Keywords: plomb pour condensateurs céramiques multicouches Ferroélectriques, Céramique sans plomb, Condensateur multicouche, Electronique chaude Lead-free ferroelectric ceramics for multilayer ceramic capacitors Ferroelectrics, Lead-free ceramics, Multilayer capacitor, Hot electronics

Céramiques ferroélectriques sans

Pour atteindre la fraction volumique et la taille de grain critiques, un agent dispersant a été utilisé lors du broyage dans la jarre de YSZ, avec du MEK et de l'éthanol comme solvants, et sans sécher les réactifs avant la pesée. Enfin, la relaxation des contraintes a été réalisée à 400°C pendant 3 heures. Trois modèles ont été utilisés pour expliquer la dispersion des propriétés diélectriques en fréquence : le modèle de Maxwell-Wagner, le modèle de Nyquist et la loi de Curie-Weiss modifiée. Les incompatibilités entre les propriétés diélectriques du NBT-BT rapportées dans la littérature ont ensuite été analysées soulignant l'importance d'avoir des méthodes de synthèse et de mesure strictes. Les trois principaux facteurs affectant les propriétés diélectriques induisant ces incompatibilités étaient la stoechiométrie, la méthode de métallisation et la fixation des fils électriques à l'aide de la laque d'argent. Des pertes diélectriques croissantes à haute température a aussi été observée après chaque cycle thermique dépassant les 300°C, indiquant une dégradation thermique des échantillons. Enfin, les monocouches céramiques ont montré une faible densité (62%) après frittage, limitant la plage de température correspondant aux spécifications d'Exxelia. Cependant, en utilisant un pressage des couches avant frittage, l'échantillon multicouche fritté présentait une densité élevée (89%). Une mesure des propriétés diélectriques doit être effectuée sur cet échantillon multicouche synthétisé, afin de déterminer sa compatibilité avec les spécifications d'Exxelia.

To achieve the critical volume fraction and surface area of the secondary phases, a dispersing agent was used during ball-milling in YSZ jar, with MEK and ethanol as solvents, and without drying the reactants prior to weighing. Finally, a strain relaxation was done at 400°C for 3 hours. Three models explained the frequency dispersion of the dielectric properties: the Maxwell-Wagner model, the Nyquist plot and the modified Curie-Weiss law. Incompatibilities between the dielectric properties of NBT-BT reported in the literature were then analysed, showing the importance of maintaining strict synthesis and measurement methods. The three main factors affected the dielectric properties, creating these incompatibilities in the bulk samples. There were the stoichiometry, the metallization method, and the fixing of the electrical leads using silver paste. An increase of the high-temperature dielectric losses after each thermal cycle reaching more than 300°C was observed, indicating a thermal degradation of the material. Finally, the sintered ceramic monolayers showed a low density (62%), limiting the temperature range corresponding to Exxelia's specifications. However, after pressing the layers together before sintering, the sintered multilayer sample showed a high density (89%). Dielectric property measurement should be carried out for these synthesized multilayers.

Before entering into the thesis itself, I would like to acknowledge some important people that were essential to the present work.

Firstly, I would like to thank Dr. Cécile Autret-Lambert, Dr. Mojca Otonicar and Dr. Raphael Haumont for accepting being a part of my thesis jury and for their valuable suggestions and comments about my work.

I would also like to thank Prof. Pierre-Eymeric Janolin, professor in CentraleSupélec and supervisor of this work, for his great scientific support during my PhD, for his patience, motivation, knowledge and for accepting supervising my thesis after the loss of my previous supervisor.

I would also like to show my gratitude to Dr. Ing. Henri Laville, responsible for the research and development in the Exxelia company during most of my PhD, for his great technical support and also for his motivation, understanding and help during difficult situations.

I would like to thank everyone in the SPMS laboratory that helped my work directly or indirectly and that made it possible. More specifically, I thank Christine Bogicevic, for her precious help in the chemical synthesis part, in the SEM analysis and also for her emotional support, Fabienne Karolak, for her help in the SEM analysis and metalization, Rossen Tchakalov, for his help with the tape casting synthesis and also for his emotional support, Dr. Pavan Nukala, for the interesting and valuable scientific discussions and for his support and Rohit Pachat, for his help and support and finally all the PhD students in the laboratory, for their support and help during my thesis.

The help of Exxelia company was also essential during my thesis. More specifically, I would like to thank Dr. Ing. Christian Ravagnani, for his support as the head of R&D during the last year of this project, Ing. Anais Anouari, for her suggestions and interesting scientific and technical discussions, Serge Le Deroff, for his help with the insulation resistance measurement, Aurélie Van De Mert, for her support and help with the MEB measurements, and Pascale Escure, for her valuable suggestions and help with the synthesis of the ceramic tapes.

I also thank Prof. Houssny Bouyanfif, professor at the University of Picardie Jules Verne and member of the laboratory of Condensed Matter Physics (LPMC) and Yaovi Gagou, also member of the laboratory of Condensed Matter Physics (LPMC) for their indispensable help with the dielectric measurements, without which this work would not be possible, and for the trust they have given me during these measurements.

I thank again Prof. Rafael Haumont, professor in the university Paris Sud and member of the Institut of Molecular and Materials Chemistry of Orsay (ICMMO), for his precious help with the XRD measurements and also Dr. Lúcio de Abreu Corrêa, doctor by the Soil, Structures and Materials Mechanics Laboratory (MSSMAT) in CentraleSupélec, for his help with the data treatment and for the emotional support.

I would also like to thank my mother Ing. Sonia Maria Mussi Toschi and my brother Ing. Guilherme Mussi Toschi, for their support and motivation during these three years.

Finally, I would like to acknowledge two people that were essential for this work and that, sadly, are not among us anymore: Prof. Jean Michel Kiat, an excellent professor and researcher on the SPMS laboratory in CentraleSupélec and my supervisor during the first year my thesis, without whom this work would not have been possible and my motivation

Introduction

The objective of this chapter is to present the context and the problematic of the thesis, to explain the industrial specifications and limitations that apply to the choice of the base material for the multilayer ceramic capacitors (MLCC).

Presentation of Exxelia

Founded in 2009, the Exxelia group is the result of the merger of five historical companies with complementary know-how (Eurofarad, Firadec, Sic Safco, Microspire and Astema). The main former company, Eurofarad, was founded in 1965 and and it was previously a world leader in the multilayer ceramic capacitors (MLCCs) production.

Since its foundation, Exxelia has continued to grow and strengthen its international presence through strategic acquisitions in the United States, Vietnam, Morocco and France. Today, Exxelia has ten entities all operating in niche industrial markets.

Exxelia specializes in the design and manufacture of high reliability passive electronic components and innovative electromechanical solutions. The products are designed and manufactured to meet the problems and constraints of demanding industrial applications: Space, Aeronautics, Defense, Security, Energy, Medical, Transport, Advanced Industries and Telecommunications. Exxelia is based on two main sites, Chanteloup-en-Brie and Marmoutier.

The Chanteloup-en-Brie main site is located close to Paris [START_REF] Yan | Microstructure evolution during sintering of multilayer ceramic capacitors: nanotomography and discrete simulations[END_REF] and it has an area of 11000m 2 . It includes the production of Film, Ceramic, Filters, Sensors and Associated Systems capacitors, as well as the Quality, Logistics, Human Resources, IT and Purchasing departments. The site is EN9100 and ISO 9001 certified.

The Marmoutier site is located in Alsace [START_REF]Technologie et caractéristiques des MLCC[END_REF] and it has a surface area of 9000 m 2 to develop its activities around Film, Filters, Sensors and Associated Systems and Precision Mechanics capacitors.

This thesis was done in cooperation with the Chanteloup-en-Brie site, where the expertise is the production of MLCCs. These capacitors have an excellent temperature resistance, volume capacity, electrical properties and reliability. Therefore, they can be used in many fields of application such as medical implants, flight controls in aeronautics, switch mode power supplies in harsh environments, oil drilling probes or space. More details on the ceramic capacitors will be presented in section 1.2.

The MLCCs are manufactured according to rigorous manufacturing procedures. These strict procedures at each production stage have enabled many Exxelia's product lines to obtain certifications, so that they comply with the most rigorous standards applied in the space, aeronautics, rail and other advanced industries.

The research and development sector of Exxelia and, more specifically, of the Chanteloupen-Brie site have also a great importance for the company. So the R&D and Innovation team are formed of expert and dedicated engineers and researchers. In this context, strategic partnerships with laboratories at universities, grandes écoles and companies in the industrial sector, like this thesis are a key point for developing new products and methods. Finally, collaborations with European and international programs also contribute to the innovative profile of Exxelia.

Innovation in Exxelia's entities is characterized by the more than 40 patents that were already registered internationally. To maintain this high performance and innovation activities, more than 7% of sales are devoted to Research and Development.

In this industrial context, this thesis was proposed by Exxelia and it was developed in partnership with the SPMS (Structures, Properties and Modeling of Solids) laboratory. The SPMS is an excellence laboratory of CentraleSupélec dedicated to the study and innovation in the fields of functional materials for energy, advanced ferroics materials and electronic structures, modelling and simulation.

Industrial Context of multilayers ceramic capacitors (MLCC)

The industrial production of MLCC is very important for the electronics industry, since MLCCs are the most consumed capacitor type in the world. Moreover, new industrial requirements are constantly created, due to the miniaturization and need for better and more reliable electronic components.

The MLCCs and their context are introduced, applications and industrial production are presented hereafter.

Presentation and importance of the MLCC for the industry

The model of the simplest capacitor is made of two conducting plates or electrodes separated by a dielectric material. This dielectric material can be characterized by its ability to store charges and by its response to an external applied electric field. The main properties we should focus on are the capacitance value and dielectric losses (linked to the real and imaginary parts of the permittivity), the insulation resistance (linked with the resistivity to a direct voltage) and the dielectric strength (breakdown field).

In the case of ceramic capacitors, the material may be paraelectric, ferroelectric, relaxor, or anti-ferroelectric.

The idea behind the production of multilayer ceramic capacitors is to increase the final capacitance of the device, by connecting in parallel many ceramic capacitors. The capacitance calculation for the MLCC will be described in the section 1.3.1.2.

The structure of a MLCC shown in Fig. 1.1 consists in alternating layers of conducting material (electrodes) and dielectric material (ceramics). Each dielectric layer represents a single mono-layer capacitor. The external electric contacts are also composed of several layers, to ensure the parallelisation of the single-layer capacitors and weldability of the MLCC. The composition and function of each layer will be explained in section 1.2.6.7.

MLCCs are known to have high volume efficiency, high reliability, and good frequency features. For this reason, MLCCs are the most consumed capacitor type in the world today, with an annual production of more than 100 billion units. [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] The market has grown around 20% each year since the beginning of the decade. One of the key factors contributing to this is the electronics production increase, driven by cell phones and personal computers. More than that, MLCCs are also intensively used in new high technology fields, such as controlling systems for transportation, aerospace, and military applications. [START_REF] Yan | Microstructure evolution during sintering of multilayer ceramic capacitors: nanotomography and discrete simulations[END_REF] For this reason, intensive efforts are being made to create capacitors that can withstand more demanding operating conditions with more controlled and reliable properties. Type I MLCCs are produced using paraelectric ceramics. For this reason, as it will be explained in details in section 1.2.5.1, their capacitance and permittivity variations with the temperature, voltage, and frequency are reduced. They do not exhibit aging or polarization. However, their dielectric constants and their capacitances are low. This type of MLCCs can be divided in 3 sub-classes depending on their temperature coefficient α (variation of the permittivity by 1 • C variation). [START_REF]Technologie et caractéristiques des MLCC[END_REF] NP0 (industrial name) or C0G (Electronic Industries Alliance classification) These MLCCs, as can be seen in Table 1.1, have the most stable permittivity in temperature, with α = 0±30 ppm/ • C, which means that the tolerance for permittivity and capacitance variations are 0.3% each 100 • C in relation to the permittivity or capacitance value at 25 • C, from -55 to 125 • C.

Note that, for current application, the value of 25 • C is defined as the reference temperature T 0 , since the usage temperature range has the room temperature as its middle point. This permittivity variation limit can be defined as:

∆ε(T ) = ε(T ) -ε(T 0 ) ε(T 0 ) (1.1)
NPO dielectrics are normally based on MgTiO 3 or Nd 2 Ti 2 O 7 . [START_REF]Technologie et caractéristiques des MLCC[END_REF] P90 and P100

The P90 and P100 MLCCs, as they are normally named in the industry, are equivalent to M7G in the EIA classification. They have α = 90 (or 100) ppm/ • C, which means that the permittivity varies linearly with temperature at a rate of 0,9 or 1% each 100 • C. These MLCC are usually based on Mg 2 TiO 4 . [START_REF]Technologie et caractéristiques des MLCC[END_REF] Others These MLCCs have a temperature coefficient, which is negative and not quite linear, with a mean value, at room temperature, ranging from -33ppm/ • C to -4700ppm/ • C.

Type II

Type II capacitors are based on BaTiO 3 (BT), which is a ferroelectric material that undergoes a phase transition from paraelectric to ferroelectric, thereby the permittivity sharply increases around the Curie temperature T c . For this reason, they can have large capacitance. However,their permittivity varies a lot under temperature, and their voltage constraints and dielectric losses present higher values. [START_REF]Technologie et caractéristiques des MLCC[END_REF] BT and standard additives In type II MLCCs, BT is the base production material. BT [START_REF] Anoufa | Nanocomposites et effet de dimensionnalité pour le stockage de l'énergie[END_REF] is a well known ferroelectric defined by the existence of a remanent polarization that can be switched by an electric field between two or more directions.

In this material, spontaneous creation of ferroelectric domains are facilitated by longrange interactions between the dipoles in each unit cell. The polarization alignment in each domain under an external electric field results in the growth of the corresponding domains that eventually occupy the entire material. After the external electric field is removed, the domain structure remains. This phenomenon is responsible for the P-E loop (polarization versus electric field cycle). The domains are also responsible for the better energy storage properties and permittivity when compared to most dielectric materials.

BT undergoes three phase transitions in temperature that are accompanied by permittivity peaks: the first one at around -90 • C, from rhomboedral to orthorhombic crystalline symmetries, the second one at around 0 • C, from orthorhombic to tetragonal and, finally, the third one, at the Curie temperature around 130 • C, from tetragonal to cubic. These phase transitions are responsible for a large variation of permittivity in temperature, especially at the Curie temperature, as can be seen in the Fig. 1.2. For the MLCC production, pure BT is not ideal, due to the large variations of permittiv-FIGURE 1.2: Phase transitions in temperature for pure BT [START_REF] Acosta | BaTiO3-based piezoelectrics: Fundamentals, current status, and perspectives[END_REF] ity in temperature. To solve this problem, modifications of the composition through additives are done, in order to increase or decrease the permittivity and to flatten its variation. [START_REF]Technologie et caractéristiques des MLCC[END_REF] Some other problems that would appear if pure BT was used in the MLCC production are:

• The aging phenomenon (steady capacitance decrease over time, as will be presented in the section 1.3.1.6), which is reversible after heating the MLCC above the Curie temperature, something that cannot be done in electronic systems;

• The decrease of the insulation resistance and the permittivity when an external continuous voltage is applied;

• The increase of the dielectric losses during phase transition, which comes from the peaks in permittivity.

Some examples of additives used in the type II MLCC are SrTiO 3 and CaZrO 3 that can be form a solid solution with BT to decrease the Curie temperature of the pure BT. The MgZrO 3 and Bi 2 Sn 3 O 9 also form a solid solution with BaTiO 3 to decrease the maximum permittivity value and the permittivity variation with temperature. Other inter-granular doping (that do not form solid solutions) that can be used in MLCC are Co 3 O 4 and MnO. These oxides have lower melting points than the BT and can form a liquid phase during sintering, which increases the final density of the ceramics. They also decrease the conductivity of the material as it will be explained in more details in section 3.4. [START_REF]Technologie et caractéristiques des MLCC[END_REF] For the variation of the permittivity with frequency, there is a relative stability for the classical operating frequencies, between 1kHz and a 100MHz.

Fluxing agents

BT is sintered only in the solid-state and the sintering temperature is higher than 1250 • C. Some fluxing agents (glass former) [START_REF]Technologie et caractéristiques des MLCC[END_REF] may be added to the composition to create a liquid phase during sintering, increasing the final density and decreasing the sintering temperature to less than 1130 • C. However, these agents can evaporate and lead to changes in composition or performance of the dielectrics, for example when using lithium salts. They can also initiate reactions with the electrodes leading to failures, for example, when bismuthbased agents or materials are used (as it will be mentioned in section 1.3.2).

MLCCs uses and advantages 1.2.4 Tuning

Tuning MLCCs are used in oscillating circuits, filters, or time constant circuits. It requires very low losses and high stability as a function of temperature, time, and DC voltage applied. Type I ceramics as well as polystyrene, polypropylene, polycarbonate, and PPS (polyphenylene sulfide) films meet these requirements. These capacitors are applied, for example, in transducer circuits.

Decoupling

Decoupling MLCCs are used to reduce or eliminate a parasitic alternating component in a high frequency domain. The capacitor must have a low impedance at the operating frequencies and therefore a high capacitance (e. g. 100 nanoFarads). Type II capacitors are the most suitable. An example of decoupling capacitor application is in output of logic signals.

Connecting

Connecting capacitors are used to ensure the connection between 2 points at different continuous potentials. It blocks the DC component and transmits the alternative component.

The capacitor must be able to withstand a high DC voltage and have a high insulation resistance. A typical application is in the output of amplifiers. Either type I or type II MLCC can be used for these applications. [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] 1.2.4.3 Filtering Filtering capacitors are used to reduce or eliminate a parasitic alternating component of the direct voltage. The capacitor must have a high capacity value as well as low resistance and inductance values. These capacitors are applied, for example, in radios. [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] 1.2.4.4 Temperature compensation Temperature compensation capacitors have a negative temperature coefficient, to compensate for the positive drift of a component, but also pre-defined and stable over time. Class I ceramics and film (polystyrene) meet these requirements. [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] 1.2.4.5 Energy storage Energy storage capacitors deliver a very high power in a very short time or a direct voltage for a very long time. An example of their applications is the development of high speed chargers.

Memory (RC)

The RC memories store information in the form of an electrical charge. As such, they must have a high insulation resistance and return the stored charge in a very short time. These memories can be used in electronic devices, such as computers and cell phones.

New applications and requirements 1.2.5.1 Industrial temperature classification

Type I and type II MLCC can be classified by their capacitance variation in temperature (temperature class). The temperature classes, expressed in code, describe the minimum operating temperature, the maximum temperature and the temperature drift. This capacitance variation in temperature represents one of the most important characteristics of the MLCC, as will be detailed in section 1.3. The EIA (Electronic Industries Alliance) is the international standard used to classify MLCCs by their temperature coefficients. It is presented in Table 1.1 for type I MLCC and Table 1.2 for type II MLCC.

REACH and RoHS

The REACH (Registration, Evaluation, Authorization, and Restriction of Chemicals) and RoHS (Restriction of Hazardous Substances) regulations are the two most important regulations in the electronics industry and, more specifically, for the MLCC production. Some specifics of those regulations will be explained here.

Products labeling (CLP) The CLP (Classification, Labelling and Packaging) [58] labeling is used to identify and to make the labeling of dangerous products. It applies to the industrial production (before the marketing of the products).

It is a complementary REACH regulation in the sense that it divides chemical products [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] into categories, based in their danger. There are 28 hazard classes: 16 classes of physical danger, 10 classes of danger to health, 1 large environmental hazard class. For certain hazards, and particularly for CMR (carcinogens, mutagens, reprotoxicants), the CLP Regulation uses the principle of classification of mixtures to limit concentrations of dangerous substances (it is the case of Pb, for example, the limit concentration is 0.15%).

REACH Regulation

The REACH (Registration, Evaluation, Authorization and Restriction of Chemicals) [START_REF]REACH -Les grands principes[END_REF] is a European Union regulation adopted with the objective of protecting human health and the environment from the risks associated with chemical substances and promoting the competitiveness and innovation.

The regulation is applied for substances present in the final product (so it does not control the products used in production lines, if they are not present in the final product). It also places the responsibility of proof on companies that have to identify and manage the risks of their products. In the long term, the most dangerous substances must be replaced by substances that are less dangerous.

The dangerous substances are defined in the CLP Regulation by the CMR and environmental dangerous products groups.

Companies must register their REACH controlled products with the ECHA (European Chemicals Agency) when they are used in quantities (1 ton) and concentrations (for each product) larger than a limit threshold, in order to be authorized to use them over a limited period (18 months). If no technically and economically viable solution is found during these 18 months, the authorization can be renewed.

The process for registering a product is long and laborious, since the ECHA agency asks for a risk management for each application of the registered substance. Since there is only one register per substance, smaller companies can pay larger ones to take part in their register.

If a new solution is found during the 18 months authorization of a registered product, the company can claim this new product solution. This will be evaluated by a technical committee and the authorization will be withdrawn. The other companies will have 18 months to stop using this previously authorized product. So, the need to find new solutions for REACH controlled products is crucial for companies that sale in Europe.

RoHS Regulation

The RoHS (Restriction of Hazardous Substances) [60] regulation deals with the electric or electronic final products (and not the substances used only during their production). It has the objective of restricting the use of 10 substances in these products: lead (Pb), mercury (Hg), cadmium (Cd), hexavalent chromium (Cr 6+ ), polybrominated biphenyls (PBB), polybrominated diphenyl ether (PBDE), bis(2-ethylhexyl) phthalate (DEHP) Butyl benzyl phthalate (BBP), dibutyl phthalate (DBP), diisobutyl phthalate (DIBP).

The maximum allowed concentrations in non-exempted products are 0.1wt% (except for Cd, which is limited to 0.01wt%). The restrictions are on each homogeneous material in the product.

In the last review of the RoHS a new category of applications was created, including all the products that have an electrical source in one of their functions, even if this function is not its main one. So, the only excluded fields are the aerospace, the military, and the industrial plant and tools.

The RoHS exemptions have between 12 and 18 months of validity. If no technically and economically viable solution is found during this period, each company should ask from a renewal of the exemption from its country authority. In order to decide if the exemption should be renewed, the authorities evaluate the substitution material and its socio-economic impact. However, if a new solution is found, the exemption can be withdrawn. So, the need of finding new solutions for RoHS controlled products is also crucial.

In conclusion, these regulations are especially important for the MLCC production since the use of lead will be soon forbidden for non military or aeroespacial applications. This creates the need to develop new lead-free material that can meet the industrial expectations for new applications.

New high temperature applications and their requirements

The MLCC industry is currently going through many technological advances to meet the requirements from modern electronics. Nowadays, investments are done into developing new processes and materials to improve the volume capacity and the capacity of working in harsh environments. [START_REF] Zednicek | Capacitors News and Trends[END_REF] In this context, the rarefaction of fossil resources, which forces to drill ever deeper and the race for miniaturization that leads to dissipate more heat in smaller volumes and, often, closer to hot sources, make the high-temperature MLCC a strategic development for the companies growth.

Some examples include the electronic control of cars or airplanes, where the key modules are placed close to the engines, the development of electric airplane that need small MLCC working constantly close to heat sources. Other examples are the braking control system used in airplanes, where it is estimated that the electronic system should be capable to work around 350 • C during every landing and the deep downhole oil and gas industry that requires today an operational temperature of 250 • C and higher temperatures in the future. [START_REF] Zednicek | Capacitors News and Trends[END_REF] It is therefore imperative to bring out new materials capable to meet the expectations of electronics in the 300-350 • C range.

Today, the high-temperature MLCC production is limited to capacitors that can operate in temperatures up to 200-250 • C. Some examples of these products are the AT Series 200 • C & 250 • C Rated high-temperature type II MLCCs from AVX company that operate at a maximum temperature of 250 • C in military and commercial applications, the Knowles HiT250 type II MLCC that works up to 250 • C, the X8R and X9M (type II) products from Murata (GCB Series) that can operate up to 200 • C, and the KEMET's High Temperature C0G (type I) that also operates at a maximum temperature of 200 • C.

All in all, the high-temperature MLCC available on the market can work in a maximum temperature of 250 • C, which will not be enough for the new market requirements in the near future.

Industrial production method and limitations

The industrial production can be described in a simplified diagram as shown in Fig. 1.3. The various steps are:

Slurry production

The first step is the preparation of the slurry [START_REF] Mistler | Tape Casting Theory and Practice[END_REF], where the ceramic powder is mixed with the solvent, a dispersing agent, a deflocculant, a binder, and a plasticizer.

• The ceramic powder is the most important component of the slurry, since it determines the final composition of the ceramic layer and its concentration and also average grain size and shape have a great influence on the final material density. • The solvents are the base of the slurry and their properties and concentrations influence the rheological properties of the slurry and the layer drying rate. These properties are extremely important for the synthesis of homogeneous and mechanically strong tapes.

• The function of the dispersing agent, which is often also used as a deflocculant, is to separate particles from each other and hold them in suspension, in order to have a stable slurry in the end. The function of the deflocculant is to avoid the formation of loosely bound groups (flocs), in order to increase solid loading, decrease the amount of solvent in the slurry, and increase the surface energy (driving force to the sintering process).

• The binder is there to keep the mechanical integrity of the ceramic sheet. So the green ceramic tape is simply a polymer matrix impregnated with a large amount of ceramics.

That is why it is the most important additive of the system.

• The function of the plasticizer is to enable the tape to be bent without cracking. They work on or around the binder polymer chains to allow motions inside the tape matrix without breaking the matrix itself, giving it more flexibility.

Tape casting and drying of the ceramic sheets

There are two possible slurry production lines, the first with an aqueous solvent and the second with an organic solvent.

For the production of the ceramic sheets, the slurry is ball-milled and then casted, by tape casting technique, over a film either in silicon-coated Mylar (for thin sheets) or in stainless steel (for thick sheets), to evaporate the solvents in a furnace at a temperature of 50 to 100 • C. The dry ceramic thick sheets are then cut and the thin ones are stored as a roll. Defects are identified visually and the thickness of the sheet is measured. Finally, the ceramic sheets are stored in a dry, air-conditioned atmosphere.

Screen printing of the electrodes

This part of the production process is where the internal electrodes are created.

Conducting materials

There are two types of conducting materials for MLCC electrodes: [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] • Base metal electrode (BME): most BMEs are composed of nickel, except in some rare cases, where the electrode is made of copper. This implies sintering in a reducing atmosphere, to avoid deterioration of the electrode. In general, the volume variation of the electrodes are more important than the one of the dielectrics during sintering. This may result in defects in the MLCC. One of the solutions is to add to the electrode ink a ceramic filler, which will reduce the volume variation of the electrode.

Method: Silkscreen and mesh The ceramic sheets are screen printed with the internal pattern electrode. In this process, the 70% Ag -30% Pd ink, composed of the metal powder, a solvent, a binder, a plasticizer, and a surfactant is applied on the raw ceramic sheet. A mesh is used to create some lines with no ink that allows the communication between two consecutive ceramic layers through small gaps in the electrode. This guarantees the mechanical integrity of the multilayer device.

Stacking, pressing, and cutting

The electrode ink is dried in a furnace before the metallized ceramic layers are stacked. After stacking, the blocks are pressed into an isostatic press, to create a block of alternating layers of ceramic and metal with good cohesion, but not yet sintered. Finally, the blocks are cut into single MLCCs.

Sintering

The co-sintering of ceramic and electrode (blocks of alternated layers of ceramic and metal) is carried out between 1000 and 1300 • C. In this process, the ceramic and the metallic ink densify and decrease in volume and a monolithic "dielectric-metal electrodes" block is obtained. Sintering is done with a gradual increase of temperature, to avoid thermal shock. To avoid contamination (for example by bismuth, which is used to reduce the melting temperature of some materials), some ceramics are sintered in dedicated furnaces.

Sintering methods

As will be detailed in section 1.3.2, the sintering is done in an industrial furnace where the heating and cooling rates can be controlled. However, the sintering atmosphere in the furnace cannot be controlled, since it is not air tight. No pressure or electric current can be applied during sintering, so the classical sintering method is used.

Polishing (Corner rounding)

After sintering, the ceramic and metal blocks are corner rounded, using a vibrating recipient where the blocks are added together with an abrasive. The corner rounding removes sharp corners, edges and the external oxidized layer, to expose the edges of the electrodes and guarantees a homogeneous dielectric layer. This step is not presented in Fig. 1.3 p. 10, even if it is a usual step for the MLCC production.

Metallization of the external electric contacts

The metallization is often a succession of several layers, so can we distinguish.

Metal contact

After polishing, the metallization of the external electric contacts [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] is done using a metal ink composed of Ag and Pd (for precious metal electrode) or Cu (for base metal electrode) and glass (silicium oxide), which will ensure the mechanical strength of the contacts by diffusion in the ceramic layers. The ink is placed on the two opposite sides of the capacitors, where the edges of the electrodes are exposed. This creates the final MLCC structure, where the single capacitors (formed by each dielectric layer) are in parallel.

The PME (Ag-Pd) capacitors are then heated at about 700 • C to sinter the metallization. In this process, the metallic particles do not melt but the metallization is densified by solid-state mass transfer (sintering) and by the formation of a liquid phase, composed mostly of bismuth and silicium oxides that accumulates at the grain boundaries and in the interface between the metallization and the MLCC, increasing the mechanical strength. This step creates a single MLCC piece.

In the case of capacitors intended for surface mount, a conductive polymer layer (silver filled epoxy) can be used to give some flexibility that allows capacitors to better withstand thermal variations.

Diffusion barrier and weldability

The next step is the surface treatment [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] where electrolytic deposition is used, to create a diffusion barrier of Ni. The role of this barrier is to prevent the dissolution of the silver-based electrical contacts into the solders. Over the Ni barrier, a Sn (or Sn-Pb) layer is added to improve the weldability of the material and to protect it against corrosion and Ni passivation.

Protective layers

The final step in the production process consists in the creation of an exterior resin coating, [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] which is made to increase the resistance of the capacitors to environmental hazards. It is necessary that these layers are waterproof and weldable. Most often Sn / Pb alloys are used (up to 40% Pb) for space and / or military applications or Sn, which is compliant with the REACH and RoHS regulations but that can generate whiskers.

In conclusion, the MLCC is the most consumed capacitor type in the world, due to the variety of applications and to the range of dielectric properties it can have.

Nowadays, the environmental requirements are growing. The most important environmental regulations concerning the MLCCs are the REACH and RoHS that control the level of lead in the final products. This created the need for developing new lead-free materials.

There is also a growing need for the development of new high-temperature MLCCs. These new capacitors would have crucial applications, such as deep oil drilling, use in train and airplane breaks, and also the creation of a new electric airplane. Moreover, the MLCC miniaturization trend intensifies the need to develop new high temperature capacitors.

So the development of a new lead-free material for high-temperature MLCCs is crucial for the electronic components industry.

Industrial Specifications and Limitations

This section presents the specific requirements for the dielectric material studied in this thesis taking into account its future lead-free high-temperature MLCC application. The requirements related to the dielectric properties and the compatibility with the industry are specified here.

Properties specifications 1.3.1.1 Temperature and frequency ranges

The storage and operating temperatures established by the industry, in which these new high-temperature capacitors should have the appropriate electric properties, are:

Temperature of storage (when the capacitor is not in use): the capacitor should not be damaged when stored at cold temperatures (-55 • C and above).

Minimum operating temperature: the expected minimum operating temperature should be the room temperature (from 0 to 25 • C). It could also be higher, up to a maximum of 100 • C, if a heating system is used. However, the lower the minimum operating temperature (up to a minimum of -55 • C) the better.

Maximum operating temperature: The maximum operating temperature should be around 300 to 350 • C in continuous operation.

The operating frequencies established by the industry, in which these new high temperature capacitors should have the appropriate electric properties, are:

For standard applications, such as oil drilling, is from 1kHz to 100MHz.

For other applications, such as classic embedded electronics, the frequency can be around 400Hz.

The industry standard is 1kHz for defining the values of the alternative current properties (permittivity and dielectric losses).

So, in general, the frequency can vary from 400Hz up to 1MHz, the standard being 1kHz to define the reference values of the dielectric properties.

Permittivity value and its variation in temperature

The capacitance C is one of the most important properties of a capacitor, because it relates to the stored charges Q and to the applied voltage V as it can be seen in equation 1.2: [START_REF]Technologie et caractéristiques des MLCC[END_REF]

Q = C * V (1.2)
The capacitance of a simple capacitor (one dielectric layer) can be calculated, based on the dielectric permittivity of the material as: [START_REF]Technologie et caractéristiques des MLCC[END_REF]

C = ε r ε 0 A l (1.3)
where ε r is the relative permittivity of the material (adimensional), ε 0 is the permittivity of the vacuum (8.85 • 10 -12 F/m), A is the surface in m 2 and l the thickness of the dielectric layer in meters.

For a multilayer capacitor, each dielectric layer behaves as a single capacitor and the set behaves as parallel capacitors, increasing the capacitance of the final capacitor. The capacitance of an MLCC containing N electrode layers in can be calculated as: [START_REF]Technologie et caractéristiques des MLCC[END_REF]

C = ε r ε 0 A(N -1) l (1.4)
In order to obtain a relatively high capacitance value and to respect the capacitance variation in temperature for the type II MLCC, the relative permittivity should ideally be of approximately 2000 and of a minimum of 1000 and flat over the operating temperature range.

Since the new MLCC developed here does not exists in the industrial standards, there is no predefined variation of the permittivity with temperature (or temperature coefficient). However, the standards for X7R ceramics, the most industrially used and produced type II ceramic capacitor have a variation of ± 15% compared to the 25 • C permittivity (reference) in the temperature range of -55 to 125 • C.

From this standard, we chose a permittivity variation of ± 15% in the operating temperature range when compared to a reference temperature within this range.

Dielectric losses value

Real capacitors can be characterized by their capacitance C, equivalent series resistance (ESR) composed of the resistance of the conductive part (electrodes, electric contacts and connections) and of the dielectric material, and its equivalent series inductance (ESL). [START_REF] Henri | Caractéristiques générales des condensateurs -Condensateurs céramiques[END_REF] The ESR and the ESL consume a part of the energy sent to the capacitors. Moreover, the relaxation time (used to polarize the dielectric material) also creates an energy loss during the application of an alternative voltage. These energy losses are transformed into heat and the real capacitor diagram can be represented as Fig. 1.4. [START_REF]Technologie et caractéristiques des MLCC[END_REF] The tan δ represents the dielectric losses of the material.

As can be seen in the Fig. 1.4, the consequence of the energy loss is to decrease the phase shift between the applied alternative voltage and the current through the capacitor from 90 • (ideal capacitor) to 90δ • Ideally, to have a low energy loss in the MLCC, the dielectric losses should be lower than tan δ < 0.5%, however the class II capacitors industrial standard for dielectric losses establishes a maximum value for tan δ of 2.5% (at 1 kHz). These are therefore the ideal and the maximum values for the dielectric losses in the operating temperatures.

Insulation resistance

The insulation resistance (IR) is the property of opposing leakage currents when a direct voltage is applied to a material. Ideally, the insulation resistance should be infinite, to avoid the capacitor discharge. However, real dielectric materials have a limited insulation resistance, due to the presence of crystalline defects and impurities in their structures. [START_REF]Technologie et caractéristiques des MLCC[END_REF] The description and origin of the conduction in dielectric materials will be discussed in the section 3.2.1.1.

The insulation resistance corresponds to the product of the material's resistivity by its corresponding permittivity in the same temperature, as detailed in section 3.1.1. So it represents the time constant of the capacitor (the time a capacitor in an opened circuit takes to drop to the value of 36.8% of its initial charge through the internal resistance). [START_REF]Capacitors -Insulation Resistance[END_REF] The low value of the insulation resistance is one of the greatest problems of ceramic capacitors that limits its use at high temperatures, since it decreases rapidly when temperature increase (mainly above 150 • C for BT-based capacitors). So the IR is an important parameter for the MLCC.

It is desirable that the minimum value of the IR for the high temperature MLCC production is of IR •C > 10ΩF from 250 to 300 • C and IR * C > 1ΩF from 300 to 350 • C.

Variation of permittivity with frequency

BT-based capacitors are normally used in the frequency range where there is no variation in capacitance and permittivity with frequency, since the dielectric material is a "normal" ferroelectric (and not a relaxor).

For that reason, there is no standard for this type of permittivity variation. However, for an ideal capacitor, a minimal variation of permittivity within the operation frequency range (10 3 to 10 8 Hz) and the operation temperature range (from room temperature to 350 • C) is desirable.

Lifetime and aging

The aging phenomenon is characterized by the gradual decrease of the dielectric properties of the capacitors, due to changes in the crystalline structure of the dielectric. It can be canceled by heating the dielectric material above its Curie temperature. However, it has to be minimal to avoid changes in the capacitor properties.

The permittivity aging, for example, can be described for a ferroelectric material by its degradation rate m: [START_REF]Technologie et caractéristiques des MLCC[END_REF]

ε r (t) = ε r (t 0 ) -m log 10 (t) (1.5)
where ε r (t) is the permittivity in time, ε r0 is the initial value of permittivity (at t = t 0 ) and t is the time.

For the new high-temperature capacitors, the expected lifetime should be at least 2000 hours of continuous work (in oil drilling, for example).

For applications in train and airplane systems, where the work is done in peaks, the cumulative lifetime under use should be of at least two months (that is, more than 1500h). For an airplane system, for example, it represents around 500 operations with short duration but high demand (this number was estimated for 500 hours of flight between two revisions, an average of one hour per flight and approximately eight flights per day, to maximize service life).

Minimal aging should be observed during the lifetime defined above. This means that the dielectric material must have a suitable reliability and, therefore, little change in permittivity and losses over time for the defined voltage, frequency and temperature operation ranges. It must, therefore, have a limited variation in capacitance and losses.

Layer thickness and grain size

The selected ceramic and grain size should allow the production of ceramic layers with a minimum thicknesses between 5 to 20 µm or less.

Normally the grain size of the ceramics used is of the order of 0.3 to 0.5 µm before sintering and between 0.5 to 2 µm after sintering.

Dielectric strength

The dielectric strength is related to the capacity of a dielectric material to withstand high electric fields.

The dielectric failure generates free electrons and, by colliding with the crystal lattice, it creates an avalanche effect resulting in a sudden current increase. This failure is irreparable and the MLCC should be changed after it happens.

The dielectric strength is a secondary parameter in the industrial requirements, because there is no minimum value in the industrial standards. The measured values for BT-based MLCC are between 25 and 30 V/µm ou MV/m for Class II capacitors and between 50 and 60 V/µm ou MV/m for Class I, which can be used as a reference for the new high temperature MLCC studied here.

Production limitations (industrial compatibility)

The compatibility with the current production method in the MLCC industry and, more specifically, in Exxelia is an important limitation, since ideally no major changes should be done to the process, for the new dielectric to be useful for industrial production with reduced costs.

Slurry preparation

As detailed in section 1.2.6.1, the slurry is composed of a mixture of ceramic powder, solvent, deflocculant, binder and plasticizer. The compatibility with the industrial production imposes requirements for the binder: the most common binder in the MLCC industry is the PVB polymer (polyvinyl butyral), so it was chosen to prepare the slurry preparation. It is necessary to verify the compatibility of the ceramic powder with this binder and its influences on the slurry properties.

Tape casting

The Tape Casting process should be used to produce the ceramic sheets, to guarantee the compatibility with the current production method.

Sintering

The heating and cooling rates of the industrial furnace can be controlled, to reduce the possibility of thermal shocks up to 1300 • C and the sintering is normally done at a maximum temperature between 1000 and 1300 • C.

The sintering atmosphere in the furnace cannot be controlled, which means that the variation of the percentage of O 2 and N 2 is in the sintering atmosphere cannot be changed. The furnace is not airtight, so having a saturated atmosphere to avoid volatilization is difficult. It is conceivable to change the furnace for a airtight one, if the new high-temperature material studied here has good properties and if a controlled atmosphere is needed for sintering.

Compatibility with the electrode materials

The compatibility of the ceramic material with the electrodes are important to allow the MLCC production.

For the BT-based MLCCs, the most common electrode type is composed of 70% of Ag and 30% of Pd, even if the percentages of each metal can vary, depending on the sintering temperature.

To guarantee a good co-sintering of the ceramic and the electrode material, the melting Finally, a special attention should be paid for Bi-containing ceramics, since they can react with the Pd of the electrode, creating defects such as cracks or lamination on the MLCCs. The reactions between the Bi and Pd are:

Ag x Pd y + 1 2 O 2 → Ag + PdO (300 • C -835 • C) (1.6) PdO + Bi 2 O 3 → Bi 2 PdO 4 (350 • C -835 • C) (1.7) Bi 2 PdO 4 → Pd x Bi y + Bi 2 O 3 + 1 2 O 2 (> 850 • C) (1.8)
Industrial experience shows that at least 30% of Ag should be added to the Pd for the Bi-containing materials in MLCC, to avoid the reactions between Bi and Pd. So, analyzing

Composition

Price limitations

The use of scandium (Sc) is not possible, because of its cost (4200 US$ / kg). For comparison some expensive minerals used industrially are the Nb, with a price of approximately 50 US$ / kg and the Ta, with a price of 100 US$ / kg. Due to the production of tantalum capacitors and doping with Nb in BaTiO 3 base ceramics, they are widely used.

Legal limitations

The ceramic used cannot contain lead (Pd), cadmium (Cd) or other heavy metals as specified in the RoHS and REACH regulations (see 1.2.5.2).

Market limitations

Some elements with very few producers or with strategic industrial applications may be subjected to drastic price increase or suddenly become unavailable. They are therefore incompatible with the industrial MLCC production. Indium is an example of such element.

Conclusion and most important properties to chose the base material

After discussing with the Exxelia's head of R&D department, the most important properties to choose the base material are:

• the permittivity value of 1000 ≤ ε r (1kHz) ≤ 2000 (the standard for comparing these values was chosen as 1kHz and 213 • C)

• the similarity of the temperature range corresponding to a variation of 15% in the value of permittivity at 200 • C and the desired operating temperature (from room temperature to 350 • C)

• the dielectric losses in the temperature and the similarity between the temperature range for having tan δ ≤ 2.5% and the desired operating temperature (from room temperature to 350 • C)

• the insulation resistance at 300 • C higher than 10 ΩF

• the industrial feasibility (tape casting synthesis with PVB as the binder, traditional sintering without a sealed oven, Ag-Pd alloy electrode compatibility and price limitation with no expensive elements)

Choice of the base dielectric material

As mentioned in section 1.2.5.2, lead-based materials are not suitable. Therefore, only lead-free materials are considered. The three main families of lead-free materials are reviewed first: they are based on BT (section 1.4.1.1), NBT (section 1.4.1.3) and KNN (section 1.4.1.2). [START_REF] Zeb | High temperature dielectric ceramics: a review of temperaturestable high-permittivity perovskites[END_REF] Table 1.3 provides a synthetic comparison of their properties with regard to Exxelia's requirements. NBT and NBT-BT solid solutions, the base material of choice, are then reviewed in more depth.

Lead-free material families

There is a growing demand for the development of new lead-free dielectric materials that can be used for MLCC production within the ever-stricter environmental constraints. For this reason, several papers have been published in recent years to study different ceramic systems that have a high and constant permittivity above 200 • C, while maintaining low dielectric losses.

In this context, three main families of lead-free materials can be used to obtain desirable dielectric properties and to increase the operating temperature limit when compared to conventional high-permittivity (class II) dielectrics, which were based on BaTiO3 until now. [START_REF] Zeb | High temperature dielectric ceramics: a review of temperaturestable high-permittivity perovskites[END_REF] The materials are analyzed hereafter taking into account their basic properties and their variation in temperature: relative permittivity, dielectric losses, and electrical resistivity. In addition to these parameters, the sintering temperature, the composition, and the production process are also analyzed with respect to their compatibility with industrial constraints and, more specifically, with Exxelia's requirements.

BaTiO 3 -based materials

The BaTiO 3 -based materials are the most commonly used materials in the industry. BaTiO 3 Curie temperature is around 130 • C, which means that, for higher temperatures, the dielectric properties are rapidly degraded. It is then necessary to modify the chemical composition, in order to increase the Curie temperature and make it useful for the production of high temperature MLCC.

(1-x) BaTiO 3 -x Bi(Mg 0.5 Ti 0.5 )O 3 (BT -x BMT) The BT -x BMT [START_REF] Zhang | Structural and Dielectric Properties of Bi (Mg1/2Ti1/2)O3-BaTiO3 Lead-Free Ceramics[END_REF] solid solution has a relaxor behavior for x ≥ 10% and for 20% ≤ x ≤ 60% of BMT, the permittivity becomes stable in temperature.

For BMT percentages of x = 10% to 20%, the material has a average relative dielectric constant between 600 and 1000 from 25 to 400 • C, but high dielectric losses with a tan δ between 5 and 10%. For higher percentages of BMT, the permittivity value increases and the losses decreases, but ceramics become less stable in temperature compared to x = 10% and the temperature range for low losses remains limited. For x = 60% for example ε r = 2200 ± 15% from 136 to 375 • C (compared to the permittivity at 200 • C) and tan δ ≤ 2% from 197 to 400 • C.

The sintering temperature of this solid solution is from 1100 to 1350 • C, so it is compatible with the industrial demands, however the sintering should be done in a air tight furnaces.

(1-x) (0.8 BaTiO 3 -0.2 CaTiO 3 ) -x BiMg 0.5 Ti 0.5 O 3 with possible NaNbO 3 addition (BCT -x BMT Substitution of 20% of barium by calcium in the BT-BMT [START_REF] Zeb | Temperature-Stable Relative Permittivity from 70C to 500C in (Ba 0.8 Ca 0.2 )TiO 3 -Bi(Mg 0.5 Ti 0.5 )O 3 -NaNbO 3 Ceramics[END_REF] solid solution stabilizes the variation of the permittivity with temperature and decreases the dielectric losses. However, it also decreases considerably the permittivity values. Considering the values for the best BCT -x BMT composition, with 55% of BMT, the optimum composition of the BT -x BMT solid solution, the BCT-BMT has an average relative permittivity value of ε r = 1000 ± 15% from 80 to 500 • C, where the value of 1000 is measured at the permittivity peak. It gives it a very low temperature coefficient of 230 ppm / • C, but also a low permittivity value. Moreover, it has a relatively high insulation resistance, from approximately 10 seconds up to 350 • C.

However, its dielectric losses are still high up to 160 • C, with tan δ ≤ 2.5% from 160 to 430 • C (measured at 100Hz). So the decrease in dielectric losses is not sufficient to meet the MLCC requirements. In addition, a small variation in the percentage of BMT can significantly deteriorate the properties, which can be a risk for industrial repeatability. Sintering is done between 1050 and 1150 • C, which is compatible with the Ag-Pd electrodes. The synthesis method is the solid-state reaction that is also compatible with the industrial production.

The addition of NaNbO 3 decreases the maximum permittivity temperature T m from 160 • C to 0 • C. This changes the lower limit of variation of ε r ± 15% of the relative permittivity (considering 200 • C as the reference temperature) to negative temperatures, resulting in ε r = 600 ± 15% from -70 to 500 • C and tan δ ≤ 2% from -20 to 400 • C for 20% of NaNbO 3 , for example. This composition also has an insulation resistance of 10s at 330 • C, compatible with Exxelia's requirements. However, the value of relative permittivity is also decreased, which is not interesting for the production of MLCC type II. The sintering temperature is 1050 to 1150 • C, which is compatible with Ag-Pd electrodes.

(1-x) (0.6 BaTiO 3 -0.4 SrTiO 3 -0.2 ZrTiO 3 ) -x Bi(Mg 0,5 Ti 0,5 )O 3 (BSZT -x BMT) The BSZT -x BMT [START_REF] Ullah | Dielectric ceramic with stable relative permittivity and low loss from -60 to 300 ÂC: A potential high temperature capacitor material[END_REF] solid solution has a wide temperature range of stable permittivity and very low values of dielectric losses, since, for the optimal composition with 20% of BMT, the relative permittivity is ε r = 500 ± 15% from -70 to 300 • C and tan δ ≤ 1.5% from -60 to 310 • C. However, it has a very low permittivity (500) at 150 • C and also a low value of insulation resistance, of 3.7s at 300 • C. The sintering temperature is 1150 • C, which is ideal for Ag-Pd electrodes and the synthesis method is solid-state reaction, compatible with the industrial production.

(1-x) BaTiO 3 -BiZn 0.5 Ti 0.5 O 3 (BT -x BZT)
The BT -x BZT [START_REF] Wang | Dielectric and Piezoelectric Properties of Lead-free BaTiO3-Bi(Zn0.5Ti0.5)O3 and (Bi0.5Na0.5)TiO3-Bi(Zn0.5Ti0.5)O3 Ceramics[END_REF] is a solid solution that has a diffuse maximum of permittivity starting from x=5% of BZT and a frequency dispersion from 20% of BZT where it becomes a relaxor. Its dielectric properties are optimal for the composition x=20% BZT, where the relative permittivity and losses are ε r = 1700 ± 15% from 80 to 310 • C and tan δ ≤ 2% from 87 to 350 • C. The temperature range can be improved to 100 to 350 • C by adding 2% barium vacancies, which also increases the insulation resistance to 1.6s at 300 • C. However, to achieve these values, the ceramic must be sintered in an oxygen flow and hot pressed (5000 psi and 1100 • C), which is not suitable for industrial production.

(1-x) (0.8 BaTiO 3 -0.2 CaTiO 3 ) -x Bi(Zn 0,5 Ti 0,5 )O 3 (BCT -x BZT) The BCT -x BZT [START_REF] Zeb | Low variation in relative permittivity over the temperature range 25-450C for ceramics in the system (1x)[Ba0.8Ca0.2TiO3]-x[Bi(Zn0.5Ti0.5)O3][END_REF] is also a solid solution, which, for a percentage of 30% of BZT, has an almost flat permittivity (that is, the variation of ± 15% in the relative permittivity takes place in a larger temperature range), with ε r = 1165 ± 15% from 25 to 425 • C. For this composition (x=30%), the material has low dielectric losses, since tan δ ≤ 2.5% from 87 to 460 • C and tan δ ≤ 1% from 110 to 420 • C. The insulation resistance value is also compatible with Exxelia's requirements (10s at 300 • C). However, the average relative permittivity value of 1030 is low and the minimum temperature to have low losses (87 • C) is high compared to the industrial demands.

The sintering temperature of this solid solution ranges from 1050 to 1400 • C, so it could be compatible with the industrial demands; however, the sintering should be done in a sealed furnace, which would require new industrial furnaces.

(1-x) BaTiO 3 -x Bi(Zn 0.5 Zr 0.5 )O 3 (BT -x BZZ)

The BT -x BZZ [START_REF] Wang | Evolution of phase transformation behavior and dielectric temperature stability of BaTiO3-Bi(Zn0.5Zr0.5)O3 ceramics system[END_REF] solid solution presents a relaxor behavior for 10% ≤ x ≤ 60% of BZZ. However, the dielectric properties of this material have not been studied and detailed. The relative permittivity is ε r = 1000 ± 15% from less than 200 to 350 • C and the dielectric losses are tan δ ≤ 2.5% from the ambient temperature to 250 • C. However, there are no studies on the insulation resistance of the material.

The sintering temperature of this solid solution is from 1100 to 1290 • C, so it is compatible with the industrial demands, however, similar to BCT -x BZT, the sintering should be done in a sealed furnace.

(1-x) BaTiO 3 -x Bi(Mg 0.5 Zr 0.5 )O 3 (BT -x BMZ)
The BT -x BMZ [START_REF] Chen | High relative permittivity, low dielectric loss and good thermal stability of BaTiO3-bi(Mg0.5Zr0.5)O3 solid solution[END_REF] is a solid solution up to a percentage of 50% of BMZ. This solid solution has a core-shell structure for 3 to 6% of BMZ, but, in this case, the relative permittivity has a value of ε r = 6200 ± 15% from 150 to 370 • C. For higher percentages of BMZ (from 30% to 40%) it has a more stable temperature permittivity of ε r = 570 ± 15% from -20 to 430 • C with low losses (tan δ ≤ 2% from 30 to 420 • C). However, in this case, the average permittivity value is too low for the MLCC application.

(1-x) BaTiO 3 -x Bi(Mg 0.67 Nb 0.33 )O 3 (BT -x BMN) The BT -x BMN [START_REF] Muhammad | BaTiO3-Bi(Mg2/3Nb1/3)O3 Ceramics for High-Temperature Capacitor Applications[END_REF] solid solution exhibits a temperature-stable behavior for compositions from 20 to 60% of BMN. The composition with 20% BMN has a very low permittivity variation but very high dielectric losses for temperatures higher than 150 • C. The compositions from 40 to 60% BMN have a greater variation in the permittivity, but much lower losses. For example, for 50% of BMN, the material has a relative permittivity of ε r = 900 ± 15% from 25 to 550 • C and dielectric losses of tan δ ≤ 2.5% from 74 to 350 • C. For this composition, the insulation resistance is approximately 2s at 250 • C, which is not sufficient considering that the IR should be of at least 10s at 350 • C. So, this ceramic does not have a sufficiently high permittivity and IR values for the manufacturing of MLCCs.

(1-x) BaTiO 3 -x BiMg 0,67 Ta 0,33 O 3 (BT -x BMTa) The BT -x BMTa [START_REF] Ma | Temperature stability, structural evolution and dielectric properties of BaTiO3-Bi(Mg2/3Ta1/3)O3 perovskite ceramics[END_REF] solid solution exhibits a stable permittivity for different ranges of temperature for to the compositions from 8 to 60% of BMTa. However, for low percentages of BMTa, the temperature range is not high enough. For example, for 10% BMTa, ε r = 1278 ± 15% from 30 to 150 • C. For larger quantities of BMTa (x > 10%), the permittivity is ε r = 1800 ± 15% from 115 to 230 • C and losses are high for temperatures larger than 263 • C. For these reasons, this solid-solution is not ideal for the production of MLCC. The KNN-based materials are, with the BT-based materials, among the most studied leadfree dielectrics. [START_REF] Zeb | High temperature dielectric ceramics: a review of temperaturestable high-permittivity perovskites[END_REF] They are promising candidates for the production of high-temperature MLCC, since KNN has a high Curie temperature between 350 and 420 • C. [START_REF] Zhao Jingbo | Improvement in the piezoelectric temperature stability of (K0.5Na0.5)NbO3 ceramics[END_REF] The dielectric properties of pure KNN vary significantly temperature, but they can be controlled by various composition changes.

However, KNN-based materials have some important disadvantages, such as the higher volatility of alkali components at high temperature (which makes the synthesis difficult and decreases the reliability of the material) and the very low sintered densities. This creates the need for doping and changing the sintering methods to obtain ceramics with interesting properties and hinders their use in the MLCC production, even though some interesting properties were reported in the literature.

(1-x) KNN -x Bi(Zn 0.75 W 0.25 )O 3 The addition of BZW to KNN lead to a solid solution with widened orthorhombic -tetragonal and tetragonal -cubic transitions compared to KNN. [START_REF] Chen | High relative permittivity, low dielectric loss and good thermal stability of novel (K0.5Na0.5)NbO3-Bi(Zn0.75W0.25)O3 solid solution[END_REF] The optimal composition, with 10% BZW, has a relative permittivity of ε r = 1300 ±15% from 120 to 350 • C. However, it has a limited temperature range of low dielectric losses, with tan δ ≤ 2.5% from 210 to 420 • C. This is not ideal for the production of MLCC as operating temperature must be extend at from below 100 to 350 • C.

(1-x) KNN -x LiTaO 3 The KNN -LiTaO 3 [START_REF] Guo | Na0.5K0.5)NbO3-LiTaO3 lead-free piezoelectric ceramics[END_REF] is a ferroelectric solid solution with a high Curie temperature of about 420 • C and a stable permittivity in temperature. The addition of LiTaO 3 to KNN decreases the transition temperature from the orthorhombic to the tetragonal phases from 200 • C in pure KNN to -50 • C for composition with 10% of LiTaO 3 . This composition has therefore a relative permittivity of ε r = 480 ± 15% from -50 to 350 • C. For x=5% of LiTaO 3 , the relative permittivity increases to ε r = 650 ± 15% from 0 to 380 • C and the dielectric losses become tan δ ≤ 2.5% from 150 to 200 • C. However, this is not high enough for the production of ceramic capacitors.

(1-x) KNN -x LaFeO 3 (KNN -x LaFeO 3 ) with possible MnO 2 addition KNN -x LaFeO 3 [START_REF] Cheng | MnO2-modified 0.98(K0.5Na0.5)NbO3-0.02LaFeO3 ceramics with low dielectric loss for high temperature ceramics capacitors applications[END_REF] is a solid solution where LaFeO 3 increases the maximum permittivity and decreases the variation of permittivity with temperature. Addition of MnO 2 improves the densification of the ceramic during sintering, which reduces dielectric losses. This doping also acts as an acceptor, increasing the maximum permittivity, decreasing the leakage current, therefore increasing the insulation resistance and making the dielectric harder. The optimal composition, which has the formula 0.98KNN -0.02LaFeO 3 -1.5mol%MnO 2 exhibits a permittivity of ε r = 2000 ± 15% from 100 to 380 • C. However, this composition has high dielectric losses, between 2.5 and 5% between 100 and 400 • C. This is not interesting for the MLCC application. Despite an intensive research effort, opened questions remain on its structures and dielectric properties, due to its high structural complexity. A more detailed literature review will be presented in section 1.4.2.1. However, it must be highlighted here that the NBT have a high Curie temperature, of around 400 • C, and it has two anomalies on its permittivity in temperature: the first one corresponding to the depolarization temperature, T d , around 200 • C and the second one corresponding to an broad permittivity maximum at T m , around 300 • C. These anomalies increase the permittivity stability compared to other ferroelectric ceramics, like BaTiO 3 , creating an extended temperature range of low dielectric losses, going from the T d to the T m .

Moreover, its properties, like the T C , the T m , and the conductivity, can be controlled by adding various dopings and by forming solid-solutions, which makes it an interesting base material for the MLCC production.

(1-x) NBT -x NaNbO 3 (NBT -x NN) The NBT -x NN [START_REF] Li | Impedance spectroscopy and dielectric properties of Na0.5Bi0.5TiO3-NaNbO3 ceramics[END_REF][START_REF] Ching | The Influences of NaNbO<sub>3</sub> on the Dielectric and Structure Characteristics of (1-X) (Na<sub>0.5</sub>Bi<sub>0.5</sub>)TiO<sub>3</sub>-x NaNbO<sub>3</sub> Ceramics[END_REF] is solid-solution. The temperature of the maximum permittivity (T m ) is shifted to lower temperatures and becomes wider with a relative percentage of 1 to 3% NN. The best properties are obtained for 20% NN, with a permittivity of ε r = 1500 ± 15% from 0 to 400 • C and dielectric losses of tan δ ≤ 2.5% from 100 to 450 • C. These properties can be further enhanced by adding dopings, such as manganese, cobalt, and copper oxides to "flatten" the permittivity and increase the insulation resistance. Strontium, calcium, and barium oxides dopings enable to control the temperature range of stable permittivity.

Due the NBT -x NN's good potential properties, there are some patents [START_REF] Arthur Schulze | High-temperature dielectric materials ans capacitors made therefrom[END_REF][START_REF] Arthur Schulze | Patent High-temperature dielectric materials and capacitors made therefrom[END_REF] presenting similar compositions, exhibiting high permittivity, wide range of usage temperature, low dielectric losses, and high insulation resistance. The optimal composition described in the Bridger patent, 2007 (US 2008/0239627 A1), for example, has a high relative permittivity (ε r ≥ 1000), low dielectric losses (tan δ ≤ 2%), high resistivity (IR * C ≥ 10s), and low permittivity variation (±15%) over a wide range of temperatures: from -30 to 200, for the fabrication of capacitors operating between 150 ± 100 • C and 350 ± 100 • C. However, these properties do not have the proper reliability for industrial production and need to be further improved. In any case, the NBT -x NN is good candidate for the production of MLCCs used at high temperatures.

(1-x) NBT -x KTaO 3 (NBT -x KTaO 3 In the NBT -x KTaO 3 [START_REF] König | Influence of the synthesis conditions on the dielectric properties in the Bi0.5Na0.5TiO3-KTaO3 system[END_REF] solid solution, KTaO 3 increases the stability of the permittivity as a function of temperature. The presence of a heat treatment before sintering and after calcination greatly reduces the dielectric losses, which becomes of tan δ ≤ 2% from 200 to 250 • C. The best properties were found for 20% of KTaO 3 and for three heating pre-treatment stages, the first at 950 • C and the next two at 1100 • C. For this composition, the relative permittivity is ε r = 1750 ± 15% from 0 to 300 • C and the dielectric losses are tan δ ≤ 2% from 50 to 320 • C. These permittivity values are close to the ones required by Exxelia for the hightemperature MLCCs. However, there is no study on the insulation resistance and on the variation of permittivity with time.

NBT -(K 0.5 Na 0.5 Nb)O 3 -(K 0.5 Bi 0.5 )TiO 3 NBT -KNN -KBT [START_REF] Zhao | Enhancement of energy-storage properties of K0.5Na0.5NbO3 modified Na0.5Bi0.5TiO3-K0.5Bi0.5TiO3 lead-free ceramics[END_REF] is a ternary solid solution and its most interesting compositions are (1-x) [0.6NBT-0.4KBT] -x KNN or (1-x) [0.84NBT-0.16KBT] -x KNN. Both solid solutions have a large temperature range of stable permittivity. The optimal composition has 12% of KNN and 16% of KBT and its relative permittivity is ε r = 2000 ± 15% from 54 to 400 • C. However, the low dielectric losses (limited to a small temperature range) are tan δ ≤ 2.5% from 70 to 230 • C. This is not ideal for the MLCC production.

From this survey of potentially interesting materials for MLCC production, a comparison of their properties with Exxelia's requirements can be made. This summary is presented in Table 1 Even though pure NBT is known since the 1960's, there is still some discussions about its structure and its actual transition temperatures. It had long been agreed that pure NBT is rhombohedral (R3c space group) at room temperature, where the Na + and Bi 3+ ions are disordered, sharing the A-site, and that it does not go through structure change up to 200 • C at least. However, recent studies indicate that the average structure is actually monoclinic (Cc space group) [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF][START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF] .

NBT was originally considered as a ferroelectric at room temperature but, recently, some studies showed that it is actually a non-ergodic relaxor (e.g. [START_REF] Huband | Depolarisation of Na0. 5Bi0. 5TiO3-based relaxors and the resultant double hysteresis loops[END_REF]). This conclusion was taking into base on its hysteresis loop, dielectric and structural properties and their changes in temperature.

On heating, the first phase transition starts at around 200 • C (depolarization temperature), when the ferroelectric domains starts to disappear. This transition can be described briefly as the formation of orthorhombic sheets (Pnma space group) within the R3c matrix, forming a modulated phase. [START_REF] Dorcet | Reinvestigation of Phase Transitions in Na 0.5 Bi 0.5 TiO 3 by TEM. Part I: First Order Rhombohedral to Orthorhombic Phase Transition[END_REF] These sheets develop between 200 and 300 • C by a micro-twining process.

The modulated phase can explain another important discussion related to the NBT properties: the double hysteresis loop between 200 and 300 • C, characteristics of anti-ferroelectric materials. The reason for this double loop was that two successive R3c domains present anti-parallel vectors in a plane perpendicular to the modulation direction, giving rise to the anti-ferroelectric-like properties(see in Fig. 1

.7).

This first phase transition was also explained in terms of a transition from a non-ergodic FIGURE 1.7: Schematic representation of the modulated phase present in NBT from 200 to 300 • C, responsible for the anti-ferroelectric-like behaviour. [START_REF] Dorcet | Reinvestigation of Phase Transitions in Na 0.5 Bi 0.5 TiO 3 by TEM. Part I: First Order Rhombohedral to Orthorhombic Phase Transition[END_REF] to ergodic relaxor [START_REF] Huband | Depolarisation of Na0. 5Bi0. 5TiO3-based relaxors and the resultant double hysteresis loops[END_REF]. Above the T d , the polar nano-regions or PNR (rhombohedral structure) are small and poorly correlated and the material behaves as an ergodic relaxor. At temperatures close to the T d , when an electric field is applied to the material, the PNRs grow and the material becomes polarized. When this electric field is then reduced, the poled structure remains stable until it reaches a threshold, when material polarization decreases rapidly. This gives rise to the anti-ferroelectric-like behaviour. As the temperature increases further (over T d ), the stability of the poled structure decreases until some PNR start to return to the initial polarization continuously as the field is reduced, forming the thin polarization loop typical of relaxors. Decreasing the temperature below the T d , the PNR grow in size and their correlation increase until it starts behaving like a non-ergodic relaxor, with a similar polarization property as a typical ferroelectric. Both explanations about the first phase transition agree with each other, since the development of a modulated phase can explain change in behaviour from non-ergodic to ergodic relaxor behaviour on NBT.

The second phase transition, from the orthorhombic phase (Pnma space group) to the tetragonal centrosymmetric one (P4/mbm space group), happens at about 320 • C. The material is then paraelectric. [START_REF] Dorcet | Reinvestigation of Phase Transitions in Na 0.5 Bi 0.5 TiO 3 by TEM. Part I: First Order Rhombohedral to Orthorhombic Phase Transition[END_REF] From 400 • C, there is a local P4 2 /mnm local structure that can be detected in the global tetragonal P4/mbm one. [START_REF] Dorcet | Reinvestigation of Phase Transitions in Na 0.5 Bi 0.5 TiO 3 by TEM. Part I: First Order Rhombohedral to Orthorhombic Phase Transition[END_REF] The Curie-Weiss law is valid for temperatures higher than 400 • C, so this can be considered as the pure NBT Curie temperature, T c . [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] Finally, the last phase transition happens at 520 • C, from the global tetragonal P4/mbm phase to the cubic Pm3m phase [START_REF] Dorcet | Reinvestigation of Phase Transitions in Na 0.5 Bi 0.5 TiO 3 by TEM. Part I: First Order Rhombohedral to Orthorhombic Phase Transition[END_REF].

Fig. 1.8 presents a schematic representation of the structure and their microscopic electric properties.

The structure of pure NBT explains the dielectric properties of this material. The per- mittivity and the dielectric losses in temperature goes through two anomalies [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF]:

• The first one (around 200 • C) is a frequency dependent transition (it shifts to higher temperatures with increasing frequency), since the NBT becomes an ergodic relaxor.

It is observed as a shoulder in the permittivity at the depolarization temperature T d around 200

• C, and it corresponds to the first phase transition described in details in section 1.4.2.1. It can also be identified as the imaginary permittivity maximum.

• The second one at higher temperature is the broad permittivity maximum at T m around 320 • C and it corresponds to the second phase transition.

The dielectric losses are initially high, between 6 and 8%, for the temperatures lower than T d . After the first phase transition they decrease and remain low, between 3 and 6%, up to about 300 • C, when the losses increase again, due to the increase of the conductivity of the material. [START_REF] Venkata | Phase Transitions Of The Ferroelectric Na0.5Bi0.5TiO3 By Dielectric And Internal Friction Measurements[END_REF] An example of typical dielectric properties for pure NBT is presented in the Fig. 1.9.

NBT-BT solid solution

NBT and BT form the most-studied solid solution based on NBT. The rhombohedral NBT-rich side of the NBT-BT solid solution is separated from the BT-rich tetragonal one by a morphotropic phase boundary (MPB).

The first unpoled NBT -x BT phase diagram [START_REF] Maurya | Synthesis-Structure-Property Relationships in Lead-Free Piezoelectric Materials[END_REF][START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF] in Fig. 1.10 shows an MPB at x=0.06-0.07 where the NBT-rich side of the MPB has a rhombohedral structure with the space group (R3c) at room temperature, as for pure NBT. The BT rich side has a tetragonal (P4mm) structure at room temperature also like the pure BT. However, for pure NBT and for NBT-rich compositions, the room temperature structure could also be the monoclinic (Cc) (see section ??.

In fact, adding barium to NBT creates a local strain in the crystal lattice, favouring the formation of tetragonal domains, depending on the percentage of Ba 2+ that is added. [START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF] The barium decreases the interaction between the PNRs and increases the crystalline disorder. These changes give rise to an interesting MPB, where the solid solution presents the maximum piezoelectric and dielectric responses. FIGURE 1.9: Typical dielectric properties of pure NBT [START_REF] Venkata | Phase Transitions Of The Ferroelectric Na0.5Bi0.5TiO3 By Dielectric And Internal Friction Measurements[END_REF] There are still some discussions about the MPB structure at room temperature and its compositional range. It was often described as having a cubic or pseudo-cubic structure with possible small tetragonal and rhombohedral distortions. However, other studies described this composition range as having single-structures such as R3m, R3c, P4bm, or different structures, such as Cc+Pm-3m. [START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF] For the compositional range, there are also disagreements, but it is generally reported to be in between 4 and 8% of BT. So, the definition of the MPB in this solid solution is difficult, due to its complex structure. However, all the MPB studies describe it as having a nearly cubic structure, which agrees with the relaxor character found in the unpoled compositions of the MPB, similarly to the relaxor characters of the pure NBT also presented in section 1.4.2 [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF].

Since there are no consensus on the NBT-BT structure at the MPB, there are still discussions about the origin of the PNR at room temperature for this composition. Many studies attribute the PNRs to a coexistence of rhombohedral and tetragonal domains, as for the pure NBT close to T d (where the tetragonal P4bm nano-domains result in anti-ferroelectric-like ordering) [START_REF] Dorcet | Reinvestigation of Phase Transitions in Na 0.5 Bi 0.5 TiO 3 by TEM. Part I: First Order Rhombohedral to Orthorhombic Phase Transition[END_REF][START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF], while a few others argue for local monoclinic distortions [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF][START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF]. In the first case, the competition between AFE and FE domains at the MPB would be the reason for its relaxor behaviour. [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] The XRD measurement [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] on the NBT-rich (rhombohedral) phase are characterized by the splitting of the pseudocubic (111)pc peak around 2θ at 39-41 The change in structure is visible from 5% of BT and it intensifies from 7% of BT, indicating the MPB composition range for this reference.

As for the pure NBT, the NBT-BT with x ≤ 0.15 presents two dielectric anomalies in temperature below 400 • C. [START_REF] Maurya | Synthesis-Structure-Property Relationships in Lead-Free Piezoelectric Materials[END_REF][START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF] The first one at around 120 • C (T d ) represents the transition from ferroelectric (or relaxor, as explained before) to anti-ferroelectric-like structure (or ergodic relaxor, as explained for the pure NBT in section 1.4.2.1). The second one is at around 300 • C (T m ) and corresponds to the transition to the paraelectric cubic structure, also like the pure NBT compound [START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF].

The comparison between the permittivities in function of temperature pure NBT, NBT-BT with 6.5% of Ba and 7% of Ba are presented in Fig. 1.12. It can be seen that, for NBT-rich compositions, BT decreases the depolarization temperature T d , and it also decreases the maximum permittivity temperature T m . It increases the mean value of the permittivity, decreases its variation in temperature, and increases its variation in frequency. This analysis suggests that substitution with low barium levels (up to 7 mol%) favors rhombohedral (ferroelectric) transition to a tetragonal (paraelectric) phase [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF].

When the BT content is greater than 7 mol% (BT-rich solid solution), the permittivity shows a frequency dispersion, the T m is shifted to high temperatures, and the variation of the permittivity with temperature increases, as it can be seen in Fig 1 .12.

For all compositions, the dielectric losses increase rapidly when the temperature is higher than 300 • C, due to the increase the electrical conductivity [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF].

Typical properties for NBT-BT at the MPB and choice of BT percentage As it was mentioned before, the MPB improves the dielectric properties of the NBT-BT solid solution. Comparing the dielectric properties of various percentages of barium in the NBT-BT composition, the advantages of the MPB appear as:

• Low depolarization temperature, since the dielectric losses are lower for the ergodic relaxor temperature range,

• Higher permittivity value, in order to produce higher capacitance MLCC, showing that the MPB is between 6.5 and 7% of BT. [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] FIGURE 1.12: Relative permittivity as a function of temperature for a) NBT-BT with 0%, 6.5% and 7% of BT and b) NBT-BT with 10% of BT [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] • Lower variation of the permittivity in temperature, in order to produce MLCC with more stable capacitance

The expected dielectric properties for the NBT-BT solid solution with 6% of BT can be seen in Fig 1 .13.

It should be noted that the dielectric measurements of poled samples are different from the unpoled ones, since there is an abrupt transition at the depolarization temperature. Below this temperature, the frequency dispersion of the poled samples disappears and the material has a ferroelectric behaviour. This shows also the interest of having a low depolarization temperature for the MLCC production. [START_REF] Maurya | Synthesis-Structure-Property Relationships in Lead-Free Piezoelectric Materials[END_REF][START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF] Finally, it will be presented in the chapter 4 that the reported dielectric properties of NBT-BT at the MPB are not necessarily compatible among them, sdue to differences in the synthesis parameters and with the stoichiometry. So the properties presented in Fig. 1.13 are only an illustration of possible properties at the MPB. The NBT-BT solid solution can be further improved thanks to the formation of new solid solutions with KNN and SBT.

NBT-BT-KNN [START_REF] Zhao | Enhancement of energy-storage properties of K0.5Na0.5NbO3 modified Na0.5Bi0.5TiO3-K0.5Bi0.5TiO3 lead-free ceramics[END_REF] is a ternary solid solution also based on NBT. The compositions studied are (1-x) [0.94NBT-0.06BT] -x KNN, since the morphotropic phase boundary of the NBT-BT is at 6% of BT. As with other complex solid solutions based on NBT, this material has a stable of permittivity within a specific temperature range. The optimal KNN composition range is from 12 to 18%. For 12% KNN, the ceramic has a high relative permittivity of ε r = 2988 ± 15% from 75 to 325 • C, average dielectric losses of tan δ ≤ 2.5% from 100 to 350 • C, insulation resistance of 17s at 250 • C and, therefore, a wide operating temperature range from about 100 to at least 250 • C. For 18%KNN, the relative permittivity is also high (ε r = 2151 ± 15% from 40 to 350 • C), dielectric losses increase rapidly, with tan δ ≤ 2.5% from 70 to 250 • C and a low resistivity of 2s at 250 • C. This composition therefore has a limited temperature range from 70 to less than 250 • C.

Due to its good electrical characteristics, compositions similar to NBT-BT-12%KNN with different percentages of BT and dopants, such as oxides of zinc, manganese and niobium, have been patented by MRA laboratories (US 8,076,257 B1). In the patented optimal composition, the percentage of BT is 6% and a total of about 1.6wt% of dopants (manganese oxide, niobium, zinc, silicon and neodymium) has been added. The resulting material exhibits a relative permittivity of about ε r = 3600 ± 15% from 150 to 350 • C, dielectric losses of tan δ ≤ 2.5% from 150 to 350 • C and a high insulation resistance of about 200s at 200 • C, but that does not have the necessary reliability for industrial production, since there are no studies on the change in its relative permittivity and its dielectric losses over time. Moreover, no studies were done in a scale larger than a laboratory one, to test the properties variation from sample to sample. These ceramics are, therefore, excellent candidates for the production of MLCCs used at high temperatures, but they must be studied and improved with respect to the temperature range and the reliability. Finally, the final material should not be in conflict with the composition and the method in the published patent.

NBT-BT-Bi 0.2 Sr 0.7 TiO 3 [START_REF] Shi | Bi deficiencies induced high permittivity in lead-free BNBT-BST hightemperature dielectrics[END_REF] is a ternary solid solution with 10% of structural strontium vacancies, to ensure electrical neutrality. Its most studied composition is based on the composition of the morphotropic phase boundary of the NBT-BT solid solution (6% BT). It has been studied for several percentages of introduced bismuth vacancies. These vacancies decrease dielectric losses and greatly increase the permittivity in the stable permittivity temperature range, but they also increase the variation of the permittivity outside this range. The optimal composition contains 7% bismuth vacancies and 26% of SBT. This composition gives a very high relative permittivity with little variation in temperature (ε r = 4884 ± 1.5% from 73 to 230 • C and ε r = 4884 ± 15% from 50 to 290 • C), a relatively low dielectric loss of tan δ ≤ 2% from 100 to 300 • C, and a insulation resistance of 5.96s at 250 • C.

Due to its good electrical characteristics, a composition similar to this ceramic, composed of a solid solution of 0.94NBT-0.06BT with oxides of manganese and niobium as doping has also been patented by MRA laboratories (US 8,076,257 B1). In the patented optimal composition, a total of about 1.6% (molar) of doping was added. This created a material with a relative permittivity of about ε r = 1900 ± 15% from 150 to over 200 • C, dielectric losses of about tan δ ≤ 2.5% from 150 to over 200 • C, and resistivity of about 10s at 200 • C. This material has good dielectric properties, but it does not have the insulation resistance necessary for industrial MLCC production. As for the NBT-BT-KNN, there are no studies on the change in the relative permittivity and the dielectric losses of NBT-BT-SBT over time and from sample to sample.

The described dielectric properties of the NBT-BT-based solid solutions can be summarized in the Table 1

NBT-6%BT choice

As it was presented in the section 1.4.2.2, the NBT-BT at its MPB is a good candidate for the MLCC production, due to its phase transitions that give it a relatively high and stable permittivity in temperature. Moreover, the NBT-BT present a relatively low dielectric loss when some additives are used.

For the undoped NBT-BT the best properties reported in the literature are ε r =2700±15% from 60 to more than 450 • C, tan δ ≤ 2.5% from 100 to 350 • C and a thin double hysteresis loop at room temperature, when an excess of bismuth and a deficiency of sodium are used. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] This stoichiometry will be detailed in section 2.3.2.6.

Comparing these properties with the ones from the other base material candidates shown in Table 1.3 p. 24, it can be seen that the pure NBT-BT material in the MPB shows the highest relative permittivity value at the reference temperature, with a small variation in temperature (only BCT-BZT, BT-BMZ, KNN-LiTaO 3 and NBT-NN show a more stable relative permittivity within Exxelia's requirements). It also shows a large temperature range for having low dielectric losses (only the BT-BZT and BT-BMZ show a larger temperature range within Exxelia's requirements). Finally, it does not require any change in the industrial synthesis method or in the furnaces industrially used, unlike almost all the other candidates, except for the BCT-BMT, BSZT-BMT and KNN-LiTaO 3 .

Moreover, other NBT-BT-base materials can be done, as shown in the Table 1.4 p. 32 and in the section 1.4.2.3, to improve its properties. It can be seen that the NBT-BT-KNN solid solution has good dielectric properties with ε r =2900±15%from 75 to 325 • C, tan δ ≤ 2.5% from 100 to 350 • C and IR of 17s at 250 • C.

Finally, the NBT-BT-SBT in its optimal composition has a high and stable permittivity with ε r = 4884 ± 1.5% from 73 to 230 • C and ε r = 4884 ± 15% from 50 to 290 • C, a low dielectric loss of tan δ ≤ 0.02 from 100 to 300 • C, and a relatively high insulation resistance of 5.96s to 250 • C.

So, the BT-BMZ is the only base material candidate having the relative permittivity stability and the low dielectric losses temperature range better than the NBT-BT within Exxelia's requirements. However, this material shows a low insulation resistance at high temperatures, contrary to the NBT-BT-based materials, that can have an insulation resistance more than twice as large.

In conclusion, the NBT-BT solid solution at the MPB was chosen as the base dielectric material, since it has interesting properties that could be used for the MLCC production.

Firstly, it presents two dielectric anomalies: the first at T d is a frequency-dependent shoulder and the second at T m is a permittivity maximum. These phase transitions give the NBT-BT a more stable permittivity in temperature when compared to most lead-free base material candidates.

Moreover, the MPB with 6% BT, which has both rhombohedral and tetragonal crystalline structures, improves the relative permittivity values, giving the NBT-BT the highest value in the reference temperature compared to other base material candidates. The MPB also improves the relative permittivity variation in temperature when compared to most base material candidates. The NBT-BT also has a double hysteresis loop between 200 • C and 300 • C, even though it is actually an ergodic-relaxor. This makes it interesting for energy storage applications. Finally, its composition can be changes by adding other lead-free ceramics, to change and improve its dielectric properties, depending on the requirements of the final MLCC.

Other possible dopants in NBT-BT

NBT-6% BT can be improved when using other dopants and additives:

• KTaO 3 [START_REF] König | Influence of the synthesis conditions on the dielectric properties in the Bi0.5Na0.5TiO3-KTaO3 system[END_REF]: It forms a solid solution with pure NBT, as shown in section 1.4.1, stabilizing the permittivity in temperature. The solid solution with NBT-BT was not studied, but the KTaO 3 could be a candidate to be used together with a heat treatment to increase the temperature range of stable permittivity.

• Isovalent doping [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF]: A good example of isovalent doping is the K + substitution of Na + , or Y 3+ and La 3+ substitution of Bi 3+ , and Zr 2+ substitution of Ti 2+ . These dopants decrease the oxide-ion conductivity in pure NBT, which comes from high mobility oxygen vacancies created by the Bi 2 O 3 loss during sintering. The decrease in the conductivity can be explained ether by compositional variations (higher volatility of K), higher bond strength with oxygen or lower polarisability of the Bi substitutes. So isovalent doping can be useful for the MLCC production, since it significantly decreases the electrical conductivity.

• Acceptor doping [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF]: normally used to increase the ionic conductivity of NBT, by inducing the formation of oxygen vacancies or p-type (hole) conduction. So, this type of doping is not interesting for the MLCC production, even if it can be useful for other applications.

• Donor doping [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF]: A frequently used donor dopant is the Nb 5+ substitution of Ti 2+ (for example, using NaNbO 3 ). Contrarily to the electronic compensation effect of the Nb substitution of BT (that increases the conductivity), the compensation effect on NBT is the ionic one that reduces significantly the conductivity, even in low doping percentages. Other than changing the NBT-BT conductivity, the NaNbO 3 doping can also help to stabilize the permittivity in temperature, as it was shown in section 1.4.1.

For this reason, the NaNbO 3 doping could be used to increase temperature range of stable permittivity.

• Co 3 O 4 and CoO [START_REF] Guo | Improved electrical properties of Co-doped 0.92 NBT-0.04 KBT-0.04 BT lead-free ceramics[END_REF][START_REF] Ming | The temperature-dependent piezoelectric and electromechanical properties of cobalt-modified sodium bismuth titanate[END_REF]: It is an industrially used interstitial additive in BT ceramics.

In NBT or NBT-BT-KBT, the Co is incorporated in the crystal lattice, substituting the Ti 4+ ions. In pure NBT 0.3wt% of CoO addition acts as a sintering aid, increasing the grain growth and the density. It also increases the temperature of the maximum permittivity to 663 • C, decreases the tan δ and stabilizes ε r for temperatures lower than 400 • C. In the solid solution NBT-BT-KBT with 4wt% of NBT and KBT, it also acts as a sintering aid when the percentage of Co 3 O 4 is ≤0,4%. In this case, the Co doping increases the depolarization temperature T d , decreases tan δ at temperatures lower than the T d and increase tan δ and ε r dispersion at higher temperatures. This indicates that doping with Co increases the conduction at high temperatures. However, it might be an interesting doping, since the properties at moderate temperatures are improved.

• MnCO 3 [START_REF] Fen | Effects of manganese additive on piezoelectric properties of (Bi 1/2 Na 1/2 )TiO 3 -BaTiO 3 ferroelectric ceramics[END_REF]: It is another industrial interstitial additive used in low quantities (≤ 0.8%). In this case, Mn acts as a sintering aid, increasing the density and the grain growth and decreasing the sintering temperature. The maximal density is reached for 0.1wt% and the minimum dielectric losses are obtained for 0,8wt% of MnCO 3 addition. The permittivity always decreases with increasing Mn content. When it is added at higher quantities, Mn form precipitates and it creates air holes at the grain boundaries, decreasing the density and deteriorating the NBT-BT properties.

Conclusion

This chapter discussed the context and the problematic of the thesis, to explain the industrial specifications and limitations that apply to the choice of the base material for the multilayer ceramic capacitors (MLCC) used for high temperature electronics.

The MLCCs are the most consumed capacitor type in the world, due to their high volumetric efficiency, good reliability, and frequency features. The annual MLCC production is more than 100 billion units and its market grew around 20% each year since the beginning of the decade. One of the key factors contributing to this is the increase of the electronics production and its use in high-technology fields, such as controlling systems for transportation, aerospace, and military applications.

However, the environmental demands for the industrial production are increasing nowadays. In this context, the REACH and RoHS regulations are especially important for the MLCC production since the use of lead in the MLCC production will be soon forbidden for non-military or aerospace applications. This creates the need to develop new lead-free materials that can meet the environmental expectations.

Moreover, new MLCC applications and industrial demands are being created everyday. In this context, the high temperature electronics demands are growing, due to new applications such as the deep oil drilling, the use in train and airplane breaks, and also the creation of a new electric airplanes. Moreover, the MLCC miniaturization trend also intensifies to the need to develop new high-temperature capacitors. It is estimated that the electronic systems should be capable to work at a maximum temperature of 300 to 350 • C.

Today, the high-temperature MLCC production are limited to capacitors that can operate in temperatures up to 200-250 • C. It is therefore imperative to bring out new lead-free materials capable of meeting the expectations of electronics at around 300-350 • C.

The MLCC production process in Exxelia is based on the tape casting of a ceramic slurry composed of a ceramic powder, a solvent, a binder and other additives, to improve the final properties of the ceramic tapes. The "green" ceramic tapes are screen printed with a Ag-Pd electrode and the blocks of alternated layers of ceramic and metal is co-sintered between 1000 and 1300 • C. Sintering is done in industrial furnaces, where the sintering atmosphere and the pressure cannot be controlled.

The compatibility with the current production method in the MLCC industry and, more specifically, in Exxelia is an important limitation, since ideally no major changes should be done to the process, for the new dielectric to be useful for industrial production with reduced costs. Some important industrial limitations include the use of a tape casting slurry, the sintering process in a furnace without the possibility of controlling the atmosphere, the pressure or other heating sources (such as electric current and microwaves), the compatibility with the Ag-Pd electrodes and the price and market limitations on the ceramic composition.

Considering these industrial limitations and the new high-temperature electronics demands, a specification document was created to sum up the specific requirements for the dielectric material studied in this thesis, taking into account its future lead-free high-temperature MLCC application.

The main objectives of this work include an operation temperature range from 25 • C to 300-350 • C, an operation frequency range from 400Hz to 100MHz with a standard measurement frequency of 1kHz, a relative permittivity between 1000 and 2000 at 1kHz, a permittivity variation of ± 15% in the operating temperature range when compared to a reference temperature within this range, a maximum loss value of tan δ < 2.5% at 1 kHz, an insulation resistance of 10s from 250 to 300 • C and 1s from 300 to 350 • C, a layer thickness between 5 to 20 µm or less, a grain size of the ceramics of 0.3 to 0.5 µm before sintering and 0.5 to 2 µm after sintering and a dielectric strength of 25 to 60 V/µm.

To achieve these objectives and considering the industrial and environmental restrictions, an extensive study of the main available lead-free dielectric families was carried-out. The choice of the final material was done considering the permittivity value, the dielectric losses and relative permittivity values, the similarity between the the desired operating temperature range and the temperature range to have tan δ ≤ 2.5% and a variation of 15% in the relative permittivity, the insulation resistance at 300 • C, and the industrial feasibility.

In this context, three families of lead-free materials were reviewed: the BaTiO 3 -based materials, the K 0.5 Na 0.5 NbO 3 -based materials and the Na 0.5 Bi 0.5 TiO 3 -based materials.

The NBT-BT solid solution at the MPB was chosen as the base dielectric material, since it has interesting properties that could be used for the MLCC production. Firstly, it presents two dielectric anomalies: the first at the depolarization temperature T d is a frequency dependent shoulder and the second at the maximum relative permittivity temperature T m is a permittivity maximum. These phase transitions give the NBT-BT a more stable permittivity in temperature when compared with BT. It also shows low dielectric losses from T d to T m .

For the undoped NBT-BT the best properties reported in the literature are ε r =2700±15%from 60 to more than 450 • C, tan δ ≤ 2.5% from 100 to 350 • C and a thin double hysteresis loop at room temperature, when an excess of bismuth and a deficiency of sodium are used. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] Moreover, the MPB between 6% and 7%BT, which has both rhombohedral and tetragonal crystalline symmetry, improves the permittivity values and its variation in temperature when compared to pure BT. Finally, the NBT-BT has a double hysteresis loop between 200 • C and 300 • C, even though it is actually an ergodic-relaxor. This makes it interesting for energy storage applications.

The NBT-BT solid solution may also be further improved through the formation of new solid solutions with KNN and SBT. Other useful dopants and additives may be used, such as isovalent doping (K + substitution of Na + or Y 3+ and La 3+ substitution of Bi 3+ , and Zr 2+ substitution of Ti 2+ ) to decrease the oxide-ion conductivity, donor doping (Nb 5+ substitution of Ti 2+ ) to decrease the conductivity and stabilize the permittivity in temperature and addition of Co and Mn in small quantities to increase the final density and decrease the dielectric losses.

Chapter 2

Synthesis method

The objective of this chapter is to develop a synthesis method that is compatible with industrial production and enables to obtain samples matching Exxelia's specifications.

The main synthesis methods are first reviwed, before their respective industrial limitations are presented. The solid-state synthesis was chosen for this thesis, but it had to be improved to meet Exxelia's requirements. The way several parameters have been studied and optimized is therefore presented.

Before the existance and afterwards the influence of secondary phases is reported, leading to an optimized synthesis route for the NBT-6%BT meeting Exxelia's requirements.

Choice of the synthesis method

The synthesis method is composed of the method used to obtain the NBT-BT powder and of the sintering method.

Currently, solid-state reaction is the most used synthesis method in industries and the one used for MLCC production in Exxelia. Different synthesis methods used for the NBT-BT synthesis are reviewed, in order to choose the most adapted one for Exxelia's specifications. [START_REF] Cernea | Sol-gel synthesis and characterization of BaTiO3-doped (Bi0.5Na0.5)TiO3 piezoelectric ceramics[END_REF][START_REF] Mercadelli | Influence of the synthesis route on the properties of BNBT ceramics[END_REF][START_REF]Sol-Gel Science for Ceramic Materials[END_REF] The sol-gel synthesis method is used because it is based on a simple reaction that only requires mild temperatures to form the gel and the properties of the materials can be easily modified. This method uses salts of A and B cations of the perovskite and involves a series of hydrolysis and condensation reactions. [START_REF]Sol-Gel Science for Ceramic Materials[END_REF] For NBT-BT, Mercadelli et al.( 2009) [START_REF] Mercadelli | Influence of the synthesis route on the properties of BNBT ceramics[END_REF] and Cernea et al.( 2010) [START_REF] Cernea | Sol-gel synthesis and characterization of BaTiO3-doped (Bi0.5Na0.5)TiO3 piezoelectric ceramics[END_REF] use the sol-gel synthesis with sodium, barium and bismuth acetate in water and acetic acid solutions or bismuth nitrate in nitric acid [START_REF] Cernea | Sol-gel synthesis and characterization of BaTiO3-doped (Bi0.5Na0.5)TiO3 piezoelectric ceramics[END_REF][START_REF] Mercadelli | Influence of the synthesis route on the properties of BNBT ceramics[END_REF].Titanium is then added by Titanium IV isopropoxide in 2-propanol and isopropanol, or by titanium acetate in nitric acid. The solutions are mixed drop-wise to produce a Bi-Na-Ba-Ti complex solution (sol). After stirring under mild heating, the gel is formed, dried, and the resulting powder is heated at temperatures around 200 and 500 • C to obtain the desired single-phase powder.

Sol-gel

Once optimized and after sintering at 1150 • C for one hour in air, this synthesis method gives a single phase material and a uniform microstructure. However, the density of the ceramics obtained from sol-gel powders is usually lower than for the ones obtained by solidstate reaction. The dielectric properties of the material are similar to those obtained by solidstate reaction and Spark-plasma sintering (see section 2.1.2). The ceramics obtained [START_REF] Cernea | Sol-gel synthesis and characterization of BaTiO3-doped (Bi0.5Na0.5)TiO3 piezoelectric ceramics[END_REF] have a permittivity of around 1200 at room temperature, a frequency dispersion for high temperatures, and an increase in ε for temperatures higher than 280 • C, which indicates an increase in the conductivity of the material (see Fig 2.1). So, even if the sol-gel synthesis method is based on a simple and easy to change chemical reaction, using powder from sol-gel method does not enable to obtain ceramics exhibiting superior properties. Moreover, this synthesis method would completely change Exxelia's production of MLCC, that is now based on the solid-state reaction and on the tape casting. So there would be no reason to adopt this synthesis method instead of the industrially used solid-state reaction.

In conclusion, the sol-gel synthesis method is not the ideal one for the industrial production of MLCC at Exxelia.

Solid-state reaction

The solid-state reaction is the most common synthesis method used for poly-crystalline materials, for example, in the industrial production of ceramic-based products, such as MLCC, as described in the section 1.3.

It consists in mixing "starting" powders hence "solid state", which are generally carbonates and oxides and then heating (calcinating) at high temperature, in order to induce the reaction. The calcinated powders are then pressed into a green body, followed by sintering to get a ceramic.

The solid-state synthesis of the NBT-BT uses TiO 2 , Bi 2 O 3 , NaCO 3 and BaCO 3 as starting powders. These powders are weighed according to the NBT-BT stoichiometric composition and then they are mixed by ball milling during one hour [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF][START_REF] Spreitzer | Sodium deficiency in Na 0.5 Bi 0.5 TiO 3[END_REF] or by vibratory milling using ethanol as a milling solvent during 8 hours [START_REF] Yusong | FABRICATION AND MECHANICAL PROPERTIES OF Na0. 5Bi0. 5TiO3-BaTiO3 LEAD-FREE PIEZOELECTRIC CE-RAMICS[END_REF]. After the mixing, the powders are dried at 80 • C.

The calcination step varies depending on the study. For Yusong et al. [START_REF] Yusong | FABRICATION AND MECHANICAL PROPERTIES OF Na0. 5Bi0. 5TiO3-BaTiO3 LEAD-FREE PIEZOELECTRIC CE-RAMICS[END_REF], the calcination is done at 900 • C for 2h, but no more details on calcination atmosphere or state of the powders is given. For Lidjici [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF], the calcination was done at 825 • C for 4h in air, with a heating ramp of 3 • C/min and the cooling done in air. Finally, for Spreitzer et al. [START_REF] Spreitzer | Sodium deficiency in Na 0.5 Bi 0.5 TiO 3[END_REF], the calcination using a uniaxially-pressed NBT-BT powder (100 MPa) is done in two steps. The first one at 800 • C for 5h and the second one at 850 • C for 5h with intermediate cooling and grinding step between the two calcinations. The uniaxial pressuring of the powders can decrease the loss of the volatile oxides (bismuth and sodium oxides).

After the calcination, the NBT-BT powder is either directly uniaxially pressed into pellets, or ball milled again. Finally, the pellets are uniaxially pressed with or without the use of a polymer, such as PVA, as a binder to improve the casting ability, before being sintered. [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF][START_REF] Spreitzer | Sodium deficiency in Na 0.5 Bi 0.5 TiO 3[END_REF][START_REF] Yusong | FABRICATION AND MECHANICAL PROPERTIES OF Na0. 5Bi0. 5TiO3-BaTiO3 LEAD-FREE PIEZOELECTRIC CE-RAMICS[END_REF] The sintering can be done using different methods to decrease the bismuth and sodium evaporation and the consequent formation of oxygen vacancies.

So, the solid-state method is the one that has been chosen for this thesis, taking into account the resulting powders and Exxelia's requirements.

Sintering

The second stage of the synthesis method is the sintering of the powder to obtain a ceramic. The main sintering techniques are revised below.

"Traditional" sintering in an atmosphere

Because of the volatility of Na and Bi, it is necessary to create a Na and Bi-rich atmosphere in the crucible during synthesis, to limit the loss through evaporation of the volatile species. The created vacancies may alter the material's properties. In the case of NBT-BT, as it will be shown in the section 3.2.1.1, the bismuth evaporation and the oxygen vacancies created, drastically increase the material conductivity, which is detrimental for the MLCC properties.

A customary method to prevent the creation of vacancies of volatile elements is to cover the sample with the same composition powder. In the case of the NBT-BT ceramics, [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] the sintering is done in a covered alumina crucible at temperatures between 1100 • C and 1200 • C.

In this study, the same "traditional" sintering atmosphere was done. Properties of the asobtained ceramics will be presented in section 2.3.4.4.

However, after the sintering, it is necessary to cut the samples with a circular-saw and then to polish it, to remove the NBT-BT powder used as an atmosphere that adhered to the ceramics. This would not be possible (either technically or economically) for the MLCC production, so the use of an NBT-BT powder was not considered ideal for the MLCC production (see section 2.3.4.4) and required an alternative that will be presented in section 2.2.1.1.

Spark Plasma Sintering sintering

The Spark Plasma Sintering (SPS) technique is normally used to get dense ceramics in a short time and with nanosized grains. It consists in loading the powder in a graphite die and passing a high AC or DC current through the graphite die and the sample, while applying a uniaxial pressure. The SPS requires a reducing atmosphere, due to the need of using the graphite dies. The heat created by Joule effect densifies the ceramics and nearly 100% relative densities can be achieved at relatively low temperature and short time (25 minutes and 727 • C [START_REF] Berbecaru | Structural and Electrical Properties of BNT-BT0 . 08 Ceramics Processed by Spark Plasma Sintering[END_REF][START_REF] Mudinepalli | Structural, dielectric and ferroelectric properties of lead-free Na0.5Bi0.5TiO3 ceramics prepared by spark plasma sintering technique[END_REF]) when compared to the traditional sintering methods, since the heating comes from an internal source.

In the case of pure NBT, this sintering method was used to decrease the sintering temperature and reduce the evaporation of sodium and bismuth. The sintering temperature of pure NBT could be decreased by 300 • C (from 1150 to 850 • C), obtaining a final relative density close to 100%. [START_REF] Mudinepalli | Structural, dielectric and ferroelectric properties of lead-free Na0.5Bi0.5TiO3 ceramics prepared by spark plasma sintering technique[END_REF] The relative permittivity at 100Hz of pure NBT sintered by SPS method was 1550 at room temperature and 6400 at its maximum value. The depolarization temperature was decreased to 180 • C (compared to 200 • C for traditionally sintered pure NBT). [START_REF] Mudinepalli | Structural, dielectric and ferroelectric properties of lead-free Na0.5Bi0.5TiO3 ceramics prepared by spark plasma sintering technique[END_REF] In the NBT-BT 8% case, the spark-plasma-sintered material showed some frequency dispersion, low relative permittivity, of about ε r = 750 at room temperature, and high conduction above 200 • C. The conduction is due to the formation of oxygen vacancies (the sintering is done in reducing atmosphere) and the formation of defects and cracks during sintering. [START_REF] Berbecaru | Structural and Electrical Properties of BNT-BT0 . 08 Ceramics Processed by Spark Plasma Sintering[END_REF] So, for the NBT-BT, the SPS does not have the expected advantages of this method (lower oxygen vacancies due to lower bismuth evaporation, leading to lower dielectric losses and conductivity). Moreover, the SPS is an expensive and energy-consuming sintering method and it requires reducing atmosphere (due to graphite die and vacuum atmosphere), which increases the vacancy formation in the final ceramics. Finally, it requires furnaces that allow the internal atmosphere control and the application of an electric current into the graphite die and, through the sample. For these reasons, this was not considered ideal for the MLCC synthesis at Exxelia.

Microwave sintering method

For the microwave sintering, [START_REF] Venkata Ramana | Synthesis of Lead Free Sodium Bismuth Titanate (Nbt) Ceramic By Conventional and Microwave Sintering Methods[END_REF] the green bodies of pure NBT were prepared using PVA as a binder and uniaxial pressure. The temperature inside the microwave furnace was controlled and the sintering was done at 950 • C for 30 minutes, with an effective heating rate of 100 • C/min, much faster than for solid-state sintering.

A more uniform grain size was obtained, compared to the traditional sintering method, as shown in [START_REF] Venkata Ramana | Synthesis of Lead Free Sodium Bismuth Titanate (Nbt) Ceramic By Conventional and Microwave Sintering Methods[END_REF]. The room temperature relative permittivity was also higher: ε r = 798 vs 720 for traditional method. Moreover, the dielectric losses decrease remarkably, from 4% for the traditional sintering to 2% for the microwave sintering at 250 • C.

However, this sintering method would require a change in industrial furnaces and it would not allow the co-sintering of the ceramics with the electrodes. So it is not possible to use microwave sintering for MLCC production.

As a consequence, none of the current sintering technique is suitable for industrial production of MLCCs. The "traditional" sintering using the same composition powder (NBT-BT) involves the removal of the NBT-BT powder that has amalgamated to the ceramic using a circular-saw. The SPS is expensive, would require a change of furnace, and results in a leaky material. The microwave sintering would also require a change of furnace and would not allow the co-sintering with the electrodes. So, a new sintering method or way to create a sintering atmosphere should be studied, in order to allow the use of NBT-BT for the MLCC production in a technically and economically applicable way, avoiding the formation of oxygen vacancies and minimizing conductivity.

Films, tape casting, and MLCC

The tape casting synthesis method is widely used for the synthesis of ceramic films and multilayer devices. The advantage of this method is that it allows the fast synthesis of thin and flat ceramic layers. [START_REF] Mistler | Tape Casting: Theory and Practice[END_REF] In this synthesis method, the ceramic suspension (slurry) is kept in a reservoir behind the doctor blade, though which the carrier (support where the films are casted) passes. The film thickness is controlled by the gap between the blade and the carrier. Section 1.2.6 shows how this method is applied in Exxelia for the MLCC production.

The slurry composition and synthesis method are a key point to obtain homogeneous films with good mechanical properties before sintering and high density after sintering. It is normally composed of a mixture of a ceramic powder, a solvent, a dispersing agent, a binder and a plasticizer. The function of each is explained in section 1.2.6.1.

The different proportions and the properties of each component material of the slurry affect its rheological properties and the properties of the final ceramic film obtained after sintering. So the optimization of the slurry is essential to obtain the adapted final material properties.

Most of the rare studies on NBT-BT films or multilayer devices prepared by tape casting are focused on piezoelectric applications. Some examples are:

• Kimura et al.synthesized NBT-BT by templated grain growth (tape casting of NBT-BT with platelet grains) to created textured material used for piezoelectric applications. [START_REF] Kimura | Preparation of crystallographically textured Bi0. 5Na0. 5TiO3-BaTiO3 ceramics by reactive-templated grain growth method[END_REF][START_REF] Song | Piezoelectric and dielectric properties in grain oriented (Bi0. 5Na0. 5) TiO3-BaTiO3 ceramics[END_REF] Even though textured materials can improve the piezoelectric properties, they are not interesting for the MLCC production, since an excessive increase in the piezoelectric coefficient may be a problem to practical capacitor applications.

• Zhang et al.synthesized NBT-BT by tape casting and sol-gel methods for piezoelectric application devices. The structure, ferroelectric and piezoelectric properties were measured. But no information is given on the dielectric properties. [START_REF] Zhang | Fabrication and Characterization of High-Frequency Ultrasound Transducers Based on Lead-Free BNT-BT Tape-Casting Thick Film[END_REF] • Yan et al.synthesized pure NBT films by sol-gel method and measured its ferroelectric properties for transducer application in high frequency piezoelectric devices. But again no information is given on the dielectric properties of the material. [START_REF] Yan | Microstructure evolution during sintering of multilayer ceramic capacitors: nanotomography and discrete simulations[END_REF] Groh et al.published the only study on NBT-BT prepared by tape casting for MLCC applications. [START_REF] Groh | High-Temperature Multilayer Ceramic Capacitors Based on 100 x (94Bi 1/2 Na 1/2 TiO 3 -6BaTiO 3 )-x K 0.5 Na 0.5 NbO 3[END_REF] The material studied was NBT-6%BT-xKNN with x = 12, 18, and 24 sintered with CuO as a sintering aid. The dielectric, structural and conductivity properties of the material were measured. The best obtained properties were a stable relative permittivity from 40 to 225 • C, low dielectric losses from 100 to 300 • C, and a high insulation resistance of 300s at 150 • C.

Even if the material's properties are promising, they still do not correspond to the industrial requirements of this work, since the usage temperature range is not sufficiently high as required by Exxelia.

In conclusion, tape casting a simple method for synthesizing ceramic layers and multilayer devices with adequate properties. It is widely used in the industry, including in Exxelia's MLCC production. However, a slurry composition and synthesis method optimization step is fundamental ftoor obtain the desired final properties.

For NBT-BT, this synthesis method was mainly studied for the development of piezoelectric devices and the results cannot be used for the MLCC applications. Only one study was published on NBT-BT prepared by tape casting for MLCC applications. However, the achieved results do not correspond the Exxelia's requirements.

Industrial limitations for each synthesis method

The industrial production and, more specifically, Exxelia's MLCC production imposes some limitations, specially due to the process and equipment available. A special attention has to be paid to the co-sintering of the dielectric and electrode layers, since this is a key point to obtain good quality MLCCs.

In this section, the industrial limitations for the synthesis method will be presented, to validate the synthesis method choice.

The production of the perovskite powder should be done with a simple synthesis method that can be carried out with the available equipment and material at Exxelia (horizontal and planetary ball-milling with different ball diameters, regulated-temperature furnace up to 1300 • C, high-temperature-resistant crucibles, blade stirrer, ZrO 2 powder to be used in high temperature processes, and slurry preparation products).

As it was shown in section 2.1.1, the sol-gel route does not present advantages, when compared to the traditional solid-state-reaction synthesis method and it is not compatible with the industrial equipment and materials. So, the only possible synthesis route for the NBT-BT-based MLCC is the solid-state route.

The production of the ceramic sheets needs to be done by tape casting of a slurry over Millard sheet, without the use of a substrate. So the templated grain growth cannot be used and show no technical interest for the production of MLCC, since low piezoelectric properties and low texture are preferable in capacitors, in order to avoid cracks.

Industrial compatibility of the sintering process

The MLCC have to be co-sintered with the electrodes in a controlled temperature furnace that can reach 1300 • C, as presented in the section 1.3. It is not possible to apply or control other parameters during the sintering, such as applying pressure and running an electric current through the sample, as in SPS. Moreover, the industrial furnaces cannot have their atmosphere controlled, since they are not sealed. Ideally, one should not have to separate the sample from the powder used to create the sintering atmosphere, even though minor surface contamination is not an issue as a polishing step is carried out after the sintering. This rules out the use of NBT-BT powder to create the sintering atmosphere.

As explained in section 2.1.2, the only sintering method that can be used for the MLCC production is the traditional sintering, using an appropriate atmosphere, to decrease the volatile species evaporation. Since the NBT-BT powder cannot be used, it is necessary to develop a new sintering method or atmosphere, in order to allow the use of NBT-BT for the MLCC, avoiding the increase of the material conductivity.

Sintering atmosphere

In this work, the sintering was done without the use of controlled atmosphere and using the NBT powder, as reported in [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF], to create the atmosphere during sintering. The results, presented in section 2.3.4.4, were used to demonstrate the need of creating a new method to control the sintering atmosphere for the NBT-BT industrial applications.

The atmosphere created from inert ZrO 2 powder was used. This powder covers the sample, thereby confining it and creating a Bi and Na saturated atmosphere around and close to the NBT-BT sample. The zirconium oxide was chosen as an inert powder due to its high melting and sintering temperatures and since it is often used in the industry, either to avoid volatile evaporation or to apply a mechanical force over the MLCC during sintering, avoiding the horizontal deformation of the capacitors. The results of using ZrO 2 to avoid volatilization will be presented in section 2.3.4.4.

In conclusion, the obvious and only choice for the synthesis method of the ceramic sheets is the tape casting with the pure perovskite powder synthesized by solid-state reaction.

Moreover, for both massive and layer NBT-BT, adding ZrO 2 powder in the crucible and covering the green body during sintering was tested to obtain NBT-BT perovskite ceramics that do not require post processing apart from polishing.

Solid-state reaction and improvements in this thesis

This section presents the synthesis method used for the NBT-BT synthesis, the improvements in the synthesis parameters studied in this thesis, and the influence of each parameter on the sample's structure, phase separation, and properties.

As it was explained in section 2.1, the solid-state reaction route was chosen as the synthesis method for NBT-BT powder. It consists in mixing oxides and/or carbonates through ball-milling, calcinating them, and sintering the samples by the traditional sintering method.

The mixing step creates an homogeneous reactant powder mixture while the calcination step promotes a solid-state reaction, forming the perovskite. For NBT-BT, this is an important step that should be done in a controlled atmosphere, to avoid evaporation of volatile species. A schematic representation of the closed crucibles and calcination atmosphere is shown in Fig. 2.2, where the atmosphere powder is composed of 50wt% of ZrO 2 , 25wt% of Bi 2 O 3 and 25wt% of Na 2 CO 3 . The role of the ZrO 2 on the atmosphere is to work as an inert high-melting-point powder, facilitating the withdrawal of the NBT-BT powder from the crucibles.

All calcinations were done at 900 • C for two hours, as discussed in section 2.1.2 and in The sintering step increases the material's density and forms the final ceramics through solid-state diffusion. This step should also be done in a controlled atmosphere, to avoid the loss of volatile. In this thesis, the sintered samples are covered by a powder to create a sintering atmosphere and obtain ceramics without the need of post processing.

Finally, for the ceramic sheets used in the MLCC, tape casting was used for shaping the layers.

Once the synthesis method is chosen, several parameters remain to be considered. The parameters analyzed and optimized in this thesis for the NBT-BT synthesis were: the weighing and drying of the reactants, the material of the ball-milling jars and balls, the size of the ball-milling balls, the ball-milling speed, time and solvent, the grain size of the starting powders, the reactants stoichiometry (or nominal stoichiometry), the use of a second ball milling after calcination, the shaping of the bulk samples (uniaxial or isostatic pressure with different values), the powder used to create the sintering atmosphere and the sintering temperature program for the ceramic samples, and the slurry composition and sintering conditions for the tape-casted samples.

Reactants weighing and drying

The first part of the synthesis consists in weighing the reactants, either in stoichiometric proportions or with an excess of volatile elements to compensate losses during calcination and sintering.

For the stoichiometric proportions and for the synthesis of 5g of powder, the weights are is presented in Table 2 ture, specially after being stored for a long time. The absorbed water does not change the appearance of the powders, however, its weight is taken into account when during weighting. Mahajan et al. (2017) showed that NBT-BT prepared with dried reactants have a larger polar phase (R3c) percentage when compared to the same material prepared with the un-dried powders. Moreover, NBT-BT prepared from un-dried powders present a larger Na deficiency, which leads to a lower depolarization temperature. Finally, the presence of more point defects in the NBT-BT prepared from un-dried powders increases the frequency dispersion and the dielectric losses at high temperature compared to the samples prepared from dried powders. [START_REF] Mahajen | Effect of processing on the Structures and Properties of Bismuth Sodium Titanate compounds[END_REF] This suggests that the drying of the reactants has a great influence on the final dielectric properties and should be evaluated in the present study.

To evaluate the average water quantity absorbed by Na 2 CO 3 and Bi 2 O 3 powders and its effect on the final material, both powders were dried during 24 hours at 400 • C. [START_REF] Mahajen | Effect of processing on the Structures and Properties of Bismuth Sodium Titanate compounds[END_REF] Initially, the weight variation during drying of Na 2 CO 3 and Bi 2 O 3 powders was evaluated. For the Bi 2 O 3 powder, the mass variation was 0.4% and for Na 2 CO 3 powder it was 2.5%. This is responsible for the Na and Bi non-stoichiometries, resulting in the change of the NBT-BT phase separation and on the dielectric properties (see section 2.3.2.6).

The influence of drying the hygroscopic reactants on the NBT-BT phase separation and its effects on the dielectric properties will be discussed on details in section 3.2.1.2. The best adapted synthesis method will, then, be defined based on Exxelia's specifications for the high temperature MLCCs.

Mixture of the reactants 2.3.2.1 Ball milling of the reactants

After weighing, the mixture is carried-out by planetary ball-milling using an yttriumstabilized zircona (YSZ) jar or a tungsten carbide (WC) jar.

The ball-milling was done either at 250 rpm during 4 hours (less energetic) or at 350 rpm during 8 hours (more energetic option). The ball-milling energy was changed to improve the homogeneity of the samples and decrease the phase separation (see sections 2.3.2.5 and 3.2.1.2). The solvent used for ball milling was either ethanol (as in [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF][START_REF] Spreitzer | Sodium deficiency in Na 0.5 Bi 0.5 TiO 3[END_REF][START_REF] Yusong | FABRICATION AND MECHANICAL PROPERTIES OF Na0. 5Bi0. 5TiO3-BaTiO3 LEAD-FREE PIEZOELECTRIC CE-RAMICS[END_REF]) or a mixture of ethanol and methyl-ethyl-ketone, as normally used in Exxelia.

Ten-millimeter-diameter balls were used for the first ball millings and no problem on the powder composition, color, or size was observed. More details on the influence of the ballmilling energy, the composition of the jar, and the solvent will be given in sections 2.3.2.2 and 3.2.1.3.

The main objective of this stage is to mix the initial powders homogeneously. However, it can result in some mechanical synthesis (that is, the formation of the product: NBT-BT) depending on the ball-milling parameters and in a decrease in the grain size of the reactant powders.

The use of a dispersing agent during ball-milling was also tested. The function of the dispersing agent is to keep particles apart from each other in the solvent (see section 1.2.6.1). During ball-milling, this improves the dispersion of the grains, affecting the final material properties, as shown in section 3.2.1.3. A commercial product called Borchi-gen-911, with a polymeric base, was used as a dispersing agent, since it is widely used industrially (including in Exxelia's MLCC production) and it does not react with the NBT-BT powder.

XRD of the ball-milled powder (250 rpm during 4h, using the dispersing agent) of sample "H" is compared with the same powder after calcination in Fig. 2.3, to check the presence of mechanical synthesis.

The partial mechanical synthesis of NBT-BT is evident on the X-ray diffractograms through the presence of some small characteristic peaks corresponding to the pseudocubic (110), the (200), the (211), and the (111) peaks of the NBT-BT (see Fig. 2.3). However, as it can be seen from the peaks intensity of the NBT-BT when compared to the peaks of the starting powders that the formation (mecanosynthesis) of NBT-BT during the first ball milling is minimal and this synthesis step can be considered mainly as a mixing step.

Moreover, no peak split can be observed in the calcined NBT-BT diffraction pattern in Fig. 2.3. This is because, as explained in section 1.4.2.1, NBT-BT is a non-ergodic relaxor at room temperature. So, when it is not polarized, as in the calcined powder, its average structure is cubic.

Influence of the jar and balls material

The jar and ball material has also a strong influence on the final properties of the sample, since the ball-milling energy (mechanical energy of the shock of the balls against the walls of the jar) is larger in the WC jar and balls, because the material is denser than the YSZ. Moreover, a possible contamination of the final material has to be taken into account.

Tungsten carbide (WC)

The effect of using the WC jar and balls for NBT-BT synthesis is evaluated by the "U-WC" sample properties. Table 2.11 p. 79 shows the synthesis conditions of "U-WC" sample (ball milling in WC jar before and after calcination for 8 hours at 350 rpm and sintered under ZrO 2 atmosphere powder for 3 hours at 1050 • C).

Formation of five different phases in the "U-WC" sample surface are observed in Fig. 2.4 and their composition, as determined by EDS, are reported in Table 2.2.

The results confirm the important contamination of the NBT-BT by the jar material.

It also shows a separation of the barium from the NBT to form secondary Ba-containing phase. This secondary phase does not result from the jar material, since it is also present in the NBT-BT milled in the YSZ jar.

Moreover, the measurements of the dielectric properties (Fig. 2.5) and the insulation resistance of this sample (0.06s at 200 • C) show that the tungsten contamination has a strong influence on the dielectric properties of the final material, decreasing the resistivity, increasing the dielectric losses, and increasing the frequency dispersion compared to the same sample prepared in the YSZ jar (sample "U" in Fig. 3 In conclusion, the WC jar and balls are not ideal for the MLCC production, since the tungsten contamination degrades the dielectric properties of the material. The grain size and the structure differences between samples "U-WC", ball milled in the WC jar, and "U", ball milled in YSZ jar, are also interesting to compare. The SEM images (Fig. 2.6) of those samples indicate that the grain size of the ceramic ball-milled in the YSZ jar is around 0.8 ± 0.05 µm and the one milled in the WC jar is around 1.5 ± 0.05 µm.

This difference in grain size is due to differences in the ball-milling energy. For both ball-millings, the same mass ratio between the balls and the powder was used, the ball mass being 10 times the powder mass. However, since the density of the WC balls are higher than that of the YZS balls, more YSZ balls were used and the ball-milling energy is also higher.

The X-ray diffraction of the as-sintered samples and samples after polishing and thermal • In the X-ray diffractograms of the sample ball-milled in the WC jar ("U WC"), the peaks are narrow and there is no change in the peak widths after polishing and relaxing strain compared to the X-ray diffractograms of the as-sintered sample (sintered samples before polishing and strain relaxing). There is also no peak splitting in both diagrams, which indicates that both samples present a pseudo-cubic structure, as expected for unpoled non-ergodic relaxors. However, both diagrams present extra peaks related to the Ba-rich and W-rich phases present in the sample surface and core.

• As-sintered samples ball-milled in the YSZ jar have narrow and more symmetrical XRD peaks when compared to the polished and strain-relaxed ones that have larger and asymmetric peaks. The as-sintered sample also show no XRD peak splitting, indicating a pseudo-cubic structure. However, polished and strain-relaxed samples present the same pseudo-cubic related peaks with the addition of a shoulder on the lower-angle side.

Kong et al.showed very recently the existence of a skin effect in NBT-BT. They claimed that due to stress differences between the sample surface (plane stress) and core (tri-axial stress), there is a lattice expansion normal to the surface. This is responsible for a stressinduced transformation that creates a phase coexistence of pseudo-cubic, rhombohedral, and tetragonal phases in the skin. [START_REF] Kong | Defect-Driven Structural Distortions at the Surface of Relaxor Ferroelectrics[END_REF] Other factors, such as the increased concentration of oxygen and bismuth vacancies at the surface, may also induce a chemical pressure and a phase coexistence, with an increase of the lattice parameter. Finally, the larger concentration of Ba and its resulting lattice deformation can also induce the same phase coexistence. [START_REF] Kong | Defect-Driven Structural Distortions at the Surface of Relaxor Ferroelectrics[END_REF] This phase coexistence may, then, be responsible for the low-angle-side shoulder peaks, reflecting a skin effect on NBT-BT. Since the effect may be due to stress differences between the core and the surface, it is always present, even after polishing. [START_REF] Kong | Defect-Driven Structural Distortions at the Surface of Relaxor Ferroelectrics[END_REF] For my NBT-BT samples prepared in the YSZ jar, the XRD presents low-angle-side shoulder peaks for the polished and strain-relaxed samples, as expected for the sample surface, due to skin effect. However, thin single peaks are observed in the as-sintered sample, contrary to what would be expected.

Detailed investigation is needed to explain why the skin effect is not present in the assintered samples. However, one hypothesis is that the variation of the local Ba concentration in the NBT-BT lattice may prevent the skin effect on the as-sintered samples. This hypothesis takes into account that the surface of the as-sintered samples show higher Na evaporation compared to Bi. So, there is an intense secondary Ba-containing phase separation in the surface of these samples (see section 2.4). This decreases the local Ba concentration in the lattice of the NBT matrix phase, creating a gradient of local Ba concentration in the A-site of the matrix phase. Finally, the internal chemical pressure and lattice deformation on the matrix phase is lower in the as-sintered sample's surface compared the their core, inhibiting the skin effect.

In conclusion, the presence of the low-angle-side peaks in the XRD of the polished and strain relaxed-samples is due to the skin effect and phase coexistence at the surface of these samples. The as-sintered samples do not show the same effect probably due to the effect of the decreased local Ba-concentration in the NBT-matrix phase owing to the increased secondary Ba-containing phases at the sample's surfaces.

ZrO 2

The "U" sample was used to evaluate the effect of using the YSZ jar and balls for the NBT-BT synthesis. Table 2.11 p. 79 shows the synthesis parameters of this sample ( ball milling in YSZ jar before and after calcination for 8 hours at 350 rpm and sintering under an atmosphere created by ZrO 2 powder for 3 hours at 1050 • C).

Separation of the barium from the NBT to secondary Ba-containing phases is illustrated in Fig. 2.8. The material of the jar is not an important factor for this phase separation, since the secondary Ba-containing phases is also seen in other samples, including the one prepared in the WC jar. Details on the secondary Ba-containing phases stoichiometries and formation are given in section 2.4.

For this specific sample, where a Bi excess and a Na deficiency are added to the reactants in order to get the nominal (reactants) stoichiometry of Na 0.44 Bi 0.48 Ba 0.06 TiO 3 , there is a separation of the Bi excess, forming a third Bi-rich phase (see Table 2.3). Fig. 2.8 also shows a small contamination with ZrO 2 , mainly on the secondary Bacontaining phases (see Table 2.3), but there is no phase formation with Zr as a main compound, contrary to the case of the "U-WC" sample. The ZrO 2 contamination on the secondary Ba-containing phases is probably due to the contact between the sample's surface and the ZrO 2 powder during sintering (see section 2.4).

The ZrO 2 used to create the sintering atmosphere is also observed on the XRD diagrams in Fig. 2.7 p. 50. It is, then, necessary to polish the sample after sintering to eliminate this ZrO 2 contamination. As the polishing is already a planned stage during the MLCC production, (see section 1.2.6), this is not a problem for industrial processing.

After polishing, the ZrO 2 peaks are not present anymore, but the diffraction peaks of the NBT-BT are large and asymmetric, due to the skin effect that induces a phase coexistence in the sample's surface (see section 2.3.2.2). Moreover, a strain is introduced during polishing, so a strain relaxation step is also needed. Details on strain relaxation will be given in section 4.2.2.1. Finally, Fig. 2.8 p. 50 also reveals a limited silicium contamination in the form of small grains. However, this Si-rich phase, coming from the polishing sand paper, is negligible for the sample structure and properties, due to its low quantity.

As a conclusion, the ball milling in the YSZ jar and balls is the best option for the NBT-BT synthesis for applications in MLCC.

The influence of the other synthesis parameters (the drying of the reactants, the ballmilling solvent, speed and time, the use of a dispersing agent during ball-milling, the grain size of the Na 2 CO 3 reactant, the strain relaxation and the powder used to create a sintering atmosphere) and the sample stoichiometry on the dielectric properties will be discussed in Chapter 3.

Influence of the solvent

Two different solvents were used during the ball milling: ethanol, the most commonly used ball-milling solvent for NBT-BT synthesis [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF][START_REF] Spreitzer | Sodium deficiency in Na 0.5 Bi 0.5 TiO 3[END_REF][START_REF] Yusong | FABRICATION AND MECHANICAL PROPERTIES OF Na0. 5Bi0. 5TiO3-BaTiO3 LEAD-FREE PIEZOELECTRIC CE-RAMICS[END_REF] (see section 2.3.2.1), and a mixture of 29.7wt% of ethanol and 70.3wt% of methyl-ethyl-ketone (MEK), as used in the MLCC production at Exxelia.

The influence of the solvent on the secondary Ba-containing phases separation (size and concentration) was analyzed based on SEM images of the polished surface of two different samples: "V" and "N". The synthesis parameters of each sample is presented in Table 2.11 p. 79 and they are the same, except for the solvent (ethanol and MEK) for sample "N" vs ethanol for sample "V".

Table 2.4 shows the size and percentage of secondary Ba-containing phases in each sample. Considering a 95% confidence interval, the average size and concentration (percentage of area) of the secondary Ba-containing phases for the two samples are similar. This implies that the solvent does not have an influence on the phase separation in the NBT-BT samples.

The structure of samples "V" and "N" can also be compared via XRD measurements, shown in Fig 2 .9.

The diffraction patterns of the two samples are similar. The extra peaks in the as-sintered samples are due to the ZrO 2 powder used to create the sintering atmosphere and have no influence on the bulk material structure (see section 2.3.2.1). FIGURE 2.9: XRD measurements of samples "V" and "N" with phase identification

To sum up, the change in the solvent from pure ethanol to the ethanol and MEK mixture does not change the phase separation nor the structure of the NBT-BT.

Influence of the grain size of the reactants

Two different Na 2 CO 3 grain sizes were used for the initial powders: the "granular" Na 2 CO 3 that has an average grain size of 380µm and the "powder" Na 2 CO 3 , with a average grain size of 0.9µm.

Two samples were prepared with un-dried initial powders, 250 rpm ball milling for 4 hours, using ethanol as a solvent and a dispersing agent during the ball milling. The "H" sample used "granular" Na 2 CO 3 while the "V" sample used "powder" Na 2 CO 3 (see Table 2 2.10, it can be concluded that both grain sizes give rise to the same NBT-BT structure. Both as-sintered samples present thin pseudo-cubic NBT-BT peaks and peaks coming from the ZrO 2 atmosphere powder and from the secondary Ba-containing phases. Both polished and strain-relaxed samples show no peaks related to the secondary Ba-containing phases or to the ZrO 2 , even though the widths of the peaks for the "V" sample ("powder" Na 2 CO 3 ) are larger than for the "H" sample ("granular" Na 2 CO 3 ), due to the skin effect (see section 2.3.2.2).

In conclusion, the grain size of the Na 2 CO 3 initial powder does not affect the phase formation nor the structure of the NBT-BT.

Influence of the speed and duration of ball milling

The speed and duration of ball milling were initially chosen as 250 rpm and four hours. To verify the influence of the ball-milling energy and to increase the homogeneity of the final samples, new samples were synthesized with 350 rpm and 8 hours. The secondary Bacontaining phases separation and the structures were compared.

For the secondary Ba-containing phases separation, three different comparisons were done between the SEM images of the polished surface: "E" vs "B" samples, "I" vs "H" samples, and "P" vs "N" samples. The synthesis parameters of each sample are presented in Table 2.11 p. 79 and the parameters that vary between the samples are summarized in Table 2.6.

From Table 2.7, it can be seen that, in the case of the samples ball-milled without dispersing agent ("B" and "E" samples), the increase in the energy of ball milling decreases drastically the average size of the secondary Ba-containing phases, but it increases the proportion of this phase. In the case of the powders ball-milled with dispersing agent in the same solvent (ethanol -"H" and "I" samples), the change in the ball-milling energy does not affect the average grain surface and volume fraction of the secondary Ba-containing phases.

The structure differences between those samples were also analyzed via XRD measurements and are presented in Figures 2.11 (as-sintered) and 2.12 (after polishing and strain relaxation). 2.7: Secondary Ba-containing phases characterization for samples "E" (dried reactants, high-energy ball-milling), "B" (dried reactants, lowenergy ball-milling), "I" (un-dried reactants, ethanol as solvent, high-energy ball-milling), "H" (un-dried reactants, ethanol as solvent, low-energy ballmilling), "P" (un-dried reactants, ethanol+MEK as solvent, high-energy ballmilling) and "N" (un-dried reactants, ethanol+MEK as solvent, low-energy ball-milling).

Sample

It can be seen that, except for sample "N", all the as-sintered samples present NBT-BT pseudo-cubic structure with some peaks coming from the powder used to create a sintering atmosphere (ZrO 2 ) and some peaks coming from the secondary Ba-containing phases. The detailed Ba-rich peaks identification will be discussed in section 2.4. The as-sintered samples show pseudo-cubic structure in agreement with the relaxor character of the material (pseudocubic structure matrix with PNR of R3c symmetry) before poling and with no induced stress or grain size peak deformation. [START_REF] Ranjan | Structure and dielectric properties of (Na0. 50Bi0. 50) 1-xBaxTiO3: 0 x 0.10[END_REF][START_REF] Schader | Stress-modulated relaxor-to-ferroelectric transition in leadfree (N a 1/2 B i 1/2) Ti O 3-BaTi O 3 ferroelectrics[END_REF] For the polished and strain-relaxed samples, peaks from the ZrO 2 and from the secondary Ba-containing phases disappear. FIGURE 2.11: XRD measurements of as-sintered samples "P", "N", "H", "I" and "B" with phase identification.

Influence of the NBT-BT stoichiometry

The Bi 3+ excess and/or the Na + deficiency in NBT-BT 6% have a great influence on the sample properties. This initially creates a pinched P-E loop, the pinching increasing with Bi-excess or Na-deficiency. Fig. 2.13 show the P-E loop of NBT-BT 7% with different Na and Bi nominal stoichiometries. Note that the behavior of NBT-BT 6% and NBT-BT 7% are similar, since both are on the morphotropic phase boundary of the NBT-BT solid solution. [START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF].

The pinched P-E loop with Bi-excess or Na-deficiency behaviour is attributed to the generation of "antiferroelectric-like" micro-regions in a macroscopic ferroelectric matrix through changes in the Na/Bi ratio. This is attributed to to the appearance of orthorhombic Pnma sheets within the rhombohedral R3c matrix, similar to the modulated phase proposed to be the origin of "relaxor AFE" behavior in pure NBT. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] An AFE-like to metastable FE reversible transition is induced by applying an external electric field, giving rise to the double P-E loop observed at room temperature for high bismuth excess and/or high sodium deficiency compositions.

The double hysteresis loop is desirable for energy storage materials, since it may increase the recoverable stored energy and it may decrease the energy losses when applying an FIGURE 2.12: XRD measurements of polished and strain-relaxed samples "P", "N", "H", "I" and "B" with phase identification.

alternated external electric field. [START_REF] Qi | Linear-like lead-free relaxor antiferroelectric (Bi 0.5 Na 0.5 )TiO 3 -NaNbO 3 with giant energy-storage density/efficiency and super stability against temperature and frequency[END_REF] The effects of stoichiometry change can also be described by a decrease in the depolarization temperature, explained in section 1.4.2. As a consequence, the minimal temperature for having low dielectric losses (T tan δ ,min in Fig. 2.14) and low permittivity reduction on poled samples (T ε,min in Fig. 2.14) are displaced to lower temperatures and the material becomes useful for MLCC applications from room temperature.

Finally the decrease in the Na/Bi ratio decreases the DC conductivity of the NBT-BT FIGURE 2.13: P-E loop for non-stoichiometric NBT-BT 7% (Na x/100 Bi y/100 Ba 0.07 TiO 3 ) [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] (see section 3.2.1.1) [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] increasing the insulation resistance of the material. This is also useful for the MLCC production, as presented in section 1.3. Guo et al.measured the dielectric properties of the nominal (reactant) composition Na 0.44 Bi 0.48 Ba 0.06 TiO 3 (see Fig. 2.15). A pinched P-E loop and no sharp anomaly on poled material, either for the permittivity or for the dielectric losses were also measured as the depolarization temperature lower than room temperature. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] For this reason, the influence of the stoichiometry on the dielectric properties of NBT-BT were tested using this composition FIGURE 2.14: Relative permittivity and loss factor showing the stoichiometry effects on the depolarization temperature, and its useful consequences on the dielectric properties for MLCC applications. Vertical lines stand for the minimal temperature for having low dielectric losses (T tan δ ,min ) and permittivity reduction (T ε,min ). [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] ("U" sample).

The "U" sample (Na 0.44 Bi 0.48 Ba 0.06 TiO 3 nominal composition) is composed of three main phases (see section 2.3.2.2) and one Si-rich phase, coming from the polishing paper and inert from a dielectric point of view, as observed in the SEM images of the polished surface and cross-section of this sample (Figures 2.8 p. 50 and 2.16 respectively). The composition of each phase was measured using EDS analysis and the results are presented in Table 2.3 p.

51.

The phases can be identified as secondary Ba-containing phases (also present in other samples), a Bi-rich phase (due to the non-stoichiometry of this composition) and a pure NBT phase (also present in other samples). The SEM image reveals the presence of the Bi-rich phase in the center of the sample, confirming the evaporation of bismuth oxide during sintering.

Comparing the volume fraction of the secondary Ba-containing phases of the "U" sample (complete synthesis parameters in Table 2.11 p. 79 ) with the sample synthesized using the same parameters, but a nominal NBT-BT 6% composition for the reactants ("P" sample), the larger bismuth concentration in the "U" sample decreases the percentage of secondary Ba-containing phases. The effect of this change in the dielectric properties of the material will be analyzed in section 2.4.

Two other samples were prepared after comparing the measured "U" sample composition with the nominal one "P": the "Y" sample, done using the same synthesis parameters as "U" but with an excess of 9.5% molar of sodium and 2.1% molar of bismuth, to obtain after sintering the nominal "U" composition (theoretical composition), the "Z" sample, with an excess of 16.9% molar of sodium, to obtain nominal NBT-BT composition after sintering.

These two samples were also observed using SEM and showed no phase separation. This implies that, not only the increase of bismuth concentration in the reactants, but also the increase of sodium concentration result in lower volume fraction of secondary Ba-containing phases.

The XRD diagrams of the three nominally non-stoichiometric samples ("U", "Y" and "Z") were compared with the one of the nominal NBT-BT 6% synthesized under the same parameters (Figures 2.17 and 2.18). The four samples after sintering show a pseudo-cubic perovskite structure and extra peaks corresponding to the ZrO 2 powder used to create the sintering atmosphere and to the secondary Ba-containing phases. The polished and strainrelaxed samples show wide and asymmetric peaks, as explained in section 2.3.2.1, but they correspond well with each other. So, the change in bismuth and sodium stoichiometry in the reactants do not change the structure of the NBT-BT ceramics.

As a summary, the changes in the stoichiometry of the reactants do not affect the final material structure but the increase in bismuth and/or sodium concentrations decreases the secondary Ba-containing phases volume fraction. The increase in the Bi/Na ratio creates a partial separation of the bismuth excess in a Bi-rich phase.

Slurry preparation and tape casting 2.3.3.1 Introduction

Unlike NBT-BT ceramics, for the synthesis of tapes, the second ball milling is done together with the slurry preparation. The slurry is composed of a mixture of powdered ceramic, solvent, deflocculant, binder and plasticizer. The function of each component is explained in section 1.2.6. The slurry preparation is the most important factor to obtain a stable, resistant, and high-density ceramic tape.

After the slurry preparation, the tape-casting method is used to produce the ceramic tapes used in MLCC production.

Slurry composition

The initial slurry composition was defined taking into account the Exxelia's slurry compositions used in the organic MLCC production line and studies on the ideal concentration of binder, plasticizer and dispersing agent in X7R slurry. [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF] PVB was chosen as binder and PEG-400 (poly-ethylene-glycol with average molecular mass of 400 g/mol) was chosen as a plasticizer, since they are widely used in the industry and they do not react with NBT-BT. A commercial product called borchi-gen-911, with a polymeric base, was used as the dispersing agent, since it is also used in Exxelia and industrially for the MLCC production and since it does not react with the NBT-BT powder.

The stability of the slurry increases with increasing amounts of PVB (binder) and PEG (plasticizer) since they are responsible for the mechanical properties of the green tapes. However, an excess of these products can decrease the relative density of the ceramic tapes after sintering. The effect of the increase in concentration of the dispersing agent is not so clear. However, the slurry has better properties when it is added, even in low concentrations. [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF] The quality of the X7R slurry can be analyzed by its sheering properties, by the tensile diagram and micro-structure of the green tape and by the relative density of the sintered tapes. After analyzing different slurry compositions, [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF] concluded that the best one was as presented in the first column of the Table 2.8 [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF].

The slurry used in BT-based MLCC organic production line in Exxelia is presented in the second column of the Table 2.8.

Considering both compositions, the initial slurry composition in this study is as presented in the third column of the same table. The PVB, dispersing agent and PEG quantities added to the final slurry were taken from Liu et al.(2012) [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF], since these parameters were FIGURE 2.17: XRD diagrams of as-sintered "P", "U", "Y" and "Z" samples with phase identification.

Ball-milling (mixing) conditions

The initial ball-milling conditions for the preparation of the slurry were based on the ZrO 2 tape-casting method and on the X7R slurry synthesis parameters.

For the X7R slurry preparation, the ceramic powder, the dispersing agent and the solvent are first mixed by stirring for four hours and, after the plasticizer and the binder are added, the slurry is mixed for 10 hours. [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF] However, for the ZrO 2 tape casting method, the ceramic powder, the dispersing agent and the solvent are ball-milled at 300 rpm for 12 hours. Then PVB and PEG are added and the mixture is again ball-milled at 300 rpm for 2 hours.

Initially, the ZrO 2 synthesis method was adopted, since it is based on a ball milling in YSZ jar and balls.

Calcination and sintering

The second part of the synthesis consists in calcinating the ball-milled powders (to promote a solid-state reaction forming the perovskite) and of sintering the powders after calcination.

The sintering step is one of the most important for the NBT-BT production. During this step, the material is densified and the organic compounds are eliminated. The surface energy and the temperature are the driving forces for the solid-state mass exchange, responsible for the densification. So, the sintering can be controles by the shaping of the samples (pressuring or tape casting), the grain size and the temperature of the sintering.

Due to the high volatility of the reactants, the sintering can significantly change the final properties of the NBT-BT. So the sintering atmosphere is crucial for improving it. The existing atmospheres used for the NBT-BT sintering are not ideal for the MLCC production (see section 2.1.2), so a new sintering method or atmosphere has been studied to allow the use of this material on MLCC production.

Density problem for ceramic samples

After calcinating and sintering of NBT-BT 6% ceramic at different sintering temperatures (sample "Density 1" in Table 2.11 p. 79 ) and without the second ball-milling step, the highest relative density was around 91.5% ± 2.5% for the sintering temperature of 1150 • C. The relative density of the sample sintered at 1050 • C (the only temperature with no second phase peak in the XRD diagram of the as-sintered samples) was around 85% ± 2.5%. These densities are not compatible with Exxelia's requirements, since the ceramics used in MLCCs should have a relative density of at least 95% to avoid interfacial defects and loss increase.

The density measurement were done using a caliper and a precision balance and the results are presented in Fig. 2.19 p. 62.

Ball milling and/or mechanical synthesis after calcination

To solve the density problem of NBT-BT ceramics, a second ball-milling step was added after calcination (see "Density 2" in Table 2.11 p. 79 ). Two sets of samples were done with the same synthesis parameters (presented in Table 2.11 p. 79 ) and different sintering temperatures during three hours and with a temperature ramp of 120 • C/h in heating and 200 • C/h in cooling. The second ball-milling, as the first one, was done in the YSZ jars, to avoid the contamination of the material with the W coming from the tungsten carbide jars (see section 2.3.2.2).

The relative densities (Fig. 2. [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF] show that the second ball-milling is useful to increase the final density of the samples. The maximum relative density after the second ball milling and after sintering is 93.5% ± 2.5% at a sintering temperature of 1150 • C and 91% ± 2.5% at 1050 • C. Considering the measurement uncertainty, the maximum density value for the NBT-BT after the second ball-milling and the sintering at 1150 • C may be sufficient for the MLCC production. However, some sintering optimization should still be done in the layer synthesis, to further increase the density of the ceramics (see Chapter 5). ders is noticed for all of the measurements carried out after the second ball-milling. This indicates a decrease in the grain size during the ball milling and also with increasing ballmilling energy as the full width at half maximum (FWHM) of the peaks from sample "H" before ball-milling is 0.56 degrees vs 0.67 degrees for sample "H" after 250 rpm and 4h ballmilling vs 0.79 degrees for sample "I" after 350 rpm and 8h ball-milling. The powders ball-milled after calcination with the 10mm-diameter balls were then heated at 400 • C for five hours in air, in order to oxidize the oxygen vacancies and relax any strain introduced during the second ball milling. The temperature choice of 400 • C was done to avoid sodium or bismuth evaporation, as it will be detailed in section 3.2.1.4. After this thermal treatment, the powder color was again white.

The oxygen vacancies cannot be easily detected in the XRD analysis [START_REF] Thangavelu | Evidence for the suppression of intermediate anti-ferroelectric ordering and observation of hardening mechanism in Na1/2Bi1/2TiO3 ceramics through cobalt substitution[END_REF] as they may increase the lattice parameter but they can change the color of an oxide, even at really low concentrations. [START_REF] Wang | Photophysical and photocatalytic properties of SrTiO3 doped with Cr cations on different sites[END_REF] So, the results indicate that the second ball milling with the 10 mmdiameter YSZ balls create oxygen vacancies in the NBT-BT that could have a negative effect in the MLCC productions, since it can result in a lower DC resistivity. [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] A Raman analysis was also done using an excitation laser with 633 nm wavelength. The ball-milled powder was measured, since a high concentration of oxygen vacancies decreases the wave number and increases the intensity of the 650-950 cm -1 ("D") band, as observed in Fig. 2.22 [START_REF] Thangavelu | Evidence for the suppression of intermediate anti-ferroelectric ordering and observation of hardening mechanism in Na1/2Bi1/2TiO3 ceramics through cobalt substitution[END_REF]. The Raman spectra at different positions for the sample before the second ball-milling (Fig. 2.23), after the second ball-milling (Fig. 2.24), and after thermal treatment (Fig. 2.25) are presented. The fit was done for bands C and D (see Fig. 2.22), using three peaks for each. [START_REF] Thangavelu | Evidence for the suppression of intermediate anti-ferroelectric ordering and observation of hardening mechanism in Na1/2Bi1/2TiO3 ceramics through cobalt substitution[END_REF] The mean peak position and intensities of each fit peak is shown in Table 2.9.

The fit for the heat-treated sample is presented in Fig. 2.26 as an example. By analyzing the peaks position, it can be seen that the difference in wavenumber between the three powders (their displacement) is not significant, since the greatest difference between the wavenumbers is 4 cm -1 . Moreover, the peaks height analysis also shows that the differences are not significant. It is concluded, therefore, that all the measurements before and after ball milling are similar. This implies that both samples are homogeneous (so the first ball-milling is enough to guarantee an homogeneity of the powders) and that the oxygen vacancies supposedly created during ball milling are not detectable by Raman, probably due to their low concentration. For the 1 mm-diameter balls, the NBT-BT powders did not change color after the second ball milling. Moreover, like for powders ball-milled with the 10 mm-diameter balls, no difference was noticed when comparing the XRD and SEM before and after ball milling (see Fig. 2.27). This indicates that there is no phase formation due to the second ball milling and that no oxygen vacancies are introduced when the powder is ball-milled using the smaller YSZ balls.

As a conclusion, the second ball milling with 1mm YSZ balls was chosen for the final synthesis method, since it increases the final relative density of the samples without changing the micro-structure, nor the phase separation nor introducing oxygen vacancies that could have a negative effect on the material properties.

Influence of the pressure before sintering

The shaping of bulk ceramic samples is done by pressing the ball-milled powders into a pellet ("green body") in an 8 mm-diameter mold using a uniaxial oil press. About 8% of PVA has to be added as a binder, to avoid cracks during the pressing.

The applied uniaxial pressure was of two or three tons. After the first uniaxial press, an isostatic press was also used to increase the density of the green body samples. Following Exxelia's MLCC pressing parameters, the isostatic press was done at 40 MPa for five minutes, with a preheating at 65 • C and a pressure ramp of 8 MPa/min.

The density of the samples "B", "C" and "D" the first one pressed uniaxially with two tons, the second one with three tons, and the third isostatically pressed were compared. The measured densities after sintering using ZrO 2 powder for three hours at 1050 • C were 92%, 91.3%, and 92.6% respectively (the uncertainty is of 2.4%). So the increase in pressure during shaping does not increase significantly the relative density of the sintered sample. The two-ton pressure is sufficient to obtain the highest possible density after standard sintering.

In summary, the uniaxial shaping pressure of two tons was chosen because it is sufficient to obtain the highest possible density after standard sintering.

Influence of the sintering temperature

The influence of the sintering temperature on the final relative density is usually done using dilatometry. However, since the sintering of the NBT-BT requires a powder to create the sintering atmosphere to avoid evaporation of volatiles, (see 2.2.1.1), the dilatometry measurement is not appropriate.

The analysis of sintering temperature was done using different NBT-BT samples prepared from the same powder A (nominally stoichiometric, un-dried reactants, 250 rpm and 4 hours ball-millings, no dispersing agent, ethanol as solvent and coarse Na 2 CO 3 reactant powder) and sintered at different temperatures.

The initial heating rate was 200 • C/h and the initial cooling rate was 300 • C/h. However, the samples sintered with those rates presented cracks, due to the fast temperature change (see Fig. 2.28). The heating rate was then changed to 120 • C/h and the cooling rate to 200 • C/h. The samples did not present cracks with those temperature rates, adopted for all the following sintering.

During the sintering heating, a 30-minute plateau at 800 • C was used to eliminate the PVA added during pressing, other possibly present organic compounds and to guarantee the complete reaction (degradation of carbonates and formation of NBT-BT) [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF].

The sintering temperature enabling a maximum density (of 94%)is 1150 • C (see Fig. In conclusion, the chosen temperature rates were 120 • C/h for the heating, with a 30minute plateau at 800 • C to eliminate organics and complete the reaction, and 200 • C/h for the cooling. The best sintering temperature in term of final relative density is 1150 • C, but in terms of purity it is 1050 • C. The temperature of 1050 • C was chosen for the bulk NBT-BT samples.

Sintering atmosphere influence

The study of a new sintering atmosphere is crucial to allow the use of the NBT-BT in the industrial MLCC production (as explained in 2.2.1.1). In this work, three different sintering atmospheres were tested:

Open crucible

In order to verify the need of an atmosphere during traditional sintering, a sample was sintered in a open crucible for tree hours at 1050 • C. It was prepared with the following synthesis conditions : un-dried reactants, 250 rpm, and four hours for the first ball milling, no second ball milling, ethanol as a solvent, a nominal stoichiometric sample.

After sintering, crystal structure was characterized by XRD (Fig. 2

.30).

There is only a minor NBT-BT formation in this sample. The major formed phase could not be identified. Hence, it is not ideal for NBT-BT synthesis.

Analyzing the dielectric properties of this sample (see Fig. 2.31), a relative permittivity of 340 and the dielectric losses of 44% were measured at 1MHz. This is also not ideal for the MLCC production due to the high dielectric losses compared to NBT-BT sintered in an atmosphere and to the industrial requirements (see section 1.3). The high dielectric losses and frequency dispersion can be explained by the bismuth and sodium evaporation that leads to the formation of a new non-identified, low permittivity, and high dielectric losses phase. In conclusion, the use of an atmosphere powder during sintering is necessary for the NBT-BT formation.

BiO 2 + Na 2 CO 3 and NBT As explained in section 2.2.1.1, the sintering with the sample with the same composition powder (NBT-BT) is the most commonly used for the NBT-BT synthesis, due to the volatility of its components. However, there is a reaction between the sample and the powders used to create an atmosphere during sintering and slicing of the sample is necessary to obtain a clean surface. [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF] In order to test this sintering-atmosphere-creation method, an NBT sample was prepared with the same synthesis parameter as the sample sintered in an open crucible (un-dried reactants, 250 rpm and 4h for the first ball milling, no second ball milling, ethanol as a solvent and nominal stoichiometric).

Identical samples were sintered on pure NBT + ZrO 2 powder or on reactants mixture + ZrO 2 powders.

Only one ceramic could be recovered after sintering and without slicing off the surface, due to the reaction between the powder used to create the sintering atmosphere and the sample surface. Fig. 2.32 shows the inomogeneous aspect of the inomogeneous as-sintered sample.

The XRD measurement of this sample was done and is shown in Fig. 2.33 together with Finally, creating a saturated atmosphere for sintering with powder of the same compo- sition as the green body would not be suitable for industrial MLCC production. The need to slice each sample would increase the production costs and would generate residues that are not ideal for the industry. Moreover, it would require the use of dedicated furnaces and crucibles, due to the high volatile concentrations during sintering. This would also imply higher production costs.

To summarize, it would not be practically possible to use a circular-saw to separate the sintered products, like in [START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF], during MLCC production. Moreover, this sintering atmosphere method would represent a cost increase for the industrial production. So, the sintering using an atmosphere created with powder of the same composition as the green body or with the reactants powder cannot be used industrially for the MLCC production and a new sintering atmosphere has to be devised.

ZrO 2
As explained in section 2.2.1.1, since the BiO 2 + Na 2 CO 3 and NBT-BT powders cannot be used to create the sintering atmosphere and since the sintering in an opened crucible does not allow to obtain NBT or NBT-BT, a new sintering atmosphere had to be used, in order to obtain NBT-BT with low vacancies concentration and using an industrially adapted method.

The ZrO 2 powder was chosen to create the sintering atmosphere, since it is widely used in the industry and it is already used by Exxelia during sintering, due to its high melting point and low reactivity with other ceramic materials. So it can cover the sample, confining it, with little, if any, chemical influence.

The sintering using ZrO 2 powder was done and promising results were obtained, as explained by the dielectric properties of the material (see section 3.2.2.1), specially for sample "U".

The influence of the ZrO 2 powder on the formation and on the composition of the secondary Ba-containing phases is explained in section 2.4.

The XRD measurement of the sample "H" is presented as an example in Fig. 2.34. It can be seen that the as-sintered material presents extra peaks coming from the secondary Ba-containing phases and from the ZrO 2 powder. However, the peaks from the secondary Ba-containing phases and from the ZrO 2 powder disappear in the polished and strain-relaxed sample. Both show a pseudo-cubic phase, characteristic of unpoled relaxors. Finally, a skin effect is responsible for the peak enlargement on the poled and strain-relaxed samples (see section 2.3.2.2). However, it does not affect the dielectric properties. In conclusion, even if the use of a ZrO 2 powder to create the sintering atmosphere increases the formation of the secondary Ba-containing phases at the surface, the final samples sintered using this atmosphere present promising dielectric properties for high-temperature MLCCs. The samples present a pseudo-cubic structure, with no ZrO 2 or secondary Bacontaining phases peaks after polishing. A skin effect is responsible for the enlargement of the XRD peaks of the poled and strain-relaxed samples, but it does not affect the final ceramic sample properties.

Phase separation and secondary Ba-containing phases formation

The secondary Ba-containing phases separation is present in almost every sample of Table 2.11 p. 79 , except for samples "Y", "Z", "Open crucible" and "NBT atm". These secondary phases can be considered as a conducting phase in an insulating matrix. For this reason, they affect considerably the dielectric properties of the samples (see section 3.2.1.2).

This section explains the secondary Ba-containing phases formation and it identifies the phase compositions. Details on the synthesis parameters affecting the phase formation (average grain surface and volume fraction) and the corresponding effects on the dielectric properties will be shown in section 3.2.1.2.

Phase formation and identification

Yang et al.showed that, contrary to the Bi evaporation that is compensated through the formation of defects, the Na evaporation creates secondary Ba-containing phases in the case of the NBT-BT (see section 3.2.1.1). [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] So the secondary Ba-containing phases formation is due to the Na evaporation during synthesis.

A similar phase separation is reported by [START_REF] Otoničar | Compositional range and electrical properties of the morphotropic phase boundary in the Na0. 5Bi0. 5TiO3-K0. 5Bi0. 5TiO3 system[END_REF] for samples of (Na 1-x K x ) 0.5 Bi 0.5 TiO 3 , where the secondary phase is composed of K 2 Ti 6 O 13 . [START_REF] Otoničar | Compositional range and electrical properties of the morphotropic phase boundary in the Na0. 5Bi0. 5TiO3-K0. 5Bi0. 5TiO3 system[END_REF] Pure NBT also has a phase separation that can be observed by the XRD of the as-sintered samples (Fig. 2.35). Similarly to NBT-BT, the phase separation in pure NBT is due to the Na evaporation. However, differently from the secondary Ba-containing phases formed in NBT-BT, the formed phase in pure NBT is a Ti-rich phase without Ba. The XRD analysis indicates that the formed Ti-rich phase in pure NBT is TiO 2 . Fig. 2.23 p. 65 and 2.24 p. 65 show the Raman spectra of the pure NBT powder after calcination and after second ball-milling. Since no difference was found between the multiple Raman measurements, it can be concluded that the powders are homogeneous and, so, that there is no phase separation during calcination. This indicates that the Ti-rich phase separation and the Na and Bi evaporation happen during sintering for the pure NBT. It can be assumed that the same happens for NBT-BT and that the secondary Ba-containing phases separation takes place during sintering as well.

To identify the secondary Ba-containing phases, XRD and EDS analyses were performed on all samples. Figures 2.36 and 2.37 present the XRD measurements for the as-sintered samples "H" and "U" with the peak identification detail. For all samples, three possible secondary Ba-containing phases were identified: Ba 2 TiO 4 , Ba 2 Ti 9 O 20 and Ba 2 Ti 9 O 20 \2BaO•TiO 2 . Table 2.10 presents the EDS measurement results for the average Ba-containing phases. The stoichiometry is close to Ba 2 Ti 9 O 20 , with extra Ba. This indicates that the main secondary Ba-containing phase formed is Ba 2 Ti 9 O 20 . However, there is a decomposition of this phase to Ba 2 TiO 4 and 2BaO•TiO 2 , increasing the Ba/Ti ratio in the average secondary Ba-containing 2.10: Secondary Ba-containing phases average composition measured via EDS considering a 9.0 stoichiometry for the Ti for samples "E", "G", "I", "P" and "U". The uncertainties are indicated in brackets.

ZrO 2 influence in secondary Ba-containing phases formation

The secondary Ba-containing phases formation is more pronounced at the sample's surface when compared to its core (up to a thickness of 20 to 30µm). This means that the volume fraction and the grain surface of the secondary Ba-containing phases are larger at the surface. This can be observed in Fig. 2.38. This can be explained by the Na evaporation being more important at the surface, when compared to the core of a sample.

However, there is another factor affecting the secondary Ba-containing phases formation apart from the Na evaporation. Figures 2.39 and 2.40 show the secondary Ba-containing phases formation and concentration close to a YSZ (Y-doped ZrO 2 ) 1mm-diameter ball attached to the sample's surface and sintered together with this sample. The secondary Bacontaining phases average grain surface and concentration are larger close to the interface between the sample and the YZS ball. This indicates that the ZrO 2 from the YSZ ball favours the secondary Ba-containing phases formation. The same effect should also be observed for interface between the ZrO 2 powder (used to create the sintering atmosphere) and the sample's surface. So, the contact between the ZrO 2 powder used to create the sintering atmosphere and the sample's surface as well as the Na evaporation are responsible for the second phase formation and for its higher concentration on the sample's surface compared to the core, as

Conclusion and sample synthesis conditions

This chapter discussed different synthesis method and parameters, to determine the best synthesis conditions for the NBT-BT, considering Exxelia's requirements.

The synthesis methods is composed of the method used to obtain the NBT-BT powder and to shape and sinter the material.

Initially, two different syntheses of the NBT-BT powder were analyzed, the sol-gel and the solid-state synthesis. Considering the industrial limitations and the expected properties of the final material, the solid-state synthesis was chosen.

Three sintering methods were then analyzed: the microwave, the SPS, and the traditional sintering methods. The microwave sintering would require a change in the furnaces and it would not allow the co-sintering of the ceramics with the electrodes. The SPS sintering is an expensive and energy-consuming method and it requires reducing atmosphere, increasing the vacancy formation in the final ceramics. So the traditional sintering method was chosen.

However, the traditional synthesis uses a way to create a sintering atmosphere that is not compatible with industrial processing. So, a novel method had to be designed.

Finally, three different methods for controlling the atmosphere during sintering and avoiding the evaporation of volatiles were analysed and tested: the sintering in air (atmosphere not controlled), the sintering using a powder of NBT or reactants + ZrO 2 to create the sintering atmosphere and the sintering using pure ZrO 2 powder. The first method resulted mainly in a material that is not NBT-BT and the second one needed post-sintering treatment other than polishing, to obtain a clean surface. So the sintering using ZrO 2 powder was chosen to control the sintering atmosphere.

The shaping of the ceramic layers was done through tape casting, since it is the only available method for Exxelia's sythesis of MLCCs.

Once the synthesis method is chosen, several parameters remain to be analyzed and optimized. In this study the considered parameters were:

• the weighing and drying of the reactants,

• the material of the ball-milling jars and balls,

• the size of the ball-milling balls,

• the ball-milling speed, time, and solvent,

• the grain size of the starting powders,

• the reactants stoichiometry (or nominal stoichiometry),

• the use of a second ball milling after calcination,

• the shaping of the bulk samples (uniaxial or isostatic pressure and their values),

• the powder used to create the sintering, atmosphere,

• the sintering temperature program for the bulk samples,

• the slurry composition and sintering conditions for the tape-casted samples.

The drying of the hygroscopic reactants intensifies the effects of the ball-milling energy, creating large grain surfaces of secondary Ba-containing phases for 250 rpm and 4h ballmilling and large volume fraction of small grain surface secondary Ba-containing phases for 350 rpm and 8h ball milling.

Two different ball-milling jars and balls material were tested: the tungsten carbide (WC) and the Yttrium-stabilized zirconia (YSZ). The ball milling with WC jars resulted in a contamination of the material with tungsten and in a high conductivity and dielectric losses. Using the YSZ jars and balls and the ZrO 2 powder to cover the sample during sintering, the final material showed some ZrO 2 contamination at the surface, that could be removed through polishing.

A skin effect at the sample's surface after polishing and strain relaxation was observed by the low-angle-side peaks on the XRD diagrams. This skin effect creates a phase coexistence (tetragonal, rhombohedral and cubic). It is not present in the as-sintered samples, due to the lower effect of the Ba at the surface (lower local concentration of Ba in the NBT lattice). This variation in the local concentration is due to the formation of secondary Ba-containing phases and concentration of these phases at the sample's surface.

All the samples showed the separation of secondary Ba-containing phases, due to the Na evaporation during sintering. These phases were identified as a mixture of Ba 2 TiO 4 , the Ba 2 Ti 9 O 20 , and the Ba 2 Ti 9 O 20 \2BaO•TiO 2 . They concentrate in the sample's surface due the the higher Na evaporation and also because the ZrO 2 favours the formation of Ba 2 Ti 9 O 20 .

Two ball-milling solvents were also tested: pure ethanol and a mixture of ethanol and methyl-ethyl-ketone (MEK). However, the change in the solvent did not affected the structure ans phase separation of the NBT-BT samples. A similar result is found when changing the Na 2 CO 3 reactant grain size.

The speed and duration of ball-milling were also investigated with a ball-milling at 250 rpm for 4h and another at 350 rpm for 8h. The effects of ball milling were evident in the samples ball-milled without the use of dispersing agent, when the increase in the energy resulted in a smaller grain surface and higher volume fraction of the secondary Ba-containing phases. This effect is not observed for the samples ball-milled with the use of a dispersing agent.

Also, in relation to the ball-milling parameters, the use of a second ball-milling after calcination was tested as well, to increase the final density of the samples. The higher relative density for the samples with no second ball-milling was 91.5% vs 93.5% for the sample prepared with a second ball-milling. The maximum densities were achieved in both cases for the sintering at 1150 • C for 3h. The temperature ramps used were 120 • C/h for the heating and 200 • C/h for the cooling, to avoid cracks during sintering.

Two ball sizes were tested for the second ball-milling: 1mm-diameter and 10mmdiameter balls. The 1mm-diameter balls were chosen, since it increases the relative density of the material without changing the micro-structure and phase separation, and without introducing oxygen vacancies.

Finally, the nominal (or reactant) stoichiometry changes of Na and Bi were also studied. The Na/Bi ratio proved having an important effect on the sample's final composition (after sintering) and properties, with no change in its structure. The increase in the Bi and Na concentrations decreased the secondary Ba-containing phases volume fraction and samples without phase separation could be obtained from samples with Na and Bi excess. The decrease in the Na/Bi ratio created a matrix with the 10% (atomic) of Bi, as expected for the stoichiometric NBT, and a separation of the bismuth excess in a Bi-rich phase concentrated in the sample's core. This resulted in important changes in the dielectric properties, reported in Chapter 3.

The last tested parameters were used for the tape casting of the NBT-BT. The second ball-milling parameters and the slurry compositions in this case were obtained by comparing the ones used by Exxelia and a slurry optimization reported for the NBT-BT. However, further optimization should still be done.

A summary of the synthesis conditions of all the samples used for this study is shown in Table 2.11 p. 79 .

Sample

Dielectric characterization and compatibility with industrial requirements

The objective of this chapter is to present the results of the dielectric characterizations and to compare them with Exxelia's specifications. Together with Chapter 2, the results presented here enable to determine the synthesis parameters needed to obtain a material meeting these specifications.

In the first part, the experimental setups, the model to calculate the complex permittivity, and the associated uncertainties will be presented.

The second part will show the dielectric and insulation properties in temperature and discuss the influence of the various synthesis parameters, and the secondary Ba-containing phases formation in these properties. The compatibility of the properties with Exxelia's requirements will be presented afterwards.

The third part will present the dielectric spectroscopy results for the various samples and the influence of the secondary Ba-containing phases, the relaxor character and the conductivity on the dielectric properties.

Finally, the influence of small additions of Co and Mn on the dielectric properties will be discussed.

Models for dielectric properties calculations and uncertainties

In this section, the measurement setup, the properties estimation model, the temperature corrections, and the measurement uncertainties will be presented.

It is important to know the details of the measurement setup, since they can influence the measured temperatures and increase the uncertainties in the impedance measurements. For this reason, error estimations are also needed to guarantee better result interpretations.

Description of electrical measurements: impedance spectroscopy and insulation resistance

The dielectric (impedance) measurements were carried out on unpoled, polished and strain-relaxed samples, with an impedancemeter connected to a temperature controlled Linkam THMS600 operating in a temperature range between -196 • C and 600 • C. In this Linkam, the temperature control is accomplished by heating or cooling a platinum support under the sample that is grounded electrically. The electric insulation of the sample from the heating device is done using a thin glass plate. Finally, the temperature is measured by a thermocouple installed close to the heating device. The picture of the measurement device is presented in Fig. 3.1.

The measurements give the complex impedance (norm and argument) as a function of temperature and were done using a Hioki 3570 impedancemeter operating in a frequency range between 5Hz and 5MHz and capable of measuring impedance between 100mΩ and 100MΩ. A RC model was adopted and will be further explained, in order to obtain the real and imaginary permittivity values.

The insulation resistance measurements were done after the permittivity measurements, to perform the latter on unpoled samples. Industrial standards were used, so the measurements were carried out using direct current by applying a direct voltage of 50V and by measuring the bulk sample resistance initially for 30 seconds. Since the 30s-measurement was not enough to saturate the sample, the DC was re-applied during 30 seconds and the resistance measurement and the insulation resistance calculations were done. So the presented values correspond to the insulation resistance at one minute.

The performed measurement gives a set of internal resistance vs temperature values for each sample. This measured resistance represents the ratio between the applied voltage and the leakage current after a fixed time when a DC is applied. The value of the fixed time should be higher than to charging time of the capacitor, so that only the leakage current is measured. [START_REF]Ceramic Capacitors FAQ[END_REF] Using this resistance value, the resistivity of the sample can be calculated from equation 3.1. The insulation resistance corresponds to the product of the calculated resistivity by its corresponding permittivity at the same temperature (or to the product of the resistance and the capacitance), as shown in equation 3.2. So the insulation resistance represents the time constant of the capacitor, which is the time that a charged capacitor in an opened circuit will take to drop to the value of 1/e of its initial charge (around 36.8% of it) through the internal resistance. [START_REF]Capacitors -Insulation Resistance[END_REF]

ρ = R internal • A e (3.1) IR = ρ(T ) • ε r (T ) • ε 0 = R internal (T ) •C(T ) (3.2)
where R internal is the internal resistance measured, A in the sample's surface, e is the sample's thickness, IR is the insulation resistance and ρ is the resistivity> Due to equipment restrictions, the measurements were performed up to a maximum temperature of 200 • C. For the higher temperature values, the curve was extrapolated supposing an exponential decrease, as it normally happens for dielectric materials at high temperature.

RC model for permittivity and dielectric losses

The parallel RC model was used to estimate the real and imaginary parts of the permittivity, as represented in Fig. 3.2. Since the material is a dielectric with losses, the permittivity is:

ε * r ( f ) = ε r -j • ε r (3.3)
In this model, the real and imaginary parts of the permittivity read:

ε r ( f ) = 1 ε 0 • Im 1 Z * ( f ) 2π f • e A (3.4) ε ( f ) = Re 1 Z * ( f ) 2π f • e A (3.5) tan δ ( f ) = ε ( f ) ε ( f ) (3.6) C * ( f ) = ε r ( f ) -j • ε r ( f ) • A • ε 0 e (3.7) Re(σ * ) = σ ( f ) = Re 1 Z * ( f ) • e A = ω • ε ( f ) (3.8)
where σ is the sample resistivity, C * is the sample complex capacitance, f is the fre-FIGURE 3.2: RC model used for the permittivity calculation from the measured system impedance quency of the AC applied during measurement, e is the sample thickness, A is the sample surface, ε 0 is the vacuum permittivity, Z * is the complex impedance, Re is the real part of the complex number and Im is the imaginary part of the complex number.

RC model validation

Graphic impedance

In order to verify that this model is adapted for our measurements and to confirm that the cables and the measurement device do not influence significantly the measurements after calibration, the impedance versus the frequency ( f ) are plotted in Fig. 3.4 and 3.5.

From a more general the RC model like the one shown in Fig. 3.3 that takes into account the resistance and the capacitance of the cables and the setup, the impedance reads:

Z * = R sample 1 + R sample • j • 2π f •C sample + R setup + j • 2π f •C setup (3.9)
So, for high frequencies in a system where the setup affects the measurements results, the lim f →∞ Z * (2π f ) is R setup + j • 2π f • C setup , so the imaginary part of the impedance tends to infinite if there is an effect of the setup capacitance. For low frequencies in the same systems, the lim f →0 Z * (2π f ) is R sample + R setup . So, for systems where the setup resistance affects the measurements, the value of Re(Z * ) for high frequencies should be negligible compared to the value of Re(Z * ) for high frequencies.

Analyzing Figures 3.4 and 3.5 that shows the real and imaginary part of the complex impedance Re(Z * ) for sample "H" respectively, it can be seen that, for high frequencies, the Im(Z * ) values tend toward zero and the value of Re(Z * ) tends to a constant value lower than 250Ω, a lot smaller than the Re(Z * ) in low frequencies. This means that C setup is negligible and R setup is small when compared to the R sample , seen in the Z value when f-→0 (over 30kΩ). A similar behaviour is found for the other NBT-BT samples. So the RC model adopted is valid for these measurements.

Bruggeman model [2, 28]

Since the NBT-BT samples have different values of relative density (see section 2.3.4.1), being all significantly lower than the fully dense material, it is interesting to consider a model that can take the density effects into account. This is important to be able to compare better the intrinsic properties of the materials, regardless of their relative density.

Bruggeman's model was developed to determine the properties of 3-0 composites from the properties of their constituents and their proportions (see section 3.2.1.2). As a singlephase ceramic but with a density less than 100% can be considered as a ceramic-air composite, the Bruggeman model can be used to estimate the permittivity and the dielectric losses for theoretical samples having 100% density. This would be important for comparing the dielectric properties of samples without taking into account the density effect in the dielectric properties.

The complex permittivity for the 100% density material can be calculated as [START_REF] Anoufa | Nanocomposites et effet de dimensionnalité pour le stockage de l'énergie[END_REF]:

ε * i = 2ε * e f f • 1-f f • ε * e -ε * e f f ε * e +2ε * e f f + ε * e f f 1 + ε * e -ε * e f f ε * e +2ε * e f f • 1-f f (3.10)
where ε * i is the complex permittivity of the 100% density material, ε * e f f is the effective (measured) complex permittivity, f if the volume fraction of ceramic in the material (relative density) and ε * e is permittivity of the air (1.0006•ε 0 ). The relative permittivity for fully-dense material can be calculated from the real part of ε * i /ε 0 and the dielectric losses can be calculated from the imaginary part of ε * i /ε 0 divided by its real part.

However, this model supposes an isotropic and homogeneous medium and spherical particles of both phases of the composite (in this approximation, spherical ceramic grains and spherical pores) with a size of the "inclusions" larger than the distance between them. [START_REF] Jylhä | Modeling of electrical properties of composites[END_REF] As it can be seen in Fig. 2.8 p. 50, for example, these conditions are not met by my NBT-BT samples. So the values estimated for samples with a 100% density would not be reliable. Moreover, for the MLCC production, the most interesting properties are the ones directly measured in the prepared samples (ε e f f ) and not the theoretical 100% density material properties. So the Bruggeman model and the 100% density properties were not used to compare the dielectric properties of the samples in this study.

Estimation of measurement uncertainties

The uncertainties and the measurement noise estimations are necessary to guarantee a better interpretation of the measured dielectric properties. In the impedance measurement, variations may be created by the faulty electric contacts due to the cables linking the Linkam to the impedance measurement setup.

The measurement noise was estimated from the "U" sample measurements, with the synthesis parameters specified in Table 2.11 p. 79. Two measurements were performed at different times for this sample. For the first one, the permittivity and the dielectric losses (tan δ ) values at room temperature and at T m are indicated in Table 3.1. For the second one, the measurement values follow two different curves "jumping" from one to the other as temperature is changed, depending on the electric contact between the Linkam and the impedance measurement setup. The permittivity and the dielectric losses values of both curves for the second measurement are indicated in Table 3.1 (as curve 1 and curve 2).

These "jumps" were used to evaluate the noise on the dielectric measurement. The relative permittivity value for this sample can be described as ε r = 1300 ± 160 at 50 • C and ε r = 2700 ± 550 at T m . So the noise on the measured relative permittivity value is around 12% at 50 • C and 13% at T m . So a 13% noise estimation was taken for the relative permittivity for all the samples.

The dielectric losses values for this sample are tan δ = 10.7 ± 0.9% at 50 • C and tan δ = 3.4 ± 0.5% at T m . So the noise on the dielectric losses value is around 7.5% at 50 • C and 14%at T m . So a 14% noise estimation was taken for the dielectric losses for all the samples. Fig. 3.6 shows the permittivity and the dielectric losses for the "U" sample and for the two consecutive measurements, the second one following two different curves, as mentioned before, depending on the electric contact.

To compare the noise estimation with the uncertainty of the dielectric properties, a second sample "X" (synthesis parameters in Table 2.11 p. 79) was also measured twice and the values of permittivity and dielectric losses of this sample on the first and the second measurements are presented in Fig. 3.7. There are no "jumps" on the measurements of the sample "X", and the maximum variation between the first and the second measurement is 2.4% for the relative permittivity and of 14% for the dielectric losses (tan δ ) for temperatures lower than 200 • C and 25% for higher temperatures. The permittivity and the low temperature dielectric losses variations from one stable measurement to another are lower than the uncertainties. This shows that the main contribution for the measurement variability comes from the measurement noise and not from the uncertainties on the sample's properties. So, the estimations of the measurement noise were associated with the measurement uncertainties.

It will be shown in chapter 4 that, for some samples, the dielectric losses at high temperatures can increase when the measurements are carried out over multiple heating and cooling cycles, depending on the sample, on the electrode, and on the maximum temperature. Those dielectric-losses increases do not come from the measurement uncertainties but from an actual change of property in the samples and electrodes.

Property

Measurement at 50 The Linkam temperature control system is based on the heating or cooling of the platinum support separated from the sample by a glass plate. For this reason, the way the wire is fixed to the bottom of the sample can create a gap between the sample and the heating system, increasing the heat transfer resistance. So, the way the wire is fixed can disturb the temperature measurement, potentially contributing to the uncertainty.

Two methods to fix the wire to the bottom electrode were tested and are discussed here after.

Silver paste on sample surface and temperature correction

The simplest method used to fix the wires was to use a silver paste drop over the wire and the bottom surface of the sample (see Fig. 3.8). This silver paste is then heated before measurement for two hours at 200 • C, as indicated in the product instructions.

Even if this method is the simplest one to implement, it can create significant tempera-FIGURE 3.8: Wire fixing method based on silver paste over the sample surface ture drifts in the measurements. The distance between the heating source (platinum) and the sample bottom surface, due to the presence of the silver paste drop, causes the temperature of the ceramic to always be lower than the temperature measured by thermocouple located close to the heating element.

In order to correct that, a reference BaTiO 3 sample was measured using the same fixing method and this measurement was compared to the reference sample properties. The measurement and the known sample properties are shown in Fig. 3.9. Two points were taken as a reference to fit a correction by the straight line. The first one was the Cutie temperature and the second one was the room temperature, considered to be correctly measured as both the heating element and the sample are thermalized at room temperature (30 • C, in that case).

Two different wires were used: a type-K thermocouple wire (Nickel-Chromium / Nickel- Alumel) with 0.20mm diameter and a gold wire with 0.05mm diameter.

For the thermocouple wire, it can be seen in Fig. 3.9 that the measured Curie temperature was 154 • C, contrary to the known sample Curie temperature of 127 • C. Considering the room temperature of 30 • C to be correct, a linear temperature correction reads:

T corrected = T meas • 0.81 + 5.50 (3.11) For the gold wire, the measured Curie temperature was 142 • C. Considering the room temperature to be correct, the linear temperature correction reads:

T corrected = T meas • 0.87 + 4.02 (3.12)
The fact that T ε,max for the gold wire is closer to the reference than T ε,max for the thermocouple wire confirms the hypothesis that the thicker the wire the larger the thermal resistances and, hence, the temperature shift in the measurements.

BaTiO 3 undergoes a first order transition. So, there is an expected difference in the temperature of the maximum permittivity, as shown in Fig. 3.10. [START_REF] Wang | Theories and Methods of First Order Ferroelectric Phase Transitions[END_REF] From T 0 to T c , the ferroelectric phase is stable and the paraelectric phase is meta-stable, from T c to T 1 , the ferroelectric phase is meta-stable and the paraelectric phase is stable. So the maximum permittivity temperature in cooling is T 0 and the maximum permittivity temperature in heating is T 1 . The difference between T 0 and T 1 for BaTiO 3 is, then, 3 • C, as illustrated in Fig. 3.10.

To analyze if there is a temperature gradient in the samples measured with the simple Ag-paste method to fix the wires on the bottom of the samples, the same BaTiO 3 sample measurements in heating and cooling were compared. If a temperature gradient is present in the sample, a greater difference in the maximum permittivity temperature is observed after comparing the heating and the cooling.

The heating and cooling measurements for the BatiO 3 show a difference of the maximum permittivity temperature of 3 • C for the gold wire (with the smaller diameter) and 6 • C for the thermocouple wire (with the larger diameter). So, there is no significant temperature gradient in the sample (especially for thinner wire) and no significant difference between the heating and cooling temperature correction.

The following measurement results carried out with this method to fix the wires will therefore be presented with corrected temperatures.

Simplified electric contact and temperature corrections

To further verify the temperature correction for the first method (when silver paste is used to fix the wires on the samples surface), its corrected temperatures were compared to other measurements using a displaced electric contact method (silver paste on copper plate).

In this method, the Cr-Au electrodes are deposited by sputtering on the sample's surfaces (see section 4.2.2.2) over the sample. Then, a copper plate is fixed to the bottom electrode of the sample with a small amount of silver paste. The wire is then fixed on the plate also with a drop of silver paste, as shown in Fig. 3.11. This creates a better thermal contact between the sample and the heating source (platinum). So the temperature correction should no longer be necessary.

The comparison was done on the T m and the T d measurements of a NBT-BT sample "N" (synthesis parameters in Table 2.11 p. 79). The simplified Ag-paste electric contact temperatures were measured and corrected using equation 3.11. These values were then compared to the measurements using a displaced electric contact method (silver paste on copper plate).

This comparison between the first method after temperature correction and the method in the measurements of temperature can be estimated as being 3.5%.

Dielectric properties with temperature

The dielectric properties vs temperature are the most important properties for the ML-CCs. In this section, the influence of synthesis parameters, second phase, polishing, and stoichiometry on these properties were studied, in order to optimize the NBT-BT properties according to Exxelia's specifications.

Influence of stoichiometry, secondary Ba-containing phases, synthesis

parameters and polishing and strain relaxation on the dielectric properties vs temperature

Stoichiometry

The stoichiometry is specially important for NBT-BT, since bismuth and sodium can evaporate during calcination and sintering. The Bi 2 O 3 loss during ceramic processing is a source of oxygen vacancies with high mobility in the final material:

2Bi x Bi + 3O x O - → 2V Bi + 3V .. O + Bi 2 O 3 (3.13)
where Bi x Bi is a bismuth ion sitting on a bismuth lattice site with neutral charge, O x O is an oxygen ion sitting on an oxygen lattice site with neutral charge, V Bi is a bismuth vacancy with triple negative charge and V ..

O is an oxygen vacancy with double positive charge, as indicated by the Kröger-Vink notation.

It could be expected that the Na evaporation also happens via defect mechanism (like for the Bi case), creating oxygen vacancies and increasing conductivity. Actually, it creates a phase separation composed of TiO 2 for pure NBT and secondary Ba-containing phases for NBT-BT, making the matrix phase deficient in Na and Ti and therefore rich in Bi. On the other hand, the resulting Na excess forms a second phase and is not incorporated in the matrix phase. So, the Na excess cannot fill the Bi vacancies to compensate for oxygen vacancies even though they occupy the same site in the perovskite unit cell. Since, there is always a Bi evaporation during processing, the matrix composition is Bi-deficient and has high-mobility oxygen vacancies. [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] In conclusion, the Na behaves contrarily to the Bi, with an increase in the conductivity for Na-rich samples and a decrease in conductivity for the Na-poor samples. So nonstoichiometry can be measured by the Na/Bi ratio, with a high conductivity when increasing the Na/Bi ratio. [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] Slight changes in Na/Bi ratio can drastically affect the dielectric properties of NBT-BT, FIGURE 3.12: Bulk conductivity of pure NBT with different Na/Bi ratios at 600 • C [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] resulting in more than 3 orders of magnitude difference in the room temperature DC conductivity. This high conductivity created in the material is one of the most important hinderances to the use of NBT-BT in MLCCs, since it also results in an increase in the dielectric losses, when used in alternating current applications. NBT-BT show three types of electrical conductivity: [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] • Type I -the nominal stoichiometric NBT-BT exhibits a high oxide-ion DC conductivity due to the oxygen vacancies created through Bi 2 O 3 loss and to their high mobility resulting from highly polarized Bi 3+ ions and weak Bi-O bonds. The increase of the Na/Bi ratio increases the oxide-ion conductivity as shown in Fig. 3.12, owing to the generation of additional oxygen vacancies.

• Type III-the decrease in the nominal Na/Bi ratio to 0.98 drastically reduces the conductivity since the Bi excess can compensate for the loss during synthesis. The material exhibits electronic conduction.

• Type II -decreasing even more the nominal Na/Bi ratio to 0.96, the material shows mixed conduction (oxide-ion and electronic conduction) because of the increase of a space-charge effect due to the formation of a Bi-rich phase.

As shown in Fig. 3.13, the changes in conductivity have a great impact on the dielectric losses (see section 3. This effect can also be shown by analyzing equations 3.5 and 3.8 of the RC model adopted for the dielectric properties estimation, indeed ε = σ /ω. Since the dielectric losses are calculated by the ratio of the real to the imaginary part of the permittivity (equation 3.6), then the increase in conductivity induces the increase of the dielectric losses.

Other interesting effects of the stoichiometry change are the creation of a pinched P-E FIGURE 3.13: Dielectric losses with temperature for the three conductivity types NBT and NBT-BT [START_REF] Yang | Defect chemistry and electrical properties of sodium bismuth titanate perovskite[END_REF] loop and a decrease of the depolarization temperature T d with decreasing Na/Bi ratio (see section 2.3.2.6). These changes are attributed to the decrease of the temperature of the FE to the "AFE-like" phase transition. However, the reason of this decrease is not well understood yet. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] In this study, three non-stoichiometric samples were prepared with the same synthesis parameters (see Table 2.11 p. 79) and compared to sample "P". The "P" sample has a nominal stoichiometric composition (the reactants were weighted in stoichiometric proportions), the "U" sample has the nominal composition of Na 0.44 Bi 0.48 Ba 0.06 TiO 3 , i.e. with a 6.38% Na-deficiency and 2.12% Bi-excess, the "Y" sample has a nominal excess of 10.5% mol of sodium and 2.1% mol of bismuth when compared to sample "U", to obtain the nominal "U" composition (Na 0.44 Bi 0.48 Ba 0.06 TiO 3 ) after sintering, and the "Z" sample has a nominal excess of 16.9% mol of sodium when compared to sample "U", to obtain nominal NBT-BT composition after sintering. The nominal and the EDS Na/BI ratios are presented in Table 3

.3.
As sodium is a light element, the EDS measurements are less precise. The uncertainties can be considered as 5% for the heavy elements (Bi and Ti) and 10% for the light elements (Na and O). The Ba measurement also has a higher uncertainty (10%), since its measurement has to be done from the M series or from the Lb series, which have lower intensity than the La series. [51] Analyzing the differences between the nominal composition and the final one analyzed 3.3: Nominal composition of samples "P", "U", "Y" and "Z", their nominal and EDS measured Na/Bi ratios, and the average final composition of the matrix phase for samples "P" and "U" and of the only phase for samples "Y" and "Z" measured by EDS. The EDS uncertainties for the Bi and Ti are 5% and for the Ba, Na and O is 10%.

by EDS, all samples have a lower Na/Bi ratio in the final composition when compared to the nominal one. This indicates that the Na losses are more important than the Bi ones, since it is more volatile. Table 3.3 shows the nominal composition of each sample and the average final composition of the matrix phase measured by EDS (where the measurement uncertainties are 5% for Bi and Ti and 10% for Na).

It can be observed that the matrix phase does not show a Ba concentration that can be measured by EDS. Since the L series of Ba and Ti are close to each other, the Ba concentration measurement has to be done from the M or the Lb series, as explained earlier in this section. This means that the detection limit is higher when compared to the other elements. However, the EDS analysis show that the majority of the Ba is in the secondary Ba-containing phases. The composition of the secondary Ba-containing phases was detailed in section 2.4 and the secondary Ba-containing phases average grain surface and fraction will be detailed in section 3.2.1.2.

The Na and Bi losses estimation for all the samples is difficult, since a part of the Ti is present on the secondary Ba-containing phases for samples "P" and "U". However, samples "Y" and "Z" do not have any phase separation, so they can be used for estimating the losses of volatile species. Analyzing Table 3.3 p. 94 and considering that no titanium is lost during the synthesis, the sodium losses average is 17% ± 9% and the average Bi losses are 2% ± 0.03%. As explained before, the Na losses are responsible for the secondary Ba-containing phases separation in the NBT-BT materials. The Bi losses are responsible for the creation of oxygen vacancies that increase the conductivity of the sample. So adding Bi to the reactants to compensate for its evaporation, as done for sample "U", and the study of the secondary Ba-containing phases effects in the NBT-BT properties, as presented in section 3.2.1.2 are the key to understand and control the dielectric properties of NBT-BT, to achieve an adapted material for the MLCC production.

Comparing now the SEM images of samples "P" and "U", it can be observed that the relative excess of Bi compensates for evaporation during synthesis (see Table 3.3) and a second Bi-rich phase is formed in the sample's core (see Fig. 2.16 p. 58).

The dielectric properties and the insulation resistance of samples "P", "U", "Y" and "Z" are presented in Figures 3.14 Comparing again samples "P" and "U", the decrease of the Na/Bi ratio in the sample "U" through Na-excess and Bi-deficiency and the consequent oxygen vacancies compensation do not decrease the dielectric losses, as it would be expected (see figures 3.14 and 3.15). This indicates that the higher evaporation of Na in sample "P" compared to the Bi evaporation, owing its Na/Bi measured ratio to be 0.88 (see Table 3.3) is sufficient to change the conduction type from type I to type II, with low dielectric losses (tan δ ≤ 2.5%) up to 300 • C.

The permittivity of the "U" sample when compared with the "P" sample is lower, but still complaint with Exxelia's specifications, and it is also more stable in temperature, so this material is more adapted to the MLCC application. The reason for this is related to the presence of a secondary Ba-containing phase and will be discussed in section 3.2.1.2.

Finally, another important difference between the "U" and the "P" samples is the depolarization temperature, around 105 • C at 10kHz for the "P" sample and around 65 • C at 10kHz for the "U" sample. This is another reason why the non-stoichiometric material is more adapted for the MLCC production. This decrease of the depolarization temperature is due to the modulated phase being more stable at lower temperature. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] Comparing now the samples "Y" and "U", the increase of the Na content inhibits the secondary Ba-containing phases separation, increasing the Ba and Ti content in the matrix and decreasing the relative Bi content. This can be seen comparing their respective SEM images (Fig. 3.17 and Fig. 2.8 p. 50), where no second phase was detected in samples "Y" and "Z".

So, the increase of the Na content and of the Na/Bi ratio in these samples enhance the dielectric losses and change the conduction type back to type I, as expected. This can be confirmed by the increase in the dielectric losses of the samples from 200 • C shown in Fig. 3.14 and by the high conductivity, specially for sample "Z" shown in Fig. 3.16.

The measured permittivity is also increased with increasing Na/Bi nominal ratio, as reported in [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF]. This can be observed by comparing the relative permittivity of samples "Z" and "P" in Fig. 3.14, for example.

The increase in the DC conductivity can be seen by the decrease in the insulation resistance of both "Y" (47s at 200 • C) and "Z" (0.3s at 200 • C) samples in Fig. 3.16.

The depolarization temperature increases from 65 • C in sample "U" to 115 • C in sample "Y", for the same reason (cf. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF]) as for sample "P".

Finally, comparing the samples "Y" and "Z", similar effects on the permittivity, dielectric losses, insulation resistance, and depolarization temperature are observed: an increase in the permittivity and in the dielectric losses, a decrease in the insulation resistance of the sample "Z" when compared to the sample "Y", and an increase in the depolarization temperature, from 115 • C in sample "Y" to 145 • C in sample "Z", due to the increase of the Na/Bi ratio.

In conclusion, the sample "U", with the lower Na/Bi ratio is the most adapted for the MLCC production due to its higher resistivity that satisfy Exxelia's requirements and lower dielectric losses, when compared to the samples "Y" and "Z". Moreover, this sample has a lower variation of permittivity with temperature when compared to the other ones. Furthermore, the increase in Na content inhibits the phase separation and, as a consequence, decreases the relative Bi content in the main phase (increases the conductivity). So, to obtain a sample with no phase separation but without increasing the conductivity, Bi and Na excess should be added, maintaining the same Na/Bi ration as sample "U", but with increased Na/Ti ratio. A suggested nominal composition would be Na 0.4818 Bi 0.5256 Ba 0.06 TiO 3 (same Na/Ti ratio as sample "Y" and same Na/Bi ratio as sample "U".)

Secondary Ba-containing phases

The second phase formation explained in section 2.4 also has an important effect on the dielectric properties and on the insulation resistance of the samples.

The samples can be analyzed as a composite, since the secondary Ba-containing phases is a conducting phase and the matrix (mostly NBT) can be considered as an insulating ferroelectric phase (see section 3.3.1).

The classical models used to estimate the effective dielectric properties of composites (Maxwell Garnett, Bruggeman Symmetric, Bruggeman Non-symmetric, Sen-Scala-Cohen, Looyenga and Lichtenecker) consider the hypothesis of spherical and isotropic particles, [START_REF] Jylhä | Equation for the effective permittivity of particle-filled composites for material design applications[END_REF] which is not the case for the secondary Ba-containing phases (see Fig. 2.40) p. 76. Moreover, these models assume that the materials of the composite are linear, which means that the induced dipole moments depend linearly on the electric eld. [START_REF] Jylhä | Equation for the effective permittivity of particle-filled composites for material design applications[END_REF] This is also not the case for NBT-BT, since the NBT matrix is a ferroelectric relaxor material. Finally, they assume that the distance between particles is larger than the particle size, which is not necessarily the case for all the samples in this study.

A correction of the Maxwell Garnett (MG) and Bruggeman Symmetric (BS) models considers ellipsoidal particles. However, this correction assumes a specific particle orientation (long axis either parallel or orthogonal to the electric field), which is also not the case for this study, since the secondary Ba-containing phases are randomly oriented. Moreover, even after correction, the MG and BS models are still restricted to linear composites. [START_REF] Jylhä | Equation for the effective permittivity of particle-filled composites for material design applications[END_REF] For the classical composite models, the increase in volume fraction of the secondary Bacontaining phases would increase the interface surface between the conductive and the nonconductive phases, increasing the electric field in the bulk material. This would increase the permittivity, the conductivity, and the dielectric losses of the sample.[75] Fig. 3.18 shows the expected evolution of the effective (measured) permittivity with the matrix volume fraction for different values of inclusion permittivities, considering the BS model. It can be seen that the permittivity presents a monotonic evolution with the matrix volume fraction, regardless of the matrix and particle permittivity values. This is not the case for the samples in this study (see Fig. 3. [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF], proving that the classical models cannot be used. The secondary Bacontaining phases volume fraction and average grain surface estimations will be presented in section 3.2.1.2.

The average inter-particle distance and the average particle size also have an important effect on the effective properties of composites. The decrease in the inter-particle separation requires a model that takes into account the interactions between particles. [START_REF] Kaufman | Permittivity effects of particle agglomeration in ferroelectric ceramic-epoxy composites using finite element modeling[END_REF] Kaufman et al.modeled during the course of this PhD the effect of BaTiO 3 particle interactions in a polymeric insulating matrix. [START_REF] Kaufman | Permittivity effects of particle agglomeration in ferroelectric ceramic-epoxy composites using finite element modeling[END_REF] The permittivity increases with decreasing particle separation when compared to all classical composite models estimations. Deepa et al.showed the effect of the conducting La 1-x Sr x CoO 3-y particles size in an insulating polymeric matrix. [START_REF] Ks Deepa | Effect of interparticle distance and interfacial area on the properties of insulator-conductor composites[END_REF] For fine grained particles, the increase in permittivity occurs for lower volume percentage of conducting phase when compared to the coarse-grained ones (Fig. 3.20). This is because, for a given volume percentage, smaller particle creates a larger interface and higher density of accumulated charges, resulting in a greater dipole moment. So, a higher permittivity can be obtained for composites with lower average grain surface. Moreover, the overlapping of interfaces occurs at lower concentrations for composites with lower average grain surface, proving the need of a model that takes this into account.

Finally, the effect of the increase in average particle size is possibly not the same depending on the studied system, since it would decrease the interface surface and increase the electric field in the material, having competing effects on the permittivity.

In conclusion, there is no classical composite model that can take into account the FIGURE 3.20: Permittivity evolution with concentration of LSCO conducting phase in the composite in a polymeric matrix for fine and coarse grained particles [START_REF] Ks Deepa | Effect of interparticle distance and interfacial area on the properties of insulator-conductor composites[END_REF] non-spherical shape of the secondary Ba-containing phases particles that are randomly oriented, the interactions between particles, the non-linear ferroelectric character of the NBT-BT, and the different average grain surfaces of the secondary Ba-containing phases at the same time. A new model could be created, for example using finite element method, as in [START_REF] Kaufman | Permittivity effects of particle agglomeration in ferroelectric ceramic-epoxy composites using finite element modeling[END_REF]. However, this was not the main aim of this work.

The effects of the secondary Ba-containing phases volume fraction have been, then, evaluated qualitatively.

Sample

Average grain surface (µm

Effects of the secondary phase on the permittivity and dielectric losses

In order to analyze the effects of the volume fraction and grain surface of the secondary Ba-containing phases on the permittivity and on the dielectric losses, samples with different synthesis parameters affecting the secondary Ba-containing phases formation were analyzed: the drying of the reactants, the grain size of Na 2 CO 3 , the ball-milling energy (speed and duration), the ball-milling solvent, the use of a dispersing agent, and the nominal stoichiometry.

The estimation of the secondary Ba-containing phases volume fraction and average grain surface was done using the SEM images of the polished samples surface. Using different color threshold for the image analysis, the average grain surface, the surface fraction and their uncertainties were estimated.

Sample "E" can be used to show an example of the image processing used to estimate the average volume fraction and grain surface of the secondary Ba-containing phases in this sample. All the image processing were done using "ImageJ" software. Fig. 3.21 shows the polished surface of the "E" sample before image processing, after a high threshold processing, after a low threshold processing and after a high threshold processing and an elimination of small "dots" with a binary "erode" and "dilate" treatments. For low threshold, light color particles and large particle's borders may be neglected, with high threshold, images imperfections may be considered as particles and for the binary treatment, small particles and imperfections are eliminated, but borders are kept. Table 3.5 show the average volume fraction and grain surface for the three image processing methods. The average grain surface and volume fraction considered are a mean of the values obtained by the three methods, and the uncertainties related to them.

It was considered that the volume fraction of the core is equal to the surface fraction of FIGURE 3.21: SEM image of the polished surface of sample "E" A -before image processing, B -after a low threshold processing, C -after a high threshold processing and D -after a high threshold processing and an elimination of small "dots" with a binary "erode" and "dilate" treatments. the polished surface. Finally, for the uncertainties, the value of two standard variations was considered (or a confidence interval of 95%).

The size and volume fraction of the secondary Ba-containing phases are presented in Table 3.4 p. 100. The two ball-milling speeds correspond to the first and second ball-milling conditions. All the 250 rpm ball-millings had a 4h duration and all the 350 rpm ball-millings had a 8h duration. Fig. 3.22 presents the relative permittivity of each sample at T m and the dielectric losses at 300 • C, both measured at 10kHz, versus the secondary Ba-containing phases volume fraction. Average secondary Ba-containing phases grain surfaces are indicated by the labels on this Figure. The 10kHz frequency was chosen since it is a stable measurement (not at the limit of the device calibration), the permittivity was measured at T m to compare the maximum values of this property and the dielectric losses were measured at 300 • C so all the sample's high temperature losses can be compared.

The increase in the secondary Ba-containing phases volume fraction initially increases the relative permittivity and decreases the dielectric losses until 2.5 ± 0.9% of secondary Bacontaining phases volume fraction. For higher volume fractions the increase in the secondary

Ba-containing phases volume fraction decreases permittivity and increases dielectric losses.

There is therefore an optimal volume fraction for dielectric properties around 2.5%. Decreasing the Na 2 CO 3 grain size changes neither the secondary Ba-containing phases volume fraction, nor the average secondary Ba-containing phases grain surface nor the dielectric losses of NBT-BT, as observed comparing samples "V" and "H". Considering the "H" and "V" sample's permittivities within their uncertainties in Fig. 3.27 p. 108, it can be concluded that the decrease in the Na 2 CO 3 grain size may slightly increases the permittivity value of NBT-BT, specially for the temperatures between T d and T m . However, due to the relatively high value of the permittivity uncertainties, it is difficult to evaluate the effect of this synthesis parameters for the entire temperature range.

Increasing the energy of ball milling from 250 rpm -4h to 350 rpm -8h on NBT-BT samples ball-milled with the use of dispersing agent and without drying of the reactant, no difference is found in the secondary Ba-containing phases volume fraction, grain surface and on their dielectric properties, as it is observed from the comparison of samples "I" and "H". This indicates that, for these samples, the second ball-milling energy does not affect the secondary Ba-containing phases formation.

Comparing now the NBT-BT samples ball-milled at 250 rpm, for 4h using a dispersing agent and with or without dried reactants (samples "G" and "H" respectively), the only observed difference is in the secondary Ba-containing phases volume fraction (1.5% for "H" and 3.1% for "G"). This indicates that the samples with dried reactants have higher volume fraction of second phase.

Finally, when comparing samples ball-milled using a dispersing agent (with different ballmilling energies and drying of the raw powders) with their equivalents ball-milled without dispersing agent, it can be observed that the increasing ball-milling energy decreases drastically the grain surface and increases the volume fraction of the secondary Ba-containing phases phase, when no dispersing agent is used. This is clear from the large grains of secondary secondary Ba-containing phases containing phases in sample "B" (250 rpm -4h) comparing to the smaller grains in sample E (350 rpm -8h);

Moreover, the use of dispersing agent also decreases the dielectric losses and increases the permittivity. This can be observed when comparing samples "G" (250 rpm ball milling, drying of reactants and use of dispersing agent), "H" (250 rpm ball milling, no drying of reactants and use of dispersing agent) and "I" (350 rpm ball milling, no drying of reactants and use of dispersing agent) with samples "B" (250 rpm ball milling, drying of reactants and no use of dispersing agent) and "E" (350 rpm ball milling, drying of reactants and no use of dispersing agent) on figures 3.22 p. 102 and 3.23 p. 104.

To conclude, adding MEK to the solvent mixture, the only observed differences are the dielectric losses that are lower for the ball-milling with ethanol and MEK as solvents, and the second phase volume fraction that is lower for the ball-milling with pure ethanol as solvent. So, the addition of MEK as a solvent together with ethanol decreases the dielectric losses and increases the secondary Ba-containing phases volume fraction. This can be observed when comparing samples "V" (ethanol as solvent) and "N" (MEK+ethanol as solvent).

The relative permittivity and the dielectric losses of samples "N", "B" and "E" for the complete temperature range measured (from room temperature to 350 • C) are shown in Fig. 3.23 p. 104. and they prove the same tendency of values showed in Fig. 3.22.

Dielectric properties of samples "H", "I" and "V" will be discussed in section 3.2.1.3.

As a summary, the increase in the secondary Ba-containing phases volume fraction initially increases the permittivity and decreases the dielectric losses until a 2.5± 0.9% volume fraction value. For higher percentages of second phase, the trend reverts.

No considerable changes are observed in secondary Ba-containing phases and in dielectric properties for different Na 2 CO 3 grain sizes and for different ball-milling energies in samples prepared with dispersing agent.

The use of dispersing agent decreases the dielectric losses, increases permittivity and mitigates the ball-milling effects on NBT-BT properties. Finally, adding MEK as a solvent decreases the dielectric losses and increases the secondary Ba-containing phases volume fraction.

Therefore, to obtain samples compliant with Exxelia requirements of high permittivity values (at least 2000) and low dielectric losses or tan δ (lower than 2.5%), an intermediary volume fraction (2.5%) and average grain surface (0.9 to 3.0µm 2 ) on the secondary Bacontaining phases should be used. Effects of the 2 nd phase on the insulation resistance Fig. 3.25 presents the evolution of the insulation resistance of sample "N", "B", "E", "G", "H", and "V" with temperature and Fig. 3.24 show the insulation resistance at 200 • C (the highest measured temperature) versus the secondary Ba-containing phases volume fraction and average grain surface.

The increase in the secondary Ba-containing phases volume fraction and average grain average surface initially increase the insulation resistance up to 2.5% and 3µm 2 . Then, for higher volume fractions and grain surfaces, the insulation resistance decreases.

Decreasing the Na 2 CO 3 grain size does not affect the secondary Ba-containing phases volume fraction and average grain surface (see section 3.2.1.2). The insulation resistance, however, decreases from 50 to 34s, as observed in samples "H" and "V" respectively. The difference in the insulation resistance between these samples is small, considering that the variation of this property in temperature is exponential. For example, for sample "V", the decrease from 50 to 34s in the insulation resistance corresponds to an increase in temperature from 193 to 200 • C, so 3.9% with respect to the temperature range from room temperature (20 • C) to 200 • C, the temperature interval over which the insulation resistance is measured. So the decrease in the Na 2 CO 3 grain size slightly decreases the insulation resistance value of

NBT-BT.

No difference is found in the secondary Ba-containing phases volume fraction and grain surface when the energy of ball milling is increased from 250 rpm -4h to 350 rpm -8h on samples ball-milled with dispersing agent and without drying the reactants (see section 3.2.1.2). However, the insulation resistance decreases from 50 to 40s, as it is observed in samples "I" and "H". This insulation resistance variation corresponds to a temperature decrease of 2.5 • C in sample "I" (from 200 to 197.5 • C) or 1.4% of the temperature range of measurement. Considering the temperature measurement uncertainties of 3.5% presented in section 3.1.5.3, a variation of 2.5 • C can be considered as being part of measurement uncertainty. This indicates that, for these samples, the second ball milling energy does not affect the insulation resistance.

The ball-milling energy drastically changes the grain surface and the volume fraction of the secondary Ba-containing phases when no dispersing agent is used (see section 3.2.1.2). Samples ball-milled without dispersing agent also show lower insulation resistance. An example is given by the comparison of sample "G" (250 rpm ball milling, dried reactants and use of dispersing agent) with sample "B" (250 rpm ball milling, dried reactants and no use of dispersing agent). The use of dispersing agent increases the insulation resistance at 200 • C from 0.7 to 24s. This is equivalent to a temperature variation of 78 • C for sample "B" or 43% of the temperature range measured. Significant insulation resistance differences are also present when comparing samples "G", "H" and "I" (with use of dispersing agent) with samples "B" and "E" (without use of dispersing agent).

Finally, the drying of the reactants for samples ball-milled at 250 rpm -4h increases the secondary Ba-containing phases volume fraction from 1.5% to 3.1% (see samples "H" and "G"). This decreases the insulation resistance from 50 to 23s, corresponding to a temperature variation of 15 • C for sample "G" (from 200 to 185 • C) or 8.3% of the total temperature range measured. This indicates that the samples with dried reactants have significantly higher volume fraction of second phase and lower insulation resistance.

To conclude, adding MEK to the solvent mixture increases the second phase volume fraction (see 3.2.1.2). It also slightly increases the insulation resistance from 33 to 45s, being equivalent to a temperature decrease of 5 • C for sample "V" (from 200 to 195 • C) or 2.7% of the temperature range measured. This can be observed when comparing samples "V" (ethanol as solvent) and "N" (MEK+ethanol as solvent). Considering again the temperature measurement uncertainties of 3.5% a variation of 5 • C can be considered as being part of measurement uncertainty.

In short, the increase in the secondary Ba-containing phases volume fraction and average grain surface initially increases the insulation resistance up to 2.5% and 3µm 2 . But, for higher volume fractions and grain surfaces, the trend reverts.

The decrease of the Na 2 CO 3 grain size and the change in the ball-milling solvent do not affect the insulation resistance. No large change is observed in secondary Ba-containing phases and in insulation resistance for different ball-milling energies in samples prepared with dispersing agent.

Finally, the use of dispersing agent and of un-dried reactants increase the insulation resistance and mitigates the ball-milling effects on NBT-BT properties. Ideal structure and 2 nd phase state and relation with the synthesis parameters

Analysing the effect of the secondary Ba-containing phases volume fraction and average grain surface on the NBT-BT dielectric properties and insulation resistance it is possible to conclude that:

• A moderate volume fraction (2.5 to 3.0%) and average grain surface (0.9 to 3.0 µm 2 ) of the secondary Ba-containing phases is desirable to obtain high permittivity, low dielectric losses, and high insulation resistance.

• It is also important to use a dispersing agent during ball-milling, to obtain high permittivity, low dielectric losses, high insulation resistance, and to mitigate the ball milling energy effects on NBT-BT properties.

• The changes in the Na 2 CO 3 grain size and in the ball milling energy when using a dispersing agent do not influence significantly the dielectric and insulation properties.

• The use of MEK and ethanol mixture of solvents also increases the insulation resistance and decreases the dielectric losses.

• The drying of the reactants is not recommended to obtain a higher insulation resistance.

Considering the dielectric and insulation properties of samples analyzed in this section ("B", "E","G", "H", "I", "N", "V", and "P"), the influence of the secondary Ba-containing phases separation on these properties and Exxelia's requirements for the high temperature MLCCs, it is possible to conclude that samples "P", "N", and "V" are the most promising ones for the MLCC production, due to their high permittivity, low dielectric losses, high insulation resistance and moderate values of secondary Ba-containing phases volume fraction and average grain surface.

As shown in Fig. 3.15 p. 96 and in Fig. 3.16 p. 97, sample "U", synthesized with the same parameters of sample "P" but with different stoichiometry, show similar dielectric and insulation properties of sample "P". However, it shows a lower T d and a more stable relative permittivity in temperature, even though the insulation resistance at 200 • C of sample "U" (87s) is slightly smaller than "P" (130s), corresponding to a temperature decrease of 8 • for sample "U". So, sample "U" is also one of the most promising samples for the MLCC production. The suitability of the properties for these samples will be detailed in section 3.2.2.

Synthesis parameters

As shown in section 3.2.1.2, the grain size of the Na 2 CO 3 initial powder and the ball milling energy for the samples synthesized with dispersing agent do not affect the average grain surface and the volume fraction of the secondary Ba-containing phases. So, these synthesis parameters effects on the material properties can be analyzed independently of this phase.

Figures 3.26 and 3.27 compare the dielectric properties of the samples "H" and "I" (used to analyze the effect of the change in ball-milling energy) and the samples "H" and "V" (used to analyze the effect of the change in the Na 2 CO 3 grain size).

It is possible to conclude that, the effects observed in section 3.2.1.2 on the dielectric properties due to the change in the ball-milling energy of samples prepared with dispersing agent are valid for the entire temperature range and frequency (i.e. it does not affect the dielectric properties of the NBT-BT as shown in Fig. 3.1.4). Additionally, the change in the grain size of the Na 2 CO 3 increases moderately the permittivity between the T d and the T m and increasing the value of T d for all frequency range (see Fig. 3

.27).

As also mentioned in section 3.2.1.2, comparing the insulation resistance of samples "H", "I", and "V" in Fig. 3.28, the sample "H", synthesized with lower ball milling energy and larger Na 2 CO 3 grain size has higher insulating resistance than the other samples for temperatures above 130 • C. However, the maximum insulation resistance difference for the entire temperature range is 39%, a value lower than the difference between samples with different stoichiometry ("U" and "Y" have a 60% difference in insulation resistance at 200 • C). So the effect of the Na 2 CO 3 grain size and the ball milling energy on the insulation resistance is not as important as the stoichiometry effect.

Polishing and strain relaxation

The samples surfaces present a higher percentage of secondary Ba-containing phases and a zirconium oxide contamination from the sintering, contrary to the core (see sections 2.4 and 2.3.2.6). For this reason, a polishing step is necessary to guarantee a more homogeneous sample and to mitigate the effects of the ZrO 2 contamination. The polishing is done in four steps, using polishing papers with decreasing grain sizes, from # 180 (average grain size of 82µm), # 800 (average grain size of 21.8µm), # 1200 (average grain size of 15.3µm) FIGURE 3.26: Relative permittivity and dielectric losses versus temperature from 1kHz to 1MHz for samples "H", "I" and "V" with the same secondary Ba-containing phases average size and volume fraction and different synthesis parameters. to # 4000 (average grain size of 5µm). The total thickness removed from the sample surface is 25µm ± 0.1µm. XRD analysis of the polished sample compared to the as-sintered sample is presented in Fig. 3.29.

The low angle side shoulder peaks after polishing are due to the skin effect and the pseudo-cubic, rhombohedral and tetragonal phases coexistence, as described in section 2.3.2.2.

After polishing, a thermal treatment is done in order to relax the strain introduced during polishing. Fig. 3.29 shows the XRD of the samples treated for one hour at 400 • C and 500 • C. The maximum temperature to relax strain without needing to use a powder to create an atmosphere during the strain relaxation and without forming parasite phases is 400 • C.

Two different polished samples ("H" and "N") were cut into four parts. Each part was thermally treated at 400 • C for a different times, going from zero to three hours, to relax strain due to polishing. XRD analysis of these samples is shown in Fig. 3.30. In order to evaluate the effectiveness of the strain relaxation and to compare the different thermal treatment times, a Williamson-Hall analysis was carried out on each diffraction pattern.

In the Williamson-Hall analysis, it is assumed that the size and the strain-induced peak broadening vary differently with Bragg's angle. This method assumes that the peak width depends on the Bragg's angle 2θ as:

β • cos θ = Cε sin θ + Kλ D (3.14)
where β is the integral breadth of the Bragg peak in radians, θ is half of the Bragg's angle, λ is the X-ray wavelength, C is the dimensionless dislocation contrast factor, K is a dimensionless shape factor, D is the diffraction domain size and ε is the strain.

From the β • cos θ versus sin θ plot of the XRD integral breadth fit of each sample, it is possible to estimate the Cε (strain) and the K D (average diffraction domain size). The Williamson-Hall fit results for each sample with different strain relaxing times are presented in Figures 3.30 and 3.31. The fit were done using only the peaks corresponding to the pseudocubic phase (see section 2.3.2.2). For both samples, the angular coefficient and, so, strain increases after the polishing. The decrease in the angular coefficient with increasing strain relaxing time shows that the strain is relaxed during the thermal treatment. Moreover, the strain reaches a similar level of strain when compared to the as-sintered sample after three hours at 400 • C to relax strains.

The diffraction domain size estimation in Williamson-Hall model is based on the Scherrer equation. When the grains are nanosized, they often contain a single diffraction domain, therefore the grain size can be estimated by the diffraction domain size. However, the average grain size of the NBT-BT samples are all around 1µm. So the average grain size estimation via Williamson-Hall model cannot be done.

The influence of the internal strain on the dielectric properties was analyzed by measuring the permittivity and the dielectric losses for each sample after different thermal treatment times. The measurement results can be observed in Figures 3.32 and 3.33. Taking into account the measurement uncertainties, there is no difference in the measured dielectric properties when comparing different strain-relaxing times (different internal strain levels).

In conclusion, the polishing and strain-relaxing steps are necessary to have a better homogeneity and a lower effect of the ZrO 2 contamination in the bulk sample, without introducing internal strains. The maximum temperature for relaxing strain is 400 • C and the internal strains are relaxed after three hours. However, the internal strains do not markedly affect the dielectric properties of the final NBT-BT samples.

Comparison of the measured properties with Exxelia's specifications

Samples "U", "P", "V", "H", and "N" have the best dielectric properties and insulating resistance compared to Exxelia's specifications (see section 3.2.1). These samples will be analyzed in details in this section, to choose the best stoichiometry and the best synthesis method that will be used for the MLCC synthesis.

Industrial layout graphics for permittivity, dielectric losses and RI versus temperature

The permittivity variation with temperature is shown in Fig. 3.34 for these samples. The chosen reference temperature is 213 • C, since it is the mean temperature between the maximum operation temperature required (350 • C) and the minimum average depolarization temperature for NBT-BT (75 • C).

Sample "U" presents the most stable permittivity in temperature, since, considering the 1kHz frequency (industrial standard), the permittivity of this sample is ε r = 2338 ± 15% (limits shown as dotted lines) from 90 to at least 300 • C.

The evolution of the dielectric losses with temperature are shown in Fig. 3.34 for the same samples, with the industrial limit of 2.5% in the operation temperature range as dotted lines.

Sample "U" also presents the lower dielectric losses and, for the frequency of 1kHz, the losses are tan δ ≤ 2.5% from 90 to at least 300 • C.

Finally, the insulation resistances with temperature (logarithme scale) are shown in Fig. 3.35. The measurements were done to a maximum temperature of 200 • C, due to equipment limitations (see section 3.1.1). The curves extrapolation were done through a exponential decrease in the insulation resistance in temperatures, as it is normally observed for MLCCs at high temperatures (see section 3.1.1).

Considering Exxelia's specifications for the insulation resistance (IR ≥ 10s from 250 to 300 • C and 1s from 300 to 350 • C), none of the samples give an expected result. However, samples "N", "P" and "U" have the highest insulation resistances at high temperature, with IR ≥ 1s up to 300 • C.

To conclude, the dielectric properties and the insulation resistance of NBT-BT in temperature were analysed, to evaluate the effects of stoichiometry, structure, phase separation, synthesis parameters and internal strain.

The dielectric and insulation properties of the material are particularly sensitive to the stoichiometry and, more specifically, to the Na/Bi ratio. The increase in the Na content inhibits the secondary Ba-containing phases formation and increases the conductivity. The increase in the Bi content initially compensates for the oxygen vacancy formation (decreasing conductivity) and then forms a second phase, increasing again the conductivity. Considering Exxelia's requirements for the high temperature MLCC, the stoichiometry of sample "U" is the most adapted one, due to its high insulation resistance and lower dielectric losses and permittivity variation in temperature when compared to others.

The phase separation and the secondary Ba-containing phases formation are due to the Na evaporation during sintering. The increase of volume fraction and in average grain surface of this phase initially increases the permittivity, decreases the dielectric losses and increases the insulation resistance, due to the elimination of oxygen vacancies, being beneficial to the MLCC applications. Above a critical fraction and grain surface for the secondary Bacontaining phases, the tendency reverts, due to the conducting character of this phase. So, an intermediary volume fraction (2.5 to 3.0%) and average grain surface (0.9 to 3.0µm 2 ) of the secondary Ba-containing phases is desirable.

To obtain this intermediary average grain surface and volume fraction of secondary Bacontaining phases, the best dielectric and insulation properties, a dispersing agent should be used during ball milling in MEK and ethanol mixture and the reactants should not be dried before weighing. In this case, the average Na 2 CO 3 grain surface and the energy of ball milling do not affect significantly the final bulk properties.

Considering Exxelia's requirements, samples "P" (un-dried reactants, ball-milled with FIGURE 3.34: Variation of the relative permittivity with respect to the reference temperature (213 • C) and dielectric losses from 1kHz to 1MHz for samples "H", "N", "P", "U" and "V" respectively and Exxelia's specifications for the high temperature MLCCs. The arrows show the increasing frequency curves. The dotted lines stand for Exxelia's requirements on relative permittivity variation in temperature, and on dielectric losses maximum value. and dielectric losses for samples "H", "N", "P", "U" and "V" and Exxelia's specifications for the high temperature MLCCs dispersing agent in ethanol and MEK mixture during 8h at 350 rpm with fine Na 2 CO 3 powder), "N" (un-dried reactants, ball-milled with dispersing agent in ethanol and MEK mixture during 4h at 250 rpm with fine Na 2 CO 3 powder) and "U" (un-dried reactants, ball-milled with dispersing agent in ethanol and MEK mixture during 8h at 350 rpm with fine Na 2 CO 3 powder and lower nominal Na/Bi ratio compared to samples "N" and "P") are the most adapted for the NBT-BT application in MLCCs in terms of synthesis parameters and secondary Ba-containing phases characteristics, confirming the synthesis parameters and phase separation analysis. Finally, the polishing and strain relaxation are an important step to have a better homogeneity and a lower ZrO 2 contamination from the powder used to create sintering atmosphere. The thermal treatment should be done at 400 • C during 3h to release the introduced strain. However, the internal strain does not affect drastically the NBT-BT dielectric properties.

Lastly, it is possible to conclude that the sample presenting the best stoichiometry, synthesis parameters, secondary Ba-containing phases average grain surface and volume fraction and strain level to obtain the most promising dielectric and insulation properties for the MLCC production is sample "U".

Dielectric spectroscopy

NBT-BT samples show a frequency dependent behaviour. Several models were considered to analyse this dependence: a composite model with a conducting phase in an insulating matrix (through the Maxwell-Wagner model, section 3.3.1), two parallel and frequency dependent RC circuits representing a grain core and grain boundary with different conductivity (through a Cole-Cole plot, section 3.3.1.1) and a relaxor behaviour (through the modifies Curie-Weiss law, section 3.3.1.2).

Maxwell-Wagner model

The Maxwell-Wagner model is used to estimate the dielectric properties and the frequency dispersion of the permittivity when an external electric field is applied to a heterogeneous system of dielectrics. This model is applied to systems in which the ratio of permittivity to conductivity is different in the various phases, at least one of the phases having a conducting behaviour and in which the inhomogeneities are on a scale that is large compared to the size of the sample. So, it describes the properties of the accumulation of charges at the boundary between one dielectric phase and one conducting phase. For that reason, this model is also called the space-charge model. [START_REF] Bokov | Dielectric relaxation in relaxor ferroelectrics[END_REF][START_REF] Fricke | The Maxwell-Wagner dispersion in a suspension of ellipsoids[END_REF] In the case of the NBT-BT, it is possible to apply the model considering that the secondary Ba-containing phases are conducting and that they have large-scale randomly-dispersed grains in a less conducting NBT matrix phase. In this case, the Maxwell-Wagner model shows the influence of the secondary Ba-containing on the dielectric properties and, more specifically, on the frequency dispersion of the NBT-BT samples.

As mentioned before, in the Maxwell-Wagner systems there is an effect of charge accumulation at the interfaces in the material related to polarization discontinuity. [START_REF] Ning | Large Dielectric Constant and M axwell-W agner Effects in BaTiO3/Cu Composites[END_REF] So the system can be modeled by an equivalent circuit of two parallel RC circuits. The equations taken into account for the modeling are similar to the Debye relaxation. However, the Debye relaxation considers only the polarization relaxation, while the Maxwell-Wagner model takes into account the interfacial polarization due to the presence of a more conducting-phase particles. So the relative permittivity, imaginary permittivity and dielectric losses can be expressed as:

ε r = 1 ε 0 • ε ∞ + ε 0 -ε ∞ 1 + ω 2 τ 2 (3.15) ε = (ε s -ε ∞ ) • ωτ 1 + ω 2 τ 2 + 1 ωC 0 (R 1 + R 2 ) (3.16) tan δ = (ε s -ε ∞ ) • ωτ ε s + ε ∞ ω 2 τ 2 + σ ωε 0 • 1 ε 0 + ε s -ε ∞ 1+ω 2 τ 2 (3.17)
where ε s and ε ∞ are the static and high frequency permittivities, τ is the relaxation time, ω is the angular frequency, C 0 is the empty cell parameter, R 1 and R 2 are the resistances of the two phases and σ is the conductivity of the material. [START_REF] Ning | Large Dielectric Constant and M axwell-W agner Effects in BaTiO3/Cu Composites[END_REF] The resulting permittivity and dielectric losses are shown in Fig. 3.36. [START_REF] Lunkenheimer | Colossal dielectric constants in transition-metal oxides[END_REF].

In order to evaluated the Maxwell-Wagner fit for samples with different volume fractions of secondary Ba-containing phases, the permittivity and the dielectric losses versus frequency for different measurement temperatures were plotted for samples "H", "P" and "U". These plots are shown in Fig. 3.37.

Due to an internal auto-scale in the impedance measurement device, the raw dielectric vs frequency data (before correction) shown in Fig. 3.38 for sample "U", presents a discontinuity for the high frequency measurements. These discontinuities are present for most samples and they represent a shift on the high temperature dielectric losses for lower values, with a delta of between 0.5 to 2%.

For this reason, the dielectric properties in frequency shown in Fig. 3.37 corrected for these high-frequency dielectric-losses shift.

It can be observed that the relative permittivity decreases with frequency, but no permittivity plateau is observed. For low temperatures (lower than 180 • C for sample "P", 132 • C The frequency ν is shown in logarthmic scale. [START_REF] Lunkenheimer | Colossal dielectric constants in transition-metal oxides[END_REF] for sample "H", and 207 • C for sample "U"), the dielectric losses increase with frequency.

For high temperatures, the losses first decrease then increase with frequency. This indicates that there may be a Maxwell-Wagner type relaxation, due to the presence of conducting secondary Ba-containing phases particles. However, for the range of frequencies measured (1kHz to 1MHz), the only measured part of the Maxwell-Wagner relaxation curve is as indicated in Fig. 3.39 with the red lines for the case of a composite BaTiO 3 -Cu composite. [START_REF] Ning | Large Dielectric Constant and M axwell-W agner Effects in BaTiO3/Cu Composites[END_REF] So, the relaxation curve could not be entirely measured and the maximum losses could no be achieved.

All the NBT-BT samples presenting secondary Ba-containing phases have similar behaviour as the ones shown in Fig. 3.37.

Considering equations 3.15 and 3.17 and Fig. 3.36, it can be seen that the Maxwell-Wagner fit for measures that do not include at least ω p or limits for low and high frequencies values would create huge uncertainties in its parameters. So the fit could not be done for the measurements shown here.

In conclusion, the Maxwell-Wagner model may be applied to explain the frequency dispersion of the dielectric properties of the samples. Even if the fit could not be done, due to a limited frequency range of measurements, the Maxwell-Wagner model is useful to confirm the hypothesis that the Ba-containing phases are more conducting that the NBT-matrix phase. So that the interfacial polarization due to the presence of this phase contributes to the increase of the dielectric properties of the material.

Nyquist analysis

The Nyquist plot is a graphic representation of the complex impedance Z * . In this plot, the real and imaginary parts of the impedance are plot in the complex plane, for different frequencies and a single temperature. Using the electrical-circuit-modeling approach, it is possible to estimate the contribution of different parts of the measured system (grain core, grain boundary and electrode, for example) for the effective properties measured, since it is possible to identify the kinetics of different steps involved in the effective properties.

In the case studied here, the Nyquist analysis could be useful to identify the contribution of the samples (grain core and grain boundary) and of the electrodes to the measured dielectric properties (calculated from the impedance). Fig. 3.40 shows the Nyquist plots for NBT-BT samples "P", "H", and "U". The scales in both axis are not the same so that the details of the curves can be observed.

The fit of the curves using an equivalent circuit cannot be done, due to the a frequency limitation (the range of frequencies used for these measurements go from 1kHz to 1MHz). So, to estimate the values of the material's properties and to separate the contributions from the grain core, grain boundary, and electrodes, a new measurement should be done including lower frequencies, as suggested in section 4.4 about future works.

For this reason, the Nyquist plots presented here will only be analyzed qualitatively. Ning et al.showed a similar Z * plot for BaTiO 3 -Cu composites, as shown in Fig. 3.41.

[49] They adopted an equivalent circuit of two parallel RC circuits, the first one related to the grains (core) and the second one related to the grain boundaries. In this case, the impedance can be calculated as:

Z = R g 1 + (ωR g C g ) 2 + R gb 1 + (ωR gb C gb ) 2 (3.18) Z = R g ωR g C g 1 + (ωR g C g ) 2 + R gb R gb 1 + (ωR gb C gb ) 2 (3.19)
where (R g , R gb ) and (C g , C gb ) are the resistance and capacitance of grains and grain boundaries, respectively. [START_REF] Ning | Large Dielectric Constant and M axwell-W agner Effects in BaTiO3/Cu Composites[END_REF] For those composites, the R gb contribution to the Z peak is much higher than the R g . This can be seen by the 25% Cu curve in Fig. 3.41, where the diameter of the semi-circle associated with the grain boundaries (left) is much higher that the one associated with the grains (right). So the composite is composed of conducting grains with resistive grain boundaries.

For the NBT-BT samples analysed here, one hypothesis to describe the Nyquist plot behaviour would be that, for the low temperature plots shown in the right side of Fig. 3.40 (up to 140 • C for sample "U", and up to 180 • C for samples "H" and "P"), the resistance associated with the grain boundaries is much higher than the one associated with the grain cores. Besides that, this grain boundary resistance increases with increasing temperature until a critical temperature in reached. Then the resistance of the grain boundaries decreases with increasing temperature, creating the high temperature plots shown in the left side of Fig.

3.40.

As mentioned before, in order to confirm this hypothesis, a measurement including lower frequencies should be done.

Once the lower frequency measurement is included and the entire Nyquist plot can be analyzed, the effects of the secondary Ba-containing phases should be taken into account. This could potentially be done using a third RC series component representing the secondary phase grains effect, with low R values.

In conclusion, the Nyquist plot model may be applied for the NBT-BT samples. It indicates that a two parallel RC circuits associated with the grain cores and the grain boundaries could be used. In this case, the resistance associated with the grain boundaries is larger than the one associated with the grain cores and it increases with temperature up to a critical temperature, where the tendency reverts. However, a new measurement including lower frequencies should be performed to confirm this hypothesis.

Relaxor character

The frequency dispersion of the real part of the relative permittivity is described for relaxors by the modified Curie-Weiss law (equation 3.20):

1 ε r - 1 ε r,m = (T -T m ) γ C (3.20)
where ε r,m is the maximum relative permittivity value, T m is the temperature of the maximum relative permittivity, ε r is the permittivity for temperatures higher than T m , T is the temperature of where ε r is measured, C is the Curie-Weiss constant and γ is the constant used to indicate if the material is a ferroelectric or a relaxor. This law predicts the permittivity behaviour for ferroelectric materials for temperatures above the paraelectric transition. Classic ferroelectrics have γ = 1 while relaxor materials have γ = 2. [START_REF] Saeed Ullah | Electrical properties of Ca-modified Na0. 5Bi0. 5TiO3-BaTiO3 ceramics[END_REF] In order to evaluate the effects of the stoichiometry and of the secondary Ba-containing phases size and volume fraction on the relaxor character of the material, samples "U", "P", "G", "H", "B", "E" and "I" where evaluated by the modified Curies-Weiss law. The relaxor characteristics for samples "N" and "V" where also evaluated, since they are part of the best candidates for the MLCC production (see section 3.2.2).

The fit was done using the linear regression for the equation:

ln 1 ε r - 1 ε r,m = γ • ln(T -T m ) -lnC (3.21)
Sample "H" is used as an example to show the plot of ln 1 ε r -1 ε r,m versus ln(T -T m ) for different frequencies and the evolution of the C and γ estimations with increasing frequency randes. From Fig. 3.42 it is possible to see that the low frequencies have a less precise estimations, when using the modified Curie-Weiss law.

The estimated C and γ values for the frequency range of 1 kHz to 1 MHz for each sample are presented in Fig. 3.43.

Except for sample "E", all other samples present a relaxor character, with γ close to 2. The mixed character of sample "E" between a relaxor and a ferroelectric shows that a high volume fraction of small-sized secondary Ba-containing phases grains affects the effective properties of the sample. This also shows that the second phase and the interaction between neighbouring grains can tune the relaxor behaviour in NBT-BT material. [START_REF] Patel | Tuning of dielectric, pyroelectric and ferroelectric properties of 0.715 Bi0. 5Na0. 5TiO3-0.065 BaTiO3-0.22 SrTiO3 ceramic by internal clamping[END_REF] A slight increase in the gamma value is observed for the sample "U" that could mean that the stoichiometry and the decrease in the Na/Bi ratio are a good way to tune the relaxor behaviour in NBT-BT material. For sample "Z", even though the Na/Bi ratio is higher than for the "U" sample, there is no second phase to decrease the relaxor character of the material, showing that the second phase effect on the relaxor properties is more important than the stoichiometric one.

In conclusion, the three frequency dispersion models for the dielectric dispersion can possibly be applied to the NBT-BT samples, to explain the frequency scattering.

The Maxwell-Wagner model fit could not be done, due to a limited frequency range of measurements. However, it was useful to confirm the hypothesis that the Ba-containing phases are more conducting than the NBT-matrix phase and that an interfacial polarization contributes to the dielectric properties of the material.

The Nyquist plot fit could not be done, also due to a limited frequency range of measurements. However, this model indicates that two circuits associated with the grain cores and the grain boundaries could be used. In this case, the resistance associated with the grain boundaries is larger and it increases with temperature up to a critical temperature.

Finally, the modified Curie-Weiss model fit could be done and it indicated that the all NBT-BT samples present a relaxor character, except for sample "E". This indicates that the secondary Ba-containing phases and the interaction between neighbouring grains can tune the relaxor behaviour in NBT-BT.

Even though the Maxwell-Wagner and Nyquist plot fits could not be done, it is not a problem for this study, since the frequency dispersion is not a part of the main requirements for the MLCC applications. 1 MHz for samples "U", "P", "G", "H", "B", "E", "N", and "V"

Co and Mn additions and properties improvement

In order to try to improve the dielectric properties of the NBT-BT, specially to decrease the dielectric losses and to increase the insulation resistance, some samples were sintered with addition of Mn and Co oxides and characterized.

Co 3 O 4

Adding Co 3 O 4 was chosen, since it can act as a sintering aid and it can increase the temperature of the maximum permittivity, decrease the dielectric losses and stabilize permittivity for temperatures lower than 400 • C (see section 1.4.2.5). Moreover, it is an additive use intensively for industrial applications and at Exxelia.

For NBT [START_REF] Ming | The temperature-dependent piezoelectric and electromechanical properties of cobalt-modified sodium bismuth titanate[END_REF] and NBT-BT-KBT, [START_REF] Guo | Improved electrical properties of Co-doped 0.92 NBT-0.04 KBT-0.04 BT lead-free ceramics[END_REF] the percentage of Co 3 O 4 added varies from 0.3 to 0.8mol%. For the pure NBT, sample with 0.3mol% of Co-addition showed good dielectric properties, with low dielectric losses and stable permittivity in temperature. [START_REF] Ming | The temperature-dependent piezoelectric and electromechanical properties of cobalt-modified sodium bismuth titanate[END_REF] For the NBT-BT-KBT, samples with 0.2 and 0.4mol% of added-Co showed good dielectric and ferroelectric properties. [START_REF] Guo | Improved electrical properties of Co-doped 0.92 NBT-0.04 KBT-0.04 BT lead-free ceramics[END_REF] In this study, two different Co 3 O 4 percentages were tested: 0.5 and 5wt% corresponding to 0.4 and 4.4mol%, respectively. Samples were prepared with 250 rpm for 4 hours ballmilling with dispersing agent, with un-dried reactants, and with sintering at 1050 • C for three hours under ZrO 2 . The Co 3 O 4 was added before the second ball-milling.

Phase separation

Initially, the structure and phase separation of the samples were analyzed. The SEM measurements in Fig. 3.44 show that the sample with 0.4% of Co 3 O 4 have a similar phase separation as the NBT-BT samples, with a secondary Ba-containing phases separation and a NBT matrix. However, the 4.4mol%-Co-addition sample does not have secondary Ba-containing phases separation, but the excess of Co forms a new Co-rich phase. The composition of each phase could not be measured with sufficient precision, however, it can be considered that the phase separation takes place similarly to the pure NBT-BT material for the 0.4mol%-Co-addition sample with a slightly higher concentration of Co on the secondary Ba-containing phases. The EDS cartography of the Co-addition as-sintered samples shows the Co separation in the 4.4mol%-Co-addition sample and the slightly higher concentration of Co on the secondary Ba-containing phases in the 0.4mol%-Co-addition sample. (see Fig. addition sample. For the the as-sintered 4mol%-Co-addition sample, however, it is possible to identify peaks from a new unidentified phase. Even if the stoichiometry and structure if this phase were not identified, by comparing the XRD and SEM results, it is possible to conclude that they correspond to the Co-rich phase. After polishing and relaxing strain of the 4.4mol%-Co-addition sample (Fig. 3.46), no extra peak was identified, but SEM images still indicate the presence of some Co-rich phase. This indicates that the Co excess and second phase are mostly concentrated at the sample's surface.

Dielectric properties in temperature

Finally, the comparison of the dielectric properties of the Co-addition samples with the equivalent pure NBT-BT (sample "H") is presented in Fig. 3.48.

For the 4.4mol%-Co-addition sample, a clear increase in the dielectric losses is ob- served, together with an increase in the relative permittivity. This indicates an increase in the sample's conductivity and the presence of a conducting second phase. The increase in the sample's conductivity is confirmed by the decrease of the insulation resistance, as observed in Fig. 3.49. For the 0.4mol%-Co-addition sample, there is a slight decrease in dielectric losses for temperatures lower than the depolarization temperature T d . However, the dielectric losses at high temperatures do not change significantly and for temperatures between T d and T m they slightly increase. The permittivity value and the conductivity also increase compared to the pure NBT-BT, as shown by the insulation resistance measurements in Fig. 3.49.

Comparing now the depolarization temperature T d and the temperature of maximum permittivity T m of the pure NBT-BT sample with the 4.4mol% and 0.4mol%-Co-addition ones in Table 3.6 and considering the temperature uncertainties of 3.5% (section 3.1.5.3), it is possible to conclude that the T m is not significantly changed, while an important increase in T d is observed with increasing Co concentration. This shows again that the Co-addition is not ideal for MLCC application of NBT-BT.

Finally, pure NBT-BT sample density was 90.1%, sample with 0.4mol%-Co addition density was 92.3%, and sample with 4.4mol%-Co addition density was 87.8%. So, it can be concluded that the Co addition act as a sintering aid when low quantities are added, even if the resulting dielectric properties do not meet the MLCCs requirements. In conclusion, the addition of Co on NBT-BT increased the NBT-BT conductivity and, for the 0.4mol%-Co-addition it did not affect significantly the dielectric losses, while, for the 4.4mol%-Co-addition increased losses are measured. So, the Co addition have not shown promising dielectric properties and it is not ideal for the MLCC production.

MnCO 3

Adding MnCO 3 was also investigated, since it is reported that it can also act as a sintering aid for NBT-BT. [START_REF] Fen | Effects of manganese additive on piezoelectric properties of (Bi 1/2 Na 1/2 )TiO 3 -BaTiO 3 ferroelectric ceramics[END_REF] For 0.1wt% Mn-addition the maximum density is achieved while for 0.8wt% Mn-addition the minimum dielectric losses are achieved. [START_REF] Fen | Effects of manganese additive on piezoelectric properties of (Bi 1/2 Na 1/2 )TiO 3 -BaTiO 3 ferroelectric ceramics[END_REF] In this study, an intermediate MnCO 3 percentage was chosen: 0.5wt%. As for the Co 3 O 4added sample, the MnCO 3 -added one was prepared with 250 rpm for 4 hours ball-milling with dispersing agent, with no un-dried reactants and with sintering at 1050 • C for three hours using ZrO 2 . The MnCO 3 was added before the second ball-milling.

Phase separation

Initially, the structure and phase separation of the sample were analyzed through SEM and XRD measurement. The results are shown in Figures 3. [START_REF] Otoničar | Compositional range and electrical properties of the morphotropic phase boundary in the Na0. 5Bi0. 5TiO3-K0. 5Bi0. 5TiO3 system[END_REF] The SEM measurements in Fig. 3.50 show that the 0.5wt%-Mn-addition sample has a similar phase separation as the NBT-BT samples, with a secondary Ba-containing phases separation and a NBT matrix. The composition of each phase could not be measured with sufficient precision, however, it can be considered that the phase separation takes place similarly to the pure NBT-BT material. Moreover, the EDS cartography of the Mn-addition as-sintered sample shows a uniform concentration of Mn on both phases (see Fig. 3.52). The XRD measurements in Fig. 3.51 show a significant amount of secondary Ba-containing FIGURE 3.52: EDS cartography of the 0.5% Mn-addition as-sintered sample.

phases and ZrO 2 in the as-sintered sample. However, the polished and strain relaxed one show no extra peaks.

Dielectric properties in temperature

Finally, the comparison of the dielectric properties of the Mn added sample with the equivalent pure NBT-BT (sample "H") is presented in Fig. 3.53.

The dielectric losses also decrease for temperatures lower than the depolarization tem-FIGURE 3.53: Comparison of relative permittivity and dielectric losses versus temperature measured at 1kHz for samples pure NBT-BT (sample "H") and for sample with 0.5wt% of Mn. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ± 13% for the dielectric losses perature T d . However, at temperatures higher than T d , the dielectric losses increase when compared to pure NBT-BT. The permittivity value also increases compared to the pure NBT-BT, indicating an increase in the conductivity. This is again confirmed by the insulation resistance measurements in Fig. 3.49 p. 128. Finally, pure NBT-BT sample density was 90.1%, sample with 0.5% Mn-addition density was 97.6%. So, it can be concluded that the Mn can act as a effective sintering aid, even if the resulting dielectric properties do not meet the MLCCs requirements.

In conclusion, the addition of Mn on NBT-BT increases the conductivity and the dielectric losses for temperature higher than T d . So, the Mn-addition does not improve dielectric properties and it is not ideal for the MLCC production.

Other compatibilities with industrial requirements

Besides the dielectric and insulation properties and the restrictions concerning the synthesis method and parameters, other factors have to be taken into account to use a material in MLCC applications. These include the dielectric strength and the ability to co-sinter the material and the electrodes.

Dielectric strength

It is important to know the dielectric strength of the material, in order to characterize the maximum electric field that can be applied to the material and the application limits of the MLCC. The dielectric strength is a secondary parameter in the industrial requirements. However, the average measured values for BaTiO 3 -based MLCC are between 25 and 30 V/µm for Class II capacitors (see section 1.3.1.8).

The dielectric strain was characterized for sample "P" as being 7.5 ± 0.5 kV/mm or V/µm. This value is lower than the average for the BT-based MLCC. However, it is possibly higher for "U" sample (the sample showing the best dielectric properties), since this sample shows lower conductivity when compared to sample "P". So a new "U" sample should be synthesized, to allow the breakdown voltage without making the existing sample unusable for further measurements.

In conclusion, the dielectric strength should be increased for the MLCC application. However, it is expected that sample "U" shows a dielectric strength higher than 7.5 V/µm.

Compatibility with the electrodes

The compatibility of the ceramics with the electrodes and the possibility of co-sintering are an important factor for the use of the materials in MLCC production.

The compatibility of NBT-BT with the Ag-Pd electrodes is specially important due to the possible reaction between the Bi and the Pd, forming Pd x Bi y et Bi 2 O 3 . This was tested for the 70% Ag -30% Pd electrode by mixing the ceramic powders with the metal powder (prepared from the dried metallic ink) in an agathe mortar. The powders mixture was, then, sintered at 1050 • C or 1200 • C for three hours under ZrO 2 in the laboratory furnace. Another sample made with the same powder mixture was sintered at 1115 • C following Exxelia's sintering temperature program in their furnace. The XRD of the sintered material and its comparison with the pure NBT-BT and the pure electrode powder diffraction patterns are presented in Fig. 3.54.

The XRD measurements show that there is no detectable formation of new phases, since the XRD of the sample prepared by the ceramic and electrode powder mix show only the peaks related to the NBT-BT and to the electrode phases. An SEM and EDS measurement was also carried-out, to confirm that there is no reaction between the NBT-BT and the electrode and there is no defect formation on the interface between the two phases. The measurement results are presented in Fig. 3.55.

The measurement results show that there is no defect formation at the interface of the two phases. Moreover, there is also no phase formation, as can be observed in the concentration profile in Fig. 3.55. Finally, the EDS point analysis of the ceramic grains show no Pd presence and a small Ag concentration (1%), probably due to the migration from the electrode grains. So, there is no reaction between the ceramic material and the electrode during the co-sintering.

Concerning the sintering temperature, the best density for the NBT-BT samples was obtained after sintering at 1150 • C and the best structure and phase separation characteristics was obtained after sintering at 1050 • C (see section 2.3.4.3). These temperatures are compatible with the maximum co-sintering temperature of the 70% Ag -30% Pd electrode of 1150 • C (see section 1.3.2). So this does not represent a limitation for the use of NBT-BT in MLCCs.

In conclusion, the NBT-BT can be co-sintered with 70% Ag and 30% Pd electrodes, since there is no chemical reaction between the Bi and the Pd and since the sintering temperature is lower than the maximum co-sintering temperature for this electrode material.

Conclusion

This chapter discussed the dielectric properties of the NBT-BT samples and their comparison to Exxelia's specifications. The results allowed the determination of the synthesis parameters needed to obtain a material meeting these specifications.

Initially, the experimental setups, the model to calculate the complex permittivity, and the associated uncertainties were presented.

After analyzing the variation of the complex impedance in frequency, it was possible to conclude that the resistance and the capacitance of the setup can be neglected. So, the RC model was used to calculate the complex permittivity from the impedance measurements.

Since the NBT-BT samples showed different relative densities, the use of the Bruggeman model was proposed to estimate the fully dense dielectric properties. However, due to the sample's microstructure, it was shown that this model cannot be used.

The dielectric properties (relative permittivity and dielectric losses) measurements uncertainties were estimated from the measurement of one sample that showed results compatible with two different curves. So a 13% uncertainty was taken for the relative permittivity and a a 14% uncertainty was taken for the dielectric losses.

Due to the method initially used to fix the wires on the bottom of the samples (silver paste on the sample surface), a temperature shift correction was also done. The correction was done after measuring one reference BaTiO 3 sample with the same fixation method and comparing the measured properties with the known properties of the BT sample. Moreover, the shift in the Curie temperature in this sample comparing the heating and the cooling measurements showed that there is no significant temperature gradient in the samples.

Finally, a new method to fix the wires on the bottom of the samples was used (Cr-Au sputtering metallization and displaced fixation over a copper plate). These measurements were used to estimate a 3.5% uncertainty in the temperature measurements.

After defining the models to calculate the dielectric properties and estimating uncertainties, the dielectric properties and the insulation resistance of the NBT-BT ceramics in temperature were analyzed. The effects of the stoichiometry, structure, phase separation, synthesis parameters, and internal strain in these properties were analyzed.

The NBT-BT properties are particularly sensitive to the stoichiometry and, more specifically, to the Na/Bi ratio. The increase in Na content inhibits the secondary Ba-containing phases separation and decreases the relative Bi content in the main phase, increasing the sample's conductivity. On the other hand, the increase in the Bi content initially compensates for the oxygen vacancy formation and decreases the conductivity before forming a second phase, increasing again the conductivity. So non-stoichiometry can be measured by the Na/Bi ratio, with a larger conductivity with increasing the Na/Bi ratio. Considering Exxelia's requirements for the high-temperature MLCC, the stoichiometry of sample "U" is the most adapted one, due to its high insulation resistance, lower dielectric losses, and permittivity variation in temperature when compared to others.

Finally, to obtain a sample with no phase separation but without increasing the conductivity, Bi and Na excess should be added, maintaining the same Na/Bi ratio as sample "U". A suggested nominal composition would be Na 0.4818 Bi 0.5256 Ba 0.06 TiO 3 .

The phase separation and the secondary Ba-containing phases formation are due to the Na evaporation during sintering. The final material can be considered as a composite where the matrix phase is composed of non-stoichiometric NBT and the inclusions are composed of the secondary Ba-containing phases. However, due the the physical characteristics and the properties of the phases, there is no classical composite model that can be applied. So the effects of the secondary Ba-containing phases volume fraction were evaluated only qualitatively.

The increase of volume fraction and of average grain surface of this phase is initially beneficial to the MLCC application, since it increases the permittivity, decreases the dielectric losses, and increases the insulation resistance, due to the elimination of oxygen vacancies. Above a critical fraction and grain surface for the secondary Ba-containing phases, the tendency reverts, due to the conducting character of this phase. So, an intermediary volume fraction (2.5 to 3.0%) and average grain surface (0.9 to 3.0µm 2 ) of the secondary Ba-containing phases is desirable.

For this reason, the effect of multiple synthesis parameters on the secondary Ba-containing phases average grain surface and volume fraction were studied, to control this phase formation and characteristics.

The Na 2 CO 3 grain size showed no considerable effects on secondary Ba-containing phases and on sample's dielectric and insulating properties.

The use of dispersing agent and of un-dried reactants mitigated the ball-milling energy effects on the secondary Ba-containing phases (i.e. decreasing average grain surface and increasing volume fraction of the secondary phase with increasing ball-milling energy). Therefore, it decreases the dielectric losses and increases permittivity .

Finally, adding MEK as a solvent increases the secondary Ba-containing phases volume fraction and decreases the dielectric losses.

So, to obtain this intermediary average grain surface and volume fraction of secondary Ba-containing phases and the best dielectric and insulation properties, a dispersing agent should be used during ball milling in MEK and ethanol mixture and the reactants should not be dried before weighing. In this case, the average Na 2 CO 3 grain size and the energy of ball milling do not affect significantly the final bulk properties.

Considering Exxelia's requirements, samples "P" (un-dried reactants, ball-milled with dispersing agent in ethanol and MEK mixture during 8h at 350 rpm with fine Na 2 CO 3 powder), "N" (un-dried reactants, ball-milled with dispersing agent in ethanol and MEK mixture during 4h at 250 rpm with fine Na 2 CO 3 powder) and "U" (un-dried reactants, ball-milled with dispersing agent in ethanol and MEK mixture during 8h at 350 rpm with fine Na 2 CO 3 powder and lower nominal Na/Bi ratio compared to samples "N" and "P") are the most adapted for the NBT-BT application in MLCCs in terms of synthesis parameters and secondary Bacontaining phases characteristics, confirming the synthesis parameters and phase separation analysis.

Finally, the polishing and strain relaxation are important step to have a lower ZrO 2 contamination from the powder used to create the sintering atmosphere, without introducing internal strains. In this case, the thermal treatment should be done at 400 • C during 3h to relax the introduced strain, even if it does not drastically affect the NBT-BT dielectric properties.

Considering now the NBT-BT properties in frequency, several hypothesis were considered: a composite model with a conducting phase in an insulating matrix (Maxwell-Wagner model), two parallel and frequency-dependent RC circuits representing a grain core and grain boundary with different conductivity (Nyquist plot) and a relaxor behaviour (modified Curie-Weiss law).

The three frequency-dispersion model could be applied for the NBT-BT samples, even if the fits could not be done for the Maxwell-Wagner and the Nyquist plot models, due to a limited frequency range of measurement.

The Maxwell-Wagner confirmed the hypothesis that the Ba-containing phases are more conducting that the NBT-matrix phase and so an interfacial polarization contributes to increase the dielectric properties and the frequency dispersion of the material.

The Nyquist indicated that two circuits associated with the grain cores and the grain boundaries could be used. In this case, the resistance associated with the grain boundaries is larger and it increases with temperature up to a critical temperature.

Finally, the modified Curie-Weiss indicated all the samples, except for sample "E", showed a relaxor character, with γ close to 2. This indicated that the secondary Ba-containing phases and the interaction between its neighbouring grains can tune the relaxor behaviour in NBT-BT.

Lastly, Co 3 O 4 and MnCO 3 were added to NBT-BT, to try to improve the dielectric properties of the samples and to act as a sintering aid. Both additions are often done in the MLCC industry. Even though an increase in density was measured with the addition of 0.4mol% of Co 3 O 4 (from 90.1% to 92.3%) and 0.5wt% of MnCO 3 (from 90.1% to 97.6%), in both cases, the conductivity was increased. The dielectric losses were either unchanged or increased after adding Co or Mn. So, it did not improve dielectric properties and it is not ideal for the MLCC production.

Besides the dielectric and insulation properties, other factors were considered, including the dielectric strength and the ability to Co-sinter the material and the electrodes.

The dielectric strength was only measured for sample "P" and the result was 7.5 V/µm. It should be increased for the MLCC application. However, it is expected that sample "U" shows a higher dielectric strength owing to its higher insulation resistance.

Finally, the NBT-BT can be co-sintered with 70% Ag and 30% Pd electrodes, since there is no chemical reaction between the Bi and the Pd and since the sintering temperature is lower than the maximum co-sintering temperature for this electrode material.

Chapter 4

Literature incompatibilities

The objective of this chapter is to identify the origin of the differences in the dielectric properties NBT-BT presented in the literature.

NBT-BT's dielectric properties are sensitive to variations in the stoichiometry, in the synthesis method and in the atmosphere used for sintering the material (see Chapter 3). These are some reasons that are responsible for the variety of measurements reported for this material.

In this chapter, some arguments and some other reasons for the incompatibilities among the reported results will be discussed and the importance of having a strict synthesis and measurement method will be presented. Those properties are what we would expect when analyzing the material structure (see section 1.4.2.2). The first phase transition from non-ergodic to ergodic relaxor presents a frequency dispersion, due to the relaxor character of the material. This happens at a temperature of T d = 120 • C. The maximum permittivity temperature T m = 280 • C represents the transition to the paraelectric structure, so no frequency dispersion is observed. For this sample, relative permittivity values are 2000 at room temperature and 9000 at T m . [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF] Kumar et al.reported dielectric properties for NBT-BT 7% (still on the MPB of the NBT-BT solid solution) as presented in Fig. 4.2. For this report, NBT-BT presents a frequency dispersion in permittivity and in dielectric losses over the temperature range measured. Moreover, the transition temperatures are at T d = 80 • C and T m = 300 • C, at odds with what would be expected from the material structure. [START_REF] Chandrasekhar | Synthesis and characterizations of BNT-BT and BNT-BT-KNN ceramics for actuator and energy storage applications[END_REF] Finally, the permittivity at room temperature is 1000 and at T m is 2500, lower than the values reported for Ge et al.( 2014) and the dielectric losses are 5% on average over the temperature range of measurements, having a higher value when compared with the reported properties by [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF]. The relative permittivity does not show a hump at T d as would be expected from the relaxor phase transition. [START_REF] Chandrasekhar | Synthesis and characterizations of BNT-BT and BNT-BT-KNN ceramics for actuator and energy storage applications[END_REF] Finally, Zhang et al.also reported the dielectric properties of NBT-BT 6% as presented in Fig. 4.3. Relative permittivity values (2000 at room temperature and 6000 at T m ) and dielectric losses tendency (decrease of the losses for temperatures higher than T d ) are more similar to the results reported by [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF]. However, the sample presents an increase in the dielectric losses at high temperatures, a frequency dispersion over the measured temperature range and no permittivity hump at T d can be observed, as would be expected from the relaxor phase transition. [START_REF] Zhang | Temperature-dependent electrical properties of 0.94 Bi0. 5Na0. 5TiO3-0.06 BaTiO3 ceramics[END_REF] These are representative examples of literature incompatibilities for the dielectric properties of the NBT-BT. To explain the differences in the relative permittivity values, in the dielectric losses values at low and high temperature, the frequency dispersion and the presence of a hump at T d , the influence of stoichiometry, phase separation, metallization, synthesis parameters, and polishing and strain relaxation on the material's dielectric properties were analyzed.

Dielectric properties differences reported in the literature

4.2 Differences in the measured sample dielectric properties 4.2.1 Influence of the stoichiometry on the dielectric properties Stoichiometry is really important to define the dielectric properties of NBT-BT, since the presence of volatile species can significantly change the final material stoichiometry depending on the synthesis and on the sintering methods used. Moreover, slight changes in the stoichiometry of these elements can significantly affect the dielectric properties and the conductivity of the material (see section 3.2.1.1).

As mentioned in Chapter 3, the increase in Na content inhibits the secondary Bacontaining phases separation (decreases the relative Bi content in the main phase) while the increase in the Bi content initially compensates for the oxygen vacancy formation before forming a second phase. For these reasons, the increase of the nominal Na/Bi ratio increases the dielectric losses at high temperature and the conductivity of the NBT-BT. It also increases the frequency dispersion and the relative permittivity values, as observed in Fig. 3.14 p. 96.

The changes in stoichiometry can also have a large effect on the transition temperature (see section 3.2.1.1). Table 4.1 show the depolarization temperature T d and the maximum permittivity temperature T m for samples "P", "U", "Y", and "Z", with different Na/Bi ratio (see Table 3.3 p. 94) . It can be concluded that the increase in the nominal Na/Bi ratio increases T d and decreases T m , due to the decrease in the stability of the "AFE-like" phase (see section 2.3.2.6). However, the reason of this decrease is not well understood yet. [START_REF] Guo | Composition-induced antiferroelectric phase and giant strain in lead-free (Nay,Biz)Ti1xO3(1x)-xBaTiO3 ceramics Yiping[END_REF] Finally, the increase in the nominal Na/Bi ratio also decreases the relative permittivity change at T d , making it less evident, due to the increase of the relative permittivity of the "AFE-like" phase. This can be observed in Fig. 3.15 p.96. Therefore, the change in stoichiometry can have an important influence on the shape and values of the relative permittivity and dielectric losses vs temperature curves of the NBT-BT.

Sample T d ( • C) T m ( • C) "U" 65
A comparison of the shape of the dielectric properties vs. temperature curves can be done, for example, between the samples "Z" and the one reported by Zhang et al. [START_REF] Zhang | Temperature-dependent electrical properties of 0.94 Bi0. 5Na0. 5TiO3-0.06 BaTiO3 ceramics[END_REF], and between the samples "P" and the one reported by Ge et al. [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF], as shown in Fig. 4.4.

Due to the high nominal Na/Bi ratio of sample "Z", it shows increased dielectric losses, especially for high temperatures, a high frequency dispersion over the entire measured temperature range and no shoulder on the relative permittivity vs temperature curve at T d . The same observations can be done for the results reported by Zhang et al.. Moreover, the reported In conclusion, the stoichiometry has a crucial effect on the dielectric properties of the NBT-BT. The increase in the nominal Na/Bi ratio increases the conductivity, the relative permittivity, the dielectric losses over, and the frequency dispersion over the entire temperature range of the measurements (from room temperature to 350 • C).

Moreover, the change in the stoichiometry also changes the shape of the relative permittivity and dielectric losses vs temperature curves, since the increase in the nominal Na/Bi ratio also increases T d , decreases T m , and decreases the relative permittivity change at T d , making it less evident.

Finally, due to the volatile character of Na and Bi, the material's stoichiometry is sensitive to the synthesis and sintering methods used. This is one of the reasons that can explain the literature incompatibilities for the dielectric properties of NBT-BT.

Differences in the dielectric properties of over first heating measurement

All the dielectric measurements shown in Chapter 3 are over the first cooling of the sample. However, these measurements were carried out in two or three temperature cycles of heating and cooling. An example of dielectric measurement vs temperature over two consecutive cycles is shown in Fig. 4.5 for sample "X" (synthesis parameters in Table 2.11 p. 79).

It can be observed that all the cycle measurements are similar, except during the first heating. So an hysteresis is observed over the first heating/cooling cycle, decreasing the permittivity value, and often increasing the measurement noise.

To explain the reason of this temperature hysteresis, the influence of the structure and secondary Ba-containing phases, the synthesis parameters, the polishing, strain relaxation, and the metallization were studied.

4.2.2.1

Influence of the structure and secondary Ba-containing phases, the synthesis parameters and the polishing and strain relaxation on the temperature hysteresis

The first hypothesis tested to explain the hysteresis of the first cycle was that it came from intrinsic properties of the samples. In this case, differences either on the structure, composition, or synthesis methods would create samples with different properties and, consequently, could decrease or eliminate the hysteresis. To test this hypothesis that samples were measured in a sequence of thermal cycles, from room temperature to 350 • C.

Analyzing in Fig. 4.6, the dielectric properties of samples "U", "Y", and "Z" with different stoichiometries (see Table 2.11 p. 79), it can be seen that a similar hysteresis on the first temperature cycle is observed for all of them. This indicates that the stoichiometry does not induce the temperature hysteresis.

Samples "B", "N", "H", and "Z" have different Na 2 CO 3 grain size, ball-milling solvents and ball-milling energy (see Table 2.11 p. 79). Sample "B" has dried reactants and no dispersing agent was used during its synthesis. Theses differences result in different secondary Ba-containing phases average grain surface and volume fraction (see Table 2.11 p. 79) and, for the case of sample "Z", no phase separation. The dielectric properties of those samples were compared and are shown in Fig. 4.7. For each sample in this figure, the first heating measurement is different from all the other measurements in temperature cycles, showing lower relative permittivity. This also indicates that the synthesis parameters and the phase From Fig. 4.8, it can be seen that the samples present similar hysteresis over the first cycle of the dielectric properties, independently of the relaxing time. This indicates that the strain introduced by polishing is not the reason for this hysteresis.

In conclusion, the hysteresis of the dielectric properties of NBT-BT over the first cycle is neither due to the synthesis method, nor to the phase separation, nor to the strain level, nor to the stoichiometry of the material. So this hysteresis should not be an intrinsic characteristics of the material.

Influence of the metallization and electric contact on the temperature hysteresis

The hypothesis that the metallization and the electric contact method are the cause of the hysteresis over the first cycle was done after verifying that it is not due to an intrinsic characteristic of the material.

To verify this hypothesis, the simple method used to fix the wires with a silver paste drop directly onto the surface of the sample, used in section 3.1.5.1, was compared to a new metallization and electrical leads contact method, as described in section 3.1.5.3 p. 91. In the first method, a silver paste drop is put over the wire and the sample's surface and both are heated for two hours at 200 • C before measurement, as indicated in the product instructions.

For the second method, the metallization is done by sputtering of Cr-Au. A copper plate is fixed to the bottom electrode of the sample with a small amount of silver paste, avoiding the drawbacks of having a direct contact of the wire underneath the sample and large silver paste thickness under the samples. Finally, the wire is fixed on the copper plate with a drop of silver paste. The dielectric properties of two "H" samples (synthesis method in Table 2.11 p. 79) were measured. A new (never before measured) "H" sample polished and strain-relaxed during 3h at 400 • C and a "H" sample also polished and strain-relaxed during 3h at 400 • C first measured using Ag paste and subsequently using Cr-Au metallization method were compared. Fig. 4.9 show the dielectric properties of these samples measurements.

The comparison of the dielectric properties of the sample measured with silver paste and Cr-Au metallization methods in Fig. 4.9 (top and middle panels) indicates that the use of silver paste on metallization compared and wire fixing is the cause of the hysteresis over the first temperature cycle.

Moreover, a decrease from 3600 to 3000 in the relative permittivity value at 300 • C is observed from the simple Ag paste metallization to the Cr-Au sputtering. This corresponds to a 16% difference in relation to the Ag paste metallization. Considering the uncertainties of 14%, it can be considered that the use of Cr-Au sputtering metallization slightly decreases the permittivity. This is not observed for the dielectric losses, since the measured values are similar.

To confirm that there is no effect of the sample's intrinsic properties due to the heating cycles, the dielectric properties of a new Cr-Au metallized "H" sample were measured. No temperature hysteresis over the first cycle is measured. This proves that the dielectric properties hysteresis is due to the use of silver paste on the metallization and the way the wire (electric lead) is fixed onto the sample.

Finally, the comparison between the two different "H" samples with the same Cr-Au metallization method (middle and bottom panels of Fig. 4.9) show that the variability from one sample to the other can be important. For the relative permittivity, this difference is of 390 (1440 for the sample first measured with Ag paste -middle panel -and 1830 for the "new" sample -bottom panel) at 50 • C, being equivalent to 21% difference. For the dielectric losses, this difference is between 1.2% at the same temperature(4.85% for the sample first measured with Ag paste and 4.91% for the "new" sample). So the variability from sample to sample is also an important factor to explain the literature differences in the relative permittivity. However, there is no difference in the dielectric properties anomalies temperatures (T d and T m ) due to the sample to sample variability. The dielectric losses behaviour is different for both samples, since the sample first measured with Ag paste show a higher dispersion and increase in the dielectric losses over consecutive measurement cycles. This behaviour change may be due to the presence of silver paste remains in the sample's surface, since the sample was not polished after removing the Ag paste electrode.

In conclusion, the use of silver paste for the metallization and the fixing of the electric wires can change the measured dielectric properties of the samples during the first temperature cycle. The measured permittivity is decreased and the measured dielectric losses noises are often increased compared to subsequent cooling/heating. Since the silver paste is a very common metallization method for research on dielectric materials and since the properties are normally reported over the first heating, the metallization and the method to contact the electric leads can also be held responsible for the literature incompatibilities of the dielectric properties of NBT-BT.

Furthermore, the variability in the measured dielectric properties from sample to sample is also an important factor to explain the differences observed in the literature.

Other dielectric properties changes during temperature cycle measurement

Other than the first cycle hysteresis, dielectric properties show other changes during measurements over temperature cycles. The middle panel of Fig. 4.9 shows the evolution of the permittivity and the dielectric losses of sample"H" with Cr-Au metallization method after three thermal cycles (from room temperature up to 325 • C).

The permittivity is stable, but an increase in the dielectric losses can be clearly observed for temperatures higher than 160 • C after each measurement cycle. Contrary to what was observed for the hysteresis over the first temperature cycle, this high-temperature dielectric losses increase is observed for all samples, regardless of the metallization and method to contact the electrical leads, the stoichiometry, the phase separation, the synthesis parameters, or the polishing and strain relaxation (see Figures 4.6 to 4.9). Fig. 4.10 compares subsequent dielectric measurements for sample "U", both using the silver paste metallization method, the first for thermal cycles up to 300 • C and the second for thermal cycles up to 360 • C. It is possible to conclude that the increase of the dielectric losses over 300 • C depends on the higher temperature reached. This indicates that a degradation takes place at high temperatures (over 300 • C).

However, even after having been heated up to 360 • C, the dielectric losses of sample "U" maintain a low value up to 260 • C.

Two possibilities are considered to explain the thermal degradation of the NBT-BT. The first one is the presence of thermally activated phenomenon, such as defect movements at high temperatures. The second one is the change in the microstructure of the material that can be permanent or not.

Analyzing Fig. 4.9 p. 146, for sample "H", it can be seen that the dielectric losses increase after the first measurement with silver paste electrode. After removing this electrode and applying a new one by sputtering of Cr-Au, the dielectric losses return to low values (even lower than for the first measurement with silver paste). However, the same losses increase is observed during measurement over consecutive thermal cycles with Cr-Au electrodes. So, analyzing only this sample, it would be possible to make the hypothesis that a change in the sample microstructure takes place while heating. This change would not be permanent, but it would take a long time to be reverted (the measurements with the different electrodes were carried out three months apart).

However, analyzing now Fig. 4.11, for sample "X", it can be seen that the dielectric losses also increase during the first measurement with silver paste electrode. The second measurement is done on the same sample without removing the electrode. For this new measurement, the dielectric losses do not return to their original value and they continue to increase at each heating and cooling cycle. This may indicate that the high temperature dielectric losses increase is due to an electrode effect.

For all measurements, an increase in the dielectric losses is observed after each heating and cooling cycle. However, for samples where the electrode is removed and a new electrode is applied, the dielectric losses return to their original value. For samples that are remeasured with the same electrodes, the dielectric losses keep increasing over each heating and cooling cycle.

This can indicate that the electrodes influence the measured dielectric losses, increasing them by changes in the electrode's morphology during heating. In this case, the presence of uneven surface can result in just a few contact points between the electrode and the NBT-BT, which adds a series surface resistance to the equivalent electric circuit, increasing the dielectric losses, specially for the high frequencies. [START_REF] Xu | Enhancements in Dielectric Response Characterization of Insulation Materials[END_REF] However, it is also possible that there is a change in the sample's microstructure influenced by the high temperature.

In order to identify the source of this increase in the dielectric losses after heating, a Cole-Cole analysis could be done. In this analysis, the electrode contribution to the permittivity and to the dielectric losses can be identified by the presence of a second semi-circle (see section 3.3.1.1). However, in order to obtain good results for this analysis, a less conductive sample is needed. Furthermore, to determine maximum temperature to avoid the dielectric losses increase, a stability of the dielectric properties over time for different temperatures should be tested (see section 4.4).

Conclusion

This chapter discussed the origin of the differences in the dielectric properties NBT-BT reported in the literature. Some arguments for these incompatibilities were discussed and the importance of having a strict synthesis and measurement method was presented. Some examples of literature incompatibilities for the dielectric properties of the NBT-BT are: Ge et al.that reported the expected properties for stoichiometric NBT-BT with a frequency dispersion for temperatures lower than T d , a shoulder in the relative permittivity vs temperature curve at T d and low dielectric losses for temperatures higher than T d ; [START_REF] Ge | Evolution of structure in Na0. 5Bi0. 5TiO3 single crystals with BaTiO3[END_REF] Kumar et al.that reported a frequency dispersion, no hump in permittivity at T d , a different shape of the dielectric losses vs temperature curve, and higher values of tan δ compared to Ge et al.( 2014); [START_REF] Chandrasekhar | Synthesis and characterizations of BNT-BT and BNT-BT-KNN ceramics for actuator and energy storage applications[END_REF] and Zhang et al.that reported an increase in the dielectric losses at high temperatures, a frequency dispersion, and no permittivity hump at T d . [START_REF] Zhang | Temperature-dependent electrical properties of 0.94 Bi0. 5Na0. 5TiO3-0.06 BaTiO3 ceramics[END_REF] To explain these differences the influence of stoichiometry, metallization, phase separation, synthesis parameters and polishing and strain relaxation on the material's dielectric properties were analyzed.

The stoichiometry has a crucial effect on the properties of NBT-BT. The increase in the nominal Na/Bi ratio and Na quantity increases the conductivity and the quantity of free charges. This increases the relative permittivity and the dielectric losses from room temperature to 350 • C. It also increases the frequency dispersion for the entire temperature range. Finally, it also changes the shape of the relative permittivity and dielectric losses vs temperature curves. In addition to the effects on the relative permittivity and dielectric losses values, the increase in the nominal Na/Bi ratio decreases the relative permittivity change at T d , making it less evident, increases T d and decreases T m .

Another important difference in the measured dielectric properties of NBT-BT samples is the temperature cycle measurement hysteresis. All the heating / cooling cycle measurements are similar, except for the first heating that shows a decreased permittivity value and may show an increased measurement noise. The hysteresis of the dielectric properties of NBT-BT over the first cycle is neither due to the synthesis method, nor to the phase separation, nor to the strain level, nor to the stoichiometry of the material. So this hysteresis should not be an intrinsic characteristics of the material.

The hypothesis that the first heating hysteresis is due to the metallization method was confirmed and it showed that it is due to the use of silver paste on metallization and electric wire fixing. Since the silver paste is a very common metallization method in research, the metallization and the method to contact the electric leads can also be held responsible for the literature incompatibilities of the dielectric properties of NBT-BT.

The variability in the measured dielectric properties from sample to sample is also an important factor to explain the differences observed in the literature depending on the heating / cooling cycle considered.

Finally, a change in the dielectric losses at high temperatures after each heating and cooling cycle is observed. Contrary to what was observed for hysteresis over the first heating, the high-temperature dielectric losses increase is observed regardless of the metallization and method to contact the electrical leads, the stoichiometry, the phase separation, the synthesis parameters, or the polishing and strain relaxation. Moreover, it is present for temperature cycles where the higher temperature reached is greater than 300 • C and it increases with increasing maximum temperatures. This indicates that a thermally degradation takes place at high temperatures (over 300 • C).

Two possibilities are considered to explain the thermal degradation of the NBT-BT. The first one is the presence of thermally activated phenomenon, such as defect movements at high temperatures. The second one is the change in the microstructure of the material that can be permanent or not.

Comparing samples with different metallization methods it was possible to conclude that the electrode influences the measured dielectric losses, increasing it by changes in its morphology during heating. However, it is also possible that there is a change in the sample's microstructure influenced by the high temperature. A new Cole-Cole analysis could be done with a less conductive sample and including lower frequencies.

Future works for bulk NBT-BT

Some synthesis improvements could still be studied, to further enhance the properties of the final material. One suggested modification that could be studied is the change in the calcination parameters, decreasing the temperature and increasing the time of calcination. Otoničar et al.used a two-step calcination with the first one at 750 • C for 10h and the second one at 850 • C for 10h with the reactant powder mixture pressed onto the crucible. [START_REF] Otoničar | Compositional range and electrical properties of the morphotropic phase boundary in the Na0. 5Bi0. 5TiO3-K0. 5Bi0. 5TiO3 system[END_REF] In this case, as the calcination is done in a temperature lower than the fusion temperature of Bi 2 O 3 , there is no liquid phase formation and potentially less Bi evaporation, improving the final material properties.

Another suggested modification that could be studied is the use of the reactants powder or the NBT powder around the sample in a sealed crucible to create a saturated sintering atmosphere, avoiding the volatile species evaporation. Differently from the studied method shown in section 2.1.3.1, the used powders would not touch the material's surface, eliminating the need of post-sintering treatment. However, as it was shown in Chapters 2 and 3, the sintering on ZrO 2 powder results in satisfying NBT-BT properties, with small Zr contamination in the sample's surface. Moreover, the sintering on ZrO 2 powder method is less costly than the one using the same composition or the reactants powder. So, it would be an academic rather than an industrial study.

In order to prove that the change in the NBT-BT powder color after the second ballmilling with the 10mm-diameter balls (section 2.3.4.1) is really due to the creation of oxygen vacancies, a band gap measurement by UV-vis absorption of the powders could be done. The change of the band gap for powders ball-milled with the 10-mm diameter balls compared to those ball-milled with the 1mm-diameter balls would confirm the presence of oxygen vacancies and therefore the inadequacy of using 10-mm diameter balls for the second ball-milling.

The increase of the dielectric losses, even if they can be temporary, represent a problem for the material application for the MLCC production. In order to identify the maximum temperature that the NBT-BT can be used and to characterize its behaviour at high temperatures, an analysis of the stability of the dielectric properties in time for different temperatures should be done, specially over 300 • C.

The stability of the dielectric properties over time and depending on the temperature would also be useful to estimate the aging and lifetime properties of this material. These are also important characteristics for the MLCC application (see section 1.3.1.6).

A Nyquist plot analysis would also be useful to identify the influence of the electrodes on the measured dielectric properties, as mentioned in section 4.2.2.3. However, this measurement requires a less conductive sample to enable the semi-circle identification. It also requires lower frequency measurements (around 1mHz), to be able to identify the semi-circle liked to the electrode's effect.

The polarization vs electric field hysteresis cycle measurements of the final NBT-BT material are also important to determine the energy storage properties of these samples. However, a less-conductive sample at high-electric fields should be obtained first, to enable the measurement of a saturated polarization vs electric-field cycle.

Finally, the measurement of the dielectric properties under constant (bias) applied electric field would also be interesting. In case the material presents stable or increasing permittivity with limited dielectric losses (lower than 2.5%) when a bias field is applied, it could be a good candidate for substituting the lead-based MLCC capacitors presenting the maximum capacitance for specific values of constant applied voltage.

Chapter 5

NBT-BT Layers

The objective of this chapter is to ensure the compatibility of the NBT-BT layers with the industrial specification and to compare the differences in structure and properties of the best samples in bulk in with the layers obtained from these powders.

Layer preparation

Best NBT-BT bulk sample

Chapters 3 and 4 analysed the dielectric and insulation properties of NBT-BT in temperature, frequency, and over thermal cycling.

The results show that the stoichiometry of sample "U" is the best one, due to its high insulation resistance, and low dielectric losses and permittivity variation in temperature. Moreover, the secondary Ba-containing phases formation with an intermediary volume fraction (2.5 to 3.0%) and average grain surface (0.9 to 3.0µm 2 ) is beneficial for the properties.

To obtain this grain surface and volume fraction of the secondary Ba-containing phases, and the best dielectric and insulation properties, a dispersing agent should be used during ball milling in MEK and ethanol mixture and the raw powders should not be dried before weighing. In this case, the average Na 2 CO 3 grain size and the energy of ball milling do not affect significantly the final bulk properties.

So, the synthesis parameters of sample "U" (nominal NBT-BT with un-dried raw powder, ball milled with dispersing agent on ethanol and MEK mixture during 8h at 350 rpm with fine Na 2 CO 3 powder) are also the most adapted ones to meet Exxelia's requirements for MLCCs (as presented in section 1.3).

Finally, for the bulk ceramic samples, the polishing and strain relaxation at 400 • C during 3h should be done to release the internal strain and to have no secondary Ba-containing phases or ZrO 2 powder concentration on the surface.

Monolayer synthesis and sintering improvements

The slurry synthesis consists in preparing a NBT-BT powder by solid-state synthesis (weighing, ball-milling, and calcination) using the synthesis parameters and the stoichiometry of the bulk "U" sample, as detailed in Chapter 2: initially the un-dried raw powders were weighed with the nominal composition of Na 0.44 Bi 0.48 Ba 0.06 TiO 3 . Then they were ball-milling during 8h at 350 rpm in an ethanol and MEK mixture with the addition of a dispersing agent. The milled powders were, then, calcinated during 2h at 900 • C.

A second ball-milling is then carried-out giving rise the slurry. The synthesis parameters used in this second ball-milling were detailed in section 2.3.3.1 and are summarized here:

The slurry composition was 60.6wt% of NBT-BT powder, 1.1wt% of PEG (poly-ethyleneglycol), 22.7wt% of MEK (methyl-ethyl-ketone), 10wt% of ethanol, 4.5wt% of PVB (polyvinyl-butyral) and 1.1wt% of dispersing agent (borchi-gen-911), as reported in Table 2.8 p. 61.

The slurry preparation was done by adding initially the solvents (ethanol + MEK), the dispersing agent and the NBT-BT powder, as for the "U" ceramic sample. The mixture was ball-milled at 300 rpm for 12 hours in an YSZ jar. Then PVB and PEG are added and the mixture is again ball-milled at 300 rpm for 2 hours (see section 2.3.3.1).

Finally, the slurry was deaerated by pumping its recipient that is, the air was removed from the slurry, to avoid defects on the tape. It was then tape casted using the setup shown in Fig. 5.1 with a thickness of the casted slurry set to 100µm.

The "green" tapes (before sintering) showed good mechanical resistance, no cracks and a uniform thickness (153 ± 24µm). This indicates that the slurry is well dispersed and stable. Initially, the sintering of the monolayers was done following the same parameters as the ones used for the bulk "U" sample (sintering under ZrO 2 for 3h with a heating speed of 120 • C/h and a cooling speed of 200 • C/h). However, the as-sintered monolayers showed a low density of 58%. For this reason, the sintering parameters were optimized for the monolayer synthesis.

The first tested parameter was the sintering time that was increased to 6h and decreased to 1h. However, the density decreased to 47% for the 6h sintering and to 49% for the 1h sintering. So the initial sintering time of 3h was maintained.

The second parameter investigated was the sintering temperature. It was decreased to 1000 • C and increased to 1150 • C. As for the bulk, the NBT-BT monolayers presented the maximum density at 1150 • C with a density of 62% while the sample sintered at 1000 • C showed a lower density of 42%. However, the 62% density is still not enough for the MLCC application. Due to the limited time available and to the fact that the relative density decreased for the bulk NBT-BT samples sintered at temperatures higher than 1150 • C, the maximum sintering temperature tested for monolayers was 1150 • C.

Finally, the last parameter changed was the temperature steps during sintering. Salam et al.showed by thermogravimetric analysis that the oxidative breakdown of the PVB structure takes place between 400 and 500 • C, achieving a complete burnout. [START_REF] Loey | Pyrolysis of polyvinyl butyral (PVB) binder in thermoelectric green tapes[END_REF] The minimum temperature to have small quantity of PVB residues after heat treatment is 450 • C. However, all The SEM images showed in Fig. 5.3 also show the presence of secondary Ba-containing phases grains. As for the bulk samples, this phase is formed due to the Na evaporation during sintering. However, the morphology of this phase is different from the one in the bulk samples, as it can be seen in Fig. 5.4, probably due to the low density of the material.

The volume fraction of the secondary Ba-containing phases could not be estimated, due to the impossibility to have a polished surface image. The average grain surface of the secondary Ba-containing phases is 2.9 ± 0.8µm 2 in the monolayer. This is in the moderate average grain surface values necessary to obtain samples compliant with Exxelia requirements (see section 3.2.1.2).

Table 5.2 presents the composition of the matrix and the secondary Ba-containing phases present in the sample sintered at 1050 sition in Table 2.3 p. 51, it can be seen that for both samples, the Bi is stoichiometric in the matrix NBT phase. However, the Na quantity in the matrix is smaller in the monolayer sample, indicating that the evaporation during sintering is more important in the monolayer when compared to the bulk. This also indicates that the secondary Ba-containing phases volume fraction should be higher in the layers, even if this could not be measured due to the low density of the samples.

Comparing now the composition of the secondary Ba-containing phases of the layer with to the bulk ones (see Table 2.10 p. 73), it can be seen that, in both cases, there is a Zr contamination in this phase. However, the contamination is more important for the monolayers, due to the higher contact surface of the material with the ZrO 2 powder during sintering. This can also explain the lower Ba quantity in the secondary Ba-containing phases of the layers. The Zr doping favours the Ba 2 Ti 9 O 20 formation over Ba 2 TiO 4 and Ba 2 Ti 9 O 20 \2BaO•TiO 2 , resulting in a lower Ba content in this phase.

Finally, the SEM analysis shows an average grain size of 2.4 ± 0.8 µm 2 after sintering and a monolayer thickness of 97 µm. The measured grain size is slightly larger than Exxelia's specifications (2 µm), but it could still be used for the MLCC production (see section 1.3.1.7). However, the monolayer thickness is considerably larger than the minimum thickness specifications (20 µm as specified in section 1.3.1.7), so the synthesis of thinner layers should also be tested after the density is increased (see section 5.6).

In conclusion, all the synthesized monolayers presented a porous structure due to their low density. This is not ideal for the MLCC production, so an optimization of the slurry synthesis is needed. This optimization can be done by changing the ceramic powder and the binder concentrations on the slurry and by pressing multiple layer together, forming a multilayer device before sintering, to obtain a higher relative density after sintering.

Moreover, the NBT-BT layers present the same secondary Ba-containing phases separation as the bulk samples. However, a more reliable estimation of the volume fraction and the grain surface average values for this secondary phase can be done only after obtaining a dense NBT-BT layer.

Dielectric properties of the monolayers in temperature

The dielectric properties were measured only for the NBT-BT monolayer sintered at 1050 • C. The results for the temperature cycling measurements and for frequencies from 1kHz to 1MHz for the second cooling are shown in Fig. 5.5.

A reliable comparison of the dielectric properties between the equivalent bulk and monolayer samples is difficult, due to the large density difference between them. So a synthesis optimization should be done before.

However, it can be seen that the relative permittivity of the monolayer is drastically smaller compared to the bulk one, with an of average half of the bulk value. The dielectric losses are also increased for temperatures higher than 150 • C on the monolayer sample compared to the bulk one. The decrease of the relative permittivity is expected due to the low density of the monolayer sample that decreases the average permittivity of the material due to the low permittivity of the air. The higher dielectric losses are also expected due to the low density of the sample. Due to the high number of pores in the material, the ionization loss coming from the air in the pores contributes to the dielectric losses. Moreover, the high concentration of impurities and defects in the low density materials creates weakly bounded ions, resulting in conduction loss. [START_REF] Lv | Study on Dielectric Properties of Aluminum Borate Whisker Reinforced Aluminum Phosphate Composite[END_REF] Nonetheless, the most important observation related to the dielectric properties of the monolayer sample is the huge temperature hysteresis when measuring it in consecutive thermal cycles. The measurement could not be properly done for temperatures higher than 275 • C thermal cycles was already shown in chapter 4 for the bulk samples. However, the effects are magnified for the monolayer samples and they are also present for the relative permittivity. The effect may be due to the influence of the silver paste electrodes and their morphology in the effective dielectric properties. It is also possible that it is due to changes in the sample's microstructure influenced by the high temperature (see section 4.2.2.3).

The SEM image of the monolayer after measuring its dielectric properties in a temperature cycle from 25 to 350 • C using silver paste metallization is shown in Fig. 5.7.

This image shows that there is a penetration of the silver coming from the silver paste electrodes in the material pores during measurement in thermal cycling. This supports the hypothesis that the electrode influences the measured dielectric properties, increasing them by changing its morphology. However, the hypothesis of the material morphology change in temperature cannot be excluded, since the low density and the high specific area of the monolayer samples increase the defect concentration and facilitate the material morphology changes.

Finally, the insulation resistance of the NBT-BT monolayer sample is shown in Fig. 5.8. Comparing the measured value at 200 • C (the highest measured value before the curve extrapolation by exponential decrease) of the monolayer sample (0.5s) with its corresponding bulk counterpart "U" (87s), an important decrease in the insulation resistance is observed for the layer sample, corresponding to a temperature variation of 100 • C. This difference is due to the low density of the sample that facilitate the creation of defects and the evaporation of volatiles during sintering, increasing the material's conductivity.

Compatibility of the dielectric properties with Exxelia's specifications

The relative density of the NBT-BT monolayer sample should be improved, to allow a more reliable assessment of NBT-BT layer properties and to meet Exxelia's MLCC requirements (see section 5.2).

However, considering the dielectric properties of this NBT-BT monolayer sample in Fig. 5.5 p. 159, it can be concluded that the losses are lower than 2.5% at 1kHz (the required maximum value for the MLCCs) from 100 to 150 • C. Considering the reference temperature as 213 • C (see section 3.2.2.1) the relative permittivity variation of ±15% takes place from 180 to 240 • C. If the reference temperature was changed to 125 • C (the middle point of the temperature rage to have tan δ ≤ 2.5% at 1kHz), the variation of ±15% would take place from 68 to 187 • C.

Considering now the minimum value of the insulation resistance allowed for the MLCCs (1s, as explained in section 1.3), the the maximum operational temperature of this sample would be 180 • C.

In conclusion, even for the low density NBT-BT monolayer sample, considering the reference temperature as 125 • C, this sample shows a compatible relative permittivity from 68 to 187 • C, a compatible dielectric losses from 100 to 150 • C and a compatible insulation resistance from the room temperature to 180 • C.

A new dielectric characterization and the comparison between the layer and the equivalent bulk samples should be done after increasing the layer's relative density. This will allow a more reliable assessment of the NBT-BT layer properties, in order to evaluate the real compatibility with Exxelia's requirements and the effect of reducing the sample's thickness on its dielectric and insulating properties.

Structure and density of the pressed multilayers

As suggested by Exxelia, the effects of pressing multiple "green" ceramic layers together before sintering, forming a multilayer device, was studied. This pressing step is normally important thereby high density ceramics, since it decreases the porosity of the "green" material.

The first step for testing the effects of the pressing step on the density and structure of the layers was to sinter a monolayer of a material that is commercially used. The sintered monolayer was then compared with its equivalent commercial MLCC. The chosen layer material is composed of BaTiO 3 doped with Bi (K2200), since it has a similar sintering temperature to the NBT-BT. The monolayer synthesis was done using the same temperature program as for the NBT-BT layer (120 • C/h heating, a plateau of 30 minutes at 800 • C, sintering at 1150 • C for 3h and 200 • C/h cooling) and it was sintered either with or without covering the monolayer with the ZrO 2 powder. The SEM images of the two sintered monolayers and the equivalent commercial MLCC are shown in Fig. 5.9.

The density of the sintered monolayers could not be measured directly due to the low thickness of the "green" layers (40 µm). However, it can be seen from Fig. 5.9 that the monolayers show a much lower density (higher porosity) compared their corresponding MLCC.

Moreover, the monolayer sintered in ZrO 2 powder also shows a lower density compared to the one sintered without using the ZrO 2 powder. This indicates that the multilayer pressing step is essential to obtain a high density material after sintering and that the use of ZrO 2 powder to control the volatile species evaporation also contributes to limit the final density of the layers.

From the results obtained for the K2200 commercial monolayers, a second test was done, sintering multiple layers of NBT-BT pressed together before sintering. To do that, the same "green" NBT-BT layers were stacked and pressed together using uniaxial pressing in the stacking machine used in Exxelia for the MLCC production. No electrode was applied between the ceramic layers. The pressed ceramic multilayers were cut into squares of around two to three millimeters side and they were sintered in ZrO 2 powder using the same temperature cycle than the 3h at 1150 • C sintering. The measured density of the sintered NBT-BT multilayer is 89.5%, much higher than the equivalent monolayer (62%) and compatible with the MLCC production. This density increase can also be observed in the SEM images of the sintered NBT-BT multilayer in Fig. 5.10, since the surface and the core of the sample show much lower porosity compared to the monolayer. Fig. 5.10 also shows a phase separation and the presence of the secondary Ba-containing phases grains. As for the bulk samples, this phase is formed of grains due to the evaporation of Na during sintering and it concentrates at the surface of the sample. Contrary to the NBT-BT monolayer, the secondary Ba-containing phases in the NBT-BT multilayer show a similar structure as in the bulk samples, with elongated grains. However a higher concentration of this secondary phase is observed in the NBT-BT multilayer compared to the bulk samples, specially at the sample's surface. This indicated that a higher Na evaporation is present in the multilayers, as expected from their lower thickness.

The average volume fraction and average grain surface of the secondary Ba-containing phases could only be estimated for the core of the sample, due to the extremely high concentration of these phases at the surface of the sample. However, since there is a polishing step planned in the MLCC production, the volume fraction and the grain surface of the secondary Ba-containing phases in the surface of the sample do not influence the final MLCC properties.

The estimated average volume fraction of the secondary Ba-containing phases in the core of the sample is 5.5 ± 2.4 % and the estimated average grain surface of these phases is 1.6 ± 0.5 µm 2 . Comparing these values with the ones for the bulk samples (1.6 ± 0.5 % of average volume fraction and 1.9 ± 1.0 µm 2 ) it is observed that the average volume fraction of the secondary Ba-containing phases in the pressed multilayers are similar to the ones in the bulk "U" samples. However, there is a great increase in the average volume fraction for the pressed multilayers, due to the higher Na evaporation during sintering. It is, then, indicated to measure the evolution of the dielectric properties as function of the temperature for the pressed NBT-BT multilayers, to evaluate the effects of this increase on the average volume fraction of the secondary Ba-containing phases.

Another difference in the structure of the pressed multilayers compared to the equivalent "U" bulk sample is that the multilayers do not show a Bi-containing secondary phase in the core of the sample, whereas the bulk samples do. This indicates that there is also a higher evaporation of Bi in the pressed multilayers, which can also affect the dielectric properties of the material. Therefore, the measurement of the evolution of the dielectric properties as function of temperature is also important for evaluating these effects.

In conclusion, the pressing of multiple "green" ceramic layers together before sintering is an important step to obtain high density NBT-BT or commercially used ceramic layers after sintering. The NBT-BT pressed multilayers showed a density of 89.5% after sintering at 1150 • C, much higher than the equivalent monolayer (62%) and compatible with the MLCC application.

The NBT-BT pressed multilayer showed a similar structure as its equivalent bulk "U" sample, with the same secondary Ba-containing phases. However, the average volume fraction of this secondary phase was higher than the one in the bulk samples and it did not show a third secondary Bi-containing phase. This indicates a higher Na and Bi evaporation during sintering and could influence the dielectric properties of the material in temperature. So a measurement of the evolution of the dielectric properties as function of temperature should be done for the pressed multilayers, to evaluate its compatibility with the industrial demands.

Anyhow, these results show that, the low density of the monolayers are not due to a problem in the slurry composition. Moreover, even though the density of the monolayers are not sufficient for the MLCC application, giving rise to dielectric properties that are not compatible with the industrial requirements, this does not mean the the multilayer device produced from these layers will have the same problem.

Conclusion

This chapter discussed the synthesis of NBT-BT layers and its compatibility with the industrial specifications and compared the differences in structure and properties of the best samples in bulk with the layer form.

Bulk sample "U" showed the best properties considering Exxelia's requirements for MLCC applications. For this reason, this sample was chosen to be studied in layer form.

For the layer synthesis, the second ball milling was adapted and the slurry was prepared based on Exxelia's slurry composition as well as a binder and additives optimization for NBT-BT reported in the literature.

The "green" tapes (before sintering) showed good mechanical resistance, no cracks, and a uniform thickness, indicating that the slurry is well dispersed and stable. However, the monolayers sintered using the same temperature program as sample "U" (30-minute temperature step at 850 • C and sintering at 1050 • C for 3h) showed low relative density of 58%.

For this reason, a sintering optimization was initiated. The sintering parameters that resulted in the highest relative density for the monolayers (62%) were a sintering with a 30 minutes temperature step at 850 • C and a sintering at 1150 • C for 3h. This is still insufficient for the MLCC applications.

Concerning the monolayers structure, the as-sintered samples showed the presence of ZrO 2 powder in surface, as for the bulk "U" sample. A XRD peak widening was observed due to a skin effect (coexistence of pseudo-cubic, rhombohedral and tetragonal phases in the skin). The same secondary Ba-containing phases as bulk samples were present with an average grain surface of 2.9 ± 0.8µm 2 , being compliant with Exxelia requirements. However, the morphology of this phase was different from the one in the bulk, due to the low density of the monolayer. Finally, a higher Zr contamination in the secondary Ba-containing phases was observed for the monolayers, being the reason for its lower Ba concentration.

An average grain size of 2.4 ± 0.8 µm after sintering and a monolayer thickness of 97 µm were obtained. These values are not compatible with Exxelia's specifications, but they could still be used for the MLCC production.

It is not possible to do a reliable comparison between bulk and monolayer sample's dielectric properties, due to the low density of the monolayers. However, for the synthesized monolayer, the measured relative permittivity is smaller and the dielectric losses for temperatures greater than 150 • C are higher than the bulk. This is expected due to the low density values. Moreover, a huge temperature hysteresis is observed when measuring it in consecutive thermal cycles, making the measurement impossible temperatures higher than 275 • C. This hysteresis and thermal degradation of the sample may be due to the influence of the electrodes and its morphology in the effective dielectric properties, since there is a penetration of the silver paste in the material pores during thermal cycling. However, it may also be due to the material morphology change in temperature, since the low density and the high specific area of the monolayer facilitates the material morphology changes.

Finally, the insulation resistance for the monolayers are lower than for the bulk corresponding to a temperature decrease of 100 • C, as expected for lower density materials.

Even for the low density NBT-BT monolayer sample, considering the reference temperature as 125 • C, this sample shows a compatible relative permittivity from 68 to 187 • C, a compatible dielectric losses from 100 to 150 • C and a compatible insulation resistance from the room temperature to 180 • C.

So, in order to make a more reliable evaluation of the NBT-BT layers and to achieve the requirements for the MLCC production, the increase in density is imperative.

Finally, as suggested by Exxelia, the effects of pressing multiple "green" NBT-BT layers together before sintering, forming a multilayer device, was studied. It was shown that a high density material (89.5%) can be obtained after sintering the pressed multilayers at 1150 • C. This indicates that the low density of the monolayers are not due to a slurry composition problem and that, even though the monolayers do not show dielectric properties compatible with the industrial demands from room temperature up to 300 or 350 • C, this does not necessarily mean that the multilayer device prepared from these layers will have the same problem. However, since the pressed NBT-BT multilayers show more Na and Bi evaporation, a new measurement of the evolution of the dielectric properties as function of temperature should be done to evaluate the temperature range of compatibility with the industrial requirements.

Future works for NBT-BT layers

Even if the NBT-BT monolayers show a relative permittivity compatible with Exxelia's specifications from 68 to 187 • C, a compatible dielectric losses from 100 to 150 • C and a compatible insulation resistance from the room temperature to 180 • C, their properties are not optimal for the MLCC production. The increase in the dielectric losses should be restricted for their industrial application. The increasing dielectric losses were also observed on a much smaller scale for the bulk NBT-BT samples. However, due to the low thickness and low density of the ceramic monolayers, they were magnified.

In order to meet the industrial density requirements (see section 1.3), to restrain the dielectric losses increase, and the material degradation at high temperatures, the key factor is the final density of the ceramic layers. A high density material was obtained after pressing multiple NBT-BT "green" layers together before sintering (see section 5.4), indicating that, even though the dielectric properties of the monolayer were only compatible with the industrial requirements from 100 to 150 • C, this does not necessarily mean that the multilayer device prepared from these monolayers will have the same temperature range restriction.

However, the higher Na and Bi evaporation in the pressed NBT-BT multulayers can affect the final dielectric properties of the material, as explained in section 5.4. So, the next step to evaluate the compatibility of the NBT-BT layers with the industrial MLCC requirements would be to do a new measurement of the evolution of the dielectric properties as function of temperature with the pressed NBT-BT multilayers.

If the density increase is not sufficient to guarantee compatible dielectric properties, an optimization of the slurry could be done, increasing the solid content and decreasing the PVA. Moreover, if the dielectric properties of the pressed NBT-BT multilayers are not compatible with the industrial demands, a modification of the reactants stoichiometry is also proposed. This would compensate for the higher Na and Bi evaporation during sintering and it would decrease the average volume fraction of the secondary Ba-containing phases, affecting the final dielectric properties.

Another parameter that should be optimized during synthesis and characterized for the industrial application is the grain-size distribution. This parameter is important since the surface energy and the sintering results vary depending on the grain-size distribution. For this reason, this is a usual information in the product specification and it is controlled by companies before the MLCC production starts. A reliable characterization of the NBT-BT powders grain size distribution was not possible during the thesis, due to the small average grain size (≤ 1 µm) that hinders the SEM resolution of separated grains. However, Exxelia requires a grain size between 300 and 500nm before sintering and between 0.5 and 2µm after sintering. So the grain size of the NBT-BT powder and layer samples agree with the required values.

To meet Exxelia's specifications and to ensure that the layers could have a thickness of a minimum between 5 and 20 µm after sintering, the thickness of the tape-casted layers should be gradually decreased.

Finally, a MLCC should be synthesized with the optimized powder synthesis method, slurry composition and reactants stoichiometry, to obtain a prototype. To do that, the industrially used Ag-Pd (70 -30) ink should be used instead of the silver paste or the Cr-Au sputtering (see section 4.2.2.2). The metallization should be done through a screening method, to guarantee that the electrodes will have a correct and homogeneous thickness and to create some electrode defects (some places without metallic ink) to allow the contact between consecutive ceramic layers and the mechanical integrity of the MLCC. The dielectric properties of this new MLCC prototype should be characterized and compared with Exxelia's specifications afterwards.

The last step of this work would be to optimize the MLCC inside Exxelia (including form and thickness of layers), to do the transition from laboratory scale to industrial scale.

Chapter 6 Conclusion

The MLCCs are the most consumed capacitor type in the world, due to their high volumetric efficiency, good reliability, and frequency features. The annual MLCCs production is more than 100 billion units and their market has grown around 20% each year since the beginning of the decade. The increase of the electronics production and its use in high-technology fields is one key factor for this accelerated growth.

Due to its importance, new requirements are constantly created to allow the miniaturization, property improvement, and reliability. In this context, the high-temperature electronics demands are growing, due to the miniaturization trend and to the new applications such as the deep oil.

However, the environmental demands are also increasing. The REACH and RoHS regulations are especially important for the MLCCs since the use of lead will be soon forbidden for non-military or aeroespacial applications.

It is estimated that the electronic systems should be capable of working at a maximum temperature of 300 to 350 • C. Today, however, the high-temperature MLCC are limited to temperatures up to 200-250 • C. It is therefore imperative to bring out new lead-free materials capable of meeting the expectations of electronics at around 300-350 • C.

The MLCC production process in Exxelia is based on the tape casting of a ceramic slurry. The "green" ceramic tapes are screen printed with a Ag-Pd electrode and the blocks of alternating ceramic and metal layers are co-sintered between 1000 and 1300 • C. Sintering is done in industrial furnaces, where the sintering atmosphere and the pressure cannot be controlled.

The compatibility with the current production methods, including the use of a tape casting, the sintering process in a furnace without controlling atmosphere, pressure or other heating sources, the compatibility with the Ag-Pd electrodes, and the price and market limitations are an important limitations.

Considering this, the objectives of this work was the study of a material that can be used for MLCCs with: an operation temperature range from 25 • C to 300-350 • C, an operation frequency range from 400Hz to 100MHz with a standard measurement frequency of 1kHz, a relative permittivity between 1000 and 2000 at 1kHz, a permittivity variation of ± 15% in the operating temperature range when compared to a reference temperature within this range, a maximum loss value of tan δ < 2.5% at 1 kHz, an insulation resistance of 10s from 250 to 300 • C and 1s from 300 to 350 • C, a layer thickness between 5 to 20 µm or less, a grain size of the ceramics of 0.3 to 0.5 µm before sintering and 0.5 to 2 µm after sintering, and a dielectric strength of 25 to 60 V/µm.

A study of the main available lead-free dielectric families was done. The choice of the final material took into account the permittivity value, the dielectric losses and the similarity between the temperature range to have tan δ ≤ 2.5% and the desired operating temperature range, the insulation resistance at 300 • C, the industrial feasibility, and the similarity of the temperature range corresponding to a variation of 15% in the permittivity at 200 • C and the desired operating temperature range.

Three important families of lead-free materials were reviewed: the BaTiO 3 -based materials, the K 0.5 Na 0.5 NbO 3 -based materials and the Na 0.5 Bi 0.5 TiO 3 -based materials.

The NBT-BT solid solution at the MPB was chosen as the base dielectric material. It presents two dielectric anomalies: the first at the depolarization temperature T d is a frequency dependent shoulder and the second at the maximum relative permittivity temperature T m is a permittivity maximum. These phase transitions give the NBT-BT a stable permittivity in temperature. It also shows low dielectric losses from T d to T m .

Moreover, the MPB with 6% BT improves the permittivity values and its variation in temperature. Finally, the NBT-BT has a double hysteresis loop between 200 • C and 300 • C, even though it is actually an ergodic-relaxor. This makes it interesting for energy storage applications.

The NBT-BT may also be improved thanks to some small quantity additives, such as Co and Mn, to increase the final density and to decrease the dielectric losses.

Different synthesis methods and parameters were studied, to determine the best synthesis conditions for the NBT-BT, considering Exxelia's requirements.

Initially, two syntheses of the NBT-BT powder were analyzed, the sol-gel and the solidstate synthesis. The solid-state synthesis was chosen, considering the industrial limitations and the expected properties of the final material.

Three sintering methods were then analyzed: the microwave, the SPS, and the traditional sintering. Considering again the industrial limitations and the required properties, the traditional sintering method was chosen.

Finally, three different methods for controlling atmosphere during sintering, avoiding the evaporation of volatiles were tested: the sintering in air (atmosphere not controlled), the sintering on powders of NBT or reactants + ZrO 2 and the sintering on pure ZrO 2 powder. The first method resulted in a material that is not NBT-BT and the second one needed postsintering treatment to obtain a clean surface. So the sintering on ZrO 2 powder was chosen to control the sintering atmosphere.

The shaping of the ceramic layers was done through tape casting, since it is the only available method for Exxelia's synthesis of MLCCs.

All the samples showed a separation of secondary Ba-containing phases, due to the Na evaporation during sintering. These phases were identified as a mixture of Ba 2 TiO 4 , the Ba 2 Ti 9 O 20 and the Ba 2 Ti 9 O 20 \2BaO•TiO 2 . They concentrate at the sample's surface due the the higher Na evaporation and also because the ZrO 2 favours the formation of Ba 2 Ti 9 O 20 .

The drying on the hygroscopic reactants was the first tested parameter. It intensified the effects of the ball-milling energy, creating large grain surfaces of secondary Ba-containing phases for 250 rpm and 4h ball-milling and large volume fraction of small grain surfaced secondary phases for 350 rpm and 8h ball milling.

Two ball-milling jars and balls materials were also tested. The ball milling with tungsten carbide jars resulted in a contaminated, high conductive, and dielectric lossy material. Using the yttrium stabilized zirconia jars and balls and the ZrO 2 powder to cover the sample during sintering, the final material showed some ZrO 2 contamination at the surface that could be removed with polishing.

A skin effect due to a phase coexistence (tetragonal, rhombohedral and cubic) was observed for the polished and strain-relaxed materials through low-angle-side peaks on the XRD diagrams. It is not present in the as-sintered samples, due to the lower local concentration of Ba in the NBT lattice at the surface.

Two ball-milling solvents were also tested: pure ethanol and a mixture of ethanol and methyl-ethyl-ketone (MEK). However, the change in the solvent did not affect the structure and phase separation of the NBT-BT. A similar result is found when changing the Na 2 CO 3 reactant grain size.

The energy (speed and duration) of ball-milling were also investigated testing a ballmilling at 250 rpm for 4h and another at 350 rpm for 8h. The effects of the ball-milling energy were evident in the samples ball-milled without using a dispersing agent, where the increase in energy resulted in a smaller grain surface and higher volume fraction of the secondary Ba-containing phases. However, this effect is not observed in samples ball-milled with a dispersing agent, since they showed intermediary secondary Ba-containing phases average grain surface and volume fraction.

The use of a second ball-milling after calcination was also tested, to increase the density of bulk ceramic samples. The higher density for samples with no second ball-milling was 91.5% vs 93.5% for the samples prepared with a second ball-milling. It was achieved in both cases for the sintering at 1150 • C for 3h. The temperature ramps used were 120 • C/h for the heating and 200 • C/h for the cooling, to avoid cracks during sintering.

Two ball sizes were tested for the second ball-milling: 1mm-diameter and 10mmdiameter balls. The 1mm-diameter balls were chosen, since their use increased the density without changing the micro-structure and phase separation, and without introducing oxygen vacancies.

Finally, the nominal stoichiometry changes of Na and Bi were also studied. The increase in the Bi and Na concentrations decreased the secondary Ba-containing phases volume fraction and samples without phase separation could be obtained with Na excess. The decrease in the nominal Na/Bi ratio created a matrix stoichiometric in Bi and a separation of the Bi excess in a Bi-rich phase concentrated in the sample's core.

To estimate the permittivity of the NBT-BT samples from their impedance measurement, an RC model was used. The analysis of the variation of the complex impedance in frequency showed that the resistance and the capacitance of the setup can be neglected and validated the use of the RC model.

The dielectric-property uncertainties were estimated through the measurement noise from the characterization of one sample that showed results compatible with two curves. This was considered since the dielectric-property uncertainties were evaluated as being lower than the measurement noise. So a 13% uncertainty was considered for the relative permittivity and a a 14% uncertainty was considered for the dielectric losses.

A temperature shift correction was also apported, due to the method initially used to fix the wires on the bottom of the samples (silver paste on the sample surface). The correction was done after measuring a reference BaTiO 3 sample. The shift in the Curie temperature in this sample comparing the heating and the cooling measurements showed that there is no significant temperature gradient in the samples.

Finally, a new method to fix the wires on the bottom of the samples was used (Cr-Au sputtering metallization and displaced fixation over a copper plate) to estimate a 3.5% uncertainty in the temperature measurements.

After estimating uncertainties, the dielectric properties and the insulation resistance of the NBT-BT in temperature were measured. The effects of the stoichiometry, structure, phase separation, synthesis parameters, and internal strain on these properties were analyzed.

The NBT-BT properties are particularly sensitive to stoichiometry and to the Na/Bi ratio. The increase in Na content inhibits the secondary Ba-containing phases separation and decreases the relative Bi content in the main phase, increasing the sample's conductivity. The increase in the Bi content initially compensates for the oxygen vacancy formation and decreases the conductivity before forming a second phase, increasing again the conductivity at higher Bi-excess. Considering Exxelia's requirements for the high-temperature MLCC, the stoichiometry of sample "U" is the most adapted one, due to its high insulation resistance, lower dielectric losses and permittivity variation in temperature when compared to others.

Due to the phase separation and the secondary Ba-containing phases, the final material can be considered as a composite where the matrix phase is composed of non-stoichiometric NBT and the inclusions are composed of the secondary Ba-containing phases. However, due the physical characteristics and the properties of the phases, no classical composite model could be applied. The increase of the volume fraction and the average grain surface of this phase initially is beneficial to the MLCCs, since it increases the permittivity, decreases the dielectric losses, and increases the insulation resistance, due to the elimination of oxygen vacancies.

Above a critical volume fraction and grain surface, the tendency reverts, due to the conducting character of the secondary phase. So, an intermediary volume fraction (2.5 to 3.0%) and average grain surface (0.9 to 3.0µm 2 ) of the secondary Ba-containing phases is desirable.

For this reason, the effect of multiple synthesis parameters on the secondary Ba-containing phases average grain surface and volume fraction were studied.

To obtain this intermediary average grain surface and volume fraction of secondary Bacontaining phases as well as the best dielectric and insulation properties, a dispersing agent should be used during ball milling in MEK and ethanol mixture and the reactants should not be dried before weighing. In this case, the average Na 2 CO 3 grain size and the energy of ball milling do not affect significantly the final bulk properties.

Finally, the polishing and strain relaxation are an important step to have a lower ZrO 2 contamination without introducing internal strains. The thermal treatment should be done at 400 • C during 3h.

Several hypothesis were considered to explain the dispersion of the dielectric properties in frequency: a composite model with a conducting phase in an insulating matrix (Maxwell-Wagner model), two parallel and frequency dependent RC circuits representing a grain core and grain boundary with different conductivity (Nyquist plot), and a relaxor behaviour (modified Curie-Weiss law).

The three frequency-dispersion models could be applied to the NBT-BT samples, even if the fits could not be done for the Maxwell-Wagner and the Nyquist plot models, due to a limited frequency range of measurement.

The Maxwell-Wagner confirmed the hypothesis that the Ba-containing phases are more conducting that the NBT-matrix phase and so, that there is an interfacial polarization.

The Nyquist plot indicated that two circuits associated with the grain cores and boundaries could be used and that the resistance associated with the grain boundaries is larger and it increases with temperature up to a critical temperature.

Finally, the modified Curie-Weiss law indicated that all the samples, except for sample "E", showed a relaxor character, with γ close to 2. Since sample "E" shows a much higher volume fraction and a much smaller average grain surface of the secondary phases, the influence of these phases and the interaction between their neighbouring grains are greater in this sample. So, the fact that this is the only sample with lower γ value indicated that the interaction between neighbouring grains of the secondary Ba-containing phases can tune the relaxor behaviour in NBT-BT.

Lastly, Co 3 O 4 and MnCO 3 were added to NBT-BT, to try to improve the dielectric properties of the samples, acting as a sintering aid. However, in both cases, the conductivity was increased and the dielectric losses were either unchanged or increased. So, it is not ideal for the MLCC production.

Besides the dielectric and insulation properties, other factors were considered: the dielectric strength and the co-sintering with the electrodes.

The dielectric strength could only be measured for sample "P" and was 7.5 V/µm. It should be increased for the MLCC application, but it is expected that sample "U" shows a higher value. The possibility to co-sinter with 70% Ag and 30% Pd electrodes was confirmed, since there is no chemical reaction between the Bi and the Pd and since the sintering temperature is lower than the maximum co-sintering temperature.

After analysing the dielectric properties vs temperature and frequency, some reasons for the origin of the incompatibilities in the dielectric properties NBT-BT reported in the literature were discussed. The importance of having a strict synthesis and measurement method was presented.

The literature reports differences in the relative permittivity and dielectric losses values, in their dispersion in frequency, in the hump of the relative permittivity at T d , and in the shape of the dielectric properties vs temperature curves. To explain these differences, the influence of stoichiometry, metallization, phase separation, synthesis parameters, and polishing and strain relaxation on the material's dielectric properties were analyzed in heating and cooling.

The stoichiometry has a crucial effect on the properties of NBT-BT. The increase in the nominal Na/Bi ratio and Na quantity increases the conductivity and the quantity of free charges. This increases, the dielectric losses and the frequency dispersion. It may also change the value of the relative permittivity, and the shape of the relative permittivity and dielectric losses vs temperature curves. Finally, the increase in the nominal Na/Bi ratio makes T d less evident in the relative permittivity curve, increases T d and decreases T m .

Another important difference in the measured dielectric properties of NBT-BT samples is the temperature cycle hysteresis. All the heating / cooling cycle measurements are similar, except for the first heating that shows decreased permittivity and may show increased noise. This is neither due to the synthesis method, nor to the phase separation, nor to the strain level, nor to the stoichiometry of the material. So this hysteresis should not be an intrinsic characteristics of the material.

The hypothesis that the first heating hysteresis is due to the silver paste metallization and electric wire fixing method was confirmed. Since the silver paste is commonly used in research, it also may be responsible for the literature incompatibilities.

The variability in the measured dielectric properties from sample to sample is also an important factor to explain the differences observed in the literature depending on the heating / cooling cycle considered.

Finally, a change in the dielectric losses at high temperatures after each heating and cooling cycle is observed. It is present regardless of the metallization and method to contact the electrical leads, the stoichiometry, the phase separation, the synthesis parameters, or the polishing and strain relaxation. Moreover, it is present for temperature cycles where the maximum temperature is greater than 300 • C and it increases with increasing maximum temperatures. This indicates that a thermally degradation takes place at high temperatures (over 300 • C).

Comparing samples with different metallization methods it was possible to conclude that changes in the electrode's morphology during heating increases the measured dielectric losses. However, it is also possible that there is a change in the sample's microstructure influenced by the high temperature.

After analysing the bulk NBT-BT samples, the synthesis of NBT-BT layers and its compatibility with Exxelia's specifications was performed.

Bulk sample "U" showed the best properties for MLCC applications. So this sample was chosen to be studied in the layer form.

For the layer synthesis, the second ball-milling was adapted and the slurry was prepared considering Exxelia's slurry composition and a binder and additives optimization for NBT-BT reported in the literature.

The "green" tapes (before sintering) showed good mechanical resistance, no cracks and a uniform thickness. However, the monolayers sintered with a 30-minute temperature step at 850 • C and a sintering at 1050 • C for 3h showed low relative density of 58%.

For this reason, a sintering optimization was done. The sintering parameters that resulted in the highest density of the monolayers (62%) were a sintering with a 30 minutes temperature step at 850 • C and a sintering at 1150 • C for 3h. This is still insufficient for the MLCC applications, so the next step would be to study the effects of pressing the NBT-BT layers together before sintering and to increase the NBT-BT powder concentration and decrease the PVB concentration in the slurry.

Concerning the monolayers structure, a XRD peak widening was observed due to a skin effect (coexistence of pseudo-cubic, rhombohedral and tetragonal phases). The same secondary Ba-containing phases as in the bulk samples were present with an average grain size of 2.9 ± 0.8µm 2 , being compliant with Exxelia requirements. However, the morphology of this phase was different from the bulk one, due to the low density of the monolayer. Finally, a higher Zr contamination from the powder used to create a sintering atmosphere in the secondary Ba-containing phases was observed, being the reason for its lower Ba concentration.

An average grain surface of 2.4 ± 0.8 µm 2 after sintering and a layer thickness of 97 µm were obtained for the monolayer. These values are not compatible with Exxelia's specifications, but they could still be used for the MLCC production.

The dielectric properties measured for the monolayer are not reliable, due to their low density. However, for the synthesized monolayer, the measured relative permittivity is smaller and the dielectric losses for temperatures greater than 150 • C are higher than the bulk. This is expected for low-density materials. Moreover, a huge temperature hysteresis is observed when measuring it over consecutive thermal cycles, making the measurement impossible at temperatures higher than 275 • C.

This hysteresis and thermal degradation may be due to the influence of the electrodes, since there is a penetration of the silver paste in the material pores during thermal cycling. However, it may also be due to the material morphology change in temperature, since the low density and the high specific area of the layer facilitates the material morphology changes.

Finally, the insulation resistance for the monolayers are much lower than for the bulk, corresponding to a temperature decrease of 100 • C, as expected for low density materials.

These properties are not yet compatible with Exxelia's requirements for the MLCC production. Nevertheless, dielectric losses are lower than 2.5% at 1kHz from 100 to 150 • C, permittivity variation of ±15% takes place from 180 to 240 • C and insulation resistance is only higher than 1s up to 180 • C.

So, to make a more reliable evaluation of the NBT-BT layers and to achieve the requirements for the MLCC production, the increase in density is imperative.

To solve this density problem, the effects of pressing multiple "green" NBT-BT layers together before sintering, forming a multilayer device, was studied. It was shown that a high density material (89.5%) can be obtained after sintering the pressed multilayers at 1150 • C. This indicates that the low density of the monolayers are not due to a slurry composition problem and that, even though the monolayers do not show dielectric properties compatible with the industrial demands from room temperature up to 300 to 350 • C, this does not necessarily mean that the multilayer device prepared from these layers will have the same temperature range limitation. However, since the pressed NBT-BT multilayers show a higher Na and Bi evaporation, a new dielectric properties measurement in temperature should be done to evaluate the temperature range of compatibility with the industrial requirements.

Appendix B

Résumé de thèse

Les MLCCs (condensateurs céramiques multicouches) sont le type de condensateur le plus consommé au monde, en raison de leur haute efficacité volumique, leur bonne fiabilité et leurs caractéristiques en fréquence. La production annuelle des MLCC s'élève à plus de 100 milliards d'unités et leur part sur le marché a augmenté d'environ 20% chaque année depuis le début de la décennie.

L'importance prise par les MLCCs implique que de nouvelles exigences soient constamment créées pour permettre la miniaturisation et l'amélioration de leurs propriétés. Dans ce contexte, les exigences en matière d'électronique haute température augmentent en raison de la tendance à la miniaturisation et également avec l'apparition de nouvelles applications telles que la perforation pétrolière profonde.

Cependant, les exigences environnementales augmentent aussi. Les réglementations REACH et RoHS sont particulièrement importantes pour les MLCCs car l'utilisation du plomb sera bientôt interdite pour des applications non militaires ou aérospatiales. On estime que les systèmes électroniques devraient être capables de fonctionner à une température maximale de 300 à 350 • C. Cependant, les MLCCs sont aujourd'hui limités à des températures allant jusqu'à 200-250 • C. Il est donc impératif d'utiliser de nouveaux matériaux sans plomb capables de répondre aux attentes de l'électronique à environ 300-350 • C.

Le processus de production des MLCCs chez Exxelia est basé sur le coulage en bande d'une suspension céramique (barbotine). Les feuilles céramiques "vertes" (non frittées) sont sérigraphiées avec une électrode d'Ag-Pd et les blocs de couches alternées de céramique et de métal sont co-frittés entre 1000 et 1300 • C. Le frittage est effectué dans des fours industriels où l'atmosphère de frittage et la pression ne peuvent être contrôlées. La compatibilité avec les méthodes de production actuelles, y compris l'utilisation du coulage en bande, le processus de frittage dans un four sans contrôle de l'atmosphère, de la pression ou d'autres sources de chauffage, la compatibilité avec les électrodes d'Ag-Pd et les limites de prix et de marché constituent des limites importantes.

Par conséquent, les objectifs de ce travail sont d'étudier un matériau sans plomb qui pourra être utilisé pour les MLCCs avec les caractéristiques suivantes : une plage de température de fonctionnement de 25 • C à 300-350 • C, une plage de fréquence de fonctionnement de 400Hz à 100MHz avec une fréquence de mesure standard de 1kHz, une permittivité relative entre 1000 et 2000 à 1kHz, une variation de permittivité de 15 Trois familles importantes de matériaux sans plomb ont été examinées : les matériaux à base de BaTiO 3 , les matériaux à base de K 0.5 Na 0.5 NbO 3 et les matériaux à base de Na 0.5 Bi 0.5 TiO 3 . Le choix du matériau final a pris en compte : la valeur de permittivité, les pertes diélectriques et la similitude entre la plage de température pour avoir tan δ ≤ 2.5La solution solide NBT-BT à la frontière morphotropique de phase (MPB) a été choisie comme matériau de base. Il présente deux anomalies diélectriques : la première, à la température de dépolarisation Td, est un épaulement dépendant de la fréquence, et la seconde, à la température Tm, est un maximum de permittivité. Ces transitions de phase confèrent au NBT-BT une permittivité stable en température. Il montre également des faibles pertes diélectriques de Td à Tm. De plus, la MPB à les pertes diélectriques et augmente la résistance d'isolement, grâce à l'élimination des lacunes d'oxygène. Au-dessus d'une fraction volumique et d'une la surface moyenne de grain critiques, la tendance s'inverse, en raison du caractère conducteur de la phase secondaire. Ainsi, une fraction de volume intermédiaire (2.5 à 3.0%) et une surface moyenne de grain (0.9 à 3.0 µm 2 ) des phases secondaires contenant du Ba est souhaitable.

Pour obtenir cette fraction volumique et cette surface moyenne de grain des phases secondaires contenant du Ba ainsi que les meilleures propriétés diélectriques et isolantes, il est recommandé d'utiliser un dispersant lors du broyage dans un mélange MEK et éthanol et de ne pas sécher les réactifs avant pesage. Dans ce cas, la granulométrie moyenne du Na 2 CO 3 et l'énergie du broyage n'affectent pas significativement les propriétés finales.

Enfin, le polissage et la décontrainte sont une étape importante pour avoir une contamination par ZrO 2 limitée sans introduire de contraintes internes. Le traitement thermique pour relaxer les contraintes doit être fait à 400 • C pendant 3h.

Plusieurs hypothèses ont été considérées pour expliquer la dispersion des propriétés diélectriques en fréquence : un modèle composite avec une phase conductrice dans une matrice isolante (modèle de Maxwell-Wagner), deux circuits RC parallèles et dépendant en fréquence représentant le coeur et les joints de grain avec des conductivités différentes (modèle de Nyquist) et un comportement relaxeur (loi de Curie-Weiss modifiée). Les trois modèles de dispersion de fréquence ont pu être appliqués aux échantillons de NBT-BT, même si les tests n'ont pas pu être effectués pour les modèles Maxwell-Wagner et Nyquist, en raison d'une gamme de fréquences de mesure limitée.

Le modèle de Maxwell-Wagner a confirmé l'hypothèse que les phases contenant du Ba sont plus conductrices que la phase matrice de NBT et donc qu'il y a une polarisation interfaciale. Le modèle de Nyquist indique que la résistance associée aux joints des grains est plus élevée et qu'elle augmente avec la température jusqu'à une température critique. Enfin, la loi de Curie-Weiss modifiée indique que tous les échantillons, à l'exception de l'échantillon "E", présentent un caractère relaxeur, avec γ proche de 2. Puisque l'échantillon "E" présente une grande fraction de volume et une petite surface moyenne de grain des phases secondaires contenant du Ba et puisqu'il a une valeur inférieure de γ, cela indique que l'interaction entre les grains voisins des phases secondaires peut influencer le comportement relaxeur dans les NBT-BT.

Enfin, du Co 3 O 4 et du MnCO 3 ont été ajoutés au NBT-BT, pour essayer d'améliorer les propriétés diélectriques des échantillons. Cependant, dans les deux cas, la conductivité a été augmentée et les pertes diélectriques ont été soit inchangées, soit augmentées. Donc, ces ajouts ne sont pas idéaux pour la production de MLCCs. En plus des propriétés diélectriques et de la résistance d'isolement, d'autres facteurs ont été pris en compte : la rigidité diélectrique et le cofrittage avec les électrodes. La rigidité diélectrique n'a pu être mesurée que pour l'échantillon "P" et elle était de 7.5 V/µm. On s'attend toutefois à ce que l'échantillon "U" montre une valeur supérieure. La possibilité de cofritter avec des électrodes 70% Ag et 30% Pd a été confirmée, puisqu'il n'y a pas de réaction chimique entre le Bi et le Pd et que la température de frittage est inférieure à la température maximale de cofrittage.

Après avoir analysé les propriétés diélectriques en fonction de la température et de la fréquence, certaines raisons expliquant l'origine des incompatibilités des propriétés diélectriques du NBT-BT rapportées dans la littérature ont été discutées. L'importance d'avoir une méthode de synthèse et de mesure stricte a été présentée. La littérature montre des incompatibilités dans les valeurs de permittivité relative et de pertes diélectriques, dans leur dispersion en fréquence, dans la permittivité relative à T d et dans l'allure de la courbe des propriétés diélectriques en fonction de la température.

Pour expliquer ces incompatibilités, l'influence de la stoechiométrie, de la métallisation, de la séparation de phases, des paramètres de synthèse, du polissage et de la décontrainte sur les propriétés diélectriques du matériau a été analysée en chauffage et refroidissement.

La stoechiométrie a un effet crucial sur les propriétés du NBT-BT. L'augmentation du rapport Na/Bi nominal et de la quantité de Na augmente la conductivité et la quantité de charges libres. Ceci augmente les pertes diélectriques et la dispersion en fréquence. Elle peut également modifier la valeur de la permittivité relative et l'allure de la courbe de permittivité et de pertes diélectriques en fonction la température. Enfin, l'augmentation du rapport Na/Bi nominal rend T d moins évident dans la courbe de permittivité relative, augmente la valeur de T d et diminue la valeur de T m .

Une autre différence importante dans les propriétés diélectriques mesurées est l'hystérésis de la permittivité en fonction de la température. Toutes les mesures de la permittivité en chauffage/refroidissement sont similaires, à l'exception de la première mesure en chauffage qui montre une diminution de la permittivité et peut montrer une augmentation du bruit. Ceci est due la métallisation par laque d'argent et à la méthode de fixation du fil électrique. Puisque la laque d'argent est couramment utilisée dans la recherche, elle peut aussi être responsable des incompatibilités rapportées dans la littérature.

La variabilité des propriétés diélectriques mesurées d'un échantillon à l'autre est également un facteur important pour expliquer les différences observées dans la littérature.

Enfin, une variation des pertes diélectriques à haute température est observée après chaque cycle de chauffage et de refroidissement. Elle est présente indépendamment de la métallisation et de la méthode de mise en contact des fils électriques, de la stoechiométrie, de la séparation de phases, des paramètres de synthèse, du polissage et de la relaxation des contraintes. De plus, elle est présente pour les cycles de température où la température maximale est supérieure à 300 • C et elle augmente avec l'augmentation des températures maximales. Ceci indique qu'une dégradation thermique a lieu à des températures élevées. En comparant des échantillons avec différentes méthodes de métallisation, il a été possible de conclure que les changements dans la morphologie de l'électrode pendant le chauffage augmentent les pertes diélectriques mesurées. Cependant, il est également possible qu'il y ait un changement dans la microstructure de l'échantillon influencé par la température élevée.

Après avoir analysé les échantillons de NBT-BT en bulk, la synthèse des couches de NBT-BT et la vérification de leur compatibilité avec les spécifications d'Exxelia ont été réalisées. L'échantillon en bulk "U" a montré les meilleures propriétés pour les applications comme MLCC. Cet échantillon a donc été choisi pour être étudié sous forme de couche. Pour la synthèse de la couche, le deuxième broyage a été adapté et la barbotine a été préparée en tenant compte de la composition utilisée par Exxelia et d'une optimisation du liant et des additifs pour NBT-BT mentionnée dans la littérature.

Les couches "vertes" présentaient une bonne résistance mécanique, une épaisseur uniforme et aucune fissure. Cependant, les monocouches frittées avec un palier de température de 30 minutes à 850 • C et un frittage à 1050 • C pendant 3h ont montré une faible densité relative de 58 Concernant la structure de la monocouche, un élargissement des pics du XRD a été observé en raison d'un effet peau, comme pour les échantillons en bulk. Les mêmes phases secondaires contenant du Ba dans les échantillons en bulk étaient présentes avec une granulométrie moyenne de 2.9 ± 0.8µm 2 , conformes aux exigences Exxelia. Cependant, la morphologie de cette phase était différente de celle du bulk, en raison de la faible densité de la monocouche. Enfin, une plus forte contamination en Zr a été observée dans les phases secondaires. Une surface de grain moyenne de 2.4 ± 0.8µm 2 après frittage et une épaisseur de couche de 97 mm ont été obtenues pour la monocouche. Ces valeurs ne sont pas compatibles avec les spécifications d'Exxelia, mais elles pourraient quand-même être utilisées pour la production de MLCCs.

Les propriétés diélectriques mesurées pour la monocouche ne sont pas fiables en raison de leur faible densité. Cependant, la permittivité relative mesurée est plus faible et les pertes diélectriques pour des températures supérieures à 150 • C sont plus élevées que le bulk. C'est ce que l'on attend pour les matériaux à faible densité. De plus, une énorme hystérésis en

FIGURE 1 . 1 :

 11 FIGURE 1.1: Schematic representation of a multilayer ceramic capacitor -Exxelia [8]

FIGURE 1 . 3 :

 13 FIGURE 1.3: Simplified diagram of the industrial synthesis method of multilayer ceramic capacitors (adapted from Exxelia's internal document)

FIGURE 1 . 4 :

 14 FIGURE 1.4: Complex impedance plane representation of the complex impedance, the equivalent series resistance (ESR), the equivalent series inductance (ESL), the real capacitors C and dielectric losses diagram for real capacitors.

FIGURE 1 . 5 :

 15 FIGURE 1.5: Phase diagram for Ag-Pd mixture (taken from:www.crct.polymtl.ca/fact/documentation/FS_All_PDs.htm ).

Fig. 1 . 5 ,

 15 FIGURE 1.6: Thermal expansion coefficient of the Ag-Pd alloy with different compositions. [3]

1. 4

 4 .1.2 K 0.5 Na 0.5 NbO 3 -based materials

1. 4 . 1 . 3

 413 Na 0.5 Bi 0.5 TiO 3 -based materials

FIGURE 1 . 8 :

 18 FIGURE 1.8: Schematic representation summarizing structural characteristics of pure NBT -the stable phases and their macroscopic electric properties.

  • and by the single (200)pc peak around 2θ = 46 -47.50 • . The measurement on the BT rich (tetragonal) phase are characterized by a single (111)pc peak at around 40 • and by the splitting of the (200)pc peak around 45 -47.50 • . The XRD in function of the percentage of BT is presented in the Fig 1.11.

FIGURE 1 .

 1 FIGURE 1.10: Original NBT-BT phase diagram with crystalline structure and ferroelectric characters. F, AF and P stand respectively for FE, AFE andparaelectric.[START_REF] Mcquade | A review of the structure-property relationships in lead-free piezoelectric (1x)Na0.5Bi0.5TiO3-(x)BaTiO3[END_REF]

FIGURE 1 . 11 :

 111 FIGURE 1.11: XRD patterns for different BT percentages in NBT-BT solidsolution showing that the MPB is between 6.5 and 7% of BT.[START_REF] Lidjici | Étude, Élaboration Et Caractérisation De Céramiques Piézoélectriques[END_REF]

FIGURE 1 . 13 :

 113 FIGURE 1.13: Dielectric properties (relative permittivity and dielectric losses) in function of the temperature for the NBT-BT solid solution with 6% of BT (at the MPB)

FIGURE 2 . 1 :

 21 FIGURE 2.1: Temperature and frequency dependence of relative permittivity (ε r ) and dielectric losses (tan δ ) of NBT-BT synthesized via sol-gel method and sintered at 1150 • C for one hour in air. [9]

FIGURE 2 . 2 :

 22 FIGURE 2.2: Schematic representation of the closed crucibles and calcination atmosphere

FIGURE 2 . 3 :

 23 FIGURE 2.3: Comparison between the X-ray diffractograms of the ballmilled powder (250 rpm during 4h, using the dispersing agent) and of the same powder after calcination, for sample "H".

FIGURE 2 . 4 :

 24 FIGURE 2.4: SEM backscattered electrons image of the "U-WC" sample, ball milled in the WC jar showing the formation of five different phases.

FIGURE 2 . 5 :

 25 FIGURE 2.5: Dielectric properties of the sample "U-WC", ball-milled in the WC jar from frequencies from 1kHz to 1MHz.

FIGURE 2 . 6 :

 26 FIGURE 2.6: SEM image at the same scale for grain size comparison of the samples a) "U-WC" ball-milled in the WC jar b) "U" ball-milled in the YSZ jar treatment at 400 • C for 1 hour are marked by differences (see Fig 2.7) p. 50. Namely:

FIGURE 2 . 7 :

 27 FIGURE 2.7: XRD diagrams of the samples "U" (ball milled in YSZ jar) and "U-WC" (ball milled in WC jar) after sintering and after polishing and strain relaxation and NBT, ZrO 2 , and W-rich phases identification

FIGURE 2 .

 2 FIGURE 2.10: XRD measurements of samples "V" and "H" with phase identification

FIGURE 2 .

 2 FIGURE 2.15: Relative permittivity and dielectric losses over temperature and frequency property for the poled Na 0.44 Bi 0.48 Ba 0.06 TiO 3 composition [23]

FIGURE 2

 2 FIGURE 2.16: Cross-section SEM picture of the "U" sample (Na 0.44 Bi 0.48 Ba 0.06 TiO 3 stoichiometry) showing three different magnifications and four different phases in the sample.

FIGURE 2 .

 2 FIGURE 2.18: XRD diagrams of polished and strain-relaxed samples "P", "U", "Y" and "Z" samples with phase identification.

FIGURE 2 . 19 :

 219 FIGURE 2.19: Relative density of samples without second ball milling and with second ball milling for different sintering temperatures (three hours sintering, 120 • C/h in heating and 200 • C/h in cooling).

FIGURE 2 .

 2 FIGURE 2.21: XRD diagram of the NBT-BT powder after the second ballmilling at 250 rpm during 4h (sample "H"), at 350 rpm during 8h (sample "I") using 1 mm-diameter balls.

FIGURE 2 . 22 :

 222 FIGURE 2.22: Raman reference spectra of NBT and NBT-Co (with oxygen vacancies). [68]

FIGURE 2 . 23 :

 223 FIGURE 2.23: Raman spectra measured on different points for the NBT powder before the second ball-milling showing the homogeneity of the Raman signal.

FIGURE 2 . 24 :

 224 FIGURE 2.24: Raman spectra measured at different points for the NBT powder after the second ball-milling. Same variations of the intensity exist for low wavenumbers, but the C and D-bands have more uniform intensities.

FIGURE 2 . 25 :

 225 FIGURE 2.25: Raman spectra measured at different points for the NBT powder after thermal treatment at 400 • C for five hours in air showing the homogeneity of the Raman signal, especially for the C and D bands.

FIGURE 2 . 26 :

 226 FIGURE 2.26: Fitting for bands C (450 -680cm -1 ) and D (650 -950cm -1 ) of the Raman spectra of the NBT sample after thermal treatment using three base peaks.

FIGURE 2 .

 2 FIGURE 2.27: XRD and SEM analysis before and after the second ball milling with the 1mm-diameter balls (using dipersing agent, ethanol as a solvent and 250 rpm during four hours).

FIGURE 2 . 28 :

 228 FIGURE 2.28: Crack on NBT-BT sample sintered at a heating rate of 200 • C/h and a cooling rate of 300 • C/h (left) and no no crack on NBT-BT sample sintered at a heating rate of 120 • C/h and a cooling rate of 200 • C/h (right).

  2.19 p. 62. Comparing the XRD of those samples (see Fig. 2.29), reveals that the sample sintered at 1050 • C (91% density) shows lower-intensity second-phase peaks compared to the

FIGURE 2 .

 2 FIGURE 2.29: XRD diagram of the NBT-BT samples sintered on ZrO 2 for 3h at 1050 and 1150 • C

FIGURE 2 .

 2 FIGURE 2.30: XRD diagram of the sample sintered in an opened crucible for 3h at 1050 • C

FIGURE 2 . 31 :

 231 FIGURE 2.31: Dielectric properties of the NBT-BT sample sintered in an open crucible (left: tan δ , right: relative permittivity).

FIGURE 2 . 32 :

 232 FIGURE 2.32: Reaction between the sample surface and the atmosphere powder in NBT-BT sample sintered using NBT + ZrO 2 powder to create the sintering atmosphere at 1050 • C resulting in an inhomogeneous sample surface.

FIGURE 2 .

 2 FIGURE 2.33: XRD diagram for the NBT-BT samples sintered at 1050 • C during 3 hours using to create the sintering atmosphere: pure ZrO 2 powder, NBT + ZrO 2 powder and in open crucible.

FIGURE 2 .

 2 FIGURE 2.34: XRD measurement of sample "H" as-sintered and after polishing and strain relaxation (same data as in Fig. 2.10)

FIGURE 2 .

 2 FIGURE 2.35: XRD analysis of the as-sintered pure NBT sample, indicating a TiO 2 phase separation.

FIGURE 2 .

 2 FIGURE 2.36: XRD measurement of the as-sintered sample "H" with the peaks identification details.

FIGURE 2 . 37 :

 237 FIGURE 2.37: XRD measurement of the as-sintered sample "U" with the peaks identification details.

FIGURE 2 . 39 :

 239 FIGURE 2.39: SEM image of the secondary Ba-containing phases concentration close to a YSZ 1 mm diameter ball attached to the "B" sample surface during sintering (YSZ ball not removed before measurement).

FIGURE 2 .

 2 FIGURE 2.40: SEM image of the secondary Ba-containing phases concentration close to a YSZ 1 mm-diameter ball attached to the "B" sample surface during sintering (YSZ ball removed before measurement).

FIGURE 3 . 1 :

 31 FIGURE 3.1: Picture of the impedance measurement device (Linkam).

FIGURE 3 . 3 :

 33 FIGURE 3.3: RC model circuit considering the influence of the cables and the setup to calculate the dielectric properties from the measured impedance

FIGURE 3 . 4 :

 34 FIGURE 3.4: Real part of the complex impedance module Re(Z * ) vs frequency for sample "H". The inset shows the low impedance values.

FIGURE 3 . 5 :

 35 FIGURE 3.5: Imaginary part of the complex impedance module Im(Z * ) vs frequency for sample "H". The inset shows the low impedance values.

FIGURE 3 . 6 :

 36 FIGURE 3.6: Relative permittivity (top) and the dielectric losses tan δ (bottom) for "U" sample over two consecutive measurements. The first (continuous line) represents the measurement that is typical for "U" sample (see Fig. ??). The second measurement (dots) either fall on the continuous line or on another evolution, shifted from the first measurement, depending on the temperature.

FIGURE 3 . 7 :

 37 FIGURE 3.7: Permittivity and dielectric losses of NBT-BT sample "X" measured at two different times with the same electrodes (silver paste). The solid lines indicate the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ± 13% for the dielectric losses (see section 3.1.4).

3. 1 . 5 Temperature drift and corrections 3 . 1 . 5 . 1

 153151 Wire fixing method

FIGURE 3 . 9 :

 39 FIGURE 3.9: Relative permittivity of a reference BaTiO 3 sample (purple curve, cooling only -data courtesy of C. Bogicevic) and measurement of the same sample using the simple Ag-paste fixation of a type-K thermocouple wire (yellow: heating, brown: cooling) and Au wire (blue: cooling only) on the bottom of the sample .

FIGURE 3 . 10 :

 310 FIGURE 3.10: Lattice parameter (top) in the rhomboedral (R), orthorhombic (O), tetragonal (T) and cubic (C) phases and relative permittivity (bottom) along a-and c-axis (left)[START_REF] Acosta | BaTiO3-based piezoelectrics: Fundamentals, current status, and perspectives[END_REF] and polarization in the first order phase transition from ferroelectric to paraelectric phase in BaTiO 3 (right)[START_REF] Wang | Theories and Methods of First Order Ferroelectric Phase Transitions[END_REF]

FIGURE 3 . 11 :

 311 FIGURE 3.11: Wire fixing method based on Cr-Au sputtering and a shifted wire contact (silver paste on copper plate).

  1.2). Type I conductivity NBT-BT shows a sharp increase in the dielectric losses from 100 • C. Type III conductivity NBT-BT exhibit low dielectric losses, with tan δ ≤ 2% from 250 to 650 • C. Finally, type II conduction NBT-BT have an intermediate behaviour, with tan δ ≤ 2% from 300 to 500 • C.

  , 3.15 and 3.16.

FIGURE 3 . 14 :

 314 FIGURE 3.14: Relative permittivity and dielectric losses versus temperature from 1kHz to 1MHz for samples "P", "U", "Y" and "Z".

FIGURE 3 . 15 :FIGURE 3 . 16 :

 315316 FIGURE 3.15: Comparison of relative permittivities and dielectric losses versus temperature measured at 1kHz for samples "P", "U", "Y" and "Z" having different stoichiometries. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ±13% for the dielectric losses (see section 3.1.4)

FIGURE 3 . 17 :

 317 FIGURE 3.17: SEM image of samples "Y" and "Z" surface showing no secondary Ba-containing phases separation

FIGURE 3 . 18 :

 318 FIGURE 3.18: Evolution of effective permittivity (εe f f ) with the matrix volume fraction ( f ) for different values of particle permittivities (ε 2 or ε e from 1 to 2500) and a matrix permittivity of ε i = 2000, considering the Bruggemen Symmetric model

FIGURE 3 . 19 :

 319 FIGURE 3.19: Relative permittivity at 10kHz and room temperature vs volume fraction of inclusions for the NBT-BT samples.

FIGURE 3 . 22 :

 322 FIGURE 3.22: Relative permittivity at T m measured at 10kHz (left) and dielectric losses at 300 • C measured at 10kHz (right) versus secondary Bacontaining phases volume fraction for the NBT-BT samples with different synthesis parameters. Labels indicate each sample and its secondary Bacontaining average grain surface red and blue labels indicate groups with similar secondary Ba-containing average grain surface and black labels indicate the group with no dispersing agent used in ball-millings. Dotted lines are a guide for the eyes.

FIGURE 3 . 23 :

 323 FIGURE 3.23: Comparison of permittivity and dielectric losses versus temperature measured at 1kHz for samples "N", "B", "E" and "G" with different secondary Ba-containing phases average size and volume fraction. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and 13% for the dielectric losses (see section 3.1.4).

FIGURE 3 .

 3 FIGURE 3.24: NBT-BT sample's insulation resistance at 200 • C (the highest measured temperature) versus the secondary Ba-containing phases volume fraction and average grain surface.

FIGURE 3 . 25 :

 325 FIGURE 3.25: Insulation resistance versus temperature of samples "N", "B", "E", "G", "H" and "V" with different secondary Ba-containing phases average size and volume fraction (logarithme scale).

FIGURE 3 . 27 :

 327 FIGURE 3.27: Comparison of permittivity and dielectric losses versus temperature measured at 1kHz for samples "H", "I" and "V" with the same secondary Ba-containing phases average size and volume fraction and different synthesis parameters. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ± 13% for the dielectric losses (see section 3.1.4).

FIGURE 3 . 28 :

 328 FIGURE 3.28: Insulation resistance versus temperature of samples "H", "I" and "V" with the same secondary Ba-containing phases average size and volume fraction and different synthesis parameters (logarithme scale).

FIGURE 3 .

 3 FIGURE 3.29: XRD analysis of NBT-BT samples as-sintered, polished, polished and strain relaxed for 1h at 400 • C and polished and strain relaxed for 1h at 500 • C.

FIGURE 3 .

 3 FIGURE 3.30: XRD measurements (top) and Williamson-Hall fits for sample "N" (bottom). The equations and the results of the fits are shown in the boxes. The color of the box indicates the corresponding fit.

FIGURE 3 . 31 :

 331 FIGURE 3.31: Williamson Hall fits for sample "H". The equations and the results of the fits are shown in the boxes. The color of the box indicates the corresponding fit.

FIGURE 3 . 32 :

 332 FIGURE 3.32: Comparison of relative permittivity and dielectric losses versus temperature measured at 1kHz for samples "H" polished, after 1h strainrelaxed at 400 • C and after 3h strain-relaxed at 400 • C. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ± 13% for the dielectric losses (see section 3.1.4).

FIGURE 3 . 33 :

 333 FIGURE 3.33: Comparison of the relative permittivity and dielectric losses versus temperature measured at 1kHz for samples "N" polished and strainrelaxed for 3h at 400 • C. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ± 13% for the dielectric losses (see section 3.1.4)

FIGURE 3 . 35 :

 335 FIGURE 3.35: Insulation resistance to the reference temperature (213 • C) and dielectric losses for samples "H", "N", "P", "U" and "V" and Exxelia's specifications for the high temperature MLCCs

FIGURE 3 . 36 :

 336 FIGURE 3.36: General behaviour of the real (ε ) and imaginary (ε ) parts of the permittivity in the Maxwell-Wagner model as a function of frequency.The frequency ν is shown in logarthmic scale.[START_REF] Lunkenheimer | Colossal dielectric constants in transition-metal oxides[END_REF]

FIGURE 3 . 37 :FIGURE 3 . 38 :

 337338 FIGURE 3.37: Relative permittivity and dielectric losses versus frequency for different temperatures and for samples "P", "H", and "U" (from the top to the bottom) with different volume fractions of secondary Ba-containing phases.

FIGURE 3 . 39 :

 339 FIGURE 3.39: Permittivity and dielectric losses vs frequency (logarithme scale) for the case of a composite BaTiO 3 -Cu composite. [49] The red lines indicate a similar frequency range from the one measured for the NBT-BT samples.

FIGURE 3 . 40 :

 340 FIGURE 3.40: Nyquist plots for NBT-BT samples "P", "H" and "U" (from top to bottom) for the high temperature (left) and low temperatures (right).

FIGURE 3 . 41 :

 341 FIGURE 3.41: Nyquist plot for BaTiO 3 -Cu composites with different Cu fractions. [49]

FIGURE 3 .FIGURE 3 . 43 :

 3343 FIGURE 3.42: Curie-Weiss law with increasing frequency for different frequencies and evolution of the C and γ estimations in frequency for sample "H"

Figures 3. 44

 44

, 3 .

 3 45 and 3.46 show the SEM and XRD measurement of samples with 0.4 and 4.4% of Co 3 O 4 .

FIGURE 3 .FIGURE 3 . 46 :

 3346 FIGURE 3.44: SEM images of the as-sintered (left) and the polished and strain relaxed (right) samples with 0.4mol% (bottom) and 4.4mol% (top) Co 3 O 4 .

FIGURE 3 . 47 :

 347 FIGURE 3.47: EDS cartography of the 4.4mol%-Co-addition as-sintered sample (top) and the 0.4%-Co-addition as-sintered sample(bottom).

FIGURE 3 . 48 :

 348 FIGURE 3.48: Comparison of relative permittivity and dielectric losses versus temperature measured at 1kHz for pure NBT-BT (sample "H"), 0.4mol%-Co-addition , and 4.4mol%-Co-addition samples. The solid lines indicates the measured values and the dotted lines indicate the uncertainties lines of ± 14% for the permittivity and ± 13% for the dielectric losses.

FIGURE 3 . 49 :TABLE 3 . 6 :

 34936 FIGURE 3.49: Insulation resistance for NBT-BT samples with 0.4mol% of Co, 4.4mol% of Co and 0.5wt% of Mn and comparison with the pure NBT-BT equivalent sample ("H"). Sample T d ( • C) at 10kHz T m ( • C) at 10kHz pure NBT-BT 104 258 4.4mol%-Co-addition undefined 260 0.4mol%-Co-addition 136 248TABLE 3.6: Depolarization temperature T d and temperature of the maximum relative permittivity T m for the pure NBT-BT, the 4.4mol%-Coaddition , and the 0.4mol%-Co-addition samples .

  and 3.51.

FIGURE 3 .FIGURE 3 . 51 :

 3351 FIGURE 3.50: SEM measurements of the as-sintered (left) and the polished and strain relaxed (right) samples with 0.5wt% MnCO 3 .

FIGURE 3 .

 3 FIGURE 3.54: XRD of the sintered NBT-BT and Ag-Pd (70-30) powder mixtures sintered at 1050 • C or 1200 • C in the laboratory furnace and at 1115 • C in Exxelia's furnace and comparison with XRD of the Ag-Pd (70-30)powder.

FIGURE 3 .

 3 FIGURE 3.55: SEM measurements of the sintered NBT-BT and Ag-Pd (70-30) powder mixtures sintered at 1200 • C on the laboratory furnace and at 1115 • C on Exxelia's furnace and concentration profile of a Ag-Pd grain on sample sintered in Exxelia.

Ge

  et al.reported the dielectric properties for NBT-BT 6% as presented in Fig. 4.1.

FIGURE 4 . 1 :

 41 FIGURE 4.1: Dielectric properties of NBT-BT 6% reported by Ge et al.(2014) [19]

FIGURE 4 . 2 :FIGURE 4 . 3 :

 4243 FIGURE 4.2: Dielectric properties of NBT-BT 7% reported by Kumar et al.(2015) [10]

FIGURE 4 . 4 :

 44 FIGURE 4.4: Dielectric properties vs. temperature curves reported by Ge et al.[19] (top left), and by Zhang et al.[86] (bottom left), and for samples "P" (top right), and "Z" (bottom right).

FIGURE 4 . 5 :

 45 FIGURE 4.5: Dielectric properties of NBT-BT sample "X" measured in subsequent thermal cycles from 25 to 325 • C.

FIGURE 4 . 6 :

 46 FIGURE 4.6: Dielectric properties of NBT-BT samples "Y", "Z" and "U", with different stoichiometries, measured in subsequent thermal cycles from 25 to 300 or 325 • C.

FIGURE 4 . 7 :

 47 FIGURE 4.7: Dielectric properties of samples "B", "N", "H" and "Z" with different Na 2 CO 3 grain size, ball-milling solvents and energy over thermal cycles from 25 to 325 or 350 • C. strain-relaxed at 400 • C for different periods of time. As mentioned in section 3.2.1.4, the Williamson-Hall analysis show that the internal strain of the unpolished NBT-BT samples is similar to the ones in samples after polishing and strain-relaxing for three hours. So the sample relaxed for one hour still show internal strains introduced during polishing. The dielectric properties of the sample after one and three hours of thermal treatment for strain relaxing are shown in Fig. 4.8.From Fig.4.8, it can be seen that the samples present similar hysteresis over the first cycle of the dielectric properties, independently of the relaxing time. This indicates that the strain introduced by polishing is not the reason for this hysteresis.

FIGURE 4 . 8 :

 48 FIGURE 4.8: Dielectric properties of sample "H" after 1 and 3h strain relaxation at 400 • C, measured over thermal cycles from 25 to 325 • C.

FIGURE 4 . 9 :

 49 FIGURE 4.9: Dielectric properties of sample "H" with Ag paste metallization and of the same and a new "H" samples with Cr-Au metallization, measured over three consecutive thermal cycles from 25 to 325 • C

FIGURE 4 . 10 :

 410 FIGURE 4.10: Dielectric properties of NBT-BT sample "U" with Ag paste metallization measured over consecutive thermal cycles from 25 to 300 (top) or 360 • C (bottom).

FIGURE 4 . 11 :

 411 FIGURE 4.11: Dielectric properties of NBT-BT sample "X" with Ag paste metallization measured in thermal cycles from 25 to 325 • C and in two different measurement series carried out three months apart.

FIGURE 5 . 1 :

 51 FIGURE 5.1: Tape casting setup.

FIGURE 5 . 2 :

 52 FIGURE 5.2: XRD measurements of the NBT-BT monolayer before and after sintering with phase identification. The insets show the pseudocubic (110) (top) and (111) (bottom peaks of the layer after sintering.

FIGURE 5 . 3 :

 53 FIGURE 5.3: SEM images of the NBT-BT monolayer sample sintered at 1050 • C for three hours. A -grain sizes in 5000x magnification image, Bmonolayer thickness and porous structure in 650x magnification image, C -sample's surface showing the secondary Ba-containing phases separation and the ZrO 2 powder grain attached to the surface in 1900x magnification image.

FIGURE 5 . 4 :

 54 FIGURE 5.4: SEM images showing the morphology of the secondary Bacontaining phases of A -NBT-BT monolayer sample sintered at 1050 • C for three hours, B -core of the NBT-BT bulk equivalent sample ("U"), C -surface of the NBT-BT bulk equivalent sample ("U").

FIGURE 5 . 5 :FIGURE 5 . 6 :

 5556 FIGURE 5.5: Relative permittivity and dielectric losses (tan δ ) for the NBT-BT "U" monolayer sample over consecutive temperature cycles from 25 to 170 • C in the first cycle and from 25 to 270 • C in the second cycle (top panel) and for the second cooling measurement over frequencies from 1kHz to 1MHz (bottom panel).

FIGURE 5 . 7 :

 57 FIGURE 5.7: SEM image of the NBT-BT monolayer surface after measuring its dielectric properties in a temperature cycle from 25 to 350 • C using silver paste metallization.

FIGURE 5 . 8 :

 58 FIGURE 5.8: Insulation resistance of the NBT-BT monolayer sample and of its bulk equivalent (sample "U").

FIGURE 5 . 9 :

 59 FIGURE 5.9: SEM images of the commercially used material (K2200) monolayers sintered in ZrO 2 powder (a), without ZrO 2 powder (b) and its equivalent commercial MLCC (c).

Fig 5 .

 5 [START_REF] Chandrasekhar | Synthesis and characterizations of BNT-BT and BNT-BT-KNN ceramics for actuator and energy storage applications[END_REF] shows the SEM images of the pressed NBT-BT multilayers and the comparison with their corresponding monolayer.

FIGURE 5 . 10 :

 510 FIGURE 5.10: SEM images of the stacked and pressed NBT-BT multilayers sintered in ZrO 2 powder in the core (a) and in the surface of the sample (b) and the equivalent NBT-BT monolayer (c).

3

  Dielectric characterization and compatibility with industrial requirements 3.1 Models for dielectric properties calculations and uncertainties . . . . . . . . 3.1.1 Description of electrical measurements: impedance spectroscopy and insulation resistance . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 RC model for permittivity and dielectric losses . . . . . . . . . . . . 3.1.2.1 RC model validation . . . . . . . . . . . . . . . . . . . . . 3.1.3 Bruggeman model [2, 28] . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Estimation of measurement uncertainties . . . . . . . . . . . . . . . 3.1.5 Temperature drift and corrections . . . . . . . . . . . . . . . . . . . 3.1.5.1 Wire fixing method . . . . . . . . . . . . . . . . . . . . . 3.1.5.2 Silver paste on sample surface and temperature correction . 3.1.5.3 Simplified electric contact and temperature corrections . . 3.2 Dielectric properties with temperature . . . . . . . . . . . . . . . . . . . . . 3.2.1 Influence of stoichiometry, secondary Ba-containing phases, synthesis parameters and polishing and strain relaxation on the dielectric properties vs temperature . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1.1 Stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1.2 Secondary Ba-containing phases . . . . . . . . . . . . . . 3.2.1.3 Synthesis parameters . . . . . . . . . . . . . . . . . . . . 3.2.1.4 Polishing and strain relaxation . . . . . . . . . . . . . . . 3.2.2 Comparison of the measured properties with Exxelia's specifications . 3.2.2.1 Industrial layout graphics for permittivity, dielectric losses and RI versus temperature . . . . . . . . . . . . . . . . . . 3.3 Dielectric spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Co and Mn additions and properties improvement . . . . . . . . . . . . . . . .4.2 MnCO 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compatibility with the electrodes . . . . . . . . . . . . . . . . . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dielectric properties differences reported in the literature . . . . . . . . . . . 4.2 Differences in the measured sample dielectric properties . . . . . . . . . . . 4.2.1 Influence of the stoichiometry on the dielectric properties . . . . . . . 4.2.2 Differences in the dielectric properties of over first heating measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2.1 Influence of the structure and secondary Ba-containing phases,

	4 Literature incompatibilities
	4.1

3.3.1 Maxwell-Wagner model . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1 Nyquist analysis . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.2 Relaxor character . . . . . . . . . . . . . . . . . . . . . . 3.4 3.4.1 Co 3 O 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.1 Phase separation . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.2 Dielectric properties in temperature . . . . . . . . . . . . . 33.4.2.1 Phase separation . . . . . . . . . . . . . . . . . . . . . . . 3.4.2.2 Dielectric properties in temperature . . . . . . . . . . . . . 3.5 Other compatibilities with industrial requirements . . . . . . . . . . . . . . . 3.5.1 Dielectric strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 the synthesis parameters and the polishing and strain relaxation on the temperature hysteresis . . . . . . . . . . . . . 4.2.2.2 Influence of the metallization and electric contact on the temperature hysteresis . . . . . . . . . . . . . . . . . . . . Chapter 1

TABLE 1 .

 1

	Temperature coefficient (ppm/ • C)	Code letter	Temperature coefficient multiplier	Code num-ber	Temperature coefficient (ppm/ • C) tolerance	Code letter
	0.0	C	-1	0	±30	G
	1.0	M	-10	1	±60	H
	1.5	P	-100	2	±120	J
	2.2	R	-1 000	3	±250	K
	3.3	S	-10 000	4	±500	L
	4.7	T	1	5	±1000	M
	7.5	U	10	6	±2500	N
			100	7
			1 000	8
			10 000	9
			1: EIA designation for type I MLCC [8]
	Minimum operating temperature ( • C)	Code letter	Maximum operating temperature ( • C)	Code num-ber	Maximum capacitance (%) variation	Code letter
	10	Z	45	2	±1.0	A
	-30	Y	65	4	±1.5	B
	-55	X	85	5	±2.2	C
			105	6	±3.3	D
			125	7	±4.7	E
					±7.5	F
					±10	P
					±15	R
					±22	S
					± 22 -	T
					± 22 -	U
					± 22 -	V

TABLE 1 .

 1

2: EIA designation for type II MLCC

•

  Precious metal electrode (PME): the PMEs normally consists of 70% of Ag and 30% of Pd and they are normally co-sintered with the ceramic layers between 1000 and 1150 • C. Different Ag and Pd percentages can be used, depending on the sintering temperature, so materials sintered at 1300 • C can have more than 30% of Pd while materials sintered at less than 1100 • C can use 90% of Ag and 10% of Pd. Sintering is done in an oxidizing atmosphere, to prevent the creation of oxygen vacancies in the ceramic.

  .3. It can be seen that none of the presented compositions have the required properties presented in sections 1.3.3 and 1.3.

	1.4.2 NBT and NBT-BT solid solution
	1.4.2.1 Pure NBT
	Base	ε r at	ε r (200 • C) ± 15%	tan δ (1)	tan δ ≤ (1)	Industrial	IR at 250
	material	200 ± 50 • C	T min ( • C) T max ( • C)	T min ( • C) T max ( • C) feasibility to 300 • C
	BT-60%BMT	2200	136	375	2.0%	197	400	Sealed furnace	no info.
	BCT-55%BMT	1000	80	500	2.5%	160	430	ok	85s at 250 • C
	BSZT-20%BMT	500	-70	300	1.5%	-60	310	ok	5.1s at 300 • C
								Sintering
	BT-20%BZT	1700	80	310	2.5%	87	460	with O 2 and	1.6s at 300 • C
								pressure
	BCT-30%BZT	1165	25	425	1.8%	97	440	Sealed furnace	10s at 300 • C
	BT-60%BZZ	1000	100	350	2.5%	25	250	Sealed furnace	no info
	BT-40%BMZ	570	-20	430	2.0%	30	420	Sealed furnace	5.4s at 250 • C
	BT-10%BMTa	1828	115	233	2.0%	115	263	Sealed furnace	no info
	KNN-10%BZW	1300	120	345	2.5%	210	420	Sealed furnace	no info
	KNN-5%LiTaO 3	650	0	380	2.5%	150	200	ok	no info
	KNN-2%LaFeO 3	2000	100	373	4.0%	100	400	Sealed furnace	no info
	KNN-BSBT	2000	108	420	2.5%	87	305	Sealed furnace	no info
	NBT-20%NN	1500	25	450	2%	100	400	ok	no info
	NBT-20%KTaO 3	1750	0	300	2.0%	50	320	Sealed furnace	no info
	TABLE 1.3: Main properties of base material candidates. The references for
				each value are given in the text.

  1.4.2.3 Possible NBT-BT solid solutions with K 0.5 Na 0.5 NbO 3 (KNN) and Bi 0.2 Sr 0.7 TiO 3

	(SBT)

  .4.

	Base	ε r at	ε r (200 • C) ± 15%	tan δ (1)	tan δ ≤ (1)	Industrial IR at 250
	material 200 ± 50 • C T min ( • C) T max ( • C)		T min ( • C)	T max ( • C)	feasibility to 300 • C
	NBT-BT-12%KNN	2900	75	325	2.5%	100	350	Sealed furnace	17s at 250 • C
	NBT-BT-26%BST	4645	50	290	2.0%	100	300	Sealed furnace	6s at 300 • C
		TABLE 1.4: Main properties of NBT-BT-based materials. The references for
			each value are given in the text.

  .1. Na 2 CO 3 and Bi 2 O 3 are hygroscopic powders, which means that they absorb the air mois-

	Reactants	Weight (g)
	Bi 2 O 3	2.5689
	Na 2 CO 3	0.5843
	TiO 2	1.8737
	BaCO 3	0.2778

TABLE 2 .

 2

1: Weight of reactants corresponding to 5g of nominal stoichiometric NBT-BT 6%.

TABLE 2 .

 2 .14).

	Phase	O	Na	Si	Ti	Ba	Bi	Zr	W
	NBT phase 1	2.48	0.51	-	1.00	-	0.55	-	-
	NBT phase 2	2.01	0.14	-	1.00	-	0.20	-	-
	W phase 1	2.56	-	-	0.04	1.04	-	-	1.00
	W phase 2	28.77	1.58	-	10.74	-	7.8	-	1.00
	Secondary
	Ba-containing	19.70	0.23	-	9	3.91	-	-	-
	phases

2: Phases composition for the "U-WC" sample, prepared in the WC jar.

  .11 p. 79 ). Table2.5 shows that the grain size of Na 2 CO 3 does not affect the secondary Ba-containing phases separation.Analyzing the differences in structure from the XRD measurements presented in Figure

	Sample	Average size (µm 2 )	Error	% area	Error
	H (granular Na 2 CO 3 )	3.35	2.35	1.51	0.24
	V (powder Na 2 CO 3 )	1.71	1.58	1.56	0.92

TABLE 2.5: Secondary Ba-containing phases SEM characterization for samples H ("granular" Na 2 CO 3 ) and V ("powder" Na 2 CO 3 )

TABLE 2 .

 2

		Dried reactants	Ball-millings	Solvent	Dispersing agent
	"B"	Yes	250 rpm 4h -250 rpm 4h Ethanol	No
	"E"	Yes	350 rpm 8h -350 rpm 8h Ethanol	No
	"H"	No	250 rpm 4h -250 rpm 4h Ethanol	Yes
	"I"	No	250 rpm 4h -350 rpm 8h Ethanol	Yes
	"N"	No	250 rpm 4h -250 rpm 4h	MEK + Ethanol	Yes
	"P"	No	350 rpm 8h -350 rpm 8h	MEK + Ethanol	Yes

6: Synthesis parameters for NBT-BT samples "E", "B", "I" "H", "P" and "N". The "ball-millings" column present the speed and time for the first (before calcination) and second (after calcination) ball-milling.

  optimized. The NBT-BT powder and the solvent quantities were based on the slurry compositions used in Exxelia, to have a high density of the layers after sintering.

	Component	Liu et al.(2012) [38]	Exxelia	Chosen composition
	NBT-BT powder	68.9%	61.5%	60.6%
	PEG	1.1%	1.5%	1.1%
	MEK	11.5%	22.8%	22.7%
	Ethanol	11.5%	9.6%	10.0%
	PVB	4.5%	3.9%	4.5%
	Dispersing agent	1.1%	0.6%	1.1%

TABLE 2 .

 2 8: Slurry compositions based on Liu et al.[START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF], where the 1.1% missing is of butyl-benzyl-phthalate, not used in this study, on the MLCC slurries used by Exxelia and the initial slurry composition used in this work.

TABLE 2 .

 2 9: Mean position and intensities of each fitted peak for the Raman spectra of NBT samples before second ball-milling, after second ball-milling and after thermal treatment at 400 • C for five hours in air.The C-and D-bands each consists in three peaks

	1)

TABLE 3 . 1 :

 31 Relative permittivity and the dielectric losses (tan δ ) values at 50 • C and at T m for "U" sample in two consecutive measurements. Curve 1 and 2 correspond to two different trends in the second measurement, depending on the electric contact.

TABLE 3 .

 3

2: Measured T d and T m for sample "H", at 10kHz for the two methods to contact the bottom electrode.

TABLE 4 .

 4 1: Depolarization temperature T d and temperature of the maximum relative permittivity T m for samples "U" (nominal Na/Bi ratio of 0.92), "P" (nominal Na/Bi ratio of 1), "Y" (nominal Na/Bi ratio of 1 and 10.5mol% Na and 2.2mol% Bi nominal excess compared to sample "U") and "Z" (nominal Na/Bi ratio of 1.06 and 16.9mol% Na nominal excess compared to sample "U").

  separation on NBT-BT are not the reason for the first heating hysteresis of the dielectric properties.Finally, sample "H" (synthesis parameters at Table2.11 p. 79) was polished and

TABLE 5 .

 5

	2: Matrix and secondary Ba-containing phases composition mea-
	sured via EDS considering stoichiometry for the Ti as 1.0 for the matrix and
	9.0 for the secondary Ba-containing phases for the NBT-BT sample after
	sintering.

TABLE 2.11: Synthesis parameters for selected bulk ceramic samples.

Acknowledgments

the thermal treatments in air led to the formation of char that is eliminated at 750 • C. [START_REF] Loey | Pyrolysis of polyvinyl butyral (PVB) binder in thermoelectric green tapes[END_REF] Therefore, a new sintering was done with the NBT-BT monolayers using two temperature plateaus, the first one at 450 • C for 12h, to oxidize the PVB, and another one at 800 • C for 30 minutes, to guarantee the elimination of all organic residues in the tape. The final step of the sintering was done at 1050 • C for 3h, as for the first one.

However, the as-sintered NBT-BT tape showed a smaller density of 53% compared to the density of the sample sintered without the 450 • C plateau. Table 5.1 show the final densities obtained for the different sintering parameters.

Table 5.1 shows that the low density of the NBT-BT monolayers is not due to a sintering problem. The "green" tapes have good mechanical resistance, no cracks and uniform thickness, as mentioned before, indicating that the parameters used in the ball-milling for slurry synthesis are adapted to the MLCC production. So, the next step to solving the density problem of the NBT-BT layers would be to press multiple "green" layer together, to decrease the porosity of the multilayer device before sintering, to increase the NBT-BT powder concentration and to decrease the PVB concentration in the slurry. [START_REF] Liu | Combinatorial study of ceramic tapecasting slurries[END_REF]

Structure and thickness of the monolayers

The XRD measurements of the monolayer before sintering and as-sintered at 1050 • C for three hours are shown in Fig. 5.2.

The measurements show no second phase peak after sintering, since the only peaks not related to the NBT-BT are the ones coming from the ZrO 2 atmosphere powder.

A peak widening similar to the ones observed for the polished and strain-relaxed bulk NBT-BT samples is also observed. The insets in Fig. 5.2 show the pseudocubic (110) and (111) peaks details. The widening is present for all the peaks as a lower-angle-side shoulder peak and is probably also related to a phase coexistence in NBT-BT (see section 2.3.2.2). So, in the as-sintered NBT-BT monolayers, there is a coexistence of pseudo-cubic, rhombohedral, and tetragonal phases at the surface.

The SEM images of the monolayer sintered at 1050 • C for three hours are shown in Fig. 5.3. Samples sintered in different conditions show similar structures.

As it can be confirmed from Fig. 5.3, the synthesised NBT-BT monolayers show low density and porous structure. Ceramic layers with low density could not be applied to MLCC production, since it would create problems such as the penetration of the electrodes in the ceramic layer, the increase in the dielectric losses, the decrease of the insulation resistance, and the decrease of the dielectric strength. So an optimization of the slurry composition and the sintering after pressing the layers together in a multilayer device are needed before being able to characterize a layer that could be used in MLCCs (see section 5.1.2).

Appendices

Appendix A Extract of patent number 17 58575 publication number 3071244

The following extract shows the patent published by Exxelia Technologies and it concerns the material studied in this thesis for the MLCC application.

The complete document can be found in: https://bases-brevets.inpi.fr/fr/document/FR3071244.html?s=1568633240025p=5cHash=8ba b94d228065aa6087dd0d15cc42d56 6% BT améliore les valeurs de permittivité et sa variation en température. Enfin, le NBT-BT a un double cycle d'hystérésis entre 200 • C et 300 • C, bien que ce soit un relaxeur ergodique. Cela le rend intéressant pour les applications de stockage d'énergie.

Différentes méthodes et paramètres de synthèse ont été étudiés, pour déterminer les meilleures conditions de synthèse pour le NBT-BT, compte tenu des exigences d'Exxelia. Dans un premier temps, deux méthodes de synthèse de la poudre de NBT-BT ont été analysées, la synthèse via sol-gel et la synthèse à l'état solide. La synthèse à l'état solide a été choisie en tenant compte des limites industrielles et des propriétés attendues du matériau final. Trois méthodes de frittage ont ensuite été analysées : le micro-ondes, le SPS et le frittage traditionnel. Compte-tenu encore une fois les limites industrielles et les propriétés requises, la méthode de frittage traditionnelle a été choisie. Enfin, trois méthodes différentes pour contrôler l'évaporation de volatiles pendant le frittage ont été testées : le frittage sous l'air (atmosphère non contrôlée), le frittage sous poudre de NBT ou réactifs + ZrO2 et le frittage sous poudre de ZrO2 pure. La première méthode a permis d'obtenir un matériau qui n'est pas du NBT-BT et la seconde a nécessité un traitement post-frittage pour obtenir une surface propre. Donc, le frittage sous poudre de ZrO2 a été choisi pour contrôler l'évaporation de volatiles pendant le frittage. La mise en forme des couches céramiques a été faite par coulage en bande, car c'est la seule méthode disponible chez Exxelia.

Tous les échantillons ont montré une séparation de phase et la formation de phases secondaires contenant du Ba, due à l'évaporation du Na lors du frittage. Ces phases ont été identifiées comme un mélange de Ba2TiO4 et Ba2Ti9O20. Elles se concentrent à la surface des échantillons en raison de l'évaporation plus élevée de Na et aussi parce que le ZrO2 favorise la formation de Ba2Ti9O20.

Le séchage des réactifs hygroscopiques a été le premier paramètre de synthèse étudié. Il a intensifié les effets de l'énergie de broyage, en créant une grande surface moyenne de grain des phases secondaires pour le broyage à 250 rpm pendant 4h et une grande fraction volumique de petits grains des phases secondaires pour un broyage à 350 rpm pendant 8h.

Deux matériaux des jarres et des billes de broyage ont également été testés. Le broyage avec la jarre et les billes en carbure de tungstène a entraîné la formation d'un matériau contaminé, hautement conducteur et avec des pertes diélectriques élevées. En utilisant la jarre et les billes de zircone stabilisées à l'yttrium (YSZ), le matériau final a montré des bonnes propriétés diélectriques et une petite contamination par Zr à la surface qui pourrait être enlevée par polissage. Le broyage avec la jarre et les billes en ZrO2 a donc été choisi pour la synthèse du NBT-BT.

Un effet de peau dû à une coexistence de phases (tétragonale, rhomboédrique et cubique) a été observé pour les matériaux polis et décontraints dû à des pics élargis et asymétriques sur les diagrammes de diffraction de rayons-X (XRD). Il n'est pas présent dans les échantillons non polis, en raison de la plus faible concentration locale de Ba dans le réseau cristallin du NBT en surface.

Deux solvants de broyage ont aussi été testés : l'éthanol pur et un mélange d'éthanol et de méthyléthylcétone (MEK). Toutefois, le changement de solvant n'a pas eu d'influence sur la structure et la séparation des phases du NBT-BT. Un résultat similaire a été obtenu en changeant la granulométrie du réactif Na2CO3.

L'énergie (vitesse et durée) du broyage a également été étudiée en utilisant un broyage à 250 rpm pendant 4h et un autre à 350 rpm pendant 8h. Les effets de l'énergie du broyage étaient évidents dans les échantillons broyés sans utiliser d'agent dispersant, où l'augmentation de l'énergie a entraîné une plus petite surface moyenne des grains et une plus grande fraction volumique des phases secondaires contenant du Ba. Toutefois, cet effet n'est pas observé dans les échantillons broyés avec un agent dispersant, qui avaient des valeurs intermédiaires de surface moyenne des grains et de fraction volumique des phases secondaires.

L'utilisation d'un deuxième broyage après calcination a été testée pour augmenter la densité des céramiques. La densité la plus élevée pour les échantillons sans deuxième broyage a été de 91,5% contre 93,5% pour les échantillons préparés avec un deuxième broyage. Dans les deux cas, la densité maximale a été atteinte le frittage à 1150 • C pendant 3h. Les rampes de température utilisées ont été de 120 • C/h pour le chauffage et 200 • C/h pour le refroidissement, pour éviter les fissures lors du frittage.

Deux diamètres de billes ont été testés pour le deuxième broyage : 1mm et de 10mm. Les billes de 1mm de diamètre ont été choisies, car leur utilisation a augmenté la densité sans modifier la microstructure et la séparation des phases, et sans introduire des lacunes d'oxygène.

Enfin, les changements de stoechiométrie nominale du Na et du Bi ont aussi été étudiés. L'augmentation de la concentration de Bi et de Na a diminué la fraction volumique des phases secondaires contenant du Ba et des échantillons sans séparation de phase ont pu être obtenus avec un excès de Na. La diminution du rapport Na/Bi nominal a créé une matrice stoechiométrique en Bi et une séparation de l'excès de Bi dans une phase riche en Bi et concentrée dans le centre de l'échantillon.

Pour estimer la permittivité des échantillons de NBT-BT à partir de leur mesure d'impédance, un modèle RC a été utilisé. L'analyse de la variation de l'impédance complexe en fréquence a montré que la résistance et la capacité du montage peuvent être négligées et a validé l'utilisation du modèle RC. Les incertitudes des mesures diélectriques ont été estimées par le bruit de mesure, considéré supérieur aux incertitudes. Ainsi, une incertitude de 13% a été prise en compte pour la permittivité relative et une incertitude de 14% a été prise en compte pour les pertes diélectriques.

Une correction du décalage en température a également été apportée. La correction a été effectuée en utilisant un échantillon de BaTiO 3 comme référence. Le changement de la température de Curie dans cet échantillon entre les mesures en chauffage et en refroidissement a montré qu'il n'y a pas de gradient de température significatif dans les échantillons.

Enfin, une nouvelle méthode de fixation des fils sur les échantillons a été utilisée (métallisation par pulvérisation cathodique de Cr-Au et fixation décalée des fils sur une plaque de cuivre) pour estimer une incertitude de 3.5% dans les mesures de température.

Après avoir estimé les incertitudes, les propriétés diélectriques et la résistance d'isolement du NBT-BT ont été mesurées en température. Les effets de la stoechiométrie, de la structure, de la séparation de phases, des paramètres de synthèse et de la contrainte interne sur ses propriétés ont été analysés.

Les propriétés du NBT-BT sont particulièrement sensibles à la stoechiométrie et au rapport Na/Bi. L'augmentation de la teneur en Na inhibe la séparation des phases secondaires contenant du Ba et diminue la teneur relative en Bi dans la phase principale, augmentant ainsi la conductivité de l'échantillon. L'augmentation de la teneur en Bi compense d'abord la formation de lacunes d'oxygène et diminue la conductivité avant de former une deuxième phase, en augmentant à nouveau la conductivité à un Bi-excès supérieur.

Considérant les exigences d'Exxelia pour les MLCCs haute température, la stoechiométrie de l'échantillon "U" (rapport Na/Bi réduit) est la plus adaptée, en raison de sa résistance d'isolation élevée, de ses pertes diélectriques plus faibles et de sa faible variation de permittivité en température par rapport aux autres stoechiométries.

En raison de la séparation de phases et des phases secondaires contenant du Ba, le matériau final peut être considéré comme un composite où la phase matrice est composée de NBT nonstoechiométrique et les inclusions sont constituées des phases secondaires contenant du Ba. Cependant, en raison des caractéristiques physiques et des propriétés des phases, aucun modèle composite classique n'a pas pu être appliqué.

L'augmentation de la fraction volumique et de la surface moyenne des grains de cette phase est d'abord bénéfique pour les MLCCs, puisqu'elle augmente la permittivité, diminue température est observée lors de sa mesure sur des cycles thermiques consécutifs, rendant la mesure impossible à des températures supérieures à 275 • C. Cette hystérésis et cette dégradation thermique peuvent être dues à l'influence des électrodes, puisqu'il y a une pénétration de la laque d'argent dans les pores du matériau pendant les cycles thermiques. Cependant, cela peut aussi être dû au changement de la morphologie du matériau en température, puisque la faible densité et la surface spécifique élevée de la couche facilitent les changements de la morphologie du matériau. Enfin, la résistance d'isolation pour les monocouches est beaucoup plus faible que pour le bulk, comme prévu pour les matériaux basse-densité.

Ces propriétés ne sont pas encore compatibles avec les exigences d'Exxelia pour la production de MLCCs. Néanmoins, les pertes diélectriques sont inférieures à 2.5% à 1kHz de 100 à 150 • C, la variation de la permittivité de ± 15% a lieu de 180 à 240 • C et la résistance d'isolement est supérieure à 1s jusqu'à 180 • C. Pour faire une évaluation plus fiable des couches NBT-BT et pour répondre aux exigences de la production de MLCCs, l'augmentation de la densité est impérative.

Pour résoudre ce problème de densité, les effets du pressage de plusieurs couches de NBTBT avant frittage, formant un dispositif multicouche, a été étudié. Il a été démontré qu'un matériau à haute densité (89,5%) peut être obtenu après le frittage des multicouches pressées à 1150 • C. Ceci indique que la faible densité des monocouches n'est pas due à un problème de composition de la barbotine et que, même si les monocouches ne présentent pas des propriétés diélectriques compatibles avec les exigences industrielles, cela ne signifie pas nécessairement que le dispositif multicouche préparé avec ces couches aura la même limitation de plage de température. Cependant, comme les multicouches NBT-BT pressées présentent une évaporation de Na et Bi plus élevée, une nouvelle mesure des propriétés diélectriques en température doit être effectuée pour évaluer la plage de température de compatibilité avec les exigences industrielles.