Fabienne Karolak

Pavan Noukala

Christine Bogicevic

Charles Paillard

Xavier Bril

Arij Vitoria Charles

Chen Yi

Henri

Pavan

Leo

Keywords: 4, 2, 2 X-ray photoelectron spectroscopy

I want to thank very much the members of the jury committee Doru Lupascu, Maël Guennou, Florence Porcher, et Nicolas Chauvin who agreed to come to my defence and spent time reading and correcting this manuscript, as well as for their inspiring questions which might help in the future development of this work.

I feel grateful to my thesis supervisors Brahim Dkhil and Ingrid Canero-Infante, who made me discover multiple topics and methods, and to move my scientific interests to the field of ferroelectrics, by helping me in discussions and giving me the possibility to go to multiple conferences and workshops to meet new people and learn new things. I am especially happy that I could spend two short-time visits of

neglected. Thus, the band gap is mostly determined by the qualities of the bond B-O. Based on this, it is interesting to substitute the B-site cation. Unlike some transparent oxide double compounds (HfO 2 -ZrO 2 ) [START_REF] Bendoraitis | Optical energy gaps in the monoclinic oxides of hafnium and zirconium and their solid solutions[END_REF], band gap value of perovskite solid solutions often evolves strongly non-linearly. There are multiple examples of such B-site substitution. First approach is to choose the transition metal atom so that it's electronic levels will be situated inside the band gap of the parent compound. The examples are Sr(Cr,Ti)O 3-δ [START_REF] Pakpoom Reunchan | Mechanism of photocatalytic activities in Cr-doped SrT iO 3 under visible-light irradiation: an insight from hybrid density-functional calculations[END_REF] where Cr - T i t 2 g orbitals are situated just above the valence band maximum, or Ba(Pd,Ce,Ti)O 3-δ , where the orbitals of Pd lie both above the VBM and below CBM which is formed by Ce [START_REF] Zhou | Pb-free semiconductor ferroelectrics: An experimental study of Ba(T i 0.75 Ce 0.125 P d 0.125 )O 3 thin films[END_REF][START_REF] Bennett | Pb-free semiconductor ferroelectrics: A theoretical study of Pdsubstituted BaT iO 3[END_REF], or (K,Ba)(Ni,Nb)O 3-δ , where the band gap was reduced from 4 eV to <1.5 eV. Calculations show that significant reduction in the band gap happens due to the formation of complexes from oxygen vacancy V •• O and adjacent N i ′′′ N b defects. Despite being efficient in band gap reduction, defects act as trapping and recombination centers for the photoconduction electrons, and the final photovoltaic efficiency is low (around 3%). In further works by Rappe, he calculated that charge redistribution in layered compounds with certain ordering of atoms, like Bi(Zn 0.5 Ti 0.5 )O 3 [START_REF] Qi | Firstprinciples investigation of the highly tetragonal ferroelectric material Bi(Zn 1/2 T i 1/2 )O 3[END_REF][START_REF] Qi | Band-gap engineering via local environment in complex oxides[END_REF][START_REF] Chen | Effect of cation arrangement on the electronic structures of the perovskite solid solutions SrT iO 3 (1 -x) -LaCrO 3 (x) from first principles[END_REF] must lower the band gap without creating defects, but the synthesis of this material in pure shape is complicated, and the solid solution 0.88 • BaTiO 3 -0.12 • Bi(Zn 0.5 Ti 0.5 )O 3 does not show the band gap decrease for some reason [START_REF] Yu | Structural characteristics and optical properties of leadfree Bi(Zn 1/2 T i 1/2 )O 3 -BaT iO 3 ceramics[END_REF].

The layered compounds like thin film multilayers, or Aurivillius phase materials, or Ruddlesden-Popper phases are actively studied [START_REF] Woo | Wide bandgap tunability in complex transition metal oxides by site-specific substitution[END_REF][START_REF] Chen | Effect of cation arrangement on the electronic structures of the perovskite solid solutions SrT iO 3 (1 -x) -LaCrO 3 (x) from first principles[END_REF]. From all the works with an accent on atomic ordering, the most successful was on Bi 2 FeCrO 6 thin films [START_REF] Nechache | Bandgap tuning of multiferroic oxide solar cells[END_REF]. There are regions of ordered superstructure inside the disordered matrix, former ones showing the decrease of band gap from 2.7 eV to 1.5 eV (by 1.2 eV), and the latter one -only by 0.5 eV. Superstructure leads to certain Jahn-Teller distortions, under which the valence of atoms changes from (Fe 3+ , Cr 3+ ) towards (Fe 2+ , Cr 4+ ). Calculations explained the drastic decrease of the band gap by effect of stress in thin films which causes the reordering of orbital directions [START_REF] Dong | Improving the optical absorption of BiF eO 3 for photovoltaic applications via uniaxial compression or biaxial tension[END_REF]. By making a trial multilayer solar cell from Bi 2 FeCrO 6 layers with different properties of ordered regions, 8% efficiency is reached, which is the highest ever made with inorganic ferroelectric and is a very promising result.

In our work, we study pure perovskite compounds Ba 2+ Ti 4+ O 2- 3 , Ba 2+ Sn 4+ O 2- 3 and their solid solutions.

1.2 Crystallographic studies of Ba(Sn,Ti)O 3 phase diagram

1.2.1 BaTiO 3
Barium titanate, BaTiO 3 , is a perovskite ferroelectric. Perovskites is the class of chemical compounds which have the general formula ABO 3 fig. 1.4. In the cubic unit cell the A-site atoms are located in the edges of a cube, the B atoms are in the center, and the O atoms are on the face centers and form the octahedron around the B-site atom. In BaTiO 3 the cubic phase is in equilibrium at high temperatures (above the Curie temperature Tc). The full phase sequence from high to low temperature is cubic (C) P m 3m, tetragonal (T) P 4mm, orthorhombic (O) Amm2, rhombohedral (R) R3m as shown in the top panel of fig. 1.5 [START_REF] Ch | Tetragonal-Orthorhombic Phase Transition in Barium Titanate via Monoclinic MC-Type Symmetry[END_REF]. In T, O and R phases the Ti atom is displaced from the center of unit cell towards the crystallographic directions <001>, <110>, and <111> [START_REF] Vanderbilt | Monoclinic and triclinic phases in higher-order devonshire theory[END_REF]. On cooling, the unit cell parameters a and c decrease stepwise during phase transitions. There is a phase transition hysteresis at the different temperatures at each phase transition: during cooling the phase transition starts at lower temperatures in comparison to heating. This is characteristic to first order phase transitions, like those of BaTiO 3 . As the displacement of central Ti ion changes, the polarization varies in the way shown in the second panel of fig. 1.5. Relative permittivity also peaks at phase transitions.

The nature of the T-C phase transition is a lot discussed in the literature. Originally, it is possible to picture it as a displacive phase transition controlled by certain phonon soft mode whose frequency tends to zero at the phase transition (basically, phase transition happens in one step). However it was shown by Raman spectroscopy that the soft mode does not reach zero frequency. It turns out that there is a significant order-disorder component (different unit cells are non-equivalent). It was shown by Itoh and coworkers [START_REF] Itoh | Crystal structure of BaT iO 3 in the cubic phase[END_REF] fig. 1.6, at Figure 1.6: Average displacements of atoms in cubic BaTiO 3 3 K above Tc deduced from refinement of XRD data [START_REF] Itoh | Crystal structure of BaT iO 3 in the cubic phase[END_REF] The nature of other two transitions has lately been questioned. In [START_REF] Ch | Tetragonal-Orthorhombic Phase Transition in Barium Titanate via Monoclinic MC-Type Symmetry[END_REF] under very slow cooling the XRD peak appears which does not belong either to O or T phase fig. 1.7a. This phase is most probably monoclinic. Monoclinic phase was before discovered in PZT [START_REF] Noheda | Stability of the monoclinic phase in the ferroelectric perovskite P bZr 1-x T i x O 3[END_REF], despite according to theoretical sixths-order expansion of free energy it should not occur [START_REF] Vanderbilt | Monoclinic and triclinic phases in higher-order devonshire theory[END_REF]. However, after 8-order expansion monoclinic phase appears to exist. It is suggested that in classical ferroelectrics like BaTiO 3 and KNbO 3 a different sequence of phases is possible than the one usually found. Either the order R-O-M A -T-C or R-M B -O-M A -T-C is possible. In addition, even the sixth-order expansion is close to predicting M C phase [START_REF] Vanderbilt | Monoclinic and triclinic phases in higher-order devonshire theory[END_REF].

BaSnO 3

BaSnO 3 end compound of Ba(Sn,Ti)O 3 solid solutions is cubic (C) P m 3m at all temperatures fig. 1.8. The slight change of slope at low temperatures (100-125 K) is caused by freezing out of atomic movements.

Ba(Sn,Ti)O 3

The Sn cation has the Shannon radius R(Sn)=0,69 in comparison to one of Ti which is smaller R(Ti)=0,605 [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. According to this, the volume of the unit cell of Ba(Sn,Ti)O 3 solid solution increases on Sn substitution. There is full solubility throughout the phase diagram [START_REF] Wei | Preparation, structure and dielectric property of barium stannate titanate ceramics[END_REF]. First two compositions, x(Sn)=0.02 and x(Sn)=0.06 preserve all the phase sequence of BaTiO 3 , while the Ti off-centering is decreased. It is explained by Sn atoms breaking the space continuity of long-term correlations in Ti-O chains [START_REF] Von Der Mühll | Dielectric investigation of a new TKWB lead free relaxor[END_REF]. Already for x(Sn)=0.11, the phase sequence changes and there is a rhombohedral phase changing to quasi-cubic, passing close to quadruple point and then turning to Figure 1.8: Temperature dependence of the unit cell parameter of BaSnO 3 [START_REF] Bévillon | Theoretical and experimental study of the structural, dynamical and dielectric properties of perovskite BaSnO 3[END_REF] cubic at much lower temperatures in comparison to BaTiO 3 [START_REF] Yao | Large piezoelectricity and dielectric permittivity in BaT iO 3 -xBaSnO 3 system: The role of phase coexisting[END_REF]. The distortions in the quasi-cubic phase are very low and it is difficult to determine their true nature as the XRD was performed on laboratory diffractometer where the resolution is not sufficient. Because of this, the refinements of laboratory XRD data with tetragonal or cubic symmetry also give satisfactory agreement factors [START_REF] Veselinovic | The effect of Sn for Ti substitution on the average and local crystal structure of BaT i 1-x Sn x O 3 (x=0...0.20)[END_REF]. As the Sn ratio increases further x(Sn)>0.11, the temperature of transition between the rhombohedral phase and cubic one decreases fig. 1.9 [START_REF] Yao | Large piezoelectricity and dielectric permittivity in BaT iO 3 -xBaSnO 3 system: The role of phase coexisting[END_REF].

CHAPTER 1. INTRODUCTION

.9: XRD patterns of Sn-rich compositions of Ba(Sn,Ti)O 3 at different temperatures, x(Sn)=0.02; 0.06; 0.11; 0.15 [START_REF] Yao | Large piezoelectricity and dielectric permittivity in BaT iO 3 -xBaSnO 3 system: The role of phase coexisting[END_REF] 1

.3 Visualizing chemical homogeneity on atomic level

The TEM allows to check the homogeneity of chemical composition. Moreover, in the High Resolution mode (HRTEM) the individual atomic displacements can be visible, averaged in each atomic column over the thickness of the sample.

Figure 1.10 shows that on the atomic scale the material is not homogeneous. The regions rich in either Ti or Sn are visible in the right panel. The Ti polar displacements in the left panel of fig. 1.10 are larger for Ti-rich regions. These regions can be called polar nanoregions (PNR). The different reaction (relaxation) of PNR impedance to AC electric field of different frequencies will be discussed in next section and is the basic property of relaxor systems. with Sn concentration for x(Sn)=0.2 (HAADF TEM image) in < 001 > polar axis [START_REF] Shi | Why Sn doping significantly enhances the dielectric properties of Ba(T i 1-x Sn x )O 3[END_REF] In fig. 1.11 one can see that regions with different Ti displacement start forming already in x(Sn)=0. [START_REF] Qi | Firstprinciples investigation of the highly tetragonal ferroelectric material Bi(Zn 1/2 T i 1/2 )O 3[END_REF], despite the average Ti off-centering is very small. In x(Sn)=0.2, the difference in Ti off-centering becomes larger, but it stays similar in x(Sn)=0. [START_REF] Aksel | Advances in lead-free piezoelectric materials for sensors and actuators[END_REF]. Nevertheless, the proportion and size of PNR with larger Ti off-centering increases. The summary of approximate PNR characteristics can be seen in table 1.1. To conclude, on the local scale the Ti displacement decreases from pure BaTiO 3 towards x(Sn)=0. [START_REF] Qi | Firstprinciples investigation of the highly tetragonal ferroelectric material Bi(Zn 1/2 T i 1/2 )O 3[END_REF], but it is larger for further compositions. To our knowledge, no such HRTEM studies 1.4. DIPOLE ORDERING AND DIELECTRIC SPECTROSCOPY 9 have been performed for x(Sn) > 0.25, for Sn-rich compositions which show well-marked relaxor behaviour.

Figure 1.11: Ti displacement in compositional serie x(Sn) = 0.16; 0.2; 0.25 (HRTEM image) in <120> polar axis [START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF] Table 1.1: Ti displacement in PNR and the average size of displaced regions x(Sn) average Ti displacement, pm PNR average size, Å 0.16 [START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF] 0 -5 40-60 0.2 [START_REF] Shi | Why Sn doping significantly enhances the dielectric properties of Ba(T i 1-x Sn x )O 3[END_REF] 10-28 16 0.2 [START_REF] Shi | Explanation of diffuse scattering mechanism based on the structure of polar nanoregions in BaT i 1-x Sn x O 3[END_REF] 8-22 16-24 0.2 [START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF] 10-20 20-30 0.25 [START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF] 10-20 30-40

The PNR size and shape can be analysed from the diffuse electron scattering around the diffraction points in TEM. The advantage of diffraction over imaging is that in the latter it is difficult to get the 3D information. The detailed analysis from [START_REF] Liu | Structured diffuse scattering and polar nano-regions in the BaT i 1-x Sn x O 3 relaxor ferroelectric system[END_REF] shows that the diffuse scattering in the series x(Sn)=0.10, 0.20, 0.225, 0.25, 0.30 and 0.50 comes from chains of polarized unit cells in < 001 > direction, with the characteristic length of chains at least 5 nm for all these compositions. With increase in Sn ratio the diffuse component becomes weaker, which is consistent with a decrease in the number of Ti off-centered atoms as well as reduction of dielectric constant.

Other work [START_REF] Shi | Explanation of diffuse scattering mechanism based on the structure of polar nanoregions in BaT i 1-x Sn x O 3[END_REF] suggests that the diffuse scattering is coming from very thin (< 1 nm) elliptic zones with long axis (∼ 2nm) parallel to the < 001 > direction.

Dipole ordering and dielectric spectroscopy

To study the transitions between different dipole orderings, dielectric spectroscopy is used. The dielectric constant ε(ω) = ε ′ (ω) + iε"(ω) peaks at every phase transition for a ferroelectric ( 1/ε tends to zero at the phase transition). In BaTiO 3 , the phase transitions are (at least partially) driven by a phonon transverse soft mode, and this causes the ε to peak: Figure 1.12: Relative permittivity of BaSn x Ti 1-x O 3 with x(Sn) = 0.02; 0.06; 0.11; 0.15 [START_REF] Yao | Large piezoelectricity and dielectric permittivity in BaT iO 3 -xBaSnO 3 system: The role of phase coexisting[END_REF]

ω 2 L ω 2 T = ε st ε ∞ (1.1)
with ω L and ω T -longitudinal and transversal phonon mode frequency, ε st and ε ∞ -dielectric permittivity at electric field frequency f=0 and at optical frequencies.

To our knowledge, only the Ti corner of the phase diagram was studied in dielectric spectroscopy. In fig. 1.12, one can see the ε shown for a compositional series BaSn x Ti 1-x O 3 . The plot for x(Sn)=0.02 has the peaks which are inherent to BaTiO 3 . On further increase of Sn ratio, the transition temperatures T 1 , T 2 and T 3 = T m (temperature of peak maximum) get closer to each other, so that for x(Sn) = 0.11 there is only one peak with the temperature of maximum Tm. For x(Sn) > 0.11 the T m is decreasing. In this compositional range the dielectric permittivity value peaks for x(Sn)=0.11. As can be seen from fig. 1.13, this is the composition close to the so-called quadruple point where four different kinds of unit cell distortion are allowed to coexist. The fact that Ti can be easily displaced to multiple directions also causes the anomaly of the piezo-electric [START_REF] Yao | Large piezoelectricity and dielectric permittivity in BaT iO 3 -xBaSnO 3 system: The role of phase coexisting[END_REF][START_REF] Kalyani | Polarization switching and high piezoelectric response in Sn-modified BaT iO 3[END_REF] and electrocaloric [START_REF] Zhang | Large electrocaloric effect in Ba(T i 1-x Sn x )O 3 ceramics over a broad temperature region[END_REF][START_REF] Luo | Enhanced electrocaloric effect in lead-free BaT i 1-x Sn x O 3 ceramics near room temperature[END_REF][START_REF] Luo | Enhanced electrocaloric effect in lead-free BaT i 1-x Sn x O 3 ceramics near room temperature[END_REF][START_REF] Sanlialp | Direct measurement of electrocaloric effect in lead-free BaSn x T i 1-x O 3 ceramics[END_REF] properties, and the mechanical compliance to happen at this temperature. [START_REF] Straube | Ultrasound Investigations of BaT i 1-x Sn x O 3 Ceramics[END_REF].

As shown in fig. 1.13, BaTiO 3 the T m equals the Curie temperature T CW , but for compositions x(Sn)>0.1 dielectric permittivity peaks become wider as characteristic of diffuse phase transition. For diffuse phase transition 1/ε does not tend to zero, so more characteristic temperatures are needed to describe the phase transition. Those parameters are T m -dielectric peak maximum, T CW -the Curie-Weiss temperature, and T Q . The T CW is determined from fit of data to equation

ε ′ = ε 0 + C T -T CW (1.2)
with C -Curie constant, ε 0 -frequency-dependent and temperature nondependent contributions (high-energy phonon modes or electronic polarization).

The T d -temperature where the static polar correlations disappear (same as T B -Burns temperature) is determined as the temperature below which the data of cubic phase deviates from the Curie-Weiss law. This signifies that on heating through this point the polar correlated regions disappear.

Just above the T m, the fit can be done with equation

ε A ε = 1 + (T -T A ) 2 2δ 2 (1.3)
with ε A , T A , δ -the parameters. In fig. 1.13, the temperature T Q is where the deviation from eq. ( 1.3) appears and the data begins to change towards the Curie-Weiss law.

The low-temperature phase is rhombohedral ferroelectric for low Sn ratio, and changes to polar glass frozen relaxor state for higher Sn ratio. The freezing temperature T V F is determined from the fit by the Vogel-Fulcher law:

f = f 0 • e -E a k(T m -T V F ) (1.4)
with f 0 -the characteristic frequency of PNR dielectric relaxation, and E a -the activation energy.

Whether the ferroelectric low-temperature phase changes to the relaxor one abruptly in the compositional series was discussed in several references. Authors of ref. [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF] found a sharp transition at x(Sn)=0.2 from the analysis of ε ′ asymmetric peak widths. However, ref. [START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF] claims that the transition is continuous. Figure 1.14 shows the dependence of an imaginary part of dielectric permittivity ε" on frequency. It shows how the energy of applied electric field is absorbed by the sample (dielectric loss), and is used to analyse processes of dielectric relaxation. For compositions x(Sn)=0.15 and 0.175 there are two relaxation processes, attributed to breathing modes of pinned domain walls and PNRs. In the latter composition, there is at the same time the highfrequency relaxation (10 8 -10 9 ), which is usually attributed to reorientation of PNR [START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF]. This work claims that the gradual transition towards the classical relaxor regime occurs for x(Sn) = 0.175...0.25, since the dynamics freezing (disappearance of high-frequency peak) occurs much below the characteristic temperature of the diffuse phase transition determined from data fit [START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF]. The first sample showing truly relaxor behaviour is x(Sn)=0.3.

MACROSCOPIC POLARIZATION

Macroscopic polarization

Since there is a diffuse transition to relaxor regime, it is possible to measure the remanent ferroelectric polarization hysteresis for intermediate compositions x(Sn)=0.1...0.3 fig. 1.15. Under 10 kV/cm, at room temperature there seems to be a polarization of ∼ 10, 9, 6, 4 µC/cm 2 for the corresponding nominal compositions 0.1; 0.12; 0.15; 0.18 [START_REF] Zhang | Large electrocaloric effect in Ba(T i 1-x Sn x )O 3 ceramics over a broad temperature region[END_REF]. Note that in ref. [START_REF] Zhang | Large electrocaloric effect in Ba(T i 1-x Sn x )O 3 ceramics over a broad temperature region[END_REF], the maximum value of dielectric permittivity is for composition x(Sn)=0.15 against x(Sn)≈0.11 which is a reproducible value from other articles. So the x(Sn)=0.18 might correspond in reality to a lower Sn ratio. Chapter 2

New phase diagram (structure and dielectric/ferroelectric properties)

In this chapter we will describe the phase transitions of our samples depending on chemical composition and on temperature and compare the solid solutions to the pure compounds BaTiO 3 and BaSnO 3 . The following sections will describe the fabrication of our samples and the study of average unit cell and ferroelectricity by X-ray diffraction, transmission electron microscopy, dielectric spectroscopy, and polarization measurement.

Methods of characterization used in this chapter

Solid state reaction synthesis implies mixing the initial chemical components in the shape of solid powders, and heating to high temperatures for chemical reaction to occur. In our case, to obtain BaSn x Ti 1-x O 3 solid solutions, we prepared the mixture according to chemical reaction:

BaCO 3 + (1 -x)T iO 2 + xSnO 2 = BaSn x T i 1-x O 3 + CO 2 (gas) (2.1)
The speed of solid state reaction and the homogenisation of products during solid state reaction are limited by the size of the powder particles and temperature. In fact, it was shown that there are several intermediate steps to the process as shown in fig. 2.1 for pure BaSnO 3 . First, BaSnO 3 crust forms on SnO 2 . On second step, the process is diffusion-guided, since the Sn and O atoms should be passing through the BaSnO 3 layer which is formed already, and so the Sn deficient phase might be forming on top of the grain. Finally, after sufficient homogenisation at high temperatures and during sufficient time, a BaSnO 3 particle is formed. Despite normally the processing conditions favor phase homogeneity, it is important to understand that some small difference in chemical composition or the amount of defects are possible between the grain bulk and the surface. The state of the grain surface can be further changed by annealing at 500 • C, since this is the temperature at which depending on the atmosphere either the loss of oxygen or the oxygen vacancy compensation happens [START_REF] Ibtessam | Oxygen stoichiometry, conductivity and gas sensing properties of BaSnO 3[END_REF].

The compositions of BaSn x Ti 1-x O 3 chosen throughout the phase diagram were x = 0, 0.1, 0.2, 0.4, 0.5, 0.6, 0.8, 0.9, 1. We took as initial components BaCO 3 (STREM 99,9% ref 56-1020 lot 21556500), TiO 2 (99% prolabo 20732,298 lot 80170), SnO 2 (99,9 % alfa products 87779 lot 00090410).

The following procedure was used to use the proper homogeneity: (a) mixing in a mortar, and then in ethanol with magnetic mixing (b) drying at 80 • C, mixing in a mortar by hand (c) calcination at 800 • C, mixing in a mortar (d) calcination at 1280 • C, mixing in a mortar Some samples which will be mentioned are studied after this step. For some other methods, however, additional steps of fabrication are needed, as follows: (e) making pellets with PVA as a binding agent and sintering at 1280-1400 • C, polishing the pellets with SiC papers of grade P800 (26 µm) and P1200 (15.3 µm) (f) grinding the pellets and annealing the powders in order to remove the mechanical stresses at 500 • C.

Details of XRD measurement in this study

The X-ray diffraction (XRD) was performed on Bruker D2 phaser diffractometer in Cu Kα 1,2 X-rays on finely ground and annealed powders. For solid solution samples, the acquisition times per step were of 10 seconds for 2Θ=20-35 • , 30 seconds for 2Θ=35-60 • , 55 seconds for 60-120 • with a step of 0.02 • . After the normalization of acquisition time and standard deviation, Jana2006

RESULTS

software for Rietveld refinement was used to obtain the composition and lattice parameters.

Dielectric spectroscopy measurement

The measurement was made on two kinds of ceramic pellets, sintered without any binding agent and with PVA. The silver paste contacts were deposited on the former ones, and the Cr/Au sputtering was performed on the second series. Note that for Sn-rich compositions around x(Sn)=0.8-1 the dark-colored layer of Cr-containing solid solution was formed at the contact interface with the sample, which agrees with Cr solubility in the perovskite structure, including the Sn-containing ones [START_REF] Muralidharan | Room temperature ferromagnetism in Cr doped SrSnO 3 perovskite system[END_REF]. Therefore, x(Sn)=0.8 with golden contacts was not measured. The measurement was performed in the cryofurnace in the temperature range 78-450 K, the temperature controlled with the help of PT100 probe. The impedancemeter HP4294 was used.

Results

Microstructure from scanning electron microscopy

Scanning electron microscopy was performed on the powders after chemical synthesis fig. 2.2 and on the pellets sintered with PVA binding agent fig. 2.3 using the microscope model Leo Gemini 1530 with field emission gun and in high resolution mode. The grains have faceted shape and even show the growth spirals fig. 2.2d, which in general shows that they are well crystalline. The grain size varies within one composition, but on average the value is 1-2 µm throughout the compositional series. The larger grains occur rarely with longer dimension reaching about 10 µm fig. 2.2c.

When sintered with PVA, high densities ρ pellet are reached (92-95 %) as determined from weighting it in water and in air:

ρ pellet = m air ρ water m air -m water (2.2)
Correspondingly, during the sintering process the grain size increases to 5-10 µm in x(Sn)=0 and 0.2, and to 20 µm for x(Sn)=0.5.

Room temperature structure of compositional series

The X-ray diffraction in fig. 2.4 shows characteristic patterns of pure perovskite compounds. No parasitic peaks are found with the laboratory source. The intensity of the peaks evolves gradually throughout all compositions. The XRD peak at 45.5 • (fig. 2.5a) consists of two components for BaTiO 3 in P 4mm space group, (200) and (002). For x(Sn)=0.1, the two components merge into one, but the shape of the peak is very wide hinting that the distortion is still present. For the rest of the compositions, the peak is quasicubic. Spectra were

CHAPTER 2. NEW PHASE DIAGRAM (STRUCTURE AND DIELECTRIC/FERROELECTRIC PROPERTIES)

analysed by LeBail fit to determine the unit cell volume (fig.

Dielectric spectroscopy

For the analysis of the dielectric spectroscopy data, we have applied the precedently described concepts of Vogel-Fulcher temperature T V F , maximum temperature Tm, temperature of deviation from quadratic law T Q and shift to Curie-Weiss law, Curie-Weiss temperature T CW , and temperature of deviation from Curie-Weiss law which T d section 1.4.

Here, we analyse the dielectric properties of the relaxor compositions in the BaSn x Ti 1-x O 3 system for x(Sn)>0.3, as well as verify the properties of x(Sn)<0.3 which have been studied before [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF][START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF].

For all the compositions in fig. 2.6 we see the single dielectric permittivity peak for single frequency. In x(Sn)=0.1 and 0.2 there in no frequency dependence of the peak, the compositions with higher Sn ratio and up to x(Sn)=0.8 all show the relaxor peak shift. The corresponding T m of dielectric permittivity at 1 MHz is given in The T m decreases first linearly for compositions until x(Sn)=0.4, and then for the remaining two compositions stays very close to 100 K. From fig. 2.7 it is visible that on frequency the T m decreases with approximately similar rate for x(Sn)=0.4 and 0.8 and faster for x(Sn)=0.5. The higher the Sn ratio, the stronger is the shift of the imaginary part ε" to lower temperatures from T m. According to this, the T V F should be low. The results of fit by Vogel-Fucher law are shown in fig. 2.7, and T V F among other results of fitting can be found in fig. 2.10.

Figure 2.8 illustrates the fit of 1/ε ′ by Curie-Weiss and quadratic laws for x(Sn)=0.4 and the determination of T d and T Q correspondingly. Note that for x(Sn)=0.4 the Curie-Weiss law well fits the data to the highest measured temperatures, while for the further compositions x(Sn)=0.5 and 0.8 in fig. 2.8 there is a deviation at high temperatures, which normally should not occur unless some dipoles of non-ferroelectric nature are present [START_REF] Maiti | Structure-Property Phase Diagram of BaZr x T i 1-x O 3 System[END_REF]. In Sn-rich samples those could be the charged defects. The temperature above which The T m and T V F decrease non-linearly. It is as low as 30.8 K and 23.6 K for x(Sn)=0.4 and 0.5, and it shifts to negative values for x(Sn)=0.8. This means that there is no polar glass state for any temperature in that composition, that the low-temperature behaviour is dominated by quantum fluctuations and is characteristic for chemical compositions in BaTiO 3 -based relaxors above the percolation point of Ti [START_REF] Maiti | Structure-Property Phase Diagram of BaZr x T i 1-x O 3 System[END_REF].

RESULTS

Figure 2.11-fig. 2.15 represent the imaginary part of dielectric permittivity, which is responsible for losses, or energy absorbed as a result of some relaxation processes. For x(Sn)=0.1 there are two relaxations in mid-frequency region(fig. 2.11). The low-frequency relaxation in the sample sintered without PVA peaks at f max =10 4 Hz and T=310 K, the high-frequency relaxation peaks at f max =10 5 Hz and T=350 K. The region 310-350 K is where T m and T CW occurs. For the pellet sintered with PVA the difference in f max between the two peaks is larger (6.9 kHz and ∼ 2 MHz), but the difference in temperature is smaller (309 K and 315 K). The presence of two different relaxations is in agreement with [START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF] and the coexistence of ferroelectric domain wall relaxation and PNR breathing mode. The relaxation characteristics might be changing between two samples because the first one has higher porosity, which is accompanied either by formation of oxygen vacancies or worse homogenisation). Note that the maximum of the loss data shifts to lower temperatures for lower frequencies. In composition x(Sn)=0.2 (fig. 2.12), to the contrary from the previous case, the low-temperature relaxation happens at higher frequencies. For the sample without PVA, on heating the first relaxation, with maximum value higher than the frequency range of experiment, is the strongest of all relaxation processes in this sample and happens at 210 K. In the region of temperatures 240-260 K the second relaxation appears with maximum below studied frequency range, and then fades at higher temperatures. In the sample with PVA, there is a similar sequence of relaxations. First one peaks at T=210 K f max =10 6 Hz, slightly larger than in x(Sn)=0.1. Second one peaks at very low frequencies at T=245 K. The second of two peaks seems to correspond to T m, but the origin of the first one is questionable.

This different behaviour of the dielectric relaxation may be due to phase DIELECTRIC/FERROELECTRIC PROPERTIES) coexistence, either extrinsic or due to diffuse phase transition. This topic is detailed in section section 2.2.5 and section 4.2.1.3.

In the pellet of x(Sn)=0.4 (fig. 2.13), sintered with PVA, the wide peak appears at 97 K and f max =1.1•10 6 Hz, which is just below the T m=118 K. It is visible that there is one more peak at even higher frequencies, which probably belongs to reorientation of dipoles in PNRs [START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF].

Overall, the behaviour of relaxation in x(Sn)=0.4 and 0.5 is very similar, together with that of x(Sn)=0.8. The first difference to notice is that in the latter sample the peak seems to be shifted to large frequencies. In x(Sn)=0.5 for both samples the maximum of relaxation lies at 778.2 kHz and 86 K. For x(Sn)=0.8 the temperature range of measurement with liquid nitrogen is above the maximum of relaxation, so the decrease in intensity of the peak is seen.

In pellets with x(Sn)=0.1, 0.5 with PVA, and 0.8 the large ε" at low temperatures and low frequencies is probably related to conductivity contribution or contact polarization. Further experiments are needed to determine the relaxation behaviour processes of these compositions.

Transmission electron microscopy

A Transmission Electron Microscope FEI Titan operated at 300 keV was used. The sample was prepared by Focused Ion Beam.

All the previous HRTEM studies section 1.3 on BaSn x Ti 1-x O 3 were performed on compositions from ferroelectric or diffuse phase transition regions. In fig. 2.16 we show our study on x(Sn)=0.4 which is a pure relaxor composi- In fig. 2.16a the TEM image is shown, and in fig. 2.16b -the corresponding crystallographic projection. The darkest regions in the image are related to Ba atoms, and the points in between -to Sn or Ti. The contrast in plane of the

RESULTS

29

figure comes from a sum of the atomic positions in atomic columns through the depth of the sample (< 30 nm). The indexing by color depth was performed in ImageJ software, so that atomic positions, marked by bright data markers, are taken at the point with the highest probability to find an atom within each column.

According to model of fig. 2.16b, within the plane of the figure Ba atoms are situated in horizontal lines, and Sn/Ti atoms are located in the middle between Ba lines. The displacement of Sn/Ti atoms along <111> crystallographic axis is along the vertical of the figure.

In fig. 2.16a, the atoms of Ba are less displaced than Sn/Ti, so we assume Ba displacement as zero. Based on the model of fig. 2.16b, the displacement of Sn/Ti atoms along the <111> axis is calculated as difference between the positions of corresponding Sn/Ti atom data markers in fig. 2.16a and 0.5d Ba-Ba .

The B-site atomic positions are plotted in colormap of fig. 2.16c. The atoms are displaced from their standard positions by the groups of 4-5 unit cells with the displacement stronger in the center. The PNRs seem to be of smaller size but with larger distortions. While in Ti-rich compositions of fig. 1.11 the displacements were reaching maximum 20 pm, in this relaxor compositions the < 111 > displacements reach 30-40 pm and even more. According to this, the trend of increasing displacements which was seen in x(Sn)=0.16...0.25 (table 1.1) continues deeper into the phase diagram, and the presence of rhombohedral distortions is confirmed.

It is interesting to note that the distortions with the lifetime sufficiently high to be detected in TEM exist in x(Sn)=0.4 above the T d (for which the deviation from Curie-Weiss law was taken with large precision). We speculate that there could be one more critical temperature T * > T d corresponding to full disappearance of any kind of static or dynamic polar correlations.

Temperature dependent laboratory X-ray diffraction studies

We studied our samples in temperature by acquisition of three XRD peaks, corresponding to (200), [START_REF] Chaves | Coupled modes with A 1 symmetry in tetragonal BaT iO 3[END_REF], and (111) crystallographic planes. These three peaks correspond to three directions of Ti atom off-centering in T, O, and R phases. The quality of acquisition permits to estimate the phase symmetry and to find the temperatures of possible phase transitions, although the absorption of Cu K β X-rays is high in BaSn x Ti 1-x O 3 , so that only the surface grains are analysed (90% of intensity is lost at the depth of 6-7 grains).

As a reference, the three peaks for BaTiO 3 are shown in fig. 2.17. Phase transitions happen at temperatures roughly corresponding to ones from references. Slight deviations can result from sample history (domain state) or grain size. The phase transition R-O is seen from ( 110) and (200) peaks at T=195-210 K. Despite the slow heating speed (∼ 0.5 K/min), the phase transition occurs not simultaneously, but within a gap of 10 K. Typically, the

CHAPTER 2. NEW PHASE DIAGRAM (STRUCTURE AND DIELECTRIC/FERROELECTRIC PROPERTIES)

28.2 28.5 upper temperature 210 K is higher than in single crystals, but is in agreement with [START_REF] Ekhard | Elastic excitations in BaT iO 3 single crystals and ceramics: Mobile domain boundaries and polar nanoregions observed by resonant ultrasonic spectroscopy[END_REF]. The next phase transition, O-T, is seen at expected temperature 285-290 K for all peaks. Finally, the T-C phase transition lies in the widest temperature interval of 370-405 K, where the 2Θ of peaks of ( 110) and especially (200) varies according to different linear dependence than at temperatures below or above. There is also a shift of peak maximum to larger 2Θ values (smaller lattice parameters) at T=470 K, where the static Ti displacements vanish [START_REF] Dul'kin | Relaxor-like behavior of BaT iO 3 crystals from acoustic emission study[END_REF], and which is close to depolarization temperature T d, determined from dielectric spectroscopy (see section 1.2.1 and section 1.4). For x(Sn)=0.2 (fig. 2.18), which corresponds to diffuse phase transition with coexistence of relaxor and ferroelectric phases, all the three crystallographic phase transitions, remanent from from BaTiO 3 , disappear. However, on heating there is possibly a change of slope from increasing to nearly constant in d 200 close to 200 K, which is close to T V F in fig. 1.13. Additionally, there is a shift to smaller value in d 110 peak at the temperature which appears to be the T d=440-460 K. It is possible to speculate that since the [START_REF] Chaves | Coupled modes with A 1 symmetry in tetragonal BaT iO 3[END_REF] peak is most sensitive to T d, the major type of distortions in PNRs are orthorhombic.

RESULTS

28.2

28.4 ), which is a truly relaxor composition, more changes are visible at 180-200 K, 260-280 K, and 380-400 K. The first region corresponds to T d=200 K as determined from dielectric spectroscopy (fig. 2.9). The d 111 starts increasing after passing through T d=200K. The further deviation present at 260-280 K, and at even higher temperatures the deviation from Curie-Weiss law happens at 380-400 K. This means that more than one process is involved above T d=200 K. At 260-280 K the d 110 and d 200 start to increase similarly to d 111 at T d=200 K. If several kinds of distortions (or phases) coexist, this temperature could correspond to disappearance of static distortions of the second type. Above T=380-400 K d 110 and d 111 start decreasing similarly to BaTiO 3 , where there is also a sharp decrease in d 110 and d 111 at T d. The deviation reaches 1.2 • 10 -5 at T x =366 K, but appears well visible by eye at 400 K (fig. 2.9a). Why the deviation happens at the temperature above the disappearance of distortions of both types is not fully clear. However, we can consider that this is related to appearance of some factor which is not related to ferroelectricity. This could be for instance the activation of defect sites, typically oxygen vacancies, coming from the BaSnO 3 sublattice.

CHAPTER 2. NEW PHASE DIAGRAM (STRUCTURE AND DIELECTRIC/FERROELECTRIC PROPERTIES)

28.0 28.1 In x(Sn)=0.8 (fig. 2.20) the changes happening to d 110 remind very much ones from x(Sn)=0.5, just the temperatures are different. The values of two high-temperature regions in this sample shift 40 K higher to give T 1 =300 K and T 2 =420 K. These values do not anymore coincide with the T d or T x which are found at much lower temperatures. The coupling between crystallographic structure and the polar order probably disappears because this composition is above the percolation limit of Ti atoms, and dielectric properties (Ti sublattice) and defect properties (Sn sublattice) are not related.

The changes of unit cell volume which are not related to ferroelectricity are also visible in BaSnO

Conclusions

The samples of BaSn x Ti 1-x O 3 are synthesized. The laboratory Xray diffraction does not show the presence of any impurities. At room temperature, the peak shape is quasicubic or cubic for all the compositions except pure BaTiO 3 . With Sn ratio increase, the unit cell parameter varies linearly.

According to our dielectric spectroscopy data combined with previous research, the phase diagram can be separated into 1) ferroelectric phase (below x(Sn)=∼0.13 %), diffuse phase transition with possible phase coexistence (x(Sn)=0.13-0.3), relaxor phase starting from x(Sn)=0.3 and further compositions until x(Sn)=0.8.

The properties vary non-linearly in relaxor compositions, including the T d, T m, T V F decreasing exponentially on x(Sn). The compositions with x(Sn)>0.5 never transform to a polar glass since T CW is negative. For Sn-rich compositions there is a high-temperature deviation from the Curie-Weiss law T x, which we attribute to the activation of some nonferroelectric mechanisms of interaction with the electric field, such as defect dipoles. The T x was not discovered for other compositions because of an upper limitation of the measurement range, and whether it exists is an opened question for more experiments.

We evidence through HRTEM in x(Sn)=0.4 the PNRs with Ti displacements along the <111> crystallographic directions, despite this is at room temperature T > T d. The full disappearance of polar correlations probably happens at higher temperatures.

The characteristic temperatures from laboratory X-ray diffraction are compared with ones from dielectric spectroscopy in fig. 2.22. With one exception for x(Sn)=0.5, the temperature values from XRD seem to correspond to the ones from dielectric spectroscopy below x(Sn)≈0.7. Above this composition, the temperatures do not coincide, as the ferroelectric (Ti) and defect (Sn) properties are probably not coupled, if this is above the possible percolation limit of Ti atom.

Optical properties

Optical Properties: Introduction

In perovskite compounds Ba 2+ Ti 4+ O 2- 3 and Ba 2+ Sn 4+ O 2- 3 the B-site atoms have the same valence. Due to this we don't expect any significant contents of compensating defects like V O , which can potentially cause the decrease of efficiency in photovoltaic materials.

One of the parent compounds for this solid solution, Barium stannate BaSnO 3 is known as a promising candidate to transparent conductive oxides industry, because the electronic structure of Sn atom assures the increased mobility of electrons in the conduction band compared to BaTiO 3 . In detail, neutral B-site atoms in the two parent compounds of the solid solution are in configuration Ti 4s 2 3d 2 and Sn 5s 2 5p 2 4d 10 . After forming the chemical bonding, the conduction band minimum is formed by Ti 3d 0 and Sn 5s 0 5p 0 , correspondingly. The s and p orbitals are known to be less localized in space than d-orbitals, providing wider conduction band with larger energy dispersion. As a result, the electron effective mass is as low as m * ≈ 0.469m 0 in BaSnO 3 [START_REF] Bouhemadou | Structural, elastic, electronic and thermal properties of the cubic perovskite-type BaSnO 3[END_REF], compared to m * ≈ 2.8m 0 in BaTiO 3 [START_REF] Dong | Electronic structures and optical dielectric functions of room temperature phases of SrT iO 3 and BaT iO 3[END_REF].

The band gaps of the two compounds are very similar, 3.2 eV for BaSnO 3 and 3.27 eV for BaTiO 3 . Whether the band gap of BaSnO 3 is direct or indirect is under discussion. As for BaTiO 3 , both in tetragonal and cubic phases indirect band gap R -Γ is very close in energy to the direct band gap Γ -Γ so it is impossible to discriminate between the two by experimental techniques [START_REF] Sanna | Barium titanate ground-and excited-state properties from first-principles calculations[END_REF][START_REF] Qi | BaT iO 3 : Energy, geometrical and electronic structure, relationship between optical constant and density from first-principles calculations[END_REF][START_REF] Si Shablaev | Band structure of oxygen-octahedral ferroelectric BaT iO 3 , SrT iO 3 and KT aO 3 derived from two-photon spectroscopy data[END_REF][START_REF] Khenata | First-principle calculations of structural, electronic and optical properties of BaT iO 3 and BaZrO 3 under hydrostatic pressure[END_REF][START_REF] Dong | Electronic structures and optical dielectric functions of room temperature phases of SrT iO 3 and BaT iO 3[END_REF]. For BaSnO 3 there is an agreement in theoretical works, as well, that the indirect band gap has lower energy than the direct one [START_REF] David | Defect engineering of BaSnO 3 for high-performance transparent conducting oxide applications[END_REF][START_REF] Bouhemadou | Structural, elastic, electronic and thermal properties of the cubic perovskite-type BaSnO 3[END_REF]. Nevertheless, few existing experimental works do not reach the same conclusion, whether by UV-visible-NIR absorption spectroscopy or by Angular resolved photoelectron emission spectroscopy (ARPES) [START_REF] Soo | Evidence for indirect band gap in BaSnO 3 using angle-resolved photoemission spectroscopy[END_REF]. Most probably, the ambiguous results of ARPES are caused by the participation of defect levels in chemical binding [START_REF] Soo | Evidence for indirect band gap in BaSnO 3 using angle-resolved photoemission spectroscopy[END_REF]. Moreover, local structure imperfections or defects could be the reason why in Raman spectroscopy the modes of orthorhombic phase 38 CHAPTER 3. OPTICAL PROPERTIES P bnm (P nma) [START_REF] Bevillon | Unstable polar mode and minimum of the dielectric constant in cubic BaSnO 3 under hydrostatic pressure[END_REF][START_REF] Stanislavchuk | Electronic band structure and optical phonons of BaSnO 3 and Ba 0.97 La 0.03 SnO 3 single crystals: Theory and experiment[END_REF] are detected while no signal should exist for the cubic P m 3m phase. It was shown that P m 3m has only slightly lower energy than the orthorhombic phase P bnm (P nma) [START_REF] Stanislavchuk | Electronic band structure and optical phonons of BaSnO 3 and Ba 0.97 La 0.03 SnO 3 single crystals: Theory and experiment[END_REF]. In such case, the diffuse component of reflection (not the specular one) is selectively collected by the specially optimized hemispherical mirrors. Assuming that the collected component is first absorbed, and then reemitted into space, and that particle size is much larger than the light wavelength d ≫ λ, for the sample surrounded by air it is possible to analyse the collected data using the Kubelka-Munk formula [START_REF] Kubelka | An article on optics of paint layers[END_REF]:

Band gap

F KM = K/S = (1 -R) 2 /2R 2 (3.1)
with F KM -Kubelka-Munk function, which is the analogy of absorption coefficient K corrected for scattering S, R -unity fraction of diffusely reflected light.

Having F KM , we recalculate it according to Tauc formula for determining the band gap Eg from the fit of the linear region close to the absorption edge [START_REF] Tauc | Optical properties and electronic structure of amorphous germanium[END_REF]:

(hνF KM ) 2 = A(hν -Eg) (3.2)
with h -Planck constant, ν -frequency, E -energy.

BAND GAP

39

It is possible to choose different assumption on the nature of the band gap, including direct allowed (n=1/2), direct forbidden (n=3/2), indirect allowed(n=2), indirect forbidden (n=3) band gaps [START_REF] Tauc | Optical properties and electronic structure of amorphous germanium[END_REF].

Since for solid solutions the nature of the absorption edge is not known, we checked all the four possible assumptions. In solid solutions, there is a second peak appearing at 5.25 eV, which is growing with increase in Sn content. In x(Sn) 0.8 it dominates the spectrum and is the only peak in the high-energy part of the spectrum in pure BaSnO 3 . Hence, it seems that energy levels, corresponding to high-energy absorption, do not hybridize or mix in between them. To the contrary, the lower-energy levels cannot be separated into Ti-and Sn-related contributions, probably consisting of multiple widened components, and possibly with some hybridization happening in between them. This group of peaks evolves in three steps, x(Sn) < 0.2, 0.2 x(Sn) 0.6, and x(Sn) > 0.8, corresponding to room-temperature regions of ferroelectricity, relaxor behavior, and the region dominated by BaSnO 3 matrix as will be shown in Chapter 4.

Results of UV-Visible-NIR spectroscopy

The Tauc plot was performed under different assumptions of the band gap nature to verify the presence of any additional absorption edges. There are no additional absorption features appearing, thus we consider the band gap as a direct allowed one, fig. Existence of two distinct trends must be related to domination of Ti or Sn levels, as seen in the high-energy region of the absorption coefficient. One possibility of why the band gap increases where Ti atoms dominate (according to the high-energy absorption region) is that the chemical stress is imposed by Sn atoms on Ti matrix. It was shown in calculations that Sn-containing perovskites are more sensitive to strain than titanates [START_REF] Li | Strain sensitivity of band gaps of Sn-containing semiconductors[END_REF]. We also evidence faster evolution of the band gap on the Sn-rich side of the diagram. In [START_REF] Li | Strain sensitivity of band gaps of Sn-containing semiconductors[END_REF], the band gap of stannates increases on hydrostatic compressive strain, however the band gap of BaTiO 3 is supposed to decrease also. Therefore, other factors probably contribute, such as the presence of polar nano-regions in the relaxor phase and the nature of the distortion inside them.

From TEM studies of x(Sn)=0.2 in the relaxor phase [START_REF] Shi | Why Sn doping significantly enhances the dielectric properties of Ba(T i 1-x Sn x )O 3[END_REF], and multiple experimental and theoretical studies of similar relaxor system Ba(Zr,Ti)O 3 [START_REF] Jeong | Ferroelectricrelaxor crossover in BaT i 1-x Zr x O 3 studied using neutron total scattering measurements and reverse Monte Carlo modeling[END_REF][START_REF] Laulhé | Random local strain effects in homovalent-substituted relaxor ferroelectrics: a first-principles study of BaT i 0.74 Zr 0.26 O 3[END_REF][START_REF] Levin | Local structure of Ba(T i, Zr)O 3 perovskitelike solid solutions and its relation to the band-gap behavior[END_REF], one can suppose that a complicated pattern of local distortions can occur in relaxor polar nanoregions (PNR), combining local distortions of tetragonal, orthorhombic, or rhombohedral types [START_REF] Jeong | Ferroelectricrelaxor crossover in BaT i 1-x Zr x O 3 studied using neutron total scattering measurements and reverse Monte Carlo modeling[END_REF]. As well, monoclinic local distortions are possible, since it was claimed to exist in pure BaTiO 3 at the phase transition between the orthorhombic and tetragonal phases [START_REF] Ch | Tetragonal-Orthorhombic Phase Transition in Barium Titanate via Monoclinic MC-Type Symmetry[END_REF]. Off- , which is known to decrease the overlap of the O 2p and B-site (Ti 3d or Sn 5s 5p) orbitals. This decreases the width of conduction band, mainly making its lower region more anti-bonding and less non-bonding, which results in an increase in the energy of the CBM and the band gap [START_REF] Wang | Band gap engineering strategy via polarization rotation in perovskite ferroelectrics[END_REF][START_REF] Mizoguchi | Probing the Electronic Structures of Ternary Perovskite and Pyrochlore Oxides Containing Sn 4+ or Sb 5+[END_REF]. Moreover, PNRs, at least in x(Sn)=0.2, correspond to Ti-rich regions distributed inside a Sn-rich matrix [START_REF] Shi | Why Sn doping significantly enhances the dielectric properties of Ba(T i 1-x Sn x )O 3[END_REF]. It can be thought as coherent particles incorporated into a matrix with slightly larger lattice parameter, thus there would be tensile stress applied on the PNRs. For rhombohedral distortions, tensile stress can add up to the effect of band gap increase [START_REF] Seo | First-principles investigations on polytypes of BaT iO 3 : Hybrid calculations and pressure dependences[END_REF]. Finally, it is under question if the nanoscopic size of PNR ( 2nm) can contribute with effects of quantum confinement like it happens in nanoparticles of BaTiO 3 or SrTiO 3 powders [START_REF] Suzuki | Optical band gap of barium titanate nanoparticles prepared by rf-plasma chemical vapor deposition[END_REF][START_REF] Yuan | Strain induced tetragonal SrT iO 3 nanoparticles at room temperature[END_REF]. It is always possible to assume that the band gap can increase due to so-called Burstein-Moss effect. Essentially, in this case Sn substitution for Ti would create the donor defects which would result in filling of the CB, so that the measured band gap would be Eg ′ = Eg + E f illed . However, in this case the conductivity is supposed to increase, which is not the

Types of disorder

As can be seen in fig. 3.3, at the low-energy limit the absorption does not start abruptly, but has a non-linear shape. Such an absorption tail most often has an exponential shape, in this case it is called an Urbach tail. Its shape and width depend a lot on imperfections of the crystalline lattice. In relaxor

CHEMICAL DISORDER-DRIVEN ABSORPTION EDGE

43 systems, this is a particularly important parameter to be analysed, since it is straightly connected to physical properties.

Studies of absorption tail started as early as 1953, when F. Urbach studied the sensitivity of photographic emulsions of multiple semiconductors (including the wide-gap ones). He noticed that low-energy part could be described closely by e 1/kT [START_REF] Urbach | The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids[END_REF]. Later studies, for instance on amorphous hydrogen-doped silicon [START_REF] Sa | Urbach tails and disorder[END_REF] concluded that any kind of disorder contributes to widen, or blur, the allowed density of states ρ of the band gap edges according to the law lnρ = E n , where n can be different depending on the kind of disorder.

In general, there can be structural static type of disorder Eu S (due to immobile defects), or the compositional disorder Eu Comp in solid solutions due to distribution of chemically substituted atoms, and temperature-related disorder Eu T [START_REF] Kranjčec | Urbach rule and disordering processes in Cu 6 P (S 1-x Se x ) 5 Br 1-y I y superionic conductors[END_REF]:

Eu = Eu T + Eu S + Eu Comp (3.
3)

The latter one Eu T most often results from thermal lattice vibrations (phonons), but is also affected by disorder phase transformations characterized by different dynamics of ions or defects:

Eu T = Eu ph + Eu dyn (3.4)
The thermal disorder is described by the formula

Eu ph = Eu 0 + Eu 1 1 e (Θ E /T ) -1 , (3.5)
with Eu 0 , Eu 1 , Θ E -constants. It is suggested that the thermal mechanism occurs mainly due to valence band electron coupling to phonons [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF]. Another approach tells that the exciton at light absorption is momentarily trapped at the vibrational levels created by phonons [START_REF] Kranjčec | Urbach rule and disordering processes in Cu 6 P (S 1-x Se x ) 5 Br 1-y I y superionic conductors[END_REF] (self-trapped ST exciton). This point of view is supported by the fact that the Urbach tail also appears in photoluminescence spectra which represent the recombination of ST exciton [START_REF] Pauporté | Electrodeposition of semiconductors for optoelectronic devices: results on zinc oxide[END_REF]. The phonons participating in the process are mainly those involving the electric field change, the longitudinal optical LO branch, where the Ti-O bond vibrates parallel to the polarization direction, so that overlap of O 2p and Ti 3d orbitals of π type is modulated [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF]. Note, same effect of electric field modulation can be caused by fast transverse acoustic phonons, which result in a so-called piezoelectric absorption edge [START_REF] Dow | Urbach's rule[END_REF]. Moreover, if this effect of changing the polarization becomes static, for instance in the phase transition from cubic (paraelectric) to tetragonal (ferroelectric) BaTiO 3 , then the band gap itself is modified [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF]. The fact that the band gap varies according to similar law as the Raman shift was pointed out by [START_REF] Zhang | Influence of Fe ions in characteristics and optical properties of mesoporous titanium oxide thin films[END_REF].

The second factor in temperature changes of Eu is the possibility of disorder phase transformations. Those are characteristic to materials with high defect concentrations, so that there are unique favorable defect positions and/or 44 CHAPTER 3. OPTICAL PROPERTIES defect mobility in the lattice of each phase. The different favorable states are separated at a critical temperature T c. The state above T c is called superionic state and is distinguished by high ionic conductivity, as for example in Cu 6 P(S,Se) 5 (I,Br) [START_REF] Chadwick | High temperature transport in fluorites[END_REF]. The characteristic large changes of Eu happen also at paraelectric to ferroelectric phase transitions, as well as at low temperature when the dynamics of the system becomes frozen, as shown in ferroelectric SbSI (fig. 3.6) [START_REF] Studenyak | On the Urbach rule in SbSI ferroelectric crystal[END_REF]. Similar shapes of E U (T) dependences were observed [START_REF] Paillard | Photo-induced effects in multiferroics[END_REF] in perovskite relaxor solid solutions [Pb(Ni Structural disorder is illustrated in the simplest way by the fact that Urbach energy decreases from amorphous to polycrystalline thin films to single crystals of semiconductors. In SnO 2 , the corresponding values are 440 meV, 230 meV, 37 meV [START_REF] Pauporté | Electrodeposition of semiconductors for optoelectronic devices: results on zinc oxide[END_REF]. Similarly, there is a trend of Eu decrease for amorphous thin films under annealing, since ordering of the structure happens. This trend was demonstrated in amorphous silicon [START_REF] Cody | Disorder and the optical-absorption edge of hydrogenated amorphous silicon[END_REF], as well as in SnO 2 [START_REF] Pauporté | Electrodeposition of semiconductors for optoelectronic devices: results on zinc oxide[END_REF]. It is interesting that for amorphous semiconductors, there is a linear dependence of band gap Eg on Urbach energy Eu, and correspondingly on the structural disorder [START_REF] Cody | Disorder and the optical-absorption edge of hydrogenated amorphous silicon[END_REF][START_REF] Pauporté | Electrodeposition of semiconductors for optoelectronic devices: results on zinc oxide[END_REF].

1/3 Nb 2/3 )O 3 ] 1-x -[PbTiO 3 ] x (PNN- PT).
The compositional contribution to the overall disorder parameter is known to follow in many materials the equation:

Eu Comp = Ax(1 -x), (3.6)
where x is the amount of chemical substitution [START_REF] Kranjčec | Urbach rule and disordering processes in Cu 6 P (S 1-x Se x ) 5 Br 1-y I y superionic conductors[END_REF].

All the three contributions to disorder were disentangled one from each other and analysed quantitatively in Cu 6 P(S,Se) 5 (I,Br) solid solutions fig. For intermediate compositions of solid solutions, Eu Comp contributes to increase Eu, Eu T decreases or stays constant, w X =Eu S due to the possibility of defect formation.

Without knowing the predominant reason for disorder, one can find the Eu value according to equations

α = α 0 e E Eu (3.7) lnα = 1 Eu E + lnα 0 (3.8)
with α -F KM in our case.

In case of structural defects, the Urbach energy Eu can be understood in terms of trapped defect states in the band gap below the conduction band minimum or above the valence band maximum [START_REF] Bai | Size and doping effect on the structure, transitions and optical properties of multiferroic BiF eO 3 particles for photocatalytic applications[END_REF]. In BiFeO 3 nanoparticles [START_REF] Bai | Size and doping effect on the structure, transitions and optical properties of multiferroic BiF eO 3 particles for photocatalytic applications[END_REF] Eu describes the properties of the particle skin layer. As the size varies, the surface strain and the polarization state changes, the defect energy is shifted, so the Eu value is size-dependent. In addition, it should reflect the sample history, such as processing and annealing atmosphere which influence the defect states. For both pure parent compounds, there is a single linear region of the plot, with no absorption below. For intermediate compositions, there is an additional shoulder at the lower-energy side. This shoulder is present for x(Sn)=0.1 to 0.6, and seems to disappear in x(Sn) 0.8. It is known that the presence of the second linear part of the Urbach plot can point at the coexistence of different phases or different types of disorder, at least in BaTiO 3 close to T c [START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF]. However, here there is no clearly defined linear region. Whether this absorption comes from defect levels inside the band gap, or from coupling to more than one phonon due to multiple kinds of distortions

CHEMICAL DISORDER-DRIVEN ABSORPTION EDGE

47

in PNRs, needs more experimental proofs and discussion.

In fig. 3.9a the fitted Eu values definitely fall into two regimes of disorder. Inside both of them, the data can be fitted with eq. (3.6). The boundary composition between the two regimes, x(Sn)=0.8, is also separating the two regimes for the band gap compositional dependence. Based on this,the band gap evolution is definitely connected to different local environments of the Bsite atoms. To stress this, we plot Eg against Eu in fig. 3.9b. As in case with amorphous SnO 2 and Si in the process of annealing, there is a linear correlation of the band gap to disorder within each of the two regimes separated by x(Sn)=0. Remarkably, the tangent is approximately the same for both regions (12.58 and 13.37), and the Sn-rich region seems to be parallelly shifted towards the higher disorder side. The reason is probably that the Sn matrix promotes the formation of structures with a lot of defects, which is specific for BaSnO 3 and which makes it a good protonic conductor at relatively low temperatures T 300 • C [START_REF] Ibtessam | Oxygen stoichiometry, conductivity and gas sensing properties of BaSnO 3[END_REF][START_REF] Wang | Synthesis and characterisation of acceptor-doped BaSnO 3 compounds as proton conductors[END_REF]. For both regions, the tangent is of opposite sign than in the temperature-dependent plot on amorphous semiconductors. In that case, lower values of Eu correspond to higher annealing temperatures, less disorder and defects, so larger band gap. In our case, larger disorder Eu corresponds to larger band gap Eg, demonstrating the clear connection between the two. The reason is probably connected to the nature of the PNR and will be explained later on. For BaTiO 3 , we are capable to deduce the non-linear temperature dependence the T c for T-C phase transformation from Eg, and the correlation of Eu with the different structural transitions and dependence on powder sample preparation.

The band gap of BaTiO 3 (fig. 3.10a) has two linear regions, below 398 K and above 550 K, which correspond to the pure tetragonal and cubic phases. In between, there is a non-linear region where the band gap decreases fast close to Tc and slowly closer to 550 K. There is a difference between the curves for sample 1 and sample 2. The linear regions are more visible in sample 1, since sample 2 is obtained by crashing the pellet and without the annealing to relax the possible mechanical strains. In sample 1, the change of Eg is ≈0.05 eV if taken in between the value at 300 K and the continuation of the linear fit of high-temperature data.

Because of different processing of sample 1 and 2, the curve for sample 2 is not the same as the one for sample 1. Both Eg and the disorder Eu are higher. Sample 2 was pressed into the pellet with the binding agent PVA and sintered at 1280 • C. As a result, the grain size could increase, the presence of PVA could change the structure of the grain boundaries, the pressure could introduce the mechanical strain so that the domain structure and twin pattern would alternate. In addition, sample 2 was measured starting from lower temperature T=240 K and heated afterwards. It means that also cooling the sample down to the orthorhombic phase could have altered the twinning state and changed the state of disorder [START_REF] Ekhard | Elastic excitations in BaT iO 3 single crystals and ceramics: Mobile domain boundaries and polar nanoregions observed by resonant ultrasonic spectroscopy[END_REF]. It also is important to note that the UV-visible absorption process is happening close to the surface of grains, so that properties of grain boundaries may contribute significantly. The Urbach tail width Eu for sample 1 (fig. 3.10b) is separated into two linear regions by the T = 420 K just above the T→C phase transition. The linear fit quality is good at 420-500K, but seems worse above 500 K. For sample 2, anomaly is visible at O→T phase transition (285 K), and the curve is nonlinear for temperature of tetragonal phase. The transition to new linear region is visible at 400 K.

TEMPERATURE EVOLUTION OF BAND GAP AND DISORDER-RELATED ABSORPTION

As we showed before on example of compositional disorder in Ba(Sn,Ti)O 3 series, the plot Eg=f(Eu) helps to distinguish more clearly the different regimes of disorder. In fig. 3.11, data points for sample 2 in Eg-Eu coordinates are shifted along the x=y diagonal according to increase of both Eg and Eu.

Sample 1

Three regimes can be seen for sample 1 (fig. 3.11): #2 linear evolution for tetragonal BaTiO 3 , non-linear phase transition region at 380-415 K, #3 low-temperature cubic phase at 415-500 K, #4 high-temperature cubic phase.

Between regions #2 and #3, the band gap non-linear variation at the tetragonal to cubic phase transition was observed for BaTiO 3 [START_REF] Hafid | Absorption spectrum in the near U.V. and electronic structure of pure barium titanate[END_REF][START_REF] Si Shablaev | Band structure of oxygen-octahedral ferroelectric BaT iO 3 , SrT iO 3 and KT aO 3 derived from two-photon spectroscopy data[END_REF][START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF] and for PbTiO 3 [START_REF] Železný | The variation of P bT iO 3 bandgap at ferroelectric phase transition[END_REF]. The origin of non-linearity is not exhaustively explained. First possibility is that it is caused by the coexistence of multiple local energetically favorable states at the same energy, the proportion of one and another being time-dependent close to T c [START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF]. A second possible reason is that the band gap change is related to a non-linear polarization change [START_REF] Železný | The variation of P bT iO 3 bandgap at ferroelectric phase transition[END_REF]. More in detail, there is a coupling between the polarization, phonon modes, and the band gap. Their relationship was studied in ref. [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF], where the absorption was measured on single crystals under polarized light, with Eg (band gap measured with light polarization parallel to the crystal polarization axis) being higher than Eg ⊥ (measured with light polarization perpendicular to the crystal polarization axis). The separation between the two band gaps plotted against P 2 was shown not to disappear fully at the phase transition, but to gradually linearly decrease above T c [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF]. It is proposed according to parallel study of Eu and Eg that both the valence band electrons and the conduction band empty states can be possibly coupled both to crystal polarization and polarization fluctuations in the cubic phase. Several works agree that the phonon participating in the process is most probably not the soft mode Slater A 1 (TO 1 ), but rather one of the LO phonons [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF][START_REF] Hafid | Absorption spectrum in the near U.V. and electronic structure of pure barium titanate[END_REF], which have the wavevectors parallel to the polarization axis. Such phonons can change the chemical bonding by modifying the dynamic hybridization between Ti and O orbitals [START_REF] Xie | The Electronic Structures, Born Effective Charges, and Interatomic Force Constants in BaM O 3 (M= Ti, Zr, Hf, Sn): A Comparative First-Principles Study[END_REF].

The very important question is why we are able to detect two regimes (#3 and #4) by optical methods for a range of temperatures where there is a cubic phase. From studies by multiple methods it is well-known that even above T c ≈400K in BaTiO 3 there are some local polar correlations [START_REF] David | Electric field gradients in BaT iO 3 and KN bO 3[END_REF][START_REF] Krakauer | Dynamic local distortions in KN bO 3[END_REF]. These correlations appear as chain-like tetragonal displacements in the column of Ti-O-Ti [START_REF] Krakauer | Dynamic local distortions in KN bO 3[END_REF]. The size of these correlation regions were determined by different techniques as several unit cells (∼ 30 Å) [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF]. Such regions should be in principle similar by their dielectric response to relaxors. Despite the temperature-dependent dielectric response of BaTiO 3 showing no frequency dependence in Hz-MHz range, it was shown that a relaxation in THz range is frequency-dependent [START_REF] Nuzhnyy | Broadband dielectric response of Ba(Zr, T i)O 3 ceramics: From incipient via relaxor and diffuse up to classical ferroelectric behavior[END_REF][START_REF] Hlinka | Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaT iO 3[END_REF][START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF]. The frequency values are close to the ones of Ti site hopping between eight rhombohedral directions, which is energetically favorable for very short times in all BaTiO 3 phases, including the cubic one [START_REF] David | Electric field gradients in BaT iO 3 and KN bO 3[END_REF].

Acoustic spectroscopy and resonant ultrasonic spectroscopy both showed that in BaTiO 3 there is a temperature above which the polar correlations disappear letting place to a purely cubic phase (T * ≈550 K) [START_REF] Dul'kin | Relaxor-like behavior of BaT iO 3 crystals from acoustic emission study[END_REF][START_REF] Ekhard | Elastic excitations in BaT iO 3 single crystals and ceramics: Mobile domain boundaries and polar nanoregions observed by resonant ultrasonic spectroscopy[END_REF]. Moreover, in the range of temperatures between T * and T c one more critical temperature T ′ =500 K can be defined, which is limiting the dynamic polar correlations for T ′ < T < T * and static polar chains for T c < T < T ′ . Most probably, T ′ can be compared to T d from ref. [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF].

TEMPERATURE EVOLUTION OF BAND GAP AND DISORDER-RELATED ABSORPTION TAIL 51

The same value of the critical temperature was found for the dielectric response of cubic BaTiO 3 . In detail, there is a shoulder in the THz range, whose behaviour changes above 550 K. This shoulder is modelled below 500 K by the oscillator responsible for short-range correlations along the <100> direction, and at higher temperatures it becomes progressively smaller and cannot be described anymore by the same model [START_REF] Ponomareva | Terahertz dielectric response of cubic BaT iO 3[END_REF]. Also from Raman spectroscopy, the low-wavenumber mode is seen to be saturating in frequency (oscillator strength) when the temperature falls below 500-550 K [START_REF] Luspin | Soft mode spectroscopy in barium titanate[END_REF]. Similar, a T * seen by different techniques is related to the behaviour of the oscillator which appears due to coupling between the Slater A 1 (TO 1 ) soft phonon mode and the Debye-like central mode (or order-disorder mode) which is due to eightsite Ti hopping. This mode is found at 100-135 cm -1 (3-4 THz) [START_REF] Hlinka | Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaT iO 3[END_REF][START_REF] Takuya | Terahertz dielectric response of single-domain BaT iO 3 measured by far-infrared spectroscopic ellipsometry[END_REF][START_REF] Shirane | Inelastic Neutron Scattering from Single-Domain BaT iO 3[END_REF][START_REF] Ponomareva | Terahertz dielectric response of cubic BaT iO 3[END_REF] and was also claimed to be related to a width of the disorder-related Urbach tail (0.025-0.075 eV) which is found in titanates.

Above T * =550 K the band gap is linear in our measurement and in agreement with ref. [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF].

Sample 2

For sample 2 (fig. 3.11), region #1 corresponds to the O phase, followed by the Eu anomaly at the phase transition, region #2 for T phase, phase transition 380-420 K, region #3 for cubic phase with polar correlations (420-500 K), and region #4 for cubic phase without polar correlations. Overall, same temperature intervals are kept for corresponding phases as in sample 1. However, the slopes of the corresponding regions differ very much, for reasons which are mentioned before.

The Eu non-continuity at the phase transitions, specifically at T c, was also seen in BaTiO 3 ref. [START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF]. Similar to our case, Eu increases during heating, and decreases during cooling [START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF].

3.4.2 BaSn 0.1 Ti 0.9 O 3 For BaSn 0.1 Ti 0.9 O 3 the analysis of Eg and Eu enables us to determine the temperature of the phase transition between the rhombohedral and the cubic phases as seen in synchrotron diffraction. In addition, we discover the correlation between Eu and peaks of dipole dynamics in dielectric spectroscopy, these peaks being related to ferroelectric and PNR coexistence.

The band gap of BaSn 0.1 Ti 0.9 O 3 behaves non-linearly but without any anomalies fig. 3.12a. The fit can be done using the Bose-Einstein formula:

Eg(T ) = Eg(0) + A(n BE (T ) + 1 2 ) (3.9) n BE (T ) = 1 e T ph T -1 (3.10)
where n BE (T ) is the Bose-Einstein factor which characterizes intensity (occupation of allowed vibrational levels) of the phonon mode with characteristic temperature T ph. The Eu values can be separated into three parts, (a) the sharp increase of disorder between 237 and 270 K, followed by (b) the non-linear region of complicated shape and (c) the linear region above 377 K.

Plotted in Eg-Eu coordinates (fig. 3.12b), the points form four distinct regions. Region #1 corresponds to rhombohedral phase according to [START_REF] Yao | Large piezoelectricity and dielectric permittivity in BaT iO 3 -xBaSnO 3 system: The role of phase coexisting[END_REF]. Then, two non-linear regions follow for temperature spans 300-324 K and 324-377 K. Above 377 K and until 450 K, there is a linear evolution of Eu.

From what is known on dielectric properties of BaSn 0.1 Ti 0.9 O 3 [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF], the T d is around 485 K. Unfortunately, our measurement stops at 450 K, so we are not able to detect the difference between the relaxor ferroelectric phase and the paraelectric one. The fact that there are two regions of disorder transition might be related to the coexistence of two different dielectric relaxation processes in x(Sn)=0.15 and a broad distribution of relaxation times in x(Sn)=0.1 [START_REF] Shvartsman | Diffuse phase transition in BaT i 1-x Sn x O 3 ceramics: An intermediate state between ferroelectric and relaxor behavior[END_REF], where the dielectric losses seem asymmetric, possibly with traces of a second dielectric relaxation.

Moreover, in our data there is a trend to double relaxation in relative permittivity ε in pellets x(Sn)=0.1, which were prepared without the binding agent. There is a first lossy process peak at ≈ 310 K and a second one at 350 K (fig. 2.11). This is similar to 308 K and 348 K in optical data (fig. 3.12b), which are the points where there is a the largest difference between the continuation of the linear fit for #4 and each of the semi-circles of the two disorder processes.

In the sample sintered with PVA (like the one studied here by UV-VIS) there are two dielectric relaxations coexisting at one temperature for a wide

TEMPERATURE EVOLUTION OF BAND GAP AND DISORDER-RELATED ABSORPTION TAIL 53

range of measurements, first peaking at 300 K and second at 315 K fig. 2.11.

The optical measurement results have critical points closer to the sample sintered without PVA, likely because the powder was previously annealed at 500 • C. Thus, both the powder in optic measurements and the porous pellet in dielectric setup have the grain boundaries more exposed to the atmosphere under heating, which could change the defect concentrations. The difference in temperature between the maxima of relaxation intensity is slightly larger in these two samples, which means that the separation in temperature between the two relaxations might depend on defect densities, for instance V O concentration. Turning back to the dielectric spectroscopy results of Chapter 1, the two relaxations in 0.1<x(Sn)<0.175 represent [START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF] ferroelectric and PNR contributions.

BaSn

0.2 Ti 0.8 O 3
For this composition, we are able to detect multiple transition temperatures, which correspond to critical temperatures of polar correlations from dielectric spectroscopy [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF].

For x(Sn)=0.2 both Eg and Eu have an anomaly close to 260-270 K fig. 3.13 . The degree of disorder decreases, and starts to increase again further. Same trend is visible for the band gap. Further, Eg decreases monotonously up to the kink at 552-570 K. The Eu has additional change of slope at 324 K, and a kink close to 493-500 K. In the inset of fig. 3.13, first the band gap decreases as disorder decreases until 260 K, then the disorder continues to decrease but the band gap shows opposite trend, and finally, starting from 275 K, the band gap decreases as disorder increases, which is a standard behavior for semiconductors [START_REF] Pauporté | Electrodeposition of semiconductors for optoelectronic devices: results on zinc oxide[END_REF][START_REF] Cody | Disorder and the optical-absorption edge of hydrogenated amorphous silicon[END_REF]. The high-temperature transition is illustrated better in fig. 3.13b, because the range of transition itself can be determined as 510-540 K.

To compare with dielectric spectroscopy data, in the porous pellet the maximum intensity of low-frequency relaxation is 260 K (and 210 K for the high-frequency one, which is out of range of optical measurement). If compared to dielectric spectroscopy data from [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF], 260 K is close to both Tm and T V F .

At 275 K there is T Q , where the 1 ε at T > T m starts to deviate from a quadratic dependence on temperature and the transition to Curie-Weiss law begins. The point 324 K is close to a characteristic temperature T CW (ideally, 315 K) above which the Curie-Weiss law fits the data [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF] fig. 3.13. The points of 293 K and the process 510-540 K might be related the disappearance of static PNR (T d=485 K in [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF]) and to the disappearance of dynamic polar correlations.

BaSn

TEMPERATURE EVOLUTION OF BAND GAP AND DISORDER-RELATED ABSORPTION TAIL 55

BaSnO 3

The band gaps of both BaSnO 3 samples shown in fig. 3.15a do not show any considerable non-linearities. Between the two samples, the rate of decrease over the temperature is different. This difference is more pronounced than in two samples of BaTiO 3 . Probably, in BaSnO 3 the defect disorder plays a much more important role for the properties than in BaTiO 3 , or the defect concentrations are higher at the same conditions. Indeed, BaSnO 3 tends to be a good ionic conductor due to high concentrations of defects [START_REF] Bévillon | Theoretical and experimental study of the structural, dynamical and dielectric properties of perovskite BaSnO 3[END_REF]. It's electronic conductivity is mainly controlled by defect-related mechanisms [START_REF] Ganguly | Mobility-electron density relation probed via controlled oxygen vacancy doping in epitaxial BaSnO 3[END_REF][START_REF] Upadhyay | Probing electrical conduction behavior of BaSnO 3[END_REF]. The Eu dependence on temperature is shown in fig. 3.15b. The plots do not coincide for the two samples. Nevertheless, despite the average slope of evolution is similar starting from above 360 K. It is however evident that the data cannot be fitted by a linear dependence, since there are some small nonlinear variations superimposed. Moreover, there seem to be unexpected large non-linearities at temperatures below 360 K for both samples, but nevertheless appearing different in the plot of fig. 3.15b.

To clarify this behavior, we plot the band gap dependence on disorder in fig. 3.16. In the close-up on the right of fig. 3.16, it is visible that around 300 K sample 1 does not behave in a similar way on heating and cooling, probably because it gets oxidized or reduced during heating, or there is a rearrangement of defect structure. In fact, both cooling during the processing of the sample and heating during this measurement is done in air, but the latter takes twice longer time and could act as annealing. The similarity between first heating for sample 1 and 2 is that both of them seem to change regime at 295-300 K. In fact, in both dielectric measurements of [START_REF] Bévillon | Theoretical and experimental study of the structural, dynamical and dielectric properties of perovskite BaSnO 3[END_REF] and [START_REF] Kumar | Ferroelectric phase transition in Te-modified BaSnO 3[END_REF] there seem to be some slight anomaly around 300 K and 324 K. Further, in our fig. 3.16 there seems to be an inflection point at 360 K. This is very close to 375 K, where the change of slope in dielectric data was noticed in [START_REF] Kumar | Ferroelectric phase transition in Te-modified BaSnO 3[END_REF]. At the same temperature, the mass loss was detected in [START_REF] Hodjati | Absorption/desorption of N O x process on perovskites[END_REF] and was tentatively ascribed to evaporation of physisorbed water.

Next, in our data there is a change of slope at 480 K. This probably corresponds to the end of the mentioned mass loss at 473 K in [START_REF] Hodjati | Absorption/desorption of N O x process on perovskites[END_REF]. Moreover, in [START_REF] Kumar | Ferroelectric phase transition in Te-modified BaSnO 3[END_REF], at 460 K there is an end of linear region of dielectric spectrum with the following strong non-linear increase of ε.

The following change of slope in our fig. 3.16 is at 580 K. In [START_REF] Ibtessam | Oxygen stoichiometry, conductivity and gas sensing properties of BaSnO 3[END_REF] the decrease of n-type conductivity starts at this temperature, apparently caused by the beginning of oxidation in their oxygen-deficient sample which was previously quenched from 1773 K. To add to the mentioned reference, in [START_REF] Kumar | Ferroelectric phase transition in Te-modified BaSnO 3[END_REF] the dielectric constant decrease finishes, giving place to a horizontal plateau.

The change of slope of our plot at 700 K could correspond to the beginning of mass loss of multiple carbon species in ref. [START_REF] Hodjati | Absorption/desorption of N O x process on perovskites[END_REF]. Otherwise, 650-670 K is the temperature where the oxidation of oxygen-deficient BaSnO 3 finishes, and the conductivity starts to increase again [START_REF] Ibtessam | Oxygen stoichiometry, conductivity and gas sensing properties of BaSnO 3[END_REF]. It is a question whether the process of oxygenation at the surface compensates the dangling bonds which are otherwise taken by carbon, and therefore the two processes are related.

There is a non-linear evolution of our plot until 820 K, and a new linear region starts after that. Despite we have no suggestions for the possible reasons, this change is not unexpected, because the mass loss which starts at around 670 K does not stop before 1173 K according to ref. [START_REF] Hodjati | Absorption/desorption of N O x process on perovskites[END_REF]. In addition, as mentioned, high temperature activates the process of oxygen loss which intensifies with temperature increase [START_REF] Ibtessam | Oxygen stoichiometry, conductivity and gas sensing properties of BaSnO 3[END_REF].

TEMPERATURE EVOLUTION OF BAND GAP AND DISORDER-RELATED ABSORPTION TAIL 57

As for sample 2, the critical points at 300 K, 360 K, 480 K, and the slight deviation at 600 K coincide with those ones in sample 1. The further characteristic temperatures cannot be verified since 600 K is the upper limit of the experimental temperature range.

Conclusions

The optical absorption was measured on BaSn x Ti 1-x O 3 powders by UV-visible-NIR absorption spectroscopy.

According to the shape of the measured spectra, the Eg levels of Sn and Ti exist separately, but the lower-energy levels cannot be distinguished, so probably they hybridize together. Despite the fact that the band gaps of BaTiO 3 and BaSnO 3 are very similar, the band gap increases until x(Sn)=0.8 by more than 0.35 eV, and then decreases. Since the band gap Eg plotted against Urbach energy Eu shows two separate regions as well, we deduce that the disorder should be responsible for the band gap increase. Moreover, there is a low-energy shoulder on the Urbach plot in compositions x(Sn)=0.1...0.6 which is probably due to some components of disorder.

We also studied the optical properties of some compositions in temperature. From complementary plots Eg=f(T) and Eg=f(Eu) the phase transition temperatures can be extracted, as well as the changes of the disorder state in a wider range around the phase transitions in ferroelectric and relaxor compositions (fig. 3.17). The T of phase transitions and the T d agree well with XRD and T CW . For x(Sn)=0.1, there are two disorder states existing in the region of diffuse phase transition, one related to process happening below T m, and the second one -up to T CW . For x(Sn)=0.2, two characteristic temperatures are also visible, and the T d is confirmed. For BaSnO 3 , the temperature points in fig. 3.17 characterize the changes of defect state. As for x(Sn)=0.5, unfortunately we are not able to make any hypothesis because of the non-coinciding temperature ranges of previous experiments. A deeper insight would need more experiments. This chapter presents the results of two spectroscopic techniques, Raman spectroscopy and X-ray photoelectron spectroscopy. These techniques allow to analyse local properties of matter. Raman spectroscopy, applied to crystalline materials, allows recording a phononic fingerprint of the material under study, which can lead to getting information of interatomic force constants, potentials, and local structure anisotropy. Only the phonon modes which cause the polarization of electronic clouds are active in Raman, or in other words those modes which cause the dynamic contribution to atomic charges. We make the bridge to X-ray photoelectron spectroscopy, since this technique also permits to qualitatively compare the atomic charges between different materials. Using these two techniques, we are interested to shine some light on the local chemical binding in BaSn x Ti 1-x O 3 compounds in connection to the local (static or dynamic) unit cell distortions.

In Raman spectroscopy, the sample probe is the monochromatic light of a laser. The photons can be inelastically scattered with the creation or absorption of a phonon vibration (Stokes process when the scattered photon has less energy than the incident, or Anti-Stokes processes when the scattered photon has more energy than the incident one), the former ones being measured in the present experiments. The scattered phonon, whose energy (wavelength λ s ) is different from the initial one (wavelength λ i ), has the Raman shift (wavenumber) of | 1/λ i -1/λ s |, which is used as abscissa in Raman spectroscopy spectra representation.

For a phonon to be active in Raman, it should be characterized by a po- The TO 1 mode, especially its component E(TO 1 ) at low wavenumbers (10-50 cm -1 ) [START_REF] Fontana | Quasimodes and a central peak in BaT iO 3[END_REF][START_REF] Freire | Lattice dynamics of crystals with tetragonal BaT iO 3 structure[END_REF], is very important to the phase transitions of BaTiO 3 . It is a so-called soft mode, whose frequency tends to zero at fully displacive phase transitions. To the contrary, in BaTiO 3 this mode never comes to zero at any phase transition [START_REF] Luspin | Soft mode spectroscopy in barium titanate[END_REF], because an order-disorder component is also involved [START_REF] Hlinka | Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaT iO 3[END_REF]. The order-disorder contribution to the phase transition is observed from dielectric experiments. Such mode arises from the hopping of Ti between the eight ground sites where it lies along the <111> directions of the unit cell [START_REF] David | Electric field gradients in BaT iO 3 and KN bO 3[END_REF][START_REF] Hlinka | Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaT iO 3[END_REF]. This mode is also called a central mode [START_REF] Ekhard | Elastic excitations in BaT iO 3 single crystals and ceramics: Mobile domain boundaries and polar nanoregions observed by resonant ultrasonic spectroscopy[END_REF]. As shown in fig. 4.4a, the triple degenerate modes soften (decrease in frequency) at each phase transition, and then reappear between 200 and 300 cm -1 .

It is claimed that at every phase transition on cooling certain degrees of freedom of Ti hopping are frozen, so the coupling between some components The spectrum of BaTiO 3 consists of three major groups of peaks (table 4.1) which lie below 450 cm -1 , between 450 and 600 cm -1 , and 700-800 cm -1 (see fig. 4

CHAPTER 4. CHEMICAL BONDING AT THE ATOMIC LEVEL

.10).

The low-frequency region is dominated by wide and dampened soft and central modes. Another wide mode A 1 (TO 1 ) strongly influences the shape of the spectra in the 270 cm -1 region.

In between those two wide modes, the spectrum is determined by the coupling of multiple modes which form the antiresonance (Breit-Wigner interference) in phases with unit cell distortions [START_REF] Buscaglia | Grain size and grain boundary-related effects on the properties of nanocrystalline barium titanate ceramics[END_REF]. Ref. [START_REF] Scalabrin | Temperature Dependence of the A, and E Optical Phonons in BaT iO 3[END_REF][START_REF] Gervais | Infrared and Raman responses in ferroelectric perovskite crystals: Apparent inconsistencies[END_REF][START_REF] Robins | Investigation of the structure of barium titanate thin films by Raman spectroscopy[END_REF] claims there is a coupling of these modes with disorder, or with polaritons. In the latter case, the coupling with polaritons is studied for modes propagating at some angle to the crystallographic axes, i.e. oblique polaritons. In ref. [START_REF] Chaves | Coupled modes with A 1 symmetry in tetragonal BaT iO 3[END_REF] it is speculated that at slight deviations from the center of the Brillouin zone, the shape of 100-300 cm -1 region could be either due to large first-order coupling between electron and phonons (polaritons) or due to the interaction between first-order phonons and second-order background. The oblique Raman modes are discussed more in detail in [START_REF] Fontana | Quasimodes and a central peak in BaT iO 3[END_REF][START_REF] Freire | Lattice dynamics of crystals with tetragonal BaT iO 3 structure[END_REF]. There is high probability that the modes at 150-195 cm -1 and 716 cm -1 are oblique (see table 4.1). The possibility of capturing the oblique Raman modes during the measurement is rather high for ceramics, since the grains are oriented differently. We will consider this hypothesis for the identification of modes in our samples. The special feature of the BaTiO 3 spectrum is the wide asymmetric shape of A 1 (T O 1 ) at 260 cm -1 , A 1 T O 3 at 512 cm -1 , and the A 1 (LO 3 ) (with possible mixture of E(LO 3 ) character) at 716 cm -1 . The reason for that is the complicated coupling between the modes and the disorder.

In addition to the mentioned modes, the wide smeared mode at 600-620 cm -1 can appear depending on the sample. In general, it is often seen in ceramics or powders with submicron grains. In bulk BaTiO 3 , this mode appears at the pressure of 4-6 GPa in the cubic phase. It is probably connected with the disordered paraelectric phase appearing at the grain boundaries [START_REF] Naik | Temperature dependence of the Raman spectra of polycrystalline Ba 1-x Si x T iO 3[END_REF][START_REF] Buscaglia | Grain size and grain boundary-related effects on the properties of nanocrystalline barium titanate ceramics[END_REF].

BaSnO 3

BaSnO 3 is a cubic compound, so ideally first-order Raman is not allowed by selection rules. Nevertheless, the spectrum with well defined modes is [START_REF] Stanislavchuk | Electronic band structure and optical phonons of BaSnO 3 and Ba 0.97 La 0.03 SnO 3 single crystals: Theory and experiment[END_REF] observed in Raman measurements, even if its intensity per second of acquisition is much lower than the BaTiO 3 spectrum. It was claimed that those could be second-order Raman peaks, or that the first-order effect appears due to defects locally breaking the symmetry, despite the so-called F 2U mode was predicted by calculations [START_REF] Bog | Hybrid functional calculation of electronic and phonon structure of BaSnO 3[END_REF]. Another possible reason for that could be that in BaSnO 3 the P bnm(P nma) orthorhombic structure with oxygen octahedra rotations is very close in energy to P m3m [START_REF] Bevillon | Unstable polar mode and minimum of the dielectric constant in cubic BaSnO 3 under hydrostatic pressure[END_REF][START_REF] Stanislavchuk | Electronic band structure and optical phonons of BaSnO 3 and Ba 0.97 La 0.03 SnO 3 single crystals: Theory and experiment[END_REF], so that alternative phonon modes characteristic for P bnm symmetry could exist in BaSnO 3 . In fig. 4.5 the modes were indexed according to the changed Brillouin zone of orthorhombic phase where first-order modes are allowed.

Solid solutions

For solid solutions, the convention will be to add * symbol to mode symmetry, to note that it might be changed if the local distortions are different from tetragonal ones as in room temperature BaTiO 3 . We keep the original symmetry notation just to distinguish between different components of same mode.

In the solid solutions BaSn x Ti 1-x O 3 the spectrum keeps the features of BaTiO 3 , but the modes become wider, fig. 4.6 [START_REF] Veselinovic | The effect of Sn for Ti substitution on the average and local crystal structure of BaT i 1-x Sn x O 3 (x=0...0.20)[END_REF][START_REF] Kumar | Investigation of local structure of lead-free relaxor BaT i 0[END_REF]. The shape of the 150-200 cm -1 region changes: the antiresonance disappears (or moves to lower wavenumbers in the Raman spectrum with λ=514 nm) and two peaks appear instead [START_REF] Kumar | Investigation of local structure of lead-free relaxor BaT i 0[END_REF]. In similar solid solutions BaZr x Ti 1-x O 3 , such a shape and the appearance of mode ∼110-130 cm -1 is associated with the local distortions of orthorhombic or rhombohedral character [START_REF] Farhi | A raman and dielectric study of ferroelectric ceramics[END_REF][START_REF] Maiti | Evaluation of experimental resume of BaZr x T i 1-x O 3 with perspective to ferroelectric relaxor family: An overview[END_REF]. Except in BaZr x Ti 1-x O 3 , it has been evidenced in single domain BaTiO 3 thin film Raman spectra with rhombohedral nanoregions [START_REF] Rubio-Marcos | Ferroelectric domain wall motion induced by polarized light[END_REF], disordered solid solutions (Ba,Sr)TiO 3 [START_REF] Ag Razumnaya | Phase transition in ferroelectric BaT iO 3 /SrT iO 3 superlattice: Raman spectroscopy studies[END_REF], amorphous BaTiO 3 [START_REF] Nuzhnyy | Properties of BaT iO 3 confined in nanoporous Vycor and artificial opal silica[END_REF], and is proved to be a component of A 1 (TO 1 ) mode coupled with Debye mode (Ti hopping) [START_REF] Liu | Intrinsic dielectric frequency dependent spectrum of a single domain tetragonal BaT iO 3[END_REF][START_REF] Hlinka | Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaT iO 3[END_REF]. As well, this mode is suggested to be of Slater character according to the frequency and the mass ratio of Zr/Ti [START_REF] Farhi | A raman and dielectric study of ferroelectric ceramics[END_REF]. The temperature studies of the A * 1 TO 3 peak in x(Sn)=0.3 showed that from Raman spectroscopy it is possible to find (from the presence of several linear regions in peak centers and the integrated intensity) the sequence of relaxor phases and the critical temperatures of phase transitions. The phase sequence is slightly different from the one obtained by dielectric spectroscopy in [START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF]. It is proposed that the phases (in the order of temperature increase) are non-ergodic relaxor, 100 K<T<200 K mature ergodic phase, 200 K<T<450 K ergodic polar cluster phase, T>450 K paraelectric phase fig. 4.7. In dielectric spectroscopy, no differentiation between mature ergodic phase and polar cluster phase was made.

In this chapter we are discussing the Raman data on other compositions of BaSn x Ti 1-x O 3 in the same frame, making references to other chapters.

Experimental details

The micro Raman spectra were acquired from ceramic pellets to reproduce XPS data using a Labram-Horiba spectrometer with He-Ne laser (632.8 nm) through an optical microscope and typically using 50X objective. Fityk software was used for fitting. For enhanced comparison of BaTiO 3 features with our solid solutions, BaTiO 3 sample was measured at temperatures 100-700 K and fitted within the same procedure after correction for Bose-Einstein population factor. We used the mathematical correction by negative Gaussian peak for the antiresonance in the 180 cm -1 region.

X-ray photoelectron spectroscopy

In laboratory based X-ray photoelectron spectroscopy, the monochromatized X-ray beam, generated with an X-ray source (typically aluminium), illuminates and is absorbed by the material. The transition to the ground state is accompanied by different desexcitation events, among others the generation of electrons (so called photoemitted electrons) fig. 4.8.

The hemispherical analyser with potential applied to it is used to separate the photoelectrons by their kinetic energy K.E. The binding energy B.E. is then recalculated as follows:

B.E. = hν XR -K.E. -φ sp (4.2)
with hν XR -energy of X-ray, φ sp -potential of spectrometer. Normally, the sample is electrically grounded, and the calibration is made with a standard, so that the potential of the spectrometer does not contribute to the peak position and the Fermi level is at the zero binding energy (see the red arrow in fig. 4.8b). By convention, the scale is normally inverted with "zero" on the right. If the value of the electronic level energy is small, the hν XR is enough to excite the electron to the Fermi level or to the vacuum level energy. The deeper in energy is the core level, the less will be the kinetic energy of the electron, larger than the B.E.. The semiconductor valence band (VB) appears in the spectrum at some energy below the Fermi level, and at some distance from the VB there are peaks corresponding to core levels or Auger processes which will not be discussed here.

Measurement details and framework of analysis

Because the electrons are extracted from the sample, it needs to be not only grounded but also well-conductive, otherwise it charges positively, and the peak positions and shape change. If a sample with low conductivity has to be studied, as it is the case in our work, it is possible to compensate the charging by using an electron gun. The intensity of the electron flow is chosen to shift the peak of the surface carbon C 1s close to its usual position, nevertheless the absolute values of the peak positions and the valence band maximum cannot be trusted because C 1s binding energy can be influenced by different interface charge distribution phenomena and C is not part of the perovskite unit cell.

In our study, we want to make the comparative qualitative analysis of the peaks. Since the absolute position is not available, we take the difference between the Ba 3d 5/2 and other levels, since Ba is present in all the samples and is supposed to be least influenced by Ti substitution fig. 4.9. One of the reasons is that the Born charge of Ba in BaTiO 3 and BaSnO 3 was calculated to be very close (+2.73 in and +2.74) [START_REF] Xie | The Electronic Structures, Born Effective Charges, and Interatomic Force Constants in BaM O 3 (M= Ti, Zr, Hf, Sn): A Comparative First-Principles Study[END_REF]120]. Note that we can distinguish contributions to Ba 3d 5/2 peak from the bulk and surface carbonates.

It is clear that in a first approach in XPS the closest electronic levels to the nucleus have larger value of binding energy. Outer orbitals have smaller value of B.E., because the Coulomb interaction between them and the nucleus is screened by electrons from deeper levels. For the same bond between metal atom and oxygen M-O, metal M electronic levels which are less oxidized/equivalently, more reduced are shifted to the smaller B.E. values. In our case, cannot evaluate the absolute values of B.E. as there is no absolute Fermi edge allowing us to define the energy reference. On the other hand, we analyse the B.E. difference between Ba 3d 5/2 (with its B.E. fixed according to calibration) and core levels of other atoms. Therefore the value of this difference will account for different atomic and electronic factors, including the average charge of the metal ion M and the bond length itself. In this work in Ba-perovskites, we consider the Ba 3d 5/2 B.E. level as constant. In addition to changes of valence state, the more intricate chemical shift could come from the property of the bond itself, such as the degree at which the electrons are localized at the atoms, or the covalency/ionicity of the bond:

∆B.E.(3d) = -∆ǫ -∆E XP S relaxation (3d) (4.3)
with ǫ -the variation of Koopman's energy (energy of monoelectronic orbital), and ∆E XP S relaxation (3d) -variation in the extra-atomic relaxation energy corresponding to a hole in the given shell [START_REF] Jollet | Influence of oxygen vacancies on the electronic structure of yttrium oxide[END_REF]. Although this dependency is deduced for monoelectronic orbitals, we can use it as a first approximation to be applied to the different core levels under study in our compounds. Therefore the extra-atomic charge has an important effect on the B.E., this effect can be imagined as outer charge screening of the core levels.

In the bond M-O the ∆B.E. is larger for a higher degree of ionicity (smaller Madelung potential) for the case of binary oxide Y 2 O 3 [START_REF] Jollet | Influence of oxygen vacancies on the electronic structure of yttrium oxide[END_REF]. However, in our case there are three pairs of such M-O bonds (Sn-O, Ti-O and Ba-O), so the charge transfer from one bond to another is possible, and care should be taken about the more complicated charge distribution.

The information on differences of the chemical bonding can be also extracted from Auger lines. For instance, the difference between OKL 23 L 23 and OKL 1 L 23 is larger for the bond which is more covalent [START_REF] Jollet | Influence of oxygen vacancies on the electronic structure of yttrium oxide[END_REF], because the different orbitals of the same atom are influenced in a different way by the distribution of electronic charge of the chemical bond.

In our experiment, we performed XPS on ceramic pellets, polished for ease of focusing. An axis Ultra DLD spectrometer with monochromatic Al Kα X-ray source together with a charge compensation electron gun were used.

Connection between XPS, phonons, and the band gap

There is an important connection between the two techniques. we have included in the results of this chapter, i.e. XPS and Raman spectroscopy.

In theoretical works, a lot of different definitions of effective charge exists to answer the question of whether the charge of an atom is localized/delocalized, static or dynamic etc [120,[START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF]. Nevertheless, in general the more accepted approach is based on using a standard quantity called the Born charge. It is defined as the change of polarization P β per unit cell along the β direction for the displacement of the atom i in direction u.

Z * i,αβ = δP β δu i , α (4.4)
with u i , α -the components of displacement. The polarization P β includes both the components of atomic rigid displacement and the charge transfer in the electronic clouds. In a crystal, this dynamic charge transfer contributes importantly to the properties of chemical bond and thus to the phonons that are related to the change in the polarizability.

The Born charge values for the different ions in BaTiO 3 and BaSnO 3 are given in table 4.2. It is remarkable that for BaTiO 3 the values are very much different from the chemical valence values due to the dynamic hybridization in Ti-O chains which are introduced by certain phonon modes [START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF]120]. Note that the O Born charge is more different from the value of chemical valence than the corresponding one from O ⊥ . In general, Z * strongly depends on the electronic distribution leading to the creation of a dipole within the Ti-O bond, and thus of an atomic distortion in other words on the kind of unit cell distortion. Most probable phonon modes to modify the effective charge distribution are probably Slater or Axe modes, since they involve movements of Ti against O. Changing the Born or effective charges, the nature and energy position of the valence band maximum and the conduction band minimum can also be changed. As a result, there might be a connection between the Raman mode characteristics and the band gap in the different Born charges, as it will be mentioned in the discussion of the results. If we concentrate on the high wavenumber region (> 650 cm -1 ), one can see that the initial LO 3 peak, remanent of BaTiO 3 , becomes weaker and disappears beyond x(Sn)=0.2. Meanwhile, a new hardened Axe LO 3 mode grows at larger frequency (737 cm -1 ), next to the LO 3 (E-A 1 ) oblique mode characteristic of tetragonal BaTiO 3 , which have smeared out due to the new chemical bonds and unit cell change introduced by the Sn-substitution. Remarkably, it is the only mode starting from x(Sn)=0.4 until x(Sn)=0.8. This mode is known to be characteristic in relaxors, including the similar system Ba(Zr,Ti)O 3 [START_REF] Farhi | A raman and dielectric study of ferroelectric ceramics[END_REF][START_REF] Maiti | Evaluation of experimental resume of BaZr x T i 1-x O 3 with perspective to ferroelectric relaxor family: An overview[END_REF]. In x(Sn)=0.9, new peaks appear which are characteristic and common to some of the modes seen in pure BaSnO 3 .

The positions of LO 3 mode(s) are plotted in fig. 4.11a. One can see that for the high-frequency mode there are two linear regions, which intercept at x(Sn)=0. [START_REF] Pauporté | Electrodeposition of semiconductors for optoelectronic devices: results on zinc oxide[END_REF]. In Ba(Zr,Ti)O 3 , this composition corresponds to percolation limit of Ti, so that further compositions represent the separate Ti-rich clusters which are surrounded by paraelectric matrix [START_REF] Maiti | Evaluation of experimental resume of BaZr x T i 1-x O 3 with perspective to ferroelectric relaxor family: An overview[END_REF]. This is in agreement with the new modes characteristic of pure BaSnO 3 appearing in x(Sn)=0.9, although other potential cause for this effect could be the existence of a phase separation. We cannot simply distinguish one from another from Raman spectroscopy and further experiments, including synchrotron radiation diffraction, are needed to answer to this question. In the part of the spectra at lower frequencies (< 650 cm -1 ) in fig. 4.10 three compositional regions of the phase diagram are as well visible.

Below x=0.2, there is a significant softening of the Slater mode A * 1 (TO 1 ) at 260 cm -1 which occurs as for the soft mode of BaTiO 3 , i.e. due to the decrease of the ferroelectric distortion and unit cell approaching quasicubic shape at around 11 % [START_REF] Frantti | A statistical model approximation for perovskite solid-solutions: A raman study of lead-zirconate-titanate single crystal[END_REF][START_REF] Chang | X-ray diffraction studies of phase transformations between tetragonal and cubic phases in the BaSn x T i 1-x O 3 system[END_REF]. Besides, modes b and c, and LO 3 are softened inside the first compositional region because of their coupling to the soft mode.

RESULTS

73

Despite the fact that the antiresonance close to mode c disappears already in x(Sn)=0.1, similarly to cubic BaTiO 3 , the B * 1 (TO 4 -TO 2 ) mode does not disappear fully but is widened, indicating probably the simultaneous presence of differently distorted polar nanoregions in relaxors or a change in the unit cell that could be compatible to a lower symmetry unit cell. Its center and FWHM are plotted in fig. 4.11b, and can be separated into three different compositional regions. The width of this mode stays approximately similar within the relaxor region, and further increases for x(Sn)=0.8 and 0.9, changing into a wide feature fig. 4.10 which is not fitted in BaSnO 3 .

For relaxor compositions, there is as well a change in relative intensity of modes b and c. While in tetragonal BaTiO 3 phase the mode b is more intense than the mode c, it is to the contrary starting from x(Sn) = 0.2, resembling the orthorhombic phase of BaTiO 3 (see fig. 4.4). The intensity ratio I(b)/I(c) is shown in fig. 4.12a, where we can clearly separate this I(b)/I(c) ratio into two regions where this ratio behaves linearly on composition -ferroelectric ones against the rest of compositions. Based on this, we can make the hypothesis that there could exist orthorhombic distortions in the Ti-rich clusters of compositions x(Sn)> 0.2. Another important characteristic of relaxor phases is There is a plateau for x(Sn)=0.2 and 0.4, and starting from x(Sn)=0.5 I(d)/I(A * 1 T O 1 ) increases strongly until x(Sn)=0.8. This might be the indication of the further increase in rhombohedral distortion value in the relaxor compositions. This is in agreement with the trend evidenced for Sn-poor compositions x(Sn)=0.16-0.4 by [START_REF] Xie | Static and dynamic polar nanoregions in relaxor ferroelectric Ba(T i 1-x Sn x )O 3 system at high temperature[END_REF] and our own study (see Chapter 2). The ratio stays unchanged for x(Sn)=0.8-0.9. Probably, this is because above the percolation limit the Ti concentration inside the PNR does not change, so that the chemical stress stays the same, and the Ti displacements as well.

Thus, we can conclude that compositions in the relaxor region of phase diagram demonstrate both orthorhombic and rhombohedral local distortions, with increasing tendency towards latter ones, unlike it was deduced before from Raman spectra without fitting procedure [START_REF] Veselinovic | The effect of Sn for Ti substitution on the average and local crystal structure of BaT i 1-x Sn x O 3 (x=0...0.20)[END_REF].

Connection between phonons and optical properties in BaTiO 3

It was discussed in introduction to this Chapter that certain phonon modes which cause the Ti electronic clouds polarization along Ti-O bonds (Slater or Axe modes) can participate in the creation of dynamic hybridization of bonds (corresponding to dynamic component of effective charge) and in this way to modify the band gap. The band gap change at the ferroelectric transition of The corresponding Raman spectra for BaTiO 3 are presented for completitude in Annex B, as well as for several other compositions. In agreement with [START_REF] Perry | Temperature Dependence of the Raman Spectrum of BaT iO 3[END_REF], there are the discontinuities in peak centers at the phase transitions according to the mode softening close to the different phase transitions on heating, and the new hardened mode appearing above the ferroelectric transition temperature.

However, there are no discontinuities in the band gap of the BaTiO 3 annealed powder in fig. 4. [START_REF] Qi | Firstprinciples investigation of the highly tetragonal ferroelectric material Bi(Zn 1/2 T i 1/2 )O 3[END_REF].

In agreement with speculations in references, there seem to be no direct connection between A 1 TO 1 mode positions and the band gap. On the other hand, the A 1 TO 3 mode seems to evolve in a way which is related to the band gap. All the three phase transitions are accompanied by the corresponding steps on both Raman and the band gap data. Therefore we conclude that in BaTiO 3 it is the Axe mode which is indicative of the change in the orbitals determining the band gap.

It is known that the static distortions cause the deviation of the Ti-O-Ti bond from 180 • and the change of orbital overlap (fig. 4.17) [START_REF] Wang | Band gap engineering strategy via polarization rotation in perovskite ferroelectrics[END_REF][START_REF] Mizoguchi | Probing the Electronic Structures of Ternary Perovskite and Pyrochlore Oxides Containing Sn 4+ or Sb 5+[END_REF]. Whether the B site atom orbital is Sn 5s or Ti 3d t2g (orbital forming the conduction band minimum in parent compounds of our solid solutions), the distortion promotes the increase of antibonding character of the chemical bond. As a result, the conduction band minimum shifts to higher values in energy, and For the atomic displacements of Axe TO 3 mode and the transverse band gap Eg ⊥ a very similar mechanism is involved (fig. 4.18). It is clear from fig. 4.14 that the lowest band gap we are measuring is of transverse nature and the interaction involved should be happening along the bonds parallel to XY plane. When four oxygen atoms lying in this plane vibrate against Ti, the alternation of pdπ bond overlap is happening. This is the type of bond which defines the conduction band minimum in BaTiO 3 according to LCAO and calculations [START_REF] Koleżyński | From the molecular picture to the band structure of cubic and tetragonal barium titanate[END_REF], so eventually the band gap is directly connected with this type of phonon, in agreement with the prediction [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF].

Connection between phonons and optical properties in

x(Sn)=0.2

We try to analyse the Raman spectra in the same framework as BaTiO 3 . In fig. 4.19 one can see the examples of fits for different temperatures. The maximum of the peak in 500 cm -1 region is in all compositions defined by the mode which arises from the A 1 *(TO 3 ) in BaTiO 3 .

In x(Sn)=0.2, at low temperature both peaks A 1 *(LO 1 ) and E*(TO 3 ) are present. However, at higher temperatures (> 280 K) the E*(TO 3 ) disappears, and simultaneously there is a steplike increase in intensity and width of a Gaussian peak at 550 cm -1 which models the asymmetric tail in the high frequency side due to mode coupling to disorder. These changes are similar to the ones happening in BaTiO

I(LO 3 ) F E /I(LO 3 ) relaxor .
Figure 4.22a shows the centers of all the peaks in 450-750 cm -1 region. Starting from the low temperatures, the first point to note is that at 200 K the decrease in frequency of the mode at 640 cm -1 which is associated to disorder at grain boundaries in pure BaTiO 3 . Therefore, this critical point is probably associated with the disorder.

In parallel, at 200 K the E*(LO 1 ) reaches the maximum of frequency. Despite in dielectric properties no characteristic features are observed at these temperatures from the XRD patterns at 200 K, there is a change of trend of the studied d 200 distance (fig. 2

.18).

Upon the increase of temperature, the peak at 640 cm -1 keeps constant frequency and then disappears between 240 K and 260 K. We speculate that between 200 K and 260 K there is a continuous process happening which leads to diffuse phase transition evidenced from dielectric spectroscopy (fig. 1.13) peaking at T m=240 K.

At T m, according to what was discussed about the E*(TO 3 ) mode disappearance (fig. 4.19), the local symmetry seems to change from rhombohedral to orthorhombic. This may be in agreement with the spectrum of x(Sn)=0.2 at 293 K, where the presence of orthorhombic phase is evidenced in fig. 4.10, while the mode d appears but its intensity is low fig. 4.12b.

Between 320 K and 340 K another significant change occurs in Axe LO 3 mode in 700 cm -1 region. Instead of two separate LO 3 peaks, one characteristic for ferroelectric phase and another for relaxors, at 340 K there is only one component. Since the position of its center does not evolve continuously, probably this change means that the anisotropy related to certain type of distortion disappears at this temperature. From fig. 1.13, this is where the T CW lies, which probably means that the diffuse phase transition is finished and the macroscopic ferroelectric phase disappeared. Nevertheless the PNRs and dynamic polar correlations could still exist.

The peak of 600 cm -1 (fig. 4.22) reacts to every of the dipole state changes which are visible in other peaks. At 480 K there is a new shift of this peak happening after the previous stabilization. According to dielectric data, this

RESULTS

must be the T d.

Thus, summarizing phonons, XRD and dielectric results from our study with local and macroscopic characterization tools, for the nominal composition x(Sn)=0.2 there is a phase which is mostly (rhombohedral) ferroelectric below 200 K, the diffuse transition until T m=260 K with the change of local distortion to orthorhombic, the region of phase coexistence (relaxor and phase with macroscopic polarization) until T CW =320-340 K, single relaxor phase until T d=480 K, paraelectric above 480 K.

Turning to optical properties of x(Sn)=0.2 (fig. 4.22b), there is a critical point for the band gap at 260 K. Despite the ranges of temperature in the experiment does not permit the measurement of Eg below 235 K, it is visible that the critical point is preceded by a fast decrease of Eg, similarly to what happens at phase transitions of BaTiO 3 . There seems to be a correlation between the decrease in Eg until 260 K, decrease of Eu until 270 K, and the changes in Raman spectroscopy, such as the decrease in the frequency of the A 1 *(TO 3 ) mode and the disappearance of E*(TO 3 ) mode.

The Eg steplike decrease at 550 cm -1 could correspond to full disappearance of dynamic polar correlations similar to BaTiO 3 [START_REF] Dul'kin | Relaxor-like behavior of BaT iO 3 crystals from acoustic emission study[END_REF].

The decrease of the Urbach tail characteristic energy, which is indicating the disorder of the transition (fig. 4.22) close to the T m (fig. 2.6b) is probably associated with the disappearance of certain phonon modes which smear less the band gap edges. At T > T m, the Urbach tail Eu is reactive to T CW =324 K by change of slope, which is probably due to coupling with LO 3 mode, or with the 600 cm -1 mode, which by the way shows the change of slope for peak position. The kink and the Eu slope alternation at T d=480 K seems as well to be connected with the beginning of frequency decrease of disorder-related mode at 600 cm -1 .

We summarize the temperature sequence of phases in x(Sn)=0.2 in fig. 4.23.

Taking into account that the most significant changes of band gap occurs when the local symmetry is changed (FE phase transitions or T m in x(Sn)=0.2), we do not present here the data for other compositions. It is nevertheless a prospective for future works to study the connection between Urbach tail and the phonons in relaxor compositions.

X-ray photoelectron spectroscopy

Figure 4.24 shows the XPS peaks for each element. The intensity of Sn 3d peak and Ti 2p is proportional to concentration, according to sensitivity factors, and there are no unidentified shoulders or satellite peaks. It is noteworthy that the Ba 3d peaks contain a contribution from both Ba-TiO 3 sublattice and surface carbonate Ba-CO 3 , which we have identified and deconvoluted according to literature expected values for peak widths and relative energy positions. Similarly, the O 1s peak is formed by the contribution from the perovskite sublattice and from the surface organic bonds with H. The B site peaks are well fitted by the single component, which confirms the correct valence state and absence of significant amounts of defects at the surface. The quantification results are shown in table 4.3. While the ratio of Ti/Ba concentrations is very close to the nominal one, there seems to be an excess of Sn, as deduced from the ratio Sn/Ba and Sn/Ti at the surface, more significant in Sn-rich samples.

We note that the effective screening on both Ti and Sn atoms increases until x(Sn)=0.8, and then decreases after x(Sn)=0. 8 (fig. 4.25). The trend and energy change are similar to those of the band gap fig. 3.4b. The former probably suggests that both B-site atoms are influenced in the similar way by local environment. Whether the latter is connected with the valence band maximum or conduction band minimum shifts, cannot unfortunately be verified with these experiments.

The difference ∆B.E.(Ba 3d -Ti 2p) and ∆B.E.(Ba 3d -Sn 2p) is larger in Sn-rich compositions, meaning that in those compositions there is more electron screening on B-site atoms. By extrapolation, the charge screening on Ti in BaTiO 3 is smaller than on Sn in BaSnO 3 , which means that Ti is more oxidized than Sn (due to dynamic hybridizations induced by phonons and/or the larger unit cell provided by the Sn-rich matrix).

The values of ∆B.E.(Ba 3d -O 1s) for pure end compounds do not follow the predicted Born charges (the Born charge of O in BaTiO 3 is in absolute value larger than in BaSnO 3 ). On one hand, this could be caused by the surface effects due to organic bonds. Other possibility can be that the defects or local structure are usually not taken into account in the calculation of electronic structure of BaSnO 3 . The Born charge absolute value could be unprecise because the very same calculations predicted no allowed Raman modes in BaSnO 3 , while there are Raman active phonons that are visible and their positions seem to be in agreement with those caused by a local orthorhombic distortion [START_REF] Stanislavchuk | Electronic band structure and optical phonons of BaSnO 3 and Ba 0.97 La 0.03 SnO 3 single crystals: Theory and experiment[END_REF][START_REF] Bevillon | Unstable polar mode and minimum of the dielectric constant in cubic BaSnO 3 under hydrostatic pressure[END_REF]. The difference ∆B.E. (Ba 3d -O 1s) increases linearly for all the compositions until x(Sn)=0.8. It stays approximately constant for x(Sn)>0.8.

The possible reason of why ∆B.E.(Ba 3d -O 1s) increases instead of decrease predicted from calculations could be proposed through the shape of the valence band of different compositions in fig. 4.26. From calculations in fig. 4.26b, hybridization with Ba contributes to the larger B.E. side of the complex valence band shape [START_REF] Qi | BaT iO 3 : Energy, geometrical and electronic structure, relationship between optical constant and density from first-principles calculations[END_REF][START_REF] Mizoguchi | Probing the Electronic Structures of Ternary Perovskite and Pyrochlore Oxides Containing Sn 4+ or Sb 5+[END_REF]. In our measured VB of BaTiO 3 , the larger intensity lies as well at larger B.E. values. For x(Sn)=0.5, the maximum of intensity shifts to higher B.E., and in BaSnO 3 forms maximum on the low-B.E. side. This contribution is caused by hybridization with Ba levels [START_REF] Sallis | Ladoped BaSnO 3 -Degenerate perovskite transparent conducting oxide: Evidence from synchrotron x-ray spectroscopy[END_REF]. The shift of Ba-O hybridized level to higher energy can mean that it benefits of higher electronic charge. Probably, the increase of O atom screening relative to Ba is happening for the same reason.

Special attention should be paid to the increase of electron screening for Ti and Sn levels above values of pure BaSnO 3 for x(Sn)=0.5-0.8. If the simple charge transfer in Ti-O bond was happening, the increase of screening for Ti and Sn would probably correspond to opposite trend for O, which depicted from our results. Within the unit cell with same characteristics, the simultaneous increase in effective charge of A-and B-site atoms in perovskites is unfavorable from the principle of Pauli repulsion between Ba-O and Ti-O hybridized orbitals [START_REF] Joseph W Bennett | Effect of symmetry lowering on the dielectric response of BaZrO 3[END_REF]. We speculate that two bonds could be involved, both Ti-O and Ba-O. The A-O bond tends to strengthen when the O-B-O octahedral angle deviates from 180 • [START_REF] Mizoguchi | Probing the Electronic Structures of Ternary Perovskite and Pyrochlore Oxides Containing Sn 4+ or Sb 5+[END_REF]. Therefore the XPS data are compatible with our conclusions from the Raman spectroscopy that rhombohedral distortions increase for compositions x(Sn)=0.5-0.8, and that the amount of distorted clusters decrease for x(Sn)=0.8-1. Everything goes in line with the band gap non-linear trend.

We also note that for Sn 4d core levels (fig. 4.25) two peaks can be observed, in contrast to the single peak measured for BaSnO 3 compound. This result is compatible with the existence of different bonding for Sn in this composition, which can be allowed in rhombohedral or orthorhombic distortions.

87

Conclusions

Raman spectroscopy well describes the polar order and the kind of distortions. With the addition of the information from previous chapters, we can picture out the next section of the phase diagram at room temperature:

• FE-like with tetragonal distortion symmetry for 0<x(Sn)≤0.1

• x(Sn)=0.2 as the only representative of a sample with a diffuse phase transition and the resulting phase coexistence at room temperature.

Both FE and relaxor-like components are detected in Raman. Note that according to dielectric measurements, at room temperature the major phase is FE-like with very weak distortions (close to T CW where the macroscopic static polarization disappears). The mixture of relaxor-like phase is evidenced only by Raman.

The symmetry deduced from Raman spectra is mainly orthorhombic, with very weak mixture of rhombohedral distortions.

• x(Sn)=0.4 -the pure relaxor composition with mainly orthorhombic distortions and a small mixture of rhombohedral ones • 0.5<x(Sn)<0.75 relaxor compositions with both orthorhombic and growing rhombohedral distortions • 0.75<x(Sn)≤0.9 clusters containing Ti within a purely paraelectric BaSnO 3 matrix. The distortions preserve the same characteristics (O + R) as just below the percolation limit, probably because within the clusters the chemical stress stays similar.

In addition to giving a clear understanding of the polar state, Raman spectroscopy allows to qualitatively explain the band gap non-linear step-like changes in temperature at the phase transitions with the massive change of distortion kind (unit cell symmetry). We observe such changes both in BaTiO 3 (phonon mode of Axe character A 1 TO 3 ) and x(Sn)=0.2 (also Axe mode E * TO 3 ). The Axe mode is responsible for dynamic component of bond hybridization in pdπ (Ti-O) or psπ (Sn-O) chemical bond, which form the conduction band minimum.

The change of unit cell symmetry and kind of distortion changes both the static and the dynamic components of the effective charge. The static component should be connected with macroscopic polarization P , however it was pointed out in [START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF] that the separation between transverse and longitudinal Eg was not straightly proportional to P 2 as it is supposed to be in the static model, but rather was connected with dynamic polarization fluctuations. Similar quantitative analysis is out of the scope of this work, as it would probably require the Raman spectra to be recorded from single crystals, as well as the comparison to theoretical calculations. We demonstrate on the example of x(Sn)=0.2 that there is a clear connection between phonons and the temperature evolution of the Urbach tail Eu. The Eu decreases at 270 K, where the phonon mode causing the band gap non-linearity dies off. Additionally, Eu changes the slope at transitions which seem to involve only the change of polar order (T CW , T d).

In agreement with the distortion-Eg connection deduced from Raman spectroscopy, we also evidence the connection between the effective charge of B-site atoms and Eg through X-ray photoelectron spectroscopy. The electron screening of core levels on Ti and Sn atoms is increasing (relative to Ba) for compositions x(Sn)<0.8 and decreasing for 0.8<x(Sn)<1, the excess of electron charge originating probably from the distortions of the unit cell and the octahedral angle O-B-O deviation from 180 • .

Chapter 5

Conclusions

The study of optical properties of perovskite solid solutions is of great interest in connection with their macroscopic structure and local polar order which can alternate the chemical bonding. The properties of ferroelectric solid solutions, including photovoltaic, piezoelectric, dielectric, electrocaloric etc. often show non-linear behaviour and potentially allow to reach new functionalities in applied devices. In our work, we have concentrated on solid solutions BaSn x Ti 1-x O 3 with the end members BaTiO 3 (ferroelectric) and BaSnO 3 (paraelectric). The similar valence of Ti and Sn (+4) should prevent large concentrations of defects, while Sn could potentially contribute to better electron mobility by its conduction band levels Sn 5s 5p.

In the first chapter, we have studied the compositional and temperature dependence of the crystallographic structure by X-ray diffraction and polar order by dielectric spectroscopy, and we had an insight into the atomic structure and local atomic distortions of the relaxor phase by using transmission electron microscopy. Despite the linear compositional dependence of the unit cell volume at room temperature, a range of different phases is discovered. Adding more Ti atoms introduces chemical stress which causes the decrease of ferroelectric distortion and increasing polar disorder. The sequence of phases is:

• ferroelectric (x(Sn)=0...0.1)

• material in diffuse phase transition state where ferroelectric and relaxor phases coexist, with quasicubic unit cell (x(Sn)=0.1...0.3)

• relaxor phase with average quasicubic unit cell but presence of nanoclusters of distorted phase from x(Sn)=0.3 to 0.8 or higher Sn ratio

The dielectric properties of Ti-rich compositions seem to be defined by polar order of ferroelectric origin, while the dipoles of non-ferroelectric (defect) origin play an important role for Sn-rich compositions.

The local atomic structure shows that the PNRs in the relaxor phase in x(Sn) = 0.4 seem smaller in size, but the distortion of the B-site atoms increases in comparison to compositions which are inside the diffuse phase transition region at room temperature. The distortion state is mixed, but a component along the <111> rhombohedral axis is present.

After characterization of the samples, in second chapter we tested the optical absorption of solid solutions at room temperature for compositional series, and with varying the temperature for chosen compositions for deeper insight into dependence of optical properties on the changing polar order.

In the compositional series, the band gap shows non-linear behaviour. It increases by ∼0.35 eV until x(Sn)=0.8 and decreases for Sn-rich compositions. From our data, the band gap seems to be defined by wide smeared feature where the Sn and Ti levels cannot be separated, we assume that the band gap is defined by mixed levels. We find a connection between the band gap and the type of disorder in the compositional series. Based on this, we also studied the temperature dependence of the band gap in connection with changing disorder regimes. In general, the band gap varies homogeneously within one phase, followed by a non-linear decrease on temperature increase around phase transitions, and followed by another linear regime. For BaTiO 3 above Tc, the slope of Eg variation differs for the phase with static polar correlations and the phase where they are absent. For Ti-rich solid solutions, the Eg and Eu react to changes of the polar state, while for BaSnO 3 and probably Snrich compositions the disorder is determined by defects which are related to oxidation/reduction of the material.

Based on the importance of local disorder for optical properties, in the last chapter of this manuscript we analysed the local structure and disorder in connection to chemical bonding. Concentrating on phase transitions, we use Raman spectroscopy to distinguish the different types of local structural distortions and their magnitude, for compositional series and in temperature. This study combined with crystallographic, dielectric, and optical data, results in our redefinition of the sequence of phases at room temperature:

• FE-like for 0<x(Sn)≤0.1

• x(Sn)=0.2 as the only representative of the sample with diffuse phase transition and the resulting phase coexistence at room temperature. Both FE and relaxor-like components are detected in Raman. Note that according to dielectric measurements, at room temperature the major phase is FE-like with very weak distortions (close to T CW where the macroscopic static polarization disappears). The mixture of relaxor-like phase is evidenced only by Raman.

The symmetry deduced from Raman spectra is mainly orthorhombic, with very weak mixture of rhombohedral distortions.

• x(Sn)=0.4 -the pure relaxor composition with mainly orthorhombic distortions and the small mixture of rhombohedral ones • 0.5<x(Sn)<0.75 relaxor compositions with both orthorhombic and growing rhombohedral distortions • 0.75<x(Sn)≤0.9 clusters containing Ti within pure cubic BaSnO 3 matrix. The distortions preserve same characteristics (O + R) as just below the percolation limit, probably because within the clusters the chemical stress stays similar.

The band gap of a single composition decreases stepwise on increase of temperature if the change of the type of local symmetry occurs (e.g. rhombohedralorthorhombic). According to our discussion, the band gap value is in significant degree dependent on the different components of phonon A * 1 T O 3 of Axe type, evidenced in Raman. The phonons of this type modify the overlap of orbitals of O and B-site atoms in ABO 3 which form the π bond that defines the energy of the conduction band minimum.

The degree of overlap of the atomic orbitals also modifies the distribution of the effective electronic charge of the atoms. This effective charge can be qualitatively analysed through X-ray photoelectron spectroscopy. Since there are distortions of the unit cell, the octahedral angle O-B-O deviates from 180 • , simultaneously, an increase of the effective electronic charge on the B site and on O becomes possible, which is energetically unfavorable in a non-distorted unit cell. This trend appears in our XPS results between x(Sn)=0 and 0.8, with excess of effective charge decreasing for x(Sn)=0.8...1. This proves that the band gap increase in the compositional series is caused by the increasing rhombohedral distortions, and the following decrease of the bad gap agrees well with the gradual disappearance of distorted phase clusters in Sn-rich compositions.

Outlook and perspectives

Since Sn should contribute to an increase of the electron mobility, it would be of interest to perform the measurement to evaluate the changes in comparison to BaTiO 3 . However, because of the microscopic size of grains, it can be experimentally complicated. To the contrary, it is possible to estimate the photovoltaic response from short-circuit current measured under laser illumination. These measurements were performed at the Institut de Ciència de Materials de Barcelona, but need additional processing before being shown to a thesis committee. The measurements were performed under lasers of different energies within the band gap of BaTiO 3 on different compositions. The short circuit current response consists of several components, including transient behaviour which might depend on defect concentrations.

The more profound analysis of this data can be performed if compared to the analysis of photoluminescence experiments which were performed at the Institut de Nanoscience de Lyon. In those experiments the electrons are excited to the energy level in the conduction band, and then recombine with the defect levels inside the band gap. The concentration of defects, including the distortion-related polarons, and the energies of levels can be analysed for better explanation of transient components as well as shift photocurrent values which depend on defect trapping.

Annex

Annex A UV-visible spectroscopy x(Sn): 0 0.1 0.2 0.4 0.5 0.6 0.8 0.9 1 x(Sn): 0 0.1 0.2 0.4 0.5 0.6 0.8 0.9 1

(E*F KM ) 1/2 E, eV (a)
(E*F KM ) 3 E, eV (c)

Résumé complet de thèse

Les études des solutions solides de structure pérovskite permettent d'établir une connexion entre leur structure macroscopique et l'ordre polaire qui influence les liaisons chimiques, et les propriétés optiques. Les propriétés (photovoltaïques, piézoélectriques, diélectriques, électrocaloriques etc.) sont souvent non-linéaires et peuvent permettre de nouvelles fonctionnalités. Dans notre travail, nous nous sommes concentrés sur la solution solide BaSn x Ti 1-x O 3 entre les composés chimiques purs BaTiO 3 (ferroélectrique) et BaSnO 3 (paraélectrique). Les valences similaires de Ti et de Sn (+4) doivent assurer l'absence de grandes concentrations de défauts. La présence de Sn peut contribuer à la meilleure mobilité des charges par la présence des niveaux électroniques Sn 5s 5p dans la bande de conduction.

Le diagramme de phases de BaSn x Ti 1-x O 3 contient des compositions très différentes du point de vue de l'ordre polaire. En première approximation, à partir des études détaillées pour 0<x(Sn)<0,3 il y a les ferroélectriques, où les dipôles électriques sont ordonnés et les phases relaxeurs où il y rupture de l'ordre polaire. Nous avons également étendu l'étude des propriétés au-delà de la composition x(Sn)=0,3.

Le premier chapitre décrit les études de la structure cristallographique par diffraction des rayons X ainsi que de l'ordre polaire par spectroscopie diélectrique. Puis, nous avons analysé une structure atomique (x=0,4) et les distorsions locales de la phase relaxeur en utilisant la Microscopie Électronique en Transmission (MET). Bien que le volume de la maille unitaire évolue linéairement avec la composition, nous avons pu préciser quelle était la séquence de phases :

• ferroélectrique (x(Sn)=0...0,1)

• les compositions présentant une transition diffuse où l'ordre ferrroélectrique et desordre coexistent, avec une maille pseudo-cubique (x(Sn)=0,1...0,3)

• les relaxeurs avec une maille pseudo-cubique qui incluent des clusters nanoscopiques avec les distorsions polaires (x(Sn)>=0,3).

Les propriétés diélectriques des compositions riches en Ti viennent des dipôles d'origine ferroélectrique. Par contre, pour les compositions riches en Sn, les dipôles de défauts peuvent jouer un rôle important.

La MET montre que les clusters polaires nanométriques des phases relaxeur x(Sn)=0,4 ont une taille plus petite que dans les compositions présentant une transition diffuse, mais les valeurs des déplacements des Ti/Sn est plus grande. On observe des distorsions complexes avec une composante rhomboédrique selon <111>.

Le deuxième chapitre présente les mesures d'absorption optique à température ambiante et en température, pour des compositions choisies, afin de relier les propriétés optiques à l'ordre polaire.

La bande interdite montre une variation non-linéaire en fonction de la composition. Elle croît d'une valeur ∼0.35 eV jusqu'à x(Sn)=0,8 et diminue pour les autres compositions. À partir de nos données, la bande interdite est définie par les états élargis où les composantes individuelles Sn ou Ti ne sont pas séparables, nous amenant à supposer une hybridation.

On trouve la connexion entre la valeur de bande interdite et le type de désordre sur x(Sn) pour les échantillons à température ambiante et en température. La bande interdite change d'une façon continue dans les limites d'une phase, puis elle diminue d'une façon non-linéaire avec l'augmentation de température près de la transition de phase, avant de reprendre une évolution linéaire. De plus, la pente de Eg(T ) change entre la phase avec les corrélations polaires statiques et la phase où elles sont absentes. La largeur de la queue d'absorption exponentielles (dites queue d'Urbach) est couplée au type de désordre polaire mais, pour les compositions riches en Sn, le désordre est défini par l'activation des défauts.

En raison de l'importance du désordre local pour les propriétés optiques, dans le dernier chapitre de ce manuscrit la structure locale et le désordre sont analysés en connexion avec la liaison chimique. Nous nous sommes concentrés sur la transition de phase et la spectroscopie Raman a été employée pour discerner les types différents de distorsions et les caractériser qualitativement. Cette étude, couplée avec les résultats des méthodes utilisées dans les chapitres précédents, nous a permis de redéfinir la séquence de phases à température ambiante :

• structures de type ferroélectrique 0<x(Sn)≤0,1

• x(Sn)=0,2 est la seule composition de notre étude présentant une transition diffuse amenant à une coexistence de phase. Une composante ferroélectrique est plus importante que la phase relaxeur selon les mesures diélectriques. La distorsion est très faible, comme x(Sn)=0.2 est juste au-dessous de T CW où la composante de polarisation macroscopique disparaît. La distorsion est orthorhombique avec une faible composante rhomboédrique.

• x(Sn)=0,4 -relaxeur avec des distorsions identique à x(Sn)=0,2

• 0,5<x(Sn)<0,75 relaxeur avec les distorsions orthorhombique et rhomboédrique, la dernière augmentant avec la composition.

• 0,75<x(Sn)≤0,9 les clusters qui contiennent les atomes de Ti dans la matrice BaSnO 3 cubique. Les distorsions préservent les caractéristiques identiques à celle juste avant la limite de percolation d'atomes Ti (O + R), probablement parce que les contraintes chimiques dans les clusters ne changent pas.

Dans les études en température Eg=f(T), la bande interdite réagit à tout changement de phase où la symétrie est modifiée (e.g. rhomboédrique -orthorhombique, comme pour x(Sn)=0.2 dans la zone de transition diffuse) et pas au désordre. Le mécanisme de la variation de la zone interdite est le couplage avec les phonons de type Axe, qui sont détectés en Raman, qui modifient une degré de superposition des orbitales d'oxygène et des atomes B de la structure-type ABO 3 . Ces orbitales forment la liaison chimique π, qui détermine l'énergie minimale de la bande de conduction. Le dégrée de superposition modifie aussi la distribution des charges électroniques effectives des atomes. On peut analyser ces charges qualitativement avec la Spectrométrie de photo-électrons X. Dans une maille distordue, l'angle de la liaison chimique O-B-O n'est pas exactement 180 • et il y a croissance simultanée des charges électroniques des atomes O et B, ce qui est interdit dans le cas cubique parfait par le principe de Pauli. Cette tendance apparaît entre x(Sn)=0 et 0,8, puis le surplus de charge diminue pour x(Sn)=0,8...1. Ceci apporte la preuve que l'augmentation de la bande interdite est causée par l'augmentation de la distorsion rhomboédrique, et la diminution qui suit est reliée à la disparition progressive des clusters polaires dans la matrice de BaSnO 3 . Abstract. The bandgap energy values for the ferroelectric BaTiO3-based solid solutions with isovalent substitution Ba1-x SrxTiO3, BaZrxTi1-xO3 and BaSnxTi1-xO3 were determined using diffuse reflectance spectra. While the corresponding unit cell volume follows Vegard's law in accordance with the different ionic radii of the ionic substitutions, the bandgap values depict non-linear compositional dependences for all the solid solutions. The effect is considerably large for BaZrxTi1-xO3 and BaSnxTi1-xO3 solutions, depicting a bandgap linear compositional dependence up to x=0.6, for x>0.6 BaZrxTi1-xO3 compounds present much larger bandgap values than BaSnxTi1-xO3 counterparts. Electronic properties have been investigated through X-ray photoelectron spectroscopy in BaSnxTi1-xO3 compounds, indicating that the Sn 3d and Ti 2p core levels shift against the Ba 3d ones within the whole compositional range with the same energy trend as that observed for the optical bandgap. Since for Ba1-x SrxTiO3 compounds no major bandgap variation is observed, we conclude that the bandgap compositional dependences observed for BaSnxTi1-xO3 compounds and BaZrxTi1-xO3 ones are originated from the structural sensitivity of the O, Ti and Sn or Zr electronic bands involved in the bandgap transition of these compounds. With this work, we underline the reliability of the bandgap determined from diffuse reflectance spectrometry experiments, as a means to non-invasively evaluate the electronic properties of powder materials.

Introduction

Since the theoretical efficiency limit of single p-n junction solar cell was calculated by Shockley and Queisser [1], there is a challenge of finding new ways to bypass it. A way to intrinsically increase the efficiency could be to use alternative materials such as ferroelectrics (FEs). Unlike p-n junctions, the potential difference in ferroelectrics arises from their non-centrosymmetric unit cell providing the so-called bulk photovoltaic effect [2]. Among them, BaTiO3 is a well-referenced, relatively cheap to produce, and environmentally friendly FE. In view of finding new ways to obtain FE-control of the optical properties, BaTiO3-solid solutions have been studied, as potentially depicting FE-order with simultaneously enhanced photoconductive properties. Here we present the work on three solid solutions with isovalent substitutions, in view of understanding the pure structural and electronic effects and minimizing the point defect contributions. With Sr 2+ substituting Ba 2+ , the Ba1-x SrxTiO3 is a family of solid solutions with ferroelectricity remaining at low temperature up to x_Sr~0.9 [3]. BaZrxTi1-xO3 and BaSnxTi1-xO3 are solid solutions with Ti 4+ being substituted by Zr 4+ and Sn 4+ , respectively, thus presenting conduction band where Zr 4d and Sn 5s 5p states will be added to Ti 3d ones, which in principle will depict much different effective mass and mobility, for the potential photoconduction properties that we are seeking. The phase diagrams of BaZrxTi1-xO3 [4] and BaSnxTi1-xO3 [5] display rich polar features, evolving at room temperature from a pure tetragonal FE in the Ti-rich region towards a paraelectric cubic structure in the Ti-poor region. In-between, the compositions are FE-relaxors characterized by polar disorder and average cubic structure.

Experimental procedures

Ba1-xSrxTiO3 (x_Sr = 0, 0.25, 0.5, 1), BaZrxTi1-xO3 (x_Zr = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1) and BaSnxTi1-xO3 (x_Sn = 0, 0.1, 0.2, 0.4, 0.5, 0.6, 0.8, 0.9, 1) samples were synthesized by solid state reaction from starting materials, BaCO3 (99.9%), SrCO3 (99.9%), TiO2 (99%), ZrO2 (99.9%), and SnO2 (99.9%). After homogenization in a mortar, by ultrasonic bath and by magnetic mixing, the powders were calcined at temperatures between 800°C and 1200°C, and subsequently ground with polyvinyl alcohol and pressed into pellets. Two annealing steps at 600°C and 800°C insured the evaporation of binding agent. The sintering was held at temperatures of 1280-1450°C adjusting the dwell times, resulting in pellet density of ~92-95%. Structural evaluation by X-ray diffraction (XRD) was performed using a Bruker D2 Phaser diffractometer on finely ground and annealed powders, with 0.02º step and acquisition times adjusted for different angular ranges (10 sec/step for 2q=20-35°, 30 sec/step for 35-60°, 55 sec/step for 60-120°). Unit cell volume was determined using Le Bail analysis through devoted crystallographic software (Jana2006). The ultraviolet-visible-near-infrared spectrometry experiments were performed on a Perkin Elmer Lambda 850 spectrometer in diffuse reflectance geometry using a Harrick's Praying Mantis TM accessory, from finely grinded and annealed powders to minimize mechanical stresses. From the raw reflectance, R, the absorption coefficient k is determined according to Kubelka-Munk reemission function FKM transformation [6], within the assumption the scattering coefficient s is independent of the photon energy:

= = 1- 2 . ( 1
)
The optical bandgap is determined from a linear fit to the onset of the absorption edge obtained after converting the FKM following Tauc formalism, which for the present study we consider as direct bandgap. X-ray photoelectron spectroscopy (XPS) studies were carried out on powder and ceramic samples. Axis Ultra DLD spectrometer with Al Kα X-ray source operated at 50W was used, together with charge neutralizer. For the analysis of the XPS data (CasaXPS), we have used the internal reference of the Ba 3d7/2 core level energy, fixed at 778.5eV, as considered to be the ion with very limited changes in its electronic state due to chemical, electronic and structural effects.

Results and Discussion

From the XRD collected (Figure 1a-c), we deduce the stabilization of a pure perovskite phase for each solid solution compound, with unit cell volume following Vegard's law (Figure 1d). The larger compositional slope for Zr-compounds than for Sn-ones is in agreement with the expected effect induced by the difference in ionic radius of Zr 4+ against Sn 4+ , depicting the Sr 2+ -compounds a volume reduction, as expected [8].

Optical properties of the different compositions are shown in Figure 2a-d. Diffuse reflectance raw data in Figure 2a point out the large absorption differences of parent compounds. Optical absorption features are seen in the Kubelka-Munk functions FKM depending of the solid solution. A large increase of FKM is characteristic of the optical absorption edge at a given photon energy, being the Zr-compounds (Figure 2c) those presenting the larger variation of the photon energy onset. No remarkable onset change is seen for Sr-compounds (Figure 2b), and weak and non-monotonic ones for Sn-compounds (Figure 2d). The chemical substitution effect on the occupied electronic states is directly investigated on Sn-based compounds through XPS core level acquisition. Using Ba3d7/2 state as the perovskite energy reference, we plot in Figure 2e-k the different characteristic O1s, Sn3d and Ti2p occupied states. Fine analysis of these levels indicate a shift of the energy positions of Sn and Ti as a function of the Sn-content (Figure 2i andk). Bandgap values as a function of Sn-or Zr-substitution (Figure 3a) account for the large differences previously noticed from direct analysis of the optical properties through FKM. Remarkably, for x_B > 0.2, both solution compounds depict polar disorder, being relaxors at room temperature, follow the same initial trend up to x_B ~ 0.6. For x > 0.6, Zr-compounds present larger bandgap values while lower ones are determined for Sn-compounds. Comparing the obtained optical bandgap values for Sn-compounds with the energy differences of the XPS Ti2p and Sn3d electronic bands (Figure 3b-c), we notice a similar substitution dependence. Moreover, these XPS energy differences are fully in agreement with the observed bandgap variation, being for optical and XPS results this energy difference of ~ 0.35eV between BaTiO3 and x_Sn = 0.8. Investigations are ongoing to determine the precise origin of this behavior and its coupling to the relaxor properties.

Conclusions

Combining structural, optical and electronic characterization tools on pure perovskite Ba1-x SrxTiO3, BaZrxTi1-xO3 and BaSnxTi1-xO3 solid solutions, we proved that we can precisely determine their bandgap values. We have successfully presented the potential of diffuse reflectance spectrometry for the determination of the optical and electronic properties of single phase perovskite oxides, and similar approaches can be exploited for investigating the optical transitions of other materials.

1 3 Figure 1 . 3 :

 1313 Figure 1.3: The efficiency chart of commercially patented solar cell technologies. Credits to NREL (https://www.nrel.gov/pv/national-center-forphotovoltaics.html)

1. 2 .Figure 1 . 7 :

 217 Figure 1.7: Possible intermediate monoclinic phase formation at O-T phase transformation: (a) XRD diagram of BaTiO 3 single crystal at cooling through T-O phase transition (293-273 K, -0.05 K/min) [23] (b) possible directions of polarization inside the BaTiO 3 unit cell[START_REF] Kalyani | Polarization switching and high piezoelectric response in Sn-modified BaT iO 3[END_REF]

Figure 1 . 10 :

 110 Figure 1.10: Correlation of Ti polar displacement in polar nanoregions (PNR)with Sn concentration for x(Sn)=0.2 (HAADF TEM image) in < 001 > polar axis[START_REF] Shi | Why Sn doping significantly enhances the dielectric properties of Ba(T i 1-x Sn x )O 3[END_REF]

Figure 1 . 13 :

 113 Figure 1.13: Phase diagram of BaSn x Ti 1-x O 3 , x(Sn)=0...0.3 from dielectric spectroscopy[START_REF] Lei | Ferroelectric to relaxor crossover and dielectric phase diagram in the BaT iO 3 -BaSnO 3 system[END_REF]

Figure 1 . 14 :

 114 Figure 1.14: Imaginary part of dielectric permittivity of BaSn x Ti 1-x O 3 withx(Sn) = 0.1; 0.15; 0.75; 0.2; 0.25; 0.3[START_REF] Shvartsman | Crossover from ferroelectric to relaxor behavior in BaT i 1-x Sn x O 3 solid solutions[END_REF]

Figure 1 . 15 :

 115 Figure 1.15: Polarization dependence on temperature and (insets) P-E hysteresis loops at different temperatures, x(Sn) = (a) 0.1 (b) 0.12 (c) 0.15 (d) 0.18[START_REF] Zhang | Large electrocaloric effect in Ba(T i 1-x Sn x )O 3 ceramics over a broad temperature region[END_REF]

16 CHAPTER 2 .Figure 2 . 1 :

 16221 Figure 2.1: Steps of solid state reaction synthesis of BaSnO 3

CHAPTER 2 .Figure 2 . 2 :Figure 2 . 3 :

 22223 Figure 2.2: SEM (secondary electrons mode) images of BaSn x Ti 1-x O 3 powder coming from grinding the pellets of x(Sn) = (a) 0, (b) 0.2, (c) 0.5, (d) 0.8, (e) 1

Figure 2 . 5 :

 25 Figure 2.5: Details of XRD data and results: (a) zoom at the region of (002) and (200) peaks, (b) the extracted unit cell volume (error bars of the Le Bail fit in green are smaller than the symbol size)

CHAPTER 2 .

 2 NEW PHASE DIAGRAM (STRUCTURE AND DIELECTRIC/FERROELECTRIC PROPERTIES)

Figure 2 . 6 :

 26 Figure 2.6: Dielectric permittivity and losses for BaSn x Ti 1-x O 3 with x(Sn): (a) 0.1, (b) 0.2, (c) 0.4, (d) 0.5 (synthesis with PVA) and (e) 0.8 (synthesis without PVA)

Figure 2 . 8 :Figure 2 .

 282 Figure 2.8: The phase transformations of BaSn 0.4 Ti 0.6 O 3 at the highertemperature limit: (a) the fit of 1/ε by Curie-Weiss law and the determination of T d (b) fit of 1/ε by quadratic law and the determination of T Q Figure 2.10 presents the summary plot with the critical temperatures taken from literature and obtained in this study. Note that T d keeps approximately constant to x(Sn)=0.3 and then decreases exponentially. Similarly, the slope of T CW changes at x(Sn)=0.3: this value is larger for relaxor compositions.

CHAPTER 2 .Figure 2 . 9 :Figure 2 . 10 :

 229210 Figure 2.9: Deviation from Curie-Weiss law plotted for x(Sn) = (a) 0.5 (b) 0.8

Figure 2 . 11 :

 211 Figure 2.11: The dielectric relaxation frequency dependence for two samples of x(Sn)=0.1: the pellet sintered (a) without PVA (b) with PVA

Figure 2 . 12 :Figure 2 . 13 :

 212213 Figure 2.12: The dielectric relaxation frequency dependence for two samples of x(Sn)=0.2: the pellet sintered (a) without PVA (b) with PVA

Figure 2 . 14 :

 214 Figure 2.14: The dielectric relaxation frequency dependence for two samples of x(Sn)=0.5: the pellet sintered (a) without PVA (b) with PVA

Figure 2 . 15 :

 215 Figure 2.15: The dielectric relaxation frequency dependence for x(Sn)=0.8 sintered without PVA

CHAPTER 2 .Figure 2 . 16 :

 2216 Figure 2.16: HRTEM study of BaSn 0.4 Ti 0.6 O 3 sintered pellet, (a) the image with atomic resolution, (b) correspondingly oriented structural model, with large green atoms -Ba, small red -O, large grey/blue -Sn/Ti; (c) color map of Ti/Sn displacement along <111>

Figure 2 . 17 :

 217 Figure 2.17: XRD peaks of BaTiO 3 from crystallographic planes (a) (110), (b) (111), (c) (200)

Figure 2 . 18 :

 218 Figure 2.18: XRD peaks of BaSn 0.2 Ti 0.8 O 3 from crystallographic planes (a) (110), (b) (111), (c) (200)

Figure 2 . 19 :

 219 Figure 2.19: XRD peaks of BaSn 0.5 Ti 0.5 O 3 from crystallographic planes (a) (110), (b) (111), (c) (200)

Figure 2 . 21 :

 221 Figure 2.21: XRD peaks of BaSnO 3 from crystallographic planes (a) (220); (b) (111); (c) (200)

CHAPTER 2 .Figure 2 . 22 :

 2222 Figure 2.22: The characteristic temperatures united from dielectric spectroscopy and laboratory X-ray diffraction

3. 2 . 1

 21 Methodology: Diffuse reflectance theory, Kubelka Munk approximation and Urbach tail To measure the optical absorption, Ba(Sn,Ti)O 3 pellets were crashed into fine powders and annealed at 500 • C to relax the possible stresses generated by mechanical grinding. Their optical properties were measured by UV-visible-NIR spectroscopy, spectrometer model Perkin Elmer Lambda 850. Powders cannot be measured by a standard transmission technique due to phenomena of reflection and refraction taking place at the multiple interfaces, and strong absorbance above the band gap energy value. Hence, we used the adapted measurement technique with the commercial accessory for diffuse reflection (fig. 3.1).

Figure 3 . 1 :

 31 Figure 3.1: The commercial accessory for diffuse reflection UV-visible-NIR spectroscopy

  Diffuse reflectance raw data in fig.3.2a point out the large absorption differences of the parent compounds. Optical absorption features are seen in the Kubelka-Munk functions F KM depending of the solid solution. A large increase of F KM is characteristic of the optical absorption edge at a given photon energy, being the Zr-compounds (fig.3.2c) those presenting the larger variation of the photon energy onset. No remarkable onset change is seen for Sr-compounds (fig.3.2b), and weak and non-monotonic ones for Sn-compounds (fig.3.2d).The absorption coefficient of BaSn x Ti 1-x O 3 at room temperature (F KM ) is plotted in fig.3.3 for a range of chemical compositions. No anomalies at the absorption edge are visible. At the same time, the onset shifts to higher energy for intermediate compositions. Overall, three peaks (possibly, groups of peaks) are visible in the spectrum of BaTiO 3 -at around 3.6 eV, 4.3 eV and 5.7 eV.

  3.4a. The rest three plots are available in fig. A1 of the Annex. Band gap values in fig. 3.4 evolve non-linearly, increasing by around 0.35 eV until x(Sn)=0.8, and then decreasing towards pure BaSnO 3 .

Figure 3 . 2 :

 32 Figure 3.2: Optical properties from BaTiO 3 -solid solutions (a) Diffuse reflectance spectra from parent compounds (BaTiO 3 , SrTiO 3 , BaSnO 3 and BaZrO 3 , bottom to top), and (b)-(d) Kubelka-Munk F KM functions vs photon energy E determined for (b) Ba 1-x Sr x TiO 3 with x(Sr)=0, 0.25, 0.5, 1 (top to bottom), (c) BaZr x Ti 1-x O 3 with x(Zr)=0, 0.2, 0.5, 1 (top to bottom), and (d) BaSn x Ti 1-x O 3 with x(Sn)=0, 0.2, 0.5, 1 (top to bottom).

Figure 3 . 3 :

 33 Figure 3.3: Absorption coefficient F KM of BaSn x Ti 1-x O 3 : compositional dependence

Figure 3 . 4 :Figure 3 . 5 :

 3435 Figure 3.4: Band gap of BaSn x Ti 1-x O 3 : compositional dependence at room temperature (a) Tauc plot under direct Eg assumption for different compositions (b) the extracted Eg values (error bar is smaller than the symbol size)

Figure 3 . 6 :

 36 Figure 3.6: Temperature dependence of Urbach tail in ferroelectric SbSI, showing tree regimes of disorder: frozen dynamics, ferroelectric, and paraelectric phases

  3.7.

Figure 3 . 7 :

 37 Figure 3.7: Compositional dependence of disentangled components of disorder parameter Eu (w T = Eu T , w X =Eu S , w C =Eu Comp ) [73]

3. 3 . 2

 32 Figure3.8 shows the Urbach plots. For both pure parent compounds, there is a single linear region of the plot, with no absorption below. For intermediate compositions, there is an additional shoulder at the lower-energy side. This shoulder is present for x(Sn)=0.1 to 0.6, and seems to disappear in x(Sn) 0.8. It is known that the presence of the second linear part of the Urbach plot can point at the coexistence of different phases or different types of disorder, at least in BaTiO 3 close to T c[START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF]. However, here there is no clearly defined linear region.

Figure 3 . 8 :

 38 Figure 3.8: Urbach-type plots for different Ba(Sn, Ti)O 3 compositions

Figure 3

 3 Figure 3.9: Urbach tail width Eu in Ba(Sn,Ti)O 3 : (a) compositional dependence (b) coupling between disorder Eu and the bandgap Eg

3. 4

 4 Temperature evolution of band gap and disorder-related absorption tail 3.4.1 BaTiO 3

Figure 3 . 10 :

 310 Figure 3.10: Optical properties of BaTiO 3 powders (straightly after solid state synthesis and after sintering as a pellet with PVA and crashing: temperature dependence of (a) band gap Eg (b) Urbach tail energy Eu (typical error bar values are shown at lowest temperatures)

1 Figure 3 . 11 :

 1311 Figure 3.11: Band gap Eg dependence on disorder Eu in BaTiO 3

Figure 3 . 12 :

 312 Figure 3.12: Optical absorption of BaSn 0.1 Ti 0.9 O 3 powders: (a) band gap and Urbach tail width temperature dependence (typical error bar values are shown at lowest temperatures) (b) band gap dependence on disorder

Figure 3 . 13 :

 313 Figure 3.13: Optical absorption of BaSn 0.2 Ti 0.8 O 3 : (b) temperature dependence of Eg and Eu (typical error bar is shown in green for lowest temperature) (b) dependence of Eg on Eu

0. 5

 5 Ti 0.5 O 3 For this composition, the band gap appears to decrease linearly on temperature fig. 3.14a. The Urbach tail width increases with three linear regions: below 420 K, 420-520 K, 520-610 K, and above this temperature. According to band gap linearity throughout the temperature span of measurement, no new critical points appear in the plot of fig. 3.14b.

Figure 3 . 14 :

 314 Figure 3.14: Optical absorption of BaSn 0.5 Ti 0.5 O 3 : (a) temperature dependence of Eg and Eu (typical error bar values are shown at lowest temperatures) (b) dependence of Eg on Eu

Figure 3 . 15 :

 315 Figure 3.15: Optical absorption of two BaSnO 3 samples: (a) temperature dependence of Eg and (b) of Eu (typical error bar values are shown at lowest temperatures)

Figure 3 . 16 :

 316 Figure 3.16: The Eg -Eu plot for the two BaSnO 3 samples

Figure 3 . 17 : 4 Chemical

 3174 Figure 3.17: The combined plot with characteristic temperatures from dielectric, XRD, and optical characterization

Figure 4 . 1 :

 41 Figure 4.1: Raman spectrum of BaTiO 3 ceramics with different grain sizes, as indicated

Figure 4 . 2 :

 42 Figure 4.2: Sketch of the difference between TO and LO phonons, the arrows indicate the amplitude of vibration, horizontal lines indicate the propagation direction (time axis) In ABO 3 perovskites, the modes can involve the vibration of different combinations of atoms fig. 4.3. The type of mode determines the index n in the mode name (LO n or TO n ). The longitudinal Slater and Axe modes (LO 1 and

Figure 4 . 3 :

 43 Figure 4.3: The classification of phonons in perovkites [95] depending on the involved atoms: (a) Slater n=1 (b) Last n=2 (c) Axe n=3 (d) O 4 torsional mode, n=4

Figure 4 . 4 :

 44 Figure 4.4: The soft mode in BaTiO 3 (a) from neutron scattering [94], (b) in Raman spectroscopy (our data)

Figure 4 . 5 :

 45 Figure 4.5: Raman spectrum of BaSnO 3[START_REF] Stanislavchuk | Electronic band structure and optical phonons of BaSnO 3 and Ba 0.97 La 0.03 SnO 3 single crystals: Theory and experiment[END_REF]

Figure 4 . 6 :

 46 Figure 4.6: Raman spectra of BaSn x Ti 1-x O 3 with x(Sn)=0.3[START_REF] Kumar | Investigation of local structure of lead-free relaxor BaT i 0[END_REF]

Figure 4 . 7 :

 47 Figure 4.7: Study in temperature of A * 1 TO 3 mode fit parameters in BaSn x Ti 1-x O 3 with x(Sn)=0.3. Note the different critical temperatures in the peak centers and the intergrated intensity[START_REF] Kumar | Investigation of local structure of lead-free relaxor BaT i 0[END_REF]

Figure 4 .

 4 Figure 4.8: X-ray photoelectron spectroscopy: (a) measurement scheme, with hν XR -the X-ray energy; and (b) the relation between the electronic bands and the XPS spectrum

Figure 4 . 9 : 1

 491 Figure 4.9: The difference between the reference energy level Ba 3d 5/2 and other levels -the parameter used for analysis of our XPS data

Figure 4 . 10 :

 410 Figure 4.10: Raman spectra at room temperature for BaSn x Ti 1-x O 3 with different Sn ratio

Figure 4 . 11 :

 411 Figure 4.11: Some of the fit parameters plotted against composition: (a) peak maxima of LO 3 modes in 700 cm -1 region; (b) the TO 2 -TO 4 mode (remanent from B 1 in BaTiO 3 ). Error bars are shown in green.

Figure 4 . 12 : 1 T O 1 )

 41211 Figure 4.12: (a) the intensity ratio I(b)/I(c), corresponding to different coupling of Last mode and soft mode; (b) the intensity ratio I(d)/I(A * 1 T O 1 ) the presence of mode d, appearing at 232 cm -1 in x(Sn) = 0.2 and becoming stronger for Sn-rich compositions. This mode appearing in BaTiO 3 spectrum is the characteristic feature of rhombohedral phase (see fig. 4.4 and discussion of fig. 4.4a), evidences the de-coupling of all the components of Slater E * TO 1 from the eight-side hopping. The fact that the coupling disappears in our spectra can be further proved by the drastic decrease of width of A * 1 TO 1 mode at 260 cm -1 fig. 4.13a. Importantly, the widening of this mode in BaTiO 3 is claimed to happen due to bond and/or chemical coupling to disorder. Addi-

Figure 4 . 13 :

 413 Figure 4.13: The FWHM of (a) A * 1 TO 1 ; (b) mode b. Error bars are shown in green.

4. 2 . RESULTS 75 BaTiO 3

 2753 was measured in several references[START_REF] Wemple | Polarization Fluctuations and the Optical-Absorption Edge in BaT iO 3[END_REF][START_REF] Hafid | Absorption spectrum in the near U.V. and electronic structure of pure barium titanate[END_REF][START_REF] Vikash Mishra | Electronic and optical properties of BaT iO 3 across tetragonal to cubic phase transition: An experimental and theoretical investigation[END_REF] fig.4.14. It is speculated that phonon driving the optical response is probably not the soft mode transverse Slater phonon A 1 TO 1 . Here we present our Raman data acquired in temperature to analyse the changes of the polar state and the possible connection to the band gap change we have determined.

Figure 4 . 14 :

 414 Figure 4.14: The band gap of BaTiO 3 at the T-C phase transition

Figure 4 . 15 :

 415 Figure 4.15: The temperature dependence of Raman A 1 TO 1 mode deduced from the peak maximum position

  3 at the R-O phase transformation fig. 4.20, and 4

Figure 4 . 16 :Figure 4 . 17 :Figure 4 . 18 :

 416417418 Figure 4.16: The connection between temperature dependences of A 1 TO 3 Raman mode and band gap for different phases of BaTiO 3 (error bar for the band gap is smaller than the symbol size)

Figure 4 . 19 :Figure 4 . 20 : 3 Figure 4 . 21 :

 4194203421 Figure 4.19: The fit of Raman spectra of x(Sn)=0.2 at different temperatures

Figure 4 . 22 :

 422 Figure 4.22: Connection between phonons and the optical absorption in x(Sn)=0.2: (a) the Raman peak maximum evolution; (b) Eg and Eu temperature dependence (reproduced from Chapter 2)

Figure 4 . 23 :Figure 4 . 24 :

 423424 Figure 4.23: The summary on phase and disorder transitions in x(Sn)=0.2, using the data from XRD and dielectric, UV-visible-NIR, and Raman spectroscopies

Figure A1 :

 A1 Figure A1: The Tauc plot under different assumptions of its origin: (a) allowed indirect band gap; (b) forbidden direct band gap; (c) forbidden indirect band gap

Figure B1 :Figure C1 :Figure D1 :Figure D2 :

 B1C1D1D2 Figure B1: Raman spectra recorder in temperature for compositions x(Sn): (a) 0; (b) 0.2, (c) 0.4, (d) 0.5

Figure 1 :

 1 Figure 1: Room temperature X-ray diffraction [(a)-(c)] powder patterns and (d) unit cell volume determined from the XRD patterns, for different BaTiO3-based compounds. [(a)-(c)]: (a) Ba1-xSrxTiO3 with x_Sr=0, 0.25, 0.5, 1 (bottom to top), (b) BaZrxTi1-xO3 with x_Zr=0, 0.2, 0.5, 1 (bottom to top), and (c) BaSnxTi1-xO3 with x_Sn=0, 0.2, 0.5, 1 (bottom to top); (d) Pseudocubic cell volume per formula unit as a function of x_B site (Zr or Sn) (symbols), corresponding linear fits are shown.

Figure 2 :

 2 Figure 2: [(a)-(d)] Optical properties from BaTiO3-solid solutions, and [(e)-(k)] X-ray photoelectron spectroscopy (XPS) core level data from Ba(Sn,Ti)O3. [(a)-(d)]: (a) Diffuse reflectance spectra from parent compounds (BaTiO3, SrTiO3, BaSnO3 and BaZrO3, bottom to top), and [(b)-(d)] Kubelka-Munk FKM functions vs photon energy E determined for (b) Ba1-xSrxTiO3 with x_Sr=0, 0.25, 0.5, 1 (top to bottom), (c) BaZrxTi1-xO3 with x_Zr=0, 0.2, 0.5, 1 (top to bottom), and (d) BaSnxTi1-xO3 with x_Sn=0, 0.2, 0.5, 1 (top to bottom).[(e)-(k)]: Core levels from BaSnxTi1-xO3 compounds (x_Sn=0, 0.2, 0.5, 1) (a) Ba3d, (g) O1s, (h) Sn3d, (i) Sn3d7/2, (j) Ti2p, (j) Ti2p3/2, together with the example on BaTiO3 sample of the different components used for Ba3d5/2 fitting (Ba within BaCO3, dash line, Ba within the perovskite -here, BaTiO3-fill line, and background, dotted line).

Figure 3 :

 3 Figure 3: (a) Bandgap values as a function of the x_B site substitution for different BaTiO3-solid solutions, determined using FKM and Tauc plot linear fits, assuming direct bandgap. Inset: Bandgap for the Ba1-xSrxTiO3 compounds vs x_Sr substitution. [(b),(c)]: B-site core level energy difference (DE) relative to the perovskite Ba3d7/2 core level position for different BaSnxTi1-xO3 compounds and as a function of the x_Sn substitution, being (b) Ti2p5/2 and (c) Sn3d7/2 (lines are a guide for the eye).

  Visualizing chemical homogeneity on atomic level . . . . . . . . 1.4 Dipole ordering and dielectric spectroscopy . . . . . . . . . . . 1.5 Macroscopic polarization . . . . . . . . . . . . . . . . . . . . . . Methods of characterization used in this chapter . . . . . . . . 2.1.1 Details of XRD measurement in this study . . . . . . . 2.1.2 Dielectric spectroscopy measurement . . . . . . . . . . . 2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Microstructure from scanning electron microscopy . . . 2.2.2 Room temperature structure of compositional series . . 2.2.3 Dielectric spectroscopy . . . . . . . . . . . . . . . . . . . 2.2.4 Transmission electron microscopy . . . . . . . . . . . . . 2.2.5 Temperature dependent laboratory X-ray diffraction studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Properties: Introduction . . . . . . . . . . . . . . . . . 3.2 Band gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Methodology: Diffuse reflectance theory, Kubelka Munk approximation and Urbach tail . . . . . . . . . . . . . . 3.2.2 Results of UV-Visible-NIR spectroscopy . . . . . . . . . 3.3 Chemical disorder-driven absorption edge . . . . . . . . . . . .

	2 New phase diagram (structure and dielectric/ferroelectric
	properties)
	2.1 3 Optical properties
	3.1

1 Introduction 1.1 Motivation: photovoltaics and ferroelectric perovskite oxides . . 1.2 Crystallographic studies of Ba(Sn,Ti)O 3 phase diagram . . . . . 1.2.1 BaTiO 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 BaSnO 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Ba(Sn,Ti)O 3 . . . . . . . . . . . . . . . . . . . . . . . . 1.3

  2.5b). The details of the fit can be found in Annex D in fig. D1 -fig. D2 and in table D1. The value increases linearly as expected due to the larger size of the Sn ion.Figure

					(Sn) :
					1
					0.9
	XRD intensity, a.u.				0.8 0.6 0.5 0.4 0.2 0.1 0
	40	60	80	100	120
			2Θ,°x

2.4: XRD patterns for different compositions of BaSn x Ti 1-x O 3 : x(Sn)=0...1 (bottom towards top)

  table 2.1 and later recalled in fig. 2.10.

	2.2. RESULTS									21
					x(Sn):
					1
					0.9
	XRD intensity				0.8 0.6 0.5 0.4 0.2 0.1
					0
	43	44	45	46	47	64	0.0	0.2	0.4	0.6	0.8	1.0
			2Θ,	°(a)

Table 2 .

 2

	1: Tm of dielectric permittivity at 1 MHz
	x(Sn) Tm, K
	0.1	320
	0.2	245
	0.4	118
	0.5	99
	0.8	109

  3 (fig. 2.21) at 230-260 K for all the three systems of crystallographic plane (d 200 , d 220 , d 111 ).

	2.2. RESULTS	33 CHAPTER 2. NEW PHASE DIAGRAM (STRUCTURE AND
				DIELECTRIC/FERROELECTRIC PROPERTIES)
		T, K:	T, K:
			480	480
	420 K		460	450
	27.75 27.90 2Θ, °300 K 57.0 2Θ,	440 420 400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 115 110 105 100 95 90 85 °230 K 34 2Θ, 400 350 57.5 260 K 300 260 230 200 190 185 180 175 170 165 160 155 150 145 140 135 130 120 110 100 80	°(b)	35 34.0 34.2 39.5 40.0 2Θ, °340 K 2Θ, °(b) 39.5 2Θ,	°260 K 230 K
	(a)		(a)			(c)	(c)

Figure 2.20: XRD peaks of BaSn 0.8 Ti 0.2 O 3 from crystallographic planes (a) (110), (b) (111), (c) (200)

Table 4 .

 4 1: Raman modes of BaTiO 3[START_REF] Fontana | Quasimodes and a central peak in BaT iO 3[END_REF][START_REF] Freire | Lattice dynamics of crystals with tetragonal BaT iO 3 structure[END_REF][START_REF] Takuya | Terahertz dielectric response of single-domain BaT iO 3 measured by far-infrared spectroscopic ellipsometry[END_REF][START_REF] Perry | Temperature Dependence of the Raman Spectrum of BaT iO 3[END_REF][START_REF] Gervais | Infrared and Raman responses in ferroelectric perovskite crystals: Apparent inconsistencies[END_REF][START_REF] Laabidi | Underdamped soft phonon in orthorhombic BaT iO 3[END_REF]

	Mode	Peak maximum, cm -1
	E(TO 1 ) mode a: Central mode	38-50 100
	mode b: A 1 (TO 2 ) -E(TO 1 ) mode c: LO 2 , TO 2 -E(TO 1 ) rhombohedral E(TO 1 ) A 1 (TO 1 ) TO 4 , TO 2	154 ∼ 180-190 250 260-270 300-307
	E(LO 4 ) A 1 (LO 1 ) E(TO 3 ) A 1 (TO 3 )	465 470 490 512
	E(LO 3 ) Oblique mode A 1 (LO 3 )-E(LO 3 ) A 1 (LO 3 )	706 716 730

Table 4 .

 4 2: Born charges of parent compounds of BaSn x Ti 1-x O 3[START_REF] Xie | The Electronic Structures, Born Effective Charges, and Interatomic Force Constants in BaM O 3 (M= Ti, Zr, Hf, Sn): A Comparative First-Principles Study[END_REF]

	Compound	Z * Ba	Z * B	Z * O	Z * O⊥
	BaTiO 3 BaSnO 3	+ 2.73 + 7.52 -5.88 -2.15 + 2.74 + 4.38 -3.35 -1.88

Table 4 .

 4 3: XPS quantification results of BaSn x Ti 1-x O 3 ceramics

	x(Sn) Sn/Ba Sn/Ba Sn/Ti Sn/Ti Ti/Ba Ti/Ba
			(theor)		(theor)		(theor)
	0					0.94	1
	0.1	0.17	0.1	0.17	0.11	0.99	0.9
	0.2	0.28	0.2	0.39	0.25	0.7	0.8
	0.4	0.58	0.4	1.05	0.67	0.55	0.6
	0.5	0.65	0.5	1.39	1	0.47	0.5
	0.6	0.79	0.6	2.29	1.5	0.35	0.4
	0.8	1.07	0.8	5.93	4	0.18	0.2
	0.9	1.25	0.9	14.96	9	0.08	0.1
	1	1.44	1.00

Table D1 :

 D1 Errors of the profile Le Bail fit for different compositions

	x(Sn) Space group	a, Å	c, Å	Rwp GOF
	0	P 4mm	3.9965 4.0325 15.99	1.4
	0.1	P m 3m	4.0179 4.0179 17.56	1.5
	0.2	P m 3m	4.0285 4.0285 16.84 1.47
	0.4	P m 3m	4.0502 4.0502 16.06 1.37
	0.5	P m 3m	4.0587 4.0587 12.38	1.5
	0.6	P m 3m	4.0693 4.0693 14.62 1.88
	0.8	P m 3m	4.0932 4.0932 13.61 1.22
	0.9	P m 3m	4.1056 4.1056 11.54 1.54
	1	P m 3m	4.1158 4.1158 16.72 1.38

  OPTICAL AND ELECTRONIC PROPERTIES IN FERROELECTRIC BARIUM TITANATE-BASED COMPOUNDSHalyna Volkova 1, * , Pascale Gemeiner 1 , Grégory Geneste 2 , Jêrome Guillot 3 , Carlos Frontera 4 , Nidal Banja 1 , Fabienne Karolak 1 , Christine Bogicevic 1 , Brahim Dkhil 1 , Nicolas Chauvin 5 , Damien Lenoble 3 , and Ingrid C. Infante 5 1 Laboratoire Structures, Propriétés et Modélisation des Solides, CentraleSupélec, CNRS-UMR8580, Université Paris-Saclay 8-10 rue Joliot-Curie, Gif-sur-Yvette, France 2 CEA, DAM DIF, Arpajon, France 3 Luxembourg Institute of Science and Technology, Materials Research and Technology Department 41 rue du Brill, Belvaux, Luxembourg 4 Institut de Ciència de Materials de Barcelona, Consejo Superior de Investigaciones Científicas Campus de la UAB, Bellaterra, Spain 5 Institut de Nanotechnologies de Lyon, CNRS-UMR5270 ECL INSA UCBL CPE, Université de Lyon 7 avenue Jean Capelle, Villeurbanne, France

	THIRD SEMINAR ON THE MECHANICS OF MULTIFUNCTIONAL MATERIALS
	1

*

Corresponding author: H. Volkova (halyna.volkova@centralesupelec.fr)

Acknowledgements

thank a lot to Nicolas Chauvin from INL, Lyon for