Maman Belge

Claire Schollaert-Nguyen

Pierre Nguyen

Meng Liao

Xiaomeng Zhang

Xiaoya Li

Shouwei Zhang

Zimin Li

Xiaoqin Gao

on lithography training and advices on the 2D exfoliation and of course, fun jokes; Seb, from all the memories of March meeting to every daily conversations we've shared, you are like walking encyclopaedia to me; and Andra, you are so earnest with generous heart, thanks for all your warm-hearted encouragement and support and all the sweets to cheer me up.

After an intensive period of four years, today is the day: writing this note of thanks is the finishing touch on my dissertation. It has been a period of intense learning for me, not only in the scientific arena, but also on a personal level. At the end of this, I should take some time to express my gratitude to those without whom this thesis would never have been possible.

First and foremost I offer my sincerest gratitude to my two enthusiastic supervisors, Prof. Benoît Hackens and Prof. Thierry Ouisse. They have taught me, both consciously and unconsciously, how good experimental physics is done. I appreciate all their contributions of time, ideas, and funding to make my Ph.D experience productive and stimulating. The joy and enthusiasm they have for the research was contagious and inspiring for me, even during tough times in the Ph.D. pursuit. My PhD has been an amazing experience and I thank Benoît and Thierry wholeheartedly, not only for their tremendous academic support, the systematic guidance that put into training me in the scientific field, but also for their patience and kindness helped me overcome tough situations. Thank you to pick me four years ago and offered me this great opportunity to work in two great labs. I would like then to take a moment to thank my thesis committee members. Thank you to Prof. Sylvain Dubois and Prof. Matthieu Verstraete for being my rapporteurs.

Also thank you to Prof. Jean-Christophe Charlier and Prof. Vincent Bayot for being examiners of my thesis. I appreciate greatly of your time investing on my thesis and valuable insights for the thesis revisions. I feel honoured that you have accepted to be on my committee.

I am grateful to LMGP members with whom I have interacted during my first stage of thesis, Didier Chaussende, Jean-Marc Dedulle and Eirini Sarigiannidou for good advices on my research, Odette Chaix for the Raman analysis, Herve Roussel for the i XRD analysis, Joseph La Manna, Serge Quessada and Lucile Parent-Bert for technical support, and Benjamin Piot (LNCMI,CNRS) for helping me with LowT measurements in Grenoble. The members of the Cristallogenese group in LMGP have contributed immensely to my personal and professional time at Grenoble. Special thanks to our closed team members: Nikolaos Tsavdaris, Kanaparin Ariyawong, Yunji Shin, Sven Tengeler, Demitrios Zevgitis, Shiqi Zhang, Hoang-Long Le Tran. From our first Christmas party at Yunji's home to the laser game, rock climbing, weekend hiking, and our magic table always with snacks and beverage at lab, I spent so many joyful and lighthearted moments with all of you. Your great support and accompany all ease the adaptation to the new changes of my life in Europe. And to my friends in Grenoble, my dear roommate Xuexin Ma and Yunxia Yao. I will never forget those moments filled with laughters and tears lighting up this snowy mountain city.

Similar, profound gratitude goes to those with whom I have interacted during my research time in UCLouvain. To members of BSMA, Prof.Luc Piraux for LowT measurement, Delphine Magnin for SEM analysis, Cécile D'Haese for AFM analysis, Sergey Basov and Pedro Sá for helping me changing Helium and endless gas and water pressure checking. Special to Pascale Lipnik for TEM analysis and thanks to your effort, I finally get the TEM results on my samples. To members of MOST, Prof. Sophie Hermans for support of all chemical experiments, Jean-François Statsyns for technical support, Koen Robeyns for crystallography analysis. Special thanks to Nadzeya Kryvutsa, for all the advices and support from chemical side and to be honest, I could not image if the time spending at Building Lavoisier without you. To members of ICTEAM, Ferran Urena Begara for valuable suggestions on the Raman analysis. To members of NAPS, Aurélie Champagne, for all your ideas and discussions on this topic. To members of Winfab, Sébastien Faniel for helps on Ebeam lithography and metal deposition, Ester Tooten for the laser machining, Milout Zitout for the wafer processing. Thank you all for helping my works in Louvain-la-neuve.

I am hugely appreciative to our fun group 'Fridge': Damien Cabosart, Thanh Nhan Bui, Andra-Gabriela Iordanescu, Boris Brun-Barrière, Sébastien Toussaint, Nicolas Moreau, Hui Shang and our previous group member Frederico Matins and Cristiane Nascimento Santos. Starting from the beginning of my presentation for FRIA, they have been a source of friendships as well as good advice and collaboration. Nhan, thank you for you've helped me so much with day and night endless recycling of cooling down and warming up, pumping vacuum and refilling Helium, and for electronic measurement advices; Damien, hey three year's officemate, thank you for your help

Introduction

MAX phases are layered early transition metal ternary carbides and nitrides so called because they are composed of M, an early transition metal, A, a group A element and X is C and/or N. MAX phase structure is composed of near close-packed planes of M atoms with the X atoms occupying all the octahedral sites between them. They combine some of the best properties of ceramics and metals. Their physical properties (stiffness, damage and thermal shock resistance, high thermal and electrical conductivity) along with the fact they are readily machinable, make them extremely attractive in terms of the potential technological applications.

In 2011, it was discovered that by immersing Al-containing MAX phases in hydrofluoric(HF) acid, it was possible to selectively etch the Al, resulting in two-dimensional (2D) materials, that were labelled MXene to denote the removal of the A-group element and make the connection to another conducting 2D material, graphene. This new member of 2D materials family owns stronger, more chemically versatile, and have higher conductivity than other materials. As such they are highly interesting on new applications, e.g. specialized in vivo drug delivery systems, hydrogen storage, or as replacements of common materials in e.g. batteries, sewage treatment, and sensors. The list of potential applications is long for these new materials.

In this thesis, as its self-telling title indicated, we present our work on the synthesis, structural characterization and the electron transport in the MAX phases and their 2D derivatives, MXenes.The manuscript is organized as follows:

Chapter 1 An general introduction of MAX phases and its derivative MXene is given, including lattice and electronic structure, experimental and theoretical research work on synthesis, characterization and properties.

Contents

For MAX phase:

Chapter 2 Motivated by the theoretically expected anisotropic properties of these layered materials, producing bulk single crystals is a natural way to obtain samples where the anisotropy of the physical properties can be experimentally probed. Also, knowledge of low-temperature behaviour of single crystal is vital because it can provide insight into MAX intrinsic physical properties. Using high temperature solution growth and slow cooling technique, several MAX phases single crystals have been successfully grown. Structural characterization confirms the single crystalline character of the samples.

Chapter 3 Experimentally, a set of experimental data are obtained from single crystals of V 2 AlC and Cr 2 AlC as a function of temperature and magnetic field. In comparison with the resistivity of polycrystalline samples, that of Cr 2 AlC and V 2 AlC, are correspondingly much lower. In particular, we obtain a substantial anisotropy ratio between the in-plane and c-axis resistivity, in the range of a few hundreds to thousands. From Magneto-resistance and Hall effect measurement, in-plane transport behaviours of MAX phases have been studied.Theoretically, a general model is therefore proposed for describing the weak field magneto-transport properties of nearly free electrons in 2D hexagonal metals, which is then modified to be applicable for the transport properties of layered MAX phases.

For MXene:

Chapter 4 We report on a general approach to etch V 2 AlC single crystal and mechanically exfoliate multilayer V 2 CT x (T= termination group, -OH, -F, =O) MXenes. We then investigate the structural characterization of the obtained MXene by means of XRD, SEM, TEM, Raman and AFM techniques. The second part of this chapter discusses the process with the aim of obtaining Ti 2 CT x MXene from Ti 2 SnC single crystals.

Chapter 5 We then further pursuit the electrical device fabrication process and proceeded with electrical measurements, performing down to low temperature, with the aim to extract electronic transport parameters. We successfully attain some first hand data on V 2 CT x MXenes, including the average value for the resistivity of V 2 CT x MXenes, the filed effect measurement indicates field effect mobility µ FE and the Hall mobility µ H , which contributes to the understanding of this class of materials.

chapter 1

From MAX phases to MXene:

Background, History and Synthesis

This introductory chapter aims to bring a brief overview of MAX phases and its derived two-dimensional (2D) material-MXene.

In the first part, the history of MAX phases is given, including the salient properties and the status of current understanding of the MAX phases. Their potential applications are also highlighted. The up-to-date theoretical and experimental understandings on the electronic transport properties of MAX phases are reviewed as well.

The second part is dedicated to the discovery of 2D MXene, encompassing both theoretical and experimental studies of relevance to their synthesis, properties and potential applications in the field of transparent conductors, environmental treatment and energy storage.

Structure of MAX phases

MAX phases acquire a hexagonal layered structure with space group P6 3 /mmc with two formula units per cell. They consist of alternate near close-packed layers of [M6X] octahedral interleaved with layers of pure group A-atoms. The [M6X] octahedral are connected to each other by shared edges. The main difference, in terms of the structures, among so called 211, 312 and 413 phase, is the numbers of M layers between every two A layers. As can be seen in Figure 1.2, two M layers are intercalated between two A layers in 211 phase, three M layers and four M layers between two A layers in 312 and 413 phase, respectively. It also shows the corresponding unit cell with nanolamelar structure where the presence of metallic M-A bonds and covalent M-X bonds results in a combination of metallic and ceramic properties.

MAX phases are typically good thermal and electrical conductors, as well as thermodynamically stable at high temperatures and oxidation resistant. MAX phases exhibit extreme thermal shock resistance, damage tolerance and are easily machinable. All these characteristics make MAX phases promising candidates for various industrial applications.

Synthesis of MAX phases

In last two decades, substantial efforts have been placed on the synthesis and characterization of MAX phases. Here we summarize the methods applied to synthesize MAX phase powders, bulk material and thin films. We can see from the Table 1.1 that, up to now, most of MAX phases are usually produced in a highly polycrystalline form, except in a limited number of reported cases dealing either with thin singlecrystalline layers [5], or single-crystalline platelets [START_REF] Etzkorn | V 2 AlC, V 4 AlC 3-x (x=0.31), and V 12 Al 3 C 8 : Synthesis, Crystal Growth, Structure, and Superstructure[END_REF]. Producing bulk single crystals is a natural way to obtain samples where the anisotropy of the physical properties can be experimentally probed, and which can also be used for developing technological processes leading in turn to the production of macroscopic two dimensional MXene samples with acceptable area. Until recently, the difficulty to produce single crystal MAX phases prohibited a thorough investigation of their physical properties. In 2011, our LMGP team found the way to produce such single crystals [START_REF] Mercier | Morphological instabilities induced by foreign particles and Ehrlich-Schwoebel effect during the two-dimensional growth of crystalline Ti 3 SiC 2[END_REF][START_REF] Mercier | Raman scattering from Ti 3 SiC 2 single crystals[END_REF], and this opened the door to new lines of research in a field which already triggers an intense international research activity. More details about the crystal growth of MAX phases will be discussed in Chapter II.

Electronic properties of MAX phases

From various aspects, MAX phases exhibit interesting and unusual properties. The present thesis will mainly focus on their electrical properties. Herein, we will summarize some of magneto-electronical transport properties of MAX phases in polycrystalline form. In order to highlight the electrical conduction mechanism in the MAX phases, Hall effect, Seebeck Effect and magnetoresistance measurement are presented.

Resistivity

In general, most of the MAX phases are excellent metal-like electrical conductors, particularly, the conductivity of MAX phases is higher than that of the corresponding binary transition metal carbides or nitrides. Some of them, such as Ti 3 SiC 2 , Ti 3 AlC 2 , are better conductors than Ti itself. Up to now, the resistivity of most studied MAX phases was found to be metallic-like: in the phonon-limited regime, the resistivity, ρ, increases linearly with increasing temperature. This behaviour can be described by a linear fit according to the relation

ρ(T) = ρ 0 [1 + β(T -T RT )] (1.1)
6

Method Example Reference

Mechanical Alloying (MA) Ti 3 SiC 2 [START_REF] Li | Fabrication of highly dense Ti 3 SiC 2 ceramics by pressureless sintering of mechanically alloyed elemental powders[END_REF] Powder Self-propagating high-Ti 3 AlC 2 [START_REF] Lopacinski | Synthesis of Ternary Titanium Alumimum Carbides Using Self-Propagating High-Temperature Synthesis Technique[END_REF] temperature synthesis(SHS) Ti 2 AlC [START_REF] Yeh | Effects of TiC and Al 4 C 3 addition on combustion synthesis of Ti 2 AlC[END_REF] (in-situ)Solid state reaction pressure-less sintering Ti 3 SiC 2 [START_REF] Yang | Reaction in Ti 3 SiC 2 powder synthesis from a Ti-Si-TiC powder mixture[END_REF][13] Ti 3 SnC 2 ,Ti 2 SnC [START_REF] Dubois | A New Ternary Nanolaminate Carbide: Ti 3 SnC[END_REF] Hot isostatic pressing (HIP) sintering Hf 2 PbC, Zr 2 PbC [START_REF] El-Raghy | Synthesis and characterization of Hf 2 PbC, Zr 2 PbC and M 2 SnC (M=Ti, Hf, Nb or Zr)[END_REF] Bulk materials V 2 AlC [START_REF] Barsoum | The M n+1 AX n phases: A new class of solids[END_REF] (Polycrystalline MAX Hot pressing (HP) sintering Cr 2 AlC [START_REF] Lin | In-situ hot pressing/solid-liquid reaction synthesis of bulk Cr 2 AlC[END_REF] and its composites Nb 2 AlC [START_REF] Zhang | Reactive Hot Pressing and Properties of Nb 2 AlC[END_REF] Spark plasma sintering (SPS) Ti 3 SiC 2 [START_REF] Zhang | Rapid fabrication of Ti 3 SiC 2 -SiC nanocomposite using the spark plasma sintering-reactive synthesis (SPS-RS) method[END_REF] Ti 2 AlC [START_REF] Shi | Fabrication, Microstructure and Mechanical Properties of TiC/Ti 2 AlC/TiAl3 in situ Composite[END_REF] Slip casting (SC) Ti 3 AlC 2 [START_REF] Sun | Surface Chemistry, Dispersion Behavior, and Slip Casting of Ti 3 AlC 2 Suspensions[END_REF] Physical vapor deposition(PVD) Ti 3 GeC 2 ,Ti 2 GeC [START_REF] Högberg | Epitaxial Ti 2 GeC, Ti 3 GeC 2 , and Ti 4 GeC 3 MAX-phase thin films grown by magnetron sputtering[END_REF] Thin film Chemical vapor deposition (CVD) Ti 3 SiC 2 [START_REF] Jacques | Pulsed reactive chemical vapor deposition in the C-Ti-Si system from H 2 /TiCl 4 /SiCl 4[END_REF] Solid-state reactions Ti 2 AlN [START_REF] Hoglunda | Topotaxial growth of Ti 2 AlN by solid state reaction in AlNaTi(0001) multilayer thin films[END_REF] Thermal spraying Ti 2 AlC [START_REF] Sonestedt | Oxidation of Ti 2 AlC bulk and spray deposited coatings[END_REF] Table 1.1: Synthesis of various forms of MAX phases.

the charge carrier concentration and type of majority charge carriers. Furthermore, most MAX phases exhibit a quadratic, positive, non-saturating magnetoresistance where the MR is defined as △ρ/ρ = ρ(B)-ρ(B=0) ρ(B=0)

.

The combination of small R H , the linearity of the Hall voltage with magnetic field and finally the parabolic non saturating magnetoresistance strongly suggested that most of the MAX phases are compensated conductors [START_REF] Finkel | Lowtemperature transport properties of nanolaminates Ti 3 AlC 2 and Ti 4 AlN 3[END_REF][START_REF] Finkel | Electronic, thermal, and elastic properties of Ti 3 Si (1-x) Ge x C 2 solid solutions[END_REF][START_REF] Finkel | Magnetotransport properties of the ternary carbide Ti 3 SiC 2 Hall effect, magnetoresistance, and magnetic susceptibility[END_REF]]. An assumption on the fact that both electron-like and hole-like states contribute approximately equal to the electrical conductivity allows to interpret the transport data by using traditional two band model. The electrical conduction is assured by electrons and holes and it is described by the relation

σ = 1 ρ = e(nµ n + pµ p ) (1.2)
where e is the electronic charge, n and p are the electron and hole densities, µ n and µ p are electron and hole mobilities.

The R H in low field limit is defined by

R H = (pµ 2 p -nµ 2
n ) e(pµ p + nµ n ) 2 (1.

3)

The magnetoresistance behaviour is described by the following expression

MR = △ρ ρ(B=0) = αB 2 (1.4)
where B is the magnetic field and α is the magnetoresistance coefficient. For two types of carriers, the two band model is required and α is given by α = npµ n µ p (µ n + µ p ) 2 (nµ n + pµ p ) 2 (1.5)

In these equations, n, p , µ n and µ p are unknown. Assuming that MAX phases are compensated conductors lead to n=p which allows simplifying the Eqs 1.2 1.3 and 1.5 where the conduction is governed by either electrons or holes, these relations are simplified to:

σ = 1 ρ = en(µ n + u p ) R H = (µ p -µ n ) en(µ p + µ n ) (1.6) α=µ n µ p (1.7)
If we assume that, µ n = µ p , then this implies that R H =0. The mobility values are close to each other as deduced from 1.6 and relatively low value of measured R H . The electron-like and hole-like mobilities were determined by Barsoum and coworkers [START_REF] Finkel | Lowtemperature transport properties of nanolaminates Ti 3 AlC 2 and Ti 4 AlN 3[END_REF][START_REF] Finkel | Electronic, thermal, and elastic properties of Ti 3 Si (1-x) Ge x C 2 solid solutions[END_REF][START_REF] Finkel | Magnetotransport properties of the ternary carbide Ti 3 SiC 2 Hall effect, magnetoresistance, and magnetic susceptibility[END_REF][START_REF] Scabarozi | Electronic and thermal properties of Ti 3 Al(C 0.5 , N 0.5 ) 2 , Ti 2 Al(C 0.5 ,N 0.5 ) and Ti 2 AlN[END_REF], the results are summarized in the Table 1.2.

From the results listed, it is suggested that MAX phases can be considered as compensated conductors and a traditional two band model seems to give the range of magnitude for the mobility and charge carrier density: charge carrier densities are typically in the range of 1.1-6.3 ×10 27 m -3 and both n and p are temperature independent due to their metal-like character. Mobilities are in the range of (0.55-9) ×10 -3 m 2 /V•s.

Electronic band structure of MAX phases

The electronic structure of a large number of MAX phases has been calculated through Density Functional Theory(DFT). In general, simulation results show that there is no gap between the valence band and the conduction band of MAX phases, which is consistent with metal-like conductivity as demonstrated experimentally. At the Fermi level, the total densities of states (TDOS) is mainly dominated by M 3d states, suggesting that the 3d states of the M element dominate the MAX phase's electronic conductivity.

In this section, we will focus on the electronic band structure and DOS of 211 phase (Cr 2 AlC and V 2 AlC) and one 312 phase (Ti 3 SiC 2 ), which are the main phases involved in the present experimental work.

Cr 2 AlC

The crystallographic, electronic, dielectric function and elastic properties of Cr 2 AlC were studied by means of pseudo-potential plane-waves method using the density functional theory. The energy band structure of Cr 2 AlC is shown in Figure 1.4(a) [START_REF] Jia | Ab initio calculations for properties of Ti 2 AlN and Cr 2 AlC[END_REF].

MAX ρ 0 R H n p µ n µ p α Ref.
(µΩ•m) (10 -11 m 3 /C) (10 27 m -3 ) (10 27 m -3 ) (10 For the case of V 2 AlC, as is shown in Figure 1.5, the metallic nature can be observed with the bands crossing the Fermi level. Also, around Fermi level, weak energy dispersions along M-L and Γ-A directions appeared, which leads to anisotropic character of the conductivity in this compound (i.e., a weaker conductivity along the c-axis).

-3 m 2 /V•s) (10 -3 m 2 /V•s) (T -2 )10 -5 m 4 /V
Previous discussions on Cr 2 AlC have demonstrated that the hybridized M 3d -C 2p states dominate the bonding of this type of MAX phase. The calculated V 2 AlC confirmed such conclusions again, and demonstrates that Al p states also contribute to the orbital bonding. Further analysis of PDOS shows that the hybridization peaks V 3d -C 2p are located at a lower range with respect to that of V 3d -Al 3p, suggesting a stronger V-C bond but a weaker V -Al bond. Actually, the valence DOS can roughly be divided into three major regions: (i) from -12 eV to -10 eV with mainly C 2s states, which is mainly because of the localized or tightly bound electrons; (ii) from -6.5 to -1.0 eV with strongly hybridized V 3d and C 2p or Al 3p states; and finally (iii) from -1.0 eV to 0 eV with mainly V 3d states. The Fermi level is situated halfway between the peak and the valley, which leads to the stability and conductivity of these materials.

In comparison between DOS of Cr 2 AlC and V 2 AlC, difference in bonding between two structures can be inferred from the weakly hybridized M 3d -A 3p states which are closer to the Fermi level for V 2 AlC (-2 eV) than for Cr 2 AlC (-2.5 eV), which indicates that the V-Al bond is slightly weaker than the Cr-Al bond. Meanwhile, similarities can also be concluded as M 3d -C 2p bonds are stronger than M 3d -A 3p bonds, which therefore is mainly responsible for the high modulus and strength of both M 2 AlC MAX phase. The metal-like behaviour of electronic properties is attribute to the M 3d states near Fermi energy level.

From the electron band structure of both cases, it is clearly indicated that, for both Cr 2 AlC and V 2 AlC, the bands are much less dispersive (or even no crossing) along the c-axis than along the basal plane, suggesting that the electronic properties of both MAX phase are anisotropic. The Fermi velocity ( ∂E ∂k ) along the basal plane is higher than that along the c-axis. Herein, we would like to discuss Ti 3 SiC 2 as representative of 312 MAX phases, whose thermopower S is almost zero over a wide range of temperature [START_REF] Yoo | Materials science: Ti 3 SiC 2 has negligible thermopower[END_REF]. First of all, it is essential to distinguish two independent type of M element: Ti(1) and Ti(2) as in the Figure 1 Two particular bands are also shown on their Fermi surface in Figure 1.7(a) [START_REF] Chaput | Anisotropy and thermopower in Ti 3 SiC 2[END_REF]. The Fermi surface of the upper band is very flat and is located around the c/2 plane. Since the velocities are normal to the Fermi surface they are mainly along the c-axis direction.

It explains the predominant role of this band along the c component and its relatively minor role in the basal plane. On the other hand, the normals to Fermi surface of downside band have large components in the ab plane and therefore contribute to the component in the basal plane. Evidence for the anisotropic thermopower of Ti 3 SiC 2 has also been given by Magnuson [38] that in the polycrystalline bulk sample, the Seebeck coefficient is about zero whereas a positive value in the range of 4-6 µV/K is measured on (000l)-oriented thin film, as shown in 1.7(b).

Figure 1.6:

Crystal structure [START_REF] Magnuson | Electronic-structure origin of the anisotropic thermopower of nanolaminated Ti 3 SiC 2 determined by polarized x-ray spectroscopy and Seebeck measurements[END_REF] and electronic band structure of Ti 3 SiC 2 [START_REF] Zhou | Electronic structure and bonding properties in layered ternary carbide Ti 3 SiC 2[END_REF]. [START_REF] Chaput | Anisotropy and thermopower in Ti 3 SiC 2[END_REF] and (b) calculated and measured Seebeck coefficients of Ti 3 SiC 2 (a (000l)-oriented thin film of Ti 3 SiC 2 (triangle) and polycrystalline sample (square) [START_REF] Magnuson | Electronic-structure origin of the anisotropic thermopower of nanolaminated Ti 3 SiC 2 determined by polarized x-ray spectroscopy and Seebeck measurements[END_REF].

PhD work on MAX phase

The primary objective of the present PhD thesis is to deal with the synthesis of single crystal MAX phases (Cr 2 AlC and V 2 AlC) and the characterization of their intrinsic properties. Thermodynamics and kinetics of crystal nucleation and growth were deduced from the synthesis of different single crystal MAX phases (See Chapter II).

The main physical properties, mainly magneto-electronic transport properties of the MAX phases were also studied and the consistency of results obtained in experiments and from simulations was checked. More specifically, probing the anisotropic properties was also achieved thanks to the crystalline samples (See Chapter III).

MXene

2D materials

2D family

Since the pioneering work on graphene, world-wide enthusiasm for 2D materials including inorganic graphene analogues (IGAs) has rapidly grown. These IGAs include hexagonal boron nitride (h-BN),transition metal oxides and hydroxides, transition metal dichalcogenides (TMD), etc. Due to the fact that the thickness is significantly smaller than the other two dimensions, which always results in dramatic changes in electronic structure and lattice dynamics, these 2D materials exhibit unique properties compared with their three-dimensional counterparts.

Top-down Approaches

Mechanical Cleavage Micromechanical cleavage, as originally used in peeling off graphene from graphite, can be extended to other layered materials with weak van der Waals (vdW) forces or hydrogen bond between layers. It proves that 2D layers can be readily exfoliated from 3D crystals mechanically by cleaving the crystals against another surface. The micromechanical cleavage was applied to the isolation of h-BN, MoS 2 , NbSe 2 , from their layered phases. The resulting 2D sheets are stable under ambient conditions, exhibit high crystal quality, with the obtained thickness ranging from 1 to 10 atomic layers.

Micromechanical cleavage has proven an easy and fast way of obtaining highly crystalline atomically thin nanosheets. However, this method produces a large quantity of thicker sheets, while the thinner or monolayer ones only reside in a very minor proportion; thus this method is not scalable to mass production for potential engineering applications. Also, the size of the 2D sheets produced by this technique is limited by the size of the parent 3D crystal and only work for weakly bonded layered materials.

Chemical Exfoliation

As an alternative method, chemically derived exfoliations, such as liquid-phase exfoliation, and ion-intercalation induced exfoliation, have been demonstrated to effectively isolate single layer and few layers from those thicker structures in large quantities. Chemical exfoliation of 3D layered material is used for the production of a wide range of 2D materials chemistries, as varied as graphene and its oxide [START_REF] Hernandez | High-yield production of graphene by liquid-phase exfoliation of graphite[END_REF], h-BN [START_REF] Zhi | Large-Scale Fabrication of Boron Nitride Nanosheets and Their Utiliza-tion in Polymeric Composites with Improved Thermal and Mechanical Properties[END_REF], TMDs [START_REF] Zeng | An Effective Method for the Fabrication of Few-Layer-Thick Inorganic Nanosheets[END_REF] metal oxide and hydroxide [START_REF] Li | Positively Charged Nanosheets Derived via Total Delamination of Layered Double Hydroxides[END_REF][START_REF] Wang | Recent Advances in the Synthesis and Application of Layered Double Hydroxide (LDH) Nanosheets[END_REF].

The principle of chemical exfoliation is to break the bonds between the layers by chemical, chemical-thermal treatment, or chemical reaction assisted by sonication procedures. Most of the chemical exfoliation processes are conducted in the aqueous environment, relying upon strong polar solvents, reactive reagents, or ion intercalation, which is versatile and up-scalable. The fabricated 2D materials can be re-dispersed in common organic solvents, or in various environments and substrates, which is not feasible for mechanical cleavage methods. These methods step up a wide range of potential large-scale preparations and applications of 2D materials for nano devices, composites, or liquid phase chemistry.

Bottom-up Approaches

Chemical Vapour Deposition (CVD)

The main technique that uses a bottom-up approach to synthesize 2D materials is CVD. 2D layers of graphene [START_REF] Reina | Large Area, Few-Layer Graphene Films on Arbitrary Substrates by Chemical Vapor Deposition[END_REF], h-BN [START_REF] Song | Large Scale Growth and Characterization of Atomic Hexagonal Boron Nitride Layers[END_REF], and MoS 2 [START_REF] Lee | Synthesis of Large-Area MoS 2 Atomic Layers with Chemical Vapor Deposition[END_REF] have been successfully obtained by using this technique. Compared to the mechanical and chemical exfoliation, the main asset of CVD method is the feasibility of scaling-up. More than 30 inch screen size graphene film used as transparent electrodes can be successfully fabricated by roll-to-roll production [START_REF] Bae | Roll-to-roll production of 30-inch graphene films for transparent electrodes[END_REF]. CVD also allows for the fabrication of electronic devices such as transistors [START_REF] Mark | Transfer-Free Batch Fabrication of Single Layer Graphene Transistors[END_REF]. Yet, compared with the simple and easily-handled chemical exfoliation methods, the CVD strategy is costly.

Surface-assisted Epitaxial Growth

Surface-assisted epitaxial growth can be regarded as a modification of CVD method, in which the substrate surface serves as a seed crystal other than a template or a catalyst. This method is alternatively considered as molecular beam epitaxy (MBE) growth. The epitaxial growth has been successfully applied to fabricate one-atom-thick Si sheets (silicene), and the un-reactive metal Ag with sixfold surface symmetry provides a promising substrate to facilitate growth of hexagonal silicene or Si nanoribbons [START_REF] De Padova | Multilayer Silicene Nanoribbons[END_REF].

Application of 2D materials

According to the definition that all 2D materials have high aspect ratios of lateral dimension compared to the thickness of few atoms, they typically result in very high specific surface areas. This unique property of 2D materials suggest that they can be applied in energy storage systems, which is a keystone in today's world technologies.

Considerable research efforts have been dedicated to exploring and developing new

anode materials for lithium ion battery (LIBs), with the aim of developing new materials with higher capacities and lifetimes than current graphite or lithium titanate anodes.

As a host materials for metal ion batteries, 2D materials have unique morphology that enables fast ion diffusion and ion insertion channels [START_REF] Liu | Two-Dimensional Nanoarchitectures for Lithium Storage[END_REF].

Another general merit is that most 2D materials show properties that differ from those of their 3D counterparts, which bring themselves wide applications: reinforcement for polymer composites to produce light weight, high strength and conductive composites [START_REF] Stankovich | Graphene-based composite materials[END_REF]; transparent flexible electronic devices due to their good electronic properties and flexibility [START_REF] Eda | Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material[END_REF].

MXenes

Structure of MXenes

Herein, a new member of 2D materials family is now introduced. MXene, a derivative of MAX phase, is a group of two-dimensional materials consisting of atomic layers of transition metal carbides, carbonitrides and nitrides, consisting of a few atomic layers of two elements (Mono-M), or more than two elements (solid-solution M or double-M element). MXenes, were denoted to emphasize the loss of the A element from the MAX parent phase and to highlight their 2D nature, which is similar to graphene. The ideal MXene composition can be described by M n+1 X n , in general, at least three different formulas have been discovered: M 2 X, M 3 X 2 , M 4 X 3 . The structure is shown in the Figure 1.9. They can be made in different forms: mono-M elements, a solidsolution of at least two different M elements or ordered double-M elements. Chemical-exfoliated MXene exhibits surface groups and is denoted M n+1 X n T x , where T x describe the surface groups, -OH, =O, -F. MXene sheets are almost stacked, where ions and/or molecules may be positioned in between sheets without strong chemical bonding (intercalants). These intercalated MXenes are described by M n+1 X n T x -IC, where IC denote the intercalants.

Since the first MXene Ti 3 C 2 T x was reported in 2011 [START_REF] Naguib | Two-Dimensional Nanocrystals Produced by Exfoliation of Ti 3 AlC 2[END_REF], up to date, over 19 MXenes have been synthesized while another 25 more have been predicted according to the Density Functional Theory (DFT) calculations. The element composition of these MXenes is also shown in the Figure 1.9, of which Ti 3 C 2 T x and Ti 2 CT x are still the most studied MXenes to date.

MXenes originate from MAX phases. That is to say, the MAX phase can be described as 2D layers of early transition metal carbides and/or nitrides stuck together with the A-element layer. Due to the fact that the M-A bond is metallic, it is difficult to separate the MX layers by simply mechanical shearing of MAX phases as graphene derivated from graphite. Nevertheless, as the M-X bond has mixed covalent/metallic/ionic bond character, which is stronger than M-A bonds, selective etching becomes possible to remove the A-element layers without destroying the M-X bonds, which is the primitive principle to access MXenes. In plane view, the structure of MXene sheets is hexagonal with space group P6 3 /mmc (See Figure 1.10). Take MXene Ti 3 C 2 as an example, the unit cell has lattice parameter a and b = 3.05 Å, while the lattice parameter c is 19.86

Åfor ideal Ti 3 C 2 [START_REF] Shi | Structure of Nanocrystalline Ti 3 C 2 MXene Using Atomic Pair Distribution Function[END_REF], while the surface groups and intercalants expand the separation between sheets and increase the lattice parameter c [START_REF] Wang | Atomic-Scale Recognition of Surface Structure and Intercalation Mechanism of Ti 3 C 2 X[END_REF].

1.2. MXene 1.2.

Synthesis of MXenes

Etching with hydrofluoric acid

Attempts on etching A layers from MAX phase have been made by heating MAX phase under vacuum or in molten salts at high temperatures, which results in the selective loss of the A element, whereas the formation of 3D M n+1 X n rock salt structure were also formed due to the detwinning of M n+1 X n layers at elevated temperature [START_REF] Farbera | The Topotactic Transformation of Ti 3 SiC 2 into a Partially Ordered Cubic TiiC0.67Si0.06) Phase by the Diffusion of Si into Molten Cryolite[END_REF]. Moreover, the operation of strong etchants, such as Cl 2 gas, at temperatures over 200 °C results in the etching of both the A and M atoms, to yield carbide derived carbons (CDC).

In 2011, the pioneering work has been done by selective etching of Al from Ti 3 AlC 2 using aqueous HF at room temperature (RT), which can be seen in Figure 1.11(a) [START_REF] Naguib | Two-Dimensional Nanocrystals Produced by Exfoliation of Ti 3 AlC 2[END_REF].

In this process, the Al atoms are replaced by O, OH and/or F atoms. The removal of the Al layers dramatically weakens the interactions between the M n+1 X n layers, which allows them to be separated. This simple selective etching of Al from the parent MAX phases was then successfully extended and yielded multi-layered Ti 2 CT x , Ta 4 C 3 T x ,

(V 0.5 Cr 0.5 ) 3 C 2 T x , Ti 3 CN x T x , Nb 2 CT x , V 2 CT x , Nb 4 C 3 T x , Mo 2 TiC 2 T x , Mo 2 Ti 2 C 3 T x , etc.
[ [START_REF] Ghidiu | Conductive two-dimensional titanium carbide /'clay/' with high volumetric capacitance[END_REF][START_REF] Yang | Two-Dimensional Nb-Based M 4 C 3 Solid Solutions (MXenes)[END_REF][START_REF] Anasori | Two-Dimensional, Ordered, Double Transition Metals Carbides (MXenes)[END_REF]. Typical MXenes accordion-like morphology are shown in Figure 1.11(b, c).

This preferential etching of the M-A bond in MAX phases with Al may be summarized as: and after (c) HF etching [START_REF] Naguib | Two-Dimensional Nanocrystals Produced by Exfoliation of Ti 3 AlC 2[END_REF].

M n+1 AlX n + 3HF → M n+1 X n + AlF 3 + 1.5H 2 (1.8) M n+1 X n + 2H 2 O → M n+1 X n (OH) 2 + H 2 (1.9) M n+1 X n + 2HF → M n+1 X n F 2 + H 2 (1.
can effectively reduce the required etching duration and/or HF concentration, the as-synthesized MAX phase powders are usually subjected to attrition or ball milling and/or sieved prior to chemical exfoliation. proved to be milder etchant as well [START_REF] Feng | Fabrication and thermal stability of NH 4 HF 2 -etched Ti 3 C 2 MXene[END_REF].

Etching with fluoride solution

Delamination and intercalation

In principle, as the strong M-A bonds are replaced by weaker bonds, intercalation and delamination of multi-layered stacked MXenes into single or few layers is possible, which is essential for exploring its 2D nature.

Multilayered MXenes have relatively stronger interlayer interactions than those in graphite or TMDs, simple mechanical exfoliation provides a low yield of single layers.

There are only two reports of Scotch tape exfoliation of multilayer MXene into single flakes [START_REF] Lai | Surface group modification and carrier transport properties of layered transition metal carbides (Ti 2 CT x , T: -OH, -F and -O)[END_REF][START_REF] Xu | MXene Electrode for the Integration of WSe 2 and MoS 2 Field Effect Transistors[END_REF].

The rest of the reports are mainly focused on the chemical intercalants which have been used successfully in other 2D materials. Figure 1.12 shows the schematic diagram of intercalation mechanism [START_REF] Mashtalir | Intercalation and delamination of layered carbides and carbonitrides[END_REF]. To date, intercalation of Ti 3 C 2 T x with a variety of organic molecules, such as hydrazine, urea and dimethyl sulphoxide (DMSO) was reported. Hydrazine can also intercalate Ti 3 CN and (Ti,Nb) 2 C. Intercalation of Ti 3 C 2 T x and Mo 2 TiC 2 T x with DMSO followed by sonication in water led to a colloidal solution of single-and few-layer MXenes [START_REF] Mashtalir | Intercalation and delamination of layered carbides and carbonitrides[END_REF][START_REF] Mashtalir | Amine-Assisted Delamination of Nb 2 C MXene for Li-Ion Energy Storage Devices[END_REF][START_REF] Mashtalir | The effect of hydrazine intercalation on the structure and capacitance of 2D titanium carbide (MXene)[END_REF]. By the use of isopropylamine or large organic base molecules such as tetrabutylammonium hydroxide (TBAOH), choline hydroxide, or n-butylamine, V 2 CT x , Nb 2 CT x and Ti 3 CNT x were delaminated [START_REF] Naguib | Largescale delamination of multi-layers transition metal carbides and carbonitrides "MXenes[END_REF].

However, TBAOH does not delaminate Ti 3 C 2 T x , possibly due to its large size. Either DMSO or an alkali metal halide salt have been used for delaminating Ti 3 C 2 T x .

MXene can also be intercalated with different metal cations by introducing aqueous solutions of ionic compounds. As etching with fluoride salt with acid, metal cations is intercalated spontaneously into layers. The possibility of intercalating MXenes with various organic molecules and metal cations goes beyond delaminating MXenes on a large scale. This phenomenon is of great significance for a range of MXene applications, from polymer reinforcements to energy storage systems.

Properties of MXenes

The main reason why the electronic properties of MXenes are of special interest is because they can be tuned by changing the MXene elemental composition and/or their surface terminations. The band structure and electron density of states (DOSs) of MXenes have been extensively studied by DFT, indicating that MXenes properties range from metallic to semiconducting. Bare MXene mono layers are predicted to be metallic, with a high charge carrier density near the Fermi level [START_REF] Khazaei | Novel Electronic and Magnetic Properties of Two-Dimensional Transition Metal Carbides and Nitrides[END_REF][START_REF] Xie | Prediction and Characterization of MXene Nanosheet Anodes for Non-Lithium-Ion Batteries[END_REF][START_REF] Tang | Are MXenes Promising Anode Materials for Li Ion Batteries? Computational Studies on Electronic Properties and Li Storage Capability of Ti 3 C 2 and Ti 3 C 2 X 2 (X = F, OH) Monolayer[END_REF]. Interestingly, the electron DOS near the Fermi level (N(E f )) for bare individual MXene layers is higher than in their parent MAX phases. Some MXenes with heavy transition metals (Cr, Mo,W) are predicted to be topological insulators [START_REF] Khazaei | Novel Electronic and Magnetic Properties of Two-Dimensional Transition Metal Carbides and Nitrides[END_REF][START_REF] Weng | Largegap two-dimensional topological insulator in oxygen functionalized MXene[END_REF] [START_REF] Anasori | Control of electronic properties of 2D carbides (MXenes) by manipulating their transition metal layers[END_REF], which means that it would be possible to tune the electronic structure of MXenes by varying termination group and transition metal.

Ferromagnetic and anti-ferromagnetic properties have been predicted for some pristine MXenes, whereas magnetism disappears with surface terminations for some cases [START_REF] Si | Half-Metallic Ferromagnetism and Surface Functionalization-Induced Metal Insulator Transition in Graphene-like Two-Dimensional Cr 2 C Crystals[END_REF]. Only two MXenes Cr 2 CT x and Cr 2 NT x have been predicted to be magnetic even with surface terminations, yet their magnetic nature is not clear, also no experimental basic electrolytes have been demonstrated to be 300-400 F•cm -3 , which is higher than the best carbon-based EDLCs [START_REF] Lukatskaya | Cation Intercalation and High Volumetric Capacitance of Two-Dimensional Titanium Carbide[END_REF]. Also, no change in capacitance was reported after 10000 cycles for Ti 3 C 2 T x electrode , indicating their excellent cyclability [START_REF] Ghidiu | Conductive two-dimensional titanium carbide 'clay' with high volumetric capacitance[END_REF].

MXene-based composites have opened a new pathway in various energy storage systems, due to the possible synergistic effect in agglomeration prevention, facilitating electronic conductivity, improving electrochemical stability, enhancing pseudo-capacitance and minimizing the shortcomings of individual components.

Other application

Energy storage systems is the primary and most studied application for MXenes, yet, due to their rich chemistries and diverse structures, there are potentially many other applications of MXene, such as hydrogen storage medium [START_REF] Hu | MXene: A New Family of Promising Hydrogen Storage Medium[END_REF],

photocatalysis [START_REF] Ran | Ti 3 C 2 MXene co-catalyst on metal sulfide photo-absorbers for enhanced visible-light photocatalytic hydrogen production[END_REF][START_REF] Zhang | Ti 2 CO 2 MXene: a highly active and selective photocatalyst for CO 2 reduction[END_REF], biosensor [START_REF] Rakhi | Novel amperometric glucose biosensor based on MXene nanocomposite[END_REF][START_REF] Liu | A novel nitrite biosensor based on the direct electrochemistry of hemoglobin immobilized on MXene-Ti 3 C 2[END_REF] and sewage purification [START_REF] Manawi | Can carbon-based nanomaterials revolutionize membrane fabrication for water treatment and desalination?[END_REF][START_REF] Guo | Heavy-Metal Adsorption Behavior of Two-Dimensional Alkalization-Intercalated MXene by First-Principles Calculations[END_REF].

Summary

For most MXenes, theoretical predictions about their electrical, thermoelectrical, magnetic and other properties should be verified experimentally, especially on the single or fewer layers MXenes. Understanding and controlling surface chemistry is of great importance to allow tailoring the material structure and properties. Regardless of the advancement of these 2D layered MXenes and their composites in Li-ion batteries (LIBs), super-capacitors, transparent conductors, environmental protection, electrocatalysts, etc, more works remain to be conducted, in particular aiming at understanding the exact mechanisms behind certain properties.

PhD work on MXenes

The second part of the PhD thesis is focused on the V 2 C MXenes derived from large V 2 AlC MAX phase crystals by using a combination of chemical modification and The high temperature growth reactor is firstly presented in this chapter.

Then the development of growth process for various MAX single crystals is introduced. Single crystalline characterization as well as the mechanical cleavage of the as-grown MAX phases single crystal are also discussed.

Single Crystal Growth

Growth setup

A modified Czochralski (Cz) puller, named "memere", has been adapted to MAX phase crystal growth. Figure 2.1 shows photo of the puller. It consists of three main parts:

(1) The Heat unit. It is composed of an induction coil, a capacitor box and a power generator.

(2) The reactor includes the growth chamber, gas lines (only Ar 99.9% was used in this work), and recycling cooling water line. Rotation units are located at the top of the chamber, as well as an optical non contact infrared temperature sensor to focus on the crucible through a quartz window to measure the temperature.

(3) The computer based monitor which contains a control panel (not listed in the figure) to tailor the growth conditions by programming heating and cooling sequences.

It is also equipped with safety elements who are able to alarm when in the absence of cooling water in the generator and chamber. Besides, a pressure meter is also applied to monitor the pressure in the chamber in order to avoid the overheating.

It is worth mentioning that two quartz windows are implanted at the side of the chamber, among which, one is used for the temperature measurement of crucible and the other is for the observation when rotating the graphite into the solution.

Three main steps can be explained as follows: firstly, meltdown of alloy (e.g. Cr and Al , V and Al) ;secondly, dissolution of carbon in the fused solution and thirdly, crystallization of MAX phase single crystal in the crucible.

The crucible kit

The crucible kit is composed of crucibles and insulators. The solution growth process is launched at high temperature, therefore the crucible material must be thermally stable for long time operation at high temperature. There are some requisite characteristics for the crucible materials: high-temperature and thermal shock resistant, high electrical and thermal conductivity, easily machinable. Therefore, the most suitable material is graphite as it fulfils all the criteria listed above. So in the previous growth experiment for Ti 3 SiC 2 [START_REF] Mercier | Morphological instabilities induced by foreign particles and Ehrlich-Schwoebel effect during the two-dimensional growth of crystalline Ti 3 SiC 2[END_REF], graphite crucible can be used when the temperature reach up to above This has two drawbacks: on one hand, this does not allow precise control of graphite incorporation, and when it comes to Al-containing MAX phase, this can lead to the unwanted formation of Al 4 C 3 during the initial heating process. On the other hand, if the temperature becomes higher than 1400 • C before the transition metal melts, then liquid Al reacts extremely fast and violently with graphite, so that in a very short time and at the hot point, most of the crucible is consumed until it breaks.

For Cr 2 AlC, this is not a problem because Cr melts before reaching 1400 • C. While in the case of V 2 AlC, it becomes crucial when using more refractory metals (such as Vanadium), as the transition metal melt before introducing the carbon. This imposes the choice of another materials for the crucible. So for this thesis, concerning the Alcontaining MAX phase growth, the alumina crucible is used instead of graphite crucible, though the highest temperature achieved is 1700-1800 • C (See The resistance of the graphite material will lead to its Joule heating. On the top of the outer graphite crucible, several pieces of titanium-zirconium alloy as oxygen absorber material are placed between graphite lip and top insulation, because they can prevent the heterogeneous nuclei from solvent due to the floating oxide particles generated from the the native oxide layers on the metal. It is proved that Zr is a very effective de-oxidizing metal, while Ti exhibit a wide range of solubility against both oxygen and nitrogen. Temperature limitation of Ti-Zr alloy is around 1520 • C, hence even it is placed far from the heating zone, it would start to melt when the growth temperature reaches up to 1800 • C.

Reactor geometry

Growth procedure

Growth is achieved by maintaining the solution for several hours at high temperature, with a partial Ar pressure p Ar =1.5 bar. Different stages of growth are summarized in Figure 2.4 for the high temperature solution growth and slow cooling methods. In general, the crucible is manually heated up to a temperature T 1 (higher than 1000 • C) which is possible to be detected by the pyrometer. From T 1 to T 2 , it is the period of meltdown alloys, T 2 is dependent on the binary phase diagram (Cr-Al, V-Al, etc.). Here, we set T 2 equals to 1600 • C for V-C system while 1650 • C for Cr-C system. The time period lasting from t 1 to t 2 varied from 40 min to 1h according to the raw materials quantities. Once crucible is heated to T 2 , a graphite rod is put into the melt with continuous rotation to dissolve carbon into the melt. The amount of carbon dissolved should be precisely calculated based on the ternary phase diagram. As long as the carbon is all dissolved in the melt, the graphite rod should be pulled out from the melt.

Done with high temperature meltdown of all raw materials, next critical procedure came out, which is slow cooling. The less nuclei, the better. Here, a pre-cooling procedure (t 3 -t 4 ) was introduced to reduce the number of nuclei .

Besides, since no seed crystal is available to be introduced, spontaneous nucleation in the flux is the key factor. A way to decrease the nucleation and increase the crystal size is to start at a temperature at which the flux can be completely converted into a liquid phase, and then to decrease the temperature slowly, so that the first nucleated crystals reduce subsequent nucleation by Ostwald ripening. This is essentially the strategy which we would follow for growth. So, a fairly slow cooling starts, which could last several hours or days (under proper monitoring conditions). In the end, when the system is cooled down to acceptable temperature, the solidified sample can be taken out from the chamber. It is worth mentioning the chamber pressure should be monitored strictly during the carbon dissolution procedure, which is at highest temperature, because the low-melting-point metal vapour will form precipitates on the monitor window, making the pyrometer unable to work in proper conditions. If the temperature indicated is much lower than the real one, the feedback power will keep increasing, leading to a destructive result. To collect the crystal from the flux "cupcake" (See Figure 2.5(a)), diluted HCl acid is applied. Alternatively, after a few weeks under air, the solidified flux hydrolysed and turns into powders as can be seen in Figure 2.5(b,c).

Cr 2 AlC crystal growth

V 2 AlC crystal growth

As for the Ti-Si-C and Cr-Al-C systems, the V-Al-C system has also been evaluated in detail, so that the isothermal sections as well as the liquids surface have been calculated

and/or measured with a reasonable accuracy. In any case, one has to find a temperature and flux composition for which the desired MAX phases is in equilibrium with a liquid phase. Figure 2.9(a) is the V-Al-C ternary phase diagram. For the V-Al-C system, this can be achieved, for example, at V mole fractions below 0.2 and temperatures above 1500

• C. As applied in the Cr-Al-C system, combined with the V-Al binary phase diagram (See Figure 2.9(b)), we tried several growth processes with different vanadium atomic ratio from 10% to 20%, the optimized value is around 15%, so we maintained this for all the following experiments.

In the case of V 2 AlC, we typically maintain the melt at 1650 • C for 1h, and then introduced and dissolved the carbon. On contrary to the case of Cr 2 AlC , the carbon solubility is not high enough. We increased temperature up to 1700-1750 • C , which did not successes due to the thermoresistant limit of the crucible. We also tried to preheat the crucible before growth in order to maintain the flux at high temperature for long time (e.g. 90 min) in order to increase the carbon solubility. Depending on the size of crucible, if we use 8 g V and 24 g Al, the melted carbon amount is around 0.44 g.

After a slow cooling stage for 7 h from 1650 • C to 1100 • C, a solidified flux was obtained. Unlike Cr 2 AlC, the solidified flux did not turn into powder after few weeks, so that in order to extract the crystals from the flux, we had to dip the flux in HCl for a few hours. Since alumina crucible is not as easy machinable as graphite one, the whole crucible was put into the concentrated HCl. From the Figure 2.10(a) showing the crucible and the crystals inside, we can see that the numbers of V 2 AlC crystals is not as high as for Cr 2 AlC, while the size and thickness are also smaller than that of

Other MAX phases crystal growth

The solution growth is clearly limited by the carbon solubility in the flux. This makes it, for instance, very difficult to grow phase such as Ti 2 SnC by this technique, because the carbon solubility is so limited, which is not even measurable in a reliable way. The most favourable case is that of Cr-Al-C, because carbon solubility can be achieve very high and better still, at very acceptable temperature. For a given crucible size, the final platelet area mainly depends on carbon solubility: in our experimental set-up, some 10 -4 cm 2 for Ti 2 SnC, some 0.25 cm 2 for Ti 3 SiC 2 , 1cm 2 for V 2 AlC and several cm 2 for Cr 2 AlC , as can be seen in Figure 2.11.

Structural characterization

Characterization details

Crystal identification was firstly achieved by X-ray diffraction, using a Siemens-Bruker D5000 diffractometer (Cu, K α1 radiation). The X-ray source was copper anode and diffraction of K α1 and K α2 lines were measured. The data was collected in the 2θ range 10°-115°, with a step size of 0.05°, duration of 2s/step. The pole figures were recorded using a setup comprising a four-circle goniometer (Schultz geometry), and an incident beam of diameter 1 mm, a nickel filter for attenuating the CuK β radiation and a point scintillation detector. The illuminated sample surface consisted of a 4 mm ×3 mm ellipse. The penetration depth corresponding to 99% of the diffraction beam was about 8-10 µm. For each pole figure, complete φ-scans (-180°up to 180°) were performed at different χ values (0°up to 90°). Our goals, by using XRD analysis, are the identification of the phases present in the as-grown sample and the determination of the crystal quality.

Micro-Raman measurement were performed at room temperature on different crystals using a He-Ne laser as the exciting line (λ=632.8 nm) of a Jobin Yvon/Horiba LabRam spectrometer equipped with a liquid nitrogen cooled CCD detector. Experiments were carried out using a laser power inferior to 1 mW with a focus spot of about 1µm 2 under the microscope to avoid sample heating.

The chemical composition of the crystals were analysed by Energy Dispersive X-ray Spectroscopy (EDS) using a BRUKER Silicon Drift Detector (SDD) mounted on a Quanta 250 FEI field Emission Gun (FEG) Scanning Electron Microscope (SEM) operated at 15

keV. Observation of the surface is achieved with an optical microscope. (2023) plane is around 0.26°, which is in the order of magnitude 0.1°. In comparison with standard industrial semiconductors materials with the FWHM 0.05°-0.1°, our single crystals are clearly not that of high quality. We attribute this to the fact that none of the platelets is perfectly flat and to the presence of defects, so that this value can be partly explained in terms of the relaxation of long range residual strain in samples with a very high aspect ratio. Our data indicate that the platelets are single crystals at least over an area of several mm 2 and a depth of order of 10 µm.

Cr 2 AlC crystal characterization

Raman spectrum

Fast identification can be achieved by Raman spectrum which is determined by the crystal structure. All samples exhibit similar spectra, and a typical Raman spectrum is reported in Figure 2.14(a). Among the four Raman active vibration modes calculated by the factor group analysis of Cr 2 AlC (2E 2g + E 1g + A 1g , See Figure 2.14(b) [START_REF] Volker Presser | Erratum: First-order Raman scattering of the MAX phases: Ti 2 AlN, Ti 2 AlC 0.5 N 0.5 , Ti 2 AlC, (Ti 0.5 V 0.5 ) 2 AlC, V 2 AlC, Ti 3 AlC 2 , and Ti 3 GeC 2[END_REF]), two well-defined Raman peaks appear at 248 and 336 cm-1, which is in agreement with values reported in the literature. Another weaker mode which exhibit as shoulder in the as-shown spectrum at 238 cm -1 can be identified to the mode at 237, 263,and 250 cm -1 according to various reports [START_REF] Wang | Raman active phonon modes and heat capacities of Ti 2 AlC and Cr 2 AlC ceramics: firstprinciples and experimental investigations[END_REF][START_REF] Spanier | Vibrational behavior of the M n+1 AX n phases from first-order Raman scattering (M=Ti,V,Cr,A=Si,X=C,N)[END_REF][START_REF] Su | Synthesis of Cr 2 AlC thin films by reactive magnetron sputtering. Fusion Engineering and Design[END_REF]. The crystal orientation of our platelet (basal plane perpendicular to the c axis) constrains the observation of E 1g modes. So these two intense peaks are determinate to be E 2g and A 1g . The large band close to 564 cm -1 can be attributed to a combination band of two modes of the first order spectrum.

Surface morphology of as grown crystals

Crystal growth in the melt can be considered as a two step-process: nucleation and growth. Nucleation can be homogeneous, in the absence of foreign particles or crystals in the solution, or heterogeneous, in the presence of foreign particles in the solution.

Both types are known as primary nucleation. Secondary nucleation takes place when nucleation is induced by the presence of crystals of the same substance. No seed crystal is introduced into our growth process, so it is assumed that the primary nucleation occurred spontaneously in the melt during the cooling down. The actual nucleation and growth mechanism of Cr 2 AlC crystal is still unclear, as crystallization occurs in the whole volume of the liquid despite the applied temperature gradient. We assumed some heterogeneous nucleation induced by foreign particles or drops [START_REF] Mercier | Morphological instabilities induced by foreign particles and Ehrlich-Schwoebel effect during the two-dimensional growth of crystalline Ti 3 SiC 2[END_REF].

Besides, growth and solidification of other compounds also happen during the cooling stage. Depending on the various growth parameters (temperature, time and cooling down rate), the Cr 2 AlC crystals can be forced to grow very close to one another, or in competition with other phases. As a consequence, the final growth stage involves usual solidification phenomena, including but not limited to dendrite growth occurring at the surface of the crystals during final solidification. The accumulation of solute and heat ahead of the interface can lead to circumstances in which the liquid in front of the solidification front is supercooled. The interface thus becomes unstable and in appropriate circumstances solidification gives rise to dendrite. A dendrite tends to branch because the interface instability applies at all points along its growth front. The branching gives it a tree-like character which is the origin of the term dendrite. The aspect of the crystal surface may therefore result in a high variety of morphologies at microscopic scale. which is roughly self-organized.

Crystal surface structure can also be the evidence to explain growth mechanism.

One of the most commonly used models was that provided by Kossel [100]. This model envisions the crystal surface as made of cubic units (See Figure 2.16) which form layers of atomic height limited by steps. These steps contain a number of kinks along their length. The area between steps is referred to as a terrace, and it may contain single adsorbed growth units, clusters, or vacancies. According to this model, growth units attached to the surface will form one bond, whereas those attached to the steps and kinks will form two and three bonds, respectively. Growth will then proceed by the attachment of growth units to kink sites in steps. Then, a new step will be formed by the nucleation of an island of monolayer height on the crystal surface. However, when the nucleation rate is faster than the time required for the step to cover the whole crystal surface, 2D nuclei will form all over the surface and on top of other nuclei. These nuclei will spread and coalesce forming layers. Growth terrace can be obviously observed on the surface of our as-grown crystal from the SEM analysis has been conducted in order to investigate the nature of the growth.

Figure 2.17 shows the typical terrace morphology of the as-grown surface, particularly the peninsulas grown on the terrace as features of 2D instability growth (highlighted with red line in Figure 2.17(b)). As already observed for other materials, it can therefore be inferred that the Ehrlich-Schwoebel (ES) effect, give rise to these Bales-Zangwill instabilities. The mechanism and models of these 2D-growth instabilities have been discussed in detail in the previous experiment of our group for the growth of Ti 3 SiC 2 [START_REF] Mercier | Morphological instabilities induced by foreign particles and Ehrlich-Schwoebel effect during the two-dimensional growth of crystalline Ti 3 SiC 2[END_REF].

In such experiments, the presence of foreign particles induces formation of elongated peninsulas or islands on terrace, followed by highly anisotropic growth parallel to the step edges. The instabilities often occur for a larger terrace width, in comparison to the stable and narrow terrace. We explain this as follows: initially, the crystals are supposed to grow totally flat inside the solution, for they are not subject to any constraint as long as they do not meet each other or the opposite crucible wall. However, upon cooling and during the final solidification stage of the flux, they are submitted to a high stress and a subsequent deformation, enhanced by their small thickness and the ease with which they can be plastically bent. We expect such an induced curvature to affect mainly the peak width along χ, whereas a coalescence of crystal planes with the same orientation of the c-axis, but rotated with respect to one another around this axis, or any rotation disorder or mosaicity in the basal plane would rather lead to a broadening of the φ-scan peaks. This explanation is also made plausible by the fact that in the case of much thicker Cr 2 AlC crystals (around 400 µm-thick), such a wide broadening along χ is not observed.

Raman spectrum

Raman measurements performed on different flat and large crystals led to the typical spectrum shown in Figure 4.19 (top spectrum). All the four Raman active optical modes predicted by the factor group analysis of V 2 AlC are observed at 158, 239, 259 and 362 cm -1 in the backscattering configuration used with the laser beam propagation along the c axis, which is in good agreement with the spectra reported by Spanier et al. [START_REF] Spanier | Vibrational behavior of the M n+1 AX n phases from first-order Raman scattering (M=Ti,V,Cr,A=Si,X=C,N)[END_REF] and Presser et al. [START_REF] Volker Presser | First-order Raman scattering of the MAX phases: Ti 2 AlN, Ti 2 AlC0.5N0.5[END_REF]. The similarity between Raman spectra of Cr 2 AlC and V 2 AlC, both compounds belonging to the same 211 MAX phase family with the same crystal structure, and the V 2 AlC mode assignment reported in [START_REF] Spanier | Vibrational behavior of the M n+1 AX n phases from first-order Raman scattering (M=Ti,V,Cr,A=Si,X=C,N)[END_REF] allow us to assign the different modes to E 2g , E 1g , E 2g and A 1g , respectively.

In our spectra, only the mode E 1g at 239 cm -1 slightly differs in intensity and position from one crystal to another one. Theoretically, this mode should not be observed in this backscattering configuration according to the Raman selection rules. Its observation probably results from some polarization leakage due to a slight misorientation between the laser beam and the crystal c axis, its amplitude varying with the misorientation angle. Together with the E 2g modes, this mode is also observed in polarized spectra collected using crossed polarization configuration (Figure 2.20, bottom), which is not predicted by the selection rules. This confirms that the crystal is not strictly horizontal.

As expected for A 1g symmetry modes, the mode pointed at 362 cm -1 is not observed in this configuration.

dislocation was further refined by Burton, Cabrera, and Frank, giving rise to what is known as the BCF theory [START_REF] Burton | The Growth of Crystals and the Equilibrium Structure of their Surfaces[END_REF]. In our experiment, the unpredictable growth process can be attribute to the absence of seed crystal and designed temperature gradient. Hence, we find there may be several nucleation and growth synergy mechanism. Investigation of the surface by means of atomic force microscope shows that the underlying surface morphology is characteristic of a step flow growth process, with well defined steps and terraces (Figure 2.22(a)). On the flat parts, the step height is most often equal to c, the lattice base vector along the c-axis (c=1.31nm), and those regions are separated by highly bunched steps. Locally, the terrace width is generally regular. The physical origin of the step flow process is still unknown, and we never found particular surface structures indicating mechanisms such as, e.g., spiral growth, nor a particular morphological pattern which might be responsible for the birth of the step and terrace structure.

It is worth noting that even if the HCl etching step used for dissolving the solidified flux does not appreciably modify the crystals, it nevertheless induces a partial etching of the step edges which is clearly visible in Figure 2.22(a) and which is substantially aggravated in regions exhibiting a higher defect density (Figure 2.22(b)). In some unusual cases, the surface can even exhibit microscopic etch pits which might indicate the presence of threading dislocations, as observed for other materials with appropriate etchants [START_REF] Thi | Critical assessment of birefringence imaging of dislocations in 6H silicon carbide[END_REF]. Immersing crystals in concentrated HF (40%) for 5 days does not appreciably change their macroscopic appearance, but modify their surface. However, we did not obtain any delamination of the MX planes by removal of the A plane. This is most probably due to the fact that in a highly polycrystalline structure, HF penetration is greatly favoured, in contrast to the case of our single crystals.

Surface morphology of platelets cleaved along the basal plane

An outstanding illustration of the MAX phase nano-lamellar structure and of the weakness of the A atomic bonds is given by the ease with which the platelets can be cleaved along the basal plane, using a process almost similar to producing graphene from graphite. Sticking a platelet onto a strong adhesive tape (gorillaTM), folding the tape onto the crystal and separating the folded parts again is enough for cleaving the platelets in the basal plane, a fact which would be clearly impossible to realize with materials characterized by a strong covalent bonding. As for graphite, the separation can occur not only because basal atomic planes are not tightly bound, but because the detached layer can be deformed without systematically breaking, so that all the "weak" detachment force is applied at the separation line, and not over the full surface (in the latter case, even bonding through van der Waals forces would be too strong to allow plane separation).

We already observed such a cleavage with Cr 2 AlC and Ti 3 SiC 2 , but it is in general not possible to obtain a separation over the full sample area for those two materials.

This can be ascribed to the fact that the Cr 2 AlC samples are rougher and thicker, so that the adhesion of the tape depends on the position and is not homogeneous. As a consequence, only some top regions of the Cr 2 AlC sample or regions devoid of surface dendrites sufficiently adhere to the tape to lead to a partial mechanical cleavage. V 2 AlC platelets are thinner and flatter, so that the adhesion is more homogeneous and so more efficient. In some cases, this allows us to obtain cleavage over the full crystal area, as exemplified by the photograph of Figure 2.23. The remaining part of this section is devoted to the AFM observation of the produced cleaved surfaces.

The surface usually exhibits terraces often ending with a triangular shape (Figure 2.23). Most terraces are separated by unit or half-unit steps, and sometimes by higher steps, but then still equal to an integer number of half-units. This strongly supports the assumption that local cleavage is always obtained at the A atomic planes, since those planes appear twice in a unit cell. In some regions, only a very few steps appear on areas as large as 50 µm ×50 µm, and in other regions the cleavage results in more disturbed patterns (Figure 2.23)).

In some regions, half-unit sharp triangular tears, either terraces or grooves, all start from a single line, and basically exhibit two different kinds of shape, as shown in Figure 2.24 for which we chose an image including both kinds of patterns. The tears are either roughly symmetrical in the direction of the pulling or asymmetrical. The crack orientation is determined by the competition of several factors, since the tearing angle corresponds to the minimum energy variation and depends on a number of other parameters, such as the initial curvature, the film thickness and the width of the flap to be delaminated [START_REF] Kruglova | How Geometry Controls the Tearing of Adhesive Thin Films on Curved Surfaces[END_REF]. We attribute the origin of asymmetrical shapes to the fact that, once a crack is initiated along a direction with a weaker number of bonds, then it goes on in that direction. Focusing on the symmetrical patterns, such tears are usually observed during the pulling of a simple adhesive tape [START_REF] Kruglova | How Geometry Controls the Tearing of Adhesive Thin Films on Curved Surfaces[END_REF] or of a graphene sheet [START_REF] Sen | Tearing Graphene Sheets From Adhesive Substrates Produces Tapered Nanoribbons[END_REF], and we also observed it with Cr 2 AlC samples. More specifically, it has been shown that if the ratio between the flap width W (i.e. the basis of our triangles) and the flap thickness t is much larger than the ratio between the adhesive energy per unit surface τ and the energy of the edge to be cracked γ, then the tear angle θ behaves as sin θ ∝ (2Bτ)1/2/2γt, where B is the bending modulus, so that it is independent of W [START_REF] Novoselov | Two-dimensional atomic crystals[END_REF].

Even if the atomic bonding between the A atoms and the M sublayer atoms is weaker than M-M or X-X bonding coming into the play for cracking the flap edge, the corresponding ratio is certainly much smaller than 2 W/c, since we observed W values larger than 0.1 µm. This implies that locally, the angle of symmetrical tears should

Ti 2 SnC crystal charaterization

Structural characterization were conducted on the as-grown Ti 2 SnC single crystals as well. In order to compare with the as-etched crystals according to the attempts on

Conclusion

Using high temperature solution growth and slow cooling technique, several MAX phase single crystals were successfully grown:

The solution growth is clearly limited by the carbon solubility in the flux. The most favourable case is that of Cr-Al-C, because carbon solubility can be achieved very high and better still, at very acceptable temperature. For a given crucible size, the final platelet area mainly depends on carbon solubility: some 10 -4 cm 2 for Ti 2 SnC, some 0.25 chapter 3

Transport properties of MAX phases

In this chapter, in-plane and out-of-plane magneto-electronic transport properties of MAX phase have been investigated experimentally and theoretically. For in-plane transport, we firstly investigated the in-plane resistivity as the function of temperature and magnetic field, followed by the Hall effect measurement. Thermal transport measurement was also conducted on MAX single crystal samples. For out-of-plane transport, out of plane resistivity was measured and a substantial anisotropy ratio was observed. Results on the out-of-plane magnetoelectronic transport are also discussed. Theoretically, a general model is proposed for describing the weak field magneto-transport properties of nearly free electrons in two-dimensional hexagonal metals. It was then modified to be applicable for the transport properties of layered MAX phases.

Experiment details

Measurement configuration

In-plane transport

Four probes method Four probes method was adopted to eliminate contact resistance for these low resistivity materials [START_REF] Valdes | Resistivity Measurements on Germanium for Transistors[END_REF]. Figure 3.1(a) is schematic of the four probes method.

ρ = R s l = R wt l = 1 σ (3.1)
where: ρ is resistivity, R is resistance obtained from the measurement (V/I), S is cross section area perpendicular to the current direction, l is distance between two side contacts, w is sample width, t: sample thickness.

Van der

-π R A R S + exp -π R B R S = 1 (3.2)
Thus, the resistivity can be calculated using ρ = R S × t, where t is the sample thickness. Here we note that for practical purposes we found that the numerical integral giving f can be replaced by an analytical approximation, which is plotted in Figure 3.3: Then, the resistivity is calculated as

Hall bar bridge

ρ c (corrected) = R × Ld t (1 -f ) -1 (3.3)
where R is the measured resistance, and L, d and t are dimensions defined in Figure 3.2(a). Once ρ c is measured, the resistivity anisotropy ratio ρ c /ρ ab is obtained by using the in-plane tranport resistivity measured from a Van der Pauw sample or a Hall bar processed from crystal issued from the same process run in order to minimize the sample quality variations.

Sample fabrication

In-plane transport

Single crystals of Cr 2 AlC, V 2 AlC, Ti 3 SiC 2 and Ti 2 SnC were successfully grown.

Among them, the size of the Ti 3 SiC 2 and Ti 2 SnC crystals remains quite small, so the data reported here are therefore restricted to Cr 2 AlC and V 2 AlC crystals of macroscopic size. The crystal plane is always perpendicular to the c-axis. The typical areas of the crystals are in the range of a few cm 2 for Cr 2 AlC, and around 1 cm 2 for V 2 AlC, with thicknesses t of order 200-300 µm for Cr 2 AlC and 30-50 µm for V 2 AlC. For all the geometries discussed above, sample has to be prepared based on following criterion:

1) sample should have flat surface with uniform and homogeneous thickness, 2) all contacts should be located at the edge of othe sample.

As demonstrated in the previous chapter, the as-grown surface of V 2 AlC is flat and its initial thickness does not vary more than a few percent over the crystal area while that of Cr 2 AlC crystals needed to be firstly polished so as to obtain a good thickness homogeneity. The samples are processed in two different ways: some are cut with a diamond wire saw so as to form parallelepiped-shaped samples with well-defined dimensions. Some others are defined by laser cut, which allows one to produce more complicated shapes, such as Hall bars with well-defined and aligned lateral arms.

Out-of-plane

For the out-of-plane transport, a metallic mask was machined by laser patterning.

(See Figure 3.5 (a)). Sample was placed in the high vacuum chamber of an E-gun Vacotec evaporation system available in the WINFAB cleanroom, Louvain-la-neuve. Then we proceeded a first metal deposition of a 5 nm-thick Ti/Cr layer followed by a second metallization of a 500 nm Cu layer. Here, the Ti/Cr layer is used as an adhesion layer, than its polycrystalline counterparts. Accordingly, this implies that single crystalline sample exhibits lower resistivity resulting from the absence of grain boundaries which consequently limits the mean free path at low temperature. Due to the imperfections of our as-grown crystals, it is highly probable that these values do not represent a lower intrinsic limit, and further improvement of the materials quality should result in an additional drop of the resistivity.

MAX phase transport properties

In-plane resistivity

More specifically, the sample preparation method can also affect the resistivity substantially, the rectangle and VdP sample obtained by diamond saw cutting are considered to create less defects than that made by laser, that's why the lowest resistivity can be achieved on VdP sample in both cases. Here we also plot one "back and forth" curve for the procedure of cooling down and warming up in By using the Mathiessens's rule, we can extract the ideal resistivity (ρ i ), which is defined as

ρ i (T) = ρ(T) -ρ residual .
Herein, if we do not considering the form factor, which is to say all contact are well connected at the edge of the sample and current pass through all the planes of the layered structure, ρ i is an intrinsic characteristic which is supposed to be only dependent on the electron-phonon-scattering mechanism. Figure 3.9 shows the ideal resistivity of both cases, indicating noticeable uniformity for Cr 2 AlC sample. As usually observed in MAX phases, ρ i varies linearly with the temperature in the range from 150 -300 K and the slope of the linear variation can be calculated. It is clear that the slopes obtained from V 2 AlC sample are smaller than those of Cr 2 AlC sample, such behaviour can be attributed to the differences between two MAX phases in terms of 1) electron-phonon coupling, 2) electron band structure and 3) charge carrier densities. Cr 2 AlC (upper figures), though the correction does not merge all curves, the maximum difference between the five samples at low T does not exceed a factor of 1.5. Most likely, this variation is attributed to the fact that the crystals are all but perfect, so that some variability between samples issued from different runs is to be expected. The ratio is plotted as a function of the temperature in order to get more insights into resistivity anisotropy. It is very substantial, in the range of a few hundreds. The anisotropy ratio increases as T decreases as long as phonon scattering prevails, which did not exhibit the sample trend of temperature coefficient, as reported in the case of oriented grown thin film and bulk Ti 2 AlC phase. This anisotropy is a combination of the Fermi surface anisotropy and that of scattering mechanisms, but a full understanding of temperature dependence of the coefficient of anisotropy is still unclear.

Out-of-plane resistivity

Plotting the same data for a V 2 AlC sample shows that the anisotropy ratio is still higher, a few thousands (Figure 3.10, bottom). The hugh anisotropy ratio still needs to be verified by more samples, here, we found for the sample with larger thickness has lower anisotropy ratio, which may be due to the higher level of defects caused by growth stress in the case of thinner sample. The anisotropies obtained for Cr 2 AlC and V 2 AlC are a spectacular illustration of the impact of the nano-lamellar structure of the MAX phases on electrical transport, and strongly support the assumption of a strong spatial confinement in the transition metal planes. The larger resistivity anisotropy found in V 2 AlC, compared with Cr 2 AlC, may come from a different topology and anisotropy of the Fermi surface itself, which could be described as more "tube-like" in one case than in the other case.

In-plane transport

In this part, three MAX phases will be discussed, including Cr 2 AlC, Ti 2 AlC, Ti 3 SiC 2 .

Magnetoresistance

Figure 3.11 shows the magnetoresistance (MR) variation with temperature at a magnetic field from 0 to 11 T. As in the case of the polycrystalline phases, we observe a magneto-resistance of a few per cent in both cases, higher for V 2 AlC and Ti 3 SiC 2 than for Cr 2 AlC. In general, MR rapidly decreases with increasing temperature. In standard metals, the Lorentz force caused by an applied magnetic field changes the electron trajectory and gives rise to a positive MR which increases quadratically with the strength of the field.

Power function y = Ax B is used to fit the MR curve and the fitting curves at low T are plotted in Figure 3.12. In the cases of V 2 AlC and Ti 3 SiC 2 , unlike Cr 2 AlC, the exponents of power-law fits are around 1.4 for both cases. For a conventional metal, the change in isothermal resistivity in an applied magnetic field (B) normally obeys a functional relation known as Kohler's law [START_REF] Luo | Kohler's rule and relaxation rates in high-Tc superconductors[END_REF]. Semiclassical transport theory based on the Boltzmann equation predicts Kohler's law to hold if there is a single type of charge carrier and the scattering time τ is the same at all points on the Fermi surface. According to Kohler's law, MR at different temperatures can be scaled by the expression:

( ∆ρ ρ 0 ) = f (Hτ) = F( B ρ 0 ) (3.4)
where ρ 0 is the zero-field resistivity at given temperature. This relation follows from the fact that scattering time 1/τ(T) ∝ ρ(T). In the low field limit, most metals exhibits a quadratic dependence of the MR , so

∆ρ ρ 0 ∝ τ 2 B 2 .
Hence, a plot of ∆ρ ρ 0 versus ( B ρ 0 ) is expected to collapse onto a single temperature-independent curve if charge carrier density is constant , regardless of the topology and geometry of the Fermi surface.

In general, this rule is applicable to single-band metals with temperature-independent charge carrier density. Thus, this condition can be satisfied most easily if there is only a single temperature-dependent scattering time. Interestingly, this rule, although derived from the semiclassical Boltzmann theory, was found to be well obeyed in a large number of metals, including the metals with two types of carriers, the pseudo gap phase of the underdoped cuprates superconductors [START_REF] Chan | In-Plane Magnetoresistance Obeys Kohler's Rule in the Pseudogap Phase of Cuprate Superconductors[END_REF] as well as some other Q1D metals [START_REF] Narduzzo | Possible Coexistence of Local Itinerancy and Global Localization in a Quasi-One-Dimensional Conductor[END_REF].

The violation is generally believed to result from the change of charger carrier density with temperature or from the fact that the anisotropic carrier scattering rates do not have the same T scaling on different sections of the Fermi surface.

Here, the Kohler plots of three MAX phases samples are shown in the Figure 3.14.

For Ti 3 SiC 2 Kohler's scaling is reasonably well obeyed below 50 K with small deviations from full scaling thereafter, which is consistent with reported (000l)-oriented thin film of Ti 3 SiC 2 [116]. So as for V 2 AlC. In contrast, for Cr 2 AlC, Kohler's rule is violated at all T. This difference in Kohler's scaling between Ti 3 SiC 2 and Cr 2 AlC, is striking if we consider the very similar ρ(T) behaviour of t both crystals. Such violation of Kohler's rule suggests several possibilities:(i) Charge carriers density is not temperature-independent while the electronic structure varies with temperature due to the formation of density waves; (ii) There is more than one type of carriers and their mobilities have different temperature dependences, in which a simple Boltzmann-type approach with its associated scattering time approximation is not valid;

(iii)The scattering times associated with the magnetoresistance are distinct and have different temperature dependences.

Hall coefficients

Hall measurement was also conducted on three MAX phase single crystals. Figure 3.15 gives an example of the Hall resistivity of V 2 AlC, measured versus magnetic field, at different temperatures. One can notice that Hall resistivity varies linearly with magnetic field, and this phenomenon is temperature independent, indicating the systems are in the weak-field limit. It is worth mentioning that within a sweep of magnetic field, four values were measured to obtain the average value for all the discussion afterwards (See sample. The sign of R H is always positive. For Cr 2 AlC and Ti 3 SiC 2 , these results are in qualitative agreement with the result found for the polycrystalline phases, but for V 2 AlC, negative R H values were always reported for polycrystals [3].

It is also worth noticing that though different samples can lead to different R H values, there seems to be no substantial variation of R H with T (See Figure 3.16 ). We ascribe the variability among samples to a change in their quality, which according to our simplified 2D model can lead to substantial variations of R H for most cases. The small value of R H makes it difficult to be measured, and we notice that a very slight temperature variation during a magnetic field sweep (less than 1K) may seriously affect the final value R H . We suspect that some fluctuations, as well as those reported in the literature, might be due to this artifact.

Charge carrier density and mobility

Using Cr 2 AlC temperature data, we have extracted the carrier densities, mobilities and α using the conventional two band model (as plotted in Figure 3.17). We obtain a decrease in carrier density with T. This is a quite anomalous behavior for isotropic bands, which can be explained in terms of a variation in the ratio between τ n and τ p in the frame of a proposed 2D model which will be discussed in next section. Also, as predicted by this 2D model (and as reported in the case of polycrystalline phases), we find apparent densities in the range of 10 27 m -3 . Apparent mobilities also correspond to what would be predicted from typical values of the relaxation time in metals, and in the range from 120 to 50 cm 2 /Vs when T is varied from 4 K to 200 K.

Thermal transport measurement of Cr 2 AlC

Thermal transport measurement was conducted on the as-grown Cr 2 AlC crystal by my previous group in Shanghai Institute of Ceramic, China. Seebeck coefficient from RT to high T were measured using an Ulvac ZEM-3, while Low T seebeck coefficient and thermoconductivity were conducted on Physical Property Measurement System (PPMS) (Quantum Design, Inc.) Unlike higher electronic conductivity of single crystalline sample compared to their polycrystalline counterparts, no significant improvement on the thermal conductivity was observed compared to the reported results on the polycrystalline samples below room temperature [3] Among measurements taken on several samples, the average thermal conductivity at RT is around 20 W/Km (See Figure 3.18). Moreover, the electron contribution to the thermal conductivity can be inferred according to the Wiedemann-Franz relation κ = σLT, where L is 2.45×10

-8 W • Ω • K -2 ,
which is theoretical value for the contribution to thermal conduction from charge carriers only. The electronic contribution of thermal conductivity is plotted in Figure 3.19(a).

Note that, experiments have shown that the value of L, while roughly constant, is not exactly the same for all materials. It is established that the Wiedemann-Franz relation is generally valid for high temperatures and for low (i.e., a few Kelvins) temperatures, but may not hold at intermediate temperatures [START_REF] Rosenberg | The Solid State[END_REF].

To investigate the phonon contribution to the thermal conductivity, according to the calculated and measured value, we should consider the Debye temperature T D of Cr 2 AlC, which is 735 K [START_REF] Jia | Ab initio calculations for properties of Ti 2 AlN and Cr 2 AlC[END_REF].Our measurement is only conducted below RT, therefore, the following discussion concerns the at low temperature limit (T D / T ≪ 1) . Under this circumstance, thermal conductivity of a perfect infinite crystal is finite at low temperatures only because of Umklapp processes(U-process). For U-process at least one of the initial phonons must have energy comparable to hω D . At T D / T ≪ 1, the number of such phonons is

n = 1 e βhω -1 ∼ = 1 e T D /T -1 ∼ e -T D /T
As T decreases, the number of phonons that can take part in U-process falls exponentially. Thermal conductivity is inversely proportional to the number of U-processes, so the effective relaxation time for thermal scattering goes as:

τ ∼ e T D /T Thus as T decreases, shows an increase till the mean free path, l , becomes limited by the scattering from the imperfections/boundaries of the crystal. Below this temperature, l becomes T-independent and is determined solely by the temperature dependence of specific heat C v . So, at very low temperatures, thermal conductivity will be determined by C v and should go as T 3 .

However, in the Cr 2 AlC, as indicated in the Figure 3.19(b, c): at low T, the deviation from Debye T 3 laws was observed. The thermal conductivity increased linearly with the temperature increased. Also, with the temperature keeping increasing, the thermal conductivity, after treaching a maximum, did not begin to fall exponentially with temperature as e T D /T . At higher temperatures, we observed the violation of 1/T power law fall of κ with increasing T.

When it goes to the Seebeck coefficient as shown in Figure 3.20, the curve does not display monotonous sign within all temperature range, which is not in agreement with Hall coefficient measurement results on Cr 2 AlC. This is therefore another hint for a departure from the conventional isotropic two-band model. Compared to the polycrystalline sample, almost identical trends were obtained: at around 50 K, there is a knee point on both curves . The dominant transport carrier characteristic of single crystalline sample changed from electron-like to hole-like in the temperature range between 200 K-250 K, while for polycrystalline is 250 K-300 K. The values for both cases are strikingly comparable. It is worth noticing that due to the high thermal conductivity and low Seebeck coefficient , at low T , it is practically difficult to build large thermal gradient to obtain measurable thermopower, leading to noisy signal at low T. Nevertheless, we consider the case in which the contribution from in-plane resistivity component is non-negligible and can be extracted from the overall magnetoresistvity, as shown in Figure 3.23 .The derived MR is between 5%-8%, a reasonable value comparable to that obtained from our in-plane measurement. Hence, we use parabolic fitting to indicate the in-plane contribution:

Out-of-plane transport

MR o = MR -(αB 2 -A)
The fitting parameter α and intercept A as function of temperature were plotted in Figure 3.24, in which one can notice that as temperature increases, both α and A However, the physical meaning of intercept value, as the amplitude of the offset to the Zero point, remains unknown.

We use different fitting equations for the residual magnetoresistance (MR) demon-strated in Figure 3.25. Among them, it seems that a Boltzmann-type equation fits better than others. Here we fixed the onset magnetic field at 2.5T, the residual magnetoresistance

MR o = A 1 1+exp( x-2.5 dx )
where the parameterA1 is equals to the intercept A in the parabolic fitting for the in-plane contribution. We now try to understand our results by referring to the literatures in which an analogous phenomenon was reported in lamellar structures. Considering the stacking of two dimensional layers in MAX phase, we firstly referred to out-of-plane magneto transport of two-dimensional electron gas in heterostructures [START_REF] Podor | Parabolic negative magnetoresistance in twodimensional electron gas in InGaAs/InP[END_REF] and graphene [START_REF] Jobst | Electron-Electron Interaction in the Magnetoresistance of Graphene[END_REF] in the temperature range from 20 mK to 4.2 K. In magnetic fields less than about 1 T and before the onset of Shubnikov-de Haas (SdH) oscillations a large negative magnetoresistance was observed, which followed a quadratic dependence on the magnetic field.

The observed negative magnetoresistance can be explained in terms of electron-electron interactions (weak localization) in two-dimension. Yet, in our case, we did not observe that the out-of-plane resistivity has a logarithmic dependence with temperature, which excludeds weak localization.

The data discussed here are somewhat anomalous to anisotropic magnetoresistance in the high-T superconductors [START_REF] Xing | Out-of-plane transport mechanism in the high-T c oxide Y-Ba-Cu-O[END_REF][START_REF] Yoo | Out-of-plane transport properties of Bi 2 Sr 2 CaCu 2 O 8 single crystals in normal and mixed states[END_REF][START_REF] Hussey | Out-of-plane magnetoresistance of La 2-x Sr x CuO 4 : Evidence for intraplanar scattering in the c-axis transport[END_REF], who also exhibit a striking feature of large anisotropic electronic properties, as our MAX phase samples. It was widely studied that the interlayer tunnelling or weak coupling were proposed for c-axis conduction and the presence of Josephson coupling between layers had been experimentally proved in Bi-based superconductor single crystals.

In our experiment, B is parallel to I, in principle, so that a macroscopic Lorentz force is zero and the Lorentz-force-driven charge motion is not expected. However, if the carrier trajectories are not straight along c-axis, and there exists some sort of misalignment between B and I, out-of-plane magnetoresistance may be produced even in the absence of Lorentz force.

It is worth mentioning another point related to defect scattering, as demonstrated in [START_REF] Crommie | Thermal-conductivity anisotropy of single-crystal Bi 2 Sr 2 CaCu 2 O 8[END_REF], the electrical conductivity anisotropy of Bi-based superconductor material is of order 10 4 and is strongly temperature dependent, which is also the case for V 2 AlC sample. A defect scattering played an important role in out-of-plane transport mechanism. At this stage these hypothesis still need to be further investigated with more experimental results.

V 2 AlC

Similar phenomena was detected in the V 2 AlC sample as well. Here we simply list the measurement results (Figure 3.26 3.27 3.28) as reference. The anisotropy ratio of V 2 AlC sample is around 10 3 . Unlike Cr 2 AlC, the onset magnetic field of negative MR for V 2 AlC is lower , at 1.8 T. Besides, up to 50 K, the negative MR could still be observed.

After extraction, we can clearly find out the MR value for V 2 AlC is much larger than Cr 2 AlC sample, which might imply that higher mobilities leading to lower resistivity.

Theoretical calculation of MAX phase transport properties

Introduction of a 2D hexagonal metal with nearly free electrons

As emphasized by N.W. Ashcroft and N. D. Mermin many years ago, the nearly free-electron-like Fermi surfaces are essential in understanding the real Fermi surfaces of many metals [START_REF] Ashcroft | Solid State Physics[END_REF]. Here we intend to argue that MAX phases probably make no exception. Determining the Fermi line of nearly free electrons in a pure 2D hexagonal metal is elementary. The origin of the hole and electron bands can be seen by plotting several Brillouin Zones (BZ) along with the Fermi circles corresponding to the filling of the free electrons states up to the Fermi energy in each zone . We focus on cases where the free electron circle extension is larger than that of the corresponding BZ. Then, restricting oneself to the first hexagonal BZ, one obtains free electron pockets at the corners of the hexagon and a hole band centred at the origin (See Figure 3.29). To get the dispersion curves is a trivial matter, obtained by solving the following secular equation (justification of this procedure can be found, e.g., in Eqs 3.5):

E 0 -E U U U U U U U E 1 -E U 0 0 0 U U U E 2 -E U 0 0 0 U 0 U E 3 -E U 0 0 U 0 0 U E 4 -E U 0 U 0 0 0 U E 5 -E U U U 0 0 0 0 E 6 -E = 0 (3.5)
where E is the unknown energy and the E i is the free electron parabolic relations of An example of dispersion curves is given in Figure 3.30. For a large number of electrons per unit cell, the first band is filled with electrons. As in the case of graphene tight-binding treatment, it is easy to demonstrate that for nearly free electrons the first band touches the second at the so-called Dirac points K's. The second band is the hole band. It is separated from the third band -the upper electron band -by an energy gap close to 3U at points K's. Here we restrict our analysis to the case where the first band is totally filled (with two electrons per unit cell), and we define N as the number of electrons per unit cell populating all higher partially filled bands. In order to compare the model to the case of the M 2 AX phases, or to compute 3D carrier densities from the 2D model, we assume that we have four 2D planes per unit cell (as a consequence, to get the number of electrons per plane in partially filled bands one must divide N by a factor of four).

E i = h2 (k -k i ) 2 /
that each band is split in two, the dispersion of the split bands along c being of the form Combining the in-plane and out-of-plane energy contributions give rise to Fermi surfaces such as that of Figure 3.32 (where we assumed that the splitting is different for the hole and electron pockets). Although not perfect, the similarity with DFT calculations is prominent, even if so simple a model can obviously not reproduce the smallest details of the Fermi surface. This approach also neglects an additional but quite small splitting, which dissociates each of the hole and electron Fermi surfaces into almost indistinguishable surfaces, and which can be attributed to the fact that two consecutive A planes are inequivalent.

E = E 0 ± (β 2 + γ 2 + 2βγcos(kc)) 1/2 .
In order to further simplify the calculation of all transport parameters, we move one last step further, and replace the 3D structure by a fully 2D model, neglecting any energy variation along c (so that our model can only predict the values of in-plane transport coefficients). This gives Fermi lines such as the one presented in the tight-binding splitting is such that the electron bands are repelled at energies high enough for being totally unoccupied [START_REF] Chaput | Thermopower of the 312 MAX phases Ti 3 SiC 2 , Ti 3 GeC 2 , and Ti 3 AlC 2[END_REF].

Although only a restricted number of Fermi surface calculations are presently available in the literature, many support the nearly-free electron explanation of the Fermi surface shape. Our purpose is therefore to use the 2D model as a reasonable approximation of the Fermi surface shape, because it allows one to simplify the calculation of the transport parameters to a considerable extent, and thus to discuss the physical aspects which govern the transport properties in a very convenient way. Apparently, this approximation restricts the analysis to in-plane transport.

Transport formalism

Here, we briefly summarize the principle used for calculating the transport coefficients. As usual, we start from Boltzmann's equation, where F is the force, including the electrical and Lorentz contributions, f 0 is the equilibrium distribution and τ is the relaxation time:

F h ∇ k ( f 0 + ∆ f ) + ∆ f τ = 0 (3.6)
From this equation, the out-of-equilibrium part ∆ f of the distribution function is expressed as

∆ f = -(1 - eτ h (v×B) ∂ ∂k ) -1 eτvE ∂ f ∂E (3.7)
where v is the velocity, B the magnetic field and E the electric field. Expanding the denominator gives (Jones-Zener approximation) [START_REF] Ziman | Electrons and phonons[END_REF] ∆

f = -(1 - eτ h (Bv y ∂ ∂k x -Bv x ∂ ∂k y ) + order2)eτvE ∂ f ∂E (3.8)
The first term inside the parenthesis gives rise to the direct conductivity σ xx (without the magneto-resistance contribution), the second term (first order in B) gives rise to the transverse conductivity σ xy , and the third term (second-order term in B) is at the origin of the magneto-resistance. ∆ f is used to compute any current component by estimating

j = e D(k)v(k)∆ f d 3 k (3.9)
With D(k) the density of states. Applying the electric field E along x, computing j x gives σ xx and the magneto-resistance, and j y leads to R H . Besides, a considerable simplification is obtained for a 2D system, since any transport integral can then be put in the form of a circulation along the Fermi line. Grouping all terms and ∂ f /∂E under the form of a function g(k), any transport integral can be put in the polar form

g(k x , k y ) ∂ f ∂E dk x dk y ∼ = g(k F ) dk F hv F = g(k F ) 1 hv F k 2 F + ( ∂k F ∂θ ) 2 dθ (3.10)
Roughly speaking, this means that for interpreting magneto-transport we just have to examine what the holes and electrons do along the Fermi line as a function of time.

From the calculations of the direct conductivities and transverse conductivities for each band of index i, one can obtain the overall resistivity and Hall coefficient values from summations of

ρ ab = ∑ i σ i xx ( ∑ i σ i xx ) 2 + ( ∑ i σ i xy ) 2 (3.11) R H = ∑ i σ i xy ( ∑ i σ i xx ) 2 + ( ∑ i σ i xy ) 2 1 B (3.12)

Predicted results for a simple 2D hexagonal metal

Herein, a simple model is introduced, not directly mimicking the MAX phase Fermi surface, so as to emphasize and isolate physical phenomena. The lattice parameters are that of Ti 2 AlC, and then, these phenomena is shown to rule in the same way the transport properties associated to more complex Fermi lines (such as that of Figure

3.33).

As a first example, if we fill our 2D system with just a few electrons per unit cell to get a free carrier system (Figure 3.35(1)). Still, the transport calculations give a substantial magneto-resistance while R H is quite small, equals to 1.178 × 10 -11 m 3 C -1 as in Figure 3. 35(1d). An isotropic 1-band model would lead to an apparent hole density n = 1 eR H = 5.30 × 10 29 m -3 , extremely far from the assumed value 2.30 × 10 28 m -3 . In order to interpret the results for the Hall coefficient and magneto-resistance, we first remind that in a semi-classical approximation, the wave vector changes with time according to h∂k/∂t = ev × B when submitted to the Lorentz force, and holes with an energy E F cycle clockwise along the Fermi line, until they are scattered to another part by a collision. If one focuses on a concave part and in contrast to this clockwise rotation, the hole velocity, which is perpendicular to the Fermi line, clearly rotates counter-clockwise with time, which means that in real space the holes are thus turning counter-clockwise, so that during a fraction of time in between two collisions they truly exhibit an electron-like behaviour (See Figure 3.35(1a)).It is only at the corners with a convex shape that their velocity rotates clockwise with time, so that they rotate clockwise with time, as free holes would do in real space. This phenomenon is discussed in [START_REF] Banik | Hall coefficient of a holelike Fermi surface[END_REF][START_REF] Ong | Geometric interpretation of the weak-field Hall conductivity in twodimensional metals with arbitrary Fermi surface[END_REF] , and it is quite understandable that this feature can dramatically affect the value of the Hall coefficient.

An elegant way to describe this is provided by Ong's theorem for 2D metals [START_REF] Ong | Geometric interpretation of the weak-field Hall conductivity in twodimensional metals with arbitrary Fermi surface[END_REF]. It states that the transverse conductivity , σ xy is given by

σ 2D xy = 2e 3 h 2 A l B (3.13)
where A l is the algebraic area spanned by the mean free path as the wavevector cycles with time over one full orbit. If the mean free path λ = v k τ k is a constant (for pure impurity scattering), one obtains a circle with the sign corresponding to the type of carriers [START_REF] Ong | Geometric interpretation of the weak-field Hall conductivity in twodimensional metals with arbitrary Fermi surface[END_REF]. However, λ may vary with k F (for instance if the relaxation time τ k is isotropic and the velocity is not constant along the Fermi line (See Figure 3.35 (1b)(2b)).

For holes, the oriented area now exhibits outer flaps affected by a negative sign (See If the flaps get bigger than the central part, the Hall coefficient can even reverse its sign, so that pure holes can be seen as electrons [START_REF] Ong | Geometric interpretation of the weak-field Hall conductivity in twodimensional metals with arbitrary Fermi surface[END_REF]. That is to say if holes partially behaving as electrons and leading to seemingly compensated transport, pure holes can obviously give rise to a magneto-resistance. This is the case of our hexagonal 2D model.

(See Figure 3.35(1d)).

It is worth noticing that using the extraction procedure assuming the existence of two types of carriers and n=p(as described in traditional two band model in Chapter I), the parameters of Figure 3.35(1) would lead to almost equal mobilities (96.2 and 93.5 cm 2 /V•s, respectively) and a concentration n= p= 7.36×10 27 m -3 . Therefore an intermediate conclusion can be drawn as already indicated in [START_REF] Banik | Hall coefficient of a holelike Fermi surface[END_REF]: the evidence of a small R H value and a substantial magneto-resistance is by no means enough to prove the presence of two kinds of carriers. As in the Figure 3.35(1), a system involving just one type of carriers can even mimic compensated transport with almost perfectly balanced electron and hole properties.

Furthermore, with a higher N, we now have both hole and electron bands, and the considerations developed above now apply to both kinds of carriers (See Figure 3.35(2)). Increasing the value of U makes the hole Fermi line smoother, and tends to reduce the flap size. However, as long as the Fermi line appreciably deviates from a circle, the mean free path curve, even if it is devoid of flaps (as that of electrons in 3.35(2c)),also departs from a circle and lead to a substantial modification of R H , as well as to magneto-resistance.

Following all above discussions, questions are generated : for such a simple system, can we rely on the extracted electron and hole densities in the frame of a conventional two-band model, and do they bear any similarity with the real values?

In order to answer it, it is instructive to plot the electron and hole densities as a function of N (Figure 3.36), as well as the n app =p app values which would be extracted by using twoband model. Figure 3.36 demonstrates that the extracted values are quite different from the ones using hexagonal 2D nearly free electron model. The Hall coefficient is quite small, and depending on N, it can be either positive or negative. This example also shows that in spite of considerable variations of the real densities at the Fermi level, n app can remain remarkably stable, whereas the sign of R H may vary as well as its magnitude.

Another message can be taken from

Predicted results for MAX phases

We simply use the lattice parameters of the MAX phases and select a set of energy parameters aimed at recovering the Fermi surface of a given MAX phase. Here we take the case of Ti 2 AlC as an example and draw general conclusions which can be applied to other MAX phases. The contributions of each band are calculated (split hole bands and split or single electron pockets) and summed. Figure 3.37 gives the results obtained for a Fermi line mimicking the full Fermi surface of Ti 2 AlC, obtained for equal electron and hole relaxation times τ n =τ p =10 -14 s, representing a common order of magnitude for metals [START_REF] Ashcroft | Solid State Physics[END_REF]. The valley degeneracy of electron g n =1, of each hole band g p =2. The fact indicates that in spite of a minor contribution of the electrons to ρ ab (as postulated in [START_REF] Mauchamp | Anisotropy of the resistivity and charge-carrier sign in nanolaminated Ti 2 AlC: Experiment and ab initio calculations[END_REF]), there is a substantial contribution of all carriers to R H and holes alone would lead to a considerably higher value . Any band, considered alone, exhibits a substantial magneto-resistance, with quite similar relative variations. But the measured magneto-resistance is due to holes, since they give the major contribution to the overall resistivity.

A two-band isotropic model would give n app =p app =3.94×10 27 m -3 (staying the case of g n =1 and g p =2), and mobilities µ p =148 cm 2 /V•s and µ n =125 cm 2 /V•s, respectively (polycrystalline samples give values around 10 27 m -3 [3]). A one-band model would give only holes with p app =4.60×10 28 m -3 . The values given by this 2D nearly free electrons model, are p=2.02×10 28 m -3 and n=3.15×10 27 m -3 .

So we can see from this case that it is quite obvious that neither a conventional 2-band model, nor a 1-band model can give reasonable estimations of the true densities.

The small value of R H and the apparent compensation must not be attributed to the fact that the hole and electron densities compensate one another, since they are indeed quite different. Firstly, the velocities remain the same order of magnitude in most parts (close to the free electron velocities). Secondly, with phonon scattering we can reasonably expect an almost isotropic scattering time. If the τ n and τ p are similar , the substantial, in the range of a few hundreds to thousands.

From MR and Hall effect measurement, in-plane transport behaviours of MAX phases have been studied. As in the case of the polycrystalline phases, we observe a magneto-resistance of a few per cent, among them, only MR curve of Cr 2 AlC exhibits parabolic-like curves, as reported for polycrystalline MAX phases. One can notice that Hall resistivity varies linearly with magnetic field, and this phenomena is temperature independent, indicating the systems are in the weak-field limit. R H is small, as previously noticed for polycrystalline samples. The extracted mobility is in the range from 50 to 120 cm 2 /Vs, which is the same order of magnitude of polycrystalline sample.

Thermal transport measurements were also conducted on Cr 2 AlC samples. Similar as higher electronic conductivity compared to its polycrystalline counterpart, higher thermal conductivity is verified. Non-monotone sign of charge carrier type was displayed in the curve of Seebeck coefficient, while similar phenomena was observed to Hall coefficient measurement. Yet this discrepancy can still be partly explained by a compensation between holes and electrons. Attempts on the out-of-plane magnetoelectronic transport were also performed. Though it is interesting to observe the anomalous magnetoresistance in the absence of Lorentz-force, the mechanism of a field-induced transport along c-axis is still unclear.

Theoretically, a general model was proposed for describing the weak field magnetotransport properties of nearly free electrons in two-dimensional hexagonal metals.

It was then modified to be applicable for the transport properties of layered MAX phases. We argue that the values of the in-plane Hall coefficient and the in-plane parabolic magneto-resistance are due to the specific shape of the Fermi surface of almost two-dimensional hole and electron bands. If the contribution of the electron pockets to in-plane resistivity is often predicted to be a minor one, in contrast, both holes and electrons should substantially contribute to the overall value of the in-plane Hall coefficient.

The Fermi surface of MAX phases has never been experimentally probed. Yet, it is only the experimental verification of its shape for various MAX phases which can ultimately prove or invalidate some of our assumptions. The striking similarity between some polycrystalline and single-crystalline extracted data is yet to be explained.

MXenes are derived from MAX phases, a class of layered ternary carbides and/or nitrides that have been introduced in the previous chapters. The motivations for extracting MXenes are multiple, as explained in the introduction, inspired by the highest metal uptake when testing V 2 CT x MXenes as electrodes for lithium battery compared to the other multilayer MXenes [START_REF] Naguib | New Two-Dimensional Niobium and Vanadium Carbides as Promising Materials for Li-Ion Batteries[END_REF]. Herein, we selected V 2 CT x as a representative M 2 XT x MXenes.

V 2 CT x MXene Synthesis

Etching

Wet hydrofluoric acid (HF) treatment of MAX phases was the first efficient method to synthesize MXenes, which allows selective dissolution of the Al layers from the MAX phases [START_REF] Naguib | Two-Dimensional Nanocrystals Produced by Exfoliation of Ti 3 AlC 2[END_REF]. Our process to synthesize V 2 CT x flakes is illustrated in Figure 4.2. First, we found that, in the case of mm-size V 2 AlC single crystals, chemical dissolution of the Al layers was extremely slow. In order to hasten the etching procedure, as-grown V 2 AlC single crystal were scratched heavily with a sharp blade to create defective surface, and then sonicated in 45% HF solutions at 80 °C for 12 h. Subsequently, dark green supernatant with V 2 CT x precipitates was collected, confirming the etching of V 2 AlC (See In our present experiment, it is worth noting that some attempts have been made

to improve the chemical etching process. First, the as-grown crystals were directly immersed into the HF without breaking into pieces, aiming at large-scale MXenes. The effect of sizes of crystals on the etching process will be discussed in the next section.

Moreover, dimethyl sulfoxide (DMSO), an effective intercalant for Ti 3 C 2 T x -MXenes as evident by the observed shift in major XRD peaks towards lower angles in the Ti 3 C 2 T x samples [START_REF] Mashtalir | Intercalation and delamination of layered carbides and carbonitrides[END_REF], was also introduced in our experiment since other organic intercalants such as thiophene, ethanol, acetone, tetrahydrofuran, formaldehyde, chloroform, toluene and hexane, were found to be unsuitable. The as-etched V 2 CT x MXenes was added to the DMSO and stirring was employed. After 24 h of intercalation, the MXenes was centrifuged and the supernatant poured out to remove most DMSO and was washed with DI water followed by 4h sonication with ethanol. The effect of DMSO on our V 2 CT x will also be discussed in the next section. However, the prospect of intercalating DMSO is severely limited by its exclusive effectiveness towards delaminating Ti 3 C 2 T x , and its difficulty of thorough removal due to high boiling point solvents. Furthermore, lamellar thickness can be undesirably increased by remnant DMSO molecules, which joined the delaminated sheets together. To date, the exact mechanism to explain how and why DMSO only interact with multi-layer Ti 3 C 2 T x remains unclear [START_REF] Mashtalir | The effect of hydrazine intercalation on the structure and capacitance of 2D titanium carbide (MXene)[END_REF].

Substrate preparation

In order to investigate the electronic properties of V 2 CT x MXene, the multilayer sheets should be isolated onto a substrate. Si/SiO 2 substrate is often used in the case of 2D crystals, as it offers the possibility to tune charge carrier densities according to the voltage applied on the backgate formed by the doped Si.

In this thesis, Si/SiO 2 substrate was used for all device fabrication. Three inches diameter doped silicon (ρ~0.001-0.005 Ω•m ) wafers with a thermally grown 90 nm or 300 nm-thick dioxide layer on both the front polished and the back surface were used, ordered from MTI Corporation.

In order to electrically contact the backgate, we first chemically etched the oxide on the wafer back side and then metallized a 300 nm-thick aluminum layer.

A grid of metallic marks [Ti(5 nm)/Au(60 nm)] with the combination of symbols and numbers was defined by optical lithography, metal deposition and lift off on the front surface to locate flakes for the following process. Then, the wafers are diced in 6

×8 mm 2 pieces in order to fit the chips used for electrical measurements.

Mechanical exfoliation

Our original focus is to isolate single large flakes of V 2 CT x MXenes, that can be examined and measured, particularly for electrical, optical and thermal properties.

As for other 2D inorganic graphene analogues discussed in the Chapter 1.2.1, we will show that mechanical cleavage as originally applied in peeling off the graphene from graphite allows to mechanically isolate fewer layer MXene flakes from as-etched

V 2 CT x MXenes.
First, as-etched V 2 CT x MXenes was placed on the sticky side of a medium-track blue tape. This residue-free tape promised to leave little to no sticky residue on the substrate(See Figure 4.4(a)). Then, the tape was folded more than 10 times so as to peel off multilayers V 2 CT x sheets. We proceed with a transfer on a fresh piece of tape. As generally known, the interlayer bond are stronger than graphite, even after the etching process. In order to maximize the shear force, it is necessary to use the fresh tape to continue the exfoliation process.

Then, the exfoliated V 2 CT x sheets stuck on the tape was directly transferred onto a piece of Si/SiO 2 substrate (See Figure 4.4(b)). The flakes can be identified by optical microscopy contrast with SiO 2 , similar as graphene. Meanwhile, the position of flakes can be identified according to the metallic mark system.

Material characterization

4.1.4.1 X-ray diffraction X-ray diffraction is an analytical technique used to characterize materials atomic structure. In a θ -2θ configuration, θ corresponds to the angle between (hkl) plane and the incident X-ray and the diffracted X-ray. The detector is placed at an angle 2θ to the incident X-ray. The results are usually presented as the intensity vs 2θ. According to the Bragg's law:

nλ = 2d hkl sinθ (4.1)
the interplane atomic spacing d hkl can be calculated from the peak position. For MXene phase, the (002) plane is one of the most intense peaks observed, whose 2θ position is therefore used to determine the c-lattice parameter.

In the present experiments, X-ray diffraction on V 2 AlC before and after HF etching were performed on a Mar345 image plate using Mo Kα radiation (l= 0.071074 nm) (Rigaku Ultra X18S rotating anode, Xenocs fox 3d mirror). Data images were integrated by Fit 2d software. Crystals were picked up using grease. For the following discussion, the data was converted under the wavelength of Cu Kα radiation in order to compare with the 2θ value in the literature.

Micro Raman

The unpolarized Raman spectra were collected on a LabRAM HR800 (Horiba Jobin-Yvon, France) equipped with an air-cooled CCD array detector in the backscattering configuration. An Argon ion laser (514.5 nm) was used as the excitation source. An objective with numerical aperture of 1.25 was used. The spot size of the laser was focused to 2 µm. The spectral resolution was grooves/mm with grating 1800, 2400 and 150.

SEM, TEM with EDS and AFM

The microstructure morphology and elemental analysis of V 2 CT x MXene sheets were characterized by a field emission scanning electron microscope (JSM-7600F, JEOL, Japan) equipped with Energy Dispersive Spectroscopy (EDS). A TEM (LEO922) also equipped with EDS detector, was used to observe the microstructure of the sample and investigate the element distribution. Flake thickness and surface topology was tested by AFM using Bruker Multimode Nanoscope VIII under using Peak-force or normal Tapping mode.

Structural characterization of as-etched V 2 AlC single crystal

SEM and EDS

Work towards isolating large single V 2 CT x MXenes flakes began with the idea that starting the process with large V 2 AlC single crystal would lead to eventual separation of large flakes. As-grown V 2 AlC crystals were firstly employed as raw materials ready for HF etching. As can be seen in Figure 4.5, showing the SEM image of V 2 AlC crystals after etching by 45%HF for two weeks, the as-produced samples were neither fully delaminated, nor were they as large as we desired. No typical accordion-like morphology of MXenes are observed, combined with EDS spectrum results, indicating that the Al was not completely removed from the parent MAX phase. It is evident that delamination has not occurred. Yet, comparing to the EDX results before and after etching, it is undeniable that that the etching process act on the V 2 AlC single crystal, though reaction kinetics are limited by the etchant concentration, crystal size as well as reaction temperature.

AFM

AFM image of the steps of as-etched V 2 AlC shows that the step height is around 1.3 to 1.4 nm, which is very close to value of the c-lattice parameter of V 2 AlC (See Figure Apparently, increasing the crystal size of the parent MAX phase makes it impossible to extract MXene flakes through chemical etching. Hence, to ease the etching process, for V 2 AlC and V 2 CT x , respectively. Such phenomenon has been attributed to the water intercalation in between the layers after delamination in an aqueous solution. Indeed, water intercalation is common and has been observed in other MXenes such as Nb 2 CT x , Nb 4 C 3 T x [START_REF] Byeon | Lithium-ion capacitors with 2D Nb 2 CTx (MXene) -carbon nanotube electrodes[END_REF][START_REF] Ghidiu | Synthesis and characterization of two-dimensional Nb 4 C 3 (MXene)[END_REF]. The value of the c-LPs is almost comparable to that reported in previous works on V 2 CT x powders, yet, the (006) (103) peaks in the present seemingly vanished [START_REF] Chen | CO 2 and temperature dual responsive "Smart" MXene phases[END_REF]. In our experiment, DMSO was also introduced as intercalant. Figure 4.9(a) shows the collected V 2 CT x (VC-p) samples with and without treatment of DMSO. We can see from the patterns that, contrary to Ti 3 C 2 T x , there is no obvious further shift of (002) peak corresponding to the expansion of interplane distance on the V 2 CT x with treatment of DMSO. Although we did not try any other intercalant molecule, we would like to mention that a relatively large molecules organic base, namely tetrabutylammonium hydroxide (TBAOH) was recently demonstrated to be effective for the delamination of Note that at early stage trials of the etching experiments, the etched samples terminated by a mixture of functional groups -F and -OH were found, as shown in the Figure 4.13. We then improved cleaning, drying and collection of the as-etched sample and it became rare to detect -F in EDS spectrum.

SEM and EDX

More and more evidences show that hydroxide groups directly bond to the MXene, with a layer of water hydrogen-bonded to the hydroxide surface while fluoride moieties bonded to the MXene surface. This is confirmed by direct measurement of surface termination groups of V 2 CT x MXenes using NMR spectroscopy [START_REF] Harris | Direct Measurement of Surface Termination Groups and Their Connectivity in the 2D MXene V 2 CT x Using NMR Spectroscopy[END_REF]. However, recent computational studies revealed more complexity in the locations and orientations of surface groups depending on the species and elemental compositions.

Xie et al. [START_REF] Xie | Role of Surface Structure on Li-Ion Energy Storage Capacity of Two-Dimensional Transition-Metal Carbides[END_REF] suggested that =O and/or -OH terminated MXenes were the most stable, because -F terminations were readily replaced by -OH groups, which could occur when they were washed and/or stored in H 2 O. During the high temperature treatments and/or metal adsorption processes, -OH was converted to =O terminations.

The structural, elemental and chemical properties of single and double sheets of native point defects such as Ti vacancies and oxidized titanium adatoms (TiO x ) are also observed [START_REF] Karlsson | Atomically Resolved Structural and Chemical Investigation of Single MXene Sheets[END_REF]. By analogy, we can infer that the absence of -F group in our end product is not surprising.

TEM

As collected V 2 CT x (VC-p) were dispersed in the DI water and isopropanol (IPA), In comparison with DI water dispersed sample exhibiting well-defined and clean edges, the IPA dispersed ones have uneven edges and easily roll up. The a -LP of this flake from SAED, inheriting the hexagonal basal plane symmetry of the parent V 2 AlC phase, is measured to be ~2.9 Å, which is similar to that of the V 2 AlC precursor [START_REF] Shi | Synthesis of single crystals of V 2 AlC phase by high-temperature solution growth and slow cooling technique[END_REF]: as found for all other MXenes synthesized to date, removing Al did not alter the in-plane structure. In addition, no Al element signal was detected with EDS spectrum (See

Raman spectrum

The Raman spectra of the untreated V 2 AlC and HF-treated V 2 CT x are shown in

E 2g (ω 1 ), E 2g (ω 2
), E 1g (ω 3 ), A 1g (ω 4 ) are labelled after fitting the spectra with Gaussian fitting. Furthermore, peak at 257.1 cm -1 is assigned to E 1g group vibration which corresponds to in-plane (shear) modes of V atoms. This peak should be observed in the V 2 CT x spectrum after etching V 2 AlC.

We observed a reduced peak intensity and broadened shape, which is probably due to the increased interlayer spacing of the MXene structure. This change in the Raman spectra can be analogous to the relatively low G band intensity in monolayer graphene.

The peak at 358.6 cm -1 is assigned to A 1g group vibration, which reflects the out-of-plane vibrations of V atoms. Therefore, if the Al interlayer is removed, the corresponding peak in MXene is expected to red-shift, broaden and change the peak shape, in analogy with the 2D-band of graphene. The E 2g modes ω 1 (155.7 cm -1 ) and ω 2 (239.5 cm -1 ) are in-plane vibration of V and Al atoms. After etching, the Al atoms are supposed to be replaced with lighter atoms (such as F, O or H), hence these peaks involving V-Al coupled vibration are more affected compared to those of E 1g , the intensities of which reduced dramatically. Also the broadening of these peaks in the Raman spectrum could be the result of the higher disorder degree of the structure due to the introduction of various surface termination. All these features present in the Raman spectrum of V 2 CT x corroborate removal of Al layer. characterization methods, such as XRD. However, it is also noticeable that the flake produced from the sample obtained after DMSO treatment is rougher along the edge and surface, which might be due to the stirring and sonication time.

Ti 2 CT x MXene

As discussed in the Charpter I, the bonds between M n+1 X n and A are weaker than those of M-X, and are thus chemically more reactive. Therefore, selectively etching only the A layers from the MAX phase is possible. An effective way to extract A layer without destroying the layered morphology is the chemical etching. Alternative method as direct mechanical exfoliation has never been proved to be successful in delamination of 2D MXene layer. It is well known that the mechanical exfoliation is closely related to the mechanical properties of materials including elastic constants C ij , bulk mechanical moduli (K, G, and E).

From the calculated elastic coefficients and mechanical properties of the MAX phase compounds (See Table 4.1), we can find that the elastic constants of MAX phases with large atomic radius A elements smaller than that with those of small atomic radius element. Here, if we compare C 33 of Ti 2 SnC to that of Ti 3 AlC 2 , it clearly indicates lower C 33 which should ease the mechanical deformation along c-axis. By checking the atomic radius of Al (143 pm) and Sn (158 pm) [144], the bond energy of Ti-Sn is weaker than that of Ti-Al. In this case, HF-etching combined with mechanical exfoliation were also applied on the as-grown Ti 2 SnC aiming at synthesizing Ti 2 CT x MXenes.

Ti 2 SnC etching

The average size of as-grown Ti 2 SnC crystal is around 10-100 µm, exhibiting hexagonal morphology (as shown in Figure 4.24). Ti 2 CT x MXene was synthesized by immersing Ti 2 SnC in 45% concentrated HF solution for 72 h at room temperature. The low yield of crystal limited the raw materials that we can use in the experiment, hence the amount of particles is not enough to form a suspension as that of V 2 CT x after rinsing with DI water.

Another method used, henceforth referred to as drop casting, consisted of filling a pipette with Ti 2 CT x MXene solution and dispensing a drop on a glass slide or Si/SiO 2 substrate that had been cleaned in ethanol. The substrate would then be left to dry in air. This was intended as a quick and easy method that might result in dispersion of colloidal MXene particles. The goal was the evidence of a potential route for non-Al containing MAX phase etching.

Theoretically, when the water in the drop dried, a thin layer of flakes might be left behind. To help with flake adhesion, positively charged hydrophilic glass slides were used, since MXene flakes are negatively charged and the aqueous solution spreading itself along the slide surface was desirable. Finally analysis consisted of optical microscopy, Raman spectroscopy, and ToF-SIMS spectrometry were performed.

Optical microscopy of HF-etching Ti 2 SnC

Unlike dry method, drop casting resulted in extremely uneven coverage of the drop area with MXenes particles as well as a very large amount of solution residues on the Si/SiO 2 substrate as can be seen in Figure 4. 25(a,b). A single droplet of MXenes solution was placed on top of the glass substrate and allowed to dry, as shown in Figure 4.25(c,d).

Raman spectroscopy of HF-etching Ti 2 SnC

Conclusion

In summary, large scale V 2 CT x MXene flakes was obtained by conventional HFetching of V 2 AlC single crystals. Mechanical delamination of multilayered V 2 CT x flakes into few layer flake and transfer on Si/SiO 2 substrate was also achieved. Structural characterization demonstrated an enlarged interplane distance, while prior DMSO intercalation seems to have no effect on this type of MXenes. Typical 2D material morphology was derived in SEM and TEM images. From EDS results, we concluded that -OH terminations on V 2 CT x is dominating, and the most energetically favourable, compared to -F and -O functional groups. Isolated V 2 CT x flake on the Si/SiO 2 substrate are suitable for the fabrication of electrical device and measurements, which will be discussed in next Chapter.

chapter 5

Electron transport in MXenes devices

In this chapter, protocols employed for fabrication of V 2 CT x MXene device suitable for electrical transport measurements will be firstly introduced. Then, methods to measure the carrier transport properties of 2D V 2 CT x MXene are discussed. Measurements have been performed from room to low temperature. First-hand electron transport data were obtained for this new 2D material and we discuss the salient features emerging from these data. µC/cm 2 ); The second one aimed for the pattering of the contact pads themselves (200 x 200 µm 2 ) as well as the path to these contacts. Due to larger working area and lower requirements for the resolutions, a smaller magnification and higher beam current were chosen to optimize the expose time (E beam ~30keV, spot 5, magnification ×400, dose ~300 µC/cm 2 ).

Following this, the sample was developed in a MIBK/IPA (1:3) solution for 90 seconds and then rinsed in the IPA for 30 seconds. After development, the sample was put in the high vacuum chamber (~2 ×10 -7 mbar) of an E-gun vacotec metal evaporation system. Then a first metal deposition of a 5 nm thick Ti layer as adhesion layer followed by a second metallization of a Au layer was performed. The deposition rate for both layers is ~1 Å/s.

The last step (lift-off) process consists in immersing the sample in an acetone solution.

The device is ready after rinsing in IPA and drying with nitrogen gun.

Thermal annealing under an inert gas flow

Prior to the bonding, the sample to be annealed was placed in the chamber of a Rapid Thermal Annealing (RTA) system (ULVAC Mila-5000) in the Winfab cleanroom.

First, the annealing chamber was purged during 10 min under inert atmosphere (a Ar/H 2 flow in our experiment). Then the sample was heated using a near-infrared lamp from room temperature to 500 °C for 1 hour and maintained at 500 °C for 4 hours, always under Ar/H 2 flow. Afterwards, the sample was cooled down back to room temperature.

Due to the lack of the reference on the contact fabrication on MXene sample, no standard protocol was available for this process. The effect of the annealing on the contact performance was still unclear. The condition applied in the sample of Ti 3 C 2 T x MXenes were varied from 140 °C to 300 °C for 15 min to 30 min [START_REF] Lipatov | Effect of Synthesis on Quality, Electronic Properties and Environmental Stability of Individual Monolayer Ti 3 C 2 MXene Flakes[END_REF][START_REF] Miranda | Electronic properties of freestanding Ti 3 C 2 T x MXene monolayers[END_REF].

The bonding

The last fabrication step is to contact the metallic leads of the device to the pins of the sample holder (Dual-in-line non-magnetic holder, 2 x 7 metallic pins) which is adapted for electrical (magneto) transport measurements in the cryostat.

First, all the pins of the chip were short circuited using a gold wire (diameter = 0.025 mm and purity of 99.99% from GoodFellow) bonded using silver epoxy (Epoxy Technology). The chip was then annealed at 140 °C for 1 h to dry the silver epoxy to become electrically conductive. This procedure, along with with the a grounded wrist band are useful to avoid the electric discharge through the device during the bonding step. In fact, according to our previous experience on mesoscopic device of graphene device, such discharge could strongly damage the device. Though seemingly the MXene device was more robust, same procedure was retained.

Then, the backgate of the sample was glued on the chip using silver paint (Agar Scientific) and contacted to one of the sample holder pins using the same gold wire and silver epoxy. After all the metallic leads were contacted to the pins, the sample was again annealed under the same conditions as for the previous step. Afterwards, the chip was plugged on the measurement setup and grounded. Finally, the wires short circuiting the pins on the chip were carefully cut using tweezer. It is worth mentioning that some very thin flakes were also electrically contacted as shown in Figure 5.4. It is, however, due to the size of the flake that can not define four contacts. In the present thesis, only devices with four contacts successfully deposited on the flakes will be discussed. In table 5.1 we list the size and characteristics of the flakes that were used to produce devices, as described below. Coherent transport calculations were performed by other researchers via a non equilibrium Green's function (NEGF) technique which have already been applied to low-dimensional system for the electron transport. The simulation results predict that the pristine MXenes are highly conductive [START_REF] Khazaei | Nearly free electron states in MXenes[END_REF]. In the first paper on Ti 3 C 2 T x , a small band gap of 0.05 eV with -OH termination and 0.01 eV with -F termination were predicted. Since then, dependence of the electronic band structure on chemical termination groups have been widely studied [START_REF] He | New two-dimensional Mn-based MXenes with room-temperature ferromagnetism and half-metallicity[END_REF][START_REF] Hu | Investigations on V 2 C and V 2 CX 2 (X = F, OH) Monolayer as a Promising Anode Material for Li Ion Batteries from First-Principles Calculations[END_REF][START_REF] Anasori | Control of electronic properties of 2D carbides (MXenes) by manipulating their transition metal layers[END_REF][START_REF] Lai | Surface group modification and carrier transport properties of layered transition metal carbides (Ti 2 CT x , T: -OH, -F and -O)[END_REF][START_REF] Guo | Ti 2 CO 2 Nanotubes with Negative Strain Energies and Tunable Band Gaps Predicted from First-Principles Calculations[END_REF][START_REF] Li | Lattice dynamics and electronic structures of Ti 2 C 2 O 2 and Mo 2 TiC 2 O 2 (MXenes): The effect of Mo substitution[END_REF][START_REF] Zhou | Electronic and transport properties of Ti 2 CO 2 MXene nanoribbons[END_REF].

According to the theoretical results, most of the functionalized MXenes are metallic or have small band gaps which could be possibly missed experimentally Specifically, for the V 2 CT x MXenes, V 2 C monolayer is predicted to be metallic with antiferromagnetic configuration, while its derived V 2 CF 2 and V 2 C(OH) 2 in their most stable configuration are small-gap antiferromagnetic semiconductor ( [START_REF] Hu | Investigations on V 2 C and V 2 CX 2 (X = F, OH) Monolayer as a Promising Anode Material for Li Ion Batteries from First-Principles Calculations[END_REF][START_REF] Gao | Monolayer MXenes: promising half-metals and spin gapless semiconductors[END_REF]). According to the calculation results of [START_REF] Hu | Investigations on V 2 C and V 2 CX 2 (X = F, OH) Monolayer as a Promising Anode Material for Li Ion Batteries from First-Principles Calculations[END_REF], Figure 5.5 shows the optimized structural geometries of the free-standing V 2 C monolayer and its fluorinated and hydroxylated derivatives.

Electrical characterization of V 2 CT x MXenes

I-V curve

First electrical characterization was carried out by sweeping the source-drain voltage, V DS , from -4 V to 4 V and record the current, I DS . Figure 5.8 shows the typical I -V curve obtained at room temperature for Device I. Current was swept through contacts 1 and 4 while the voltage difference between contact 2 and 3 was measured. An ohmic character is observed with a constant resistivity 2.46 ×10 -2 Ω•m which is two orders of magnitude higher than reported value of Ti 2 CT x MXenes [START_REF] Lai | Surface group modification and carrier transport properties of layered transition metal carbides (Ti 2 CT x , T: -OH, -F and -O)[END_REF] and one order of magnitude higher than reported value of Ti 3 C 2 T x [START_REF] Miranda | Electronic properties of freestanding Ti 3 C 2 T x MXene monolayers[END_REF]. The contact resistance in our first trial is relatively high, staying in the range of few MΩs, which might be due to the PMMA residuals after contact fabrication and some attempts are therefore made to improve the contact and lower the contact resistance.

Improvement on the contact fabrication procedure were achieved after several attempts on the device measurement. It is confirmed that thermal annealing is a way to get rid of organic contaminants. The detailed process can be referred to the experimental part: Section 5.1.2.

Temperature dependency of resistivity

To investigate the carrier transport properties of the V 2 CT x MXenes, the resistivity as the function of temperature was measured on the devices with four contacts after annealing procedure. Current was swept through contacts 1 and 4 while the voltage between contact 2 and 3 was measured as in the previous configuration. Ω•m and 2.20 ×10 -5 Ω•m at 10 K, as measured respectively, for device II and device III.

Clearly, the resistance increases with the increasing temperature, unlike the reported temperature dependence reported for Ti 3 C 2 T x [START_REF] Miranda | Electronic properties of freestanding Ti 3 C 2 T x MXene monolayers[END_REF] and Ti 2 CT x [START_REF] Lipatov | Effect of Synthesis on Quality, Electronic Properties and Environmental Stability of Individual Monolayer Ti 3 C 2 MXene Flakes[END_REF], where in both cases, the resistance decreased with increasing temperature.However, the change in temperature is rather modest, compared e.g. to that observed in the corresponding MAX phase. with decreasing temperature, the resistance first decreases until about 250 K and then increases slightly all the way down to 2.5 K. We can see that the results varied from sample to sample dramatically, though different regimes of the resistance variation with the temperature were reported.

In the case of V 2 CT x MXenes, two regimes were also clearly observed from our plots where there exist two slopes of linear variation dependence, one sharper than another.

Metallic behaviour (decreasing resistance with decreasing temperature) is observed in both samples. However, one would expect the resistance to reach a constant value at low temperature due to impurity scattering, which is not observed. Moreover, the the top part) then it could happen that, with temperature, the inter-stack resistance is gradually reduced. In that case, one could imagine that in the high temperature regime, only the top stack contributes to the measured resistance, while in the low temperature regime, the whole MXene crystal contributes to transport, and the resistance becomes smaller (as in Figure 5.9).

Another hypothesis is that the anisotropy ratio (ρ ab /rho c ) in the case of V 2 CT x MXene follows the same trend as in the V 2 AlC MAX phases (see Figure 3.10). In that case, since the anisotropy factor exhibits a factor-of-two change between room temperature and low temperature, this could explain a transition between different regimes in the temperature dependence of the in-plane resistance of V 2 CT x , especially if the electrical contacts to each MXene layer inside the stack are not homogeneous (i.e. better contacts to some layers).

We compared resistivity values of two samples in Figure 5.12. As demonstrated, the shape of the flake is irregular, leading to non homogeneous. Considering the maximum and minimum value used for the calculation of resistivity, the error bar is calculated and shown in Figure 5.12(a). From the data on both measured samples, we can find out the average value of resistivity of V 2 CT x is around 2×10 -5 Ω•m. To the best of our knowledge, this is the highest-conductivity MXene device ever reported. More details can be found in the Table 5.2. Furthermore, from Figure 5.12 (b), the residual resistivity varies quite strongly depending on the amount of impurities and other crystallographic defects. In our present test, it implies that the thinner flake device has better quality than thicker one. Therefore, the resistivity of V 2 CT x MXene is highly sensitive to defects and also to the layers thickness.

Field effect of V 2 CT x MXene device

Using the Si substrate as backgate electrode, transport in V 2 CT x MXene device II was investigated by sweeping the backgate voltage, V G . As can be observed in Figure 5.13(b). We can see that the transfer characteristics of the V 2 CT x MXene device exhibits p-type behavior, as Ti 2 CT x [START_REF] Lai | Surface group modification and carrier transport properties of layered transition metal carbides (Ti 2 CT x , T: -OH, -F and -O)[END_REF].

From a linear fit of the data, the field effect mobility, µ FE can be determined from the standard relation

µ FE = ∆I D ∆V G t ǫV DS L W (5.1)
where t and ǫ are the thickness and permittivity of the SiO 2 layer, L and W are the length and width of the MXene device, respectively. Based on the results shown in Figure 5.13(a), a 1.6 K field effect mobility µ FE , 22.7 ± 10 cm 2 /V•s is calculated the error bar is due to the error on linear fitting), which does not seem unphysical, considering the reported values of mobility in the literature : 0.6 cm 2 /V•s [START_REF] Miranda | Electronic properties of freestanding Ti 3 C 2 T x MXene monolayers[END_REF], 4.23 cm 2 /V•s [START_REF] Lipatov | Effect of Synthesis on Quality, Electronic Properties and Environmental Stability of Individual Monolayer Ti 3 C 2 MXene Flakes[END_REF] for Ti 3 C 2 T x and 10215 cm 2 /V•s for Ti 2 CT x [START_REF] Lai | Surface group modification and carrier transport properties of layered transition metal carbides (Ti 2 CT x , T: -OH, -F and -O)[END_REF].

From σ = µn 0 e, we calculate that the charge carrier density n 0 of V 2 CT x MXene is 1.66×10 20 cm -3 , while the density of Ti 3 C 2 T x MXenes was measured to be 8×10 21 cm -3 [START_REF] Miranda | Electronic properties of freestanding Ti 3 C 2 T x MXene monolayers[END_REF]. value of 2×10 -5 Ωm is of the same order of magnitude as reported other MXene sample (thickness 20-30 nm), and about 2 orders of magnitude higher than its corresponding MAX phase sample, where the charge carrier concentration deduced from field-effect measurement is 1 order of magnitude lower than the reported data.

Conclusion

We can conclude that we successfully obtained some first hand transport data on V 2 CT x MXenes. The average value for the resistivity of Device II and Device III is 2×10 -5 Ω•m, not far from value reported other MXene samples. The temperature dependence is relatively small and unusual compared to a normal metal, but is also sample dependent, so it is probably related to defects and the corresponding conduction mechanism between layers. The field effect measurement indicates field effect mobility µ FE , 22.7 ± 10 cm 2 /V•s. The magnetoresistance surprisingly does not show any feature nor a clear classical parabolic dependence which could allow to extract very reliable information on charge carriers. We obtained the µ H is in the order of magnitude 10 2 cm 2 /V•s, comparable to its parent MAX phase.

As demonstrated in the literature [START_REF] Ouisse | Magnetotransport in the MAX phases and their 2D derivatives: MXenes[END_REF], understanding magneto-transport in MXenes (c) The possible presence of a large fraction of defects in the 2D sheets, especially when aggressive etchants such as 50% HF are used, also limit the reproducibility of experimental results from sample to sample.In solids, in general and 2D solids in particular it is difficult to characterize and quantify point defects.

It is assured that with further knowledge of the structure of MXenes, their electronic transport properties will be further understood thoroughly.

Conclusion and perspectives

At the end of this thesis, let us look back on our initiatives of this project: the primary objective is firstly involving the crystal growth of single crystal MAX phases and the characterization of their intrinsic physical properties, mainly magneto-electronic transport properties and more specifically, probing the anisotropic properties. Then, second objective of this project is focused on the synthesis of MXenes derived from MAX phase single crystals by a combined chemical etching and mechanical exfoliation. Then, MAX devices for in-plane and out-of-plane transport measurement were fabricated. A full set of experimental data were consequently obtained from single crystals of V 2 AlC and Cr 2 AlC as a function of temperature and magnetic field. In comparison with the resistivity value of polycrystalline samples, the resistivity of Cr 2 AlC single crystal is three times lower, while for that of V 2 AlC, four times lower. In particular, we obtain a very high ratio between the in-plane and parallel to the c-axis resistivity, which is very substantial, in the range of a few hundreds to thousands. From MR and Hall effect measurement, in-plane transport behaviour of MAX phases have been studied.As in the case of the polycrystalline phases, we observe a magneto-resistance of a few per cent, among them, only MR curve of Cr 2 AlC exhibits parabolic-like curves, as reported for polycrystalline MAX phases. One can notice that Hall resistivity varies linearly with magnetic filed, and this phenomena is temperature independent, indicating the systems are in the weak-field limit. R H is small, as previously noticed for polycrystalline samples. The extracted mobility is in the range from 50 to 120 cm 2 /Vs, which is the same order as magnitude of polycrystalline sample. Thermal transport measurement was also conducted on Cr 2 AlC samples. Similar as higher electronic conductivity compared to its polycrystalline counterpart, higher thermal conductivity is verified. The sign of Seebeck coefficient is not in consistent with that of Hall coefficient in which this discrepancy can still be partly explained by a compensation between holes and electrons. Attempts to measure the out-of-plane magnetoelectronic transport were also performed. Though we observed an interesting anomalous magnetoresistance in the absence of Lorentz-force, the mechanism of a field-induced transport along c-axis is still unclear. Theoretically, a general, yet simple model was proposed for describing the weak field magneto-transport properties of nearly free electrons in two-dimensional hexagonal metals. It was then modified to be applicable for the transport properties of layered MAX phases. We argue that the values of the in-plane Hall coefficient and the in-plane parabolic magneto-resistance are due to the specific shape of the Fermi surface of almost two-dimensional hole and electron bands. If the contribution of the electron pockets to in-plane resistivity is often predicted to be a minor one, in contrast, both holes and electrons should substantially contribute to the overall value of the in-plane Hall coefficient.

Additionally, large scale V 2 CT x MXene flakes were successfully synthesized by conventional HF-etching of V 2 AlC single crystals. Efforts have been made on the optimization of reaction conditions and general protocol for etching V 2 AlC was proposed.

Mechanical delamination of multilayered V 2 CT x flakes into few layer flake and transfer on Si/SiO 2 substrate was also achieved. Structural characterization demonstrated an enlarged interplane distance, while prior DMSO intercalation seems to have no effect on V 2 CT x MXenes. Typical 2D material morphology was found in SEM and TEM images. From the XRD pattern , one observed an evident shift of 2θ from 13.5°to 7.4°, corresponding to c-LPs changing from 13.107 Åto 23.872 Å. Such phenomenon has been attributed to the water intercalation in between the layers after delamination in an aqueous solution.The a -LP of this flake from SAED, inheriting the hexagonal basal plane symmetry of the parent V 2 AlC phase, is measured to be ~2.9 Å, which is similar to that of the V 2 AlC precursor.

In the end, we detailed the electrical device fabrication process and proceed with electrical measurements result. We can conclude that -OH terminations on V 2 CT x is dominate, and the most energetically favourable, compared to -F and -O functional groups. Finally, we can conclude that we successfully obtained some first hand transport data on V 2 CT x MXenes, though compared to other reported MXenes, the average value for the resistivity of Device II and Device III is 2×10 -5 Ω•m, which is in consistent with reported other MXene samples. The temperature dependence is unusual compared to a normal metal, but is also sample dependent, so it is probably related to defects and the corresponding conduction mechanism between layers. The field effect measurement indicates field effect mobility µ FE , 22.7±10 cm 2 /V•s. The magnetoresistance surprisingly does not show any feature nor classical parabolic dependence which could allow to get more information on charge carriers. The obtained µ H is in the same order of magnitude as its parent MAX phase.

At the end of this work, one can also point out a few directions that could be investigated in future studies, in light of the difficulties and hindrances that I have faced, and of the new opportunities that emerged.

The first aspect concerns sample fabrication including improvement of single crystal growth. The crystal size matters in all the following measurements. In order to understand the anisotropic magneto resistance, the crystal size is the prerequisite.

Sample fabrication also involves the fabrication of MXene device. To the best of our knowledge, among synthesis methods of MXene, there are very rare reports on the mechanical exfoliation of MXene. Up to now, no single layer MXene is obtained by mechanical exfoliation. As explained in the last chapter, understanding magneto-transport in MXenes is undoubtedly challenging. The terminations group characterization is still under exploration,which limits the understanding of relationship between chemical function and electronic properties, let alone the effect of defects introduced due to the harsh etchant. So as to get the high quality flake for the device fabrication, dry method would definitely be more favourable than wet method. Micro-mechanical exfoliation could be approached in the future.

Due to the lack of single-crystalline/single flake transport data on the MAX phases and MXenes, there is still much to be done before a thorough picture of the physical mechanisms governing magnetotransport. Here list some future work: i) thorough investigation of magnetotransport properties in magnetic MAX phases; ii)assess correlation between anisotropy ratio and crystal quality; iii) out-of-plane magnetoelectronic transport; iv) deep understanding of the termination group of MXenes according to different fabrication process; v) more experimental endeavours on MXene electronic measurement.

Figure 1 . 2 :

 12 Figure 1.2: Unit cell of representative MAX phase for (a) 211 (b) 312 (c) 413 [4].

  crossing the Fermi level along the short H-K, Γ-A and M-L directions (c-axis direction) whereas many bands are crossing the Fermi level along the Γ-K and Γ-M directions (directions located in the basal plane). Such result suggests a very strong anisotropy of the electronic properties (might give zero conductivity along the c-axis direction).The DOS and LDOS of Cr 2 AlC is shown in Figure 1.4(b). The lowest states around 10 eV below the Fermi level, originate from C 2s states, which are separated from the upper part of the valence band. The upper part of the valence band mainly consists of Cr 3d, C 2p, Al 3s and Al 3p states. The Cr 2 AlC valence band shows the hybridizations of Cr 3d -C 2p(from -7 to -3.7 eV) and Cr 3d -Al 3p (from -3.1 to -1.6 eV), implying strong ionic-covalent Cr-C bonds and weaker Cr-Al ones. At the Fermi level, pure Cr d states are predominant, indicating that, in a first approximation, the electronic properties of Cr 2 AlC are dominated by the Cr d states. The charge density contour is shown in Figure 1.4(c) for the Cr-C bonds in Cr 2 AlC and the metastable rock salt structure CrC with space group Fm 3m. Comparing the charge density of the Cr-C bonds in both phases the similarity is prominent. The ionic and covalent contribution to the overall bond character in the cubic CrC phase are essentially conserved in Cr 2 AlC, as can be seen from the charge density around Cr andbetween the Cr and C atoms in both structures. It can be concluded that the bonding is characterized by covalent and ionic contributions and that this character is essentially conserved in the M 2 AC ternaries. The chemical bonding in both materials therefore appears to be rather similar.

Figure 1 . 4 :

 14 Figure 1.4: (a) Energy band structure of Cr 2 AlC [31] (b)Total and local DOS of Cr 2 AlC [32] (c) Charge density contour for the Cr-C bond. upper image:in Cr 2 AlC for a cut in the plane marked in left structure. down image: in rock salt structure CrC for a cut in the (100) plane [33] (d) Primitive Brillouin zone of the hexagonal unit cell.

Figure 1 . 5 :

 15 Figure 1.5: Band structure of V 2 AlC via first principles under different pressures [34] (upper image) and TDOS and PDOS (down image)of V 2 AlC [35].

  .6(a) illustrating the crystal structure and the electronic orbitals across and in the laminate plane for Ti 3 SiC 2 . In general, Ti(2) 3d states less contributes to the Ti 3d-Si 3p chemical bonding because Ti(2) atoms are located in between two octahedral layers. Electronic band structure of Ti 3 SiC 2 presented in the Figure 1.6(b) exhibits similar anisotropic features as 211MAX phases, in which near Fermi level there is almost no band crossing the Γ-A, M-L and few along H-K direction while there are large numbers of bands crossing along Γ-K, Γ-M. Moreover, it is demonstrated by theoretical calculation that Ti 3 SiC 2 presents holelike properties along the basal plane and electron-like properties along the c-axis, as experimentally proved by the different sign of Seebeck coefficient along two directions.

Figure 1 . 7 :

 17 Figure 1.7: (a) Fermi surfaces for two adjacent bands crossing Fermi level indicating hole-like (upper) and electron-like features (down)[START_REF] Chaput | Anisotropy and thermopower in Ti 3 SiC 2[END_REF] and (b) calculated and measured Seebeck coefficients of Ti 3 SiC 2 (a (000l)-oriented thin film of Ti 3 SiC 2 (triangle) and polycrystalline sample (square)[START_REF] Magnuson | Electronic-structure origin of the anisotropic thermopower of nanolaminated Ti 3 SiC 2 determined by polarized x-ray spectroscopy and Seebeck measurements[END_REF].

  Figure 1.8 represents current 2D materials families.

Figure 1 . 8 :

 18 Figure 1.8: Current 2D material library [40].

Figure 1 . 11 :

 111 Figure 1.11: (a) Schematic describing the synthesis process of MXenes from microcrystalline MAX phase by HF selectively etching. SEM images of Ti 3 AlC 2 before (b) and after (c) HF etching [55].

Figure 1 . 12 :

 112 Figure 1.12: (a) Schematic representation of the intercalation mechanism (b) Particle size distribution in aqueous colloidal solution; inset shows Tyndall scattering effect in the solution (c) Scanning electron microscope image of d-Ti 3 C 2 single flake on alumina membrane [68].

  2000 • C. The carbon content was obtained by partial dissolution of the graphite walls (See Figure 2.2(a)).

Figure 2 . 1 :

 21 Figure 2.1: (a) Photo of the puller with heat unit and reactor (computer control panel not included) (b) schematic diagram of the experimental set-up used for high temperature solution growth.

Figure 2 .

 2 2(b)).

Figure 2 . 2 :

 22 Figure 2.2: (a) Graphite crucible (for Ti 3 SiC 2 , Ti 2 SnC) (b) Alumina crucible (for Cr 2 AlC,V 2 AlC) and the raw materials used for growth of Cr 2 AlC.

Figure 2 .

 2 Figure 2.3 shows the details of the reactor geometry. The crucible can be separated in two parts: the inner alumina crucible where growth takes place and the outer graphite crucible, which is directly heated by the electromagnetic field applied by induction coil.

Figure 2 . 3 :

 23 Figure 2.3: Reactor configuration indicating the melt solvent and crucible structure.

Figure 2 . 4 :

 24 Figure 2.4: Experimental process profile of all the crystal growth in the current work.

Figure 2 .

 2 Figure 2.6(a) is the Cr -Al-C ternary phase diagram, in which a liquid surface expands along the Al-Cr line of the isothermal sections at a temperature higher than the melting point of Al. At temperature in the 1400 • C range, and starting from a binary Cr-Al melt with a Cr atomic fraction roughly below χ Cr =0.4, dissolving a small amount of carbon in the melt allows one to obtain a composition for which the liquid is in equilibrium either

Figure 2 . 5 :

 25 Figure2.5: (a) Flux "cupcake" taken immediately from crucible after cooling process (b) Flux "cupcake" after immersed in the dilute HCl for few hours (c) Flux "cupcake" standing in the air after for few weeks.

Figure 2 .

 2 Figure 2.7 shows the cross section of the flux cake with different molar ratio of Al:Cr:C. It is obvious that by changing the carbon dissolution amount in the solvent, the numbers of nuclei and size of the crystals vary.Figure 2.7(a) shows that if the dissolution

Figure 2 .

 2 7(a) shows that if the dissolution amount is too low, there is no sufficient carbon resource to grow continuously, which leads to a small amount of crystals. On the contrary, excessive carbon will result in plenty of nuclei and form the undesirable by-products Al 4 C 3 which appeared as gold color phase in Figure2.7(b).

Figure 2 .

 2 7(c, d) give the optimized example with 7.2at% of carbon, before and after washing with HCl acid, from which we can determine the nucleation is generated from the bottom and wall of the crucible.

Figure 2 . 6 :

 26 Figure 2.6: Phase diagrams of (a) Cr-Al-C[92] (b) Cr-C.

Figure 2 . 7 :

 27 Figure 2.7: Cross section images of various flux cupcakes with different molar ratio of raw materials (a) n(Cr) : n(Al) : n(C) = 37.5% : 56.9% : 5.6% (b) n(Al) : n(Cr) : n(C) = 53.9% : 33.5% : 12.6% (c) n(Cr) : n(Al) : n(C) = 35.6% : 57.2% : 7.2% (d) etching of (c).

Figure 2 . 8 :

 28 Figure 2.8: Photo of as-grown crystals.

Figure 2 .

 2 Figure 2.8 shows the photos of the as-grown Cr 2 AlC crystals, with an average size in the centimeter range. We can see from the photos that the crystals are platelet-like, indicating a highly anisotropic high-oriented growth.

Cr 2

 2 AlC. As shown in Figure 2.10(b), this process results in the complete dissolution of the flux, leaving the crystals free and almost unaffected by the acid treatment. After the reduction of the solidified flux, the remaining platelets were cleaned and sonicated in ethanol or propanol.

Figure 2 . 9 :

 29 Figure 2.9: Phase diagrams of (a) V-Al-C [93](b) V-Al [94].

Figure 2 . 10 :

 210 Figure 2.10: Optical photos of V 2 AlC single crystal growth (a) solidified flux after immersed in diluted HCl acid for several hours and (b) single crystal after washed with ethanol or propanol and rinsed with water.

Figure 2 . 11 :

 211 Figure 2.11: Photos of different MAX crystals showing the typical sizes.

2. 2 . 1 . 1

 211 Crystal structure and identification Three different kinds of pole figures were obtained, among which, each one corresponding to one or two different plane orientations with same interplane distance:(a) (0006) (1 peak) and 1013 (6 peak), (b) 1019 (6 peak), (c) (2023) (6 peaks) and (1126)

( 6

 6 peaks) (See Figure2.12). Particularly, the 1013 pole figure displays exhibits the expected peaks, all located at the apex of a hexagon. It is noticeable that the interplane distance of the (0006) planes is very close to that of the (1013) planes, (0.214073 nm and 0.214592 nm, respectively), so that for the crystal orientation along c-axis, an additional diffraction peak appears at the origin. For the other crystal orientations, we obtained a set of diffraction peaks which are scattered over the circle including the hexagonal distribution expected from a single crystal.

Figure 2 . 12 :

 212 Figure 2.12: X-ray pole figure of Cr 2 AlC platelet with an area of several mm 2 .

Figure 2 . 13 :

 213 Figure 2.13: FWHM of φ-scan pattern of (2023) plane.

Figure 2 .

 2 Figure 2.13 shows that the FWHM (width at half-peak maximum) of φ-scans of the

Figure 2 . 14 :

 214 Figure 2.14: (a) Raman spectrum of Cr 2 AlC platelet with an excitation laser parallel to the c-axis (b) Assignment of atomic displacements to the different Raman active vibrational modes in 211MAX phases[95].

Figure 2 .

 2 Figure 2.15 shows the optical microscope images of various samples observed in the Normarski mode.Figure 2.15(a) shows the bumpy and tangled surface of the as-grown

Figure 2 .

 2 15(a) shows the bumpy and tangled surface of the as-grown crystals after cleaning. The dendrite islands can be clearly observed in Figure2.15(b),

Figure 2 . 15 :

 215 Figure 2.15: Optical microscope views of the surface of the Cr 2 AlC crystals obtained in the Nomarski mode (Differential interference contrast (DIC) microscopy) (a) Bumpy and tangled surface of the as-grown crystals after cleaning (b) Dendrite islands (c-e) Dendrite morphology and (f) Growth terrace.

Figure 2 .

 2 [START_REF] El-Raghy | Synthesis and characterization of Hf 2 PbC, Zr 2 PbC and M 2 SnC (M=Ti, Hf, Nb or Zr)[END_REF](f) , we can see the transport and diffusion of solute on the crystal surface. Concurrently, no clear spirals growth phenomenon were obtained.

Figure 2 . 16 :

 216 Figure 2.16: Kossel model of a crystal surface[101].

Figure 2 . 17 :Figure 2 .

 2172 Figure 2.17: SEM images of as-grown Cr 2 AlC crystal surface.

Figure 2 . 18 :

 218 Figure 2.18: XRD pattern of as-grown V 2 AlC platelet.

Figure 2 . 19 :

 219 Figure 2.19: X-ray pole figures measured from a V 2 AlC platelet and obtained from different interplane distances. Diffraction peak indexations are shown in the figures.

Figure 2 . 21 :

 221 Figure 2.21: Optical microscope views of the surface of V 2 AlC crystals obtained in the Nomarski mode(a) Flat surface (b) Heterogeneous nuclei (c) Dendrite structure (d) Etch pits.

Figure 2 . 22 :

 222 Figure 2.22: AFM topographic images of the surface of V 2 AlC platelets after dissolution of the solidified flux in concentrated HCl during several hours. A terrace and step structure characteristic of a step flow growth process is visible. In both images all the step heights are equal to c.

Figure 2 . 23 :

 223 Figure 2.23: The left photograph shows the two parts of a V 2 AlC crystal after cleavage with a strong adhesive tape (the tape has been cut around the cleaved crystal and corresponds to the white color). The right image is an AFM topography of the cleaved surface in a region with a high density of tears.

Figure 2 . 25 :

 225 Figure 2.25: AFM images of the top surface of a terrace (the color range corresponds to a much smaller height than in the previous figures). The extracted RMS value of the roughness is 0.18 nm for image (a) and 0.06 nm for image (b).

Ti 2 C

 2 MXene from Ti 2 SnC in Chapter IV, some results are briefly demonstrated in Figure2.26. The hexagonal morphology of the crystal as resulted from the SEM micrographs, combined with the EDX results, undoubtedly prove the harvest of Ti 2 SnC crystals. Due to the lack of reported data on the Raman spectrum of Ti 2 SnC, we can only refer to our results on other M 2 AX MAX phase, the peak at 246.8 cm -1 can be assigned to E 2g mode, which is generated by the M-A atoms in-plane vibrations.

Figure 2 . 26 :

 226 Figure 2.26: (a) SEM image indicating the hexagonal morphology of the crystal (inserted EDX results showing the atomic ratio of Ti:Sn:C) and (b) Raman spectrum of Ti 2 SnC.

cm 2 for

 2 Ti 3 SiC 2 , 1 cm 2 for V 2 AlC and several cm 2 for Cr 2 AlC were obtained in in our experiment set-up. Structural characterization confirms the single crystalline character of the samples by X-ray measurements and Raman spectroscopy. The surface morphology of V 2 AlC crystals is flat without dendrites observed on the surface of Cr 2 AlC. Well defined steps and terraces indicates a step flow growth process. Emphasis is put on the mechanical cleavage of the sample which can be achieved in the basal plane thanks to the existence of the weakly bonded Al atomic planes. The nano-lamellar structure of the crystals permits to cleave the platelets parallel to the basal plane just by sticking and folding a strong adhesive tape on each face. The initial flatness of the crystal surface allowed us to obtain cleaved areas almost equal to that of the entire platelet. Since the transformation of HF-treated, polycrystalline V 2 AlCinto MXene nano-or micro-crystals has already been proved, our crystals might be used as a starting basis for forming MXenes with macroscopic area. This will be the main objective of next step work, along with the assessment of the transport properties.

  Pauw geometry A schematic of a square Van der Pauw configuration is shown in Figure 3.1(b) [109]. In our exeriment, the Van der Pauw geometry was used for the temperature dependency of resitivity, not for Hall measurement. Four voltage measurements yield the following four values of resistance R 21,34 = V 34/ I 21 , R 32,14 = V 41/ I 32 , R 43,21 = V 12/ I 43 , R 14,23 = V 14/ I 23 , Then the two characteristic resistance can be written as R A = (R 21,34 + R 43,21 )/2 , R B = (R 32,41 + R 14,23 )/2 , Van de Pauw demonstrated that R A and R B determinate the sheet resistance R S through the Van der Pauw equation: exp

Figure 3 .

 3 1(c) is a typical Hall bar geometry, the Hall coefficient is defined as R H = V H t IB , where t is sample thickness.

Figure 3 . 1 :

 31 Figure 3.1: Geometry of in-plane measurements: (a) Four probe (b) Van der Pauw [109] (c) Hall bar bridge.

Figure 3 . 2 :

 32 Figure 3.2: Geometry of out-of-plane measurement: (a) Contact configuration and (b) Derivation of current lines along the edge.

Figure 3 . 3 :

 33 Figure 3.3: Correction function curve.

Figure 3 .

 3 Figure 3.4(a,b) shows the samples fabricated by these two different ways. In order to investigate the effect of high power laser on the samples, optical microscopic photos were shown as well , indicating that the sample did not burn heavily or not too many defects were generated in spite of few oxidation layers along the cutting edge.

Figure 3 . 4 :

 34 Figure 3.4: (a) Diamond saw cutting of V 2 AlC (b) Laser cutting of Cr 2 AlC; Optical microscopic photos of the heat affect area of laser cutting of (c) V 2 AlC and (d) Cr 2 AlC.

Cr seemed perform better for Cr 2

 2 AlC sample than Ti. The deposition rate for Ti/Cr is 1 Å/s, for Cu is 3 Å/s. Meanwhile, a standard silicon sample was also prepared as reference (See Figure 3.5(b)).

Figure 3 .

 3 5(c) shows the optical microscopic view of contacts on the Cr 2 AlC sample.

Figure 3 . 5 :

 35 Figure 3.5: (a) Metalization mask for contact deposition and designed for different size of MAX phase samples (b) Standard silicon sample (c) Microscopic photo of as-prepared Cr 2 AlC sample.

Figure 3 . 6 :

 36 Figure 3.6: Four probes measurement with Lock-in amplifiers in the present experiments.

Figure 3 . 7 :

 37 Figure 3.7: Ratio of in-phase and out of phase signal (example: raw curve of V 2 AlC out-of-plane resistivity measurement).

Figure 3 .

 3 Figure 3.8 summarizes the temperature dependency of in-plane resistivity obtained in both cases of Cr 2 AlC and V 2 AlC. First of all, in the 100 K-300 K temperature range, there is a linear dependence of ρ as a function of T as generally observed of almost all MAX phases compounds[3]. The evolution is qualitatively similar to that already reported for polycrystalline phases, but the resistivity values are much smaller in the case of the single crystals. This typical metal-like behaviour is assumed to be simply due to the large density of states at Fermi level as explained in the Chapter I. Note that variations between the absolute in plane resistivity values measured among different samples are not negligible. Possible cause for these variations include different levels of defects (e.g. related to slightly different synthesis conditions), as well as imperfect electrical contacting of all the planes constituting the structure.In comparison with the resistivity value of polycrystalline samples for both cases (1.5×10 -7 Ω•m (4 K) and 7.4×10 -7 Ω•m (300 K) for Cr 2 AlC, 4×10 -8 Ω•m (4 K) and 2.5×10 -7 Ω •m (300 K) for V 2 AlC[3]), we can find that, for single crystal samples, though the value varies among samples, the resistivity of Cr 2 AlC is three times lower, being 2.5×10 -7 Ω•m (300K) and 5×10 -8 Ω• m (4K). As for case of V 2 AlC, the RT and 4K resistivity, being 1×10 -7 Ω•m (300K) and 1 ×10 -9 Ω•m (4K) are four times lower

Figure 3 . 8 (

 38 left), which indicates that the contacts are robust during cooling process and the curves are reproducible.

Figure 3 . 8 :

 38 Figure 3.8: Temperature dependence of in-plane resistivity of (a) Cr 2 AlC and (b) V 2 AlC.

Figure 3 . 9 :

 39 Figure 3.9: Corresponding ideal resistivity of Cr 2 AlC and V 2 AlC.

Figure 3 .

 3 Figure 3.10 summarizes the temperature variation of corrected value ρ c versus T. For

Figure 3 . 10 :

 310 Figure 3.10: Out-of-plane resistivity (all the values are corrected using correction functions) and anisotropy ratio ρ c /ρ ab of Cr 2 AlC and V 2 AlC.

Figure 3 . 11 :

 311 Figure 3.11: Temperature dependency of magnetoresistance MR of Cr 2 AlC, V 2 AlC and Ti 3 SiC 2 .

Figure 3 . 12 :

 312 Figure 3.12: Power fitting of MR of V 2 AlC and Ti 3 SiC 2 in comparison with to parabolic MR of Cr 2 AlC.

Figure 3 . 13 :

 313 Figure 3.13: Temperature dependence of exponent of power fitting for MR of V 2 AlC and Ti 3 SiC 2 .

Figure 3 .

 3 Figure 3.15(b)) . Following by linear fitting, Hall coefficient (R H ) can be deduced from the slope of the fitting curves.

Figure 3 . 16 :

 316 Figure 3.16: Temperature dependency curves of Hall coefficient of R H of Cr 2 AlC, V 2 AlC and Ti 3 SiC 2 .

Figure 3 . 17 :

 317 Figure 3.17: Two band model density (a), mobilities(b) and fitting parameter α(c) as a function of temperature for Cr 2 AlC Hall bar.

Figure 3 . 18 :

 318 Figure 3.18: (a) Thermal conductivity of Cr 2 AlC single crystal and (b) In comparison with polycrystalline sample[3]).

Figure 3 . 19 :

 319 Figure 3.19: (a)Electronic contribution and (b,c) Plotting curves indicating phonon behaviour to thermal conductivity of Cr 2 AlC.

Figure 3 . 20 :

 320 Figure 3.20: Seebeck coefficient of Cr 2 AlC single crystal (In comparison with polycrystalline sample [3]).

Figure 3 .

 3 Figure 3.21 shows the measurement configuration of out-of-plane magneto-electronic transport of MAX phases (modified Montgomery contact configuration[START_REF] Crommie | Thermal-conductivity anisotropy of single-crystal Bi 2 Sr 2 CaCu 2 O 8[END_REF]), where B//c, I//c. According to the function of Lorentz force: F = qE + qv × B, when B//v, no magnetic force is applied on charge carriers. Hence, ideally, no magnetoresistance will be observed.Yet, it is not the case of our experimental results. For magnetic field applied perpendicular to the basal (a-b) plane, the out-of-plane (c-axis) resistivity displays a magnetic enhancement.

Figure 3 . 21 :Figure 3 .

 3213 Figure 3.21: Measurement configuration of c-axis magneto-electronic transport.

Figure 3 . 22 :

 322 Figure 3.22: Out-of-plane resistivity of Cr 2 AlC (B//c. I//c) (a) magnetoresistivity (b) Zero field ρ c (T).

Figure 3 . 23 :

 323 Figure 3.23: Extraction the in-plane contribution from out-of-plane magnetoresistance.

Figure 3 . 24 :

 324 Figure 3.24: Fitting parameters of in-plane contribution for out-of-plane magnetoresistivity vs T (a) α (b) A and its relation with corresponding charge moblity.

Figure 3 . 25 :

 325 Figure 3.25: (a) Residual magnetoresistance vs T and (b) various fitting curves.

Figure 3 . 26 :

 326 Figure 3.26: Out-of-plane resistivity of V 2 AlC (B//c. I//c) (a) ρ c (B) (b) magnetoresistance at 1.5K and (c) Zero field ρ c (T).

Figure 3 . 27 :

 327 Figure 3.27: Extraction the in-plane contribution from out-of-plane magnetoresistance and the fitting of residual magnetoresistance.

Figure 3 . 28 :

 328 Figure 3.28: Fitting parameters of in-plane contribution for out-of-plane magnetoresistivity vs T (a) α (b) A. 88

  2m 0 centred in the first BZ (index zero, k 0 =0) and all BZ's adjacent to it (See Figure3.29(a) ). In the latter expressions k is the wave vector and the k i 's coordinates are that of the centres of the BZ's. U represents the Fourier component of the periodic potential for a wave vector joining the centres of two adjacent hexagonal BZ's. If the cell dimensions are specified, U is the only adjustable parameter. It splits the free electron curves into a hole band and electron pockets (Figure3.29(b)). Close to the corners of the hexagon, the secular equation might be reduced to the determinant of a 3×3 matrix, leading to analytical relationships between E and k. The E vs k relation can be plotted for any value of k, and the Fermi surface is computed by finding the line segments which satisfy E=E F , where the Fermi energy E F is determined by finding the level for which the sum of electrons in all bands is equal to the number of electrons per unit cell.

Figure 3 . 29 :

 329 Figure 3.29: Reproduction of adjacent Brillouin zones of a two-dimensional hexagonal lattice with the corresponding free electron disks (left) and Fermi line of the same lattice in the first Brillouin zone for nearly free electrons.

Figure 3 . 31 :

 331 Figure 3.31: 1D-tight-binding with 2 atomic planes per unit cell showing large splitting.

Figure 3 . 33 (

 333 red line). Comparing it to the projection of a full numerical computation in the basal plane demonstrates that in the case of Ti 2 AlC(See Figure3.33 right), only the small features are not reproduced. In the case of Ti 2 AlC, the roughest approximation is to consider that the electron pockets form open tubes, which is actually not predicted by An interesting point is that compiling the published expectations for other Ti-based MAX phases shows that the overall structure of the Fermi surface is always formed by hexagonally-shaped hole bands in the center of the zone, and trigonal electron pockets extending over three hexagonal BZ's and centred at the corners of the BZ hexagon[START_REF] Chaput | Thermopower of the 312 MAX phases Ti 3 SiC 2 , Ti 3 GeC 2 , and Ti 3 AlC 2[END_REF][START_REF] Chaput | Anisotropy and thermopower in Ti 3 SiC 2[END_REF][START_REF] Mauchamp | Anisotropy of the resistivity and charge-carrier sign in nanolaminated Ti 2 AlC: Experiment and ab initio calculations[END_REF](Figure 3.34) .Very often, the electron pockets form open tubes too. The number of bulges appearing in the open tubes over one unit cell is a direct function of the integer n appearing in the M n+1 AX n formula. In one extreme case (Ti 3 AlC 2 ),

Figure 3 . 34 :

 334 Figure 3.34: Fermi surface of Ti 3 AlC 2 , Ti 3 SiC 2 ,Ti 3 GeC 2 [126]and Ti 2 AlC[125].

Figure 3 .

 3 Figure 3.35 (1c)), corresponding to the electron-like parts of the Fermi line. They must be subtracted from the hole-like contribution (the central part of the Figure 3.35 (1c)).

Figure 3 . 35 :

 335 Figure 3.35: (1) Top: from left to right: (a) Fermi line, (b) polar plot of the velocity along the Fermi line, (c) polar plot of the mean free path and (d) magneto-resistance of a 2D hexagonal system of nearly free electrons with a low number of electrons per unit cell (N=2, τ p =10 -14 s, U=0.25eV, four 2D planes per unit cell with c=1.36 nm and a=0.304 nm).(2) Bottom: from left to right: (a) Fermi line, (b) radial plot of the velocity and (c) mean free path for a higher value of N (N=6, τ p =τ n =10 -14 s, U=0.75 eV, four 2D planes per unit cell with c=1.36 nm and a=0.304 nm).

Figure 3 .

 3 [START_REF] Yoo | Materials science: Ti 3 SiC 2 has negligible thermopower[END_REF] and from the nearly-free electron model which can explain a relative insensitivity of n app to the electron band filling. A small value of R H can indeed attribute to multiple reasons. It may be induced by a compensation between holes and electrons, or to a larger number of only one type of carriers. Yet, it is only in the isotropic case that the common observation of a small value of R H indicate the presence of two types of carriers. free path curves of the hole band and one of the two electron pockets almost contract one another, and what remains is the net contribution to σ xy of the second electron pocket (See Figure3.35(2c)). Since the velocity does not considerably vary with the filling, R H exhibits a plateau, whose value is fixed by the electron pocket per unit cell which remains uncompensated. Yet the hole density substantially decreases, whereas the electron density does the opposite.

Figure 4 .

 4 1 shows the principle of the removal of Al from the V 2 AlC 3D structure.

Figure 4 . 1 :

 41 Figure 4.1: Schematic diagram of Al removal from V 2 AlC.

Figure 4 .

 4 3(a)). Those not fully etched large crystals at the bottom of the beaker were immersed in fresh HF solutions with same concentration at room temperature for 120 h. The collected suspension was separated by centrifugation at 6000 rpm for 10 min and washed by deionized water several times until the pH value of solution reached above 5. Thereafter, the wet sediment were vacuum dried at 40 °C for 24 h, marked as VC-p indicating the powder-like morphology (See Figure4.3(b). The same rinsing procedure was applied for the larger crystals as well, marked as VC-f indicating the flake-like morphology (See Figure4.3(c)), both can be referred to V 2 CT x , where T x stands for terminated-surface groups.

Figure 4 . 2 :

 42 Figure 4.2: Schematic diagram of synthesis process.

Figure 4 . 3 :

 43 Figure 4.3: (a)Dark green supernatant and collection of (b)VC-p (powder-like) and (c)VC-f (flake-like).

Figure 4 . 4 :

 44 Figure 4.4: Blue tape exfoliation. (a) Status of exfoliation after ~10 times of foldingunfolding of the tape on VC-f. (b) Transfer on a piece of Si/SiO 2 .

Figure 4 . 5 :

 45 Figure 4.5: (a) SEM image and (b) the corresponding EDS spectrum of as-etched V 2 AlC single crystal.

4. 6 )

 6 . No clear change of interlayer space was detected after two weeks etching.

Figure 4 . 6 :

 46 Figure 4.6: AFM image indicating the step height of the V 2 AlC crystal after etching for 14 d.

Figure 4 . 8 :

 48 Figure 4.8: XRD patterns of V 2 AlC and V 2 CT x (VC-p and VC-f).

V 2

 2 CT x (See in the Figure 4.9(b,c)). The (002) peak shifted from a 2θ of 8.9°to 4.6°(c-LP from 19.9 Åto 38.6 Å) after 2 h mixing in TBAOH solution. By doubling the time to 4 h, a very slight down shift in the (002) peak position was observed (shifted down to 4.56°). Also this intercalant works well for large-scale delamination of carbonitrides MXene, such as Ti 3 CNT x as well.

Figure 4 . 9 :

 49 Figure 4.9: (a) XRD patterns of V 2 CT x MXenes with and without treatment of DMSO and (b,c) XRD patterns of Ti 3 CNT x and V 2 CT x before and after mixing with TBAOH [71].

Figure 4 .

 4 Figure 4.10 shows the cross-section SEM images of the mechanically disrupted V 2 AlC single crystals after sonication in 45% HF at 80 • C for 12 h. Apparently, the etching

Figure 4 . 10 :

 410 Figure 4.10: Cross-section SEM images of the as-mechanically destructed V 2 AlC single crystals after sonication in 45% HF at 80 • C for 12h.

Figure 4 . 11 :

 411 Figure 4.11: Cross-section SEM images of the as-etched V 2 CT x after immersed in 45% HF for 120 h.

Figure 4 .

 4 Figure 4.12(a) showed the distribution of V 2 CT x MXene grain sizes after sonication, from few micrometers to hundreds of micrometers. Comparing to small delaminated V 2 CT x particles[START_REF] Chen | CO 2 and temperature dual responsive "Smart" MXene phases[END_REF], and even most well-studied case Ti 3 C 2 T x with grain sizes of tens of micrometers, Figure4.12(b) demonstrates that the crystals with grain size larger than 100 µm could be successfully exfoliated by HF acid. From the magnified image (Figure4.12(c)) of the area marked in the Figure 4.12(b), we can clearly see the delaminated accordion-like delaminated morphology. EDS spectra was acquired under low magnification, on the sample of Figure 4.12(b). The results indicate that Al is almost completely removed from the etched samples (See Figure 4.12(d)). No fluorine was detected in the sample, which is a probable indication that -OH groups functionalize most of the V 2 CT x surface.

Figure 4 . 12 :

 412 Figure 4.12: SEM images indicating (a) V 2 CT x MXenes with various sizes and (b) 100 µm large particles, (c) Enlarge part of areas marked in (b) and (d) EDS spectrum of (b).

Figure 4 . 13 :

 413 Figure 4.13: EDS spectrum of as-etched sample in the early stage of our experiments.

Ti 3 C

 3 2 T x by aberration-corrected atomic-resolution scanning transmission electron microscopy (STEM)-electron energy loss spectroscopy (EELS), and confirmed that the inherited close-packed structure of Ti 3 C 2 T x is observed as atomic positions of two Ti 3 C 2 T x sheets remained laterally aligned and coverage of O-based surface groups,

Figure 4 . 14 :

 414 Figure 4.14: The considered types of -OH terminated Ti 3 C 2 T x MXenes (a) -OH groups are placed at the hollow site between three neighbouring carbon atoms, (b) -OH groups are placed at the top site of the carbon atom.

  respectively. Digital photos of V 2 CT x nano sheets dispersed in water and IPA with typical Tyndall effect indicates their excellent hydrophilicity and dispersity (See Figure4.15). Furthermore, a drop of the colloidal solution of V 2 CT x MXenes were placed on a lacey carbon coated TEM copper grid and allowed to dry in the vacuum at 40 °C overnight, ready for the TEM observation.

Figure 4 . 15 :

 415 Figure 4.15: Optical photos of dispersed colloidal solution of V 2 CT x MXenes.

Figure 4 .

 4 Figure 4.16 shows TEM micrographs of DI water dispersed V 2 CT x nanosheets. Electron transparent sheets of different lateral sizes, from hundreds of nanometres

Figure 4 . 16 :

 416 Figure 4.16: TEM images and SAED pattern of V 2 CT x nanosheets (DI water dispersed colloidal solution).

Figure 4 .

 4 Figure 4.17 shows the TEM and corresponding EDS of IPA dispersed V 2 CT x nanosheets.

Figure 4 .

 4 Figure 4.17(c)).

Figure 4 . 17 :

 417 Figure 4.17: TEM images and SAED patterns (a,b) and EDS spectrum (c) of V 2 CT x nanosheets (IPA dispersed colloidal solution).

Figure 4 .

 4 [START_REF] Zhang | Rapid fabrication of Ti 3 SiC 2 -SiC nanocomposite using the spark plasma sintering-reactive synthesis (SPS-RS) method[END_REF] shows the morphology of the electron transparent monolayer V 2 CT x flake.

Figure 4 . 18 :

 418 Figure 4.18: TEM images of individual monolayer V 2 CT x flake.

Figure 4 .

 4 Figure 4.19(a) and the corresponding optical images in Figure 4.19(b). In comparison to clean flat crystal surface before etching, highly defective surfaces were obtained, especially etching holes tend to appear at those places where there are more growth defects. The Raman spectrum of original V 2 AlC has consistent peak position as previously reported. The observed vibration modes of certain symmetry groups of V 2 AlC,

Figure 4 . 19 :

 419 Figure 4.19: Raman spectra (a) and corresponding optical images (b) of the V 2 AlC, as-etched V 2 CT x and as-exfoliated flake on the Si/SiO 2 substrate.

Figure 4 . 21 :

 421 Figure 4.21: AFM images indicating sizes and thickness distributions of isolated V 2 CT x flake on the Si/SiO 2 substrate starting from the as-etched V 2 CT x MXene treated with intercalant DMSO.

Figure 4 . 22 :

 422 Figure 4.22: AFM images of the flake indicating tape residue.

Figure 4 . 23 :

 423 Figure 4.23: AFM images of two typical flakes: (a) 5-7 nm thick, smaller than 5 µm (b) 15-20 nm thick, larger than 10 µm.

Figure 4 . 24 :

 424 Figure 4.24: Optical micrographs of Ti 2 SnC.

Figure 4 .

 4 Figure 4.26 is the Raman spectrum of Ti 2 SnC before and after HF-etching. The peaks at 243.2 cm -1 and 365.1 cm -1 in the Ti 2 SnC spectrum can be assigned to E 2g and A 1g modes, where E 2g involves the in-plane vibration of Ti-Sn atoms while A 1g involves out of plane vibration of Ti. After etching with HF acid, the E 2g peaks vanished by removing the Al. Meanwhile, two peaks appears centred at 403.3 cm -1 and 650.4 cm -1 , close to the Raman peaks found for Ti 2 CT x MXene in the literature, representing the vibration modes which can be assigned to nonstoichiometric titanium carbide[START_REF] Ahmed | H 2 O 2 assisted room temperature oxidation of Ti 2 C MXene for Li-ion battery anodes[END_REF][START_REF] Cai | TiCx-Ti 2 C nanocrystals and epitaxial graphene-based lamellae by pulsed laser ablation of bulk TiC in vacuum[END_REF].

Figure 4 . 25 :

 425 Figure 4.25: Drop coat with MXene solution on (a,b) Si/SiO 2 substrate and (c,d) Glass substrate.

Figure 4 . 26 :

 426 Figure 4.26: Raman spectra of Ti 2 SnC before and after HF-etching (on the Si/SiO 2 substrate).

Figure 4 . 27 :

 427 Figure 4.27: Raman spectrum of Ti 2 CT x MXene on different substrates.

Figure 5 . 2 :

 52 Figure 5.2: Schematic diagram of the steps for electrical contact fabrication: (a) Side view of the sample (b) Spin-coating of PMMA layer on the sample (c) EBL writing the electrical contact pattern on PMMA layer (d) Development for removing the nonexposed PMMA areas (e) deposition of the Ti/Au layer (f) Lift-off to remove the rest of PMMA layer.

Figure 5 .

 5 Figure 5.3 shows a micrograph of as-contacted device at the end of this process. Note

Figure 5 . 3 :Table 5 . 1 :

 5351 Figure 5.3: Optical images of electrically contacted V 2 CT x MXene device.

Figure 5 . 4 : 5 . 2 . 1

 54521 Figure 5.4: Two contacts on the V 2 CT x MXenes flakes.

Figure 5 . 5 :

 55 Figure 5.5: Optimized structural geometries of the free-standing V 2 C monolayer and its fluorinated and hydroxylated derivatives. (a) Side view of the bare V 2 C monolayer consists of a triple-layer with V(1) CV(2) stacking sequence. (b) Top view of the V 2 C monolayer with T5 magnetic configuration. (c-h) Side views of (c) I-V 2 CF 2 , (d) II-V 2 CF 2 , (e) III-I-V 2 CF 2 , (f) I-V 2 COH 2 , (g) II-V 2 COH 2 , and (h) III-V 2 COH 2 . (i, j) top views of I-V 2 CF 2 and II-V 2 CF 2 [151].

Figure 5 .

 5 [START_REF] Etzkorn | V 2 AlC, V 4 AlC 3-x (x=0.31), and V 12 Al 3 C 8 : Synthesis, Crystal Growth, Structure, and Superstructure[END_REF] shows the total density of states (TDOS) of V 2 C, V 2 CF 2 and V 2 C(OH) 2 monolayer. For bare V 2 C, the resulting DOS indicates that it is metallic with antiferromagnetic configuration. In contrast, when V 2 C is passivated by F or OH, the generated V 2 CF 2 or V 2 C(OH) 2 monolayer would turn into a semiconductor regardless of the specific adsorption configurations of functional groups. The calculated DOS results showed that the C atoms have almost no contribution to states near the Fermi level, namely, the metallic electronic character is determined by free electrons from V atoms. The termination group -F or -OH could saturate the free electrons of V atoms, resulting in the nonmetal character of fluorinated and hydroxylated of V 2 C monolayer.Different adsorption configurations merely result in different band gaps.

Figure 5 . 6 :

 56 Figure 5.6: TDOS of (a) V 2 C (b) I-V 2 CF 2 (c) III-V 2 CF 2 (d) I-V 2 C(OH) 2 (e) II-V 2 C(OH) 2 and (f) III-V 2 C(OH) 2 .The Fermi levels are set to zero. In each panel, the upper curve and the lower curve correspond to the DOS of the two spin species.[START_REF] Hu | Investigations on V 2 C and V 2 CX 2 (X = F, OH) Monolayer as a Promising Anode Material for Li Ion Batteries from First-Principles Calculations[END_REF]

Figure 5 . 7 :

 57 Figure 5.7: Electronic band structures of (a) V 2 C, (b) V 2 CF 2 , (c) V 2 C(OH) 2 and (d) V 2 CF(OH) in their high-symmetric configuration. The Fermi level is fixed as the reference of zero energy [157].

Figure 5 . 8 :

 58 Figure 5.8: (a) Optical microscopy (OM), (b) AFM image, (c) Dimensions and (d) Current-voltage (I-V) characteristic of V 2 CT x MXene device I measured at room temperature.

Figure 5 . 9 andFigure 5 .

 595 Figure 5.10 present the resistance as a function of the temperature for the two annealed samples : the high-temperature value is three orders of magnitude below the resistivity value for the samples which was not annealed. With decreasing temperature, a drop on the resistivity from, 1.68 ×10 -5 Ω• m and 2.35 ×10 -5 Ω• m at 200 K, to 1.66 ×10 -5

Figure 5 . 9 :

 59 Figure 5.9: (a,b) AFM profile of as contacted flake,(c) Optical micrograph of the device and (d) Resistivity versus temperature curve of V 2 CT x MXene device II.

Figure 5 . 10 :

 510 Figure 5.10: (a,b) AFM profile of as contacted flake , (c) Optical micrograph of the device and (d) Resistivity versus temperature curve of V 2 CT x MXene device III.

Figure 5 . 11 :

 511 Figure 5.11: Resistance versus temperature curves of (a) Ti 2 CT x [66] and (b) Ti 3 C 2 T x [148].

Figure 5 . 12 :

 512 Figure 5.12: Temperature dependency of resistivity of Device II and III (a)Resistivity (b)Residual-resistance.

Figure 5 . 13 :

 513 Figure 5.13: (a)Schematic diagram of the MXenes transistor (b,c,d) functional dependence of source-drain current I DS (for a constant V DS ) on backgate voltage on different MXenes device (b) V 2 CT x (c) T 2 CT x [66](d) Ti 3 C 2 T x [148].

Figure 5 . 14 :

 514 Figure 5.14: Effect of magnetic fields on V 2 CT x MXenes device.(a) Magnetoresistance of Device II at 1.6K (b) Magnetoresistance of Device III at 1.6 K(c) Magnetoresistance after symmetry and fitting with MR = αB 2

  is undoubtedly challenging for several reasons: (a) When the A layers are etched from MAX phase, they are replaced by =O, -F and -OH terminations. With different surface chemical termination, the transport properties certainly vary. The terminations group characterization is still under exploration, which limits the understanding of relationship between chemical function and electronic properties. (b) The interlayer space is intercalated by cations and water molecules, and the exact arrangement of stacking in multilayered particles can vary from flake to flake, from device to device.

Fabrication

  of MXene-based nano device and electronic properties cryo measurement are also proposed in the beginning of the thesis. Then, it is the time to examine the degree of completion of this project: First of all, several MAX phase single crystal have been successfully grown by using high temperature solution growth and slow cooling technique, including Ti 2 SnC, Ti 3 SiC 2 , V 2 AlC and Cr 2 AlC. Structural characterization confirms the single crystalline character of the samples by X-ray measurements and Raman spectroscopy. The most favorable case is that of Cr-Al-C, attributed to its extreme high carbon solubility. Fortunately, the size of as-obtained crystals are only limited by the size of the crucible, leading to relatively large Cr 2 AlC crystals ready for the subsequent device measurement. V 2 AlC, as a starting basis for forming MXenes with macroscopic area, permits the selective etching after HF-treatment and cleavage of the platelets parallel to the basal plane.

3. 12

 12 Power fitting of MR of V 2 AlC and Ti 3 SiC 2 in comparison with to parabolic MR of Cr 2 AlC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.13 Temperature dependence of exponent of power fitting for MR of V 2 AlC and Ti 3 SiC 2 . 75 3.14 Kohler's scaling for sample Ti 3 SiC 2 , V 2 AlC and Cr 2 AlC at different temperatures. 77 3.15 (a) Hall resistivity vs magnetic field at different temperature and (b) the variation of Hall coefficient with temperature ( noting: considering the sweep direction, values computed from within one sweep of magnetic field (-11T-11T) are also demonstrated. 77 3.16 Temperature dependency curves of Hall coefficient of R H of Cr 2 AlC, V 2 AlC and Ti 3 SiC 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.17 Two band model density (a), mobilities(b) and fitting parameter α(c) as a function of temperature for Cr 2 AlC Hall bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.18 (a) Thermal conductivity of Cr 2 AlC single crystal and (b) In comparison with polycrystalline sample[3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.19 (a)Electronic contribution and (b,c) Plotting curves indicating phonon behaviour to thermal conductivity of Cr 2 AlC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.20 Seebeck coefficient of Cr 2 AlC single crystal (In comparison with polycrystalline sample [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.21 Measurement configuration of c-axis magneto-electronic transport. . . . . . . . . . 84 3.22 Out-of-plane resistivity of Cr 2 AlC (B//c. I//c) (a) magnetoresistivity (b) Zero field ρ c (T). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.23 Extraction the in-plane contribution from out-of-plane magnetoresistance. . . . . . 85 3.24 Fitting parameters of in-plane contribution for out-of-plane magnetoresistivity vs T (a) α (b) A and its relation with corresponding charge moblity. . . . . . . . . . . . 86 3.25 (a) Residual magnetoresistance vs T and (b) various fitting curves. . . . . . . . . . 86 3.26 Out-of-plane resistivity of V 2 AlC (B//c. I//c) (a) ρ c (B) (b) magnetoresistance at 1.5K and (c) Zero field ρ c (T). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.27 Extraction the in-plane contribution from out-of-plane magnetoresistance and the fitting of residual magnetoresistance. . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.28 Fitting parameters of in-plane contribution for out-of-plane magnetoresistivity vs T (a) α (b) A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.29 Reproduction of adjacent Brillouin zones of a two-dimensional hexagonal lattice with the corresponding free electron disks (left) and Fermi line of the same lattice in the first Brillouin zone for nearly free electrons. . . . . . . . . . . . . . . . . . . . 90 3.30 Dispersion curves of nearly free electrons in a 2D hexagonal lattice (parameters are inserted in the graph and defined in the text). . . . . . . . . . . . . . . . . . . . . 91 3.31 1D-tight-binding with 2 atomic planes per unit cell showing large splitting. . . . 92

Table 1

 1 .2 is a summary of the available Hall constants for MAX phases at room temperature. We can see from Table 1.2 that R H of MAX phases, like most other metallic conductors, has quite small value. The measured Hall coefficients tend to fluctuate around zero and give either slightly positive or negative values.

  2

Table 1 . 2 :

 12 Summary of electrical transport parameters of some MAX phases that have been measured.The Fermi level is set to 0 eV. One can notice that there are many bands crossing the Fermi level, no gap between the valence band and conduction band, suggesting that Cr 2 AlC would demonstrate metallic conductivity.Moreover, these bands around Fermi energy are mainly from Cr 3d states, indicating Cr 3d states dominate the conductivity of Cr 2 AlC. One can also notice that, no band is

  Generally, synthesis techniques for 2D materials can be classified into two approaches:

	1.2. MXene
	1.2.1.2 Synthesis of 2D materials

  CT x , Ti 2 CT x , Cr 2 TiC 2 T x , Mo 2 TiC 2 T x , Mo 2 Ti 2 C 3 T x , Mo 2 CT x ,

	Instead of HF, different etchants were introduced for the etching of MAX phase. Even with various synthesis conditions and chemical reagents, fluoride compounds work as a decisive factor to produce 2D MXenes. Fluoride salts, such as lithium fluoride (LiF), sodium fluoride (NaF), potassium fluoride (KF), caesium fluoride (CsF), could be added into hydrochloric acid (HCl) or sulphuric acid (H 2 SO 4 ) to produce the etchant solution [64]. It is convincing that a precise balance of etching conditions for different combinations with acid and salt, can potentially bring out multi-layered early transition metal carbides modified by surface chemistries and diverse pre-intercalated ions. This one-step method has been successfully applied to produce multi-layered Nb 2 1.2. MXene etc [62, 63, 64]. Moreover, bifluoride solution (e.g., NaHF 2 , KHF 2 or NH 4 HF 2 ) were

Application of MXenes Energy storage application

	1.2. MXene
	Cr-MXene have been successfully synthesized except for Cr-Ti-containing MXenes. on improving their volumetric capacity, i.e. energy density per volume. Depending on
	their charge-discharge mechanisms, supercapacitors are classified as either electrical High Seebeck coefficients were predicted for MXenes by DFT calculations [72]. double-layer capacitors (EDLCs) or pseudo-capacitors. In general, pseudo-capacitors Thermoelectric calculations based on the Boltzmann theory imply that semiconducting possess higher volumetric capacitances and lowered cycling stability. MXenes, with MXenes attain very large Seebeck coefficients at low temperatures, which opens a novel their 2D characteristics, large surface areas, present themselves as promising electrode potential applications for these surface terminated MXenes. materials for super-capacitors. Ti 3 C 2 T x is the most studied MXenes for super-capacitors,
	The mechanical properties of MXenes are also of great interest as the M-C and/or the volumetric capacitances of free standing Ti 3 C 2 T x MXene electrodes in neutral and
	M-N bonds are some of the strongest known. M 2 X MXenes are predicted to be stiffer
	and stronger than their M 3 X 2 and M 4 X 3 counterparts. Though experimental mechanical
	testing has been conducted only for MXene films and not for single-layer, a cylinder with
	walls made of 5 µm thick Ti 3 C 2 T x film can support over 4000 times of its own weight [81].
	MXenes/polymer composites have also been developed with improved mechanical
	and electrical properties. Thin films of MXenes are transparent and its optoelectronic
	properties can be tuned by the chemical and electro-chemical intercalation of cations,
	which implies that MXenes films can be applied in transparent conductive coatings and
	optoelectronics [82].
	1.2.2.4 Battery: Similar to graphene, MXene are promising candidate electrode materials for
	Lithium-ion battery (LIBs) and super-capacitors by the intercalation of Li ions into the
	MXene layers. Owing to their wide chemical variety, it has more tunable performance
	compared to the elementary graphene. MXenes are promising LIB anode materials,
	since they have excellent electronic conductivity, low operating voltage range, low
	diffusion barriers which are favourable for high rate performance and exceptional
	mechanical properties that are invariant to Li adsorption. Unlike typical diffusion
	limited battery electrode materials, intercalation of ions in MXenes can paradoxically
	occur at a high rate, without significantly depreciating their energy storage capacities.
	Based on the theoretical calculations, it is proved that MXenes with low formula weights
	(M 2 X MXenes) are the most promising in terms of theoretical gravimetric capacity.
	Encouraged by the first application of HF-etched multilayered Ti 2 CT x as anode material
	in LIBs, other MXene materials, such as Ti 3 C 2 T x , Mo 2 TiC 2 T x , Nb 2 CT x , V 2 CT x , Nb 4 C 3 T x ,
	and Mo 2 CT x , have also been examined as potential anode for LIBs.[63, 69, 76, 83]
	Supercapacitor: Supercapacitors provide alternative energy storage with rapid power
	density but low energy density compared to batteries. Research efforts have been made

chapter 2 MAX Phase Single Crystal Growth and Characterization

	1.2. MXene
	ultrasonic technique. "Large"( >10 µm) and homogeneous V 2 C MXenes were obtained
	by following mechanical exfoliation method. Synthesis and characterization of V 2 C
	MXenes are detailed in Chapter IV. MXene-based devices were fabricated and their
	electronic properties were examined down to low temperature and in high magnetic
	field as discussed in Chapter V.
	In the present work, several MAX single crystals were grown from liquid
	phase by high temperature solution growth and slow cooling technique.

Table 4 . 1 :

 41 Calculated elastic coefficients and mechanical properties of the 20 MAX phase compounds (Unit:GPa)[145].

  . While Sc 2 CT 2 (T= F, OH, and O), Ti 2 CO 2 , Zr 2 CO 2 and Hf 2 CO 2 become semiconducting with the surface functionalization. The energy gaps are estimated to be 1.03, 0.45 and 1.8 eV for Sc 2 CT 2 with T= F, OH, and O, respectively, 0.24 eV for Ti 2 CO 2 , 0.88 eV for Zr 2 CO 2[START_REF] Khazaei | Novel Electronic and Magnetic Properties of Two-Dimensional Transition Metal Carbides and Nitrides[END_REF].

Table 5 .

 5 2 lists the electronic transport of MXene device and comparison with the MAX phases. Undoubtedly, electronic transport data on this new family of 2D material is still deficient. Even, the reported results of mostly studied Ti 2 CT x and Mo 2 CT x varies dramatically. If we compare the resistivity of our V 2 CT x samples, the average Resistivity, Hall mobility, Field effect mobility, Concentration, Ref ρ,Ω • m µ H , cm 2 /V•s µ EF , cm 2 /V•s n, cm -3

	V 2 CT x	(1.68-2.22)×10 -5	97.3 ; 145.2	22.7	1.66×10 20
	Ti 3 C 2 T x (f)	(2.22-3.92)×10 -5				[158]
	Mo 2 C T x (p)	0.02-20				[76]
	Mo 2 C T x (p)	3.37×10 -5				[159]
	Ti 3 C 2 T x (s)			0.7 ± 0.2	8 ± 3 × 10 21	[148]
	Ti 3 C 2 T x (m) sheet resistivity, 1590		4.23		[77]
	Ti 2 CT x (m)		9375	>10000		[66]
	V 2 AlC	2 × 10 -7	(80-120)		(2 -4) × 10 21

*NOTE f:film; p:paper; s:single layer; m:multi-layer

Table 5 . 2 :

 52 Electronic transport data of MXenes device.

1.1. MAX phases

Acknowledgements

DFT calculations . This means that the simplified model will probably slightly overestimate the contribution of electrons to in-plane transport. Such case can be empirically improved by finding a set of energy parameters which slightly underestimates the extent of those electron pockets. [START_REF] Mauchamp | Anisotropy of the resistivity and charge-carrier sign in nanolaminated Ti 2 AlC: Experiment and ab initio calculations[END_REF] along with the fitting Fermi line given by the 2D model using U=0.35eV and an appropriate splitting between the hole bands and electron pockets (red line). chapter 4

MXenes synthesis and characterization

In this chapter, we report a general approach to etch V 2 AlC single crystal and mechanically exfoliate multilayer V 2 CT x MXenes. We then detail the structural characterization of the obtained MXenes. Up to our knowledge, all MXenes reported up to now have been derived from the Al-containing MAX phases, the second part of this chapter discusses the process with the aim of obtaining Ti 2 CT x MXene from Ti 2 SnC single crystals. a simple mechanical disruption was introduced to break apart the large single crystal by using sharp tweezers to scratch the surface. Figure 4.7 shows the optical images of the same sample before and after mechanical disruption. Additional macro and micro cracks are generated by the mechanical force during sonication process and lead to acceptable size for chemical etching. The effect of these intentional defects on the improvement of preferential etching will be discussed in the following part. The structure and phase composition before and after HF exfoliation were characterized by XRD. The typical XRD patterns of the raw material V 2 AlC and V 2 CT x samples are presented in Figure 4.8. Here, it is worth mentioning that the broaden peaks at 11°is the signal from the grease on sample holder from the XRD patterns of VC-p. Similar as other MAX phase to MXenes transformation, the degree of order as measured by XRD clearly decreased and VC-p exhibit a more disordered structure than that of VC-f. The (002) peaks on both VC-p and VC-f samples broaden and shift to lower angles after acid treatment, indicating the larger d spacings. Yet, from the XRD pattern of VC-f, we can still observe the (002) peak with decreased intensity comparing to the original crystal, indicating unreacted crystals. From the XRD pattern of VC-p, one observed an evident shift of 2θ from 13.5°to 7.4°, corresponding to c-LPs changing from 13.107 Åto 23.872 Å, The Raman spectrum of V 2 CT x flake transferred on the Si/SiO 2 substrate exhibits the same peaks at the same positions as those observed on the "bulk MXene" materials, in addition to peaks characteristic of phonon modes of the substrate.Yet, it is intriguing to find that, when the layer thickness is down to below 10 nm, the signal of Raman spectrum could not be detected on the thin layers.

AFM

The thickness and shapes of the flakes produced by mechanical exfoliation and transferred on Si/SiO 2 were investigated by atomic force microscopy (AFM), as can be seen Figure 4.20. The AFM height profiles measured along the color lines showed that V 2 CT x flakes have the similar heights of ≈ 10-20 nm and are identified as multilayers.

The lateral sizes of flakes is several µm. It is worth mentioning that the measured AFM height of the flake relative to the Si/SiO 2 substrate is overestimating the actual height due to the presence of surface adsorbates, such as water molecules, that are trapped under the V 2 CT x flake; similar observations have been previously reported for other 2D materials as well [START_REF] Diaz | Interface properties of CVD grown graphene transferred onto MoS 2[END_REF][START_REF] Ochedowski | Graphene on Mica -Intercalated Water Trapped for Life[END_REF]. Here, electron beam lithography (EBL) was performed using a SEM (FEI/Philips XL30 FEG) equipped with a Raith laser interferometer controlled stage and the Elphy Plus software (remote control for Ebeam writing). This equipment is capable of writing patterns with a resolution down to 10 nm.

A metallic mark close to the flake was firstly located by SEM imaging in TLD mode (~10 KeV, magnification of ×2000, spot 3). SEM imaging corrections including wobble, astigmatism and focus, were performed as the alignment and focus are closely related to the precision of beam writing. It is worth mentioning that a calibration is necessary to know the relative position of the electron beam with respect to the mark coordinate system in Elphy Plus. Based on the SEM image of the target flake, one can easily draw the flake shape in the Elphy Plus layout editor according to the values of the cartesian coordinates. Once the drawing of flake was done in the Elphy Plus file, the electrical contacts were designed by using Layout Editor.

Once the pattern file is ready, the process of electrical contact fabrication is conducted in sequence.