Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In ferromagnets, magnetic entropy change is written by function that starts (in Ti = 0) and finish (in Tf ? 8) in zero after going through a maximum (the transition temperature TC). The enclosed area is thus A = Z Tf?8Ti=0SdT wherein S =Z HfHi ?M?T!HdH. AsM ? 0 writing for high temperatures independent of values of accessible field, the area is A =Z HfHi M(Ti ,H)dH defining the so-called rule of areas. This rule states that the enclosed areais defined by the values M(Ti,H) in the interval [Hi,Hf ]. Of course that it can be used at any interval [Ti, TF ]. This suggests that in a narrow region of temperatures around TC, A shouldvary with H (assuming Hi = 0) according to a power law: A ? Hm. The fact M(Ti,H) define the area is evident because the ferromagnet in question must follow an equation of state. Thus,M(Ti,H) and M(TF ,H) contains the information of the area A between Ti and TF . In this issue we consider since the equation of state more simple for a ferromagnet (Brillouin function) up to corresponding to systems that present crystal field effects and subject to hydrostatic pressure too. We analyze compounds RAl2 (R: Dy, Nd and Pr) and we have determined the values of the exponent m. We check the universality curvas of magnetocaloric potential (isothermal S ? Hn and adiabatic T ? Mp), of its areas and the exponents m and n. Finally, we obtain the usual critical exponents, analyzed the graphs of Arrott of the magnetic curves, based on the criteria Banerjee, and using the method Kouvel-Fisher. Main result is that, despite the application of pressure tends to induce discontinuous transitions, there are regions of applied field, in that is observed the collapse S curves. The scaled curves also suggests a continuous-discontinuous way with the definition of a tricritical point (he case ofPrAl2 under pressure 3,8 kbar). / Em ferromagnetos, a variação de entropia magnética é uma função que inicia (em Ti = 0 ) e termina (em Tf ? 8) no zero após passar por um máximo (na temperatura de transição TC). A área encerrada é assim dada por A =Z Tf?8Ti=0SdT em que S =Z HfHi?M?T!HdH. Como M ? 0 para temperaturas altas, independente dos valores de campo acessíveis, a área resulta A =Z HfHiM(Ti ,H)dH definindo a chamada regra das áreas. Esta regra estabelece que a área encerrada fica definida pelos valores M(Ti ,H) no intervalo [Hi,Hf ]. É claro que a mesma pode ser usada em qualquer intervalo [Ti, Tf ] . Isto sugere que em uma região estreita de temperaturas, ao redor de TC, A deve variar com H (supondo Hi = 0) segundo uma lei de potência: A ? Hm. O fato de M(Ti,H) definir a área é evidente pois o ferromagneto em questão deve seguir uma equação de estado. Desta forma, M(Ti,H) e M(Tf ,H) contém a informação da área A entre Ti e Tf. Neste trabalho consideramos desde a equação de estado mais simples para um ferromagneto (a função de Brillouin) até a correspondente a sistemas que apresentam efeitos de campo cristalino e ainda sujeitos a pressão hidrostática. Analisamos os compostos RAl2 (R: Dy, Nd e Pr) e determinamos os valores do expoente m. Verificamos a universalidade nas curvas dos potenciais magnetocalóricos (isotérmico S ? Hn e adiabático T ? Mp), de suas áreas e dos expoentes m e n. Finalmente, para a obtenção dos expoentes críticos usuais, analisamos os gráficos de Arrott das curvas magnéticas, com base no critério de Banerjee, e usando o método Kouvel-Fisher. Um dos principais resultados é que, apesar da aplicação de pressão tender a induzir transições descontínuas, existem regiões de campo aplicado em que é observado o colapso das curvas de S. As curvas reescaladas também sugerem a passagem contínua-descontínua com a definição de um ponto tricrítico (caso do PrAl2 sob pressão de 3,8 kbar).

Dans cette thèse, l’étude de plusieurs modèles de systèmes magnétiques frustrés a été couverte. Leur racine commune est le modèle de la glace de spin, qui se transforme en modèle de la glace sur réseau kagome (kagome ice) et réseau en damier (square ice) à deux dimensions, et la chaîne d’Ising à une dimension. Ces modèles ont été particulièrement étudiés dans le contexte de transitions de phases avec un ordre magnétique induit par les contraintes du système : en effet, selon la perturbation envisagée, les contraintes topologiques sous-jacentes peuvent provoquer une transition de Kasteleyn dans le kagome ice, ou une transition de type vitreuse dans la square ice, due à l’émergence d’un ordre ferromagnétique dans une chaîne d’Ising induit seulement par des effets de taille fini. Dans tous les cas, une étude détaillée par simulations numériques de type Monte Carlo ont été comparées à des résultats théoriques pour déterminer les propriétés de ces transitions. Les contraintes topologiques du kagome ice ont requis le développement d’un algorithme de vers permettant aux simulations de ne pas quitter l’ensemble des états fondamentaux. Une revue poussée de la thermodynamique et de la réponse de la diffraction de neutrons sur kagome ice sous un champ magnétique planaire arbitraire, nous ont amené à une compréhension plus profonde de la transition de Kasteleyn, et à un modèle numérique capable de prédire les figures de diffraction de neutrons de matériau de kagome ice dans n’importe quelles conditions expérimentales. Sous certaines conditions, ce modèle a révélé des propriétés thermodynamiques quantifiées et devrait fournir un terreau fertile pour de futurs travaux sur les conséquences des contraintes et transitions de phases topologiques. Une étude combinée du square ice et de la chaîne d’Ising a mise en lumière l’apparition d’un ordre sur réseau potentiellement découplé de l’ordre ferromagnétique sous-jacent, et particulièrement pertinent pour les réseaux magnétiques artificiels obtenus par lithographie. / In this thesis a series of model frustrated magnets have been investigated. Their common parent is the spin ice model, which is transformed into the kagome ice and square ice models in two-dimensions, and an Ising spin chain model in one-dimension. These models have been examined with particular interest in the spin ordering transitions induced by constraints on the system: a topological constraint leads, under appropriate conditions, to the Kasteleyn transition in kagome ice and a lattice freezing transition is observed in square ice which is due to a ferromagnetic ordering transition in an Ising chain induced solely by finite size effects. In all cases detailed Monte Carlo computational simulations have been carried out and compared with theoretical expressions to determine the characteristics of these transitions. In order to correctly simulate the kagome ice model a loop update algorithm has been developed which is compatible with the topological constraints in the system and permits the simulation to remain strictly on the groundstate manifold within the appropriate topological sector of the phase space. A thorough survey of the thermodynamic and neutron scattering response of the kagome ice model influenced by an arbitrary in-plane field has led to a deeper understanding of the Kasteleyn transition, and a computational model that can predict neutron scattering patterns for kagome ice materials under any experimental conditions. This model has also been shown to exhibit quantised thermodynamic properties under appropriate conditions and should provide a fertile testing ground for future work on the consequences of topological constraints and topological phase transitions. A combined investigation into the square ice and Ising chain models has revealed ordering behaviour within the lattice that may be decoupled from underlying ferro- magnetic ordering and is particularly relevant to magnetic nanoarrays.

À l'approche d'un point critique, la divergence de la longueur de corrélation des fluctuations peut être tronquée par le confinement du système. Cette troncature engendre des effets de taille finie présentant des caractères universels au sein d'un classe de transitions de phases.Nous nous sommes intéressés particulièrement à la classe d'universalité du modèle d'Ising, regroupant notamment les transitions de phase ferro/paramagnétique pour les systèmes magnétiques uniaxiaux, la transition liquide/gaz et encore la démixtion de mélanges binaires. Nous présentons tout d'abord une introduction aux phénomènes critiques, à l'universalité, au « finite-size scaling » et aux simulations Monte Carlo du modèle d'Ising, sur lesquelles se fondent la majeur partie de ce travail.Un effet de taille finie ayant attiré une grande attention durant les dernières dizaines d'années est la force de Casimir critique. Les travaux théoriques et numériques concernant cette force ont, dans leur quasi totalité, été menés dans des systèmes magnétiques modèles, tel que les modèles d'Ising ou XY. Par contre, les approches expérimentales ont toutes été réalisées dans des systèmes fluides, tels que des mélanges binaires ou de l'hélium IV proche de la transition superfluide.Une motivation de ce travail a été de chercher a résoudre cette situation paradoxale en proposant, d'une part, un protocole expérimental pour la mesure de la force de Casimir dans une couche mince magnétique et, d'autre part, une approche numérique dans un mélange binaire de type Lennard-Jones. Cette dernière approche présente l'avantage d'ouvrir la porte à des études des fluctuations de la force de Casimir ou encore hors-équilibre. / Approaching a critical point, the divergence of the correlation length of fluctuations can be cut-off by a confinement of the system. This truncation fosters finite size effects with universal features in a class of continuous phase transitions. We are particularly interested in the Ising universality class, regrouping transitions such as the ferromagnetic/paramagnetic transition for uniaxial magnetic systems, the liquid/gas tran- sition and the demixing of binary mixtures. We will first present an introduction to critical phenomena, universality, finite-size scaling and Monte Carlo simulations of the Ising model, on which a major part of this work relies.A finite size effect that has particularly drawn attention in the past decades is the critical Casimir force. On the one hand, theoretical and numerical works on the subject have almost systematically been performed in magnetic model systems, such as the Ising or XY models. On the other hand, experimental approaches were all realized in fluid systems, such as binary mixtures or helium IV close to the superfluid transition.A motivation of this work was to bridge this gap by proposing, firstly, an experimental protocol for measuring the critical Casimir force in a magnetic layer and, secondly, a numerical approach in a Lennard-Jones binary mixture. The latter is of particular interest as it could lead the way to studying fluctuations of the Casimir force or out-of-equilibrium phenomena.

Ferroelectric materials are very promising for a variety of applications such as high-permittivity capacitors, ferroelectric memories, pyroelctric sensors, piezoelectric and electrostrictive transducers and electro-optic devices, etc. In the area of ferroelectric ceramics, lead-based compounds, which include lead zirconatetitanate (PZT) solid solutions, occupy an important place because of their superior physical properties. However, due to the toxicity of lead, there is an increasing concern over recycling and disposing of the devices made out of these compounds, which has compelled the researchers around the globe to search for lead-free compounds with promising piezo and ferroelectric properties. Ferroelectric materials that belong to Aurivillius family of oxides have become increasingly important from the perspective of industrial applications because of their high Curie-temperatures, high resistivity, superior polarization fatigue resistanceand stable piezoelectric properties at high temperatures. These bismuth layer-structured ferroelectrics (BLSF) comprise an intergrowth of [Bi2O2]2+ layers and [An+1Bn O3n+1]2- pseudo-perovskite units, where ‘n’ represents the number of perovskite-like layers stacked along the c-axis. ‘A’ stands for a mono-, di- or trivalent ions or a combination of them, ‘B’ represents a small ion with high valencysuch as Ti4+, Nb5+, Ta5+or a combination of them.Ferroelectricity in the orthorhombic phase of these compounds was generally attributed to the cationic displacement along the polar a-axis and the tilting of octahedra around the a- and c-axes. Sr2Bi4Ti5O18(SBT) is ann = 5 member of the Aurivillius family and possess promising ferroelectric and piezoelectric properties that could be exploited for a wide range of applications, including ferroelectric random access memories (FeRAM), piezoelectric actuators, transducers and transformers. Reports in the literaturereveal that the ferroelectricand piezoelectric properties of these oxides can be tuned depending on synthesis routes vis-a-vis micro-structural aspects (texture, grain size) and site specific dopant substitutions.In the present study, textured SBT ceramics were fabricated using pre-reacted precursors and their anisotropic dielectric, piezoelectric and ferroelectric properties were demonstrated. Grain size tunability with regard to their physical properties was accomplished in the ceramics, fabricated using fine powders obtained from citrate assisted sol-gel synthesis. The grain size dependent second harmonic generation activity of SBT ceramics was investigated. Enhancement in the piezoelectric and ferroelectric properties of SBT ceramics was achieved by substituting A site ions (Sr2+) with a combination of Na+ and Bi3+. From the perspective of non-linear optical device applications, physical properties associated with the SBT crystallized in a transparent lithium borate glass matrix were studied. The results obtained in the present investigations are organized as follows, Chapter 1 gives a brief exposure to the field of ferroelectrics. The emphasis has been on the ferroelectric oxides belonging to the Aurivillius family. Structural aspects and the underlying phenomena associated with ferroelectricity in these compounds are discussed. A brief introduction to the glasses, thermodynamic aspects of glass formation and fabrication of glass- ceramics are included. Basic principles involved in the non-linear optical activities are highlighted. Chapter 2 describes the various experimental techniques that were employed to synthesize and characterize the materials under investigation. The experimental details pertaining to the measurement of various physical properties are included. Chapter 3 deals with the fabrication of Sr2Bi4Ti5O18 ceramics using the pre-reacted Bi4Ti3O12 and SrTiO3 powders viasolid-state reaction route. These in stoichiometric ratio were uniaxially pressed and sintered at 1130oC for 3 h resulting in textured Sr2Bi4Ti5O18 ceramics. The obtained dense ceramics exhibited crystallographic anisotropy with prominent c-axis oriented grains (Lotgering factor of 0.62) parallel to the uniaxially pressed direction. The resultant anisotropy in the ceramics was attributed to the reactive template-like behavior of Bi4Ti3O12 that was used as a precursor to fabricate Sr2Bi4Ti5O18 ceramics. Dielectric, ferro and piezoelectric properties measured on the ceramics in the direction perpendicular to the uniaxially pressed axis were found to be superior to that measured in the parallel direction. Chapter 4 reports the details pertaining to the synthesis of strontium bismuth titanate (Sr2Bi4Ti5O18) powders comprising crystallites of average sizes in the range of 94–1400 nm via citrate-assisted sol-gel route. X-ray powder diffraction, Transmission Electron Microscopy (TEM) and Raman spectroscopy were employed for the structural studies. A crystallite size-dependent variation in the lattice parameters and the shift in the Raman vibration modes were observed. Second harmonic signal (532 nm) intensity of the Sr2Bi4Ti5O18 powders increased with the increase in the average crystallite size and the maximum intensity obtained in the reflection mode was 1.4 times as high as that of the powdered KH2PO4. Piezo force microscopic analyses carried out on an isolated crystallite of size 74 nm, established its single domain nature with the coercive field as high as 347 kV/cm. There was a systematic increase in the d33 value with an increase in the size of the crystallite and a high piezoelectric coefficient of ~27 pm/V was obtained from an isolated crystallite of size 480 nm. Chapter 5 illustrates the details concerning the fabrication of Sr2Bi4Ti5O18(SBT) ceramics with different grain sizes (93 nm–1.42 μm) using nano-crystalline powders synthesized via citrate assisted sol-gel method. The grain growth in these powder compacts was found to be controlled via the grain boundary curvature mechanism, associated with anactivation energy of 181.9 kJ/mol. Interestingly with a decrease in grain size there was an increase in the structural distortion which resulted in a shift of Curie-temperature (phase transition) towards higher temperatures than that of conventional bulk ceramics. Extended Landau phenomenological theory for the ferroelectric particles was invoked to explain experimentally observed size dependent phase transition temperature and the critical size for SBT is predicted to be 11.3 nm. Grain size dependent dielectric, ferroelectric and piezoelectric properties of the SBT ceramics were studied and the samples comprising average grain size of 645 nm exhibited superior physical properties that include remnant polarization (2Pr) = 16.4 μC cm-2, coercive field (Ec) = 38 kV cm-1, piezoelectric coefficient (d33) = 22 pC N-1 and planar electromechanical coupling coefficient (kp) = 14.8 %. In Chapter 6, the studies pertaining to the fabrication of Sr(2-x)(Na0.5Bi0.5)xBi4Ti5O18 (SNBT) ceramics for various x values (0, 0.1, 0.25, 0.3, 0.4 and 0.5), using fine powders synthesized via sol-gel route are dealt with. X-ray powder diffraction, transmission electron microscopy and Raman spectroscopic studies were carried out to confirm composition dependent structural changes taking place in the SNBT ceramics. Scanning electron microscopic studies carried out on ceramics revealed that dopants played an important role in inhibiting the grain growth. Dielectric constants of the ceramics were found to decrease with an increase in ‘x’. The increase in Curie temperature with increase in ‘x’ is attributed to the decrease in the tolerance factor. Particularly,x = 0.3 composition of the SNBT ceramics exhibited better piezo and ferroelectric properties with a higher Curie-temperature (569 K). The piezoelectric coefficient (d33) and the planar electromechanical coupling coefficient (kp) of SNBT(x = 0.3) were enhanced by 25% and 42% respectively as compared to that of the undoped ceramics. Chapter 7 deals with the glasses in the system (100 –x) {Li2O + 2B2O3} ─x {2SrO + 2Bi2O3 +5TiO2} (where, x = 10, 25 and 35) fabricated via conventional melt-quenching technique. The amorphous and glassy characteristics of the samples were confirmed respectively using X-ray diffraction (XRD) and differential scanning calorimetric (DSC) methods. All the compositions under investigation exhibited two distinct crystallization peaks (exothermic peaks in the DSC traces): the first peak at ~ 545 °C and the second at ~610 °C that were found to be associated with the crystallization of the phases (as confirmed from the XRD studies) Sr2Bi4Ti5O18 (SBT)and Li2B4O7 (LBO) respectively. Non-isothermal crystallization kinetics (using modified Ozawa-type plots) for SBT crystallization in the LBO glass matrix for the compositions x = 10 and 35, indicated three dimensional growth of the crystallites from pre-existing nuclei present in the as-quenched samples and their effective activation energies for crystallization were found to be around 686 ± 85 kJ/mol and 365 ± 53 kJ/mol, respectively. The optical band gap of the as-quenched glasses for the composition x = 35 was 2.52 eV, is less than that of the composition x = 10 (2.91 eV). The Urbach energies for the as-quenched glasses of compositions x = 10, 25 and 35 were found to be 118 ± 2 meV, 119 ± 2 meV and 192 ± 1 meV respectively.The glasses associated with the composition x = 35, on controlled heat-treatment at 515 °C for various durations (1―20 h), yielded glass-ceramics comprising SBT nano-crystals (18―28 nm) embedded in the LBO glass matrix. Compressive strain in the nano-crystallites of SBT, analyzed using Williamson-Hall method was found to decrease with an increase in the crystallite size. The second harmonic generation signal (532 nm) intensity emanating from glass-nanocrystal composites comprising 22.1 nm SBT crystallites was nearly 0.3 times that of a KDP single crystal. Although each chapter is provided with conclusions and a list of references, thesis ends with a separate summary and conclusions.

The dissertation covers phase transitions in the realm of the Anderson model of localization on topologically disordered Voronoi-Delaunay lattices. The disorder is given by random connections which implies correlations due to the restrictive lattice construction. Strictly speaking, the system features "strong anticorrelation", which is responsible for quenched long-range fluctuations of the coordination number. This attribute leads to violations of universal behavior in various system, e.g. Ising and Potts model, and to modifications of the Harris and the Imry-Ma criteria. In general, these exceptions serve to further understanding of critical phenomena. Hence, the question arises whether such deviations also occur in the realm of the Anderson model of localization in combination with random Voronoi-Delaunay lattice. For this purpose, four cases, which are distinguished by the spatial dimension of the systems and by the presence or absence of a magnetic field, are investigated by means of two different methods, i.e the multifractal analysis and the recursive Green function approach. The behavior is classified by the existence and type of occurring phase transitions and by the critical exponent v of the localization length. The results for the four cases can be summarized as follows. In two-dimensional systems, no phase transitions occur without a magnetic field, and all states are localized as a result of topological disorder. The behavior changes under the influence of the magnetic field. There are so-called quantum Hall transitions, which are phase changes between two localized regions. For low magnetic field strengths, the resulting exponent v ≈ 2.6 coincides with established values in literature. For higher strengths, an increased value, v ≈ 2.9, was determined. The deviations are probably caused by so-called Landau level coupling, where electrons scatter between different Landau levels. In contrast, the principle behavior in three-dimensional systems is equal in both cases. Two localization-delocalization transitions occur in each system. For these transitions the exponents v ≈ 1.58 and v ≈ 1.45 were determined for systems in absence and in presence of a magnetic field, respectively. This behavior and the obtained values agree with known results, and thus no deviation from the universal behavior can be observed. / Diese Dissertation behandelt Phasenübergange im Rahmen des Anderson-Modells der Lokalisierung in topologisch ungeordneten Voronoi-Delaunay-Gittern. Die spezielle Art der Unordnung spiegelt sich u.a. in zufälligen Verknüpfungen wider, welche aufgrund der restriktiven Gitterkonstruktion miteinander korrelieren. Genauer gesagt zeigt das System eine "starke Antikorrelation", die dafür sorgt, dass langreichweitige Fluktuationen der Verknüpfungszahl unterdrückt werden. Diese Eigenschaft hat in anderen Systemen, z.B. im Ising- und Potts-Modell, zur Abweichung vom universellen Verhalten von Phasenübergängen geführt und bewirkt eine Modifikation von allgemeinen Aussagen, wie dem Harris- and Imry-Ma-Kriterium. Die Untersuchung solcher Ausnahmen dient zur Weiterentwicklung des Verständnisses von kritischen Phänomenen. Somit stellt sich die Frage, ob solche Abweichungen auch im Anderson-Modell der Lokalisierung unter Verwendung eines solchen Gitters auftreten. Dafür werden insgesamt vier Fälle, welche durch die Dimension des Gitters und durch die An- bzw. Abwesenheit eines magnetischen Feldes unterschieden werden, mit Hilfe zweier unterschiedlicher Methoden, d.h. der Multifraktalanalyse und der rekursiven Greensfunktionsmethode, untersucht. Das Verhalten wird anhand der Existenz und Art der Phasenübergänge und anhand des kritischen Exponenten v der Lokalisierungslänge unterschieden. Für die vier Fälle lassen sich die Ergebnisse wie folgt zusammenfassen. In zweidimensionalen Systemen treten ohne Magnetfeld keine Phasenübergänge auf und alle Zustände sind infolge der topologischen Unordnung lokalisiert. Unter Einfluss des Magnetfeldes ändert sich das Verhalten. Es kommt zur Ausformung von Landau-Bändern mit sogenannten Quanten-Hall-Übergängen, bei denen ein Phasenwechsel zwischen zwei lokalisierten Bereichen auftritt. Für geringe Magnetfeldstärken stimmen die erzielten Ergebnisse mit den bekannten Exponenten v ≈ 2.6 überein. Allerdings wurde für stärkere magnetische Felder ein höherer Wert, v ≈ 2.9, ermittelt. Die Abweichungen gehen vermutlich auf die zugleich gestiegene Unordnungsstärke zurück, welche dafür sorgt, dass Elektronen zwischen verschiedenen Landau-Bändern streuen können und so nicht das kritische Verhalten eines reinen Quanten-Hall-Überganges repräsentieren. Im Gegensatz dazu ist das Verhalten in dreidimensionalen Systemen für beide Fälle ähnlich. Es treten in jedem System zwei Phasenübergänge zwischen lokalisierten und delokalisierten Bereichen auf. Für diese Übergänge wurde der Exponent v ≈ 1.58 ohne und v ≈ 1.45 unter Einfluss eines magnetischen Feldes ermittelt. Dieses Verhalten und die jeweils ermittelten Werte stimmen mit bekannten Ergebnissen überein. Eine Abweichung vom universellen Verhalten wird somit nicht beobachtet.

Vanadium oxides are being used as the thermal sensing layer because of their applications in infrared detectors. They have high temperature coefficient of resistance, favorable electrical resistance and compatibility with the MEMS technology. Of all oxides of vanadium, only vanadium dioxide (VO2)has been highly investigated as it shows first order transition (semiconducting to metal transition-SMT)at 68 oC. First order transition is understood as the sharp change in the electrical resistance. The change in resistivity in this case is of the order of 105 over a temperature change of 0.1 oC at 68 oC in a single crystal. Doping vanadium oxides with elements like Mo and W reduce the transition temperature. This is very important for room temperature electrical and optical detection. Though most of the research groups subscribe to PLD, cost-effective methods with large area deposition are major focus of this research. Hence for synthesizing VO2 in bulk and thin films, Solution Combustion Synthesis (SCS), Ultrasonic Nebulized Spray Pyrolysis of Aqueous Combustion Mixture (UNSPACM) Chemical vapour deposition (CVD)and microwave are explored. Synthesis of doped VO2 films in CVD has not been done extensively to yield optical quality thin films. Chapter I surveys the use of phase transition in oxides system for a variety of practical applications. In particular, Vanadium dioxide (VO2) is chosen as it is found to be very useful for infrared and metamaterials based applications. VO2 is known for its first-order semiconducting to metallic transition (SMT). This chapter attempts to explain the influence of processing, doping, annealing, etc on the SMT characteristics. Important aspects such as the idea of hysteresis in VO2 and similarity to martensitic transformation are discussed. The scope and objectives of the thesis are discussed here. Chapter II explains in detail the materials and methods used to synthesize VO2 both in bulk and in thin lm form and methods used to study their characteristics. Brief description on the principle and the working of the home-built experimental set up needed for this study is elicited. In chapter III, attempts were made to understand the phase stability of VO2 and the evolution of crystal structures during the phase transition. VO2 crystallizes in P21/c space group at room temperatures with lattice parameters a=5.752 Ab=4.526 Ac=5.382 Aα=90 β=122.60 γ=90 . Precise control of synthesis parameters is required in stabilizing pure phase in bulk as well as thin lm form. This study focuses on the novel large scale two step synthesis of VO2 using Solution Combustion Synthesis. This involves synthesis of product utilizing redox reaction between metal nitrate and suitable fuel. Generally the products are nanocrystalline in nature due to self-propagation of the exothermic combustion reaction. First step involved the synthesis of V2O5 by combustion reaction between Vanadyl nitrate and urea. In the second step, the as-synthesized V2O5 has been reduced by a novel reduction technique to form monophasic VO2. The presence of competing phases like M1, M2, M3 and R are investigated by XRD, Raman spectroscopy, DSC, Optical and high temperature X-ray diffraction. Chapter IV deals with the reduction in phase transition temperature by doping the SCS synthesized VO2 with W and Mo. Effect of doping on the transition temperature was studied using differential scanning calorimetry (DSC) in both W and Mo. Electrical characteristics of Mo doped VO2 and Optical characteristics of the W-doped VO2 were also studied using four probe resistivity measurements and UV-VIS Spectroscopy respectively. W addition was found to be more effective in reducing the phase transition temperature. To understand further more on the W addition, X-ray photo-electron spectroscopy measurements were performed. W-addition alters the V4+-V4+ bonding and with W addition it is observed that V was present in V3+state. W was present in W6+ state. The addition of W to VO2 introduces more electrons to the systems and disturbs the V4+-V4+ thus reducing the phase transition temperature of VO2. Chapter V describes the large scale, large area deposition of thin films of VO2 by a cost effective method. A novel technique to deposit vanadium dioxide thin films namely, UNSPACM is developed. This simple two-step process involves synthesis of a V2O5 lm on an LaAlO3(LAO) substrate followed by a controlled reduction to form single phase VO2. The formation of M1 phase (P21/c) is confirmed by Raman spectroscopic studies. A thermally activated metal{insulator transition (MIT) was observed at 61 oC, where the resistivity changes by four orders of magnitude. The infrared spectra also show a dramatic change in reflectance from 13% to over 90% in the wavelength range of 7-15 m. This indicates the suitability of the films for optical switching applications at infrared frequencies. A trilayer metamaterial absorber, composed of a metal structure/dielectric spacer/vanadium dioxide (VO2) ground plane, is shown to switch reversibly between reflective and absorptive states as a function of temperature. The VO2 lm, which changes its conductivity by four orders of magnitude across an insulator{metal transition, enables the switching by forming a resonant absorptive structure at high temperatures while being inactive at low temperatures. The fabricated metamaterial shows a modulation of the reflectivity levels of 58% at a frequency of 22.5 THz and 57% at a frequency of 34.5 THz. Chapter VI explains the W doped VO2 thin films synthesized by UN-SPACM. Morphology of the thin films was found to be consisting of globular and porous nanoparticles having size 20 nm. Transition temperature decreased with the addition of W. 1.8 at. %W doping in VO2 transition temperature has reduced upto 25 oC. It is noted that W-doping in the pro-cess of reducing the transition temperature, alters the local structure and also increases room temperature carrier concentration. The presence of W, as was seen in Chapter IV, altered V4+-V4+ bonds and introduced V3+. W was found to be in W6+ state suggesting W addition increased the carrier concentration. Hall Effect measurements suggested the increased carrier con-centration. The roughness of the synthesized films were very high for them to be of de-vice quality, despite encouraging results obtained by electrical measurements. Hence in order to further improve the smoothness and thereby the optical quality of thin films, Chemical Vapour Deposition (CVD) is employed. Chapter VII outlines the effect of processing parameters and post pro-cessing annealing on the semiconductor-metallic transition of VO2. Here in this chapter, the influence of substrate temperature on the SMT properties of VO2 is explored. At different substrate temperatures, the percentage of phase fraction of V in V3+, 4+ and V5+ differed. Besides, the morphology also varied with substrate temperatures. Similarly it is observed that with annealing the VO2 film deposited on glass substrates, SMT properties enhanced which was attributed to filling out of oxygen vacancies. Si based substrates and non-Si based substrates were used for depositing VO2 thin films by CVD. Their temperature coefficient of resistance and SMT properties were studied in order to understand their potential in bolometer and thermal to optical valve based applications. Chapter VIII involves the study of VO2 thin films for thermal to optical valves. ITO coated glass substrates were used for the purpose. Thin films were deposited by both UNSPACM and CVD. It was observed that the reflectivity pro les of the films synthesized by the above said methods were very different. Hence in the process of understanding the huge difference in the reflectivity pro les, classical harmonic oscillator, Lorentzian model was employed to t the experimental data at room temperature whereas Drude-Lorentzian model was used to t the data at higher temperature (at 100 oC- after transition). With this fitting plasma frequencies of the CVD films were calculated. It was observed that defect chemistry of films synthesized by these methods were different. In order to further improve the smoothness of the films, microwave method was proposed in Chapter IX. The preliminary results showed the presence of uniform spheres and 3 D hierarchical structures of VO2 consisting of nanorods. This was extended to deposit VO2 thin films on ITO. DSC and Infrared reflectance pro le of VO2 nanopowder suggested the phase transition. Chapter X summarizes the work done for the thesis and provides insights to the applications and to the future work. The work reported in this thesis has been carried out by the candidate as part of the Ph.D.program. She hopes that this would constitute a worth-while contribution towards development of VO2 thin film technology and its challenges for reliable infrared device applications.

Ce manuscrit porte sur la modélisation et la simulation numérique d’écoulements diphasiques compressibles. Dans ce contexte, les méthodes d’interfaces diffuses sont aujourd’hui bien acceptées. Cependant, un progrès est encore attendu en ce qui concerne la précision de la capture numérique de ces interfaces. Une nouvelle méthode est développée et permet de réduire significativement cette zone de capture. Cette méthode se place dans le contexte des méthodes numériques de type “MUSCL”, très employées dans les codes de production, et sur maillages non-structurés. Ces interfaces pouvant être le lieu où une transition de phase s’opère, celle-ci est considérée au travers d’un processus de relaxation des énergies libres de Gibbs. Un nouveau solveur de relaxation à thermodynamique rapide est développé et s’avère précis, rapide et robuste y compris lors du passage vers les limites monophasiques. En outre, par rapport aux applications industrielles envisagées, une extension de la thermodynamique des phases et du mélange est nécessaire. Une nouvelle équation d’état est développée en conséquence. La formulation est convexe et est basée sur l’équation d’état “Noble-Abel-Stiffened-Gas”. Enfin, sur un autre plan la dispersion de fluides non-miscibles sous l’effet de la gravité est également abordée. Cette problématique fait apparaître de larges échelles de temps et d’espace et motive le développement d’un nouveau modèle multi-fluide de type “shallow water bi-couche”. Sa résolution numérique est également traitée / This manuscript addresses the theoretical modeling and numerical simulation of compressible two-phase flows. In this context, diffuse interface methods are now well-accepted but progress is still needed at the level of numerical accuracy regarding their capture. A new method is developed in this research work, that allows significant sharpening. This method can be placed in the framework of MUSCL-type schemes, widely used in production codes and on unstructured grids. Phase transition is addressed as well through a relaxation process relying on Gibbs free energies. A new instantaneous relaxation solver is developed and happens to be accurate, fast and robust. Moreover, in view of the intended industrial applications, an extension of the thermodynamics of the phases and of the mixture is necessary. A new equation of state is consequently developed. The formulation is convex and based on the “Noble-Abel-Stiffened-Gas” equation of state. In another context, the dispersion of non-miscible fluids under gravity effects is considered as well. This problematic involves large time and space scales and has motivated the development of a new multi-fluid model for “two-layer shallow water” flows. Its numerical resolution is treated as well

Cette thèse s'inscrit dans l'étude mathématique de la percolation, qui regroupe une famille de modèles présentant une transition de phase. Des avancées majeures au cours des quinze dernières années, notamment l'invention du SLE et la preuve de l'invariance conforme de la percolation de Bernoulli critique, nous permettent aujourd'hui d'avoir une image très complète de la percolation de Bernoulli sur le réseau triangulaire. Cependant, de nombreuses questions demeurent ouvertes, et ont motivé notre travail.La première d'entre elle est l'universalité de la percolation plane, qui affirme que les propriétés macroscopiques de la percolation plane critique ne devraient pas dépendre du réseau sous-jacent à sa définition. Nous montrons, dans le cadre de la percolation Divide and Color, un résultat qui va dans le sens de cette universalité et identifions, dans ce contexte, des phénomènes macroscopiques indépendants du réseau microscopique. Une version plus faible d'universalité est donnée par la théorie de Russo-Seymour-Welsh (RSW), et sa validité est connue pour la percolation de Bernoulli (sans dépendance) sur les réseaux plans suffisamment symétriques. Nous étudions de nouveaux arguments de type RSW pour des modèles de percolation avec dépendance. La deuxième question que nous avons abordée est celle de l'absence d'une composante connexe ouverte infinie au point critique, une question importante du point de vue physique, puisqu'elle traduit la continuité de la transition de phase. Dans deux travaux en collaboration avec Hugo Duminil-Copin et Vladas Sidoravicius, nous montrons que la transition de phase est continue pour la percolation de Bernoulli sur le graphe Z^2x{0,...,k}, et pour la percolation FK sur le réseau carré avec paramètre q inférieur ou égal à 4. Enfin, la dernière question qui nous a guidés est la localité du point critique : la donnée des boules de grands rayons d'un graphe suffit-elle à identifier avec une bonne précision la valeur du point critique? Dans un travail en collaboration avec Sébastien Martineau, nous répondons de manière affirmative à cette question dans le cadre des graphes de Cayley de groupes abéliens. / This thesis is part of the mathematical study of percolation theory, which includes a family of models with a phase transition. Major advances in the 2000s, including the invention of SLE and the proof of conformal invariance of critical Bernoulli percolation, provide us with a very complete picture of the Bernoulli percolation process on the triangular lattice. Fortunately, many questions remain open, and motivated our work.The first of these is the universality of planar percolation, which states that the macroscopic properties of critical planar percolation should not depend on the underlying graph. We study this question in the framework of Divide and Color percolation, and prove in this context a result that goes in the direction of universality. A weaker universality statement is given by the theory of Russo-Seymour-Welsh (RSW), which is known to hold for planar Bernoulli percolation (without dependence) on sufficiently symmetric graphs. We study new RSW-type arguments for percolation models with dependence.The second question is the absence of an infinite cluster at the critical point, an important question from a physical point of view, equivalent to the continuity of the phase transition. In two different joint works with Hugo Duminil-Copin and Vladas Sidoravicius, we show that the phase transition is continuous for Bernoulli percolation on the graph Z^2 x {0,...,k} and for FK percolation on the square lattice with parameter q smaller than or equal to 4.Finally, the last question that guided us is the locality of the critical point: is it possible to determine with good accuracy the critical value for Bernoulli percolation on a graph if we know only the balls with large radii? Jointly with Sébastien Martineau, we answer positively to this question in the framework of Cayley graphs of abelian groups.

In this work, atomic scale investigation of pressure-induced transformations in the solid state have been carried out. A series of compounds including GaN, ZnO, CaF2, and AgI, in addition to elemental phosphorus have been studied. The corresponding transition mechanisms have been elucidated with a clear description of atomic displacements and intermediate structures involved therein. In the first group of compounds, the long standing debate on the transition path of the wurtzite(WZ)-to-rocksalt(RS) transition in semiconductors, GaN and ZnO was resolved using geometrical modeling combined with molecular dynamics (MD) simulations conducted in the frame of transition path sampling (TPS) method. In GaN, a two-step mechanism through a metastable intermediate phase with a tetragonal structure iT has been revealed from simulations. In ZnO, the tetragonal intermediate structure was kinetically less stable, although still part of the real transition mechanism. It appeared at the interface between WZ and RS as consequence of a layers shearing. The transition regime in ZnO was characterized by a competition between iT structure and another hexagonal intermediate with hexagonal symmetry iH. Although possible, the latter is not functional for the transition. In both cases, GaN and ZnO, two points of agreement with experiments have been revealed. The tilting of structures after transition, and the phonon mode softening associated with atomic displacements leading to the tetragonal structure iT In the second group of compounds, the investigation of transitions in superionic conductors, CaF2 and AgI, demonstrated a different and particular behavior of atomic motion under pressure. The solid-solid reconstruction of CaF2 structure was shown to be initiated and precedented by high disorder of the anionic sublattice. The percolation of fluoride ions through voids in the fluorite structure created a thin interface of liquid like state. The sparce regions caused by the departure of anions facilitates the cation sublattice reconstruction. In AgI, ion diffusion during the wurtzite/zincnlende(ZB)$rocksalt transition was more pronounced due to the extended stacking disorder WZ/ZB. The Ag+ ions profited not only from the structure of the interface but used the combination of interstitial voids offered by both phases, WZ and ZB, to achieve long diffusion paths and cause the cation sublattice to melt. Clearly, a proper account for such phenomena cannot be provided by geometry-designed mechanisms based on symmetry arguments. In phosphorus, the question of how the stereochemically active lone pairs are reorganized during the orthorhombic (PI) to trigonal (PV) structural transition was answered by means of simulations. Computation was performed at different levels theory. First, the mechanism of the transition was obtained from TPS MD simulations. MD runs were performed within density functional tight binding method (DFTB). The analysis of atomic displacements along the real transformation path indicated a fast bond switching mechanism. In a second step, the nature of the interplay between orbitals of phosphorus during the bond switching was investigated. A simultaneous deformation of lone pair and P−P bond showed a mutual switching of roles during the transformation. This interplay caused a low dimensional polymerization of phosphorus under pressure. The corresponding structure formed as zigzag linear chain of fourfold coordinated phosphorus atoms (· · ·(P(P2))n · · ·) at the interface between PI and PV phases. A further result of this work was the development of a simulation strategy to incorporate defects and chemical doping to structural transformations. On top of the transition path sampling iterations, a Monte Carlo like procedure is added to stepwise substitute atoms in the transforming system. Introducing a chemically different dopant to a pure system represents a perturbation to the energy landscape where the walk between different phases is performed. Therefore, any change in the transition regime reflects the kinetic preference of a given structural motif at times of phase formation. This method was applied to the elucidation of WZ-RS transition mechanism in the series of semiconducting compounds AlN, GaN, and InN. Simulations showed that In atoms adopt the same transformation mechanism as in GaN and favor it, while Al atoms demonstrated a significant reluctance to the path going through tetragonal intermediate iT. The difference between transition regime in mixed systems InxGa1−xN and AlxGa1−xN is in agreement with experiments on high pressure behavior of AlN, GaN, and InN. While transitions in GaN and InN are reversible down to ambient conditions, AlN is stable. The work presented in this thesis constitutes the seed of new perspectives in the understanding of pressure-induced phase transformations in the solid state, where the physics and the chemistry are brought together by means of computer simulations.

Les matériaux de Dirac constituent une classe intéressante de systèmes pouvant subir une transition de phase quantique à température nulle, lorsqu’un paramètre non-thermique atteint un point critique quantique. À l’approche d’un tel point, les observables physiques sont affectées par les importantes fluctuations thermiques et quantiques. Dans ce mémoire, on utilise des techniques de théorie conforme des champs afin d’étudier le tenseur de conductivité électrique dans des théories en 2 + 1 dimensions contenant des fermions de Dirac près d’un point critique quantique. À basse énergie, ces dernières décrivent de façon adéquate de nombreux matériaux de Dirac ainsi que leur transition de phase quantique. La conductivité est étudiée dans le régime des hautes fréquences, à température non-nulle et lorsque le paramètre non-thermique est près de sa valeur critique. Dans ce projet, l’emphase est mise sur les points critiques quantiques invariants sous la parité et le renversement du temps. Dans ce cas, l’expansion de produit d’opérateurs (Operator product expansion en anglais) ainsi que la théorie des perturbations conforme permettent d’obtenir une expression générale pour l’expansion à grandes fréquences des conductivités longitudinales et transverses (de Hall) lorsque le point critique quantique est déformé par un opérateur scalaire relevant. Grâce à ces dernières, nous sommes en mesure de déduire des règles de somme exactes pour ces deux quantités. À titre d’exemple, nos résultats généraux sont appliqués dans le cadre du modèle interagissant de Gross-Neveu, où nous obtenons l’expansion des deux conductivités ainsi que les règles de somme pour un nombre de saveurs de fermions de Dirac N arbitraire. Ces mêmes expressions sont ensuite obtenues par un calcul explicite à N = infini, permettant la comparaison avec les résultats pour un N quelconque. Par la suite, des résultats généraux similaires sont obtenus dans le cas où le point critique quantique est déformé par un opérateur pseudoscalaire relevant. Ces derniers sont finalement appliqués à une théorie de fermions de Dirac libres perturbée par un terme de masse. / Dirac materials constitute an interesting class of systems that can undergo a quantum phase transition at zero temperature, when a non-thermal parameter reaches a quantum critical point. As we approach such a point, physical observables are altered by the important thermal and quantum fluctuations. In this thesis, conformal field theory techniques are used to study the electrical conductivity tensor in theories with Dirac fermions in 2+1 dimensions close to a quantum critical point. At low energies, these adequately describe various Dirac materials as well as their quantum phase transition. In this project, we focus on theories that have a quantum critical point invariant under parity and time-reversal. In this case, the operator product expansion and conformal perturbation theory allow to obtain a general expression for the large frequency expansion of the longitudinal and transverse (Hall) conductivities when the quantum critical point is deformed by a relevant scalar operator. Using these, we are able to deduce exact sum rules for both quantities. As an example, our general results are applied to the Gross-Neveu model, where we obtain the large frequency expansion for both conductivities and the associated sum rules for an arbitrary number of Dirac fermion flavors N. The same expressions are then obtained by an explicit calculation at N = infinity, allowing to compare with our results for any N. Afterwards, analogous general results are obtained for theories where the quantum critical point is deformed by a relevant pseudoscalar. These are finally applied to a theory of massless free Dirac fermions perturbed by a mass term.