In this dissertation, we will study solvent-vapor induced spherulitic growth in multicomponent thin films modeled as prestressed elastic solids. The interface between the crystalline phase and the amorphous phase will be treated as an evolving thermodynamic system and no diffusion of any component will be considered. The dissertation is divided into three parts. In Part I we will determine necessary conditions of thermodynamic equilibrium between the two solid phases, the inter- face, and the vapor. In Part II we will derive the thermodynamic driving force for spherulitic growth in multicomponent elastic thin films. In Part III we will investigate the effect of prestress on the directional dependence of the growth. There a formula that delineates how the prestress affects the shape of the spherulite will be proposed.

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete β functions. The motivation of calculating the discrete β functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare the distribution of Fisher zeros for lattice gauge models with four and twelve light fermion flavors. We also briefly discuss the scaling of the zeros and its connection with the infrared fixed point (IRFP) and the mass anomalous dimension. Conventional numerical simulations suffer from the critical slowing down at the critical region, which prevents one from simulating large system. In order to reach the continuum limit in the lattice gauge theories, one needs either large volume or clever extrapolations. TRG is a new computational method that may calculate exponentially large system and works well even at the critical region. We formulate the TRG blocking procedure for the two dimensional O(2) (or XY ) and O(3) spin models and discuss possible applications and generalizations of the method to other spin and lattice gauge models. We start the thesis with the introduction and historical background of the RG in general.

A blue sky, a white cloud or a red sunset are explained by classical multiple scattering theory of light. However, these phenomena neglect interference occurrence. Once it is taken into account, interference in a disordered medium may actually put a halt to the propagation of light, an effect known as Anderson Localization. Until now, experimental reports of Anderson Localization of light in 3D systems have not been conclusive. Our goal is to understand what are the underlying obstacles, and look for new insights from a theoretical point of view. In this dissertation, the properties of a cloud of two-level atoms scattering light are investigated. The dipole-dipole interaction generates collective modes, some of them, being localized. We found that finite-size effects dominate the lifetime of the localized modes, specifically by the ratio of localization length to their distance to the system boundaries. Localized modes saturates at maximum of 20% even above phase transition. Studying the steady-state regime, the coupling between localized modes and light is weak. Both results agrees with the difficulty of experimental evidence of light localization and promote the link of experiments and theory. / Um céu azul, uma nuvem branca ou um por do sol vermelho são explicados pela teoria clássica de espalhamento múltiplo da luz. No entanto, esses fenômenos negligenciam a ocorrência de interferências. Uma vez levada em conta, a interferência em um meio desordenado pode interromper a propagação da luz, um efeito conhecido como Localização de Anderson. Até agora, relatos experimentais de Anderson Localização de luz em sistemas 3D não foram conclusivos. Nosso objetivo é entender quais são os obstáculos fundamentais, e buscar novos insights do ponto de vista teórico. Nesta dissertação, as propriedades de uma nuvem de átomos de dois níveis espalhando luz de é investigado. A interação dipolo-dipolo gera modos coletivos, alguns deles, sendo localizados. Descobrimos que os efeitos de tamanho finito dominam o tempo de vida dos modos localizados, especificamente pela razão entre o comprimento da localização e sua distância até os limites do sistema. Os modos localizados saturam no máximo 20%, mesmo acima da transição de fase. Estudando o regime de estado estacionário, o acoplamento entre modos localizados e luz é fraco. Ambos os resultados concordam com a dificuldade da evidência experimental da localização da luz e promovem a ligação entre experimentos e teoria.

A liga de FeRh apresenta uma transição de fase magneto-estrutural de primeira ordem próxima da temperatura ambiente, fazendo deste material um forte candidato para aplicações de gravação magnética termicamente assistida ou em refrigeradores magnéticos. Em baixas temperaturas o FeRh apresenta uma fase antiferromagnética enquanto em altas temperaturas apresenta uma fase ferromagnética. Cientes disto, neste trabalho foram analisados as transições de fase de filmes de FeRh, porém quando na presença de nanofios de Ni. Para isso foram fabricados filmes de FeRh, próximos da composição equiatômica, sobre uma matriz nanoporosa de Al 2 O 3 com nanofios de Ni. A matriz nanoposora foi produzida por um processo de anodização em dois passos, sendo preenchido os poros com Ni via eletrodeposição. O filme de FeRh foi crescido por deposição via magnetron sputtering, em duas temperaturas distintas, 525 e 600 o C. Um tratamento térmico in situ a 600 o C, por uma hora, foi feito no filme depositado na mesma temperatura. Curvas de magnetização em função de campo magnético aplicado, em temperaturas fixas, mostraram comportamentos característicos de filmes ou nanofios quando medidos nas direções preferenciais de cada componente, respectivamente, sugerindo um forte acoplamento via magnetoestrição entre os elementos. Foi analisada a dependência da transição de fase com relação a condições de magnetização dos nanofios de Ni, sendo observado clara dependência do comportamento da transição de fase com relação à estas condições. A transição de fase do FeRh é dada por nucleações e, posteriormente, por um deslocamento das paredes de domínio adjacentes a nucleação. Este comportamento é bem descrito pela somatória de duas distribuições gaussianas, sendo ajustadas na primeira derivada da magnetização em função da temperatura. Estes ajustes mostraram um claro comportamento da distribuição de nucleação com relação a magnetização remanente dos nanofios. Tal comportamento não tinha sido relatado até este momento. O filme depositado em 525 o C se mostrou mais suscetível a magnetização remanente dos nanofios do que o filme depositado em 600 o C. Posteriormente, medidas de transição de fase sob campo magnético intenso mostraram uma forte relação entre as temperaturas críticas de transição e a intensidade de campo aplicado, sendo deslocada a curva de transição para temperaturas mais baixas devido o incremento do campo. O filme depositado em 525 o C apresentou uma transição mais larga e uma menor magnetização em altas temperaturas do que o filme depositado em 600 o C. / The FeRh alloy presents a first order magnetic-structural phase transition close the room temperature, making this material a strong candidate to heat-assisted magnetic recording or magnetic refrigerators. At low temperaturas the FeRh the FeRh shows a antiferromagnetic phase while at high temperatures shows a ferromagnetic phase. Aware of this, in this work were analyzed the FeRh films phase transition, but under the Ni nanowires presence. For this were maked FeRh films, close the equiatomic composition, over a nanoporous matrix of Al 2 O 3 with Ni nanowires. The nanoporou matrix were produced by a two-step anodization process and the nanoporou fille with Ni via eletrodeposition. The FeRh film were grown by deposition via magnetron sputtering at two different temperatures, 525 e 600 o C. Annealing in situ at 600 o C for one hour was done in the film deposited at same temperature. Magnetization curves as function of applied magnetic field, at fixed temperatures, showed characteristic behaviors of the films or nanowires where measured in the preferential direction of each componente, respectively, suggest a strong magnetostriction coupling between elements. The phase transition dependence was analyzed with respect to magnetization conditions of Ni nanowires, been observed a clear dependence of the phase transition behavior with these conditions. The FeRh phase transition is given by nucleations and followed by a displacement of domain walls adjacents to the nucleation. This behavior is well defined for the sum of two gaussians distributions, been fitted to the first derivative of magnetization as function of temperature. These fittings showed a clear behavior of the nucleation distribution with repect to a nanowires remanent magnetization. Such behavior has never been reported before. The film deposited at 525 o C showed more susceptible to nanowires remanentc magnetization than film deposited at 600 o C. Subsequently meadures of phase transition under high magnetic fields showed a strong relation between the critical temperatures of depostion and the field intensity, being displaced to lower temperatures the transition curve with the field increment. The film deposited at 525 o C presented a broader transition with lower magnetization at high temperatures than film deposited at 600 o C.

Doctor of Philosophy(PhD) / This project focuses on the examination of the structures of lanthanide containing double perovskites of the type Ba2LnB'O6-d (Ln = lanthanide or Y3+ and B' = Nb5+, Ta5+, Sb5+ and/or Sn4+) using synchrotron X-ray and neutron powder diffraction. The first part of this project examined the relative stability of R3 rhombohedral and I4/m tetragonal structures as the intermediate phase adopted by the series Ba2LnB'O6 (Ln = lanthanide (III) or Y3+ and B' = Nb5+, Ta5+ or Sb5+). It was found that I4/m tetragonal symmetry was favoured when B' was a transition metal with a small number of d electrons, such as Nb5+ or Ta5+. This is due to the presence of p-bonding in these compounds. In the Ba2LnNbO6 and Ba2LnTaO6 series R3 rhombohedral symmetry was, however, favoured over I4/m tetragonal symmetry when Ln = La3+ or Pr3+ due to the larger ionic radius of these cations. The incompatibility of the d0 and d10 B'-site cations in this family of compounds was indicated by significant regions of phase segregation in the two series Ba2Eu1-xPrxNb1-xSbxO6 and Ba2NdNb1-xSbxO6. In the second part of this project the compounds in the series Ba2LnSnxB'1-xO6-d (Ln = Pr, Nd or Tb and B' = Nb5+ or Sb5+) were examined to understand the relative stability of oxygen vacancies in these materials compared to the oxidation of the lanthanide cations and to determine if any oxygen vacancy ordering occurred. It was found, using a combination of structural characterisation, X ray Absorption Near Edge Structure and Ultra-Violet, Visible and Near Infrared spectroscopies, that with Ln = Pr or Tb increased Sn4+ doping results in a change in the oxidation state of the Ln3+ cations to Ln4+. This leads to those series containing little or no oxygen vacancies. A loss of B site cation ordering was found to accompany this oxidation state change and phase segregation was found to occur in the Ba2PrSnxSb1-xO6-d series most likely due to the Pr3+ and Pr4+ cations segregating into different phases. The Nd3+ cations in the series Ba2NdSnxSb1-xO6-d, however, can not oxidise to the tetravalent state so the number of oxygen vacancies rises with increasing x. It was found that oxygen vacancies concentrate onto the axial site of the compounds with x = 0.6 and 0.8 at ambient temperature. In Ba2Sn0.6Sb0.4O5.7 the oxygen vacancies were found to change to concentrating on the equatorial site at higher temperatures and it is suggested that this oxygen vacancy ordering plays a role in the adoption of I2/m monoclinic symmetry.

<p>This thesis presents a theoretical study of bulk materials using <i>ab initio</i> methods based on the density functional theory (DFT).</p><p>Crystallographic structural phase transformations and phase stability for 5f-dioxides, ABO₃ perovskites, and ABO₄ compounds have been extensively studied. Different approaches such as static total energy calculations, elastic stability and dynamical stability (phonon calculations) criteria have been used to determine the phase stability. As a special case, the lattice dynamics of solid Xe has been studied as a function of pressure.</p><p>Dielectric functions and optical constants have been calculated for solar energy cell system CuIn_1-xGa_xSe₂ with concentrations x=0, 0.25, 0.5 and 1.0 as well as for C₆₀, PbWO₄and δ-AlOOH. The absorption coefficient provides information about the optimum solar energy conversion efficiency. We have derived absorption coefficients for a number of compounds. Comparisons between the calculated and experimental dielectric functions and absorption coefficients have been made.</p><p>The main part of this thesis focuses on the nanolayered ternary compounds M _N+1AX_N(MAX), where N = 1, 2 or 3, M is an early transition metal, A is an A-group (mostly IIIA and IVA) element, and X is either C and/or N. These ternary carbides and nitrides combine unusual properties of both metals and ceramics. They exhibit high hardness, but fully reversible plasticity, and negligible thermoelectric power. These excellent properties make the MAX phases another new class of materials with versatile technological applications. Our work presents a systematic study of the electronic, bonding, elastic and optical properties of the MAX phases. A new MAX phase-Ti₄SiC_3,is calculated to be stable, and at the same time also been synthesized by experimentalists. Surface energy calculations have also been performed for the (0001) surface of the Ti-Si-C system. The general relations between the electronic structure and materials properties of the MAX phases have been elaborated in the thesis.</p>

Ab Initio calculations suggest that partially lithiated layered LixMnO₂ transforms to spinel in a two-stage process. In the first stage, a significant fraction of the Mn and Li ions rapidly occupy tetrahedral sites, forming a metastable intermediate. The second stage involves a more difficult coordinated rearrangement of Mn and Li ions to form spinel. This behavior is contrasted to LixCoO₂. The susceptibility of Mn for migration into the Li layer is found to be controlled by oxidation state which suggests various means of inhibiting the transformation. These strategies could prove useful in the creation of superior Mn based cathode materials. / Singapore-MIT Alliance (SMA)

This thesis is focused upon chemistry as a school subject and students' interpretations and use of formally introduced teaching models. To explore students' developing repertoire of chemical models, a longitudinal interview study was undertaken spanning the first year of upper secondary school chemistry. Matter in its different states was selected as the target framework for this study. The results presented are derived from both generalisations of groups of students as well as a case study describing an individual learner's interpretation of formal content. The results obtained demonstrated that the formal teaching models provided to the students included in this study were not sufficient to afford them a coherent framework of matter in its different states or for chemical bonding. Instead, students' expressed models of matter and phase change were to a high degree dependent on electron movement (Paper I), anthropomorphism (Paper II) and, for one student, a mechanistic approach based on small particles and gravitation (Paper III). The results from this study place focus on the importance of learners' prior learning (previous experiences) and the need to develop a coherent framework of formal teaching models for the nature of matter and phase change.

This thesis presents a theoretical study of bulk materials using ab initio methods based on the density functional theory (DFT). Crystallographic structural phase transformations and phase stability for 5f-dioxides, ABO3 perovskites, and ABO4 compounds have been extensively studied. Different approaches such as static total energy calculations, elastic stability and dynamical stability (phonon calculations) criteria have been used to determine the phase stability. As a special case, the lattice dynamics of solid Xe has been studied as a function of pressure. Dielectric functions and optical constants have been calculated for solar energy cell system CuIn1-xGaxSe2 with concentrations x=0, 0.25, 0.5 and 1.0 as well as for C60, PbWO4 and δ-AlOOH. The absorption coefficient provides information about the optimum solar energy conversion efficiency. We have derived absorption coefficients for a number of compounds. Comparisons between the calculated and experimental dielectric functions and absorption coefficients have been made. The main part of this thesis focuses on the nanolayered ternary compounds M N+1AXN (MAX), where N = 1, 2 or 3, M is an early transition metal, A is an A-group (mostly IIIA and IVA) element, and X is either C and/or N. These ternary carbides and nitrides combine unusual properties of both metals and ceramics. They exhibit high hardness, but fully reversible plasticity, and negligible thermoelectric power. These excellent properties make the MAX phases another new class of materials with versatile technological applications. Our work presents a systematic study of the electronic, bonding, elastic and optical properties of the MAX phases. A new MAX phase-Ti4SiC3, is calculated to be stable, and at the same time also been synthesized by experimentalists. Surface energy calculations have also been performed for the (0001) surface of the Ti-Si-C system. The general relations between the electronic structure and materials properties of the MAX phases have been elaborated in the thesis.

This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.