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Quantum Chromodynamics (QCD) is generally assumed to be the fundamental theory underlying nuclear physics. In recent years there is progress towards investigating the nucleon structure from first principles of QCD. Although this structure is best revealed in Deep Inelastic Scattering, a consistent analysis has to be performed in a fully non-perturbative scheme. The only known method for this purpose are lattice simulations. We first sketch the ideas of Monte Carlo simulations in lattice gauge theory. Then we comment in particular on the issues of chiral symmetry and operator mixing. Finally we present our results for the Bjorken variable of a single quark, and for the second Nachtmann moment of the nucleon structure functions.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23509号 / 工博第4921号 / 新制||工||1769(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 田中 功, 教授 中村 裕之, 教授 安田 秀幸 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This study seeks to evaluate the temperature effects on the electronic properties of thermoelectric materials, using first principles Density Functional Theory (DFT) calculations by incorporating the temperature effects on structural properties of the material. Using the electronic properties attained, the charge carrier scattering relaxation times were determined. The effect of interface between PbTe and SrTe on the charge carrier mobility was studied by finding out the relative alignment of energy bands at the semiconductor heterojunction. The crystal shape of the SrTe precipitates in the PbTe host matrix was evaluated from the interface energies using the Wulffman construction. We also attempted to develop a relation between the interface energies and electronic band alignment for different interface orientations. In this research, we incorporated the temperature effects on the structural properties of PbTe to get the temperature dependence of electronic properties like energy bandgap and effective masses of charge carriers. We used the values of bandgap and effective masses to determine the charge carrier scattering relaxation time at different temperatures which is used in evaluating the transport properties of thermoelectric materials like the Seebeck coefficient and electrical conductivity. / Master of Science

Difficulties in learning and understanding statistics in college education have led to a reform movement in statistics education in the early 1990s. Although much work has been done, there is more work that needs to be done in statistics education. The progress depends on how well the educators bring interesting real-life data into the classroom. The goal was to understand how course design based on First Principles of Instruction could facilitate tertiary-level students' conceptual understanding when learning introductory statistics in a technology-enhanced learning environment. An embedded single descriptive case design was employed to investigate how integrating technology and real data into a tertiary level statistics course would affect students' statistical literacy, reasoning, and thinking. Data including online assignment postings, online discussions, online peer evaluations, a comprehensive assessment, and open-ended interviews were analyzed to understand how the implementation of First Principles of Instruction affected a student's conceptual understanding in a tertiary level introductory statistics course. In addition, the teaching and learning quality (TALQ) survey was administered to evaluate the teaching and learning quality of the designed instruction from the student's perspective. Results from both quantitative and qualitative data analyses indicate that the course designed following Merrill's First Principles of Instruction contributes to a positive overall effectiveness of promoting students' conceptual understanding in terms of literacy, reasoning, and thinking statistically. However, students' statistical literacy, specifically, the understanding of statistical terminology did not develop to a satisfactory level as expected.

This thesis is a theoretical study of configurational disorder in icosahedral boron-rich solids, in particular boron carbide, including also the development of a methodological framework for treating configurational disorder in such materials, namely superatom-special quasirandom structure (SA-SQS). In terms of its practical implementations, the SA-SQS method is demonstrated to be capable of efficiently modeling configurational disorder in icosahedral boron-rich solids, whiles the thermodynamic stability as well as the properties of the configurationally disordered icosahedral boron-rich solids, modeled from the SA-SQS method, can be directly investigated, using the density functional theory (DFT). In case of boron carbide, especially B4C and B13C2 compositions, the SA-SQS method is used for modeling configurational disorder, arising from a high concentration of low-energy B/C substitutional defects. The results, obtained from the DFT-based calculations, demonstrate that configurational disorder of B and C atoms in boron carbide is not only thermodynamically favored at high temperature, but it also plays an important role in altering the properties of boron carbide − for example, restoration of higher rhombohedral symmetry of B4C, a metal-to-nonmetal transition and a drastic increase in the elastic moduli of B13C2. The configurational disorder can also explain large discrepancies, regarding the proper- ties of boron carbide, between experiments and previous theoretical calculations, having been a long standing controversial issue in the field of icosahedral boron- rich solids, as the calculated properties of the disordered boron carbides are found to be in qualitatively good agreement with those, observed in experiments. In order to investigate the configurational evolution of B4C as a function of temperature, beyond the SA-SQS level, a brute-force cluster-expansion method in combination with Monte Carlo simulations is implemented. The results demonstrate that configurational disorder in B4C indeed essentially takes place within the icosahedra in a way that justifies the focus on lowenergy defect patterns of the superatom picture. The investigation of the thermodynamic stability of icosahedral carbon-rich boron carbides beyond the believed solubility limit of carbon (20 at.% C) demonstrates that, apart from B4C generally addressed in the literature, B2.5C represented by B10Cp2(CC) is predicted to be thermodynamically stable with respect to B4C as well as pure boron and carbon under high pressure, ranging between 40 and 67 GPa, and also at elevated temperature. B2.5C is expected to be metastable at ambient pressure, as indicated by its dynamical and mechanical stabilities at 0 GPa. A possible synthesis route of B2.5C and a fingerprint for its characterization from the simulations of x-ray powder diffraction pattern are suggested. Besides modeling configurational disorder in boron carbide, the SA-SQS method also opens up for theoretical studies of new alloys between different icosahedral boron-rich solids − for example, (B6O)1−x(B13C2)x and B12(As1−xPx)2. As for the pseudo-binary (B6O)1−x(B13C2)x alloy, it is predicted to display a miscibility gap resulting in B6O-rich and either ordered or disordered B13C2-rich domains for intermediate global compositions at all temperatures up to melting points of the materials. However, some intermixing of B6O and B13C2 to form solid solutions is also predicted at high temperature. A noticeable mutual solubility of icosahedral B12As2 and B12P2 in each other to form B12(As1−xPx)2 disordered alloy is predicted even at room temperature, and a complete closure of a pseudo-binary miscibility gap is achieved at around 900 K. Apart from B12(As1−xPx)2, the thermodynamic stability of other compounds and alloys in the ternary B-As-P system is also investigated. For the binary B-As system, zincblende BAs is found to be thermodynamically unstable with respect to icosahedral B12As2 and gray arsenic at 0 K and increasingly so at higher temperature, indicating that BAs may merely exist as a metastable phase. This is in contrast to the binary B-P system, in which zinc-blende BP and icosahedral B12P2 are both predicted to be stable. Owing to the instability of BAs with respect to B12As2 and gray arsenic, only a tiny amount of BAs is predicted to be able to dissolve in BP to form BAs1−xPx disordered alloy at elevated temperature. For example, less than 5% BAs can dissolve in BP at 1000 K. As for the binary As-P system, As1−xPx disordered alloys are predicted at elevated temperature − for example, a disordered solid solution of up to ∼75% As in black phosphorus as well as a small solubility of ∼1% P in gray arsenic at 750 K, together with the presence of miscibility gaps. The thermodynamic stability of three different compositions of α-rhombohedral boron-like boron subnitride, having been proposed so far in the literature, is investigated. Those are, B6N, B13N2, and B38N6, represented respectively by B12(N-N), B12(NBN), and [B12(N-N)]0.33[B12(NBN)]0.67. It is found that, out of these sub- nitrides, only B38N6 is thermodynamically stable from 0 GPa up to ∼7.5 GPa, depending on the temperature, and is thus concluded as a stable composition of α-rhombohedral boron-like boron subnitride.

Os métodos de primeiros princípios dentro da Teoria do Funcional Densidade têm se desenvolvido bastante, devido aos avanços computacionais ocorridos nas últimas décadas. Por outro lado, a Termodinâmica e a Mecânica Estatística têm representado um papel importante na compreenssão da Física de Materiais, em especial no estudo dos materiais intermetálicos ordenados. A aliança entre estas duas abordagens têm se tornado cada vez mais factível, uma vez que os cálculos de estrutura eletrônica de primeiros princípios são hoje capazes de proporcionar resultados extremamente precisos para energias de formação de compostos estequiométricos. É dentro deste contexto que neste trabalho investigamos o diagrama de fases composição-temperatura do sistema Fe-Al-Mo, na estrutura cúbica de corpo centrado utilizando o método Full-Potential Linear Augmented Plane Wave (FP-LAPW) aliado ao Método Variacional de Clusters (CVM) na aproximação do tetraedro irregular. Através do método FP-LAPW determinamos a energia total de configurações cristalinas do sistema Fe-Mo-Al cúbico de corpo centrado. Estes valores são utilizados como parâmetros de entrada do CVM para determinação do potencial termodinâmico do sistema em suas diferentes fases e os correspondentes equilíbrio entre estas fases em função da composição e da temperatura, ou seja, o diagrama de fases do sistema. Embora o Fe-Al tenha grande interesse tecnológico, o seu comportamento magnético é bastante complicado e normalmente mal descrito pelos métodos de cálculos usuais. Este trabalho procura enfrentar este problema com ferramentas \"estados de arte\" e apontam para as limitações inerentes ao procedimento geral aqui utilizado. / First-principles methods within the framework of Density Functional Theory, have been developed sufficiently, due to the computational advances occurrences in the last decades. On the other hand, the Thermodynamics and the Statistical Mechanics have represented an important role in the understanding of the Physics of Materials, in special in the study to ordered intermetallic compounds. The alliance between these two approaches has become each more feasible with the time due to the fact that electronic structure calculations of first principles are today to provide almost exact results for the formations energies of stoichiometric compounds. It is inside of this context that in this work we investigate the composition-temperature phases diagram of the Fe-Al-Mo system, in the body centered cubic structure (BCC), using the Full-Potential Liner Augmented Plane Wave (FP-LAPW) method allied to the Cluster Variation Method (CVM) in the irregular tetrahedron approximation. Through the FP-LAPW method we determined the total energy of crystalline configurations of BCC Fe-Mo-Al system. These values are used as input parameters of the CVM for the determination of the thermodynamic potential of the system in its different phases and corresponding to the equilibria between these phases as a function of the composition and the temperature, that is the phase diagram of the system. Although the Fe-Al has great technological interest, its magnetic behavior is complicated and badly described by the methods used in the actual ab-initio calculations. This work faces this problem with state-of-art tools and points to the inherent limitations of the general procedure used here.

A superfície (100) do Silício é estudada através de métodos de primeiros princípios, baseados na Teoria do Funcional da Densidade e no Método dos Pseud.opotenciais. Estudamos as propriedades eletrônicas e estruturais das principais reconstruções desta superfície. Obtivemos os principais sítios ligantes para pequenas estruturas de Germânio adsorvidas sobre ela. Para um átomo adsorvido o sítio mais estável encontrado foi o sítio M, semelhante a resultados existentes na literatura. A diferença está na configuração dos dímeros de Si da superfície. Observamos que diferentes configurações destes dímeros nos forneciam diferentes sítios metaestáveis. O deslocamento dos dímeros da superfície é tratado então como um novo grau de liberdade para a adsorção de átomos, além da posição destes sobre a superfície. Também foi estudada a adsorção de alguns trímeros de Ge sobre a superfície, sendo que a estrutura encontrada como sendo a mais estável concorda muito bem com outros resultados teóricos e experimentais. / The (100) surface of Silicon is studied using First Principles methods, based on the Density Functional Theory and on the Pseudopotential method. We obtained the electronic and structural properties of the most important reconstructions of this surface and we also obtained the main bonding sites for the adsorption of small Ge structures on the surface. Site M was found as being the most stable for the monomers adsorption, similar to previous results on the literature. The main difference is on the buckling of the silicon surface dimers. We observed that different configurations of these buckling gave us different metastable adsorption sites. We then insert a new degree of freedom for this kind of adsorption, related to the buckling of the silicon surface dimers. \\Me also studied the adsorption of Ge trimers on the surface, and the structure found as being the most stable agree very well with previous theoretical and experimetal results.

In this work we exploit the unique characteristics of a Dirac semimetal material to be symmetry-protected, to investigate dierent topological phase transitions provided by chemical dopings, focusing in particular on the electronic, magnetic and topological properties of the doped systems, studied by the mean of rst-principles methods based on density functional theory (DFT) approach. In particular these doped systems, besides being of interest for investigating the role of topology in solid state physics, could have a great potential for practical application since the dierent topological phases that come along with the chemical dopings allow one to exploit the unique properties of topological materials. The starting point for our study will be the material called cadmium-arsenide (Cd3As2), an example of a topological Dirac semimetal, which is chemically stable at ambient conditions. Chapter I presents a general introduction to topology, especially in condensed matter physics, and to the main physical properties of the topological materials we mentioned. Then, in chapter II, we briey present the methods and the computational tools that we used for our study. In chapter III a more detailed introduction to our work is given, along with a schemetic view of the path we followed, together with the results that we obtained for pristine Cd3As2, which we use as bench mark for our computational methods. Finally, in chapter IV and V, the results for the doped systems are presented and discussed, respectevely for the non-magnetic (IV) and magnetic (V) dopings. Our study has enabled us to discern how doping can give rise to see dierent topological phase transitions. Specically our work shows that dierent realizations of non-magnetic doping gives rise to dierent topological phases: the topological Weyl semimetal phase, which is of great interest since it can support a robust quantum spin Hall eect, and a very special mixed Dirac + Weyl phase, where surprisingly both a Dirac and a Weyl phase can coexist in the same system. Furthermore, magnetically doped systems show the emergence of a magnetic Weyl phase, which can support a quantum anomalous Hall eect. Our work can be the starting point for future studies, both theoretical and experimental, in which the unique physical properties we found in the doped Cd3As2 systems can be further investigated, in order to exploit them for practical applications.