Transition metal alloys are an important class of materials in heterogeneous catalysis due in no small part to the often greatly enhanced activity and selectivity they exhibit compared to their monometallic constituents. A host of experimental and theoretical studies have demonstrated that, in many cases, these synergistic effects can be attributed to atomic-scale features of the catalyst surface. Realizing the goal of designing -- rather than serendipitously discovering -- new alloy catalysts thus depends on our ability to predict their atomic configuration under technologically relevant conditions. This dissertation presents original research into the development and use of computational tools to accomplish this objective. These tools are all based on a similar strategy: For each of the alloy systems examined, cluster expansion (CE) Hamiltonians were constructed from the results of density functional theory (DFT) calculations, and then used in Metropolis Monte Carlo (MC) simulations to predict properties of interest. Following a detailed description of the DFT+CE+MC simulation scheme, results for the AuPd/Pd(111) and AuPt/Pt(111) surface alloys are presented. These two systems exhibit considerably different trends in their atomic arrangement, which are explicable in terms of their interatomic interactions. In AuPd, a preference for heteronuclear, Au-Pd interactions results in the preferential formation of Pd monomers and other small ensembles, while in AuPt, a preference for homonuclear interactions results in the opposite. AuPd/Pd(100) and AuPt/Pt(100) were similarly examined, revealing not only the effects of the same heteronuclear/homonuclear preferences in this facet, but also a propensity for the formation of second nearest-neighbor pairs of Pd monomers, in close agreement with experiment. Subsequent simulations of the AuPd/Pd(100) surface suggest the application of biaxial compressive strain as a means increasing the population of this catalytically important ensemble of atoms. A method to incorporate the effects of subsurface atomic configuration is also presented, using AuPd as an example. This method represents several improvements over others previously reported in the literature, especially in terms of its simplicity. Finally, we introduce the dimensionless scaled pair interaction, whereby the finite-temperature atomic configuration of any bimetallic surface alloy may be predicted from a small number of relatively inexpensive calculations. / text

The interaction of intense laser pulses with nanometer scale atomic clusters has been an active area of study since the advent of amplified femtosecond lasers. In the case of infrared irradiation of noble gas clusters, direct field-driven ionization results in the ejection of energetic electrons, high ion charge states, and Coulomb explosion of the ion core of the clusters. These processes result from electron motion driven by the cluster potential and the large ponderomotive potential of the laser field. When extreme ultraviolet (XUV) pulses interact with clusters, the mechanisms responsible for the infrared response are 'turned off' because the ponderomotive potential is very small. We have conducted cluster experiments at 38nm using focused XUV pulses produced by high harmonic generation with a 15TW Ti:Sapphire laser. We measured the charge states and kinetic energy spectra of ions produced in the interaction, and observe substantial ion population up to Xe⁵⁺, with a small number of Xe⁶⁺-Xe⁸⁺ ions produced by collisional ionization by hot plasma electrons. The ion kinetic energy spectrum indicates a hydrodynamic expansion at an ion temperature of 8eV. This is in stark contrast to intense infrared/cluster interactions, where clusters are stripped of electrons to a large degree and expand by Coulomb forces, resulting in far higher ion kinetic energy for similar degrees of ionization. / text

At the interface of quantum information and condensed matter physics, the study of entanglement in quantum many-body systems requires a new toolset which combines concepts from each. This thesis introduces a set of computational methods to study phases and phase transitions in lattice models of quantum systems, using the Renyi entropies as a means of quantifying entanglement. The scaling of entanglement entropy can give valuable insight into the phase of a condensed matter system. It can be used to detect exotic types of phases, to pinpoint transitions between phases, and can give us universal information about a system. The first approach in this thesis is a technique to measure entanglement in finite size lattice systems using zero-temperature quantum Monte Carlo simulations. The algorithm is developed, implemented, and used to explore anomalous entanglement scaling terms in the spin-1/2 Heisenberg antiferromagnet. In the second part of this thesis, a new and complementary numerical technique is introduced to study entanglement not just in finite size systems, but as we approach the thermodynamic limit. This “numerical linked-cluster expansion” is used to study two different systems at their quantum critical points — continuous phase transitions occurring at zero temperature, at which these systems exhibit universal properties. Remarkably, these universal properties can be reflected in the scaling of entanglement. Entanglement offers a new perspective on condensed matter systems, one which takes us closer to genuinely understanding what goes on in these materials at the quantum mechanical level. This thesis demonstrates the first steps in developing an extensive list of computational tools that can be used to study entanglement over a wide range of interacting quantum many-body systems. With the ever increasing computational power available, it may be only a matter of time before these tools are used to create a comprehensive framework for the characterization of condensed matter phases and phase transitions.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20368号 / 工博第4305号 / 新制||工||1667(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 乾 晴行, 教授 邑瀬 邦明 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Atomistic modelling has widely been applied for studying structures and properties of materials. There are various methods to perform atomistic modelling. This master thesis presents a combined density functional theory (DFT) and cluster expansion (CE) study of Gd2O3 and Gd2O3-CeO2 interface (GCI) relevant for solid oxide fuel cells (SOFCs).    The energy differences (ΔE) of Va-O exchanges in C-type Gd2O3 and at GCI are calculated using both DFT and CE methods. We also calculated the migration energy (Emig) of Va jumps in Gd2O3 and at GCI by DFT. The comparison between the CE and DFT results demonstrates that the CE method provides a relatively accurate estimation of ΔE while it requires less computational resources. Furthermore, the CE method is used to study the Va migration in the vicinity of the Gd2O3-CeO2 interface. The potential energy landscapes of different types of paths are studied. / Atomistisk modellering har i stor utsträckning använts för att studera strukturer och  egenskaper  hos  material.  Det  finns  många  olika  metoder  för  att  utföra atomistisk   modellering.   Detta   masterprojekt   presenterar   en   kombinerad density functional theory (DFT) och   cluster expansion (CE) studie av Gd2O3- och Gd2O3-CeO2 gränssnittet (GCI), relevant för fastoxidbränsleceller (SOFC). Energiskillnaderna (ΔE) för Va-O-utbytet i C-typ Gd2O3 och vid GCI beräknas med   användning   av   både   DFT-   och   CE-metoder.   Vi   beräknade   också migrationsenergin   (Emig)   av   Va-hopp   i   Gd2O3   och   vid   GCI   med   DFT. Jämförelsen  mellan  CE  och  DFT-resultaten  visar  att  CE-metoden  ger  en relativt    noggrann    uppskattning    av ΔE    samt    att    den    kräver    mindre beräkningsresurser.   Vidare   används   CE-metoden   för   att   studera   Va- migrering  i   närheten   av   Gd2O3-CeO2-gränssnittet.   Det   potentiella   energilandskapet  för olika vägar studeras.

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This thesis discusses structural and ferroelectric properties of two well-known classes of materials, perovskite oxides and Hydrogen bonded ferroelectrics, using first-principles calculations. Certain aspects of first principles calculations are central to the problems presented in this thesis. Such as the ability to calculate polarization based on the modern theory of polarization and calculation of ferroelectric property under finite electric displacement field. Therefore, these fundamental theoretical approaches are discussed following an opening section on the basic methodology of density-functional theory. In addition to the discussion on theoretical methods, a brief review of different phenomena and techniques crucial to alter/enhance ferroelectric properties at the interfaces of perovskite materials has been presented along with examples. The first problem presented in this thesis proposes and validates an alternative quantitative measure of ferroelectric(FE) and antiferrodistortive(AFD) instabilities by means of calculating inverse capacitance and layer inverse capacitance of layered perovskites. The presented methodological approach is applied to BaTiO$_{3}$/CaTiO$_{3}$ and PbTiO$_{3}$/SrTiO$_{3}$ superlattices and it precisely estimates FE and AFD instabilities. Here we also present an approach to accurately predict the ferroelectric instabilities in large period superlattices from the statistical coefficients obtained from short period superlattices. In the second problem, we study ferroelectricity in an organic crystal(croconic acid) for which ferroelectric polarization is close to that of bulk BaTiO$_{3}$. We employ new meta-GGA functional named SCAN and revisit all structural and ferroelectric properties. Calculated X-ray absorption spectra(XAS) qualitatively and quantitatively agrees well with experimental O K-edge spectra. By discussing the origin of each XAS peak and their characteristic we demonstrate with a systematic approach the connection between ferroelectricity and XAS in croconic acid. Best to our knowledge such relation has not been realized in past. This study could prove XAS as a new way to measure ferroelectric instability in hydrogen-bonded organic ferroelectrics. / Physics

A point process is a mechanism, which realizes randomly locally finite point measures. One of the main results of this thesis is an existence theorem for a new class of point processes with a so called signed Levy pseudo measure L, which is an extension of the class of infinitely divisible point processes. The construction approach is a combination of the classical point process theory, as developed by Kerstan, Matthes and Mecke, with the method of cluster expansions from statistical mechanics. Here the starting point is a family of signed Radon measures, which defines on the one hand the Levy pseudo measure L, and on the other hand locally the point process. The relation between L and the process is the following: this point process solves the integral cluster equation determined by L. We show that the results from the classical theory of infinitely divisible point processes carry over in a natural way to the larger class of point processes with a signed Levy pseudo measure. In this way we obtain e.g. a criterium for simplicity and a characterization through the cluster equation, interpreted as an integration by parts formula, for such point processes. Our main result in chapter 3 is a representation theorem for the factorial moment measures of the above point processes. With its help we will identify the permanental respective determinantal point processes, which belong to the classes of Boson respective Fermion processes. As a by-product we obtain a representation of the (reduced) Palm kernels of infinitely divisible point processes. In chapter 4 we see how the existence theorem enables us to construct (infinitely extended) Gibbs, quantum-Bose and polymer processes. The so called polymer processes seem to be constructed here for the first time. In the last part of this thesis we prove that the family of cluster equations has certain stability properties with respect to the transformation of its solutions. At first this will be used to show how large the class of solutions of such equations is, and secondly to establish the cluster theorem of Kerstan, Matthes and Mecke in our setting. With its help we are able to enlarge the class of Polya processes to the so called branching Polya processes. The last sections of this work are about thinning and splitting of point processes. One main result is that the classes of Boson and Fermion processes remain closed under thinning. We use the results on thinning to identify a subclass of point processes with a signed Levy pseudo measure as doubly stochastic Poisson processes. We also pose the following question: Assume you observe a realization of a thinned point process. What is the distribution of deleted points? Surprisingly, the Papangelou kernel of the thinning, besides a constant factor, is given by the intensity measure of this conditional probability, called splitting kernel. / Ein Punktprozess ist ein Mechanismus, der zufällig ein lokalendliches Punktmaß realisiert. Ein Hauptresultat dieser Arbeit ist ein Existenzsatz für eine sehr große Klasse von Punktprozessen mit einem signierten Levy Pseudomaß L. Diese Klasse ist eine Erweiterung der Klasse der unendlich teilbaren Punktprozesse. Die verwendete Methode der Konstruktion ist eine Verbindung der klassischen Punktprozesstheorie, wie sie von Kerstan, Matthes und Mecke ursprünglich entwickelt wurde, mit der sogenannten Methode der Cluster-Entwicklungen aus der statistischen Mechanik. Ausgangspunkt ist eine Familie von signierten Radonmaßen. Diese definiert einerseits das Levysche Pseudomaß L; andererseits wird mit deren Hilfe der Prozess lokal definiert. Der Zusammenhang zwischen L und dem Prozess ist so, dass der Prozess die durch L bestimmte Integralgleichung (genannt Clustergleichung) löst. Wir zeigen, dass sich die Resultate aus der klassischen Theorie der unendlich teilbaren Punktprozesse auf natürliche Weise auf die neue Klasse der Punktprozesse mit signiertem Levy Pseudomaß erweitern lassen. So erhalten wir z.B. ein Kriterium für die Einfachheit und eine Charackterisierung durch die Clustergleichung für jene Punktprozesse. Unser erstes Hauptresultat in Kapitel 3 zur Analyse der konstruierten Prozesse ist ein Darstellungssatz der faktoriellen Momentenmaße. Mit dessen Hilfe werden wir die permanentischen respektive determinantischen Punktprozesse, die in die Klasse der Bosonen respektive Fermionen Prozesse fallen, identifizieren. Als ein Nebenresultat erhalten wir eine Darstellung der (reduzierten) Palm Kerne von unendlich teilbaren Punktprozessen. Im Kapitel 4 konstruieren wir mit Hilfe unseres Existenzsatzes unendlich ausgedehnte Gibbsche Prozesse sowie Quanten-Bose und Polymer Prozesse. Unseres Wissens sind letztere bisher nicht konstruiert worden. Im letzten Teil der Arbeit zeigen wir, dass die Familie der Clustergleichungen gewisse Stabilitätseigenschaften gegenüber gewissen Transformationen ihrer Lösungen aufweist. Dies wird erstens verwendet, um zu verdeutlichen, wie groß die Klasse der Punktprozesslösungen einer solchen Gleichung ist. Zweitens wird damit der Ausschauerungssatz von Kerstan, Matthes und Mecke in unserer allgemeineren Situation gezeigt. Mit seiner Hilfe können wir die Klasse der Polyaschen Prozesse auf die der von uns genannten Polya Verzweigungsprozesse vergrößern. Der letzte Abschnitt der Arbeit beschäftigt sich mit dem Ausdünnen und dem Splitten von Punktprozessen. Wir beweisen, dass die Klassen der Bosonen und Fermionen Prozesse abgeschlossen unter Ausdünnung ist. Die Ergebnisse über das Ausdünnen verwenden wir, um eine Teilklasse der Punktprozesse mit signiertem Levy Pseudomaß als doppelt stochastische Poissonsche Prozesse zu identifizieren. Wir stellen uns auch die Frage: Angenommen wir beobachten eine Realisierung einer Ausdünnung eines Punktprozesses. Wie sieht die Verteilung der gelöschten Punktkonfiguration aus? Diese bedingte Verteilung nennen wir splitting Kern, und ein überraschendes Resultat ist, dass der Papangelou-Kern der Ausdünnung, abgesehen von einem konstanten Faktor, gegeben ist durch das Intensitätsmaß des splitting Kernes.

L’hydrogénation sélective de l’acétylène est un processus fondamental pour l’industrie pétrochimique qui permet la purification de l’éthylène utilisé dans les réactions de polymérisation. Ce processus est promu par des catalyseurs au palladium, qui présentent une bonne sélectivité en éthylène par rapport au produit d’hydrogénation totale, c’est-à-dire l’éthane. Les catalyseurs de palladium pur sont malheureusement désactivés par des oligomères qui se forment comme sous-produits de la réaction d’hydrogénation. Les catalyseurs d’usage industriel sont, pour cette raison, plutôt des alliages de palladium avec d’autres métaux, comme par exemple, l’argent. Ces alliages réduisent la production des oligomères, sans pour autant les supprimer complètement. Ce travail de thèse a été focalisé sur la compréhension à l’échelle moléculaire de la formation de ce mélange d’oligomères, souvent appelée « huile verte ». Pour commencer, une approche de champ moyen a été développée pour déterminer rapidement l’état de la surface catalytique de l’alliage Pd-Ag en condition de réaction. Ce modèle a montré que l’acétylène est capable de réorganiser la couche de la surface et de générer des îles de palladium. Pour confirmer cette prédiction, nous avons effectué des simulations Monte Carlo en utilisant un Hamiltonien modèle. Ces calculs ont produits des résultats similaires au modèle analytique simple. Ayant attribué la formation des oligomères aux domaines de palladium ainsi obtenus, les étapes de d’oligomérisation ont été étudies et comparés à celles qui décrivent l’hydrogénation de l’acétylène. Les calculs, réalisé avec l’approximation de la théorie de la fonctionnelle de la densité (DFT), ont montré que la formation des oligomères est compétitive avec l’hydrogénation. En plus, les oligomères sont plus faciles à hydrogéner que l’acétylene et pourraient, donc, impacter négativement sur l’hydrogénation sélective de l’acétylène. Le rôle exact des îles de palladium sous conditions réalistes est encore à clarifier, sachant que le palladium est recouvert d’une grande variété d’espèces chimiques. Les techniques d’intelligence artificielle peuvent aider à atteindre ce but : nous avons ainsi démontré qu’il est possible d’interpoler les résultats des calculs DFT d’une façon automatique et de décrire l’énergie du système en série de coefficients « cluster ». Ceci permet de prendre en compte les interactions latérales entre espèces chimiques à la surface du palladium. / Selective hydrogenation of acetylene in ethylene-rich flows is a fundamental process in the petrochemical industry since it allows the purification of ethylene for polymer applications. The reaction is catalyzed by Pd, which features acceptable selectivity towards ethylene compared to the total hydrogenation product, ethane. Pure Pd is, however, deactivated by oligomeric byproducts, known as ”green oil” in the literature. Therefore, most industrial catalysts are Pd-Ag alloys, where Ag helps to suppress the secondary reactions. This work addresses the formation of initial oligomers on Pd and Ag-Pd catalysts. A mean field based theoretical model was built to efficiently screen the topology of the topper most layer of the alloy catalyst under relevant conditions. This model gave evidence for strongly favored Pd island formation. To confirm this result, the system was then re-investigated by means of Monte Carlo simulations including the effect of segregation. Emergence of large domains of Pd were confirmed over large ratios of Ag to Pd. Green oil is expected to form on these catalytically active islands. To obtain a detailed view on the oligomerization process, activation energies were computed both for hydrogenation and oligomerization steps by periodic density functional theory on Pd(111). Oligomerization was found to be competitive with hydrogenation, with the hydrogenation of the oligomers being among the fastest processes. The role of Pd domains to green oil formation is still to be clarified under realistic conditions, where the surface is covered by many different species. A step forward to this goal was taken by developing a machine-learning tool which automatically interpolates model Hamiltonians on graphical lattices based on DFT computations, accounting for lateral interactions and distorted adsorption modes on crowded surfaces.