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INVESTIGATING INTERFACIAL FERROMAGNETISM IN OXIDE HETEROSTRUCTURES USING ADVANCED X-RAY SPECTROSCOPIC AND SCATTERING TECHNIQUESPaudel, Jay, 0000-0002-3173-3018 12 1900 (has links)
In this dissertation, we utilized a wide range of complementary synchrotron-based X-ray spectroscopic and scattering techniques, notably X-ray absorption spectroscopy (XAS), hard X-ray photoelectron spectroscopy (HAXPES), standing-wave X-ray photoelectron spectroscopy (SW-XPS), and X-ray resonant magnetic reflectometry (XRMR), to understand and control the phenomenon of emergent interfacial ferromagnetism in strongly-correlated oxide heterostructures. This field holds great promise for the development of next-generation spintronic devices. In the heterostructures we investigated, neither of the parent oxide layers exhibits inherent ferromagnetism. Yet, when these layers are combined in an epitaxial film stack, charge-transfer phenomena give rise to an emergent ferromagnetic state at the interface. Throughout my graduate studies, I focused on studying such charge-transfer phenomena as the driving force for stabilizing interfacial ferromagnetism. This dissertation is structured around two main projects. The first project delves into the intriguing possibility of tuning the emergent interfacial ferromagnetism. More specifically, we investigated the mechanisms for suppressing interfacial charge transfer to gain control over and manipulate this magnetic phenomenon. In our second project, we explored a different facet of interfacial ferromagnetism, focusing on the origins of the imbalance in the magnitudes of the magnetic moment between the top and bottom interfaces in the same layer. Our investigation aimed to uncover the possible causes of this imbalance, ultimately leading us to scrutinize the role of defect states in this magnetic asymmetry.
In the first part of this dissertation, we investigated the thickness-dependent metal-insulator transition within LaNiO3 and how it impacts the electronic and magnetic states at the interface between LaNiO3 and CaMnO3. We present a direct observation of a reduced effective valence state in the interfacial Mn cations. This reduction is most pronounced in the metallic LaNiO3/CaMnO3 superlattice, where the above-critical LaNiO3 thickness of 6-unit cells triggers this phenomenon, facilitated by the charge transfer of the itinerant Ni 3d eg electrons into the interfacial CaMnO3 layer. In contrast, when we examine the insulating superlattice with a LaNiO3 thickness below the critical value (2-unit cells), we observe a homogeneous effective valence state of Mn throughout the CaMnO3 layers. This homogeneity is attributed to the suppression of charge transfer across the interface.
The second part of this dissertation delves deeply into the complexities of interfacial magnetism within the CaMnO3/CaRuO3 superlattices. Our experimental investigation unveiled an unexpected asymmetry in the strength of magnetism at these interfaces. Our findings suggest that within the superlattice CaMnO3/CaRuO3, the lower interface (CaRuO3/CaMnO3) exhibits a weaker magnetic moment when compared to the upper interface (CaMnO3/CaRuO3). This observation, supported by XRMR and XAS experimental data, was further clarified by first-principles density functional theory (DFT) calculations. Our calculations suggest that the observed magnetic asymmetry may be linked to the presence of oxygen vacancies at the interfaces. Our study significantly contributes to our understanding of interfacial ferromagnetism, potentially paving the way for controlling and manipulating this emergent property. This may be achieved by utilizing engineered defect states, offering exciting prospects for applications in the field of spintronics devices. / Physics
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Structure and electronic properties of atomically-layered ultrathin nickelate filmsGolalikhani, Maryam January 2015 (has links)
This work presents a study on stoichiometry and structure in perovskite-type oxide thin films and investigates the role of growth–induced defects on the properties of materials. It also explores the possibility to grow thin films with properties close or similar to the ideal bulk parent compound. A novel approach to the growth of thin films, atomic layer-by-layer (ALL) laser molecular beam epitaxy (MBE) using separate oxide targets is introduced to better control the assembly of each atomic layer and to improve interface perfection and stoichiometry. It also is a way to layer materials to achieve a new structure that does not exist in nature. This thesis is divided into three sections. In the first part, we use pulsed laser deposition (PLD) to grow LaAlO3 (LAO) thin films on SrTiO3 (STO) and LAO substrates in a broad range of laser energy density and oxygen pressure. Using x-ray diffraction (θ-2θ scan and reciprocal space mapping), transmission electron microscopy (TEM) and x-ray fluorescence (XRF) we studied stoichiometry and structure of LAO films as a function of growth parameters. We show deviation from bulk–like structure and composition when films are grown at oxygen pressures lower than 10-2 Torr. We conclude that the discussion of LAO/STO interfacial properties should include the effects of growth–induced defects in the LAO films when the deposition is conducted at low oxygen pressures, as is typically reported in the literature. In the second part, we describe a new approach to atomically layer the growth of perovskite oxides: (ALL) laser MBE, using separate oxide targets to grow materials as perfectly as possible starting from the first atomic layer. We use All laser MBE to grow Ruddlesden–Popper (RP) phase Lan+1NinO3n+1 with n = 1, 2, 3 and 4 and we show that this technique enables us to construct new layered materials (n=4). In the last and main section of this thesis, we use All laser MBE from separate oxide targets to build the LaNiO3 (LNO) films as near perfectly as possible by depositing one atomic layer at a time. We study the thickness dependent metal-insulator transition (MIT) in ultrathin LNO films on an LAO substrate. In LNO, the MIT occurs in thin films and superlattices that are only a few unit cells in thickness, the understanding of which remains elusive despite tremendous effort devoted to the subject. Quantum confinement and structure distortion have been evoked as the mechanism of the MIT; however, first-principle calculations show that LaNiO3 remains metallic even at one unit cell thickness. Here, we show that thicknesses of a few unit cells, growth–induced disorders such as cation stoichiometry, oxygen vacancies, and substrate-film interface quality will impact the film properties significantly. We find that a film as thin as 2 unit cells, with LaO termination, is metallic above 150 K. An oxygen K-edge feature in the x-ray absorption spectra is clearly inked to the transition to the insulating phase as well as oxygen vacancies. We conclude that dimensionality and strain are not sufficient to induce the MIT without the contribution of oxygen vacancies in LNO ultrathin films. Dimensionality, strain, crystallinity, cation stoichiometry, and oxygen vacancies are all indispensable ingredients in a true control of the electronic properties of nanoscale strongly–correlated materials. / Physics
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Scattering of vibrationally excited NO from vanadium dioxideMeling, Artur 21 January 2020 (has links)
No description available.
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Iontronic - Étude de dispositifs à effet de champ à base des techniques de grilles liquides ioniques / Iontronics - Field effect study of different devices, using techniques of ionic liquid gatingSeidemann, Johanna 20 October 2017 (has links)
Les liquides ioniques sont des fluides non volatiles, constitués de cations et d’anions, qui sont conducteurs ioniques, isolants électriques, et peuvent avoir des valeurs de capacité très élevées. Ces liquides sont susceptibles non seulement de remplacer les électrolytes solides, mais également de susciter des champs électriques intenses (>SI{10}{megavoltpercentimetre}) au sein d’une couche dite double couche électronique (electric double layer, EDL) à l’interface entre le liquide et le matériau sur lequel il est déposé. Ceci conduit à une injection de porteurs de charge bidimensionelle avec des densités allant jusqu’à SI{e15}{cm^{-2}}. Cet effet de grille remarquablement fort des liquides ioniques est réduit en présence d’états piégés ou de rugosité de surface. À cet égard, les dicalchogénures de métaux de transitions, de très haute qualité cristalline et atomiquement plats, font partis des semi-conducteurs les plus adaptés aux grilles EDL.Nous avons réalisé des transistors à effet de champ avec des EDL dans des nanotubes multi-couches de ce{WS2}, avec des performances comparables à celles de transistors EDL sur des ilots de ce{WS2}, et meilleurs que celles de nanotubes de ce{WS2} avec une grille solide. Nous avons obtenu des mobilités allant jusqu’à SI{80}{squarecentimetrepervoltpersecond} pour les porteurs n et p, et des ratios de courants on/off dépassant SI{e5}{} pour les deux polarités. Pour de forts dopages de type électron, les nanotubes ont un comportement métallique jusqu’à basse température. De plus, utiliser un liquide ionique permet de créer une jonction pn de manière purement électrostatique. En prenant avantage de cet effet, nous avons pu réaliser un transistor photoluminescent dans un nanotube.La possibilité de susciter de très forte densités de charges donne la possibilité d’induire des phases métalliques ou supraconductrices dans des semi-conducteurs a large bande interdite. Nous avons ainsi réussi à induire par effet de champ une phase métallique à basse température dans du diamant intrinsèque avec une surface hydrogénée, et nous avons obtenu un effet de champ dans du silicone dopé métallique.Les liquides ioniques offrent beaucoup d’avantages, mais leur champ d’application est encore réduit par l’instabilité du liquide, ainsi que par les courants de fuites et l’absorption graduelle d’impuretés. Un moyen efficace de s’affranchir de ces inconvénients, tout en conservant la possibilité d’induire de très fortes densités de porteurs, est de gélifier le liquide ionique. Nous sommes allés plus loin en fabriquant des gels ioniques modifiés, avec les cations fixés sur une seule surface et les anions libres de se mouvoir au sein du gel. Cet outil nous a permis de réaliser une nouvelle diode à effet de champ de faible puissance. / Ionic liquids are non-volatile fluids, consisting of cations and anions, which are ionically conducting and electrically insulating and hold very high capacitances. These liquids have the ability to not only to replace solid electrolytes, but to create strongly increased electric fields (>SI{10}{megavoltpercentimetre}) in the so-called electric double layer (EDL) on the electrolyte/channel interface, which leads to the injection of 2D charge carrier densities up to SI{e15}{cm^{-2}}. The remarkably strong gate effect of ionic liquids is diminished in the presence of trapped states and roughness-induced surface disorder, which points out that atomically flat transition metal dichalcogenides of high crystal quality are some of the semiconductors best suited for EDL-gating.We realised EDL-gated field-effect transistors based on multi-walled ce{WS2} nanotubes with operation performance comparable to that of EDL-gated thin flakes of the same material and superior to the performance of backgated ce{WS2} nanotubes. For instance, we observed mobilities of up to SI{80}{squarecentimetrepervoltpersecond} for both p- and n-type charge carriers and our current on-off ratios exceed SI{e5}{} for both polarities. At high electron doping levels, the nanotubes show metallic behaviour down to low temperatures. The use of an electrolyte as topgate dielectric allows the purely electrostatic formation of a pn-junction. We successfully fabricated a light-emitting transistor taking advantage of this utility.The ability of high charge carrier doping suggests an electrostatically induced metal phase or superconductivity in large gap semiconductors. We successfully induced low temperature metallic conduction into intrinsic diamond with hydrogen-terminated surface via field-effect and we observed a gate effect in doped, metallic silicon.Ionic liquids have many advantageous properties, but their applicability suffers from the instability of their liquid body, gate leakage currents and absorption of impurities. An effective way to bypass most of these problems, while keeping the ability of ultra-high charge carrier injection, is the gelation of ionic liquids. We even went one step further and fabricated modified ion gel films with the cations fixed on one surface and the anions able to move freely through the film. With this tool, we realised a novel low-power field-effect diode.
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MULTISCALE MODELING OF POLYMER PROCESSING AND ELECTRONIC MATERIALSShukai Yao (17419314) 20 November 2023 (has links)
<p dir="ltr">Computational materials science has emerged as a powerful technique to discover and develop new materials in past decades, primarily because accurate computational modeling can act as guidance before performing experiments that are expensive and time-consuming. However, modeling material behaviors across different scales of length and time poses a challenge, accentuating the importance of choosing appropriate levels of approximations and theories. First principles calculations based on density functional theory (DFT) are essential to predict the electronic structure of periodic crystalline systems. We will discuss a prediction of chemical doping induced metal-to-insulator transition (MIT) of transition metal perovskites owing to the variation of the electronic occupation. Nevertheless, electronic structure predictions based on DFT are not without limitation as it fails when treating strongly correlated electronic system due to the over-delocalization of valence electrons. In principle, adding on-site Hubbard U corrects this error with a low computational cost. Using an example of a two-dimensional rare-earth MXene, we demonstrate the essence of choosing the appropriate U value self-consistently for the prediction of electronic and magnetic configurations. Furthermore, molecular dynamics (MD) can be employed to study the dynamic evolution of complex condensed systems with thousands to millions of atoms at the atomistic and molecular levels. Carbon fiber manufacturing is an established industry, though the fiber produced achieves only 10% of its theoretical tensile strength. Therefore, optimizing the carbon fiber processing is a pressing topic. To achieve this, we study two steps, spinning and stabilization, of polyacrylonitrile (PAN)-based fiber fabrication at the molecular level using MD. We will discuss the realistic molecular structure of the spun PAN and the properties affected by its structural heterogeneity. Moreover, for the following step, we develop a PAN stabilization simulator, an automated workflow that addresses the underlying chemistry and the molecular-level structure-property relationship, often inaccessible through experiments.</p>
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Electrical Transport in Si:P and Ge:P δ-doped SystemsShamin, Saquib January 2015 (has links) (PDF)
Doped semiconductor systems have for decades provided an excellent platform to study novel concepts in solid state physics such as quantum hall effect, metal-to-insulator transition (MIT), weak localization and many body interaction effects. Doped Si, in particular and doped Ge has been studied extensively to study MIT as a function of dopant concentration or uniaxial stress. Spin transport phenomena have also been probed in bulk doped Si. All the previous studies involved bulk doped semiconductors where the dopants are spread through the bulk of the material. However spatial confinement of dopants in one or more dimensions may lead to a range of exotic quantum phenomena such as an absence of Anderson localization in one and two dimensions, hole-mediated (Nagaoka) ferromagnetism and new modes of quantum transport, when the Fermi energy lies at or close to centre of the band. Since many of these phenomena are inherent to lower dimensions, it has been hard to observe these experimentally in bulk doped crystals of Si and Ge. Recent advances in the monolayer doping techniques with atoms that closely pack on a surface, has made it possible to design a new class of 2D electron systems (2DES) in elemental semiconductors, such as Si and Ge, where the dopant (P) atoms are confined within a few atomic planes. The uniqueness of these systems lies not merely in the planar doping profile in bulk semiconductors that allow versatile designs of nanodevices, such as 1D wires, tunnel gaps and quantum dots, but also that it is now possible to study the interplay of wavefunction overlap and commensurability effects in 2D with unprecedented control. From an application perspective as well these systems are technologically important as they are aimed at being the building blocks of a solid state quantum computer. This thesis deals with investigating the electrical transport properties, both average (resistance) and dynamic (noise) of doped semiconductor systems in 2D delta layers, 1D wires and 0D quantum dots.
We find that the 2D δ-layers shows suppressed low frequency noise and the Hooge parameter of delta doped Si is about five to six orders of magnitude lower when compared to bulk doped Si in metallic regime. At low temperatures, the noise arises in these systems due to universal conductance fluctuations. For 1D wires as well we find that the Hooge parameter is one of the lowest among various 1D systems including carbon
nanotubes. We identify that charge traps in the Si/SiO2 are responsible for causing noise in δ-doped systems. Then we study the noise and transport in 2D delta layers as a function of doping density (and hence carrier density and interaction). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting a spontaneous breaking of time reversal symmetry driven by strong Coulomb interactions. At low doping density we observe metal-like dependence of resistance on temperature at low temperatures, raising the possibility of a metallic ground state in 2D at 0 K in doped semiconductors. Finally we probe the low density devices (with broken time reversal symmetry) using superconducting Al as ohmic contacts. Anomalous increase in resistance below the superconducting transition temperature of Al and magnetoresistance with a sharp peak at 0 T is observed. Additionally we find that when the Al is superconducting, there exists a non-local resistance in low doped devices.
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Etude des états fondamentaux dans des systèmes supraconducteurs désordonnés de dimension 2 / Study of accessible ground states in two-dimensional disordered superconductorsHumbert, Vincent 16 June 2016 (has links)
Un matériau 3D, initialement supraconducteur, peut avoir différents états fondamentaux dépendamment de son degré de désordre : supraconducteur, métallique ou isolant. A dimension réduite (2D), la localisation d’Anderson interdit théoriquement tout état métallique. La modification du désordre induit alors une Transition directe Supraconducteur-Isolant (TSI). La présence de fortes interactions électroniques, non prises en compte dans les théories conventionnelles, pourrait cependant remettre en cause ce paradigme et laisser émerger des états métalliques 2D, complexifiant l’image généralement admise de la TSI. Ainsi, des travaux récents ont révélé la présence de deux phases métalliques distinctes dans les films minces de a-NbxSi1-x, s’intercalant entre les états supraconducteur et isolant.Durant cette thèse, nous avons étudié les propriétés de transport électronique à basse fréquence et à très basse température (T<1K) de films minces de NbxSi1-x amorphes afin de caractériser l’évolution de l’état fondamental en fonction du désordre. Celui-ci a été modifié dans nos films en jouant sur la température de recuit, l’épaisseur et la composition. Nous nous sommes alors attardés sur la destruction de ces états métalliques vers un état isolant. L’analyse des lois de conduction dans le régime isolant nous a permis de quantifier l’évolution de ses propriétés – notamment des énergies caractéristiques – en fonction du désordre. Nous avons alors pu conclure que la phase isolante pouvait être essentiellement décrite par un modèle fermionique. A moindre désordre, dans la phase métallique 2D adjacente à l’isolant, nous avons mis en évidence des signes précurseurs de l’état isolant qui évoluent continument jusqu’à et à travers la Transition Métal 2D-Isolant. Nous proposons une interprétation de l’ensemble de nos résultats impliquant deux canaux parallèles dont l’importance relative est déterminée par le désordre : l’un est fermionique, l’autre gouverné par des fluctuations supraconductrices qui persistent même lorsque la cohérence macroscopique a disparu. L’état métallique est alors dominé par ces dernières, alors que, dans l’isolant, la localisation des excitations fermioniques l’emporte.Une seconde partie de la thèse s’est concentrée sur le développement expérimental d’un dispositif de calibration large bande dédié à l’étude de films minces en réflectométrie haute fréquence (GHz) à basses températures (T<4K). Ce dispositif a pour but, lors d’une unique mise à froid, de mesurer successivement la réflexion de références connues ainsi que de l’échantillon. La calibration obtenue permet ainsi de s’affranchir de l’environnement micro-onde et d’obtenir la valeur absolue de l’impédance complexe de ces films. Les résultats obtenus sur des films minces supraconducteurs de Vanadium, comparés aux théories de la supraconductivité, permettent une première validation du dispositif et de son principe de fonctionnement en vue d’une utilisation sur des systèmes plus complexes, tels que les films minces proches de la TSI. / An initially superconducting 3D material can have different ground states, depending on its disorder : superconducting, metallic or insulating. At lower dimensionality, Anderson localization theoretically forbids any metallic state. A change in disorder then induces a direct Superconductor-to-Insulator Transition (SIT). The presence of strong Coulomb interactions, which are not taken into account in conventional theories, may disrupt this paradigm and enable the emergence of 2D metallic phases, thus complicating the generally admitted picture for the SIT. Indeed, recent work has revealed the existence of two distinct metallic phases in a-NbxSi1-x thin films, in between the superconducting and insulating states.During this work, we have studied the low frequency transport properties of amorphous NbxSi1-x films at low temperatures (T<1K), in order to characterize the evolution of their ground state with disorder. In our films, disorder has been tuned by varying the heat treatment temperature, the thickness or the composition. We have then focused on the destruction of these metallic states, giving rise to an insulating state. Through the analysis of conduction laws in the insulating regime, we have quantified the evolution of its properties – in particular its characteristic energies – as disorder is varied. We could then conclude that the insulating phase can essentially be accounted for by a fermionic model. At lower disorder level, in the 2D metallic phase neighboring the insulator, we have evidenced precursor signs of the insulating state which continuously evolve until and through the 2D Metal-to-Insulator Transition. We offer an interpretation of all our results implying the existence of two parallel channels which relative importance is determined by the sample disorder level : one is fermionic, the other governed by superconducting fluctuations which persist even when the macroscopic phase coherence is lost. The metallic state is then dominated by the latter, whereas, in the insulator, fermionic excitations prevail.In a second part, we report on the experimental development of a calibration device for the broadband reflectometry measurement of thin films at microwave frequencies (GHz) and low temperatures (T<4K). This apparatus aims at measuring, during a single cool down, the reflection of known references as well as of the sample. The obtained calibration enables to obtain the absolute value of the films complex impedance, independently of the microwave environment. The results obtained on superconducting Vanadium films, compared with theories of superconductivity, enabled a first validation of the setup and of its working principle. This calibration device is therefore operational to measure more complex systems, such as thin films in the vicinity of the SIT.
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X-ray magnetic circular dichroism in iron/rare-earth multilayers and the impact of modifications of the rare earth's electronic structure / Magnetischer Röntgendichroismus in Eisen/Seltene Erd-Vielfachschichten und der Einfluß von Veränderungen der elektronischen Struktur der Seltenen ErdeMünzenberg, Markus 24 October 2000 (has links)
No description available.
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Electronic transport properties of thermoelectric materials with a focus on clathrate compoundsTroppenz, Maria 12 October 2021 (has links)
Thermoelektrische Bauelemente ermöglichen die Erzeugung von Elektrizität aus überschüssiger Wärme, wie sie in großen Mengen in Geräten und Prozessen entsteht. Effiziente Thermoelektrika benötigen eine hohe thermoelektrische Gütezahl, die durch elektronische und thermische Transporteigenschaften der Materialien bestimmt wird. Die Dissertation untersucht zunächst die elektronischen Transporteigenschaften zweier hochaktueller thermoelektrischer Materialien, des Schichtsystems SnSe und einer komplexen Klathrat-Legierung. Deren theoretische Beschreibung benötigt unterschiedliche Methoden, die während dieses Dissertationsprojektes implementiert, erweitert oder entwickelt wurden. Die Temperaturabhängigkeit der Leitfähigkeit von SnSe wurde mittels der Boltzmann-Transportmethode in Relaxationszeitnäherung untersucht. Wir zeigen, dass nur bei gleichzeitiger Einbeziehung von thermischer Ausdehnung des Kristallgitters und Elektron-Phonon-Streuprozessen eine gute Übereinstimmung mit Experimenten erreicht wird. Die Eigenschaften des Typ-I-Klathrats Ba8AlxSi46-x sind sowohl von der Stöchiometrie als auch von der Al-Konfiguration, d.h. der Anordnung der Al-Atome im Wirtsgitter, abhängig. Für x=16 wurde der Grundzustand als hableitend bestimmt, während Konfigurationen mit höheren Energien metallisch sind. Wir erhalten eine zuverlässige Beschreibung der elektronischen, strukturellen und Transporteigenschaften von Ba8AlxSi46-x bei endlichen Temperaturen durch Mittlungen über Konfigurationen. Mittels einer neu entwickelten Methode zur Berechnung der temperaturabhängigen effektiven Bandstruktur von Legierungen beobachten wir ein temperaturbedingtes Schließen der Bandlücke bei x=16, was mit einem Phasenübergang von partieller Ordnung zu Unordnung bei 582K einher geht. Basierend auf Gedächtnisfunktions-Modellen präsentieren wir ferner eine neue Ab-initio-Methode zur Berechnung der elektrischen Leitfähigkeit von Festkörpern mit einem Unordungspotential beliebiger Kopplungsstärke. / Thermoelectric devices convert heat into electricity, thus enabling the reuse of waste heat produced by all kinds of engines. To make this conversion process profitable, materials with a high thermoelectric figure of merit, ZT, are demanded. ZT depends on electronic and thermal transport properties. In this thesis, we study the electronic transport properties of two emerging thermoelectric materials, the layered material SnSe and a complex type-I clathrate alloy. Their reliable description requires different methodologies, that has been implemented, extended, or developed during this PhD project. For SnSe, the temperature dependence of the conductivity and the Seebeck coefficient is studied using the Boltzmann transport approach in the relaxation time approximation. We show that only by simultaneously accounting for thermal lattice expansion and electron-phonon coupling, a good agreement with experiment is reached. The properties of the type-I clathrate Ba8AlxSi46-x are determined, on the one hand, by its composition, and, on the other hand, by the configuration, i.e., the arrangement of the Al atoms in the host lattice. At the charge-compensated composition x=16, the ground-state configuration is found to be semiconducting, while configurations higher in energy are metallic. We obtain a realistic description of the electronic, structural, and transport properties of Ba8AlxSi46-x at finite temperature by using configurational thermodynamic averages. From a newly developed method to compute the finite-temperature effective band structure of alloys, we observe a temperature-driven closing of the band gap for x=16, which is concomitant with a partial order-disorder phase transition at 582K. We further present a novel ab initio memory-function approach for solids that enables the calculation of the electrical conductivity of solids in a disorder potential at arbitrary coupling strength. An application of the developed formalism is demonstrated with the example of sodium.
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