Aim of this work is a systematic investigation of the modes of thermal convection (onset of convection, stationary solutions, periodic solutions, chaotic states) in a material whose properties vary with depth like the material of Earth mantle; the problem was solved in Cartesian geometry. The Stokes equation set was consistently formulated in the spectral region not only horizontally but also vertically, and thus in the model consisting of layers with a constant viscosity but with general course of velocity and temperature in each layer. This equation set was solved with matrix method for each wave vector. Thermal equation was solved in the spatial domain and the transition of velocity and temperature between spectral and spatial domains was performed using the fast Fourier transform. This procedure allows a straightforward parallelization, thereby opening the possibility of not only two-dimensional but also three-dimensional modeling and modeling of chaotic regimes. On the basis of the numerical difficulties of method presented here an model investigated in finite elemens was used. The basic modes of thermal convection were then investigated using model assembled in the software Comsol. Powered by TCPDF (www.tcpdf.org)

Title: Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics Author: Hana Šustková Department: Department of Geophysics Supervisor: doc. RNDr. Ctirad Matyska, DrSc. Abstract: This thesis concerns the study of convection in Cartesian models in two and three dimensions. Specifically, it deals with the systematic monitoring of critical Rayleigh numbers based on the geometry model, on the functional dependence of the viscosity or of other parameters. Models has been created with layered viscosity and constant or temperature- and depth- dependent parameters (thermal expansion and conductivity). The system has been described by conventional dimensionless Boussinesq approximation. Part of the work is devoted to the application of matrix method for solving the appropriate Stokes flow and use of Euler's method for solving the thermal equation. The actual calculations were then performed in an environment of commercial software Comsol and thus by using the finite element method. It was shown that the dominant influence on the critical Rayleigh numbers has a viscosity model (with increasing viscosity the critical Rayleigh numbers increase), other important parameter is system's geometry (larger size and dimension of the geometry reduce the critical Rayleigh number). The...

Halbleitermaterialien sind in den elektrischen Anwendungen der heutigen Zeit unerlässlich geworden. In dieser Arbeit wird der Fokus auf die Untersuchung der elektrischen und thermischen Eigenschaften von zwei Halbleiterklassen gelegt. Zum einen wird mit -Ga2O3 ein Mitglied der Klasse der transparenten leitfähigen Oxide untersucht.Hier wurden die elektrischen Eigenschaften von dünnen Schichten (Dicke von 28nm-225nm) und Volumenkristallen temperaturabhängig untersucht.Dabei zeigt sich bei Volumenkristallen und mindestens 150nm dicken Schichten eine Steigerung der elektrischen Leitfähigkeit bis 100K durch die Streuung von Elektronen an Störstellen und bei Temperaturen über 100K wieder ein Abfall der elektrischen Leitfähigkeit durch Elektron-Phonon-Wechselwirkung. Die Untersuchung der thermische Leitfähigkeit von beta-Ga2O3 zeigt ein anisotropes Verhalten mit minimalen Werten in [100]-Richtung und maximalen Werten in [010]-Richtung. Die Temperaturabhängigkeit der thermischen Eigenschaften zeigt eine Verringerung der thermischen Leitfähigkeit und der thermischen Diffusivität mit steigender Temperatur. Eine zweite untersuchte Materialklasse ist die der Kesterite. Zu dieser Kristallstruktur wurden zwei Elementkonfigurationen untersucht, Kupfer-Zink-Zinn-Sulfid und Kupfer- Zink-Zinn-Selenid. Der Transport bei Raumtemperatur und darunter findet über verschiedene Tunnelprozesse lokalisierter Ladungsträger statt. Zusätzlich wird auf die Veränderung der elektrischen Eigenschaften durch die Kristallinität und Komposition eingegangen. Die thermischen Eigenschaften zeigen analog zum beta-Ga2O3 eine Dominanz der Phonon-Phonon-Umklapp-Streuung bei hohen Temperaturen, während bei niedrigen Temperaturen Streuung an Störstellen und Grenzflächen vorherrscht. Methodisch zeigt diese Arbeit unterschiedlichste Messmethoden zur Charakterisierung der elektrischen und thermischen Eigenschaften, welche die Standardmethoden sowohl nutzen, als auch sinnvoll erweitern. / Semiconductors are essential for electronic applications nowadays. Here, the electrical and thermal properties of two semiconductor classes with huge application potential are investigated. As a transparent conducting oxide beta-Ga2O3 is investigated. In this work, the temperature dependent electrical properties were investigated for bulk materials and thin films. An increase in the electrical conductivity until 100K is found through electron-impurity-scattering and a decrease at higher temperatures through electron-phonon-scattering for for films with a thickness of at least 150nm. The investigation of the thermal properties of -Ga2O3 show an anisotropy for the different crystal orientations with minimal primary axis values for the [100]-direction and maximal values for the [010]-direction. The temperature-dependence of the thermal properties shows a decease in conductivity and diffusivity for increasing temperature. For temperatures over 150K phonon-phonon-Umklapp-scattering can explain the measured values. For low temperatures phonon-impurity scattering is most likely the dominant scattering mechanism. A second investigated material class are kesterites. For this crystal structure two configurations were investigated, copper-zinc-tin-sulfide and copper-zinc-tin-selenide. The electrical properties show semiconducting characteristics with p-type conduction. The transport processes are defined through localised thermal activated tunneling within the band gap. Other reductions of the mobility are found by the crystalinity and the composition of the materials. The thermal properties show dominant phonon-phonon- Umklapp-scattering at higher temperatures and phonon-impurity-scattering for lower temperatures in a similar way as in beta-Ga2O3. This work shows new implemented measurement methods for investigating electrical and thermal properties as extentions to common methods.

Kolmaterial, såsom kolfibrer och kolskum, används som värmeisolatorer i applikationer vid höga temperaturer. För närvarande härleds dessa material från fossilbaserade källor, vilket tyder på ett behov av att hitta alternativa kandidater baserade på förnybara källor. Detta examensarbete undersökte möjligheten att använda kraftlignin som ett förnyelsebart startmaterial för framställning av kolskum med värmeisoleringsegenskaper. Två kraftligniner av barrträd med olika molekylvikter och ett kraftlignin av lövträd användes. De tre kraftligninerna karboniserades vid 1000°C efter att ha blandats i olika förhållanden och kombinationer (formuleringen av råmaterialet). Formuleringen av råmaterialet påverkade densiteten och porositeten hos de erhållna materialen, vilket i sin tur ledde till skillnader i kompressionsstyrkan och värmeledningsförmågan hos de erhållna kolskummen. Kolskummen hade olika värmeledningsförmåga (0,11-0,35 W/mK), porositet (80,55-97,53%) och densitet (0,08-0,42 g/cm3). För skummet med den högsta densiteten uppskattades krossstyrkan till cirka 10,03 MPa vilket är jämförbart med kommersiellt använda kolskum för högtemperaturisolerande applikationer. Kolskummens värmeledningsförmåga var inom omfånget för kommersiellt använda kolskum för högtemperaturapplikationer. Detta arbete visar möjligheten att tillverka kolskum från 100% kraftlignin som har liknande egenskaper som kommersiellt tillgängliga termiska isoleringsmaterial för högtemperaturapplikationer. / Carbon materials, such as carbon fibres and carbon foams, are used as thermal insulators in high-temperature applications. At present, these materials are derived from fossil-based sources, which suggests a need of finding alternatives candidates based on renewables. This thesis work investigated the possibility of using kraft lignin as a renewable starting material for the preparation of carbon foams with thermal insulation properties. Two softwood kraft lignins with different molecular weights and a hardwood kraft lignin were used. The three kraft lignins were carbonized at 1000°C after being mixed in different ratios and combinations (precursor formulation). The precursor formulation affected the density and porosity of the obtained materials, which in turn led to differences in compression strength and thermal conductivity of the carbon foams derived. The obtained carbon foams had different thermal conductivities (0.11-0.35 W/mK), porosity (80.55-97.53%) and density (0.08-0.42 g/cm3). For the foam with the highest density, the crushing strength was estimated to approximately 10.03 MPa which is comparable to commercially used carbon foams for high-temperature insulating applications. The thermal conductivity of the prepared carbon foams was in the range of commercially used carbon foams for high-temperature applications. This work demonstrates the possibility of preparing carbon foams from 100% kraft lignin which has properties similar of commercially available insulating materials for high-temperature applications.

<div>The recent decades have witnessed increased efforts to push the efficiency of energy systems beyond existing limits in order to keep pace with the rising global energy demands. Such efforts involve finding bulk materials and nanostructures with desired thermal properties such as thermal conductivity (k). For example, identifying high k materials is crucial in thermal management of vertically integrated circuits (ICs) and flexible nanoelectronics, which will power the next generation personal computing devices. On the opposite end of the spectrum, designing ultra-low k materials is essential for improving thermal barrier coatings in turbines and creating high performance thermoelectric (TE) devices for waste heat harvesting. In this dissertation, we identify nanostructures with such extreme thermal transport properties and explore the underlying phonon and photon transport mechanisms. Our approach follows two main avenues for evaluating potential candidates: (a) high fidelity atomistic simulations and (b) rapid machine learning-based property prediction and design optimization. The insight gained into the governing physics enables us to theoretically predict new materials for specific applications requiring high or low k, propose accelerated design optimization pathways which can significantly reduce design time, and advance the general understanding of energy transport in semiconductors and dielectric materials.</div><div><br></div><div>Bi2Te3, Sb2Te3 and nanostructures have long been the best TE materials due to their low κ at room temperatures. Despite this, computational studies such as molecular dynamics (MD) simulations on these important systems have been few, due to the lack of a suitable interatomic potential for Sb2Te3. We first develop interatomic potential parameters to predict thermal transport properties of bulk Sb2Te3. The parameters are fitted to a potential energy surface comprised of density functional theory (DFT) calculated lattice energies, and validated by comparing against experimental and DFT calculated lattice constants and phonon properties. We use the developed parameters in equilibrium MD simulations to calculate the thermal conductivity of bulk Sb2Te3 at different temperatures. A spectral analysis of the phonon transport is also performed, which reveals that 80% of the total cross-plane k is contributed by phonons with mean free paths (MFPs) between 3-100 nm. </div><div><br></div><div>We then use MD simulations to calculate phonon transport properties such as thermal conductance across Bi2Te3 and Sb2Te3 interface, which may account for the major part of the total thermal resistance in nanostructures. By comparing our MD results to an elastic scattering model, we find that inelastic phonon-phonon scattering processes at higher temperatures increases interfacial conductance by providing additional channels for energy transport. Finally, we calculate the thermal conductivities of Bi2Te3/Sb2Te3 superlattices (SLs) of varying period. The results show the characteristic minimum thermal conductivity, which is attributed to the competition between incoherent and coherent phonon transport regimes. Our MD simulations are the first fully predictive studies on this important TE system and pave the way for further exploration of nanostructures such as SLs with interface diffusion and random multilayers (RMLs).</div><div><br></div><div>The MD simulations described in the previous section provide high-fidelity data at a high computational cost. As such, manual intuition-based search methods using these simulations are not feasible for searching for low-probability-of-occurrence systems with extreme thermal conductivity. In view of this, we use machine learning (ML) techniques to accelerate and efficiently perform nanostructure design optimization within such large design spaces. First, we use a Genetic Algorithm (GA) based optimization method to efficiently search the design space of fixed length Si/Ge random multilayers (RMLs) for the structure with lowest k, which is found to be lower than the SL k by 33%. By comparing thermal conductivity and interface resistances between optimal and sub-optimal structures, we identify non-intuitive trends in design parameters such as average period and degree of randomness of layer thicknesses. </div><div><br></div><div>While machine learning (ML) has shown increasing effectiveness in optimizing materials properties under known physics, its application in discovering new physics remains challenging due to its interpolative nature. We demonstrate a general-purpose adaptive ML-accelerated search process that can discover unexpected lattice thermal conductivity (k) enhancement in aperiodic superlattices (SLs) as compared to periodic superlattices, with implications for thermal management of multilayer-based electronic devices. We use molecular dynamics simulations for high-fidelity calculations of k, along with a convolutional neural network (CNN) which can rapidly predict k for a large number of structures. To ensure accurate prediction for the target unknown SLs, we iteratively identify aperiodic SLs with structural features leading to locally enhanced thermal transport and include them as additional training data for the CNN. The identified structures exhibit increased coherent phonon transport owing to the presence of closely spaced interfaces.</div><div><br></div><div>We also demonstrate the application of ML in optimization of photonic multilayered structures with enhanced reflectivity to radiation heat flux, which is required for applications such as high temperature thermal barrier coatings (TBCs). We first perform a systematic variation of design parameters such as total thickness and average layer thickness of CeO2-MgO multilayers, and quantify their influence on the spectral and total reflectivity. The effect of randomization of layer thicknesses is also studied, which is found to increase the reflectivity due to localization of photons in certain spatial regions of the multilayer structure. Next, we employ a GA search method which can efficiently identify RML structures with reflectivity enhancements of ~22%, 20%, 20% and 10% over that obtained in randomly generated RML structures for total thicknesses of 5,10,20 and 30 microns respectively. We also calculate the spectral reflectivity and the field intensity distribution within the optimal and sub-optimal RML structures. We find that the electric field intensity can be significantly enhanced within certain spatial regions within the GA-optimized RMLs in comparison to non-optimized and periodic structures, which implies the high degree of randomness-induced photon localization leading to enhanced reflectivity in the GA-optimized structures.</div><div><br></div><div>In summary, our work advances the design or search for materials and nanostructures with targeted thermal transport properties such as low and high thermal conductivity and high reflectivity. The new insights provided into the underlying physics will guide the design of promising nanostructures for high efficiency energy systems. </div><div><br></div>

Cette thèse de doctorat porte sur l'étude théorique de la conductivité thermique du réseau dans le bismuth semi-métallique et sur les stratégies pour réduire la conductivité thermique en vue d'applications pour réduire l'échauffement dans les circuits électroniques, et pour la thermoélectricité. J'ai utilisé des méthodes avancées de résolution de l'équation de transport de Boltzmann pour les phonons, et de calcul ab initio des éléments de matrice de l'interaction phonon-phonon. J'ai calculé la dépendance en température de la conductivité thermique du réseau dans le matériau en volume en excellent accord avec les rares expériences disponibles. J'ai obtenu une description très précise, à l'échelle microscopique, du transport de la chaleur et j'ai quantifié la contribution des porteurs de charge à la conductivité thermique totale. J'ai démontré que la nano-structuration et la photo-excitation sont des moyens très efficaces dans le bismuth de contrôler la diffusion des phonons qui portent la chaleur, respectivement par interaction avec les bords de l'échantillon, et par interaction phonon-phonon. En contrôlant l'équilibre entre ces deux derniers effets, j'ai prédit de façon exhaustive l'effet de réduction pour différentes températures et tailles de nanostructures, pour des mono et poly-cristaux, semi-conducteurs ou semi-métalliques. Enfin, j'ai étudié l'élargissement anharmonique des phonons acoustiques et optiques, et j'ai déterminé pour chacun les interactions majeures qui contribuent à l'élargissement. L'atténuation du son a été prédite dans le bismuth pour de futures expériences. L'approximation des grandes longueurs d'ondes [long-wave approximation (LWA)] a été validée pour le bismuth et ses limites ont été déterminées. / This work is devoted to the theoretical investigation of the heat conduction in bulk bismuth and the possible strategies for its reduction. Thermal properties of Bi are extremely interesting because of its low thermal conductivity that makes this material suitable for the thermal management applications. Moreover, bismuth is an excellent model substance for the study of thermoelectricity and bismuth-based compounds such as Bi2 Te3 and Bi2 Se3 which are typical thermoelectric materials used in industrial applications.In collaboration with L. Paulatto (IMPMC), G. Fugallo (Ecole Polytechnique), F. Mauri(IMPMC) and M. Lazzeri (IMPMC) I have applied the recently developed advanced methods of the solution of the Boltzmann transport equation (BTE) and of the phonon-phonon matrix elements calculation to describe thermal transport in bismuth. I have obtained the temperature dependence of the lattice thermal conductivity which is in excellent agreement with experiment. Moreover I am able to predict the lattice thermal conductivity (LTC) at temperatures at which it has not been measured. I have found that most of heat is carried by the acoustic phonons. However, the optical phonons were shown to play an important role by modulating the magnitude of the acoustic-optical phonon interaction (AOPI) and thus the value of the lattice thermal conductivity. Furthermore, I have shown that the available experimental data for the lattice thermal conductivity for polycrystalline thin-films are remarkably explained by my calculations, which enables me to predict the effect of the LTC size reduction for various temperatures and nanostructure shapes and sizes.The methods I use contain no empirical fitting parameters and give a direct insight into the microscopic mechanisms determining the transport and anharmonic properties of the materials. This allows me to analyze the anharmonic broadening that is inversely proportional to the phonon lifetime, for the various phonon modes along the high symmetry directions in the Brillouin zone and show what are the major scattering channels for coalescence/decays of phonons that govern the thermal transport in Bi.

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Oxid uraničitý (UO2) je v současnosti nejčastěji používaným materiálem jakožto palivo v komerčních jaderných reaktorech. Největší nevýhodou UO2 je jeho velmi nízká tepelná vodivost, a protože se při štěpení UO2 v jaderném reaktoru vytváří velké množství tepla, vzniká v UO2 peletě velký teplotní gradient. Tento teplotní gradient způsobuje vznik velkého tepelného napětí uvnitř pelety, což následně vede k tvorbě trhlin. Tyto trhliny napomáhají k šíření štěpných plynů při vysoké míře vyhoření paliva. Tvorba trhlin a zvýšený vývin štěpného plynu posléze vede ke značnému snížení odolnosti jaderného paliva. Tato práce se zabývá problematikou zvyšování tepelné vodivosti jaderného paliva na modelu materiálu (CeO2). V této práci jsou studovány podobnosti chování CeO2 a UO2 při konvenčním slinováním a při „spark plasma sintering.“ Způsob jak zvýšit tepelnou vodivost použitý v této práci je včlenění vysoce tepelně vodivého materiálu, karbidu křemíku (SiC), do struktury CeO2 pelet. Od karbidu křemíku je očekáváno, že zvýší tok tepla z jádra pelety, a tím zvýší tepelnou vodivost CeO2. V této práci je také porovnávána podobnost chování SiC v CeO2 matrici s chováním SiC v UO2, které bylo popsáno v literatuře.

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