Niobium (Nb) is a fascinating element, that when it is in a solid state has remarkable properties. This is believed to be a result of its electronic configuration that has partially filled 4d and 5s sub-shells. Nb has a melting temperature of 2750 K, a high strength at high temperature, and a good wear resistance. Because of these properties, Nb is used as material for components of rockets and jet engines, and for strengthening steel. In the phonon dispersion relations, Kohn anomalies are experimentally observed to weaken with increased temperature, which is related to the superconducting properties of Nb. I include anharmonicity when I calculate the thermodynamic properties of Nb and relate this to the electronic structure. In this thesis I show that anharmonicity can not be neglected when considering thermodynamic properties of Nb. I observe broadening in the electronic band structure with increasing temperature, correlated with the gradual weakening of the Kohn anomalies in the phonon dispersion relations. Kohn anomaly in the phonon dispersion relation can be observed at 300 K and is completely absent at 1200 K. The observation of the Kohn anomaly's disappearance in the calculations is of great importance because it cannot be repeated by approaches that do not include anharmonic effects, meaning that properties that are directly related to phonon dispersion, like elastic constants, can be calculated more accurately with this approach.

We conduct a comprehensive and systematic study of the Fermi-Pasta-Ulam (FPU) model using both equilibrium and non-equilibrium molecular dynamics simulations, with the aim being to explain the cause of the anomalous energy-transport behaviour in the model. In the equilibrium scenario, our motivation stems from the lack of a complete understanding of the effects of initial conditions on the energy dissipation among Fourier modes. We also critically reconsider the ????probes' that had been widely used to quantitatively describe the types of energy sharing in a system, and then decide on a preferred choice to be used in our equilibrium study. We establish, from strong numerical evidence, that there exists a critical energy density of approximately 0:1, above which the energy dissipation among the modes becomes independent of initial conditions and system parameters, and that the full equipartition of mode energy is never attained in the FPU model. We report, for the first time, the violation of particle positions in the FPU model at high energies, where the particles are found to pass through one another. In the non-equilibrium scenario, we critically review the Nos???Se-Hoover algorithm thermostatting method largely used by other works, and identify its weaknesses. We also review some other alternative methods and decide on the most appropriate one to be implemented throughout our work. We confirm the divergence of the thermal conductivity of the FPU model as the chain length increases, and that kfpu [symbol] No.41, in agreement with other works. Our study further shows that there exists an upper limit of the anharmonicity in the FPU model, and that any attempt to increase the strength of this anharmonicity will not succeed. We also introduce elastic collisions into the original FPU model and find that the Modified model (FPUC) still exhibits anomalous thermal conductivity. We conclude that a one-dimensional FPU-type model with ????only' nearest-neighbour interaction, regardless of being soft or hard, does not exhibit a finite thermal conductivity as the system size increases, due to the non-chaotic nature of its microscopic dynamics, the origin of which we are unable to account for. Finally, we briefly outline possible research directions.

We conduct a comprehensive and systematic study of the Fermi-Pasta-Ulam (FPU) model using both equilibrium and non-equilibrium molecular dynamics simulations, with the aim being to explain the cause of the anomalous energy-transport behaviour in the model. In the equilibrium scenario, our motivation stems from the lack of a complete understanding of the effects of initial conditions on the energy dissipation among Fourier modes. We also critically reconsider the ????probes' that had been widely used to quantitatively describe the types of energy sharing in a system, and then decide on a preferred choice to be used in our equilibrium study. We establish, from strong numerical evidence, that there exists a critical energy density of approximately 0:1, above which the energy dissipation among the modes becomes independent of initial conditions and system parameters, and that the full equipartition of mode energy is never attained in the FPU model. We report, for the first time, the violation of particle positions in the FPU model at high energies, where the particles are found to pass through one another. In the non-equilibrium scenario, we critically review the Nos???Se-Hoover algorithm thermostatting method largely used by other works, and identify its weaknesses. We also review some other alternative methods and decide on the most appropriate one to be implemented throughout our work. We confirm the divergence of the thermal conductivity of the FPU model as the chain length increases, and that kfpu [symbol] No.41, in agreement with other works. Our study further shows that there exists an upper limit of the anharmonicity in the FPU model, and that any attempt to increase the strength of this anharmonicity will not succeed. We also introduce elastic collisions into the original FPU model and find that the Modified model (FPUC) still exhibits anomalous thermal conductivity. We conclude that a one-dimensional FPU-type model with ????only' nearest-neighbour interaction, regardless of being soft or hard, does not exhibit a finite thermal conductivity as the system size increases, due to the non-chaotic nature of its microscopic dynamics, the origin of which we are unable to account for. Finally, we briefly outline possible research directions.

This thesis presents work done on the calculation of the effects of anharmonic nuclear motion on the properties of solid materials from first principles. Such anharmonic effects can be significant in many cases. A vibrational self-consistent field (VSCF) method is used as the basis for these calculations, which is then improved and applied to a variety of solid state systems. Firstly, work done to improve the efficiency of the VSCF method is presented. The standard VSCF method involves using density functional theory (DFT) to map the Born-Oppenheimer (BO) energy surface that the nuclei move in, a computationally expensive process. It is shown that the accurate forces available in plane-wave basis DFT can be used to help map the BO surface more accurately and reduce the computational cost. This improved VSCF+f method is tested on molecular and solid hydrogen, as well as lithium and zirconium, and is found to give a speed-up of up to 40%. The VSCF method is then applied to two different systems of physical interest. It is first applied to the case of the neutral vacancy in diamond, in order to resolve a known discrepancy between harmonic ab initio calculations and experiment -- the former predict a static Jahn-Teller distortion, whilst the latter leads to a dynamic Jahn-Teller effect. By including anharmonic corrections to the energy and nuclear wavefunction, we show that the inclusion of these effects results in agreement between first-principles calculations and experiment for the first time. Lastly, the VSCF method is applied to barium titanate, a prototypical ferroelectric material which undergoes a series of phase transitions from around 400 K downwards. The nature of these phase transitions is still unclear, and understanding them is an active area of research. We describe the physics of the phase transitions of barium titanate, including both anharmonicity and the effect of polarisation caused by long wavelength vibrations, to help understand the important physics from first principles.

Monte Carlo based statistical approach to solve Boltzmann Transport Equation (BTE) has become a norm to investigate heat transport in semiconductors at sub-micron regime, owing mainly to its ability to characterize realistically sized device geometries qualitatively. One of the primary issues with this technique is that the approach predominantly uses empirically fitted phonon dispersion relations as input to determine the properties of phonons so as to predict the thermal conductivity of specified material geometry. The empirically fitted dispersion relations assume harmonic approximation thereby failing to account for thermal expansion, interaction of lattice waves, effect of strain on spring stiffness, and accurate phonon-phonon interaction. To circumvent this problem, in this work, a coupled molecular mechanics-Monte Carlo (MM-MC) platform has been developed and used to solve the phonon Boltzmann Transport Equation (BTE) for the calculation of thermal conductivity of several novel and emerging nanostructures. The use of the quasi-anharmonic MM approach (as implemented in the open source NEMO 3-D software toolkit) not only allows one to capture the true atomicity of the underlying lattice but also enables the simulation of realistically-sized structures containing millions of atoms. As compared to the approach using an empirically fitted phonon dispersion relation, here, a 17% increase in the thermal conductivity for a silicon nanowire due to the incorporation of atomistic corrections in the LA (longitudinal acoustic) branch alone has been reported. The atomistically derived thermal conductivity as calculated from the MM-MC framework is then used in the modular design and analysis of (i) a silicon nanowire based thermoelectric cooler (TEC) unit, and (ii) a GaN/InN based nanostructured light emitting device (LED). It is demonstrated that the use of empirically fitted phonon bandstructure parameters overestimates the temperature difference between the hot and the cold sides and the overall cooling efficiency of the system, thereby, demanding the use of the BTE derived thermal conductivity in the calculation of thermal conductivity. In case of the light-emitting device, the microscopically derived material parameters, as compared to their bulk and fitted counterparts, yielded ~3% correction (increase) in optical efficiency. A non-deterministic approach adopted in this work, therefore, provides satisfactory results in what concerns phonons transport in both ballistic and diffusive regimes to understand and/predict the heat transport phenomena in nanostructures.

No description available.

No description available.

Les pérovskites hybrides halogénées (ABX3) sont utilisées depuis cinq ans comme couches absorbantes pour de nouvelles cellules solaires à bas coût combinant les avantages des matériaux organiques (molécule A) et inorganiques (métal B et halogène X). Très récemment, des cellules solaires à boîtes quantiques à bases de pérovskites purement inorganiques ont également montré des efficacités prometteuses, ce qui en fait une alternative potentiellement stable et efficace à leurs cousins hybrides.Le but de cette thèse de doctorat est d'étudier et de mieux comprendre les instabilités structurelles et thermodynamiques de ces pérovskites halogénées, avec un focus sur la pérovskite purement inorganique CsPbI3.Dans un premier temps les propriétés vibrationnelles et électroniques des différentes phases de CsPbI3 sont étudiées grâce à différentes techniques ab-initio, dont la plupart sont basées sur la théorie de la fonctionnelle de la densité (DFT) et son approche en réponse linéaire (DFPT). Alors que la phase γ noire, cruciale pour les applications photovoltaïques, se comporte de manière harmonique autour de l'équilibre, pour les trois autres phases nos calculs de phonons froids révèlent une instabilité de double puits au centre de la zone de Brillouin. Nos calculs montrent également que le terme d'entropie d'ordre-désordre lié à ce double puits est crucial pour empêcher la formation de la phase pérovskitoïde jaune. Nous analysons ensuite en détail les changements structurels et l’effet Rashba dynamique le long de trajectoires de dynamique moléculaire à la lumière de ces résultats.La seconde partie de la thèse porte sur la stabilité thermodynamique de la pérovskite hybride MAPbI3. Notre étude expérimentale par ellipsométrie apporte une meilleure compréhension de la décomposition chimique de MAPbI3 en ses deux précurseurs, l’iodure de méthylamonium et l'iodure de plomb, que nous avons prédite grâce à des calculs de diagrammes de stabilité DFT et que nous confirmons par diffraction des rayons X. Enfin, nous démontrons que la pérovskite hybride MAPbI3 se comporte davantage comme les composés inorganiques (grande constante diélectrique, faible énergie de liaison des excitons) que comme les matériaux organiques (faible constante diélectrique, forte énergie de liaison d'exciton). / Hybrid halide perovskites (ABX3) have emerged over the past five years as absorber layers for novel high-efficiency low-cost solar cells combining the advantages of organic (molecule A) and inorganic (metal B, halogen X) materials. Very recently, fully inorganic perovskite quantum dots also shown promising efficiencies, making them a potentially stable and efficient alternative to their hybrid cousins.The aim of this PhD thesis is to study and better understand both the structural and thermodynamic instabilities of these halide perovskites, with a specific focus on purely inorganic CsPbI3 structures.We first use various ab-initio techniques, the majority of which are based on Density Functional Theory (DFT) and its linear-response approach (DFPT), to investigate the vibrational and electronic properties of the different phases of CsPbI3. While the black γ-phase, crucial for photovoltaic applications, is shown to behave harmonically around equilibrium, for the other three phases frozen phonon calculations reveal a Brillouin zone center double-well instability. We also show that avoiding the order-disorder entropy term arising from these double-well instabilities is key in order to prevent the formation of the yellow perovskitoid phase, and evidence a Rashba effect when using the symmetry breaking structures obtained through frozen phonon calculations. We then analyze the structural changes and the dynamical Rashba splitting along molecular dynamics trajectories in the light of our findings.In a second phase, we investigate the thermodynamical stability of hybrid perovskite MAPbI3. Our experimental ellipsometry-based study brings better understanding of the chemical decomposition of MAPbI3 into its two precursors, methylammonium and lead iodides, which we predicted using DFT stability diagram calculations and which we confirm by X-Ray diffraction. Last, we prove that hybrid perovskite structure MAPbI3 behaves more like inorganic compounds (high dielectric constant, low exciton binding energy) than like organic materials (low dielectric constant, high exciton binding energy).

We study the time evolution of driven quantum systems using analytic, algebraic, and numerical methods. First, we obtain analytic solutions for driven free and oscillator systems by shifting the coordinate and phase of the undriven wave function. We also factorize the quantum evolution operator using the generators of the Lie algebra comprising the Hamiltonian. We obtain coupled ODE's for the time evolution of the Lie algebra parameters. These parameters allow us to find physical properties of oscillator dynamics. In particular we find phase-space trajectories and transition probabilities. We then search for chaotic behavior in the Lie algebra parameters as a signature for dynamical chaos in the quantum system. We plot the trajectories, transition probabilities, and Lyapunov exponents for a wide range of the following physical parameters: strength and duration of the driving force, frequency difference, and anharmonicity of the oscillator. We identify conditions for the appearance of chaos in the system.

Die Thermodynamik von Adsorptionsvorgängen wurde mittels quantenchemischer Methoden und der statistischen Thermodynamik untersucht. Eine neue rechentechnische Methode wird vorgestellt, die den Mangel an Genauigkeit vorhandener Methoden zur Untersuchung periodischer Systeme, wie z. B. der Dichte-Funktional-Theorie, behebt, und es ermöglicht thermodynamische Funktionen mit chemischer Genauigkeit zu bestimmen. Das im Rahmen dieser Arbeit entwickelte Protokoll besteht aus verschiedenen rechentechnischen Schritten, als da wären, eine Strukturoptimierung in Normalkoordinaten anstatt in kartesischen Koordinaten, eine numerische Berechnung der harmonischen Frequenzen durch Abtasten der Potentialenergieoberfläche entlang der Normalkoordinaten und anschließender anharmonischer Korrektur. Die Normalkoordinatenoptimierung garantiert eine korrekte Relaxation der Struktur mit ausschließlich reellen harmonischen Frequenzen. Die anharmonischen Korrekturen ermöglichen eine gute Beschreibung der Schwingungsstrukturen von Systemen die durch eine besonders Flache PES gekennzeichnet sind. Gleichzeitig, wird durch die Verwendung eines QM:QM-Hybridverfahrens zur Bestimmung des elektronischen Anteils der Adsorptionsenergie eine höhere Genauigkeit in der Bestimmung der Korrelationsenergie im Vergleich zu DFT garantiert. Der elektronische Anteil der Adsorptionsenergie, sowie der Schwingungsthermische Anteil werden abschließend kombiniert um einen genauen Wert der thermodynamischen Funktionen zu erhalten. / The thermodynamic of adsorption is investigated from the vibrational point of view using quantum chemical methods via statistical mechanics. Due to the lack of accuracy of the present available methods for investigating periodic systems, such as plane-wave density functional theory (DFT), a novel computational strategy is presented to overcome these limitations and bring the estimate of the thermodynamic functions within chemical accuracy limits. The protocol presented in this work consists of different computational steps, namely a structure optimization using normal mode coordinates instead of Cartesians, a numerical harmonic frequency calculation via sampling of the potential energy surface along the normal mode coordinates and the inclusion of anharmonic correction to the latter. The normal mode coordinate optimization ensures a proper relaxation of the structure and a reliable set of real harmonic frequencies while the anharmonic corrections account for a proper description of the vibrational structure of a system characterized by a very flat potential energy surface. Parallel to these calculations the electronic part of the adsorption energy is corrected using a hybrid QM:QM scheme to account the electronic correlations effects more accurately than DFT. The hybrid electronic adsorption energy and the vibrational thermal contributions obtained using anharmonic corrections are finally combined to get accurate estimate of the adsorption thermodynamic functions.