The work in this thesis is basically divided into two related but separate investigations. The first part treats simple chemical reactions of adsorbate molecules on metallic surfaces, induced by means of a scanning tunneling probe (STM). The investigation serves as a parameter free extension to existing theories. The theoretical framework is based on a combination of density functional theory (DFT) and non-equilibrium Green's functions (NEGF). Tunneling electrons that pass the adsorbate molecule are assumed to heat up the molecule, and excite vibrations that directly correspond to the reaction coordinate. The theory is demonstrated for an OD molecule adsorbed on a bridge site on a Cu(110) surface, and critically compared to the corresponding experimental results. Both reaction rates and pathways are deduced, opening up the understanding of energy transfer between different configurational geometries, and suggests a deeper insight, and ultimately a higher control of the behaviour of adsorbate molecules on surfaces. The second part describes a method to calculate STM images in the low bias regime in order to overcome the limitations of localized orbital DFT in the weak coupling limit, i.e., for large vacuum gaps between a tip and the adsorbate molecule. The theory is based on Bardeen's approach to tunneling, where the orbitals computed by DFT are used together with the single-particle Green's function formalism, to accurately describe the orbitals far away from the surface/tip. In particular, the theory successfully reproduces the experimentally well-observed characteristic dip in the tunneling current for a carbon monoxide (CO) molecule adsorbed on a Cu(111) surface. Constant height/current STM images provide direct comparisons to experiments, and from the developed method further insights into elastic tunneling are gained.

A modified source and dipole panel method to calculate the flow properties around an oscillating arbitrary body in the presence of a free surface is proposed. To demonstrate the feasibility of the method the problem of a pulsating line source submerged under a free surface is treated. The technique chosen is based on Green's identity whereby the boundary-value problem is expressed as a boundary integral equation which is solved numerically. The near field of the water surface is represented by singularity panels with constant strength. The work was motivated by the reported large computing times for existing programs using Green's functions satisfying the free surface boundary condition. The present approach uses free-space Green's function. The free surface boundary condition is applied to surface singularity panels using Green's theorem. Thus free surface effects are included in the solution while panel integrations are simplified considerably by the use of simpler Green's function. The matrix equations resulting from Green's identity were solved by using IMSL routines for Gaussian Elimination, and the behavior of the influence coefficient matrix was tested by using LINPACK routines. The depth of the submerged-source and wave number was kept constant while the length of near field and the number of panels per wavelength was varied systematically. A minimum of 10 panels per wavelength and paneled water surface length of 2 wavelengths gives good agreement with the known exact solution. Computing times were low, indicating the feasibility of the technique for application to unsteady ship problems. / Ph. D.

Ces dernières décennies, l'urgence croissante de la crise énergétique et la prise de conscience qu'une grande partie de l'énergie utilisée dans le monde est dissipée sous forme de chaleur ont provoqué un engouement pour le développement de modules thermoélectriques performants. Ces dispositifs pourraient récupérer la chaleur provenant de procédés industriels ou d'autres sources, transformant un gradient de température en voltage grâce à l'effet Seebeck. Les matériaux thermoélectriques performants doivent posséder une faible conductivité thermique, une haute conductivité électrique et un grand coefficient Seebeck. L'optimisation simultanée de ces paramètres est un défi majeur pour la physique de la matière condensée et la science des matériaux. Dans l'optique d'améliorer les propriétés thermoélectriques de plusieurs matériaux prometteurs, nous explorons plusieurs stratégies dans lesquelles les défauts (substitutions atomiques, lacunes…), le désordre et le confinement dimensionnel jouent un rôle central. Nous réalisons des calculs en théorie de la fonctionnelle densité et des projections sur des orbitales de Wannier afin de construire des Hamiltoniens et des matrices dynamiques réalistes décrivant leur structure électronique et vibrationnelle dans l'espace réel. Ces paramètres sont ensuite utilisés pour calculer les propriétés de transport thermoélectrique en utilisant le formalisme de Kubo, l'équation de Boltzmann, le formalisme de Landauer et la méthode Chebyshev polynomial Green's function, qui permet un traitement exact du désordre. Nous étudions les propriétés de transport électronique et les performances thermoélectriques de deux matériaux prometteurs pour la production d'énergie à hautes températures, le titanate de strontium et l'oxyde de titane rutile. Nous obtenons un très bon accord entre nos prédictions et un grand nombre de données expérimentales. Nous montrons que l'augmentation du coefficient Seebeck observée dans les superlayers de titanate de strontium, jusque-là attribuée à des effets de confinement quantique, est en réalité très bien expliquée par l'hypothèse d'électrons délocalisés. Nous explorons les effets généraux des états résonant sur le transport électronique dans le cadre d'une étude modèle, et nous trouvons une augmentation d'un facteur six des performances thermoélectriques. Nous examinons ensuite le cas particulier du titanate de strontium, et nous montrons que les performances sont détruites par des effets de localisation si des atomes de Vanadium sont introduits comme impuretés résonantes. Nous étudions l'influence des défauts dans les matériaux bidimensionnels. Contrairement aux adatomes, nous montrons que les substitutions dans les dichalcogénures de métaux de transition ont pour effet de localiser les porteurs de charge. Nous étudions l'effet des lacunes sur le transport de phonons dans le graphène, et nous déterminons les taux de diffusion phonon-lacune. Nous obtenons un très bon accord entre notre théorie et des mesures de conductivité thermique dans des échantillons de graphène irradiés et de tailles finies / Over the past decades, the increasingly pressing need for clean energy sources and the realization that a huge proportion of the world energy consumption is wasted in heat have prompted great interest in developing efficient thermoelectric generation modules. These devices could harvest waste heat from industrial processes or other sources, turning a temperature gradient into a voltage through the Seebeck effect. Efficient thermoelectric materials should exhibit a low thermal conductivity, a high electrical conductivity and a high Seebeck coefficient. Simultaneously optimizing these parameters is a great challenge of condensed matter physics and materials science. With a view to enhance the thermoelectric properties of several promising materials, we explore several strategies in which defects (atomic substitutions, vacancies…), disorder and dimensional confinement play a crucial role. We perform density functional theory calculations and projections on Wannier orbitals to construct realistic Hamiltonians and dynamical matrices describing their electronic and vibrational structure in real space. These parameters are then used to compute the thermoelectric transport properties using the Kubo formalism, the Boltzmann transport equation, the Landauer formalism, and the Chebyshev polynomial Green's function method that allows for an exact treatment of disorder. We investigate the electronic transport properties and thermoelectric performances of two promising materials for high-temperature power generation, strontium titanate and rutile titanium dioxide. Comparison of our predictions with a wealth of experimental data yields a very good agreement. We show that the increase of the Seebeck coefficient observed in strontium titanate superlayers, until now attributed to quantum confinement effects, is in fact well explained assuming delocalized electrons. The general effects of resonant states on electronic transport are explored in a model study, showing a sixfold increase of the thermoelectric performances. The particular case of strontium titanate is then examined, and localization effects are shown to destroy the performances if Vanadium atoms are introduced as resonant impurities. The influence of defects in two-dimensional materials is investigated. Contrary to adatoms, substitutions in transition metal dichalcogenides are shown to localize the charge carriers. We study the effect of vacancies on phonon transport in graphene, and determine the phonon-vacancy scattering rate. Comparison with thermal conductivity data for irradiated and finite-size graphene samples yields a very good agreement between theory and experiments

A system with two magnetic molecules embedded in a junction between non-magnetic leads was studied. In this system electrons tunnel from the localized energy level in region one to the localized energy level in region two generating a flow of electric charge through the quantum dot system. The current density and thus the conductance changes depending on the molecular spin moment. In this work we studied molecules with either spin "up" or spin "down" and with symmetric coupling strengths. The results indicate that the coupling strength between energy level and molecule together with the tunneling rate through the insulating layer play a major role when switching from parallel to anti-parallel molecular spin, for a specific combination of the coupling strength and tunneling rate we could observe a decrease in the current by 99.7% in the non-gated system and 99.4% in the gated system.

FREIRE, Márcio de Melo. Funções de Green em Mecânica Estatística. 2014. 56 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-09-12T19:48:53Z No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-09-12T19:50:01Z (GMT) No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) / Made available in DSpace on 2014-09-12T19:50:01Z (GMT). No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) Previous issue date: 2014 / Neste trabalho estabeleceremos as definições das funções de Green em mecânica estatística e suas propriedades básicas. Estas funções dependem duplamente do tempo e da temperatura. Isto pode ser observado por meio de suas definições, onde aparecem os valores médios dos produtos de operadores. Neste caso a média é feita sobre o ensemble grão-canônico. Os operadores envolvidos nestas funções satisfazem a equação de movimento de Heisenberg, o que nos permite descrever as equações de evolução para as funções de Green. Por meio da representação espectral das funções de correlação temporal, que é feita através da introdução de uma transformada de Fourier para mudar o sistema do espaço dos tempos para o espaço das frequências, podemos obter as representações espectrais para as funções de Green retardada, avançada e causal. Por último, faremos o uso da função de Green retardada para descrever a condutividade elétrica de um sistema de elétrons submetido a um campo elétrico externo dependente de tempo, em outras palavras, descreveremos o tensor de condutividade elétrica em termos da função de Green retardada e, por último, calcularemos a condutividade elétrica de um sistema de elétrons e fônons.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-02-24T17:38:27Z No. of bitstreams: 1 jonathanestebanarroyosilva.pdf: 3851364 bytes, checksum: 7341b01ce42c37de611bb2df24f9012c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T19:29:14Z (GMT) No. of bitstreams: 1 jonathanestebanarroyosilva.pdf: 3851364 bytes, checksum: 7341b01ce42c37de611bb2df24f9012c (MD5) / Made available in DSpace on 2017-03-06T19:29:14Z (GMT). No. of bitstreams: 1 jonathanestebanarroyosilva.pdf: 3851364 bytes, checksum: 7341b01ce42c37de611bb2df24f9012c (MD5) Previous issue date: 2014-02-24 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / Este trabalho apresenta um novo esquema de marcha no tempo capaz de reduzir oscilações espúrias através de amortecimento numérico para problemas de propagação de ondas elásticas no âmbito da Aproximação Explícita de Green (\Explicit Green's Approach" (ExGA)) [1]. A expressão integral referente ao ExGA é escrita em termos das funções de Green e Degrau. Seus cálculos são realizados de forma independente por meio da formulação semi-discreta do MEF e o método Diferença Central. Devido ao princípio da causalidade, as funções de Green e Degrau possuem um suporte compacto ao redor dos pontos fonte para um intervalo de tempo suficientemente pequeno que é usualmente Empregado nos métodos explícitos clássicos de integração temporal aplicados à modelagem de propagação de ondas. Neste sentido, as funções de Green e Degrau em t = Δt podem ser eficientemente calculadas localmente através de subdomínios pequenos. Cada subdomínio local com sua respectiva submalha cobre somente pontos nodais onde os valores das funções de Green e Degrau são não nulos. A precisão e eficiência da metodologia proposta é demostrada ao analisar três exemplos numéricos. / This work presents a new time-marching scheme able to reduce spurious oscillations by means of numerical damping for elastic wave propagation problems in the framework of the Explicit Green's Approach (ExGA) [1]. The integral expression concerned with the ExGA is written in terms of the Green's and the Step response functions. Their computations are carried out independently by means of the semidiscrete FEM and the Central difference method. Due to the principle of causality, the Green's and Step response functions admit a compact support surround the source points for a small enough time step that is usually employed in common explicit time integration methods applied to wave propagation modeling. In this sense, the Green's and Step response functions at t = Δt can be e ciently computed locally through small subdomains. Each local subdomain with its respective submesh covers only nodes whose Green's and Step response function values do not vanish. The accuracy and e ciency of the proposed methodology are demonstrated by analyzing three numerical examples.

Une méthode améliorant le calcul des facteurs d’intensité de contrainte en mode I par hybridation de deux fonctions de poids est présentée et appliquée aux cas de fissures elliptiques sous différents chargements. L'hybridation consiste à utiliser l'une ou l'autre des deux fonctions dans la zone de la fissure où la fonction est la plus efficace. La délimitation des zones est faite après optimisation des paramètres géométriques de la fissure. Afin d’étendre l’utilisation de cette approche à la modélisation des fissures semi-elliptiques, son couplage avec la PWFM (Point Weight Function Method) pour tenir compte de l’effet de la surface libre a été réalisé. L’utilisation des lois de propagation de fissure (de Paris et de Sih) a permis l’extension de l’application de l’approche d’hybridation aux problèmes de fatigue. La qualité des résultats trouvés pour les fissures elliptiques et semi-elliptiques est bonne aussi bien pour les chargements quasi-statiques que pour ceux de fatigue. / A method improving the evaluation of the stress intensity factor by hybridization of two weight functions is presented and applied for embedded elliptical cracks under various loadings. The hybridization consists in using one or another function in the zone of the crack where it is the most efficient. The delimitation of the zones is achieved after optimizing the geometrical parameters of the crack. In order to extend the use of this approach to the modeling of semi-elliptical surface cracks, its coupling with the PWFM (Point Weight Function Method) to take account of the free edge effect were carried out. The use of the fatigue crack growth laws (Paris law and Sih law) allowed the extension of the application of the hybrid approach to the fatigue problems. The quality of the results found for the elliptical and the semi-elliptical cracks is good for the static loads as well as for the fatigue ones.

This work analyzes partial slip contact problems in the theory of linear viscoelasticity using both the semi-analytical method and nite element method. Such problems arise in metal-polymer contacts in orthopedic implants and similar applications. The boundary conditions of such problems are inherently mixed and vary with time, thus restricting the use of classical correspondence principle, which have been the basic approach for most of the solved problems in viscoelasticity. In the present semi-analytical approach, the governing equations for the vis-coelastic partial-slip contact are formulated as a pair of coupled Singular Integral Equations (SIEs) for a pin-plate geometry using the viscoelastic analogues of Green's functions. The formulation is entirely in the time-domain, avoiding Laplace transforms. Both Coulomb and hysteretic e ects are considered, and arbitrary load histories, including the bidirectional pin loads and remote plate stresses, are allowed. Moreover, the contact patch is allowed to advance and recede with no restrictions. The presence of viscoelastic behavior necessitates the application of the stick zone boundary condition in convolved form, and also introduces additional convolved gap terms in the governing equations, which are not present in the elastic case. Transient, as well as steady-state contact tractions, are obtained under load-hold, unload-hold, unload-reload, cyclic bidirectional (fretting) and remote plate loading for a three-element delayed elastic solid. A wide range of loads, loading rates, friction coeficients and the conforming nature of the contact are considered. The contact size, stick-zone size, indenter approach, maximum pressure, Coulomb energy dissipation are tracked during fretting. The edge-of-contact stresses and the subsurface stresses for the viscoelastic plate due to the contact tractions are determined by solving an equivalent traction boundary value problem. It is found that the viscoelastic fretting contact tractions for materials with delayed elastic nature shakedown just like their elastic counterparts. However, the number of cycles to attain shakedown states is strongly dependent on the ratio of the load cycle time to the relaxation time constant of the viscoelastic material. In monotonic load-hold case, the viscoelastic steady-state tractions agree well with the tractions from an equivalent elastic analysis using the shear modulus at infinite time. Whereas, the viscoelastic fretting tractions in shakedown differ considerably from their elastic counterparts. This is due to the fact that the contact patch does not increase monotonically in fretting-type(cyclic) loading. Hence, an approximate elastic analysis misleads to an incorrect edge-of-contact stresses. During fretting, the edge-of-contact hoop stress also shakedown and reaches its peak value at the trailing edge-of-contact when the horizontal pin load reaches its maximum. Moreover, the peak tensile of the edge-of-contact hoop stress increases with the increase in the Coulomb friction coefficient. In cyclic loading, Coulomb dissipation in a cycle at steady-state is almost independent of the rate at which the load is cycled. However, the viscous energy dissipated in a cycle is a strong function of the ratio of the load cycle time to the relaxation time constant. The steady-state cyclic hysteretic energy dissipation typically dominates the cyclic Coulomb dissipation, with a more pronounced difference at slower load cycling. However, despite this, it is essential to model an accurate viscoelastic fretting contacts including the effects of both viscous and Coulomb friction dissipation to obtain accurate contact stresses. A 12-element generalized Maxwell solid with long time scales representing a well characterized viscoelastic material like PMMA is also studied. The material chosen is of slowly relaxing nature and the ratio of the instantaneous shear modulus(G0) to the modulus at the infinite time(G1) is almost equal to 1000. In such cases, the material is effectively always in a transient state, with no steady edge-of-contact. As a consequence, the location of the peak hoop stress keeps on shifting when the load cycle is repeated. Interestingly, the rate at which the viscoelastic material relaxes affects the contact tractions. It is observed that the rapidly relaxing materials show qualitatively different tractions in the partial slip, with local traction spikes close to the edges-of-contact and concomitant high-stress gradients. On the other hand, finite element method is also used to analyze the partial slip viscoelastic contacts. In FEA, the pin-plate geometry is modeled using a custom mesh maker, where a 2D-continuum plane strain element is used for the plate and rigid element for the pin. The technique uses 'ABAQUS Standard' solver to solve the contact problem. Finite element analysis for a wide range of loads comparable with the SIE technique is performed. The tractions and contact sizes for various load cases such as unload-reload, fretting-type cyclic loads from both SIE and FEA agrees well. In certain conditions, there exist multiple contact arcs or stick zones that are currently difficult to solve with SIE's. However, such problems are treated using FEA and one such problem is illustrated.

The development of materials with tailored functionalities and with continuously shrinking linear dimensions towards (and below) the nanoscale is not only going to revolutionize state of the art fabrication technologies, but also the computational methodologies used to model the materials properties. Specifically, atomistic methodologies are becoming increasingly relevant in the field of materials science as a fundamental tool in gaining understanding on as well as for pre-designing (in silico material design) the behavior of nanoscale materials in response to external stimuli. The major long-term goal of atomistic modelling is to obtain structure-function relationships at the nanoscale, i.e. to correlate a definite response of a given physical system with its specific atomic conformation and ultimately, with its chemical composition and electronic structure. This has clearly its pendant in the development of bottom-up fabrication technologies, which also require a detailed control and fine tuning of physical and chemical properties at sub-nanometer and nanometer length scales. The current work provides an overview of different applications of atomistic approaches to the study of nanoscale materials. We illustrate how the use of first-principle based electronic structure methodologies, quantum mechanical based molecular dynamics, and appropriate methods to model the electrical and thermal response of nanoscale materials, provides a solid starting point to shed light on the way such systems can be manipulated to control their electrical, mechanical, or thermal behavior. Thus, some typical topics addressed here include the interplay between mechanical and electronic degrees of freedom in carbon based nanoscale materials with potential relevance for designing nanoscale switches, thermoelectric properties at the single-molecule level and their control via specific chemical functionalization, and electrical and spin-dependent properties in biomaterials. We will further show how phenomenological models can be efficiently applied to get a first insight in the behavior of complex nanoscale systems, for which first principle electronic structure calculations become computationally expensive. This will become especially clear in the case of biomolecular systems and organic semiconductors.

Les excellentes propriétés électroniques, thermiques et mécaniques du graphène confèrent à ce matériau planaire (bi-dimensionnel) un énorme potentiel applicatif, notamment en électronique. Néanmoins, ce matériau présente de sérieux inconvénients qui pourraient limiter son champ d'applications. Par exemple, sa structure de bandes électronique sans bande interdite rend difficile le blocage du courant dans un dispositif. De plus, pour les applications thermoélectriques, sa forte conductance thermique est aussi une forte limitation. Il y a donc beaucoup de défis à relever pour rendre ce matériau vraiment utile pour des applications. Cette thèse porte sur l'étude des propriétés électroniques et thermoélectriques dans les hétérostructures planaires constituées de graphène et de nitrure de bore hexagonal (BN). Différentes configuration de ce nouveau matériau hybride permettent de moduler la bande interdite, la conductance thermique et le coefficient Seebeck. Cette étude a été menée au moyen de calculs atomistiques basés sur les approches des liaisons fortes (TB) et du modèle à constantes de force (FC). Le transport d'électrons et de phonons a été simulé dans le formalisme des fonctions de Green hors équilibre. Les résultats montrent que, grâce à la modulation de la bande interdite, des transistors à base d'hétérostructures de BN et de graphène peuvent présenter un très bon rapport courant passant / bloqué d'environ 10⁴ à 10⁵. En outre, nous montrons l'existence d'états quantiques hybrides à l'interface zigzag entre le graphène et le BN donnant lieu à des propriétés de transport électronique très intéressantes. Enfin, ce travail montre qu'en agençant correctement des nano-flocons de BN sur les côtés d'un nanoruban de graphène, la conductance des phonons peut être fortement réduite alors que l'ouverture de bande interdite conduit à un accroissement important du coefficient Seebeck. Il en résulte qu'un facteur de mérite thermoélectrique ZT plus grand que l'unité peut être réalisé à température ambiante. / Graphene is a fascinating 2-dimensional material exhibiting outstanding electronic, thermal and mechanical properties. Is this expected to have a huge potential for a wide range of applications, in particular in electronics. However, this material also suffers from a strong drawback for most electronic devices due to the gapless character of its band structure, which makes it difficult to switch off the current. For thermoelectric applications, the high thermal conductance of this material is also a strong limitation. Hence, many challenges have to be taken up to make it useful for actual applications. This thesis work focuses on the theoretical investigation of a new strategy to modulate and control the properties of graphene that consists in assembling in-plane heterostructures of graphene and Boron Nitride (BN). It allows us to tune on a wide range the bandgap, the thermal conductance and the Seebeck coefficient of the resulting hybrid nanomaterial. The work is performed using atomistic simulations based on tight binding (TB), force constant (FC) models for electrons and phonons, respectively, coupled with the Green's function formalism for transport calculation. The results show that thanks to the tunable bandgap, it is possible to design graphene/BN based transistors exhibiting high on/off current ratio in the range 10⁴-10⁵. We also predict the existence hybrid quantum states at the zigzag interface between graphene and BN with appealing electron transport. Finally this work shows that by designing properly a graphene ribbon decorated with BN nanoflakes, the phonon conductance is strongly reduced while the bandgap opening leads to significant enhancement of Seebeck coefficient. It results in a thermoelectric figure of merit ZT larger than one at room temperature.