Este trabalho explora a utilização do algoritmo genético de minimização global por Evolução Diferencial (ED) como método de determinação de parâmetros de potenciais interatômicos (PIs) usados no cálculo de propriedades físicas de materiais. Dois compostos foram utilizados como estudo de caso: a berlinita (AlPO4) e a fase cúbica do tungstato de zircônio ( -ZrW2O8 ). Em ambos os casos, o potencial interatômico considerado foi uma combinação de potenciais de Buckingham, covalente exponencial e harmônico de três corpos, além do modelo casca-caroço de Dick-Overhauser para os átomos de oxigênio. Os parâmetros livres do potencial foram ajustados de modo a fornecer estimativas para os parâmetros de rede, posições atômicas e constantes elásticas de ambas as estruturas que mais se aproximassem dos valores experimentais. O algoritmo de evolução diferencial foi capaz de encontrar potenciais que melhor reproduzem as propriedades atérmicas em ambos os casos, quando comparados com PIs previamente publicados. Os potenciais encontrados para a fase cúbica do tungstato de zircônio foram aplicados à cálculos de dinâmica de rede para avaliar a influência da temperatura no seu parâmetro de rede. O algoritmo de ED encontrou um conjunto de parâmetros para potenciais com modelos analíticos relativamente simples, porém capaz de descrever com razoável precisão a expansão térmica negativa do -ZrW2O8 em baixas temperaturas. A evolução diferencial mostrouse um método capaz de explorar exaustivamente o espaço de parâmetros, o que indica que as limitações encontradas na descrição da estrutura possam ser superadas com a adição de termos ao PI ou com o uso de outra forma analítica. / This work explores the use of the genetic algorithm differential evolution (DE) for global minimization as a method for determining the interatomic potential (IP) parameters used in the calculation of physical properties of materials. Two compounds were used as a case study: Berlinite (AlPO4) and the cubic phase of zirconium tungstate ( -ZrW2O8 ). In both cases, the IP was built as a combination of Buckingham, covalent exponential, and three body harmonic potentials, together with the Dick-Overhauser core-shell model for the oxygen atoms. The free parameters of the potential were adjusted to estimate the lattice parameters, atomic positions and elastic constants of both structures that were closest to experimental values. The DE algorithm was able to find potentials that are better in describing the athermal properties for both compounds when compared to previously published IPs. The potentials found for the cubic phase of zirconium tungstate were applied in lattice dynamics calculations in order to assess the temperature influence in the lattice parameter. The DE found a relatively simple IP, but capable of describing the negative thermal expansion of -ZrW2O8 at low temperatures with reasonable precision. The DE has shown to be a method capable to exhaustively explore the parameter space of the PI, which indicates that the limitations found in describing the zirconium tungstate structure modifications as a function of temperature can be surpassed with additional terms in the potential or with another, more complex, analytical form.

The goal of this PhD research project is to devise a robust interatomic potential for large scale molecular dynamics simulations of carbon materials under extreme conditions. This screened-environment dependent reactive empirical bond order potential (SED-REBO) is specifically designed to describe carbon materials under extreme compressive or tensile stresses. Based on the original REBO potential by Brenner and co workers, SED-REBO includes reparametrized pairwise interaction terms and a new screening term, which serves the role of a variable cutoff. The SED-REBO potential overcomes the deficiencies found with the most commonly used interatomic potentials for carbon: the appearance of artificial forces due to short cutoff that are known to create erroneous phenomena including ductile fracture of graphene and carbon nanotubes, which contradicts the experimentally observed brittle character of these materials. SED-REBO was applied in large scale molecular dynamics simulations of nanoindentation of graphene membranes and shock-induced compression of diamond. It was shown in the first computational experiment that graphene membranes exhibit a non-linear response to large magnitude of indentation, followed by a brittle fracture in agreement with experiments. The strength of graphene was determined using the kinetic theory of fracture, and the crack propagation mechanisms in the material were identified. It was found in large-scale shock simulations that SED-REBO improves the predictive power of MD simulations of carbon materials at extreme conditions.

No description available.

No description available.

The research reported in this dissertation focuses on the response of grain boundaries in polycrystalline metallic nanostructures to applied strain using molecular dynamics simulations and empirical interatomic force laws. The specific goals of the work include establishing how local grain boundary structure affects deformation behavior through the quantitative estimation of various plasticity mechanisms, such as dislocation emission and grain boundary sliding. The effects of strain rate and temperature on the plastic deformation process were also investigated. To achieve this, molecular dynamics simulations were performed on both thin-film and quasi-2D virtual samples constructed using a Voronoi tessellation technique. The samples were subjected to virtual mechanical testing using uniaxial strain at strain rates ranging from 105s-1 to 109s-1. Seven different interatomic embedded atom method potentials were used in this work. The model potentials describe different metals with fcc or bcc crystal structures. The model was validated against experimental results from studying the tensile deformation of irradiated austenitic stainless steels performed by collaborators at the University of Michigan. The results from the model validation include a novel technique for detecting strain localization through adherence of gold nanoparticles to the surface of an experimental sample prior to deformation. Similar trends with respect to intergranular crack initiation were observed between the model and the experiments. Simulations of deformation in the virtual samples revealed for the first time that equilibrium grain boundary structures can be non-planar for model potentials representing fcc materials with low stacking fault energy. Non-planar grain boundary features promote dislocation as deformation mechanisms, and hinder grain boundary sliding. This dissertation also reports the effects of temperature and strain rate on deformation behavior and correlates specific deformation mechanisms that originate from grain boundaries with controlling material properties, deformation temperature and strain rate. / Ph. D.

No description available.

The development of interatomic potentials for magnetic transition metals, and particularly for iron, is difficult, yet it is also necessary for large-scale atomistic simulations of industrially important iron and steel alloys. The magnetism of iron is especially important as it is responsible for many of the element's unique physical properties -- its bcc ground state structure, its high-temperature phase transitions, and the mobility of its self-interstitial atom (SIA) defects. Yet an accurate description of itinerant magnetism within a real-space formalism is particularly challenging and existing interatomic potentials based on the Embedded Atom Method are suited only for studies of near-equilibrium ferritic iron, due to their restricted functional forms. For this work, the magnetic analytic Bond-Order Potential (BOP) method has been implemented in full to test the convergence properties in both collinear and non-collinear magnetic iron. The known problems with negative densities of states (DOS) are addressed by assessing various possible definitions for the bandwidth and by including the damping factors adapted from the Kernel Polynomial Method. A 9-moment approximation is found to be sufficient to reproduce the major structural energy differences observed in Density Functional Theory (DFT) and Tight Binding (TB) reference calculations, as well as the volume dependence of the atomic magnetic moments. The Bain path connecting bcc and fcc structures and the formation energy of mono- and divacancies are also described well at this level of approximation. Other quantities such as the high-spin/low-spin transition in fcc iron, the bcc elastic constants and the SIA formation energies converge more slowly towards the TB reference data. The theory of non-collinear magnetism within analytic BOP is extended as required for a practical implementation. The spin-rotational behaviour of the energy is shown to converge more slowly than the collinear bulk energy differences, and there are specific problems at low angles of rotation where the magnitude of the magnetic moment depends sensitively on the detailed structure of the local DOS. Issues of charge transfer in relation to magnetic defects are discussed, as well as inadequacies in the underlying d-electron TB model.

Aluminas have had some form of chemical and industrial use throughout history. For little over a century corundum (α-Al2O3) has been the most widely used and known of the aluminas. The emerging metastable aluminas, including the γ, δ, η, θ, κ, β, and χ polymorphs, have been growing in importance. In particular, γ-Al2O3 has received wide attention, with established use as a catalyst and catalyst support, and growing application in wear abrasives, structural composites, and as part of burner systems in miniature power supplies. It is also growing in importance as part of the feedstock for aluminium production in order to affect both the adsorption of hydrogen fluoride and the feedstock solubility in the electrolytic solution. However, much ambiguity surrounds the precise structure of γ-Al2O3. Without proper knowledge of the structure, understanding the properties, dynamics and applications will always be less than optimal. The aim of this research was to contribute towards settling this ambiguity. This work was achieved through extensive computer simulations of the structure, based on interatomic potentials with refinements of promising structures using density functional theory (DFT), and a wide range of supporting experiments. In addition to providing a more realistic representation of the structure, this research has also served to advance knowledge of the evolution of the structure with changing temperature and make new insights regarding the location of hydrogen in γ-Al2O3. / Both the molecular modelling and Rietveld refinements of neutron diffraction data showed that the traditional cubic spinel-based structure models, based on m Fd3 space group symmetry, do not accurately describe the defect structure of γ-Al2O3. A more accurate description of the structure was provided using supercells of the cubic and tetragonal unit cells with a significant number of cations on c symmetry positions. These c symmetry based structures exhibited diffraction patterns that were characteristic of γ-Al2O3. The first three chapters of this Thesis provide a review of the literature. Chapter One provides a general introduction, describing the uses and importance of the aluminas and the problems associated with determining the structure of γ-Al2O3. Chapter Two details the research that has been conducted on the structure of vi γ-Al2O3 historically. Chapter Three describes the major principles behind the computational methods employed in this research. In Chapter Four, the specific experimental and computational techniques used to investigate the structure of γ-Al2O3 are described. All preparation conditions and parameters used are provided. Chapter Five describes the methodology employed in computational and experimental research. The examination of the ~ 1.47 billion spinel-based structural possibilities of γ-Al2O3, described using supercells, and the selection of ~ 122,000 candidates for computer simulation, is detailed. This chapter also contains a case study of the structure of κ-Al2O3, used to investigate the applicability of applying interatomic potentials to solving complex structures, where many possibilities are involved, and to develop a systematic procedure of computational investigation that could be applied to γ-Al2O3. Chapters Six to Nine present and discuss the results from the experimental studies. / Preliminary heating trials, performed to determine the appropriate preparation conditions for obtaining a highly crystalline boehmite precursor and an appropriate calcination procedure for the systematic study of γ-Al2O3, were presented in Chapter Six. Chapter Seven details the investigation of the structure from a singletemperature case. Several known structural models were investigated, including the possibility of a dual-phase model and the inclusion of hydrogen in the structure. It was demonstrated that an accurate structural model cannot be achieved for γ-Al2O3 if the cations are restricted to spinel positions. It was also found that electron diffraction patterns, typical for γ-Al2O3, could be indexed according to the I41/amd space group, which is a maximal subgroup of m Fd3 . Two models were presented which describe the structure more accurately; Cubic-16c, which describes cubic γ-Al2O3 and Tetragonal-8c, which describes tetragonal γ-Al2O3. The latter model was found to be a better description for the γ-Al2O3 samples studied. Chapter Eight describes the evolution of the structure with changing calcination temperature. Tetragonal γ-Al2O3 was found to be present between 450 and 750 °C. The structure showed a reduction in the tetragonal distortion with increasing temperature but at no stage was cubic γ-Al2O3 obtained. Examination of the progress of cation migration indicates the reduction in the tetragonal nature is due to ordering within inter-skeletal oxygen layers of the unit cell, left over from the breakdown of the hydroxide layers of boehmite when the transformation to γ-Al2O3 occurred. Above 750 °C, δ-Al2O3 was not observed, but a new phase was identified and designated γ.-Al2O3. / The structure of this phase was determined to be a triple cell of γ-Al2O3 and is herein described using the 2 4m P space group. Chapter Nine investigates the presence of hydrogen in the structure of γ-Al2O3. It was concluded that γ-Al2O3 derived from highly crystalline boehmite has a relatively well ordered bulk crystalline structure which contains no interstitial hydrogen and that hydrogen-containing species are located at the surface and within amorphous regions, which are located in the vicinity of pores. Expectedly, the specific surface area was found to decrease with increasing calcination temperature. This trend occurred concurrently with an increase in the mean pore and crystallite size and a reduction in the amount of hydrogen-containing species within the structure. It was also demonstrated that γ-Al2O3 derived from highly crystalline boehmite has a significantly higher surface area than expected, attributed to the presence of nano-pores and closed porosity. The results from the computational study are presented and discussed in Chapter Ten. Optimisation of the spinel-based structural models showed that structures with some non-spinel site occupancy were more energetically favourable. However, none of the structural models exhibited a configuration close to those determined from the experimental studies. Nor did any of the theoretical structures yield a diffraction pattern that was characteristic of γ-Al2O3. This discrepancy between the simulated and real structures means that the spinel-based starting structure models are not close enough to the true structure of γ-Al2O3 to facilitate the derivation of its representative configuration. / Large numbers of structures demonstrate migration of cations to c symmetry positions, providing strong evidence that c symmetry positions are inherent in the structure. This supports the Cubic-16c and Tetragonal-8c structure models presented in Chapter Seven and suggests that these models are universal for crystalline γ-Al2O3. Optimisation of c symmetry based structures, with starting configurations based on the experimental findings, resulted in simulated diffraction patterns that were characteristic of γ-Al2O3.

O Tungstato de Zircônio (ZrW2O8) é um material que exibe Expansão Térmica Negativa (ETN), isotrópica em um amplo intervalo de temperatura (0,3 a 1050 K). Apesar de amplamente estudado, existem controvérsias acerca dos mecanismos microscópicos responsáveis por este comportamento. A fase cúbica deste composto, denominada a-ZrW2O8, já foi motivo de estudo através de simulações computacionais utilizando Potenciais Interatômicos (PI) e Dinâmica de Rede na Aproximação Quasi-Harmônica (DRQH). Nos dois PI distintos propostos na literatura conseguiu-se reproduzir a ETN da a-ZrW2O8, mas não a dependência com a temperatura do tensor de elasticidade. É partindo desta observação que este trabalho pretende avaliar o desempenho de PI existentes e de novos PI em simulações computacionais visando a descrição da dependência com a temperatura do tensor de elasticidade da a-ZrW2O8 entre 0 e 300 K. Utilizaram-se dados experimentais, tais como posições atômicas, parâmetros de rede e o tensor de elasticidade da a-ZrW2O8 em temperaturas entre 0 e 300 K e, em outra série de cálculos, a hipersuperfície de energia ab initio no limite atérmico para obter os parâmetros dos PI. Diferentes estratégias foram empregadas na busca pelos parâmetros dos PI incluindo minimização em linha, Newton-Raphson/BFGS e Algoritmo Genético (AG). Concluiu-se que não é possível descrever as propriedades estruturais e elásticas da a-ZrW2O8 em função da temperatura com PI simples e que esta incapacidade não está relacionada a qualquer limitação da DRQH ou dos parâmetros dos PI, mas à forma analítica dos PI empregados. Isto sugere que se deve ter cautela na interpretação de resultados obtidos com estes potencias já disponíveis na literatura. Como alternativas para a solução deste problema, pode-se considerar o uso de redes neurais para a representação da hipersuperfície de energia ab initio, o uso de PI mais sofisticados que levam em consideração a vizinhança atômica (bond order potentials) e, também, cálculo ab initio a T > 0, este último a um custo computacional muito mais elevado. / Submitted by Marcelo Teixeira (mvteixeira@ucs.br) on 2014-05-28T17:16:32Z No. of bitstreams: 1 Dissertacao Emiliano Chemello.pdf: 1343523 bytes, checksum: 46461698a2b6139def916307ab93478f (MD5) / Made available in DSpace on 2014-05-28T17:16:32Z (GMT). No. of bitstreams: 1 Dissertacao Emiliano Chemello.pdf: 1343523 bytes, checksum: 46461698a2b6139def916307ab93478f (MD5) / Zirconium tungstate (ZrW2O8) is a material that exhibits negative thermal expansion (NTE), over a wide temperature range (0.3 at 1050 K). Although thoroughly studied, controversies still remain concerning the microscopic mechanisms responsible for this behavior. The cubic phase of this compound, denominated a-ZrW2O8, was already the subject of study through computer simulations using interatomic potentials (IP) and lattice dynamics in quasiharmonic approximation (LDQH). In two different IPs proposed in the literature succeeded in reproducing the a-ZrW2O8 NTE, but not the dependence with temperature of the elasticity tensor. Starting from this observation, this work intends to evaluate of existent IPs and same proposed new IPs in computer simulations aiming the calculation of the tensor of elasticity for a-ZrW2O8 between 0 and 300 K. Experimental data (such as atomic positions, lattice parameters and the tensor of elasticity of a-ZrW2O8 at 0 and 300 K) and, in another series of calculations, the ab initio energy hypersurface in the athermic limit, were used to obtain the parameters of the IPs. Different strategies were used in the search for the parameters of IP, including line minimization, Newton-Raphson/BFGS and genetic algorithm (GA). At the end of an exhaustive search we were led to conclude that it is not possible to describe the structure and elastic properties of a-ZrW2O8 as a function of temperature with simple IPs and that this incapacity is not related the any limitation of LDQH or of the parameters of the IPs, but instead to the analytical form of the tested IPs. This suggests that same results obtained with IPs already available in the literature may be unreliable. As alternatives for the solution of this problem, it can be considered the use of a neural network for the representation of the ab initio energy hypersurface, the use of more sophisticated IPs than take into account the atomic neighborhood (bond order potentials) and even (with a computational cost much higher) ab initio calculations at T > 0.

O Tungstato de Zircônio (ZrW2O8) é um material que exibe Expansão Térmica Negativa (ETN), isotrópica em um amplo intervalo de temperatura (0,3 a 1050 K). Apesar de amplamente estudado, existem controvérsias acerca dos mecanismos microscópicos responsáveis por este comportamento. A fase cúbica deste composto, denominada a-ZrW2O8, já foi motivo de estudo através de simulações computacionais utilizando Potenciais Interatômicos (PI) e Dinâmica de Rede na Aproximação Quasi-Harmônica (DRQH). Nos dois PI distintos propostos na literatura conseguiu-se reproduzir a ETN da a-ZrW2O8, mas não a dependência com a temperatura do tensor de elasticidade. É partindo desta observação que este trabalho pretende avaliar o desempenho de PI existentes e de novos PI em simulações computacionais visando a descrição da dependência com a temperatura do tensor de elasticidade da a-ZrW2O8 entre 0 e 300 K. Utilizaram-se dados experimentais, tais como posições atômicas, parâmetros de rede e o tensor de elasticidade da a-ZrW2O8 em temperaturas entre 0 e 300 K e, em outra série de cálculos, a hipersuperfície de energia ab initio no limite atérmico para obter os parâmetros dos PI. Diferentes estratégias foram empregadas na busca pelos parâmetros dos PI incluindo minimização em linha, Newton-Raphson/BFGS e Algoritmo Genético (AG). Concluiu-se que não é possível descrever as propriedades estruturais e elásticas da a-ZrW2O8 em função da temperatura com PI simples e que esta incapacidade não está relacionada a qualquer limitação da DRQH ou dos parâmetros dos PI, mas à forma analítica dos PI empregados. Isto sugere que se deve ter cautela na interpretação de resultados obtidos com estes potencias já disponíveis na literatura. Como alternativas para a solução deste problema, pode-se considerar o uso de redes neurais para a representação da hipersuperfície de energia ab initio, o uso de PI mais sofisticados que levam em consideração a vizinhança atômica (bond order potentials) e, também, cálculo ab initio a T > 0, este último a um custo computacional muito mais elevado. / Zirconium tungstate (ZrW2O8) is a material that exhibits negative thermal expansion (NTE), over a wide temperature range (0.3 at 1050 K). Although thoroughly studied, controversies still remain concerning the microscopic mechanisms responsible for this behavior. The cubic phase of this compound, denominated a-ZrW2O8, was already the subject of study through computer simulations using interatomic potentials (IP) and lattice dynamics in quasiharmonic approximation (LDQH). In two different IPs proposed in the literature succeeded in reproducing the a-ZrW2O8 NTE, but not the dependence with temperature of the elasticity tensor. Starting from this observation, this work intends to evaluate of existent IPs and same proposed new IPs in computer simulations aiming the calculation of the tensor of elasticity for a-ZrW2O8 between 0 and 300 K. Experimental data (such as atomic positions, lattice parameters and the tensor of elasticity of a-ZrW2O8 at 0 and 300 K) and, in another series of calculations, the ab initio energy hypersurface in the athermic limit, were used to obtain the parameters of the IPs. Different strategies were used in the search for the parameters of IP, including line minimization, Newton-Raphson/BFGS and genetic algorithm (GA). At the end of an exhaustive search we were led to conclude that it is not possible to describe the structure and elastic properties of a-ZrW2O8 as a function of temperature with simple IPs and that this incapacity is not related the any limitation of LDQH or of the parameters of the IPs, but instead to the analytical form of the tested IPs. This suggests that same results obtained with IPs already available in the literature may be unreliable. As alternatives for the solution of this problem, it can be considered the use of a neural network for the representation of the ab initio energy hypersurface, the use of more sophisticated IPs than take into account the atomic neighborhood (bond order potentials) and even (with a computational cost much higher) ab initio calculations at T > 0.