Thesis (Ph.D.)--Case Western Reserve University, 2009 / Department of Materials Science and Engineering Available online via the OhioLINK ETD Center

Orientador: Maurice de Koning / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T12:17:48Z (GMT). No. of bitstreams: 1 PenaArdila_LuisAldemar_M.pdf: 3312905 bytes, checksum: da0a7b28a57fc4d8a5a1639bdf9f9473 (MD5) Previous issue date: 2010 / Resumo: O método Monte Carlo de integrais de trajetória (PIMC) é um sofisticado método para simular sistemas quânticos de muitos corpos. Em particular, é usado para a simulação de sistemas bosônicos como o 4He. O principal objetivo deste trabalho de Mestrado é aplicar o método PIMC para determinar as constantes elásticas do 4He sólido na sua fase hcp. Estas propriedades são muito importantes por estarem envolvidas num possível novo estado da matéria que foi descoberto no hélio sólido: a fase supersólida. Para realizar este objetivo, empregamos o pacote computacional PIMC++, que é uma implementação do método PIMC na linguagem C++, desenvolvido no grupo do Prof. David Ceperley. Primeiro realizamos testes básicos, calculando a energia total e a capacidade térmica para bósons livres, para as quais existem resultados exatos. Em seguida, consideramos a fase líquida do 4He, determinando propriedades como a energia, a fração de condensado e a densidade superfluida para o 4He líquido abaixo de 4K às condições de pressão de vapor saturado. Além disso, determinamos a função de correlação de pares e o fator de estrutura. Todas as propriedades apresentam boa concordância com dados experimentais. Após estes testes iniciais, determinamos as propriedades elásticas do 4He sólido na sua fase hcp descrito pelo potencial de pares de Aziz. Para realizarmos isso, implementamos o esquema de Parrinello e Rahman para permitir a utilização de células computacionais não-ortorrômbicas no pacote PIMC++. Além disso, desenvolvemos e implementamos a expressão para a observável tensorial tensão na linguagem de integrais de trajetória. Após estes desenvolvimentos técnicos, determinamos as constantes elásticas através de uma série de deformações de extensão/compressão e de cisalhamento, determinando o estado de tensão interno correspondente. Depois, usando a definição em termos da relação linear entre tensão e deformação, calculamos as constantes elásticas. Os resultados obtidos para 3 diferentes densidades e uma temperatura de 1 K demonstram que o modelo de Aziz captura as características fundamentais das propriedades elásticas do 4He na fase hcp / Abstract: The path-integral Monte Carlo (PIMC) method is a sophisticated approach for the simulation of many-body quantum systems. In particular, it has been extensively used for the study of manybody bosonic systems such as 4He. The main objective of the present dissertation is to apply the PIMC method to determine the elastic constants of solid 4He in its hcp phase. These properties are very important in view of their apparent involvement in the phenomenon of supersolidity in solid 4He. To realize this objective we utilize the software package PIMC++, which is an implementation of the PIMC method written in C++, developed in the group of Prof. David Ceperley. First, we carry out a number of basic tests, computing the total energy and heat capacity of an ideal gas of bosons, a system for which analytical results are available. Subsequently, we consider the liquid phase of 4He described by the Aziz pair potential, determining the energy per particle, the condensate fraction and superfluid density below 4 K under conditions of saturated vapor pressure. In addition, we compute the pair correlation function and the structure factor. All properties show good agreement with experimental data. After these preliminary tests, we determine the elastic constants of solid 4He in its hcp phase. To this end we implement the scheme due to Parrinello and Rahman, which allows the use of non-orthorhombic computational cells in PIMC++. In addition, we develop and implement an expression for the stress tensor observable within the path-integral formalism. After these technical developments, we determine the elastic constants by means of a series of tension/compression and shear deformations, measuring the corresponding internal stress states. Next, using the definition in terms of the linear relationship between stress and strain, we compute the elastic constants. The results obtained for 3 different densities at a temperature of 1K demonstrate that the Aziz model captures the fundamental characteristics of the elastic properties of 4He in the hcp phase / Mestrado / Física da Matéria Condensada / Mestre em Física

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The present work provides a micromechanics approach based on the generalized self-consistent composite cylinders method as a non-Eshelby approach towards for assessing the impact of carbon nanotubes on the multi-functional nature of nanocom-posites in which they are a constituent. Emphasis is placed on the effective elastic properties as well as electrical and thermal conductivities of nanocomposites con-sisting of randomly oriented single walled carbon nanotubes in epoxy. The effective elastic properties of aligned, as well as clustered and well-dispersed nanotubes in epoxy are discussed in the context of nanotube bundles using both the generalized self-consistent composite cylinders method as well as using computational microme-chanics techniques. In addition, interphase regions are introduced into the composite cylinders assemblages to account for the varying degrees of load transfer between nanotubes and the epoxy as a result of functionalization or lack thereof. Model pre-dictions for randomly oriented nanotubes both with and without interphase regions are compared to measured data from the literature with emphasis placed on assessing the bounds of the effective nanocomposite properties based on the uncertainty in the model input parameters. The generalized self-consistent composite cylinders model is also applied to model the electrical and thermal conductivity of carbon nanotube-epoxy nanocomposites. Recent experimental observations of the electrical conductivity of carbon nanotube polymer composites have identified extremely low percolation limits as well as a per-ceived double percolation behavior. Explanations for the extremely low percolation limit for the electrical conductivity of these nanocomposites have included both the creation of conductive networks of nanotubes within the matrix and quantum effects such as electron hopping or tunneling. Measurements of the thermal conductivity have also shown a strong dependence on nanoscale effects. However, in contrast, these nanoscale effects strongly limit the ability of the nanotubes to increase the thermal conductivity of the nanocomposite due to the formation of an interfacial thermal resistance layer between the nanotubes and the surrounding polymer. As such, emphasis is placed here on the incorporation of nanoscale effects, such as elec-tron hopping and interfacial thermal resistance, into the generalized self-consistent composite cylinder micromechanics model.

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The structural and mechanical properties of s-I methane hydrate have been investigated by first principles calculations. For the first time, the fully elastic constant tensor of s-I methane hydrate is obtained entirely ab-initio. The calculated lattice parameter, bulk modulus, and elastic constants were found to be in good agreement with experimental data at ambient pressure. The Young modulus, Poisson ratio and bulk sound velocities are estimated from the calculated elastic constants and compared with wave speed measurements available.

This thesis describes procedures and theory for a family of one-sided ultrasonic methods for determining third order elastic constants (TOEC) using sets of angle-beam wedges mounted on one side of a specimen. The methods are based on the well-known acoustoelastic effect, which is the change of wave speed with applied loads and is a consequence of the mechanical nonlinearity of a material. Increases in material nonlinearity have been correlated to the progression of damage, indicating that tracking changes in TOECs may provide a practical means of monitoring damage accumulation at the microstructural level prior to formation of macroscopic defects. Ultrasonic methods are one of the only ways to measure TOECs, and most prior techniques have utilized wave propagation paths parallel and perpendicular to the loading directions. A few additional ultrasonic techniques reported in the literature have employed oblique paths but with immersion coupling. These reported techniques are generally unsuitable for field implementation. The one-sided contact approach described here is applicable for in situ measurements of TOECs and thus lays the foundation for tracking of TOECs with damage. Theory is reviewed and further developed for calculating predicted velocity changes, and thus time shifts, as a function of uniaxial tensile loading for longitudinal, shear vertical, and shear horizontal waves in the context of angle-beam transducers mounted on the surface of the specimen. A comparison is made to published results where possible. The inverse problem of determining the three TOECs of an isotropic material from three measurements employing three different angle beam configurations is comprehensively analyzed. Four configurations providing well-posed solutions are identified and examined. A detailed sensitivity analysis is carried out to identify the best mounting configuration, wave mode combinations, refracted angles and geometry requirements for recovering the three TOECs. Two transducer mounting configurations are considered: (1) attached (glued-on) transducers potentially suitable for in situ monitoring, and (2) floating (oil-coupled) transducers potentially suitable for single measurements. Limited experimental results are presented for the attached case using two longitudinal measurements and one shear vertical measurement. The floating case experiments utilized three of the four well-posed solutions, and measurements were made on several aluminum alloys and low carbon steel. Key experimental issues are identified and discussed for both transducer mounting configurations.

Pastilhas de dióxido de urânio (UO2) são empregadas como combustível nos reatores nucleares de potência, onde as condições operacionais introduzem elevados gradientes térmicos nas pastilhas. Potências elevadas propiciam a fusão da parte central das pastilhas. O inchamento das pastilhas de dióxido de urânio (UO2), decorrente dos produtos de fissão, pode causar o trincamento do material, em função disso, o estudo do seu comportamento mecânico é importante. Esse trabalho avaliou a aplicação de método ultrassônico na obtenção de constantes elásticas. Em função das dificuldades no manuseio do material nuclear, optou-se por um estudo comparativo em pastilhas de alumina (Al2O3). Foram fabricados e usados dois conjuntos de 10 pastilhas de Al2O3 com densidades de 92% e 96%. Foi desenvolvida técnica ultrassônica por transmissão obtendo medidas do tempo de percurso de ondas ultrassônicas, longitudinais e transversais, usadas para a determinação das constantes elásticas do material. Equações relacionando a velocidade da onda ultrassônica ao módulo de elasticidade, módulo de cisalhamento e coeficiente de Poisson, permitiram obter essas constantes elásticas, que apresentaram excelente concordância com a literatura disponível para o Al2O3.

Pastilhas de dióxido de urânio (UO2) são empregadas como combustível nos reatores nucleares de potência, onde as condições operacionais introduzem elevados gradientes térmicos nas pastilhas. Potências elevadas propiciam a fusão da parte central das pastilhas. O inchamento das pastilhas de dióxido de urânio (UO2), decorrente dos produtos de fissão, pode causar o trincamento do material, em função disso, o estudo do seu comportamento mecânico é importante. Esse trabalho avaliou a aplicação de método ultrassônico na obtenção de constantes elásticas. Em função das dificuldades no manuseio do material nuclear, optou-se por um estudo comparativo em pastilhas de alumina (Al2O3). Foram fabricados e usados dois conjuntos de 10 pastilhas de Al2O3 com densidades de 92% e 96%. Foi desenvolvida técnica ultrassônica por transmissão obtendo medidas do tempo de percurso de ondas ultrassônicas, longitudinais e transversais, usadas para a determinação das constantes elásticas do material. Equações relacionando a velocidade da onda ultrassônica ao módulo de elasticidade, módulo de cisalhamento e coeficiente de Poisson, permitiram obter essas constantes elásticas, que apresentaram excelente concordância com a literatura disponível para o Al2O3.