The work presented here is an experimental investigation of the effect of cylindrical geometry on electrical conductivity, in which single-crystal samples of cadmium at the temperature of liquid helium are used, with the diameter on the order of the electron mean free path.

Phonon transport analysis in nano- and micro-porous materials is critical to their energy-related applications. Assuming diffusive phonon scattering by pore edges, the lattice thermal conductivity can be predicted by modifying the bulk phonon mean free paths with the characteristic length of the nanoporous structure, i.e., the phonon mean free path (Lambda(pore)) for the pore-edge scattering of phonons. In previous studies (Jean et al., 2014), a Monte Carlo (MC) technique have been employed to extract geometry determined Lambda(pore) for nanoporous bulk materials with selected periods and porosities. In other studies (Minnich and Chen, 2007; Machrafi and Lebon, 2015), simple expressions have been proposed to compute Lambda(pore). However, some divergence can often be found between lattice thermal conductivities predicted by phonon MC simulations and by analytical models using Lambda(pore). In this work, the effective Lambda(pore) values are extracted by matching the frequency-dependent phonon MC simulations with the analytical model for nanoporous bulk Si. The obtained Lambda(pore) values are usually smaller than their analytical expressions. These new values are further confirmed by frequency-dependent phonon MC simulations on nano porous bulk Ge. By normalizing the volumetric surface area A and Lambda(pore) with the period length p, the same curve can be used for bulk materials with aligned cubic or spherical pores up to dimensionless p.A of 1.5. Available experimental data for nanoporous Si materials are further analyzed with new Lambda(pore) values. In practice, the proposed model can be employed for the thermal analysis of various nanoporous materials and thus replace the time-consuming phonon MC simulations.

Materials in proximity to quantum critical points (QCPs) experience strong fluctuations in the order parameter associated with the transition and often, as a result, display interesting properties. In this dissertation, we have used a variety of experimental probes such as Shubnikov-de Haas quantum oscillations, thermal conductivity and heat capacity, to better understand two such materials — $A_3T_4$Sn$_{13}$ and YFe$_2$Ge$_2$. $A_3T_4$Sn$_{13}$ ($A$ = Ca, Sr; $T$ = Ir, Rh) is a family of quasi-skutterudite superconductors with moderate $T_c$’s between 4 and 8 K. Although the superconductivity is believed to be phonon-mediated with s-wave pairing symmetry, an unusual second-order structural transition makes this material family fascinating to study. Whether this structural transition is a result of three distortions with perpendicular wavevectors resulting in a cubic-to-cubic transformation, or each wavevector acting independently giving rise to cubic-to-tetragonal transformations and formation of twinned domains is a disputed issue. We have measured quantum oscillations in the resistivity of Sr3Ir4Sn13 and compared it to density functional theory (DFT) calculations for both scenarios. Our results strongly suggest that the former interpretation is correct. The structural transition temperature $T^*$ in $A_3T_4$Sn$_{13}$ can be suppressed to zero by tuning with physical or chemical pressure. In (Ca$_x$Sr$_{1−x}$)$_3$Rh$_4$Sn$_13$, the quantum critical point can be accessed purely by chemical substitution at x ~ 0.9. In the vicinity of the QCP, we expect large fluctuations of the order parameter at low temperatures, which for a structural transition could manifest as a structural disorder. We have measured thermal conductivity at temperatures much lower than $T_c$ and found that it is well described by a single power law with suppressed exponents near the QCP. The heat capacity, however, remains ~ $T^3$. After excluding conventional phonon scattering mechanisms, we propose the possibility of intrinsic quasi-static spatial disorder that is related to the structural QCP. YFe$_2$Ge$_2$ is closely linked to the “122” family of iron-based superconductors like KFe$_2$As$_2$, although it has a significantly lower $T_c$ ~ 1 K. It has a rather three-dimensional Fermi surface which closely resembles that of KFe$_2$As$_2$ in the pressure-induced collapsed tetragonal phase. YFe$_2$Ge$_2$ is in proximity to several types of magnetic order which are predicted by DFT calculations to have lower energy than the non-spin polarised case. Even though YFe$_2$Ge$_2$ is non-magnetic, its superconductivity could be strongly affected by magnetic fluctuations. Through a collaboration with researchers at the University of Waterloo, we have measured the thermal conductivity of YFe$_2$Ge$_2$ down to millikelvin temperatures and up to 2.5 T in field. Our results suggest that YFe$_2$Ge$_2$ is a nodal superconductor. This result could assist in the explanation of the unconventional superconductivity in iron-based superconductors.

Polycrystalline geological materials are not normally single phase materials and commonly contain second phases which are known to influence the grain size and mechanical properties of bulk material. Despite the well documented significance of second phases, there are relatively few detailed systematic experimental studies of the effect of second phases on isostatic high temperature grain growth in geological materials. Grain growth is a process that is fundamental to our understanding of how rocks behave in the lower crust / upper mantle where grain size is considered to play an important role in the localization of deformation in addition to determining the strength of materials at these pressure and temperature conditions. Furthermore, the effect that the spatial distribution and grain size of the second phases have on the mechanical properties of rocks is generally acknowledged, but it is not well constrained. Spatial variation is particularly significant in geological systems where a strength contrast exists between phases. With these two things in mind, a two-part study is presented in which the influence of a pore second phase on the microstructural evolution of halite during grain growth (Part I), and the influence of a calcite second phase on the mechanical behaviour of two phase calcite + halite aggregates (Part II), is investigated. In Part I, high temperature (330 °-600 °C), high confining pressure (200 MPa) isostatic grain growth experiments were carried out on 38-125 μm reagent grade halite (99.5%+ NaCl) powder over durations of 10 secs up to 108 days. After hot-pressing, the halite displays a foam texture. Some porosity remained along the grain boundaries, the size and distribution of which appears to impact significantly on the resulting grain size, growth mechanism and kinetics of halite grain growth. Halite grain growth was found to be well described by the normal grain growth equation: d^(1/n)-d0^(1/n)=k0(t-t0)exp(-H/RT) where t is the duration of the growth period, t0 is the time at which normal growth begins, d is the grain size, d0 is the grain size at t0, k0 is a constant, H is the activation enthalpy for the growth controlling process, R is the universal gas constant,T is temperature and n is a growth constant. At 330 °-511 °C, the data is best described by n = 0.25 indicating growth controlled by surface diffusion around pores that lie on the grain boundaries. An activation enthalpy of 122±34 kJ/mol was obtained using the grain size data from these data sets. At 600 °C the data is best described by n = 0.5, suggesting that a transition to interface controlled growth takes place between 511 °C and 600 °C. To investigate the impact of porosity, the Zener parameter (Z = pore size/pore volume fraction) was determined for individual grains in 10 samples. A general trend of increasing with increasing halite grain size is observed, indicating pore elimination keeps pace with pore accumulation in the growing grains. In some samples, the largest grains display a decrease in the Zener parameter corresponding with an increase in pore volume fraction. These grains are interpreted as having experienced a short-lived, abnormal growth phase shortly after t0 during which pore accumulation outpaced pore elimination. A model of pore controlled grain growth is proposed with a view to explaining these observations. In Part II, calcite + halite aggregates of constant volume fraction (0.60 calcite : 0.40 halite) and varying calcite clast size (6 μm 361 μm) were axially deformed to <1% bulk strain at room temperature in a neutron diffraction beamline. Elastic strain and stress in each phase was determined as a function of load from the neutron diffraction data. The strain (and stress) behaviour correlates well with the microstructural parameters: 1) halite mean free path and 2) calcite contiguity. Both phases behaved elastically up to aggregate axial stresses of 20-37 MPa, above these stresses the halite yielded plastically while the calcite remained elastic. Once yielding began, the rate of enhanced load transfer from halite to calcite with increasing applied load decreased with halite mean free path and increased calcite with contiguity. A Hall-Petch relationship between halite mean free path and aggregate yield stress was observed.

The objective of this research is to demonstrate the impact of interconnect process variations, line-edge roughness and size effects on interconnect effective resistivity and ultimately chip performance. The investigation is accomplished through five tasks. In Task I, a new closed-form effective resistivity model, which is a function of line-edge roughness (LER), surface specularity and grain boundary reflectivity, is derived. In Task II, a critical path model is enhanced by including interconnect parasitics using the model in Task I. This enhancement also involves an extensive survey of foundry process data to shed light on the device resistance estimation used in the critical path model in Task II. Task III develops a Monte Carlo (MC) simulation framework called the Fast Interconnect Statistical Simulator (FISS). Using the latest International Technology Roadmap for Semiconductors (ITRS) projections, the FISS projects the impact of interconnect process variations and size effects onto high performance microprocessor units (HP-MPUs). Task IV fabricates metallic interconnect test structures with sub-100nm line-widths. The fifth task statistically calibrates the model from Task I using resistivity data measured from the test structures in Task IV.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

Made available in DSpace on 2014-12-17T14:07:08Z (GMT). No. of bitstreams: 1 EgnilsonMM_TESE.pdf: 6816418 bytes, checksum: d3184a3bc2d81353458b49364682badc (MD5) Previous issue date: 2011-06-30 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this work we developed a computer simulation program for physics porous structures based on programming language C + + using a Geforce 9600 GT with the PhysX chip, originally developed for video games. With this tool, the ability of physical interaction between simulated objects is enlarged, allowing to simulate a porous structure, for example, reservoir rocks and structures with high density. The initial procedure for developing the simulation is the construction of porous cubic structure consisting of spheres with a single size and with varying sizes. In addition, structures can also be simulated with various volume fractions. The results presented are divided into two parts: first, the ball shall be deemed as solid grains, ie the matrix phase represents the porosity, the second, the spheres are considered as pores. In this case the matrix phase represents the solid phase. The simulations in both cases are the same, but the simulated structures are intrinsically different. To validate the results presented by the program, simulations were performed by varying the amount of grain, the grain size distribution and void fraction in the structure. All results showed statistically reliable and consistent with those presented in the literature. The mean values and distributions of stereological parameters measured, such as intercept linear section of perimeter area, sectional area and mean free path are in agreement with the results obtained in the literature for the structures simulated. The results may help the understanding of real structures. / Neste trabalho foi desenvolvido um programa de simula??o computacional f?sica de estruturas porosas com base em linguagem de programa??o C++ utilizando uma placa Geforce 9600 GT com o chip da Physx, originalmente desenvolvida para jogos eletr?nicos. Com essa ferramenta, a capacidade de intera??o f?sica entre os objetos simulados ? ampliada, possibilitando simular uma estrutura porosa, como por exemplos, rochas reservat?rios ou estruturas com alta densidade. O procedimento inicial para desenvolvimento da simula??o porosa ? a constru??o de uma estrutura c?bica constitu?da de esferas com um ?nico tamanho e com tamanhos variados. Al?m disso, podem ser ainda simuladas estruturas com variadas fra??es de volumes. Os resultados apresentados est?o divididos em duas partes: a primeira, as esferas ser?o consideras como gr?os s?lidos, ou seja, a fase matriz representa a porosidade; a segunda, as esferas est?o sendo considerada com poros. Neste caso a fase matriz representa a fase s?lida. As simula??es nos dois casos s?o as mesmas, mas as estruturas simuladas s?o intrinsecamente distintas. Para validar os resultados apresentados pelo programa, foram realizadas simula??es variando a quantidade de gr?os, a distribui??o de tamanhos de gr?os e a fra??o de vazio na estrutura. Todos os resultados apresentados mostraram-se estatisticamente confi?veis e em concord?ncia com os apresentados na literatura. Os valores m?dios e as distribui??es dos par?metros estereol?gicos mensurados, como intercepto linear, per?metro de se??o de ?rea, ?rea de se??o e livre caminho m?dio est?o de acordo com os resultados obtidos na literatura para as estruturas simuladas. Os resultados podem auxiliar a compreens?o de estruturas reais.