<p> This thesis addresses the use of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model for better understanding of kinetics of crystallization of the beta-phase in sensitized aluminum alloys. Three acoustic parameters: longitudinal velocity, transverse velocity, and attenuation coefficient for longitudinal waves, are modeled as a function of time as the beta-phase volume fraction increases. The acoustic parameters were previously measured in the same laboratory with two ultrasonic techniques, Resonant Ultrasound Spectroscopy (RUS) and Pulse Echo (PE), on sensitized samples of Al5083-H116 and Al5456-H116. In this investigation, a comparative study of beta-phase kinetics in terms of the phase transformation rate constant, <i>k,</i> and Avrami exponent, n, was performed on the three acoustic parameters, to understand their evolution with the degree of sensitization. The values of n indicate a combination of 2D to 1D growth at the grain boundaries and at their intersections. The values of <i>k</i> grow non-linearly with the heat-treatment temperature; <i>k</i> is higher for the attenuation coefficient as compared with that for velocity.</p><p>

<p> Ferromagnetic nanostructures are under considerable interest for producing larger capacity magnetic storage devices. Denser magnetic storage leads to finer magnetic grains and smaller bit size, however, as bit size shrinks it approaches a limit, such that, a single magnetic grain is only capable of holding a single bit of information. Therefore, changes in nanoscale morphology can produce different magnetic properties, so characterizing nanostructures is crucial. Atomic force microscopy (AFM) is a common way to model the morphology of ferromagnetic thin films atop of nanosphere templates. In our research, we used AFM images of polystyrene nanospheres on top of silicon substrates to define the morphology of the AFM tip geometry. We calculated &thetas;L to be approximately 4.30 &plusmn; 1.07&deg;, &thetas;R to be approximately 21.14 &plusmn; 0.33&deg;, the tip apex radius r to be 37.87 &plusmn; 2.43 nm, and a total angle of 25.44&deg; with an error of 15.2% from manufacture specifications. After analyzing the same sample scanned at 4 different angles, 0&deg;, 45&deg;, 90&deg;, and 135&deg;, relative to the cantilever, we determined the optimal scan direction for our samples was 0&deg; relative to the cantilever, due to the geometry of the AFM tip. After scanning several samples containing 600 nm nanospheres with 20 nm and 40 nm of Permalloy thin film deposited on top, the AFM images were obtained. Further research is needed, such as, modification of the geometrical relationship between the tip and the layers atop of the nanospheres to clearly model the structure of Py atop of nanospheres.</p><p>

<p> The concept of the geometric Berry phase of the quantum mechanical wave function has led to a better theoretical understanding of natural phenomena in all fields of fundamental physics research. In condensed matter physics, the impact of this theoretical discovery has been particularly profound: The quantum Hall effect, the anomalous Hall effect, the quantum spin Hall effect, magnetic skyrmions, topological insulators, and topological semimetals are but a few subfields that have witnessed rapid developments over the three decades since Michael Berry's landmark paper. In this thesis, I will present and discuss the results of three experiments where Berry's phase leads to qualitatively new transport behavior of electrons or magnetic spin excitations in solids.</p><p> We introduce the theoretical framework that leads to the prediction of a thermal Hall effect of magnons in Cu(1,3-bdc), a simple two-dimensional layered ferromagnet on a Kagom&eacute; net of spin <i>S</i> = 1/2 copper atoms. Combining our experimental results measured down to very low temperatures <i>T</i> = 0.3 K with published data from inelastic neutron scattering, we report a quantitative comparison with the theory. This confirms the expected net Berry curvature of the magnon band dispersion in this material.</p><p> Secondly, we have studied the thermal Hall effect in the frustrated pyrochlore magnet Tb₂Ti₂O₇, where the thermal Hall effect is large in the absence of long-range magnetic order. We establish the magnetic nature of the thermal Hall effect in Tb₂Ti₂O₇, introducing this material as the first example of a paramagnet with non-trivial low-lying spin excitations. Comparing our results to other materials with zero thermal Hall effect such as the classical spin ice Dy₂Ti₂O₇ and the non-magnetic analogue Y₂Ti₂O₇, we carefully discuss the experimental limitations of our setup and rule out spurious background signals.</p><p> The third and final chapter of this thesis is dedicated to electrical transport and thermopower experiments on the half-Heusler material GdPtBi. A careful doping study of the negative longitudinal magnetoresistance (LMR) establishes GdPtBi as a new material platform to study the physical properties of a simple Weyl metal with only two Weyl points (for magnetic field along the crystallographic &lang;111&rang; direction). The negative LMR is associated with the theory of the chiral anomaly in solids, and a direct consequence of the nonzero Berry curvature of the energy band structure of a Weyl semimetal. We compare our results to detailed calculations of the electronic band structure. Moving beyond the negative LMR, we report for the first time the effect of the chiral anomaly on the longitudinal thermopower in a Weyl semimetal.</p><p>

This thesis presents a study of two basic modes of deformation of a thin sheet: wrinkling and crumpling, viewed primarily in the context of an elastic sheet confined by capillary forces on a drop of liquid. First, it provides a brief conceptual background in the relevant physics of thin sheet mechanics and capillarity and introduces the general principles of wrinkling and crumpling. The problem of confining a circular sheet on an increasingly curved spherical drop is presented as a vehicle to explore these principles. At finite curvature, the sheet is seen to wrinkle around its outer edge. At large confinement, characteristic features of crumpling gradually dominate the pattern. The experimental observations in both regimes are analyzed separately. Analysis of images of the sheet in the wrinkled regime yield data for the number and length of the wrinkled zone, as a function of the experimental control parameter, the pressure. The length of the wrinkles is correctly described by a far-from-threshold theory, which describes a limiting regime in thin-sheet mechanics, distinguished by high 'bendability'. The validity of this theory is verified by the data for highly bendable, ultrathin sheets for the first time. The theory is based on the assumption that the wrinkles completely relax compressive stresses and therefore preserve the cylindrical symmetry of the stress field. The emergence of crumpling from the wrinkled shape is explored via evolution of visible features in the sheet as well as gaussian curvature measurements obtained by analyzing height maps from optical profilometry. The emergence of several length scales, increasing asymmetry in curvature distribution, the failure of wrinkle extent prediction and formation of d-cones associated with crumpling are all measured to locate the transition to a crumpled state. The value of gaussian curvature at the center of the sheet appears to follow the cylindrically symmetric prediction over the whole range of the experiment, suggesting that the onset of crumpling events does not affect the global shape of the sheet. Finally, analogous wrinkling and crumpling behavior of particle-laden interfaces is discussed. The spontaneous formation of conical defects in a curved 2D crystal is compared to the crumpling of a sheet on a drop, and insight from thin sheet mechanics is applied to the mysterious wrinkling of particle rafts. Some future directions for measuring wrinkling of sheets on negative curvature surfaces and deformations of fluid interfaces are proposed.

In this dissertation, we study velocity distributions in granular gases. For granular systems at low density, kinetic theory reduces to the Boltzmann equation which is based on the assumption of molecular chaos. At large velocity scales, stationary solutions with power-law tails, f( v) ∼ v–σ, have been derived from the Boltzmann equation for spatially homogeneous granular systems [6]. The behavior of power-law tail is complete generic, holding for arbitrary dimension, arbitrary collision rules, and general collision rates. We find the non-Maxwellian steady states using event-driven molecular dynamics simulations. Firstly, power-law steady states are observed in driven systems where energy is injected rarely at large velocity scale V . The range of power-law tail shrinks when we increase the heating-dissipation ratio [special characters omitted], where NI and NC are number of injections and number of collisions, respectively. Then a crossover from a power-law to a stretched exponential distribution is developed when the heating-dissipation ratio [special characters omitted] is close to 1. It is the energy cascade from a few energetic particles to the overwhelming majority of slowly moving particles that causes the non-Maxwellian velocity distributions. Steady states with power-law tail are robust as long as the injection velocity scale V is essentially separated from the typical velocity scale v0. These steady states are shown to exist for a wide range of number densities, different combinations of injection velocities and injection rates. The injection velocity scale V, the typical velocity scale v0, and the injection rate per particle are related by energy balance. This energy balance relation is confirmed by data collapse of velocity distributions for various choices of parameters.

In this work, we have developed a self-consistent field theory (SCFT) for polyelectrolytic systems and studied four important problems of contemporary interest: microphase separation in the melts of charged-neutral diblock copolymers, confinement effects on flexible polyelectrolytes, counterion adsorption on single flexible polyelectrolyte chain and the origin of translocation barriers in polyelectrolytic systems. Using the theory, we have been able to capture the effects of the degree of ionization, salt concentration, electrostatic and the excluded volume interaction strengths, degree of polymerization, role of architecture and solvent quality on these polyelectrolytic systems. Within saddle-point approximation, the polyelectrolyte chain configuration is described as a walk in the presence of fields coming from the excluded volume interactions and the other effects such as incompressibility in addition to the electrostatic potential. The electrostatic potential, on the other hand, is obtained from Poisson-Boltzmann like equation. So, in contrast to the SCFT for neutral polymers, there are two coupled non-linear equations namely modified diffusion equation describing the walk in the fields and the Poisson-Boltzmann equation, which have to be solved self-consistently. In this work, we have developed various numerical schemes to solve these coupled non-linear sets of equations. Furthermore, comparison of the SCFT results with a previous developed variational theory for polyelectrolytes has been carried out. Also, systematic expansions around the saddle-point results have been carried out to capture the effects of the density fluctuations of the small ions in the systems.

Nowadays, solid “filler” particles can be found in many manufactured polymeric materials because of the enhanced thermal and mechanical properties these particles can offer. However, the influence of the “filler” particles, especially those with size on a nanoscopic scale, on the structural evolution of multicomponent systems, is still poorly understood. In this thesis, the spinodal decomposition (SD) of polystyrene/poly(vinyl methyl ether) (PS/PVME) polymer blend system mixed with different nanoparticles have been investigated by the small angle light scattering (SALS) technique. Interpreting the data using the Cahn-Hilliard linear theory and the scaling theory on early stage and late stage, respectively, we concluded that the addition of nanoparticles into the pure polymer blends can cause a retardation of the phase separation. Furthermore, experiments on polystyrene/poly(2-vinyl pyridine) (PS/P2VP) polymer blends mixed with polystyrene-covered gold nanoparticles (Au-PS) have shown that during the spinodal decomposition these Au-PS nanoparticles can self-assemble at the continuous PS/P2VP interface, due to the tendency to reduce interfacial energy, making it possible to create the so-called “bijel” structure (bicontinuous interfacially jammed emulsion jel). We believe that the “bijel” structures have a huge potential of being used in areas such as photovoltaics and catalysis, because of their large surface areas.

It has been realized that a p-wave order parameter can emerge in a synthetic superconductor constructed from a semiconductor and an s-wave superconductor, provided that fermion doubling is removed. In one dimension, the required electron spectrum consists of two counter-propagating modes with opposite spin orientations, so-called helical channels. Helical channels can be realized in nanowires with spin-orbit interactions in the presence of magnetic field, topological insulators, at the edges of the quantum spin Hall system, or in the integer and fractional quantum Hall effect regimes. This thesis will discuss the formation and control of helical states in different systems.

First principles calculations, using the density-functional theory and particularly the local density approximation (LDA), have achieved remarkable success in studying the properties of solid state systems. Although the basic results of these calculations are the electronic structures (eigenvalues, eigenfunctions, etc.) and the total energy of ground state, many other related physical properties can be deduced from them by investigating their response under external perturbations. Using the linear response method with linearized-augmented-plane-wave (LAPW) basis, we have calculated lattice dynamical properties of important semiconductors CuCl, SiC and ferroelectric KNbO{dollar}\sb3.{dollar} CuCl is known to exhibit large anharmonic effects and possibly a complicated multi-well Born Oppenheimer surface reminiscent of the instabilities in perovskite ferroelectrics and the high-temperature cuprate superconductors. However, we have determined its phonon dispersion from first-principles calculations and find it to be in good agreement with the low temperature experimental results. For zincblende SiC, the calculated phonon dispersions, Grunensen's parameters, dielectric constant, Born effective charge, elastic constants, and the equation of state agree very well with the available experimental data. Additionally, we find that its dielectric constant decreases with pressure and Born effective charge increases with pressure up to 80 GPa without any saturation, calling into question the recent interpretation of experimental results to the contrary. Our calculations for KNbO{dollar}\sb3{dollar} find unusually large Born effective charges on Nb and O that originate from the strong covalent interactions between Nb 4d and O 2p orbitals. The Born effective charges and dielectric tensors are found to change up to 20% from the cubic structure to the rhombohedral structure, demonstrating that the polarizability of the perovskite ferroelectrics is very sensitive to the small atomic displacements involved in the transitions. The phonon modes for the cubic and rhombohedral structures are also calculated and their implications are discussed.

Accurate determination of the onset of structural transitions in complex physico-chemical systems is of crucial importance in condensed matter science and materials engineering. As direct access to such responses is typically difficult to attain experimentally, computational techniques such as molecular dynamics (MD) have become powerful tools for probing the underlying atomic-scale dynamics and determining the transition onsets. While the most appealing feature of MD lies in its ability to provide dynamic information with atomistic resolution, integrating all the degrees of freedom over observable length and time scales remains a major challenge in computational materials science. The problem is compounded when the underlying physical processes are governed by rare events. In recent years, a variety of new techniques, such as accelerated dynamics, transition path sampling, metadynamics, and equation-free methods have been proposed to address long-time dynamics issues directly through atomistic simulation. In this thesis, new equation-free-based (i.e., time-stepper-based) coarse molecular-dynamics (CMD) methods are developed and implemented to analyze and determine the onsets of structural transitions in condensed-matter systems. In CMD, coarse-grained information is estimated on the fly from many short and properly initialized independent replica MD simulations. This information can then be used to predict transition points in the physical behavior of the complex systems under consideration. The method is based on the description of the evolution of the probability density, P (ψ, t), as approximated by the Fokker-Planck equation where ψ ( t) is an appropriate coarse-grained observable that describes the state of the system. Specific problems that have been analyzed in this thesis include the thermodynamic melting of crystalline materials, the pressure-induced polymorphic transformation of metallic crystals, and the thermally induced order-to-disorder transition of inert-gas layers physisorbed on graphite substrate surfaces. The analysis focuses on the construction of the underlying effective free-energy landscapes and leads to accurate and computationally efficient determination of the corresponding transition onsets.