Kinetic Monte Carlo (KMC) Algorithm for Nanocrystals

<p>This thesis uses the kinetic Monte Carlo (KMC) algorithm to examine the growth morphology and structure of nanocrystals. Crystal growth in a supersaturated gas of atoms and in an undercooled binary melt is investigated. First, in the gas phase, the interplay of the deposition and surface diffusion rates is studied. Then, the KMC algorithm is refined by including solidification events and finally, by adding diffusion in the surrounding liquid. A new algorithm is developed for modelling solidification from an undercooled melt. This algorithm combines the KMC method, which models the change in shape of the crystal during growth, with a macroscopic continuum method that tracks the diffusion of material through solution towards the crystal. For small length and time scales, this approach provides simple, effective front tracking with fully resolved atomistic detail of the crystal-melt interface. Anisotropy is included in the model as a surface diffusion process and the growth rate of the crystal is found to increase monotonically with increase in the surface anisotropy value. The method allows for the study of multiple crystal nuclei and Ostwald ripening. This method will aid researchers to explain why certain crystal shapes form under particular conditions during growth, and may enable nanotechnologists to design techniques for growing nanocrystals with specific shapes for a variety of applications, from catalysis to the medicine field and electronics industry. This will lead to a better understanding of the atomistic process of crystal growth at the nanoscale.</p>

Kinetic Monte Carlo (KMC) Algorithm for Nanocrystals

<p>This thesis uses the kinetic Monte Carlo (KMC) algorithm to examine the growth morphology and structure of nanocrystals. Crystal growth in a supersaturated gas of atoms and in an undercooled binary melt is investigated. First, in the gas phase, the interplay of the deposition and surface diffusion rates is studied. Then, the KMC algorithm is refined by including solidification events and finally, by adding diffusion in the surrounding liquid. A new algorithm is developed for modelling solidification from an undercooled melt. This algorithm combines the KMC method, which models the change in shape of the crystal during growth, with a macroscopic continuum method that tracks the diffusion of material through solution towards the crystal. For small length and time scales, this approach provides simple, effective front tracking with fully resolved atomistic detail of the crystal-melt interface. Anisotropy is included in the model as a surface diffusion process and the growth rate of the crystal is found to increase monotonically with increase in the surface anisotropy value. The method allows for the study of multiple crystal nuclei and Ostwald ripening. This method will aid researchers to explain why certain crystal shapes form under particular conditions during growth, and may enable nanotechnologists to design techniques for growing nanocrystals with specific shapes for a variety of applications, from catalysis to the medicine field and electronics industry. This will lead to a better understanding of the atomistic process of crystal growth at the nanoscale.</p>

A Korteweg–DeVries type model for helical soliton solutions for quantum and continuum phenomena

Quantum mechanical states are normally described by the Schrödinger equation, which generates real eigenvalues and quantizable solutions which form a basis for the estimation of quantum mechanical observables, such as momentum and kinetic energy. Studying transition in the realm of quantum physics and continuum physics is however more difficult and requires different models. We present here a new equation which bears similarities to the Korteweg–DeVries (KdV) equation and we generate a description of transitions in physics. We describe here the two- and three-dimensional form of the KdV like model dependent on the Plank constant [Formula: see text] and generate soliton solutions. The results suggest that transitions are represented by soliton solutions which arrange in a spiral-fashion. By helicity, we propose a conserved pattern of transition at all levels of physics, from quantum physics to macroscopic continuum physics.

The random walk: Universality and continuum limit

The first chapter discusses the asymptotic properties at large time and space of the familiar example of the random walk. The universality of a large scale behaviour and, correspondingly, the existence of a macroscopic continuum limit emerge as collective properties of systems involving a large number of random variables whose individual distribution is sufficiently localized. These properties, as well as the appearance of an asymptotic Gaussian distribution when the random variables are statistically independent, are illustrated with the simple example of the random walk with discrete time steps. The emphasis here is on locality, universality, continuum limit, path integral, Brownian motion, Gaussian distribution and scaling. These properties are first derived from an exact solution and then recovered by renormalization group (RG) methods. This makes it possible to introduce all the RG terminology.

A non-affine electro-viscoelastic microsphere model for dielectric elastomers: Application to VHB 4910 based actuators

Dielectric elastomers belong to a larger group of materials, the so-called electroactive polymers, which have the capability of transforming electric energy to mechanical energy through deformation. VHB 4910 is one of the most popular materials for applications of dielectric elastomers and therefore one of the most investigated. This paper includes a new micromechanically motivated constitutive model for dielectric elastomers that incorporates the nearly incompressible and viscous time-dependent behaviour often found in this type of material. A non-affine microsphere framework is used to transform the microscopic constitutive model to a macroscopic continuum counterpart. Furthermore the model is calibrated, through both homogeneous deformation examples and more complex finite element analysis, to VHB 4910. The model is able to capture both the purely elastic, the viscoelastic and the electro-viscoelastic properties of the elastomer and demonstrates the power and applicability of the electromechanically coupled microsphere framework.