Computational Study of and Model Development for Morphological Evolution in Metallic-Nanostructure Heteroepitaxy.

Abstract

In this thesis, we describe computational studies relevant to morphological evolution in metallic-nanostructure heteroepitaxy. Our first contribution focuses on the understanding of the thermodynamic driving force behind morphological evolution of the magnetic thin-film system. Specifically, we study the stability of thin single-crystal, internal-defect-free Fe films on Mo(110) and W(110) substrates through calculations of energetics including contributions from the misfit strain, interfacial misfit dislocations, film surface and interface. It is found that the combined energetics gives rise to a driving force for solid-state dewetting for a single-crystal, internal-defect-free film, i.e., an instability of a flat film that leads to formation of thicker and thinner regions.

Our second contribution lies in the development of numerical methods for the classical density functional theory (CDFT) and the phase-field crystal (PFC) method, both of which are promising tools for modeling metallic-nanostructure hetereoepitaxy. We introduce a new approach to represent a two-body direct correlation function (DCF) in order to alleviate the computational demand of CDFT and enhance the predictive capability of the PFC method. The approach utilizes a rational function fit (RFF) to approximate the two-body DCF in Fourier space. We use the RFF to empirically parameterize the two-body DCF allows us to obtain the thermodynamic properties of solids and liquids that agree with the results of CDFT simulations with the full two-body DCF without incurring significant computational costs. In addition, the RFF can also be used to improve the representation of the two-body DCF in the PFC method.

Our third contribution involves an investigation of procedures for calculating isothermal elastic constants using the PFC method. We find that the conventional procedure used in the PFC method for calculating the elastic constants are inconsistent with those defined from a theory of thermoelasticity of stressed materials. Therefore, we present an alternative procedure for calculating the elastic constants that are consistent with the definitions from the thermoelasticity theory, and show that the two procedures result in different predictions. The second and third contributions together will provide necessary modeling capability for quantitative and accurate simulations of morphological evolution in metallic thin films.