The Immersed Interface Method


Book Description

This book provides an introduction to the immersed interface method (IIM), a powerful numerical method for solving interface problems and problems defined on irregular domains for which analytic solutions are rarely available. This book gives a complete description of the IIM, discusses recent progress in the area, and describes numerical methods for a number of classic interface problems. It also contains many numerical examples that can be used as benchmark problems for numerical methods designed for interface problems on irregular domains.













Phase-field Models for Simulating Physical Vapor Deposition and Microstructure Evolution of Thin Films


Book Description

The focus of this research is to develop, implement, and utilize phase-field models to study microstructure evolution in thin films during physical vapor deposition (PVD). There are four main goals to this dissertation. First, a phase-field model is developed to simulate PVD of a single-phase polycrystalline material by coupling previous modeling efforts on deposition of single-phase materials and grain evolution in polycrystalline materials. Second, a phase-field model is developed to simulate PVD of a polymorphic material by coupling previous modeling efforts on PVD of a single-phase material, evolution in multiphase materials, and phase nucleation. Third, a novel free energy functional is proposed that incorporates appropriate energetics and dynamics for simultaneous modeling of PVD and grain evolution in single-phase polycrystalline materials. Finally, these phase-field models are implemented into custom simulation codes and utilized to illustrate these models' capabilities in capturing PVD thin film growth, grain and grain boundary (GB) evolution, phase evolution and nucleation, and temperature evolution. In general, these simulations show: grain coarsening through grain rotation and GB migration such that grains tend to align with the thin film surface features and GBs migrate to locations between these features so that each surface feature has a distinct grain and orientation; the incident vapor flux rate controls the density of the thin film and the formation of surface and subsurface features; the substrate phase distribution initially acts as a template for the growing microstructure until the thin film becomes sufficiently thick; latent heat released during PVD increases the surface temperature of the thin film creating a temperature gradient within the thin film influencing phase evolution and nucleation; and temperature distributions lead to regions within the thin film that allow for multiple phases to be stable and coexist. Further, this work shows the sequential approach for coupling phase-field models, described in goals (i) and (ii) is sufficient to capture first-order features of the growth process, such as the stagnation of GBs at the valleys of the surface roughness, but to capture higher-order features, such as orientation gradients within columnar grains, the single free energy functional approach developed in goal (iii) is necessary.







Advances in Modeling of Chemical Vapor Infiltration for Tube Fabrication


Book Description

The forced flow/thermal gradient chemical vapor infiltration process (FCVI) can be used for fabrication of tube-shaped components of ceramic matrix composites. Recent experimental work at Oak Ridge National Laboratory (ORNL) includes process and materials development studies using a small tube reactor. Use of FCVI for this geometry involves significant changes in fixturing as compared to disk-shaped preforms previously fabricated. The authors have used their computer model of the CVI process to simulate tube densification and to identify process modifications that will decrease processing time. This report presents recent model developments and applications.







Evolution of Thin Film Morphology


Book Description

The focus of this book is on modeling and simulations used in research on the morphological evolution during film growth. The authors emphasize the detailed mathematical formulation of the problem. The book will enable readers themselves to set up a computational program to investigate specific topics of interest in thin film deposition. It will benefit those working in any discipline that requires an understanding of thin film growth processes.