Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids

Report No. ARL-TR-4002
Authors: John D. Clayton; Peter W. Chung; Michael A. Greenfield; William D. Nothwang
Date/Pages: December 2006; 40 pages
Abstract: A theory for charged vacancy diffusion in elastic dielectric materials is formulated and implemented numerically in a finite difference code. The governing equations consist of Maxwell?s equations of electrostatics coupled with kinetic equations for vacancy diffusion, with the chemical potential accounting for both mixing energy of vacancies and electrostatically-driven charge migration. A second-order accurate implicit scheme is used to solve Maxwell?s parabolic equations, while an explicit method is used to integrate the elliptic evolution equations for transient vacancy concentration. In addition to the theoretical background and numerical methodology, user documentation is included for the computer implementation, presently limited to one-dimensional analysis. Provided here are descriptions of the code structure, user instructions, and a representative application of the software for analysis of barium strontium titanate thin films containing charged oxygen vacancies. The source code is included in the appendix.
Distribution: Approved for public release
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Last Update / Reviewed: December 1, 2006