Calculating ternary diffusivities with dominant cross terms

Abstract

A pattern search method has been developed to calculate ternary diffusivities for situations in which one of the cross-term coefficients dominates, because previous methods provded unable to handle such a situation. The method employs direct calculation of concentrations and residuals instead of approximating them through a Taylor series expansion. Weighting factors are included in order to reduce the statistical importance of the larger concentration changes caused by the magnitude of the cross-term diffusivity relative to that due to the main-term diffusivity. Results show that this method is indeed superior for systems with large cross-term diffusivities and that this method gives identical results for systems in which the cross-term diffusivities are smaller than the main terms.