A novel approach to calculate diffusion matrix in ternary systems: Application to Ag-Mg-Mn and Cu-Ni-Sn systems

Diffusion behavior is of fundamental importance in material science and engineering. As a result, extensive attention has been paid to develop methodologies for obtaining the composition-dependent interdiffusivities. The present work proposed a novel approach with two steps to extract the interdiffusion coefficients from a single ternary diffusion couple. The concept of basis function is introduced, and this novel method is based on the utilization of both finite element method and optimization algorithm. Utilizing eight groups of diffusion couples together with electron probe microanalysis technique, the composition-dependent interdiffusion coefficients in fcc Ag-Mg-Mn alloys at 973 and 1073 K were determined via both the present method and Matano-Kirkaldy method. A home-made code is written to implement the novel numerical approach. The obtained interdiffusion coefficients based on the present method agree with the reliable ones from the Matano-Kirkaldy method better than previous methods for fcc Ag-Mg-Mn alloys in the present work as well as fcc Cu-Ni-Sn alloys from the literature, especially for the main interdiffusivities. In most cases, the presently computed main interdiffusivities by means of the composition-dependent diffusivities agree with the reliable ones from the Matano-Kirkaldy method within 50%, Besides, the sign of cross interdiffusivities using this novel method is usually the same as that from the Matano-Kirkaldy method. Such a high calculation precision and efficiency cannot be obtained using previous methods.