A transfer matrix analysis of quaternary diffusion

Abstract

A transfer matrix method (TMM), developed recently by Ram-Mohan and Dayananda, has been employed for the first time to generate error function solutions for quaternary diffusion in solid–solid metallic diffusion couples. The method was validated with the aid of a hypothetical couple with known quaternary interdiffusion coefficients and applied to two experimental Cu–Ni–Zn–Mn quaternary couples annealed at 775°C. Quaternary interdiffusion coefficients were determined by the Dayananda analysis from the concentration profiles of the couples over selected composition ranges in the diffusion zone and employed for the subsequent TMM calculation of error function solutions. For the hypothetical test couple, identical sets of constant interdiffusion coefficients were determined on either side of the Matano plane and utilized for the calculation of concentration profiles by TMM. For the experimental Cu–Ni–Zn–Mn couples, interdiffusion coefficients determined over selected regions in the diffusion zone were employed for the TMM generation of the concentration profiles.

Acknowledgements

This work was supported by the National Science Foundation under Grant No. DMR-0304777.