Ternary diffusion: The (2~D) matrix of an ideal solid solution

Abstract

The elements (~Dik3) of the (2~D) matrix of an interdiffusing ideal ternary solid solution have been determined for Manning’s random alloy model, and the relationships among the elements and the tracer diffusion coefficients (Di*’s) of the atom species have been examined. It is shown that for physically realistic choices of tracer diffusion coefficients a quasi-linear relationship exists between the ~Dik3 of the ith atom species and its atom fraction over the entire composition triangle. It is also, shown that a ~Dii3 diagonal element will never be negative for any physically realistic values of the Di*’s. Finally, the implications of the equality ~D223 = ~D223 are demonstrated.