On Negative Diagonal Elements in the Diffusion Coefficient Matrix of Multicomponent Systems

In multicomponent systems the diffusion coefficient turns into a matrix. The diagonal elements represent diffusion of a species caused by its own concentration gradient. In a thermodynamically stable binary alloy it is easy to see that this diagonal element must be positive but in a multicomponent system it is less obvious. The sign of the diagonal elements in the general case is discussed in this report. It is shown that the sign of an individual diagonal element has no physical meaning but can be changed by changing the dependent concentration variable. Only the sum of all the diagonal elements need to be positive in a stable system.