Consider a diffusion couple composed of two semi-infinite solids of the same metal, and that each side of the diffusion couple has a different concentration of the same elemental impurity; furthermore, assume each impurity level is constant throughout its side of the diffusion couple. For this situation, the solution to Fick's second law (assuming that the diffusion coefficient for the impurity is independent of concentration), is as follows:


In this expression, when the x = 0 position is taken as the initial diffusion couple interface, then C1 is the impurity concentration for x < 0; likewise, C2 is the impurity content for x > 0.
A diffusion couple composed of two silver-gold alloys is formed; these alloys have compositions of 98 wt% Ag-2 wt% Au and 95 wt% Ag-5 wt% Au. Determine the time this diffusion couple must be heated at 750ºC (1023 K) in order for the composition to be 2.5 wt% Au at the 50 mm position into the 2 wt% Au side of the diffusion couple. Preexponential and activation energy values for Au diffusion in Ag are 8.5 × 10-5 m2/s and 202,100 J/mol, respectively.