Solute diffusion in a dilute alloy can be treated with a simple assumption that the environment the solute sees while diffusing almost entirely consists of host lattice atoms. The same is not true for a diffusion couple, say metal A and metal B brought together and held at elevated temperatures for longer time. Diffusion across the interface (A/B) will take place, and diffusion parameters such as the jump frequency and vacancy concentration will depend on the position and time. For explaining such a case, Darken defined a diffusivity term, chemical interdiffu­sion coefficient (D), to describe the diffusion that takes place in the diffusion cou­ple. It is given by the following relation:

D — xaDb + xb Da, (2.49)

where xa and xb are the atom fractions of A and B, respectively, at the point the interdiffusion coefficient is measured, and the intrinsic diffusion coefficients of A and B are DA and DB at the same point, and are not necessarily constant. More refinement of this model has been done by incorporating activity coefficients, known as the Darken-Manning relation. Readers are referred to Refs [3, 7, 9-11] for more information.

Intuitively, it is clear now that the diffusion rate of A into B is in general different from the diffusion rate of B into A. Kirkendall has conducted a famous experiment to elucidate the operation of vacancy diffusion in metals. A number of experimental and theoretical research studies have since then followed and expanded the under­standing of diffusion in a significant way. In this experiment, molybdenum wires were wound around an alpha-brass (70Cu-30Zn, wt%) block and then plated with a copper coating of appreciable thickness (Figure 2.50). The molybdenum wires act

as inert marker to locate the original interface. When the sample is kept in a fur­nace and sufficient diffusion is allowed, Kirkendall noticed that the wire markers present on the opposite sides ofbrass moved toward each another. This observation implied that more material has moved away from brass to copper than what entered from copper to brass. Now let us think about the atomic picture of the situ­ation. Direct interchange mechanism and ring mechanism of diffusion require that the net number of atoms crossing the interface is zero. But this is clearly not the case. The vacancy mechanism of diffusion is the only plausible explanation for this behavior. When zinc diffuses by a vacancy mechanism, there is a net flux of zinc atoms going in the opposite direction. That is, an equal number of vacancies are entering the brass block. However, this enhanced concentration of vacancies is thermodynamically unstable. There are many vacancy sinks (such as grain bounda­ries and dislocations) in the material, so the vacancy concentration does not go above the equilibrium vacancy concentration. Thus, it means that zinc leaves brass and the excess vacancies in brass get annihilated at the preexisting sinks in brass. So the natural result of the event is that the volume ofbrass decreases and the wire markers move closer together. It is true that similar event is also happening in cop­per plating, but because the diffusion rate of zinc is higher than that of copper, the net effect of diffusion of the latter does not show up.

2.3.6