Analysis of atomic concentration profiles in interdiffusion and access to non-equilibrium vacancy concentrations

It is generally assumed that sources and sinks of vacancies are sufficient numerous that an equilibrium concentration of vacancies is established during interdiffusion in a binary alloy. The formation of vacancy pores or Kirkendall porosity shows that this assumption is not always valid. In this paper, we avoid this assumption by taking a very general phenomenological approach to interdiffusion. For the commonly encountered small vacancy concentration case our strategy centres on directing the information about the driving force associated with the non-equilibrium vacancies (which is effectively not measurable) onto the velocity of inert marker(s) in the diffusion zone. By assuming there is access to independent knowledge of the two tracer diffusivities we derive expressions for the transport coefficient (for the case of non-equilibrium vacancies) using an analysis along Boltzmann-Matano lines. Using the random alloy diffusion kinetics model we show that in principle it is possible to measure the relative concentration of non-equilibrium vacancies produced during interdiffusion.