Mass transport at interfaces in single component systems

Abstract

Mass transport at interfaces is induced by a gradient of chemical potential along the interface; typically, at surfaces, this is caused by a gradient in curvature and, at grain boundaries, by a gradient of normal stress. In addition, interface mass transport in metallic conductors is induced by strong electric fields/currents. On a sufficiently small scale, depending on the temperature, this interface transport dominates bulk diffusion. Continuum equations that specify the interface fluxes in terms of the preceding driving forces and continuity equations that describe the consequences of a divergence of these fluxes are presented; the chemical potential whose gradient is used as a driving force is that in local equilibrium with an element of interface. The equations are subject to boundary conditions at interface junctions that require the total emerging flux to vanish and that require, at junctions that pass flux freely, the chemical potential to be continuous. With the use of several approximations, solutions of the equations are given to describe, in a unified way, basic models of surface morphological evolution, Coble creep and diffusion-based models of sintering, and electromigration. Some of the approximations, not necessarily made simultaneously, are (1) isotropy of interface properties, both within the interface and with regard to the interface orientation; (2) surface slopes everywhere small compared to a reference plane; and (3) steady-state stress in grain boundaries. Limitations and possible extensions of the framework are discussed.