Surface Morphologies due to Grooves at Moving Grain Boundaries Having Stress-Driven Fluxes
Robert F. Sekerka, William J. Boettinger, Geoffrey B. McFadden
We examine the possibility that hillock growth of Sn coatings on Cu substrates is related to grain boundary fluxes caused by biaxial compressive stresses. We modify a previous steady state description developed by Genin [J. Appl. Phys. 77, 5130-5137 (1995)] for a grain boundary groove moving with a prescribed speed in a material subject to in-plane stress and a resultant grain boundary flux. The arbitrary assumption that the grain boundary flux is equally delivered to (or extracted from) the two adjacent free surfaces of the grains is replaced by a condition that requires continuity of surface chemical potentials at the grain boundary. Analytical results for the small slope approximation as well as nonlinear results for large slopes are computed numerically for the steady state motion at specified groove speed. We apply these results to a "partial loop" grain boundary geometry that moves by mean curvature induced by the groove conditions. In contrast to the ordinary effect that a grain boundary surface groove retards grain boundary motion, the presence of a compressive stress and resultant grain boundary flux toward the free surface promotes grain boundary motion. The surface elevation and pushing of grain boundary by an outward grain boundary flux due to compressive stress was examined with respect to the formation of Sn hillocks observed on Sn electrodeposits. The observed hillock heights and the growth of hillock grains do not appear to be explained by using parameters for Sn that are extrapolated to room temperature.
moving grain boundary groove, grain boundary flux, hillocks, Sn electrodeposits