Paradoxical grain boundary motion in a wedge-shaped aluminum bicrystal

Abstract

We provide an explanation, within the framework of a model based on standard mean curvature grain-boundary motion coupled with somewhat unusual boundary conditions, for the paradoxical experimental results reported by Rath and Hu (Trans Am Inst Min Eng, 245:1577, 1969) regarding grain boundary migration in aluminum bicrystals. In their experiments, they measured the velocity of the grain boundary in a wedge-shaped bicrystal of aluminum, and assuming that rt ∝ − r−n, where r is the radius of the grain boundary as measured on the external surface, they found that 3.3 < n < 4, despite the fact that according to much well-established theory and extensive experimental data to be found elsewhere, n should be equal to one. We undertake a theoretical study of the dynamics of an initially cylindrical grain embedded in a 3D-single crystal film. The grain boundary is assumed to maintain axisymmetry and to move by mean curvature motion. Boundary conditions for the grain boundary are taken to be determined by the experimental results of Rath and Hu. We find a solution using a combination of analytical and numerical methods. Our analytical model predicts that rt ∝ fn, where f, the force applied by the grain boundary on the triple junction, is given by \(f=\gamma_{\rm gb} \sin \theta\), where γgb is the grain boundary energy and θ is the tilt angle of the grain boundary at the triple junction, and n satisfies 3.3 < n < 4 as earlier. This power law prediction is not in accordance with classical Mullins’ theory; however, it should be possible to test experimentally, thus allowing our approach to be checked for consistency with experiment. We suggest that the unusual kinetics observed in the experiment are due to grain boundary interaction at the surface triple junction with an external surface covered with aluminum oxide.