Grain boundary grooving at finite grain size

Simple analytical solutions have been obtained for the linearized partial differential equations which describe grain boundary grooving by evaporation or by surface diffusion in finite systems. It is found that the groove profile shape predicted by infinite geometry solutions is closely approximated in the early. stages of groove formation, but that this shape is distorted toward a shape of constant surface curvature at long times as expected by equilibrium considerations. © 1988 Pergamon Press plc