During the creep of polycrystals, individual grains may undergo shape changes, grain boundary sliding and grain rotation. Theoretical studies have focused on the first 2 of these processes but only recently has the theory of rotation received detailed attention. Diffusional rotation had been analysed for a bicrystal with orthorhombic grains of dimensions X, Y and Z with the common boundary in the yz plane and with Z>>X,Y. Rate equations were derived and the stress profile over the common boundary predicted, for cases where grain boundary and lattice diffusion predominated. Here, the analyses were extended using numerical methods, to the full 2- and 3-dimensional cases for boundary and lattice diffusion, respectively. For boundary diffusion, the results for Z/Y>>1 reproduce those obtained by analytical means and this was regarded as a verification of the numerical method. When Z/Y=1, the rotation rates were shown to be about 30% faster, due to the additional diffusion contribution in the z direction. This contribution increased with decreasing values of Z/Y. The stress patterns at the rotating boundary were derived. For lattice diffusion, the stress pattern at the boundary, the shapes of the vacancy potential contours and the variation of the rotation rate with the ratios X/Y and Z/Y were presented.

Theory of Diffusional Rotation about the Common Boundary of a Bicrystal. B.Burton: Philosophical Magazine, 2005, 85[17], 1901-19