Dislocation Models of Crystal Grain Boundaries

The energies and motions of grain boundaries between two crystallites are investigated theoretically using the dislocation model of grain boundaries. Quantitative predictions made for simple boundaries for cases in which the plane of the boundary contains the axis of relative rotation of the grains appear to agree with available experimental data. The quantitative expression for energy per unit area for small angles is approximately $[\frac{\mathrm{Ga}}{4\ensuremath{\pi}(1\ensuremath{-}\ensuremath{\sigma})}]\ensuremath{\theta}[A\ensuremath{-}\mathrm{ln}\ensuremath{\theta}]$ where $G$ is the rigidity modulus, $a$ the lattice constant, $\ensuremath{\sigma}$ Poisson's ratio, $\ensuremath{\theta}$ the relative rotation and $A$ approximately 0.23. Grain boundaries of the form considered may permit intercrystalline slip and may act as stress raisers for the generation of dislocations.