Roughening of Low-Angle Grain Boundaries

The possibility of roughening in low-angle grain boundaries is investigated. By exhibiting an analogy between grain-boundary steps which do not have long-range strain and steps on solid surfaces, I argue that a grain-boundary roughening transition, of the same type as for solid surfaces, is possible. It is found that, as the grain-grain misorientation $\theta$ goes to zero, the energy of such a grain-boundary step diverges as ln ($\frac{1}{\theta }$). From this divergence I argue that, for sufficiently small $\theta$, the solid will melt before the grain boundary has a chance to roughen as the temperature increases.