A unified approach to motion of grain boundaries, relative tangential translation along grain boundaries, and grain rotation

Abstract We postulate that almost any motion of an interface between two crystals can produce a coupled tangential motion of the two crystals relative to each other which is proportional to the normal motion of the interface. Such translations can produce grain rotations; the special case of the rotations of shrinking included circular cylindrical grains which increase misorientation, as seen in the molecular dynamics simulations, is reinterpreted with this postulate. When this postulate is added to other principles of interface motion, several phenomena associated with grain boundary mechanics and motion are unified into a single theoretical formulation: normal motion of a grain boundary resulting from a shear stress applied tangential to it which results in tangential motion and its converse, tangential motion resulting from coupling to normal motion; rigid sliding of one grain with respect to the other along a “greased” boundary; grain rotation due to tangential motion along curved grain boundaries, produced by either by sliding or by coupling to the normal motion. When the motion is driven by the reduction in the total surface free energy ∫γ da, if the grain rotation is due to sliding alone, then γ itself (the surface free energy per unit area) is reduced; if it is due to coupled motion, then increases in γ can occur if there is a large enough decrease in area that ∫γ da is decreased. We explore the predictions for rotations of circular cylindrical grains moving to reduce total surface free energy. Among the surprising results is that certain combinations of coupling and surface free energy functions can result in increases rather than decreases in radii; these conditions, if achievable, can only occur far from small tilt misorientations. We also show that sliding alone must lead to misorientations with minimum γ – or no misorientation – before the crystal shrinks to zero radius. For coupling alone, limiting misorientations (which need not, and often do not, coincide with minima in γ) are never reached for non-zero radii. A more thorough exploration of sliding and coupling, including application to non-circular crystals and a variational model, is being published elsewhere.