It was proposed that almost any motion of an interface between 2 crystals could produce a coupled tangential motion, of the 2 crystals relative to each other, which was proportional to the normal motion of the interface. Such translations could produce grain rotations. The special case of the rotation of shrinking included circular cylindrical grains which increased misorientation, as seen in molecular dynamics simulations, was re-interpreted. When this modification was added to other principles of interface motion, several phenomena which were associated with grain-boundary mechanics and motion could be unified into a single theoretical form. This was the normal motion of a grain boundary, resulting from a shear stress applied tangentially to it, which resulted in tangential motion. There was also a converse case: a tangential motion resulting from coupling to normal motion, rigid sliding of one grain with respect to the other along a so-called greased boundary and grain rotation due to tangential motion along curved grain boundaries; produced by sliding or by coupling to the normal motion. When the motion was driven by the reduction in total surface free energy ∫γda, and if the grain rotation was due to sliding alone, then γ itself (the surface free energy per unit area) was reduced. If it was due to coupled motion, increases in γ could occur if there was a large decrease in area; such that ∫γda decreased. One surprising result was that certain combinations of coupling and surface free-energy functions could result in increases rather than decreases in radii. These conditions could occur only far from small tilt misorientations. It was also shown that sliding alone had to lead to misorientations with minimum γ – or with no misorientation – before the crystal shrank to zero radius. For coupling alone, limiting misorientations (which did not need to, and often did not, coincide with minima in γ) were never reached for non-zero radii.

A Unified Approach to Motion of Grain Boundaries, Relative Tangential Translation along Grain Boundaries and Grain Rotation. J.W.Cahn, J.E.Taylor: Acta Materialia, 2004, 52[16], 4887-98