Thermodynamics of Translational States in the Sigma 3 Grain Boundary System

The structure and symmetry of grain boundary translational states in the Sigma3 {110}// {111} and {110}// {112} bicrystals are reported. Symmetry-dictated extrema in interfacial energy with respect to "in-plane" translation are found. Atomic level calculations are performed to construct a complete gamma surface for the cell of non-identical displacements of the system. The thermodynamics of interfaces is extended to include translation as a degree of freedom. The conditions of equilibrium between translational states are then investigated. These conditions in conjunction with the gamma surface are used to explain experimental observations of translational states along boundaries in the Sigma3 system. It is shown that under certain constraints, segments of boundary which are unstable with respect to translation may exist. This is consistent with experimental observations.