Rigid-body displacement of asymmetric grain boundaries

The importance of asymmetric grain boundaries has made it necessary to examine the reference frame for rigid body translations in asymmetric GBs. It is proposed that the volume expansion is determined relative to the interplanar spacing that maintains the bulk density at the GB and which is given by the average of the interplanar spacings of the planes that are joined at the GB, di = (d1 + d2)/2. When d1 ≠ d2, s is the case for most asymmetric GBs, the coincidence site lattice construction increases the atomic density at the GB to higher than bulk values. The bulk density can be restored either by a O'th order rigid-body translation or by the removal of a suitable number of lattice planes at the GB. HREM appears to be a useful tool for determinations of rigid-body translation components perpendicular to the tilt axis in low index tilt GBs. Information on the detailed atomic structure of the GB core is necessary for absolute determinations of the volume expansion and the total excess volume of the GB