Relationships between grain boundary structure and energy

Abstract

The Read-Shockley equation describing the dependence of the grain boundary energy on misorientation of the grains, has been reformulated using the recently developed structural unit model of the atomic structure of grain boundaries, so that it is applicable to general high angle boundaries. The boundary energy then consists of the energy of a reference structure, and of the core and elastic energies of the corresponding DSC dislocations. While the latter part of the boundary energy is determined using the elastic theory of dislocations the former two parts are determined on the basis of atomistics of grain boundaries employing the structural unit model. In the framework of this analysis the minimum number of reference structures in a given misorientation range as well as the extent of misorientations related to a given reference structure are determined unambiguously. Hence, the positions of cusps in the energy vs misorientation dependence and their relative depths and extents are also determined uniquely. The validity of this model is demonstrated for the [001] and [111̄] symmetrical tilt boundaries which have been studied by atomistic computer simulations.