Misorientation dependence of the energy of symmetrical tilt boundaries in hcp metals: prediction by the disclination-structural unit model

Abstract

The misorientation dependence of the energy of grain boundaries in hcp metals is predicted by application of the disclination-structural unit model and continuum solutions for interfacial disclination dipoles in elastically anisotropic and inhomogeneous bicrystals. For symmetrical tilt boundaries in cobalt and titanium, it is shown that the dipole stress field and the grain-boundary energy depend strongly on the misorientation. In particular, the dipole stress field is more localized in large-angle boundaries than in small-angle boundaries, severe distortion of the stress field results from even a small inhomogeneity, and homogeneous isotropic solutions fail to capture the dependence of the stress field on misorientation. The energy–misorientation curve is characterized by cusps associated with favoured boundaries, local energy maxima between the cusps, and regions of high and low average energies demarcated by the favoured boundary. The maximum energy occurs near the misorientation of 23° corresponding to the () plane. The grain-boundary energy of cobalt is approximately twice that of titanium for most misorientations.