Survey of Grain Boundary Energies in Tungsten and Beta-Titanium at High Temperature

Heat treatment is a necessary means to obtain desired properties for most of the materials. Thus, the grain boundary (GB) phenomena observed in experiments actually reflect the GB behaviors at relatively high temperature to some extent. In this work, 405 different GBs were systematically constructed for body-centered cubic (BCC) metals and the grain boundary energies (GBEs) of these GBs were calculated with molecular dynamics for W at 2400 K and β-Ti at 1300 K and by means of molecular statics for Mo and W at 0 K. It was found that high temperature may result in the GB complexion transitions for some GBs, such as the Σ11{332}{332} of W. Moreover, the relationships between GBEs and sin(θ) can be described by the functions of the same type for different GB sets having the same misorientation axis, where θ is the angle between the misorientation axis and the GB plane. Generally, the GBs tend to have lower GBE when sin(θ) is equal to 0. However, the GB sets with the <110> misorientation axis have the lowest GBE when sin(θ) is close to 1. Another discovery is that the local hexagonal-close packed α phase is more likely to form at the GBs with the lattice misorientations of 38.9°/<110>, 50.5°/<110>, 59.0°/<110> and 60.0°/<111> for β-Ti at 1300 K.