Molecular dynamics investigation on tilt grain boundary energies of beta-titanium and tungsten at high temperature

Abstract

The grain boundary energies (GBEs) of symmetric tilt grain boundaries (STGBs) and asymmetric tilt grain boundaries (ATGBs) for W at 0 and 2400 K and β-Ti at 1300 K were calculated by means of molecular statics and dynamics simulations to investigate the effects of temperature on GBE and the relationships between GBEs and grain boundary (GB) planes. Generally, the variation trends of GBE with the tilt angle are similar for the three cases, when the tilt axis is specified. It is of course that these similarities result from their similar GB microstructures in most cases. However, the variation trends of GBE with tilt angle are somewhat different between β-Ti at 1300 K and W at 2400 K for STGBs with <100> and <110> tilt axes. This difference mainly stems from the following two reasons: firstly, the GB microstructures of W at 2400 K and β-Ti at 1300 K are different for some STGBs; secondly, the atoms at the STGB of β-Ti at 1300 K tend to evolve into the local ω- or α-like structures distributed at the STGB for some STGBs with <110> tilt axis, which makes the corresponding STGBs more stable, thereby decreasing the GBEs. Furthermore, a geometric parameter θ, the angle between the misorientation axis and the GB plane, was defined to explore the relationships between GBEs and GB planes. It was found that the relationships between GBEs and GB planes can be described by some simple functions of sin(θ) for the GBs with definite lattice misorientation, which can well explain and predict the preferred GB planes for the GBs having the same lattice misorientation. Our calculations not only extend the investigation of GBs to higher temperature, but also deepen the understanding on the temperature contributions to the microstructure evolution at GBs and on the relationships between GBEs and possible geometric parameters.