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 static method and Molecular dynamic simulations to investigate the effects of high temperature and grain boundary (GB) planes on the GBE. Generally, the variation trends of GBEs functioned with tilt angle are similar in 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 β-Ti at 1300 K are somewhat different from that of 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 STGB of β-Ti at 1300 K tend to evolve into the local ω- or α-like structures distributed at STGBs, which make the corresponding STGBs more stable, thereby decreasing the GBEs. Furthermore, a geometric parameter θ, an angle between misorientation axis and GB plane, was defined to explore the effects of GB planes on GBEs. It was found that the relationship between GBEs and sin(θ) 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 with specific lattice misorientation. Our calculations not only extend the investigation of GBs to higher temperature, but also deepen the understanding on the temperature contribution to the microstructure evolution at GBs and on the relationship between GBE and possible geometric parameters.