Theoretical and experimental grain boundary energies in body-centered cubic metals

Grain boundary energy (GBE) and its temperature dependence in body-centered cubic (bcc) metals are investigated using ab initio calculations. We reveal a scaling relationship between the GBEs of the same grain boundary structure in different bcc metals and find that the scaling factor can be best estimated by the ratio of the low-index surface energy. Applying the scaling relationship, the general GBEs of bcc metals at 0 K are predicted. Furthermore, adopting the Foiles’s method which assumes that the general GBE has the same temperature dependence as the elastic modulus c44 [Scr. Mater., 62 (2010) 231–234], the predicted general GBEs at elevated temperatures are found in good agreement with available experimental data. Reviewing two experimental methods for determining the general GBEs, we conclude that the two sets of experimental GBEs for bcc metals correspond to different GB structural spaces and differ by approximately a factor of 2. The present work puts forward an efficient methodology for predicting the general GBEs of metals, which has the potential to extend its application for homogeneous alloys without strong segregation of the alloying element and facilitates GB engineering for advanced alloy design.