Effect of faceting on the thermal grain-boundary grooving of tungsten

Thermal grain boundary grooving with anisotropic surface free energy in three dimensions

“…What we observe in Example 3 may explain the experimental observation that some facets coarsen rapidly in the initial development and then change slowly or become static in the later evolution; see Ref. [15].…”

“…These facets are similar to those in the experimental observations reported in Refs. [8,15]; see Table 1 Examples of the simulation of periodic surfaces using an anisotropic surface free energy g ¼ 1 À aðm 4 1 þ m 4 2 þ m 4 3 Þ (Eq. (6)) with a {1 1 0} crystallographic orientation for the flat surface u ¼ 0 through the Euler angles…”

“…3; see Refs. [8,15]. Here, we do not attempt to match the dimensionless time in the simulation to the real time in the experiments.…”

“…The computational domain is chosen as ½0; 2p  ½0; 2p: We assign the dihedral angles 1351 (a value in the range of the experimental results in Ref. [15]) at each of the two grain boundaries, x ¼ 0 and y ¼ 0: We assign the initial flat surface a {1 1 0} crystalline orientation through the Euler angles f 1 ¼ f 2 ¼ p=4 and f 3 ¼ 0 in Eq. (7).…”

“…[3] to demonstrate the characteristic effects of anisotropy and we compare the simulation to the experiments reported in Refs. [8,15]. Finally, we discuss potential applications of the model and the simulation, and future work to advance this study.…”