Figure 1

The $x$, $y$, and $z$ axes are a right-hand coordinate system in the $[11\overline{2}]$, $[111]$, and $[1\overline{1}0]$ crystallographic directions, respectively. (a) The structure of three $(111)$ planes in a bicrystal with a faceted grain boundary. The blue line shows two facets joined at a facet junction. The black arrows show the elementary excitation that can occur only at the facet junction. One “orange” atom moves into the vacancy at the facet junction and a “yellow” atom moves into the created space, transforming the structure to that shown in (b) with three facet junctions. (c) A schematic representation of 15 $(111)$ type planes made up of two layers as in (a), one layer as in (b), and two more layers as in (a). Such a configuration is mapped onto a matrix $h_{xy}$.Reuse & Permissions

Figure 2

(a) The structure of the grain boundary from the Monte Carlo simulation at 545 K. (b) The structure of the grain boundary at 590 K. There is an abrupt phase transition at a temperature of 570 K, in reasonable agreement with experiment. (Note that the size and orientation of the figures have been changed slightly to help visibility.) Axes are defined as in Fig. 1.Reuse & Permissions