Relationship between coincidence site lattice, boundary plane indices, and boundary energy in nickel

Abstract

This paper reports an analysis both by coincidence site lattice (CSL) categorisation and interface–plane categorisation of a large data set of grain boundary geometry in nickel. The analysis showed that whereas two-thirds of Σ3 and Σ9 CSLs were classed as having ‘special’ geometry (i.e. related to low energy), very few other CSLs had ‘special’ geometries. It was found that for Σ3s there was an empirical relationship connecting the frequency of occurrence of specific planes (mostly asymmetrical tilt types on the 011 zone), the average interplanar spacing at the boundary (d(eff)), and the boundary energy. Σ3 boundaries having a planar coincidence site density (PCSD) of unity were much more poorly represented in the data set than Σ3s having PCSD = 3, indicating the far greater importance of boundary planes than the PCSD. The occurrence of ‘special’ planes at Σ9 boundaries is considered to be partly a geometrical consequence of their contiguity with Σ3s.