A new formulation for the generation of coincidence site lattices (CSL's) in the cubic system

Abstract

The generation of tables of CSL's in the cubic system is presented with three parameters giving easy and rapid access to all the significant data characterizing a CSL" it is given by the rotation matrix from which the rotation axis and the rotation angle are easily determined. A method for the experimental determination of a CSL is presented, based on this new formulation.

Use of the CSL symmetrically equivalent descriptions tables in the DSC lattice base computation

“…For the simple cubic lattice direct and reciprocalspace vectors are expressed by the same indices and the rotation matrix R*-= R. The analytical form of this matrix has been extensively studied by Bleris & Delavignette (1981). They have shown that the elements of the matrix are a function of the multiplicity of the CSL, 2, of the Miller indices of the rotation axis, u, v, w, and of three integer parameters m, n, a whose conditions limiting their possible values have been established.…”

“…Its expression is given in equation (31a) of Bleris & Delavignette (1981). By computing the products R~=g~R, j= 1,2,...,24,…”

N-Dimensional coincidence-site-lattice theory

“…Attempts at finding the general solution of this equation were made by Santoro & Mighell (1973) and by Bonnet & Cousineau (1977); and special methods were developed for two identical cubic lattices (Grimmer, 1974b;Bleris & Delavignette, 1981) and hexagonal lattices (Bonnet et al, 1981). In the following discussion, it will be assumed that a particular rational solution X 0 of this equation has been determined.…”

“…Most of the work has been on CSL's of two identical three-dimensional lattices, especially cubic lattices (Ranganathan, 1966;Fortes, 1972;Grimmer, 1973;Grimmer, Bollmann & Warrington, 1974;Bleris & Delavignette, 1981) and hexagonal lattices (Fortes, 1973;Warrington, 1975;Bonnet, Cousineau & Warrington, 1981), although attention has also been given to the general case of two different three-dimensional lattices (Bucksch, 1972;Santoro & Mighell, 1973;Grimmer, 1976;Iwasaki, 1976;Bonnet & Cousineau, 1977;Fortes, 1977;Bacmann, 1979). These lattices are, of course, of special importance in solid-state physics and metallurgy, but recently attention has been given to lattices of higher dimension (e.g.…”

Symmetries of coincidence site lattices of cubic lattices

“…[3,4,5,6,7] and they are well understood. In particular one knows the coincidence rotations and has a handy parameterization for them, one knows the coincidence index Σ, the number of different CSLs for a given Σ, the generating functions, etc.…”