The calculation of lattice constants in crystal statistics

Systematic methods of evaluating and checking certain lattice constants which arise in cooperative phenomena associated with crystal lattices are discussed, with the most important being the use of a ‘no immediate return’ random walk problem, and theUse of finite close-packed clusters for checking the evaluations.

Abstract

Abstract It is the purpose of the present paper to discuss systematic methods of evaluating and checking certain lattice constants which arise in cooperative phenomena associated with crystal lattices. Many of these constants have been evaluated previously, but little systematic description of methods used exists in the literature, and there are discrepancies between results obtained by different authors. Several new suggestions are put forward, the most important being the use of a ‘no immediate return’ random walk problem, and the use of finite close-packed clusters for checking the evaluations.