Symmetry Properties of the Macroscopic Scalar Potential.

TLDR: In this paper, the authors examined the group properties of the macroscopic scalar potential of an alkali halide derived previously by Ritter and Markham, and they considered the point group symmetry of the σ i f i 2 ( r ) without regards to the q i's.

Abstract: Abstract This Communication examines the group properties of the macroscopic scalar potential of an alkali halide derived previously by Ritter and Markham. The potential has the form σ i f i ( r ) q i , where f i is a function of space and q i is a normal coordinate. It does not consider in detail the properties of the potential at a site, since Ritter and Markham omit all higher order terms in an expansion. This makes the origin arbitrary. The potential has space group symmetry. One desires point group symmetry when working with point imperfections. Hence, here we consider the point group symmetry of the σ i f i 2 ( r ) without regards to the q i 's. We believe that f 2 i is more appropriate than just the f i . Our interest is limited to the Φ + 1 , Φ + 3 , Φ - 4 and Φ + 5 irreducible representations of O h , and the lengthy calculations were made only for KCl. The γ + 1 part of the potential dominates, especially near the arbitrary origin where the other parts of the potential go to zero.