Nonequivalence of general tensor force and Clark, Gazis, and Wallis angular force models

Abstract

The general tensor force (GTF) model, the general scalar force (GSF) model as well as the Clark, Gazis, and Wallis (CGW) angular force model are analyzed by resolving the atomic displacements along three mutually perpendicular directions. It is shown that the GTF model that neglects three-body and mixed neighbor interactions confined to the plane of a triangle but incorporates two-body interactions perpendicular to the plane, is not equivalent to the CGW model that incorporates the former while neglecting the latter. However, the relations between the tensor force constants of the former and the scalar constants of the latter, deduced by exploiting the basic differences in their transformation properties, reveal that the GTF model is equivalent to the GSF model in the case of bcc and fcc structures, and all earlier claims regarding its equivalence with the CGW model are therefore spurious. The role played by the coordinate axes transformations, the relations between these and other force constant models, as well as the equivalence between their force constants, are discussed.