A classification of harmonic force constants

Abstract

Classification enables the maximum possible information to be obtained from experimentally determined force constant tensors. In finite systems, mathematical arguments show that there are only three distinct classes; the author argues that the 'best' physical classification corresponds to this, i.e. isotropic, traceless pairwise, and antisymmetric forces. The latter violate Newton's third law and imply nonrigid behaviour of the electrons. The way the classification distinguishes between the microscopic contributions to the force, i.e. the contribution of the different parts of the generalised pseudoatom, is shown. In particular the deformation of the pseudoatom is shown to give traceless pairwise and antisymmetric contributions and so cannot be described in terms of dipolar, quadrupolar, etc., contributions. In ionic crystals it is shown that it is not possible to move the ions independently, but that in all crystals it is still possible to define interionic force constants. These can be classified in the same way as in finite systems; the presence of real or imaginary parts of the crystalline force constants depends on the crystal structure. The classification also shows the need for more experimental data in order to determine the validity of various theoretical models.