Trace Relations for Tensors Relating Electric Fields and Elastic Strains to Nuclear Quadrupole Effects

Abstract

The effects of electric field and elastic strain on the nuclear quadrupole interactions in crystals have been described by means of third- and fourth-rank tensors relating the change of the electric field gradient tensor components ${\ensuremath{\varphi}}_{\mathrm{ij}}$ to the components ${E}_{k}$ of the applied electric field and to the components ${e}_{\mathrm{lm}}$ of the strain tensor. Usual symmetry relations reduce the number of independent components of the coupling tensors. In addition to the relations due to symmetry, other relations among the components of the coupling tensor have been usually obtained from the assumption that the change in the trace $\ensuremath{\Sigma}{i}^{}{\ensuremath{\varphi}}_{\mathrm{ii}}$ due to applied electric field or strain is equal to zero. We show that the number, but not the interpretation, of the independent tensor coefficients is independent of the assumption about the trace.