Influence of quadrupolar deformability on phonon dispersion in silver and copper halides

The quadrupolar deformability (QD) shell model is extended to calculate the phonon dispersion relation of silver and copper halides (AgCl, AgBr, AgI, CuCl, and CuBr). The QD is derived explicitly from the virtual d–s excitation of Ag and Cu ions induced by the crystal-field change of neighboring anions. The eight parameters (four short-range force constants, four shell parameters) are so economically determined that the QD shell model well reproduces the experimental phonon dispersion relations of these compounds. The QD shell model leads to the remarkable deviation from the Cauchy relation for elastic constants. We found that this QD effect is stronger in AgCl and AgBr than in AgI, CuCl and CuBr.