Theory of ligand distortions—Application to the study of nuclear quadrupole interactions of the excited states ofCd111andIn117inCdCl2

Abstract

Theory required for estimating the electric field gradients (EFGs) in ionic solids incorporating the effects of the ligand distortions due to the internal crystalline electric fields has been described. The EFGs have been derived from the distorted electronic charge distributions surrounding the nucleus under consideration in addition to the appropriate contributions from the multipole distributions in the lattice. Application of the theory has been made to study extensively the nuclear quadrupole interactions of the excited states of $^{111}\mathrm{Cd}$ and $^{117}\mathrm{In}$ in ${\mathrm{CdCl}}_{2}$. The results have been compared with those obtained under the cases: (i) "without ligand distortion"---which neglects the distortions of the ligands but considers the electronic as well as the "monopole and dipole" distributions in the crystal in a manner described previously, (ii) "monopoles and dipoles only" on the entire lattice, and (iii) "monopoles only" on the entire lattice. The ligand-distortion effects have been found to be very significant and the net EFGs change sign because of the ligand distortions. The need for obtaining the experimental sign of the quadrupole interaction frequencies in ${\mathrm{CdCl}}_{2}$ has been emphasized to understand the ligand-distortion effects on the EFG. Analysis of the EFGs from the cases considered reveals that the electronic contributions are dominant. This requires reanalysis of the experimental quadrupole interaction frequencies observed by the time-differential perturbed-angular-correlation technique in some Cd salts. The reanalysis yields the quadrupole moment $|Q(^{111}\mathrm{Cd})|$ very close to that obtained by Behrend and Budnick from the study of the circular polarization of the 247-keV $\ensuremath{\gamma}$ ray of $^{111}\mathrm{Cd}$.