Non-ionic contributions to the electric-field gradient at $^{181}$Ta and $^{111}$Cd impurity sites in R$_2$O$_3$ (R= Sc, In, Lu, Yb, Tm, Er, Y, Ho, Dy, Gd, Eu, Sm) bixbyites

The time-differential perturbed-angular-correlation (TDPAC) technique was applied to the study of the internal electric-field gradient (EFG) in Eu- and Ho-sesquioxides in their cubic bixbyite phases. The results, as well as previous characterizations of the EFG at $^{181}$Ta sites in oxides with the bixbyite structure, were compared to those obtained in experiments using $^{111}$Cd as probe, and to point-charge model and {it ab initio} results calculations for the EFG tensor at impurity sites in binary oxides. These studies provide quantitative information about electronic processes and the structural relaxations induced by the presence of impurity probes in the host lattices, and confirm the existence of nonionic contributions to the EFG in these systems. Our FP-LAPW calculations show that this nonionic contribution to the EFG is the dominating one, and that it is originated in the population of {it p} states (5{it p} in the case of Cd, 6{it p} for Ta).