The effect of the ionic radius of trivalent impurities on the reorientation parameters of tetragonal charge-compensation centers in Ca${\mathrm{F}}_2$ is studied. As it has been found in an earlier paper that electrical dipole-dipole interaction between the centers significantly modifies the reorientation behavior of dipoles, we have included this perturbation in our analysis of the results of the ionic-thermocurrents experiments. From the results we conclude that in $\mathrm{Ca}{\mathrm{F}}_2:R^{3+}$ there is an appreciable tendency of the impurities to coagulate to clusters; in contrast to results given in the literature the characteristic relaxation time ${\tau }_0$ associated with the jumping dipoles does not depend on the size of the trivalent impurity. The activation energy $E_0$ however increases with increasing $R^{3+}$ radius and the trend found for tetragonal centers in Ca${\mathrm{F}}_2$ is the same as for Sr${\mathrm{F}}_2$ observed by van Weperen and den Hartog. It is suggested that the variations are due to changes in the screening of the effective positive charge of the trivalent impurity.

• Received 31 October 1978

DOI:https://doi.org/10.1103/PhysRevB.19.4162