Dipolar complexes in rare-earth-doped strontium fluoride

The complex dielec ric constant has been measured at five audio frequencies over the temperature range 5.5-390 K for various concentrations of Ce, Eu, Gd, and Er in Sr${\mathrm{F}}_2$. Three principal relaxations are observed, two of which have been studied by previous workers. The shift in relative population between the two peaks with ion size, observed previously, has been verified and the ratio of the dipole moment is found to be approximately 2.8, which is consistent with the identification of the two relaxations as type-I and type-II dipoles. In addition, under the assumption of thermal equilibrium, enthalpy differences for the two species in Sr${\mathrm{F}}_2$: Gd and Sr${\mathrm{F}}_2$: Eu are found to be 0.049 and 0.078 eV, respectively, which is also consistent with the previous identifications. The thrid relaxation is a low-activation-energy process which occurs for large concentrations (> 0.1 mol%) of small rare-earth ions. Consequently, it is concluded that the new relaxation is cluster-associated. A similar relaxation, $R_{\mathrm{III}}$, is known to occur for small rare earths in calcium fluoride; however, the relaxation exists at smaller concentrations in calcium fluoride and is and is stable for larger rare earths in strontium fluoride.