Dielectric constants of silicate garnets and the oxide additivity rule

The dielectric constants and dielectric loss values of a series of garnets were measured at l MHz using a two-terminal method and empirically determined edge corrections. The results are five intermediate pyrope-almandine samples, k'=11.96-12.35; spessartine, k'=11.65; two andradite samples, k'=10.53-10.59; and three grossular samples, k'=8.53-8.8l. \nThe deviations of measured dielectric polarizabilities as determined using the Clausius-Mosotti equation from those calculated using the sum of oxide polarizabilities according \nto ɑ_D(M_2M'X_4) = 2ɑ_D(MX) + ɑ_D(M'X_2) is +5.0 to 6.5% for the pyrope-almandine samples,+ 1.9% for spessartine, -2.3% of or the andradite samples, and -5.5 to -7.0% for \ngrossular. These deviations from additivity are believed to result from garnet structural constraints leading to "rattling" Mg ions and "compressed" Ca ions.