Dielectric constants of silicate garnets and the oxide additivity rule

ROBERT D. SHANNON

E.I. Du Pont de Nemours and Co., Inc., Central Research and Development Department, Experimental Station
Wilmington, Delaware 19880-0356, U.S.A.

GEORGE R. ROSSMAN

Division of Geological and Planetary Sciences, California Institute of Technology
Pasadena, California 91125, U.S.A.

ABSTRACT

The dielectric constants and dielectric loss values of a series of garnets were measured at 1 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;
three grossular samples, k' = 8.53 - 8.81.

The deviations of measured dielectric polarizabilities as determined using the Clausius Mosotti equation from those calculated using the sum of oxide polarizabilities according to a_D(M₂M'X₄) = 2a_D(MK) + a_D(M'X₂) is +5.0 to +6.5% for the pyrope-almandine samples, +1.9% for spessartine, -2.3% for the andradite samples, and -5.5 to -7.0% for grossular. These deviations from additivity are believed to result from garnet structural constraints leading to "rattling" Mg ions and "compressed" Ca ions.

American Mineralogist, Volume 77, pages 94-100, 1992