Elasticity of grossular and spessartite garnets by Brillouin spectroscopy

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Abstract
The single‐crystal elastic moduli of natural samples of grossular (99.0 mol % Ca3Al2Si3O12) and spessartite (94.8 mol % Mn3Al2Si3O12) have been measured by Brillouin spectroscopy under ambient conditions. From these results the adiabatic bulk moduli Ks and shear moduli μ are calculated to be Ks = 168.4 ± 0.7, μ = 108.9 ± 0.4 for grossular, and Ks = 178.8 ± 0.8, μ = 96.3 ± 0.5 for spessartite (all in units of gigapascals). A calibration of our spectrometer by determination of the elastic properties of MgO indicates that these modulus values are accurate to within twice the stated rms error. Of the major rock‐forming silicate garnets, spessartite has the largest bulk modulus, and grossular has the largest shear modulus, with the possible exception of majorite (a high‐pressure form of pyroxene). Approximate values for the bulk and shear moduli of common aluminosilicate garnet solid solutions can be obtained with an estimated uncertainty of less than 3% from a linear molar average of the end‐member properties. The elastic properties of pure almandite garnet (Fe3Al2Si3O12), which have thus far not been measured, are estimated as Ks = 177 ± 3 and μ = 97 ± 1 GPa by a linear regression analysis of extant measurements on garnet solid solutions and end‐members. These same data imply, however, that a linear modulus‐composition relationship may not be appropriate for all silicate garnet compositions.