Elasticity of uvarovite and andradite garnets

The adiabatic single-crystal elastic properties of synthetic end-member uvarovite garnet (Ca3Cr2Si3O12) and a natural sample of 96% andradite garnet (Ca3Fe2Si3O12) have been measured at ambient conditions by Brillouin spectroscopy. The bulk modulus (Ks) and shear modulus (μ) of andradite (And) are Ks = 158 ± 2 GPa, μ = 90 ± 1 GPa, and those of uvarovite (Uv) are Ks = 165 ± 2 GPa and μ = 94 ± 1 GPa. Observed trends of the single-crystal elastic moduli (Cij) as a function of composition, and specifically the deviation from the Cauchy relation c12 = C44 are analogous between the Ca-bearing garnets grossular (Gr = Ca3Al2Si3O12)-And-Uv and other chemical systems such as the rock salt and corundum structure oxides, whereas other silicate garnets exhibit distinctly different behavior. Ks of andradite is substantially higher than previously estimated from data on garnet solid solutions. Garnets on the Gr-And join show a pronounced minimum in the Ks-composition relationship at a composition of approximately Gr24And76, indicating that ideal linear mixing of end-member elastic properties is inadequate to explain the elasticity of garnet solid solutions. The elastic properties of Gr-And and Al2O3-Cr2O3 solid solutions can be explained by incorporating a composition-dependent volume of mixing term into the expression for solid-solution elasticity. An evaluation of elasticity systematics relating the bulk sound speed and mean atomic weight, or Ks and molar volume, indicates that these relationships yield closer estimates of garnet elastic properties than does the seismic equation of state of Anderson (1967).

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