Elasticity of uvarovite and andradite garnets

Abstract

The adiabatic single‐crystal elastic properties of synthetic end‐member uvarovite garnet (Ca 3 Cr 2 Si 3 O 12 ) and a natural sample of 96% andradite garnet (Ca 3 Fe 2 Si 3 O 12 ) have been measured at ambient conditions by Brillouin spectroscopy. The bulk modulus (K s ) and shear modulus (μ) of andradite (And) are K s = 158 ± 2 GPa, μ = 90 ± 1 GPa, and those of uvarovite (Uv) are K s = 165 ± 2 GPa and μ = 94 ± 1 GPa. Observed trends of the single‐crystal elastic moduli (C ij ) as a function of composition, and specifically the deviation from the Cauchy relation c 12 = C 44 are analogous between the Ca‐bearing garnets grossular (Gr = Ca 3 Al 2 Si 3 O 12 )‐And‐Uv and other chemical systems such as the rock salt and corundum structure oxides, whereas other silicate garnets exhibit distinctly different behavior. K s 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 K s ‐composition relationship at a composition of approximately Gr 24 And 76 , 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 Al 2 O 3 ‐Cr 2 O 3 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 K s and molar volume, indicates that these relationships yield closer estimates of garnet elastic properties than does the seismic equation of state of Anderson (1967).