Abstract
Abstract The elastic constants of sixteen garnet specimens of wide variety in chemical composition are accurately determined by means of the rectangular parallelpiped resonance method. The dependence of the elastic properties on chemical composition is analyzed using the present data and those for seven garnets investigated by other authors. The property Xi of a garnet solid solution i is given by a linear addition law in terms of the mole fraction nij of component j; Xi = ΣnijXj where the Xj's are the properties of the end-members j (j = pyrope, almandine, spessartine, grossular and andradite). The Xj's are determined for density ρ, bulk modulus K, and shear moduli Cs = (C11 − C12)/2 and C44. No systematic deviation is observed from the linear addition law for the elastic moduli nor for other quantities such as the elastic wave velocities. The extrapolated elastic moduli (Mbar) of the end-members are: Almandine Pyrope Spessartine Grossular Andradite K 1.779 ± 0.008 1.730 ± 0.009 1.742 ± 0.009 1.691 ± 0.008 1.379 ± 0.017 C s 0.981 ± 0.004 0.925 ± 0.004 0.964 ± 0.004 1.106 ± 0.004 0.979 ± 0.007 C 44 0.958 ± 0.005 0.919 ± 0.005 0.937 ± 0.005 1.017 ± 0.006 0.827 ± 0.010 The elasticity systematics such as Birch's, Anderson-Anderson's, and their modifications hold only approximately in a garnet solid solution. For example, Anderson-Anderson's relation on the constancy of the bulk modulus and molar volume product holds as a general trend, but it does not satisfy the data in the almandine-pyrope series. It is pointed out that the elastic properties of pyralspite (pyrope-almandine-spessartine) and of ugrandite (uvarovite-grossular-andradite) are markedly different. Based on the present data and the approximate elasticity systematics, an estimation of the elastic parameters of garnet in the upper mantle is given; νP ≅ 8.9 km/s and νS ≅ 5.0 km/s almandine-pyrope garnet in the uppermost mantle, and νP = ∼8.9–9.0 km/s and νS ≅ 5.1 km/s for complex garnet in the deep upper mantle.
Published Version
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