Elastic properties of garnet solid-solution series

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 X_i of a garnet solid solution i is given by a linear addition law in terms of the mole fraction n_ij of component j; X_i = Σn_ijX_j where the X_j's are the properties of the end-members j (j = pyrope, almandine, spessartine, grossular and andradite). The X_j's are determined for density ρ, bulk modulus K, and shear moduli C_s = (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
$\text{K}$	1.779 ± 0.008	1.730 ± 0.009	1.742 ± 0.009	1.691 ± 0.008	1.379 ± 0.017
$\text{C}{}_{\mathrm{<mtext>s</mtext>}}$	0.981 ± 0.004	0.925 ± 0.004	0.964 ± 0.004	1.106 ± 0.004	0.979 ± 0.007
$\text{C}{}_{\mathrm{<mtext>44</mtext>}}$	0.958 ± 0.005	0.919 ± 0.005	0.937 ± 0.005	1.017 ± 0.006	0.827 ± 0.010
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