P–V–T equation of state of spessartine–almandine solid solution measured using a diamond anvil cell and in situ synchrotron X-ray diffraction

Abstract

The pressure–volume–temperature (P–V–T) equation of state (EoS) of two natural garnet samples along spessartine–almandine (Spe–Alm) join has been measured at high temperature up to 800 K and high pressures up to 15.46 and 16.17 GPa for Spe₆₄Alm₃₆ and Spe₃₈Alm₆₂, respectively, using in situ angle-dispersive X-ray diffraction and diamond anvil cell. Analysis of room-temperature P–V data to a third-order Birch–Murnaghan EoS yields: V ₀ = 1,544.4 ± 0.4 Å³, K ₀ = 180 ± 3 GPa and $K_{0}^{{\prime }}$ = 4.0 ± 0.4 for Spe₃₈Alm₆₂, and V ₀ = 1,557.5 ± 0.3 Å³, K ₀ = 176 ± 2 GPa and $K_{0}^{{\prime }}$ = 4.0 ± 0.3 for Spe₆₄Alm₃₆. Fitting of our P–V–T data by means of the high-temperature third-order Birch–Murnaghan EoS gives the thermoelastic parameters: V ₀ = 1,544.6 ± 0.6 Å³, K ₀ = 180 ± 4 GPa, $K_{0}^{{\prime }}$ = 4.0 ± 0.4, (∂K/∂T) _P  = −0.028 ± 0.005 GPa K⁻¹ and α ₀ = (3.16 ± 0.14) × 10⁻⁵ K⁻¹ for Spe₃₈Alm₆₂, and V ₀ = 1,557.7 ± 0.9 Å³, K ₀ = 176 ± 4 GPa, $K_{0}^{{\prime }}$ = 4.0 ± 0.5, (∂K/∂T) _P  = −0.029 ± 0.005 GPa K⁻¹ and α ₀ = (3.04 ± 0.16) × 10⁻⁵ K⁻¹ for Spe₆₄Alm₃₆. The results confirm that almandine content increases the bulk modulus of the spessartine–almandine join following a nearly ideal mixing model. The relation between bulk modulus and almandine mole fraction (X _Alm) in this garnet join is derived to be K ₀(GPa) = 171.6(±2.6) + 10.9(±1.8)X _Alm. Present results are also compared with previously studies determined the thermoelastic properties of other garnets.