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 A3, K 0 = 180 ± 3 GPa and $$ K_{0}^{{\prime }} $$ = 4.0 ± 0.4 for Spe38Alm62, and V 0 = 1,557.5 ± 0.3 A3, 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 A3, 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 A3, 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.