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

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: V0 = 1,544.4 ± 0.4 Å3, K0 = 180 ± 3 GPa and K0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K_{0}^{{\prime }} $$\end{document} = 4.0 ± 0.4 for Spe38Alm62, and V0 = 1,557.5 ± 0.3 Å3, K0 = 176 ± 2 GPa and K0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K_{0}^{{\prime }} $$\end{document} = 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: V0 = 1,544.6 ± 0.6 Å3, K0 = 180 ± 4 GPa, K0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K_{0}^{{\prime }} $$\end{document} = 4.0 ± 0.4, (∂K/∂T)P = −0.028 ± 0.005 GPa K−1 and α0 = (3.16 ± 0.14) × 10−5 K−1 for Spe38Alm62, and V0 = 1,557.7 ± 0.9 Å3, K0 = 176 ± 4 GPa, K0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K_{0}^{{\prime }} $$\end{document} = 4.0 ± 0.5, (∂K/∂T)P = −0.029 ± 0.005 GPa K−1 and α0 = (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 (XAlm) in this garnet join is derived to be K0(GPa) = 171.6(±2.6) + 10.9(±1.8)XAlm. Present results are also compared with previously studies determined the thermoelastic properties of other garnets.