Equations of state for Fe₃²⁺Fe₂³⁺Si₃O₁₂“skiagite” garnet and Fe₂SiO₄‐Fe₃O₄spinel solid solutions

Abstract

The equations of state of Fe 3 2+ Fe 2 3+ Si 3 O 12 , or “skiagite” garnet, and two Fe 2 SiO 4 ‐Fe 3 O 4 spinel solid solutions were determined from room temperature hydrostatic compression experiments up to 11 GPa performed at the European Synchrotron Radiation Facility. These data indicate that there are no first‐order phase transitions or changes in compression mechanism in skiagite garnet or Fe 3+ ‐bearing silicate spinel solid solutions up to 11 GPa at room temperature. Skiagite garnet has an isothermal bulk modulus K 0 T = 157.4(3.0) GPa and a pressure derivative of the isothermal bulk modulus K 0 T = 6.7(8), where numbers in parentheses represent 1 estimated standard deviation of these values. Combination of this result with those for other silicate garnets reveals an inverse linear relationship between the octahedral cation‐oxygen (Y‐O) bond length and the bulk modulus. The dominating effect of the octahedral site on the bulk compression of garnet can be understood by considering that the octahedral‐tetrahedral network has no rigid unit modes and that no cation substitution occurs on the tetrahedral sites in these garnets. It is apparent that the incorporation of Fe 3+ and Cr acts to lower the bulk modulus of aluminosilicate garnets. Consideration of the effect of compression on the molar volume results in nonsystematic changes in calculated oxygen fugacity for garnet‐bearing mantle peridotites that equilibrated at high pressures. The pressure‐volume data obtained from two Fe 3+ ‐bearing silicate spinel solid solutions with compositions X fay = 0.45 and X fay = 0.57 (fay, fayalite component) yielded similar enough values of K 0 T and K ′ 0 T to warrant a combined refinement with the data points scaled to the appropriate zero‐pressure volumes. This gave K 0 T = 168.9(1.2) GPa and K ′ 0 T = 5.7(1.2) with χ W 2 = 4.6 (weighted χ 2 ) and K 0 T = 175.5(1.4) GPa when K 0 T is fixed equal to 4 (χ W 2 = 4.9). Our solid solutions have significantly lower bulk moduli than either magnetite or Fe 2 SiO 4 spinel end‐members or indeed many other spinels.