Abstract
P–V–T equations of state (EoS) of synthetic garnet solid solutions with ternary grossular–almandine–pyrope compositions relevant to the Earth’s upper mantle have been determined in order to examine whether garnet properties can be accurately interpolated from those of the end-members. Volumes have been measured as a function of pressure using single-crystal X-ray diffraction measurements performed inside a diamond anvil cell. Isothermal bulk moduli and first pressure derivatives were obtained by fitting the P–V data using a third-order Birch–Murnaghan equation of state. Two nominally eclogitic garnets (Prp47Alm19Grs31And3 and Prp53Alm19Grs18And3Sps7) were found to have isothermal bulk moduli (KT0) and pressure derivatives (K′T0) of 170(3) GPa, 4.1 (4) and 173 (2) GPa, 3.8 (5), respectively. KT0 and K′T0 for an almandine-rich garnet (Prp26Alm63Grs6And5) were found to be 175 (3) GPa and 3.7 (7), respectively. High-temperature compression experiments at 703 K and 823 K were carried out on sample Prp47Alm19Grs31And3, resulting in the high-temperature EoS term (∂KT/∂T)P = − 0.025 (6) and a thermal expansion (α0) of 2.86 (4) × 10−5 K−1. The results imply that the bulk moduli of aluminous garnet solid solutions stable at upper mantle conditions can be deduced from the properties of the end-members with minimal uncertainty. We show that the difference in the bulk sound velocity determined for a multicomponent eclogitic garnet composition and obtained for the same composition from the end-member properties is better than 0.5% for pressures and temperatures corresponding to Earth’s upper mantle.
Highlights
Ga−rnet minerals usually crystallize in the cubic space group Ia3d and consist of a three-dimensional network of alternating corner-sharing tetrahedra and octahedra among which large distorted eightfold coordinated cubes reside
The general crystal-structural formula of garnet is X3[8]Y2[6]Z3[4]O12, where X is the eightfold coordinated site mainly occupied by large divalent cations such as Mg, Ca, Fe2+, or Mn2+; Y is the octahedral site mainly occupied by medium size trivalent cations such as Al, Fe3+, or Cr3+, and Z is the tetrahedral site usually occupied by Si, minor Fe3+ and H+ may substitute at this position
Only a few studies stand out because they report KT0 values which are either significantly larger, e.g. Zhang et al (1999) report 185 (3) GPa for Alm, or smaller, e.g. Du et al (2015) and Xu et al (2019) report values in the range 160 (2) GPa for Prp—Grs and Prp—Grs—Alm solid solutions, respectively. These inconsistencies cannot be attributed to obvious chemical variations and are, hard to include in a consistent scheme of aluminous garnet compressibility
Summary
Ga−rnet minerals usually crystallize in the cubic space group Ia3d and consist of a three-dimensional network of alternating corner-sharing tetrahedra and octahedra among which large distorted eightfold coordinated cubes reside. The general crystal-structural formula of garnet is X3[8]Y2[6]Z3[4]O12, where X is the eightfold coordinated site mainly occupied by large divalent cations such as Mg, Ca, Fe2+, or Mn2+; Y is the octahedral site mainly occupied by medium size trivalent cations such as Al, Fe3+, or Cr3+, and Z is the tetrahedral site usually occupied by Si, minor Fe3+ and H+ may substitute at this position. Earth’s upper mantle will depend in part on its elastic properties. End-member properties and binary systems of aluminous garnet solid solutions have been studied in some detail Table A1), only a few studies have attempted to examine the elastic properties of more complex solid solutions (Duba and Olinger 1972; Babuška et al 1978; O’Neill et al 1989; Chai et al 1997; Jiang et al 2004; Xu et al 2019), such as those representative of naturally occurring garnets found in mantle xenoliths.
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