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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 (Prp 47 Alm 19 Grs 31 And 3  and Prp 53 Alm 19 Grs 18 And 3 Sps 7 ) were found to have isothermal bulk moduli ( K  T0 ) and pressure derivatives ( K ′ T0 ) of 170(3) GPa, 4.1 (4) and 173 (2) GPa, 3.8 (5), respectively.  K  T0  and  K ′ T0  for an almandine-rich garnet (Prp 26 Alm 63 Grs 6 And 5 ) 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 Prp 47 Alm 19 Grs 31 And 3 , resulting in the high-temperature EoS term ( ∂K  T  /∂T )  P   = − 0.025 (6) and a thermal expansion ( α  0 ) 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.

High-pressure and high-temperature single-crystal X-ray diffraction of complex garnet solid solutions up to 16 GPa and 823 K