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 (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 (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 (∂K_T/∂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.

确定了与地球上地幔有关的具有三元总卵磷脂-金刚烷-吡啶类组成的合成石榴石固溶体的P–V–T状态方程（EoS），以检查是否可以从末尾的石榴石特性中准确地对其进行内插。成员。使用在金刚石砧座内部执行的单晶X射线衍射测量，已测量了体积随压力的变化。等温体积模量和第一压力衍生物通过拟合所获得的P-V使用状态的三阶桦木-Murnaghan状态方程数据。两个名义上的渐晕石榴石（Prp ₄₇ Alm ₁₉ Grs ₃₁和₃和Prp ₅₃ Alm ₁₉ Grs₁₈个₃ SPS ₇）被发现有等温体积弹性模量（ķ _T0）和压力衍生物（ķ ' _T0的170（3）GPA，4.1（4）和173（2）GPA，3.8（5），分别地）。ķ _T0和ķ ' _T0为富含铁铝石榴石（PRP ₂₆ Alm的₆₃ GRS ₆和₅）被发现分别175（3）GPA和3.7（7），要。对样品Prp ₄₇ Alm ₁₉ Grs ₃₁和₃进行了703 K和823 K的高温压缩实验，产生高温的EoS术语（∂K _Ť /∂T）_P  = - 0.025（6）和热膨胀系数（α ₀的2） 。86（4）×10 ^-5  K ^-1。结果表明，可以从末端构件的性质中以最小的不确定性推导在上地幔条件下稳定的铝石榴石固溶体的体积模量。我们表明，对于多组分的渐近性石榴石组合物，从相同的组合物通过端部成员的性质确定的体声速差，在对应于地球上地幔的压力和温度下，均优于0.5％。