Garnet-group minerals, with their wide range of compositions, play a significant role in Earth's crust and upper mantle, participating in various petrological and geochemical processes. Oxygen isotope fractionation factors between garnets and other minerals hold crucial implications in these contexts. In this work, vibration frequencies were measured via Raman spectra on five garnet mineral samples in the pyrope-almandine-spessartine ternary system and four synthetic pyrope-grossular solid solutions at temperatures up to 1000 °C and pressures up to 17 GPa. Isobaric () and isothermal () mode Grüneisen, as well as anharmonic () parameters, were determined for the observed modes. Our study shows that the vibration bands tend to shift to lower frequencies with increasing temperature and to higher frequencies with increasing pressure. Moreover, the anharmonic correction has been found to contribute positively to equilibrium oxygen isotope fractionation factors in garnets, typically within 0.5 ‰ above 1000 K. The 10∙ln() factors calculated from vibration spectra (considering points only) align closely with those from theoretical calculations (including all frequencies in the Brillouin zone). Contributions from phonon dispersion (including none- points) are typically smaller than the uncertainties propagated from frequency measurements. Additionally, the pressure effect on the oxygen isotope fractionation in garnet, evaluated from the isothermal Grüneisen parameters, is found to be insignificant under crustal and upper mantle conditions, consistent with thermodynamic expectations. Using published oxygen isotope fractionation factors for quartz and calcite, the equilibrium oxygen isotope fractionation factors (10∙ln) are calculated between garnets of diverse compositions and any of these phases as functions of temperature, pressure and fraction of garnet endmembers. Considering composition effects helps to reduce the discrepancies among experimental and empirical calibrations of oxygen isotope fractionation factors between garnet and quartz. As an example application, oxygen isotope fractionation factors 10∙ln(, ) between garnets and forsterite were calculated under upper mantle conditions. Our findings suggest that these fractionation factors are predominantly dependent on temperature and garnet compositions, with minor influence from pressure. Compared with our calculated fractionation factors between garnet and olivine, the oxygen isotope exchange equilibrium may have been reached in some in kimberlite and mantle xenolith samples between garnet and olivine. However, in other samples, the fractionation factors cannot be explained solely by the composition effect, likely due to metasomatism. Our results underscore the importance of considering garnet compositions when interpreting their oxygen isotope compositions.

中文翻译：

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石榴石与石英/方解石/橄榄石之间的成分对平衡氧同位素分馏因子的影响：高温高压下石榴石振动频率的含义


石榴石族矿物成分广泛，在地壳和上地幔中发挥着重要作用，参与各种岩石学和地球化学过程。石榴石和其他矿物之间的氧同位素分馏因素在这些情况下具有重要意义。在这项工作中，通过拉曼光谱测量了镁铝榴石-铁铝榴石-锰铝榴石三元系统中的五种石榴石矿物样品和四种合成镁铝榴石-钙铝榴石固溶体在高达 1000 °C 的温度和高达 17 GPa 的压力下的振动频率。针对观察到的模式确定了等压 () 和等温 () 模式 Grüneisen 以及非谐波 () 参数。我们的研究表明，随着温度的升高，振动带倾向于转向较低的频率，而随着压力的增加，振动带倾向于转向更高的频率。此外，我们发现非谐校正对石榴石中的平衡氧同位素分馏因子有积极贡献，通常在 1000 K 以上的 0.5 ‰ 范围内。根据振动谱（仅考虑点）计算出的 10∙ln() 因子与理论值紧密一致。计算（包括布里渊区的所有频率）。声子色散（包括非点）的贡献通常小于频率测量传播的不确定性。此外，根据等温 Grüneisen 参数评估，压力对石榴石中氧同位素分馏的影响在地壳和上地幔条件下并不显着，这与热力学预期一致。 使用已发布的石英和方解石氧同位素分馏因子，计算不同成分的石榴石和任何这些相之间的平衡氧同位素分馏因子 (10∙ln)，作为温度、压力和石榴石端元分数的函数。考虑成分效应有助于减少石榴石和石英之间氧同位素分馏因子的实验和经验校准之间的差异。作为应用示例，计算了上地幔条件下石榴石和镁橄榄石之间的氧同位素分馏因子 10∙ln(, )。我们的研究结果表明，这些分馏因素主要取决于温度和石榴石成分，压力的影响较小。与我们计算的石榴石和橄榄石之间的分馏因子相比，金伯利岩和地幔捕虏体样品中的一些石榴石和橄榄石之间可能已经达到了氧同位素交换平衡。然而，在其他样品中，分馏因子不能仅用成分效应来解释，可能是由于交代作用。我们的结果强调了在解释石榴石氧同位素组成时考虑石榴石组成的重要性。