We report the results of spinel-magnesite Mg isotope exchange experiments at 600, 700, and 800 °C and 1 GPa to establish the equilibrium Mg isotope partitioning between magnesite (MgCO₃) and spinel as a function of Cr substitution for Al in the spinel phase. We used the three-isotope method to obtain equilibrium fractionation factors between MgAlCrO₄ and magnesite and MgCr₂O₄ and magnesite. The experimentally-determined temperature-dependent Mg isotope fractionations are ${\mathrm{\Delta }}^{26}{\text{Mg}}_{{\text{MgAlCrO}}_{\text{4}}\text{- Mgs}}$ = 0.96 ± 0.22 × 10⁶/T² and ${\mathrm{\Delta }}^{26}{\text{Mg}}_{{\text{MgCr}}_{\text{2}}{\text{O}}_{\text{4}}\text{- Mgs}}$ = 0.55 ± 0.08 × 10⁶/T² (2 s.e.). When combined with the previous experimentally determined fractionation between forsterite and magnesite (Macris et al., 2013), the corresponding Mg isotope fractionations between these two Cr-bearing spinel compositions and forsterite are ${\mathrm{\Delta }}^{26}{\text{Mg}}_{{\text{MgAlCrO}}_{\text{4}}\text{- Fo}}$ = 0.84 ± 0.23 × 10⁶/T² and ${\mathrm{\Delta }}^{26}{\text{Mg}}_{{\text{MgCr}}_{\text{2}}{\text{O}}_{\text{4}}\text{- Fo}}$ = 0.43 ± 0.10 × 10⁶/T². The experimentally determined isotopic fractionation relationship between magnesiochromite and magnesite agrees with theoretical predictions based on the crystal chemical environment of Mg in these minerals. By combining these new results with the existing experimental calibration of equilibrium Mg isotope exchange between pure spinel and forsterite, we arrive at the temperature-dependent Mg isotope fractionation between spinel and forsterite as a function of Cr concentration in the spinel:${\mathrm{\Delta }}^{26}M{g}_{\text{Mg}{\left({\text{Al}}_{\text{1 - x}}{\text{Cr}}_{\text{x}}\right)}_{\text{2}}{\text{O}}_{\text{4}}\text{- Fo}}=\left[\left(-0.67\pm 0.26\right)x+1.10\pm 0.23\right]{10}^6/T^2$

When applied to natural samples, the combination of measured Mg isotope fractionation between spinel and forsterite, the Cr concentrations of the spinels, and estimates of temperature from independent geothermometers can be used to identify differences in closure temperatures between Mg isotope exchange and cation exchange, or the presence of disequilibrium in these systems.

我们报告了在600、700和800°C和1 GPa下尖晶石-菱镁矿Mg同位素交换实验的结果，以建立菱镁矿（MgCO ₃）和尖晶石之间的平衡Mg同位素分配，作为Cr替代尖晶石中Al的函数相。我们使用三同位素方法获得MgAlCrO ₄和菱镁矿以及MgCr ₂ O ₄和菱镁矿之间的平衡分馏因子。实验确定的温度依赖性镁同位素分馏为${\mathrm{\Delta }}^{26}{\text{镁}}_{{\text{镁铝铬}}_{\text{4}}\text{-镁}}$ = 0.96±0.22×10 ⁶ / T ²和${\mathrm{\Delta }}^{26}{\text{镁}}_{{\text{镁铬}}_{\text{2}}{\text{Ø}}_{\text{4}}\text{-镁}}$ = 0.55±0.08×10 ⁶ / T ²（2 se）。当与先前通过实验确定的镁橄榄石和菱镁矿之间的分级分离结合时（Macris等人，2013），这两种含铬尖晶石成分与镁橄榄石之间的相应的Mg同位素分级为${\mathrm{\Delta }}^{26}{\text{镁}}_{{\text{镁铝铬}}_{\text{4}}\text{-佛}}$ = 0.84±0.23×10 ⁶ / T ²和${\mathrm{\Delta }}^{26}{\text{镁}}_{{\text{镁铬}}_{\text{2}}{\text{Ø}}_{\text{4}}\text{-佛}}$ ＝ 0.43±0.10×10 ⁶ / T ²。实验确定的镁铬铁矿和菱镁矿之间的同位素分馏关系与基于这些矿物中Mg的晶体化学环境的理论预测相符。通过将这些新结果与纯尖晶石和镁橄榄石之间平衡Mg同位素交换的现有实验校准相结合，我们得出了尖晶石和镁橄榄石之间的温度依赖性Mg同位素分馏与尖晶石中Cr浓度的关系：${\mathrm{\Delta }}^{26}\mathrm{中号}{G}_{\text{镁}{\left({\text{铝}}_{\text{1-x}}{\text{铬}}_{\text{X}}\right)}_{\text{2}}{\text{Ø}}_{\text{4}}\text{-佛}}=\left[\left(--0.67\pm 0.26\right)X+1.10\pm 0.23\right]{10}^6/{Ť}^2$

当应用于天然样品时，可以使用测得的尖晶石和镁橄榄石之间的Mg同位素分馏，尖晶石的Cr浓度以及来自独立地热仪的温度估算值的组合来确定Mg同位素交换和阳离子交换之间的闭合温度差异，或者这些系统中存在不平衡。