We present a new force constants approach that combines experimental and theoretical data to constrain the reduced partition function ratio (\(\beta\)-factor) of tetrahedrally coordinated silicon (\(^{IV}\)Si) in the crust and upper mantle minerals. Our approach extends the experiment-based general moment approach, which relies on nuclear resonant scattering and is only applicable to Mössbauer-active elements, to Mössbauer-inactive elements such as Si. We determine the resilience of \(^{IV}\)Si from the Debye–Waller factor, which is derived from the temperature dependence of single crystal X-ray diffraction data, and calculate the stiffness of \(^{IV}\)Si from the density-functional theory results. The relationship between the resilience the stiffness is calibrated, and we have used an experimentally measurable parameter, the effective coordination number of the \(\hbox {SiO}_4\) tetrahedron, to correct the stiffness. The correction is most pronounced for pyroxenes (\(\sim 2\%\)). The corrected stiffness is used to calculate the equilibrium isotope fractionation \(\beta\)-factor of each mineral, and the \(\alpha\)-factors is calculated by taking the ratio of \(\beta\)-factors of different minerals. We calculate the ln\(\alpha _{Si30/28}\) between minerals that contains \(\hbox {SiO}_4\) tetrahedra, and our results are consistent with DFT calculations and mass spectrometry results. Our results suggest that the Si isotopic equilibrium temperature between cristobalite and pyroxene in lunar basalt was underestimated by \(\sim\)250 \(^\circ\)C, and the pyroxene sample in IL-14 marble is in equilibrium with \(\beta\)-quartz.

我们提出了一种新的力常数方法，该方法结合实验和理论数据来约束地壳和上部四面体配位硅（\(^{IV}\) Si）的减少配分函数比（\(\beta\) -factor）。地幔矿物。我们的方法扩展了基于实验的一般矩方法，该方法依赖于核共振散射，仅适用于穆斯堡尔活性元素，扩展到穆斯堡尔非活性元素，如 Si。我们根据德拜-沃勒因子确定\(^{IV}\) Si的弹性，该因子源自单晶 X 射线衍射数据的温度依赖性，并计算\(^{IV}\)Si 来自密度泛函理论的结果。弹性与刚度之间的关系被校准，我们使用了一个实验可测量的参数，\(\hbox {SiO}_4\)四面体的有效配位数，来校正刚度。辉石（\(\sim 2\%\)）的校正最为明显。校正后的刚度来计算的平衡同位素分馏\（\测试\）各矿物的α-因子，和\（\阿尔法\） -因子是通过取的比率计算\（\测试\） -因子的不同矿物质。我们计算含有\(\hbox {SiO}_4\) 的矿物之间的 ln \(\alpha _{Si30/28} \)四面体，我们的结果与 DFT 计算和质谱结果一致。我们的研究结果表明，月球玄武岩中方石英和辉石之间的 Si 同位素平衡温度被低估了\(\sim\) 250 \(^\circ\) C，并且 IL-14 大理石中的辉石样品与\( \beta\) -石英。