Iron represents the principal constituent of the Earth’s core, but its high-pressure melting diagram remains ambiguous. Here we present a simple analytical approach to predict the melting properties of iron under deep-Earth conditions. In our model, anharmonic free energies of the solid phase are directly determined by the moment expansion technique in quantum statistical mechanics. This basis associated with the Lindemann criterion for a vibrational instability can deduce the melting temperature. Moreover, we correlate the thermal expansion process with the shear response to explain a discontinuity of atomic volume, enthalpy, and entropy upon melting. Our numerical calculations are quantitatively consistent with recent experiments and simulations. The obtained results would improve understanding of the Earth’s structure, dynamics, and evolution.

中文翻译：

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铁的高压熔炼性能的高效分析方法

铁是地核的主要成分，但它的高压熔化图仍然不明确。在这里，我们提出了一种简单的分析方法来预测深地条件下铁的熔化特性。在我们的模型中，固相的非谐自由能由量子统计力学中的矩展开技术直接确定。这个与振动不稳定性的林德曼准则相关的基础可以推导出熔化温度。此外，我们将热膨胀过程与剪切响应相关联，以解释熔化时原子体积、焓和熵的不连续性。我们的数值计算与最近的实验和模拟在数量上是一致的。获得的结果将提高对地球结构、动力学和演化的理解。