The pressure-induced spin crossover of iron in ferropericlase, the Fe-bearing MgO, is a key to understanding the seismological observations in the lower mantle. However, the experimentally measured spin-crossover pressure zone (SCPZ) shows large variations, which disagree with the theoretically predicted values that are generally less than half of experimental ones. Here, we resolve this outstanding controversy by revealing the critical role of Fe distribution in MgO in broadening the Fe SCPZ, using comprehensive first-principles calculations combined with cluster expansion approach and Monte Carlo simulations. By employing a large supercell containing up to $\sim {10}^6$ atoms, we derive the spin-crossover pressures as functions of Fe concentration for different Fe distributions. We determine a critical temperature of $T_c\sim 900\mathrm{K}$, below which Fe segregation (clustering) occurs, in accordance with the thermodynamic phase diagram. Above $T_c$, an entropy-driven randomized Fe distribution creates large variations in Fe local environments, which in turn broadens the SCPZ, such as 17.5 GPa for 25 mol % Fe-bearing MgO in good agreement with experiments. Therefore, the broad SCPZ, rendering a smooth change of ferropericlase mechanical properties during the spin crossover, should be mainly caused by entropy, consistent with the high-temperature state of the lower mantle.

中文翻译：

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铁方镁石中自旋交叉压力的熵展宽

铁方镁石中铁的压力诱导自旋交叉，即含铁的 MgO，是理解下地幔地震观测的关键。然而，实验测量的自旋交叉压力区（SCPZ）显示出很大的变化，这与通常小于实验值一半的理论预测值不一致。在这里，我们使用综合的第一性原理计算结合簇扩展方法和蒙特卡罗模拟，通过揭示 MgO 中 Fe 分布在扩大 Fe SCPZ 中的关键作用来解决这一悬而未决的争议。通过使用包含多达$～{10}^6$原子，我们推导出自旋交叉压力作为不同 Fe 分布的 Fe 浓度的函数。我们确定临界温度为${吨}_C～900\mathrm{钾}$，根据热力学相图，在其下方发生 Fe 偏析（簇化）。以上${吨}_C$，熵驱动的随机 Fe 分布在 Fe 局部环境中产生了很大的变化，这反过来扩大了 SCPZ，例如 17.5 GPa 对于 25 mol% 含 Fe 的 MgO 与实验非常吻合。因此，广阔的 SCPZ 在自旋交叉过程中呈现铁方镁石力学性能的平滑变化，这主要是由熵引起的，与下地幔的高温状态一致。