Abstract The initial cooling stage and crystallization of a magma ocean were significantly affected by the thermodynamics and viscosity of iron silicate liquid. Here, we use first-principles molecular dynamics based on density functional theory plus the Hubbard U method to study the structures, thermodynamics and viscosities of Fe2SiO4 liquid at 3000–6000 K under pressure conditions spanning the entire mantle. Our calculations show that the compressibility of Fe2SiO4 liquid is weakened at pressures above 50 GPa. The densification of Fe2SiO4 liquid under compression is mainly manifested by a decrease in the distance among Si–O polyhedra and an increase in the cation-anion coordination number. We find that the viscosity of the Fe2SiO4 liquid has a positive pressure dependence, and the effect of pressure on viscosity decreases with increasing temperature. The predicted behaviour of viscosity coefficients of the Fe2SiO4 liquid at different P-T conditions can be described well as: η(P,T) = exp[ − 7.89 + 0.0042 P − 0.0000632 P 2 + ( 3800 + 61.6 P + 0.18 P 2 ) / ( T − 1000 ) ]. Compared to Mg2SiO4 liquid, the viscosity of Fe2SiO4 liquid is lower under the pressure of the lower mantle along isotherms. We calculate the adiabat of the Fe2SiO4 liquid in a magma ocean, and the results show that the iron content has little effect on the adiabats of (Mg,Fe)2SiO4 liquid in the magma ocean. Combining our calculated thermodynamic properties and viscosities with those of previous studies, the physical properties of an early magma ocean were constrained. The upper bound of the potential temperature for magma ocean crystallization is 3250 K. We constructed the range of the viscosity profile of a magma ocean and found that the lower viscosity of iron-rich silicate liquid would maintain the viscosity of an early magma ocean in the range of several mPa s. As the magma ocean starts to crystallize, the lower bound of the viscosity at the surface and the core-mantle boundary are 0.0020 Pa s and 0.0068 Pa s, respectively. The weakening of the viscosity of the iron silicate liquids would have a significant impact on the evolution of the magma ocean.

中文翻译：

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受硅酸铁液体热力学和粘度约束​​的早期岩浆海洋物理状态

摘要 岩浆海洋的初始冷却阶段和结晶过程受硅酸铁液的热力学和粘度的显着影响。在这里，我们使用基于密度泛函理论的第一性原理分子动力学加上哈伯德 U 方法来研究 Fe2SiO4 液体在 3000-6000 K 下在整个地幔的压力条件下的结构、热力学和粘度。我们的计算表明，Fe2SiO4 液体的压缩性在高于 50 GPa 的压力下减弱。Fe2SiO4 液体在压缩下的致密化主要表现为 Si-O 多面体之间距离的减小和阳离子-阴离子配位数的增加。我们发现 Fe2SiO4 液体的粘度具有正压力依赖性，压力对粘度的影响随温度升高而减小。Fe2SiO4 液体在不同 PT 条件下的粘度系数预测行为可以很好地描述为： η(P,T) = exp[ − 7.89 + 0.0042 P − 0.0000632 P 2 + ( 3800 + 61.6 P + 0.18 P 2 ) / (T-1000)]。与 Mg2SiO4 液体相比，Fe2SiO4 液体在下地幔压力下沿等温线的粘度较低。我们计算了岩浆海中Fe2SiO4液体的绝热，结果表明铁含量对岩浆海中(Mg,Fe)2SiO4液体的绝热影响不大。将我们计算的热力学性质和粘度与先前研究的热力学性质和粘度相结合，早期岩浆海洋的物理性质受到了限制。岩浆海洋结晶的潜在温度上限为 3250 K。 我们构建了岩浆海洋的粘度剖面范围，发现富铁硅酸盐液体的较低粘度将保持早期岩浆海洋的粘度。数 mPa s 的范围。随着岩浆海洋开始结晶，地表黏度下限和核幔边界分别为 0.0020 Pa s 和 0.0068 Pa s。硅酸铁液体粘度的减弱将对岩浆海洋的演化产生重大影响。地表黏度下限和核幔边界分别为 0.0020 Pa s 和 0.0068 Pa s。硅酸铁液体粘度的减弱将对岩浆海洋的演化产生重大影响。地表黏度下限和核幔边界分别为 0.0020 Pa s 和 0.0068 Pa s。硅酸铁液体粘度的减弱将对岩浆海洋的演化产生重大影响。