Fe-3.24%Si的状态方程和声速的第一性原理计算:地球内核Si元素的约束

First-Principles Calculations of the Equation of State and Sound Velocity of Fe-3.24%Si:Implications for the Composition of Earth’s Inner Core

硅(Si)被认为是地球内核的主要轻元素,但其在内地核中的含量仍然存在争议。为了探索内地核中Si的含量,应用第一性原理方法对Fe-3.24%Si(Si的质量分数为3.24%)进行了研究。构造了4种Fe-3.24%Si的超晶胞,研究了不同的晶胞大小和自旋对优化结构的影响。结果表明:在100 GPa以上,自旋对Fe-3.24%Si的密度无影响;而在100 GPa以下,考虑自旋时的计算结果更接近实验值。基于0 K下的声速、状态方程和相关热力学参数,计算了Fe-3.24%Si在内地核条件下的密度和声速。研究发现:Fe-3.24%Si的密度低于纯铁的密度,略高于内地核的密度;纵波声速及剪切波声速与纯铁的声速很接近,但均明显高于内地核声速,因此排除了内地核含有大量Si元素的可能性。

Silicon(Si)is considered as one major light element in Earth’s inner core,but its content is still controversy.In order to constrain its content in the inner core,using first-principles calculation method,we constructed four different supercells of Fe-3.24%Si and investigated the effects of cell size and spin on geometry optimization.It is found that the spin doesn’t affect the equation of state of Fe-3.24%Si above 100 GPa,and below 100 GPa,the calculated results with the spin are closer to the experimental data.Based on the equation of state,the sound velocity at 0 K and the corresponding thermodynamic parameters,the density and sound velocity of Fe-3.24%Si are obtained under the conditions of the inner core.The density of Fe-3.24%Si is lower than that of pure iron and slightly higher than that of the inner core.The sound velocities of longitudinal wave and shear wave for Fe-3.24%Si are very close to that of pure iron,but both are significantly higher than that of the inner core.Therefore,we could exclude the possibility that Earth’s inner core contains a large amount of Si.