Brodholt John P, Oganov A R, Price G D
Department of Earth Sciences, University College London, Gower Street, UK.
Philos Trans A Math Phys Eng Sci. 2002 Nov 15;360(1800):2507-20. doi: 10.1098/rsta.2002.1078.
The inherent uncertainties in modern first-principles calculations are reviewed using geophysically relevant examples. The elastic constants of perovskite at lower-mantle temperatures and pressures are calculated using ab initio molecular dynamics. These are used in conjunction with seismic tomographic models to estimate that the lateral temperature contrasts in the Earth's lower mantle are 800 K at a depth of 1000 km, and 1500 K at a depth of 2000 km. The effect of Al(3+) on the compressibility of MgSiO(3) perovskite is calculated using three different pseudopotentials. The results confirm earlier work and show that the compressibility of perovskites with Al(3+) substituted for both Si(4+) and Mg(2+) is very similar to the compressibility of Al(3+)-free perovskite. Even when 100% of the Si(4+) and Mg(2+) ions are replaced with Al(3+), the bulk modulus is only 7% less than that for Al(3+)-free perovskite. In contrast, perovskites where Al(3+) substitutes for Si(4+) only and that are charge balanced by oxygen vacancies do show higher compressibilities. When corrected to similar concentrations of Al(3+), the calculated compressibilities of the oxygen-vacancy-rich perovskites are in agreement with experimental results.
利用地球物理相关实例，对现代第一性原理计算中固有的不确定性进行了综述。使用从头算分子动力学计算了下地幔温度和压力下钙钛矿的弹性常数。这些弹性常数与地震层析成像模型结合使用，估计地球下地幔在1000公里深度处的横向温度差为800K，在2000公里深度处为1500K。使用三种不同的赝势计算了Al(3+)对MgSiO(3)钙钛矿压缩性的影响。结果证实了早期的研究工作，并表明用Al(3+)取代Si(4+)和Mg(2+)的钙钛矿的压缩性与不含Al(3+)的钙钛矿的压缩性非常相似。即使100%的Si(4+)和Mg(2+)离子被Al(3+)取代，其体积模量也仅比不含Al(3+)的钙钛矿低7%。相比之下，Al(3+)仅取代Si(4+)且由氧空位电荷平衡的钙钛矿确实显示出更高的压缩性。当校正到相似的Al(3+)浓度时，计算得到的富氧空位钙钛矿的压缩性与实验结果一致。
