高压下Py-FeO<sub>2</sub>、Py-FeOOH和ε-FeOOH晶体结构与弹性特征的第一性原理研究

顾小雨; 刘雷

doi:10.11858/gywlxb.20210789

高压下Py-FeO₂、Py-FeOOH和ε-FeOOH晶体结构与弹性特征的第一性原理研究

doi: 10.11858/gywlxb.20210789

顾小雨,
刘雷^*, ,

中国地震局地震预测研究所高压物理与地震科技联合实验室，北京　100089

基金项目: 中国地震科学实验场基金（2021IEF0101-01）

详细信息

作者简介:
顾小雨（1996－），女，硕士研究生，主要从事高温高压下矿物物性模拟研究.E-mail：gxy.cea.2018@gmail.com

通讯作者:
刘　雷（1980－），男，博士，副研究员，主要从事高温高压下矿物物性模拟研究.E-mail：liulei@ief.ac.cn

中图分类号: O521.2
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出版历程
- 收稿日期: 2021-05-10
- 修回日期: 2020-06-15

First-Principles Calculation on Crystal Structure and Elastic Properties of Py-FeO₂, Py-FeOOH and ε-FeOOH under High Pressures

GU Xiaoyu,
LIU Lei^{*
, ,}

The United Laboratory of High-Pressure Physics and Earthquake Science, Institute of Earthquake Forecasting, CEA, Beijing 100089, China

摘要

摘要: Py-FeO₂、Py-FeOOH和ε-FeOOH是地幔及核幔边界的重要成分，其在高温高压下的物性演化特征对了解地幔物质组成和结构及动力学过程有重要意义，为此利用第一性原理方法计算了 0～350 GPa条件下Py-FeO₂和Py-FeOOH以及0～170 GPa条件下ε-FeOOH的晶体结构与弹性性质。Py-FeO₂和Py-FeOOH的晶格常数随压强的增加呈逐渐减小趋势，而ε-FeOOH的晶格常数随压强增加而减小，其中c轴更容易被压缩。Py-FeO₂、Py-FeOOH和ε-FeOOH的晶胞密度随压强增加而增大，按照密度由大到小依次为Py-FeO₂、Py-FeOOH、ε-FeOOH。3相的体积模量随压强的增加线性增加，Py-FeO₂和Py-FeOOH的剪切模量随压强的增加线性增加。对比体积模量可知，Py-FeO₂的体积模量最高，Py-FeOOH和ε-FeOOH的体积模量在高压下几乎一致；而Py-FeO₂的剪切模量最大，ε-FeOOH的剪切模量最小。Py-FeO₂、Py-FeOOH和ε-FeOOH的压缩波速随压强的增加而增加，Py-FeO₂的剪切波速随压强的增加而增加。Py-FeOOH的剪切波速在0～2000 km深度范围内随深度增加而减小，在2000～6000 km深度范围内变化较小（在5.8～6.0 km/s之间）；ε-FeOOH的剪切波速在33 GPa（约900 km深度）发生突变。3相中ε-FeOOH的波速最低，而Py-FeO₂的波速最高。综合计算结果表明，Py-FeO₂和Py-FeOOH具有高密度、低波速的特点，与地幔超低速区的性质一致。Py-FeO₂和Py-FeOOH在形成之后可能富集下沉到核幔边界，成为超低速区的来源。ε-FeOOH在超过33 GPa压强条件下发生的氢键对称化给ε-FeOOH的结构带来显著变化，同时氢键对称化会影响原子间相互作用，进而影响ε-FeOOH的弹性性质以及地震波速。
- ε-FeOOH /
- Py-FeOOH /
- Py-FeO₂ /
- 晶格结构 /
- 弹性特征 /
- 第一性原理计算
Abstract: Py-FeO₂, Py-FeOOH and ε-FeOOH are important components of mantle and core-mantle boundary. Their physical evolution characteristics at high temperature and high pressure are important for understanding the composition, structure and dynamic process of mantle. The crystal structures and elastic properties of Py-FeO₂ and Py-FeOOH at 0−350 GPa and ε-FeOOH at 0−170 GPa were calculated by first principles in this study. The Py-FeO₂and Py-FeOOH belong to the cubic crystal system, their lattice constants decrease gradually with increasing pressure. The ε-FeOOH belongs to orthorhombic crystal system, and its lattice constants decrease with increasing pressure, however, a and b axes bump up at 33 GPa, while c axis swoop at 33 GPa. The cell densities of Py-FeO₂, Py-FeOOH and ε-FeOOH increase with pressure, and the relative cell density among these three phases is Py-FeO₂ > Py-FeOOH > ε-FeOOH. The bulk moduli of Py-FeO₂, Py-FeOOH and ε-FeOOH increase linearly with pressure, and the shear moduli of Py-FeO₂ and Py-FeOOH increase linearly with pressure, but the shear modulus of ε-FeOOH mutates at 33 GPa. Py-FeO₂ has the highest bulk modulus, and Py-FeOOH and ε-FeOOH have almost the same bulk modulus at high pressures. In addition, Py-FeO₂ has the largest shear modulus, and ε-FeOOH has the smallest shear modulus. The compression wave velocities of Py-FeO₂, Py-FeOOH and ε-FeOOH decrease gradually with the increasing pressure, while the shear wave velocities of Py-FeO₂ increase gradually with the increasing pressure. The shear wave velocity of Py-FeOOH decreases with the increasing depth in the range of 0−2000 km, and the variation is small in the range of 2000−6000 km (5.8 km/s < v_s < 6.0 km/s). The shear wave velocities of ε-FeOOH mutate at 33 GPa (about 900 km depth). The wave velocity of ε-FeOOH is the lowest, while that of Py-FeO₂ is the highest. Based on comprehensive theoretical calculations, it is found that Py-FeO₂ and Py-FeOOH have the high density and low wave velocity characteristics, which are consistent with the properties of the mantle ultra-low velocity zone (ULVZs). Py-FeO₂ and Py-FeOOH may enrich and sink to the core-mantle boundary after formation, becoming the source of the ULVZs. The hydrogen bond symmetry of ε-FeOOH under 33 GPa may affect the crystal structure of ε-FeOOH, the atomic interactions of ε-FeOOH, and then the elastic properties and seismic wave velocity of ε-FeOOH.
- ε-FeOOH /
- Py-FeOOH /
- Py-FeO₂ /
- crystal structure /
- elastic properties /
- first-principles calculation

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图 1 Py-FeO₂、Py-FeOOH和ε-FeOOH的晶体结构

Figure 1. Crystal structure of Py-FeO₂, Py-FeOOH and ε-FeOOH

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图 2 Py-FeO₂、Py-FeOOH和ε-FeOOH的晶格常数随压强的变化

Figure 2. Lattice parameters of Py-FeO₂, Py-FeOOH and ε-FeOOH under high pressures

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图 3 ε-FeOOH结构中羟基键长和氧氧键长随压强的变化

Figure 3. Hydroxyl bond length and oxygen bond distance of ε-FeOOH under high pressures

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图 4 Py-FeO₂结构中氧氧键长随压强的变化

Figure 4. Oxygen bond length of Py-FeO₂ under high pressures

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图 5 Py-FeO₂、Py-FeOOH和ε-FeOOH的密度随深度的变化

Figure 5. Variation of density of Py-FeO₂, Py-FeOOH and ε-FeOOH with depth

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图 6 Py-FeO₂、Py-FeOOH和ε-FeOOH的弹性常数（C₁₁、C₁₂、C₄₄）随压强的变化

Figure 6. Elastic constants (C₁₁, C₁₂, C₄₄) of Py-FeO₂, Py-FeOOH and ε-FeOOH under high pressures

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图 7 ε-FeOOH的弹性常数（C₁₃、C₂₃、C₂₂、C₃₃、C₅₅、C₆₆）随压强的变化

Figure 7. Elastic constants (C₁₃, C₂₃, C₂₂, C₃₃, C₅₅, C₆₆) of ε-FeOOH under high pressures

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图 8 Py-FeO₂、Py-FeOOH和ε-FeOOH的弹性模量随压强的变化

Figure 8. Bulk and shear moduli of Py-FeO₂, Py-FeOOH and ε-FeOOH under high pressures

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图 9 Py-FeO₂、Py-FeOOH和ε-FeOOH的地震波速随深度的变化

Figure 9. Variations of seismic wave velocities of Py-FeO₂, Py-FeOOH and ε-FeOOH with depth

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表 1 Py-FeO₂、Py-FeOOH和ε-FeOOH的晶格参数和体积模量

Table 1. Lattice parameters and bulk moduli of Py-FeO₂, Py-FeOOH and ε-FeOOH

Garnet	Pressure & Temperature	a/Å	b/Å	c/Å	V·Z ^–1/Å³	Bulk modulus	Method	Ref.
Py-FeO₂	70 GPa, 0 K	4.3370			20.391		Sim.	This study
	76 GPa	4.3310			20.308		Sim.	Ref.[5]
	76 GPa	4.4420			20.745		Exp.	Ref.[5]
	Maximum deviation/%	2.4			1.7
Py-FeOOH	120 GPa, 0 K	4.3540			20.635		Sim.	This study
	120 GPa, 0 K				21.110		Sim.	Ref.[7]
	119 GPa, 2300 K	4.3447			20.503		Exp.	Ref.[6]
	119 GPa, 300 K	4.3626			20.758		Exp.	Ref.[7]
	Maximum deviation/%	0.4			2.3
ε-FeOOH	0 GPa, 0 K	4.7054	4.2510	2.8970	28.970	172	Sim.	This study
					28.900	187	Sim.	Ref.[25]
	0 GPa, 300 K	4.9540	4.4540	3.0001	33.100	126	Exp.	Ref.[23]
	0.001 GPa, 300 K	4.9544	4.4594	2.9999	33.139	135	Exp.	Ref.[24]
		4.937	4.432	2.994	32.636		Exp.	Ref.[18]
	Maximum deviation/%	4.8	4.7	3.4	14.0	32

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