NaPO<sub>3</sub>高压结构行为的第一性原理理论研究

陈炜珊; 谭毅; 谭大勇; 肖万生

doi:10.11858/gywlxb.20240755

NaPO₃高压结构行为的第一性原理理论研究

doi: 10.11858/gywlxb.20240755

陈炜珊^{1, 2, 3,},
谭毅^{1, 2, 3},
谭大勇⁴,
肖万生^{1, 2,*, ,}

1.
中国科学院广州地球化学研究所矿物学与成矿学重点实验室, 广东广州 510640
2.
广东省矿物物理与材料研究开发重点实验室, 广东广州 510640
3.
中国科学院大学, 北京 100049
4.
深圳综合粒子设施研究院, 广东深圳 518107

基金项目: 国家自然科学基金（42172046）

详细信息

作者简介:
陈炜珊（1998－），女，硕士研究生，主要从事高压矿物学研究. E-mail：chenweishan0921@163.com

通讯作者:
肖万生（1968－），男，博士，研究员，主要从事高压矿物学研究. E-mail：wsxiao@gig.ac.cn

中图分类号: O521.2
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出版历程
- 收稿日期: 2024-03-19
- 修回日期: 2024-04-03
- 录用日期: 2024-04-08
- 刊出日期: 2024-09-29

First-Principles Theoretical Study on the Structure Behaviors of NaPO₃ under Compression

CHEN Weishan^{1, 2, 3
,},
TAN Yi^{1, 2, 3},
TAN Dayong⁴,
XIAO Wansheng^{1, 2,*
, ,}

1.
Key Laboratory of Mineralogy and Metallogeny, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640, Guangdong, China
2.
Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou 510640, Guangdong, China
3.
University of Chinese Academy of Sciences, Beijing 100049, China
4.
Institute of Advanced Science Facilities, Shenzhen 518107, Guangdong, China

摘要

摘要: 探索PO₆配位八面体的高压晶体化学行为是理解磷的高压化学性质、了解磷在下地幔中可能的赋存方式及磷的地球化学循环的重要基础。在0～80 GPa压力范围内，对MgSiO₃等电子体的NaPO₃开展第一性原理密度泛函理论研究，通过对其常压β相（P2₁/n）、透辉石相（C2/c）、钛铁矿相（R$ \overline 3 $）、斜方钙钛矿相（Pnma）和立方钙钛矿相（Pm3m）的几何优化和总能对比，获得了NaPO₃的结构相变序列及相变压力：P2₁/n → C2/c （2 GPa） → R$ \overline 3 $ （20 GPa）→ Pnma（50 GPa），相变导致的体积变化分别为7.1%、11.5%和9.0%。Pm3m-NaPO₃的声子色散曲线在R点和M点呈现出显著且相似的虚频，而Pnma-NaPO₃在整个布里渊区均表现为实频，表明Pnma-NaPO₃动力学稳定。Pnma-NaPO₃的晶格常数、P―O键长、P―O―P键角、${{\mathrm{NaO}}_{12}} $和${{\mathrm{PO}}_6} $多面体体积比$V_{{\mathrm{NaO}}_{12}} $/$V_{{\mathrm{PO}}_6} $与压力的关系表明，PO₆八面体在计算的整个压力范围内都较规则，且NaO₁₂多面体的压缩性比PO₆八面体的压缩性更大。电子结构计算表明，在Pnma-NaPO₃的PO₆八面体中，P的3p和3s轨道与O的2p轨道强烈混合，P―O键表现出的强共价性对稳定其斜方钙钛矿结构发挥了关键作用。
- NaPO₃ /
- PO₆配位八面体 /
- 第一性原理 /
- 高压相变 /
- 斜方钙钛矿 /
- 晶格动力学
Abstract: Exploring the high-pressure crystal chemical behaviors of the PO₆ coordinated octahedron is an important basis for understanding the high-pressure chemistry, the possible occurrence in the lower mantle, and the geochemical cycle of the phosphorus element. In this study, NaPO₃, which is isoelectronic with the major component of the lower mantle MgSiO₃, was studied with the first-principle density functional theory in the pressure range of 0–80 GPa. By ways of geometric optimization and total energy comparison of its ambient pressure β phase (P2₁/n), diopside phase (C2/c), ilmenite phase (R$ \overline 3 $), orthorhombic (Pnma) and cubic (Pm3m) perovskite phases, the structural phase transformation sequence and phase transformation pressures were obtained: P2₁/n→C2/c (2 GPa)→R$ \overline 3 $ (20 GPa)→Pnma (50 GPa), with the unit-cell volume changes of 7.1%, 11.5% and 9.0%, respectively. The phonon dispersion curves of Pm3m-NaPO₃ show remarkable and similar imaginary frequencies at R and M points, while the orthorhombic perovskite structure shows real frequencies throughout the whole Brillouin zone reflecting its dynamic stability. The pressure dependence of lattice constants, P―O bond lengths, P―O―P bond angles and $V_{{\mathrm{NaO}}_{12}} $/$V_{{\mathrm{PO}}_6} $ polyhedron volume ratio of Pnma-NaPO₃ shows that the PO₆ octahedron is regular in the whole calculated pressure range, and the compressibility of NaO₁₂ polyhedron is greater than that of PO₆ octahedron. The electronic structure calculation shows that the 3p and 3s orbitals of P are strongly mixed with 2p orbitals of O in the PO₆ octahedron of Pnma-NaPO₃, and the P―O bond exhibits strong covalency, which plays a key role in stabilizing the orthorhombic perovskite structure.
- NaPO₃ /
- PO₆ coordinated octahedron /
- first principles /
- high-pressure phase transition /
- orthorhombic perovskite /
- lattice dynamics

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图 1 常压下NaPO₃的P2₁/n (a)、Pmcn (b)和I4₁/a (c)晶体结构示意图

Figure 1. Crystal structures of NaPO₃ with P2₁/n (a), Pmcn (b) and I4₁/a (c) space groups at ambient pressure

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图 2 NaPO₃的常压β相（P2₁/n）、透辉石相（C2/c）、钙钛矿相（Pnma斜方相和Pm3m立方相）与钛铁矿相（R${ \overline 3} $）的焓差与压力关系

Figure 2. Pressure dependence of enthalpy difference for NaPO₃ with P2₁/n, C2/c, Pnma, Pm3m and R${ \overline 3} $ structures

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图 3 计算获得的NaPO₃的5种结构的单位化学式体积-压力关系

Figure 3. Pressure dependence of volume per formula for the five structures of NaPO₃

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图 4 NaPO₃钙钛矿结构Pm3m (a)和Pnma (b)的晶体结构

Figure 4. Crystal structures of NaPO₃ with cubic Pm3m (a) and orthorhombic Pnma (b) perovskites structures

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图 5 计算得到的0 GPa下NaPO₃ 钙钛矿结构的Pm3m立方相(a)和Pnma斜方相(b)的声子谱

Figure 5. Calculated phonon spectra of NaPO₃ with cubic Pm3m (a) and orthorhombic Pnma (b) perovskite structures at 0 GPa

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图 6 常压下Pnma-NaPO₃的总态密度和分态密度

Figure 6. Density of state (DOS) and partical density of state (PDOS) of Pnma-NaPO₃ at 0 GPa

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图 7 NaPO₃斜方钙钛矿（Pnma）结构随压力的变化

Figure 7. Structural variations of NaPO₃ with orthorhombic perovskite structure (Pnma) as a function of pressure

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表 1 0 GPa下NaPO₃的5种结构在几何优化后的结构参数

Table 1. Structural parameters of five phases for NaPO₃ at 0 GPa

Phase	VZ⁻¹/(Å³·formula⁻¹)	a/Å	b/Å	c/Å	β/(°)	Atom	Wyckoff site	x	y	z
P2₁/n	66.460	11.445	6.074	7.669	85.91	Na1	4e	0.1949	0.9249	0.6067
						Na2	4e	−0.0001	0.3295	0.8093
						P1	4e	0.1918	0.4206	0.4687
						P2	4e	0.0963	0.1538	0.1823
						O1	4e	0.1914	0.3465	0.6561
						O2	4e	0.1559	0.1988	0.3661
						O3	4e	0.1243	0.6207	0.4222
						O4	4e	0.1723	0.9435	0.1085
						O5	4e	0.1136	0.3513	0.0643
						O6	4e	0.0236	0.9388	0.7763
C2/c	60.831	10.193	10.040	4.804	98.15	Na1	4e	0.5000	0.3967	0.2500
						Na2	4e	0.5000	0.2112	0.7500
						P	8f	0.2825	0.0880	0.2236
						O1	8f	0.1338	0.0912	0.1854
						O2	8f	0.3631	0.2083	0.3163
						O3	8f	0.3358	0.0361	−0.0639
R$ \overline 3 $	48.990	4.618		15.915		Na	6c	0	0	0.3556
						P	6c	0	0	0.1646
						O	18f	0.3308	0.0527	0.2278
Pm3m	40.691	3.440				Na	1a	0	0	0
						P	1b	0.5000	0.5000	0.5000
						O	3c	0.5000	0.5000	0
Pnma	40.604	4.848	6.885	4.866		Na	4c	0.0240	0.2500	0.0042
						P	4b	0.5000	0	0
						O1	4c	−0.0053	0.2500	0.5567
						O2	8d	0.2810	0.0285	0.2848

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表 2 拟合得到的NaPO₃的5种结构的状态方程参数

Table 2. Fitted parameters of equation of state for the five structures of NaPO₃

Phase	V₀/Å³	K₀/GPa	$K_0' $
P2₁/n	531.84(32)	31.7(5)	5.16(13)
C2/c	486.07(32)	47.8(5)	5.78(7)
$R \overline 3 $	293.35(12)	116.7(7)	4.81(3)
Pnma	162.34(4)	215.7(1.1)	4.55(4)
Pm3m	40.67(1)	235.6(1.2)	4.58(4)

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表 3 0 GPa下Pnma-NaPO₃的键长和键角

Table 3. Bond distances and bond angles of NaPO₃ with orthorhombic perovskite structure (Pnma) at 0 GPa

Structure	Type	Bond distance/Å	Bond angle/(º)
PO₆	P―O(1) [×2]	1.729
	P―O(2) [×2]	1.744
	P―O(2) [×2]	1.757
	P―O1―P		161.62
	P―O2―P [×2]		160.23
	O1―P―O2		89.76
	O1―P―O2		89.65
	O2―P―O2		89.18
NaO₁₂	Na―O(1)	2.181
	Na―O(1)	2.301
	Na―O(2) [×2]	2.184
	Na―O(2) [×2]	2.390
	Na―O(2) [×2]	2.396
	Na―O(1)	2.583
	Na―O(1)	2.693
	Na―O(2) [×2]	2.800

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