辉石结构与相变的第一性原理研究

韩林; 马麦宁; 徐志双; 周晓亚

doi:10.11858/gywlxb.2017.02.004

辉石结构与相变的第一性原理研究

doi: 10.11858/gywlxb.2017.02.004

韩林^{1, 2,},
马麦宁^{1, 2,*, ,},
徐志双^{1, 2},
周晓亚^{1, 2}

1.
中国科学院计算地球动力学重点实验室，北京 100049
2.
中国科学院大学地球科学学院，北京 100049

基金项目:

国家自然科学基金 41274091

国家自然科学基金 41674089

详细信息

作者简介:
韩林(1990—)，女，硕士研究生，主要从事矿物物理计算研究.E-mail:hanlin13@mails.ucas.ac.cn

通讯作者:
马麦宁(1972—)，男，博士，副教授，主要从事岩石、矿物物理研究.E-mail:mamn@ucas.ac.cn

中图分类号: P574.1;O521.2
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出版历程
- 收稿日期: 2016-02-05
- 修回日期: 2016-04-16

Structural Properties and Phase Transition of Pyroxene Polymorphs from First-Principles

HAN Lin^{1, 2
,},
MA Mai-Ning^{1, 2,*
, ,},
XU Zhi-Shuang^{1, 2},
ZHOU Xiao-Ya^{1, 2}

1.
Key Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing 100049, China
2.
College of Earth Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

摘要

摘要: 利用第一性原理方法研究了Mg端员辉石(MgSiO₃)低压相(Pbca、P2₁/c)和高压相(C2/c、P2₁ca)在不同压力下(0~30 GPa)的结构。首先计算得到了不同压力下各相的晶胞体积，并由状态方程拟合得到了体积模量，结果显示在零温零压条件下Pbca和P2₁/c(低压单斜相)的体积模量相近，C2/c的体积模量最大(比Pbca的大3%)，而P2₁ca作为高压相其体积模量却比Pbca小很多。其次分析了Mg端员辉石3个轴向的压缩性，发现C2/c相的c轴比a轴难压缩，与前人研究的透辉石(MgCaSi₂O₆)的表现相反。P2₁/c、C2/c、P2₁ca的链角随着压力的增大而减小；Pbca其中一种链角的变化趋势和其他3个相一样，而另一种链角先随着压力的增大而减小，在达到7 GPa后开始增大，可能表示相的不稳定或开始相变。最后通过研究不同相之间的焓值差，讨论了Mg端员辉石在低温高压下可能存在的相变情况。
- 第一性原理 /
- 辉石 /
- 相变 /
- 体积模量 /
- 轴向压缩性
Abstract: In order to evaluate the structures of magnesium end-member pyroxene polymorphs (MgSiO₃) under different pressures, first-principles theoretical calculation on low- and high-pressure phases, with space group Pbca, P2₁/c, C2/c, P2₁ca respectively, was conducted under pressures up to 30 GPa.The bulk moduli of polymorphs were obtained from fitting the third-order Birch-Murnaghan equation with calculated pressure-volume data.The C2/c phase had the largest modulus (an increase of 3% compared to Pbca) under zero-temperature and zero-pressure, whereas little difference was observed between moduli of Pbca and P2₁/c, and the high-pressure phase P2₁ca showed a smaller value than Pbca.Moreover, the results of axial compression showed that the c-axis was harder to compress than a-axis in C2/c, which was opposite to the previous first-principle results on diopside (MgCaSi₂O₆).The angels of SiO₄ tetrahedral chains in P2₁/c, C2/c, and P2₁ca decreased monotonically as a function of pressure while in Pbca, which had two kinds of angles, one showed the same trend as the aforementioned three polymorphs and the other increased monotonically above 7 GPa, implying an unstable structure or the onset of a new phase transition.The static enthalpy differences among the four polymorphs indicated the possible phase transitions of the pyroxene under low-temperature and high-pressure.
- first-principles /
- pyroxene /
- phase transition /
- bulk modulus /
- axial compression

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图 1 Mg端员辉石Pbca、P2₁/c、C2/c和P2₁ca在不同压力下晶胞体积的第一性原理计算结果

(P2₁/c和C2/c为两倍晶胞体积)

Figure 1. First-principles results on unit cell volumes of Mg end-member pyroxenes Pbca, P2₁/c (2×unit cell), P2₁ca, and C2/c (2×unit cell) under different pressures

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图 2 不同压力下，Pbca、P2₁/c以及C2/c的晶胞体积计算结果和实验结果的比较(左图和右图分别为加压力校正前和加压力校正后；为了方便与实验数据对比，对于Pbca和P2₁/c，计算的压力范围为-3~15 GPa)

Figure 2. Comparisons of unit cell volumes of Pbca, P2₁/c and C2/c under different pressures from first-principles and experiments (The pressure ranged from -3 GPa to 15 GPa and a pressure correction of 2.7 GPa was applied to all first-principles results in right figures)

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图 3 辉石a、b、c轴的轴向压缩率

Figure 3. Axial compression ratios of a, b and c axis of pyroxene polymorphs

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图 4 辉石(P2₁/c)的四面体链链角

Figure 4. Tetrahedral chain angels of pyroxene (P2₁/c)

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图 5 辉石的超胞结构(Pbca、P2₁ca：1×2×2个晶胞；P2₁/c、C2/c：2×2×2个晶胞)

Figure 5. Super cells of pyroxenes (Pbcas, P2₁ca:1×2×2;P2₁/c, C2/c:2×2×2)

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图 6 不同压力下辉石的硅氧四面体链角

Figure 6. SiO₄ tetrahedral chain angels under pressures up to 30 GPa

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图 7 不同压力下P2₁ca、P2₁/c、C2/c与Pbca之间的焓值差ΔH

Figure 7. Static enthalpy differences (ΔH) of pyroxene polymorphs under different pressures

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表 1 Mg端员辉石晶胞体积、体积模量的计算结果(0 K)和实验结果(室温)

Table 1. Unit cell volumes and elastic moduli of Mg end-member pyroxene polymorphs from first-principles results (at 0 K) and experiments (at room temperature)

Space group	V/(nm³)	K/(GPa)	K′	Reference
Pbca	0.813 8	130.8(0.6)	5.2	This study (LDA)
	0.812 239(90)	129		Kung et al., 2004 (2.7 GPa)^[15]
	0.812 5(1)			Periotto et al., 2012 (2.69 GPa)^[33]
	0.832 918(114)	108(1)	7.2(7)	Kung et al., 2004 (Ambient condition)^[15]
P2₁/c	0.407 4	131.0(0.4)	5.2	This study (LDA)
	0.409			Yu et al., 2010 (LDA)^[29]
	0.397			Jahn, 2008 (LDA)^[17]
	0.407			Jacobsen et al., 2010 (2.58 GPa)^[34]
	0.415 78	113(2)	6.6(9)	Jacobsen et al., 2010 (Ambient condition)^[34]
	0.416 7			Kung et al., 2004 (Ambient condition)^[15]
C2/c	0.395 4	134.7(0.5)	5.5	This study (LDA)
	0.382 3			This study (LDA; 4.98 GPa)
	0.375 6			This study (LDA; 8.0 GPa)
	0.379 1			Yu et al., 2010 (LDA; 7.9 GPa)^[29]
	0.382 317(57)	163		Kung et al., 2004 (Room temperature, 7.6 GPa)^[15]
P2₁ca	0.805 8	121.7(2.5)	5.7	This study (LDA)
	0.753 6			This study (LDA; 10 GPa)
	0.733 9			Jahn, 2008 (LDA; 10 GPa)^[17]

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表 2 辉石的轴向体积模量以及轴向压缩性比值

Table 2. Axial moduli and compressibility ratios of pyroxenes

Space group	K_{a 0}/(GPa)	K_{b 0}/(GPa)	K_{c 0}/(GPa)	β_a:β_b:β_c
Pbca	160.7	106.1	135.1	0.66:1.00:0.79
P2₁/c	132.6	106.7	138.9	0.80:1.00:0.77
C2/c	124.2	111.9	150.5	0.90:1.00:0.74
P2₁ca	152.3	110.4	102.1	0.72:1.00:1.08

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