Structural Properties and Phase Transition of Pyroxene Polymorphs from First-Principles
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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。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.
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Key words:
- first-principles /
- pyroxene /
- phase transition /
- bulk modulus /
- axial compression
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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)
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] 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 Ka 0/(GPa) Kb 0/(GPa) Kc 0/(GPa) βa:βb:βc 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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