First-Principles Investigations on Materials Properties of Mo under High Pressure
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摘要: 在平面波赝势密度泛函理论的框架下，利用广义梯度近似(GGA)计算了体心立方(bcc)和双层密排六方(dhcp)结构的Mo在不同体积下的总能和焓值，算得的等温压缩线与前人的计算结果符合较好。对焓值作差，预测了620 GPa压强附近bcc→dhcp的结构相变。根据声子谱的计算结果可知，在高压下，bcc结构可能会向dhcp或9R结构转变。力学稳定性的计算结果进一步显示，在620 GPa以上，dhcp-Mo是能够稳定存在的相。结合准谐德拜模型研究了Mo在高压下的热力学性质，计算结果表明，在620 GPa附近，bcc和dhcp结构Mo的热力学性质并无显著差异。Abstract: The total energy and enthalpy of bcc- and dhcp- Mo with different volumes were calculated using the generalized gradient approximation (GGA) within the framework of plane wave psudopotential density functional theory. Our calculated isotherms agree well with the previous results. Based on the comparison of enthalpy of bcc and dhcp structures, a bcc→dhcp structural transition was predicted. According to the results of phonon dispersions, the bcc phase may change into dhcp or 9R structures under high pressure. The calculations of mechanical stability also confirm that the dhcp structure is stable under pressures that are above 620 GPa. We also studied the thermodynamic properties of Mo such as Debye temperatures, isochoric heat capacity, and thermal expansion with the quasi-harmonic Debye model. Our calculated results show that the thermodynamic properties of bcc and dhcp structures do not differ significantly around 620 GPa.
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Key words:
- first-principles /
- phase transition /
- phonon dispersion /
- thermodynamic properties /
- Mo
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图 1 bcc和dhcp钼的零温焓值之差ΔH随外界静水压的变化关系
Figure 1. Enthalpy difference between bcc and dhcp Mo vs. pressure
图 2 不同温度下计算得到的bcc和dhcp钼的等温压缩线
Figure 2. Calculated isotherms of bcc and dhcp Mo at given temperatures
图 5 不同静水压下bcc-Mo的声子色散关系
Figure 5. Phonon dispersions of bcc-Mo under different pressures
图 6 bcc-Mo在925和950 GPa下的声子色散关系
Figure 6. Phonon dispersions of bcc-Mo at 925 and 950 GPa
图 7 不同静水压下dhcp-Mo的声子色散关系
Figure 7. Phonon dispersions of dhcp-Mo under different pressures
图 8 bcc-Mo的力学稳定性随压力的变化关系
Figure 8. Mechanical stability of bcc-Mo as a function of pressure
图 9 不同温度下Mo的德拜温度随压力的变化关系
Figure 9. Debye temperature of Mo vs. pressure at different temperatures
图 10 不同温度下Mo的熵随压力的变化关系
Figure 10. Entropy of Mo as a function of pressure at different temperatures
图 11 不同温度下Mo的热膨胀系数随压力的变化关系
Figure 11. Thermal expansions of Mo vs. pressure at different temperatures
图 12 不同温度下Mo的热容量随压力的变化关系
Figure 12. Isochoric heat capacity of Mo as a function of pressure at different temperatures
表 1 1 000 GPa范围内dhcp-Mo的力学稳定性
Table 1. Mechanical stability of dhcp-Mo up to 1 000 GPa
p/
(GPa)${{\tilde C}_{44}} $/
(GPa)$\left( {{{\tilde C}_{11}} - \left| {{{\tilde C}_{12}}} \right|} \right)$
(GPa)$[{{\tilde C}_{33}}({{\tilde C}_{11}} + {{\tilde C}_{12}}) - 2\tilde C_{13}^2]$/
(1018Pa2)0 -45.797 9 -145.371 95 158 259.745 7 100 49.418 2 -13 143.735 75 1 740 024.352 0 200 123.159 0 -455.594 85 1 482 513.300 0 300 233.533 7 -247.279 80 2 577 710.463 0 400 338.946 7 185.314 70 4 205 526.928 0 500 422.381 2 467.430 95 6 525 467.545 0 600 498.987 5 567.412 80 8 155 593.123 0 700 590.033 1 686.572 20 10 213 355.090 0 800 669.932 4 884.307 65 13 658 179.890 0 900 729.620 3 1 148.540 90 17 596 671.990 0 1 000 777.745 6 1 210.616 65 19 716 829.140 0 
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[1] HIXSON R S, BONESS D A, SHANER J W, et al.Acoustic velocities and phase transitions in molybdenum under strong shock compression [J].Phys Rev Lett, 1989, 62(6):637. doi: 10.1103/PhysRevLett.62.637 [2] VOHRA Y K, RUOFF A L.Static compression of metals Mo, Pb, and Pt to 272 GPa:Comparison with shock data [J].Phys Rev B, 1990, 42(13):8651. doi: 10.1103/PhysRevB.42.8651 [3] SANTAMARÍA-PÉREZ D, ROSS M, ERRANDONEA D, et al.X-ray diffraction measurements of Mo melting to 119 GPa and the high pressure phase diagram [J].J Chem Phys, 2009, 130(12):124509. doi: 10.1063/1.3082030 [4] MORIARTY J A.Ultrahigh-pressure structural phase transitions in Cr, Mo, and W [J].Phys Rev B, 1992, 45(5):2004. doi: 10.1103/PhysRevB.45.2004 [5] BOETTER J C.Relativistic effects on the structural phase stability of molybdenum [J].J Phys:Condens Matter, 1999, 11(16):3237. doi: 10.1088/0953-8984/11/16/005 [6] BELONOSHKO A B, BURAKOVSKY L, CHEN S P, et al.Molybdenum at high pressure and temperature:Melting from another solid phase [J].Phys Rev Lett, 2008, 100(13):135701. doi: 10.1103/PhysRevLett.100.135701 [7] CAZORLA C, ALFÈD, GILLAN M J.Constraints on the phase diagram of molybdenum from first-principles free-energy calculations [J].Phys Rev B, 2012, 85(6):064113. doi: 10.1103/PhysRevB.85.064113 [8] WANG B, ZHANG G B, WANG Y X.Predicted crystal structures of molybdenum under high pressure [J].J Alloys Compd, 2013, 556:116-120. doi: 10.1016/j.jallcom.2012.12.006 [9] PAYNE M C, TETER M P, ALLAN D C, et al.Iterative minimization techniques for ab initio total-energy calculations:Molecular dynamics and conjugate gradients [J].Rev Mod Phys, 1992, 64(4):1045. doi: 10.1103/RevModPhys.64.1045 [10] WU Z, COHEN R E.More accurate generalized gradient approximation for solids [J].Phys Rev B, 2006, 73(23):235116. doi: 10.1103/PhysRevB.73.235116 [11] VANDERBILT D.Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J].Phys Rev B, 1990, 41(11):7892. doi: 10.1103/PhysRevB.41.7892 [12] MONKHORST H J, PACK J D.Special points for Brillouin-zone integrations [J].Phys Rev B, 1976, 13(12):5188. doi: 10.1103/PhysRevB.13.5188 [13] PFROMMER B G, CÔTÉ M, LOUIE S G, et al.Relaxation of crystals with the quasi-Newton method [J].J Comput Phys, 1997, 131:233-240. doi: 10.1006/jcph.1996.5612 [14] REFSON K, TULIP P R, CLARK S J.Variational density-functional perturbation theor for dielectrics and lattice dynamics [J].Phys Rev B, 2006, 73(15):155114. doi: 10.1103/PhysRevB.73.155114 [15] LIN J S, QTEISH A, PAYNE M C, et al.Optimized and transferable nonlocal separable ab initio pseudopotentials [J].Phys Rev B, 1993, 47(8):4174. doi: 10.1103/PhysRevB.47.4174 [16] OTERO-DE-LA-ROZA A, PÉREZ D A, LUAÑA V.GIBBS2:A new version of the quasiharmonic model code.Ⅱ.Models for solid-state thermodynamics, features and implementation [J].Comput Phys Commun, 2011, 182(10):2232-2248. doi: 10.1016/j.cpc.2011.05.009 [17] HIXSON R S, FRITZ J N.Shock compression of tungsten and molybdenum [J].J Appl Phys, 1992, 71(4):1721. doi: 10.1063/1.351203 [18] WANG Y, CHEN D, ZHANG X.Calculated equation of state of Al, Cu, Ta, Mo, and W to 1 000 GPa [J].Phys Rev Lett, 2000, 84(15):3220. doi: 10.1103/PhysRevLett.84.3220 [19] FARBER D L, KRISCH M, ANTONANGELI D, et al.Lattice dynamics of molybdenum at high pressure [J].Phys Rev Lett, 2006, 96:115502. doi: 10.1103/PhysRevLett.96.115502 [20] GRIMVALL G, KÖPE B M, OZOLINŠ V, et al.Lattice instabilities in metallic elements [J].Rev Mod Phys, 2012, 84:945. doi: 10.1103/RevModPhys.84.945 [21] KRASILNIKOV O M, BELOV M P, LUGOVSKOY A V, et al.Elastic properties, lattice dynamics and structural transitions in molybdenum at high pressures [J].Comput Mater Sci, 2014, 81:313. doi: 10.1016/j.commatsci.2013.08.038 [22] SIN'KO G V, SMIRNOV N A.Ab initio calculations of elastic constants and thermodynamic properties of bcc, fcc and hcp Al crystals under pressure [J].J Phys:Condens Matter, 2002, 14:6989. doi: 10.1088/0953-8984/14/29/301 -
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