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采用基于粒子群优化算法的结构预测程序CALYPSO, 并结合第一性原理的VASP程序, 在175 GPa发现NbSi2的奇异立方高压相. 在此结构中, Nb原子形成金刚石结构, 而Si原子则形成正四面体镶嵌在金刚石结构中. 声子谱计算结果表明该结构是动力学稳定的. 电子结构分析表明, 六角相和立方相NbSi2均为金属, 对金属性贡献较大的是Nb原子, 而且Nb和Si原子之间存在明显的p-d杂化现象, 电荷更多地聚集在Si四面体中. 利用“应力应变”方法, 计算了NbSi2的弹性常数, 分析了其体积模量、剪切模量、杨氏模量和德拜温度等热动力学性质随压力的变化并进行了详细的讨论. 根据剪切模量和体积模量的比值分析了NbSi2两种相结构的脆性和延展性, 发现压力会导致六角相NbSi2的延展性增加, 但对立方相结构的延展性影响较小; 采用经验算法计算了NbSi2两种相结构硬度变化情况, 结合这一比值进行了详细的分析. 弹性各向异性计算结果表明, 随着压力增加, 六角结构的各向异性增强, 而立方结构的各向异性减小.Applying the particle swarm optimization algorithm to the crystal structure prediction, we first predict a novel high pressure phase of NbSi2 with Si tetrahedron embedded diamond structure of Nb. NbSi2 alloy undergoes a first-order phase transition from hexagonal phase to cubic phase at about 175 GPa with a volume collapse of 4.1%, indicating the first-order transition. New predicted NbSi2 phase is dynamically stable in the absence of any imaginary phonon frequency in the whole Brillouin zone of phonon spectrum. The calculations of total and partial density of states indicate that the NbSi2 is in hexagonal phase at 0 GPa and it is in cubic structure at 180 GPa, both of which exhibit metal behaviors, which is dominated by Nb atom. There exists obviously the p-d hybridization between Nb and Si, and more charges accumulate in Si tetrahedron. Based on the “stress-strain” method, elastic constants, bulk modulus, shear modulus, Young's modulus, and Debye temperature of NbSi2 in two phases under pressure are systematically investigated using first principles calculations combined with the quasi-harmonic Debye model. To evaluate the ductile and brittle characteristics of NbSi2 alloy, pressure dependence of G/B ratio is investigated. Furthermore, the values of hardness and percent anisotropy AB and AG and the universal anisotropic index AU (inset) for NbSi2 alloy in hexagonal and cubic structures are also calculated. Our results show that external pressure has different effects on the values of ductility and hardness and anisotropy of the two phases. External pressure can improve the ductility of hexagonal phase, while it has a negligible effect on that of cubic phase. The hardness values of two phases of NbSi2 are analyzed in detail by using the G/B ratio. As pressure increases, the elastic anisotropy of hexagonal phase increases rapidly, while that of cubic phase remains unchanged.
[1] Shah D M, Anton D L, Pope D P, Chin S 1995 Mater. Sci. Eng. A 192-193 658
[2] Subramanian P R, Mendiratta M G, Dimiduk D M, Stucke M A 1997 Mater. Sci. Eng. A 239-240 1
[3] Zhang D Y 2001 Rare Metal Lett. 3 17 (in Chinese) [张德尧 2001 稀有金属快报 3 17]
[4] Schlesinger M E, Okamoto H, Gokhale A B, Abbaschian G J 1993 J. Phase Equilibria 14 502
[5] Geng T, Li C R, Du Z M, Guo C P, Zhao X Q, Xu H B 2011 J. Alloys Compd. 509 3080
[6] Fernandes P B, Coelho G C, Ferreira F, Nunes C A, Sundman B 2002 Intermetallics 10 993
[7] Meng X X, Fan J, Bao K, Li F F, Huang X L, Li Y, Tian F B, Duan D F, Jin X L, Zhu P W, He Z, Zhou Q, Gao C X, Liu B B, Cui T 2014 Chin. Phys. B 23 016012
[8] San X J, He Z, Ma Y M, Cui T, Liu B B, Zou G T 2008 Chin. Phys. B 17 2222
[9] Wang Y C, L J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116
[10] Wang Y, L J, Zhu L, Ma Y 2012 Comput. Phys. Commun. 183 2063
[11] L J, Wang Y C, Zhu L, Ma Y M 2011 Phys. Rev. Lett. 106 015503
[12] Wang H B, Li Q, Wang H, Liu H Y, Cui T, Ma Y M 2010 J. Phys. Chem. C 114 8609
[13] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[14] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[15] Blöchl P E 1994 Phys. Rev. B 50 17953
[16] Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
[17] Kubiak R, Horyn R, Broda H, Lukaszewich K 1972 Bull. Acad. Pol. Sci. Ser. Sci. Chim. 20 429
[18] Papadimitriou I, Utton C, Scott A, Tsakiropoulos P 2014 Intermetallics 54 125
[19] Schubert K 1964 Kristallstrukturen Zweikomponentiger Phasen (Berlin, Heidelberg: Springer-Verlag)
[20] Nye J F 1985 Physical Properties of Crystal (Oxford: Oxford University Press)
[21] Voigt W 1928 Lehrburch der Kristallphysik (Leipzig: Teubner Press)
[22] Reuss A, Angew Z 1929 Math. Mech. 9 49
[23] Hill R 1952 Proc. Phys. Soc. 65 350
[24] Anderson O L 1963 J. Phys. Chem. Solids 24 909
[25] Pugh S F 1954 Philos. Mag. 45 823
[26] Niu H Y, Wei P Y, Sun Y, Chen X Q, Franchini C, Li D Z, Li Y Y 2011 Appl. Phys. Lett. 99 031901
[27] Chung D H, Buessem W R 1968 Anisotropy in Single-crystal Refractory Compounds: Proceedings (New York: Plenum Press)
[28] Ranganathan S I, Starzewski M O 2008 Phys. Rev. Lett. 101 055504
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[1] Shah D M, Anton D L, Pope D P, Chin S 1995 Mater. Sci. Eng. A 192-193 658
[2] Subramanian P R, Mendiratta M G, Dimiduk D M, Stucke M A 1997 Mater. Sci. Eng. A 239-240 1
[3] Zhang D Y 2001 Rare Metal Lett. 3 17 (in Chinese) [张德尧 2001 稀有金属快报 3 17]
[4] Schlesinger M E, Okamoto H, Gokhale A B, Abbaschian G J 1993 J. Phase Equilibria 14 502
[5] Geng T, Li C R, Du Z M, Guo C P, Zhao X Q, Xu H B 2011 J. Alloys Compd. 509 3080
[6] Fernandes P B, Coelho G C, Ferreira F, Nunes C A, Sundman B 2002 Intermetallics 10 993
[7] Meng X X, Fan J, Bao K, Li F F, Huang X L, Li Y, Tian F B, Duan D F, Jin X L, Zhu P W, He Z, Zhou Q, Gao C X, Liu B B, Cui T 2014 Chin. Phys. B 23 016012
[8] San X J, He Z, Ma Y M, Cui T, Liu B B, Zou G T 2008 Chin. Phys. B 17 2222
[9] Wang Y C, L J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116
[10] Wang Y, L J, Zhu L, Ma Y 2012 Comput. Phys. Commun. 183 2063
[11] L J, Wang Y C, Zhu L, Ma Y M 2011 Phys. Rev. Lett. 106 015503
[12] Wang H B, Li Q, Wang H, Liu H Y, Cui T, Ma Y M 2010 J. Phys. Chem. C 114 8609
[13] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[14] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[15] Blöchl P E 1994 Phys. Rev. B 50 17953
[16] Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
[17] Kubiak R, Horyn R, Broda H, Lukaszewich K 1972 Bull. Acad. Pol. Sci. Ser. Sci. Chim. 20 429
[18] Papadimitriou I, Utton C, Scott A, Tsakiropoulos P 2014 Intermetallics 54 125
[19] Schubert K 1964 Kristallstrukturen Zweikomponentiger Phasen (Berlin, Heidelberg: Springer-Verlag)
[20] Nye J F 1985 Physical Properties of Crystal (Oxford: Oxford University Press)
[21] Voigt W 1928 Lehrburch der Kristallphysik (Leipzig: Teubner Press)
[22] Reuss A, Angew Z 1929 Math. Mech. 9 49
[23] Hill R 1952 Proc. Phys. Soc. 65 350
[24] Anderson O L 1963 J. Phys. Chem. Solids 24 909
[25] Pugh S F 1954 Philos. Mag. 45 823
[26] Niu H Y, Wei P Y, Sun Y, Chen X Q, Franchini C, Li D Z, Li Y Y 2011 Appl. Phys. Lett. 99 031901
[27] Chung D H, Buessem W R 1968 Anisotropy in Single-crystal Refractory Compounds: Proceedings (New York: Plenum Press)
[28] Ranganathan S I, Starzewski M O 2008 Phys. Rev. Lett. 101 055504
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