高压下钒的结构相变的第一性原理计算研究
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摘要
同一种物质有着不同的晶体结构,不同的晶体结构对其作为材料的性能有很大的影响,所以结构相变及其相变机制的研究对于许多领域如材料科学,地球科学,化学物理科学是非常重要的。结构相变及其相变机制的研究是最近实验和理论研究的热点,如对相变材料Ge2Sb2Te5和GeTe,固态氧,磁电材料BiFeO3,低维的离子晶体的结构相变研究以及对锕类金属钚Pu结构相变机制的研究等。
过渡金属钒由于有较高的超导转变温度Tc ,最近成为实验和理论研究的主题,对钒在高压下的结构相变研究文献中存在分歧。本文运用基于密度泛函理论的第一性原理计算研究了钒在高压下的结构相变,结构相变序列为体心立方结构-菱面体结构-体心立方结构,相变压强分别为70GPa和380GPa。具体做了以下的工作:
1、对钒的基态几何结构进行了优化,常压下钒为体心立方结构,优化得到的平衡晶格常数、体模量与实验理论符合较好。给出了约化体积随着压强变化的关系图,随着压强的增大,约化体积是逐渐减小的,减小的程度随压强的增大而变小,这些和实验上的结果定性符合的很好。
2、计算研究了体心立方结构的钒在高压下发生什么结构相变。通过对体心立方结构的钒在不同压强下剪切弹性系数C 44的计算,发现当压强约95GPa时剪切弹性系数小于0,说明体心立方结构的钒在此条件下是不稳定的。通过计算后发现钒在高压下不会发生体心立方到简立方的结构相变,而是发生体心立方到菱面体的结构相变,相变压强约为70GPa,与实验得到的结果符合较好(Phys.Rev.Lett.98,085502)。当压强约为380GPa时,将会发生菱面体到体心立方结构的相变,这提供了一个理论性的预言有待实验的进一步检验。
3、分析了钒在高压下发生体心立方到菱面体的结构相变原因。主要是由于费米面在第三能带的带内嵌套,另外s, p-d电子跃迁和带的Jahn-Teller扭曲也是该结构相变原因。不同压强下钒的s, p, d壳层电子占据数计算表明,高压导致的s, p-d电子跃迁使费米能级移到电子稳定范围之外,从而使体心立方结构的钒不稳定。本文首次给出钒的菱面体结构在高压下的能带结构,结果表明发生了带的Jahn-Teller效应即原来三重简并的Γ25,发生分裂并导致总能减少。当压强增大到120GPa时,一个分裂的能级移到费米能级以下导致费米能级处的态密度减少,这可能对在120GPa时钒的超导转变温度Tc反常研究给出了重要信息。
The same material has different crystal structures, the different crystal structures greatly impact on the the performances of the material, so the study of the structural phase transition and its mechanism is very important for many areas such as materials science, earth science and physical chemistry。This is the hotspot of recent experimental and theoretical study , such as the researchs of structural phase transitions of phase-change materials Ge2Sb2Te5 and GeTe,solid oxygen,magnetoelectric material BiFeO3,low-dimensional ion crystals and structural phase transition mechanism of Pu.
The transition metal vanadium has recently been the subject of numerous experi -mental and theoretical studies due to the high superconducting transition temperature Tc . There are differences in the literatures on the study of structural phase transition of vanadium under high pressure. In this paper, structural phase transition of vanadium under high pressure has been calculated by use of the First principles on the basis of the density function theory. The sequence of structures of vanadium is bcc (body centered cubic)- rhombohedral-bcc with increasing pressure, the transition pressure is 70GPa and 380GPa separately. The main contents are the following:
1、The ground-state geometry structure of vanadium has been optimized. Vanadium is bcc structure at normal pressure. The calculated equilibrium lattice constand and the isothermal bulk modulus at normal pressure agree well with experiment and theoretical works. The reduced volume is decreased and the degree of decreasing get smaller with the increase of pressure, this is qualitatively good with the experiment.
2、What structure phase transition of bcc vanadium under high pressures has been calculated and studied. A mechanical instability in the shear elastic constant ( C 44) is found for bcc vanadium at about 95Gpa, which indicates the existence of the structural transition. By calculation and analysis, we found that there is no bcc-sc (simple cubic) structure transition but a bcc-rhombohedral structure transition at the 70GPa, which is consistent with the experiment data in Phys. Rev. Lett. 98, 085502. Our calculations also firstly give a rhombohedral-bcc structure transition at about 380GPa, which needs to be verified by the experiment.
3、The reasons for bcc- rhombohedral structure transition of vanadium under high pressures has been discussed. The primary reason is the nesting properties of the Fermi surface in the 3rd band (intra-band nesting), s, p-d transition and band Jahn-Teller effects are also reasons. Electrons in s, p, and d shells of vanadium at different pressures have been calculated. As a function of compression an s, p-d ttransition shifts the Fermi level beyond the region of electronic instability, thus destabilizing the bcc phase in vanadium. We firstly gave the band structures of vanadium in rhombohedral lattice under high pressures, the results display band Jahn-Teller effects or the initially triple -degenerateΓ25, splitting. One split level goes down below the Fermi level causing the DOS at the Fermi level to decrease when the pressure attaining 120Gpa. This may provide essential information for proper reevaluation of the Tc anomaly at 120Gpa.
过渡金属钒由于有较高的超导转变温度Tc ,最近成为实验和理论研究的主题,对钒在高压下的结构相变研究文献中存在分歧。本文运用基于密度泛函理论的第一性原理计算研究了钒在高压下的结构相变,结构相变序列为体心立方结构-菱面体结构-体心立方结构,相变压强分别为70GPa和380GPa。具体做了以下的工作:
1、对钒的基态几何结构进行了优化,常压下钒为体心立方结构,优化得到的平衡晶格常数、体模量与实验理论符合较好。给出了约化体积随着压强变化的关系图,随着压强的增大,约化体积是逐渐减小的,减小的程度随压强的增大而变小,这些和实验上的结果定性符合的很好。
2、计算研究了体心立方结构的钒在高压下发生什么结构相变。通过对体心立方结构的钒在不同压强下剪切弹性系数C 44的计算,发现当压强约95GPa时剪切弹性系数小于0,说明体心立方结构的钒在此条件下是不稳定的。通过计算后发现钒在高压下不会发生体心立方到简立方的结构相变,而是发生体心立方到菱面体的结构相变,相变压强约为70GPa,与实验得到的结果符合较好(Phys.Rev.Lett.98,085502)。当压强约为380GPa时,将会发生菱面体到体心立方结构的相变,这提供了一个理论性的预言有待实验的进一步检验。
3、分析了钒在高压下发生体心立方到菱面体的结构相变原因。主要是由于费米面在第三能带的带内嵌套,另外s, p-d电子跃迁和带的Jahn-Teller扭曲也是该结构相变原因。不同压强下钒的s, p, d壳层电子占据数计算表明,高压导致的s, p-d电子跃迁使费米能级移到电子稳定范围之外,从而使体心立方结构的钒不稳定。本文首次给出钒的菱面体结构在高压下的能带结构,结果表明发生了带的Jahn-Teller效应即原来三重简并的Γ25,发生分裂并导致总能减少。当压强增大到120GPa时,一个分裂的能级移到费米能级以下导致费米能级处的态密度减少,这可能对在120GPa时钒的超导转变温度Tc反常研究给出了重要信息。
The same material has different crystal structures, the different crystal structures greatly impact on the the performances of the material, so the study of the structural phase transition and its mechanism is very important for many areas such as materials science, earth science and physical chemistry。This is the hotspot of recent experimental and theoretical study , such as the researchs of structural phase transitions of phase-change materials Ge2Sb2Te5 and GeTe,solid oxygen,magnetoelectric material BiFeO3,low-dimensional ion crystals and structural phase transition mechanism of Pu.
The transition metal vanadium has recently been the subject of numerous experi -mental and theoretical studies due to the high superconducting transition temperature Tc . There are differences in the literatures on the study of structural phase transition of vanadium under high pressure. In this paper, structural phase transition of vanadium under high pressure has been calculated by use of the First principles on the basis of the density function theory. The sequence of structures of vanadium is bcc (body centered cubic)- rhombohedral-bcc with increasing pressure, the transition pressure is 70GPa and 380GPa separately. The main contents are the following:
1、The ground-state geometry structure of vanadium has been optimized. Vanadium is bcc structure at normal pressure. The calculated equilibrium lattice constand and the isothermal bulk modulus at normal pressure agree well with experiment and theoretical works. The reduced volume is decreased and the degree of decreasing get smaller with the increase of pressure, this is qualitatively good with the experiment.
2、What structure phase transition of bcc vanadium under high pressures has been calculated and studied. A mechanical instability in the shear elastic constant ( C 44) is found for bcc vanadium at about 95Gpa, which indicates the existence of the structural transition. By calculation and analysis, we found that there is no bcc-sc (simple cubic) structure transition but a bcc-rhombohedral structure transition at the 70GPa, which is consistent with the experiment data in Phys. Rev. Lett. 98, 085502. Our calculations also firstly give a rhombohedral-bcc structure transition at about 380GPa, which needs to be verified by the experiment.
3、The reasons for bcc- rhombohedral structure transition of vanadium under high pressures has been discussed. The primary reason is the nesting properties of the Fermi surface in the 3rd band (intra-band nesting), s, p-d transition and band Jahn-Teller effects are also reasons. Electrons in s, p, and d shells of vanadium at different pressures have been calculated. As a function of compression an s, p-d ttransition shifts the Fermi level beyond the region of electronic instability, thus destabilizing the bcc phase in vanadium. We firstly gave the band structures of vanadium in rhombohedral lattice under high pressures, the results display band Jahn-Teller effects or the initially triple -degenerateΓ25, splitting. One split level goes down below the Fermi level causing the DOS at the Fermi level to decrease when the pressure attaining 120Gpa. This may provide essential information for proper reevaluation of the Tc anomaly at 120Gpa.
引文
[1]余海湖,余丁山,周灵德二氧化钛微晶结构相变与光致发光发光学报2006 27(2)239-242
[2]李美俊氧化锆和掺杂氧化锆物相及其变化的紫外拉曼光谱研究中国科学院研究生院博士学位论文2002,
[3]冯端金国浚凝聚态物理学(上卷)2006
[4]吕梦雅压力下硅锗及其合金结构与电子性质的计算机模拟燕山大学工学博士学位论2006
[5]宫秀敏相变理论基础及应用武汉理工大学出版社2004,
[6]刘宗昌等金属固态相变教程冶金工业出版社2003
[7] J Akola1, R O Jones Phys. Rev. B 2007 76 235201
[8] Yuan-Hua Lin, Qinghui Jiang, Yao Wang et al Appl. Phys. Lett 2007 90 172507
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[10] D. Errandonea,D. Martínez-García, A. Segura et al Phys. Rev. B 2008 77 045208
[11]Shmuel Fishman, Gabriele De Chiara,Tommaso Calarco Phys. Rev. B 2008 77 064111
[12] A. Bussmann-Holder, H. Buttner, and A. R. Bishop Phys. Rev. Lett 2007 99 167603
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[17] Nirmala Louis C, Iyakutti K Phys. Rev. B 2003 67 094509 .
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[22] Vaitheeswaran G, Shameen Banu I B, Rajagopalan M Solid State Commun 2000 116 401.
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[2]徐光宪,黎乐民,.量子化学—基本原理和从头计算法(中册).北京:科学出版社.2001
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[5]冯端金国浚凝聚态物理学(上卷)2006
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[7] D. P. Wernette et al., Chem. Mater. 2003,15, 1441
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[6] Nirmala Louis C, Iyakutti K Phys. Rev. B 2003 67 094509 .
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[2]李美俊氧化锆和掺杂氧化锆物相及其变化的紫外拉曼光谱研究中国科学院研究生院博士学位论文2002,
[3]冯端金国浚凝聚态物理学(上卷)2006
[4]吕梦雅压力下硅锗及其合金结构与电子性质的计算机模拟燕山大学工学博士学位论2006
[5]宫秀敏相变理论基础及应用武汉理工大学出版社2004,
[6]刘宗昌等金属固态相变教程冶金工业出版社2003
[7] J Akola1, R O Jones Phys. Rev. B 2007 76 235201
[8] Yuan-Hua Lin, Qinghui Jiang, Yao Wang et al Appl. Phys. Lett 2007 90 172507
[9] Duck Young Kim S. Lebègue. Moysés Araújo Phys. Rev. B 2008 77 092104
[10] D. Errandonea,D. Martínez-García, A. Segura et al Phys. Rev. B 2008 77 045208
[11]Shmuel Fishman, Gabriele De Chiara,Tommaso Calarco Phys. Rev. B 2008 77 064111
[12] A. Bussmann-Holder, H. Buttner, and A. R. Bishop Phys. Rev. Lett 2007 99 167603
[13] G. Shirane and Y. Yamada, Phys. Rev. 1969 177 858 .
[14] T. Lookman, A. Saxena, R. C. Albers PRL 2008 100, 145504
[15] Takemura K Sci. Technol. High Pressure 2000 443
[16] Suzuki N, Otani M J. Phys. Condens. Matter 2002 14 10869
[17] Nirmala Louis C, Iyakutti K Phys. Rev. B 2003 67 094509 .
[18]Landa A, Klepeis J, S?derlind P et al J. Phys. Condens. Matter 2006 18 5079 .
[19] Landa A, Klepeis J, S?derlind P et al J. Phys. Chem. Solids 2006 67 2056
[20] Y Ding, Rajeev Ahuja, Shu J F Phys. Rev. Lett 2007 98 085502
[21] Ishizuka M, Iketani M, Endo S Phys. Rev. B 2000 61 R3823
[22] Vaitheeswaran G, Shameen Banu I B, Rajagopalan M Solid State Commun 2000 116 401.
[1]吕梦雅压力下硅锗及其合金结构与电子性质的计算机模拟燕山大学工学博士学位论文2006
[2]徐光宪,黎乐民,.量子化学—基本原理和从头计算法(中册).北京:科学出版社.2001
[3]Hohnberg P, Kohn W, Inhomogeneous electron gas, Rev, B,1964,136:864-871
[4]Kohn W, Sham L J. Phys. Rev. A, 1965, 140:1133-1138
[5]冯端金国浚凝聚态物理学(上卷)2006
[6] V. Petkov et al., Phys. Rev. Lett. 2002,89, 75502
[7] D. P. Wernette et al., Chem. Mater. 2003,15, 1441
[8] T.Asada and K.Terakura, Phys.Rev.,B 46,13599(1992)
[9]Ellis D E , Painter G S. Computational Methkds in Band Theory. New York, Plenum. 1971.
[10]Bloch F Z. Quantum mechanics of electrons in crystal lattices Physik. 1928,52:555-600
[11]Slater J C, Koster G F. Phys. Rev. 1954, 94:1498-1524
[12]Herring C, Hill A G. Phys. Rev.,1940,58:132-162
[13]Ihm J, Zunger A, Cohen M L. Momentum-space formalism for the total energy of Solids. J. Phys. C, 1979,12:4409-4422
[14]Payne M C, Teter M P, Ahan D C,et al. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients Rev. Mod. Phys.,1992,64:1045-1097
[15]Herman F, Killman S. Atomic Structure Calculation. Englewood Cliffs. New Jersey, Prentice-Hall Inc, 1963
[16]Korringa J. On the calculation of the energy of a Bloch wave in a metal. Physica, 1917,13(6-7):392-400
[17]Kohn W, Rostoker N. Solution of the Schr?dinger Equation in Periodic Lattices with an Application to Metallic Lithium. Phys. Rev., 1954, 91:1111-1120
[18]Anderson O K. Linear methods in band theory. Phys. Rev. B, 1975,12:3060-3083
[19]Skiver H L. The LMTO method. Ed. by M. Cardona and P. Fulde. Heidelberg.
[20]Ihm J, Zunger A, Cohen M L. J. Phys. C, 1979,12:4409-4422
[21]Payne M C, Teter M P, Ahan D C,et al. Rev. Mod. Phys.,1992,64:1045-1097
[22]Appelbaum J A, Hamann D R. Phys. Rev. B,1973,8(4):1777-1780
[23]Selluter M, Chelikowsky J R, Louie S G, et al..Phys.Rev.Lett.,1975,34(22):1385-1388
[24]Kleinman L, Bylander D M. Efficacious form for model pseudopotentials. Phys. Rev. Lett., 1982,48:1425-1428
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