摘要
在高压下固体物质结构(晶格结构和电子结构)的改变会对它们的弹性、电学以及光学等性质产生影响。研究固体物质在高压下的物理性质对人们认识自然有推动作用。本文分两个部分分别就Al_2O_3和Cu在高压下的一些物理性质进行研究。
第一部分内容是基于第一性原理计算方法,得到了三种Al_2O_3理想晶体结构的能带结构以及能隙(或禁带宽度)随压力的变化关系;同时计算并分析了光学性质(包括高压下的光吸收系数、介电函数的虚部与实部、反射谱与吸收谱以及能量损失谱);进一步分析了高压下三种Al_2O_3理想晶体结构的电子态密度和力学性质。这些计算的目的是尝试对在冲击实验中观测到的蓝宝石电导率突增以及光学透明性降低现象的认识提供一些可能的物理机理。
本部分的主要工作和结果如下:
1)基于密度泛函理论框架下的第一性原理平面波超软赝势方法,结合局域密度近似(LDA),计算了纯Al_2O_3理想晶体的三个结构相(Corundum相、Rh_2O_3(II)相以及CaIrO_3相)在高压下的电子能带结构,并根据此导出了Al_2O_3的三个结构相的能隙随压力变化关系。从这个计算结果发现在0K时,Corundum相到Rh_2O_3(II)相以及Rh_2O_3(II)相到CaIrO_3相的结构相变将导致Al_2O_3的带隙分别减少大约7-8%以及18-20%。另外,还发现在CaIrO_3相区,带隙随压力是微弱地减小,而在Corundum和Rh_2O_3(II)相区,带隙随压力是明显地增加。
2)通过冲击实验观测到的蓝宝石电导率突增的温压条件与Al_2O_3在高温高压下Rh_2O_3(II)结构和CaIrO_3结构的相边界线比较,可以说明,蓝宝石电导率突增与压力大约为130GPa以及温度大约为1500K的Rh_2O_3(II)相到CaIrO_3相的结构相变存在密切关系。估算表明,在这个温压条件下,Rh_2O_3(II)到CaIrO_3的结构相变将导致蓝宝石电导率增加的量值大约为△lnσ～6.49。这些信息说明实验观测到的蓝宝石电导率突增可能是起因于在这个温压条件下蓝宝石从Rh_2O_3(II)到CaIrO_3的相变所引起的能隙明显地减少。而且,带隙随压力变化关系可以被用于解释实验中得到的蓝宝石电导率数据轨迹。这指明,在91-220GPa的冲击压力范围内,电子导电是蓝宝石主要的电导机理。
3)基于Al_2O_3的CaIrO_3相与MgSiO3的后钙钛矿相在晶体结构和Raman光谱上的相似性,Al_2O_3的能带结构计算结果建议,MgSiO3从钙钛矿到后钙钛矿的相变也可能导致MgSiO3的能隙减少,这对探索在下地幔底部具有异常高的电导率的机理有重要意义。
4)利用密度泛函理论框架下的第一性原理平面波超软赝势方法,结合局域密度近似(LDA),还计算了纯Al_2O_3理想晶体的三个结构相在高压下的光吸收系数。结果指明,在0-220GPa的压力范围内以及在冲击波高压实验中所采用的光波段内(大约200-1000nm),Al_2O_3吸收系数始终为零。这说明冲击实验在大约130-172GPa范围内所观测到的蓝宝石光学透明性降低与它的相变无关。
5)本文的计算数据强化了Al_2O_3从Corundum到Rh_2O_3(II)的结构相变可能引起它的电导率变化的建议,但不支持这个相变可能改变蓝宝石光学透明性的推测。本论文第二部分运用分子动力学方法,采用嵌入原子模型(EAM)描述原子之间的相互作用势,在0-35GPa压强范围,对面心立方(FCC)结构金属铜中空位密度对其弹性性质的影响进行了计算模拟。为使缺陷可以在整个空间运动,采用了周期性边界条件。模拟均在0K温度下进行,对于温度的控制,采用的是Nose-Hoover方法,对于应力的控制则采用了Parrinello-Rahman等压方法。
本部分的主要工作和结果如下:
1)运用分子动力学方法对8×8×8原子数为2048的系统从0GPa到35GPa应力范围内的弹性系数进行了研究,得到了弹性系数随压强线性变化的关系。利用Murnagahan等温状态方程对压强和体积关系进行了拟合,得到铜在零压下的体模量。
2)分别对5×5×5、6×6×6、7×7×7、8×8×8的四种晶胞中各拿走一个点阵上的原子形成空位时各体系在零温零压下的弹性系数进行模拟计算,得到金属铜的弹性系数随空位浓度的变化规律。
3)对8×8×8的晶胞中含一个空位的系统在0-35GPa应力范围的弹性系数进行了模拟,并与无空位时相同大小的晶胞的弹性系数进行比较,得到相同空位浓度下,压强对有缺陷晶体弹性性质的影响。
The structural change of the solid materials under high pressures (including crystal and electronic structures) will affect their elastic, electrical and optical properties. Studying their physical properties under high-pressure is important for understanding nature. This paper is divided into two parts, studying on some physical properties of Al_2O_3 and Cu under high pressure respectively.
In the first part of this thesis,using first-principles calculations, band structure and the pressure dependence of the band gap of perfect Al_2O_3, and investigate the optical properties (optical absorption coefficient, the real and imaginary parts of the dielectric function, reflection and absorption spectrum and the energy loss spectrum), and study the electronic density of states and mechanical properties of Al_2O_3 without defects at high pressures. By these calculations, some possible physical mechanisms for the transparency loss and the onset of the electrical conductivity, observed by shock-wave experiments, are presented.
The main work and results of this part are as follows:
1) Based on the plane-wave pseudopotential method in the frame-work of the density function theory and the local density approximation of Ceperly and Adler by the parametrization of Perdew and Zunger (LDA-CA-PZ), the author determines the pressure dependence of the band gap for the three perfect Al_2O_3 structure phases at 0 K, and the band-gap data may be obtained from the corresponding calculated energy-band structures. It is found that Corundum-Rh_2O_3(II) and Rh_2O_3(II)-CaIrO_3 transitions in alumina at 0 K cause about 7-8% and 18-20% band-gap reductions, respectively. The band gap decreases slightly with pressure in the CaIrO_3 phase region but increases in Corundum and Rh_2O_3(II) phase regions.
2) While the onset point (the temperature and pressure condition) of the observed conductivity increase is compared with the phase boundary line between the Rh_2O_3(II) and CaIrO_3 structures, the conductivity increase of shocked Al_2O_3 at about 130 GPa is associated closely with this transition at about 130GPa and 1500 K. Estimations indicate that the conductivity increase (△lnσ), produced by the band-gap reduction due to the Rh_2O_3(II)-CaIrO_3 transition at ~130 GPa and ~1500 K, may be estimated through a relationship:△lnσ～6.49 if the effect of the Rh_2O_3(II)-CaIrO_3 transition on the band gap of Al_2O_3 is considered. This information implies that the onset of the conductivity increase is attributed possibly to a band-gap decrease due to the Rh_2O_3(II)-CaIrO_3 transition at ~130 GPa and ~1500 K. Moreover, the band gap-pressure relations may just explain the trajectory of experimental conductivity data, which shows that the predominant conduction mechanism of sapphire at shock pressures of 91-220 GPa is electronic conduction.
3) Because of similarities of the crystal structures and Raman spectra of Al_2O_3-CaIrO_3 and MgSiO3 post-perovskite, the calculations of Al_2O_3 suggest that a perovskite to post-povskite transition in MgSiO3 causes perhaps a band-gap reduction as well, which makes MgSiO3 post-perovskite possess the high conductivity. This has significant implications for exploring the source of fairly large electrical conductivity at the Earth’s lowermost mantle.
4) Using the plane-wave pseudopotential method in the frame-work of the density function theory and the local density approximation of Ceperly and Adler by the parametrization of Perdew and Zunger (LDA-CA-PZ), the author has performed static first-principles calculations of optical absorption coefficients of perfect Al_2O_3 under high pressures. Results indicate that optical absorption coefficients of Al_2O_3 at 0-220GPa are always zero within the wavelength range adopted in shock experiments (~250-1000nm). The phase transitions in alumina at high pressure and temperature might not be responsible for its optical transparency degradation observed at shock pressures of about 130-172GPa.
5) The calculated data reinforce the suggestion that the Corundum-Rh_2O_3(II) transition change the electrical conductivity of alumina but don’t support the inference that this transition causes its transparency loss.
In the second section of this thesis, the effect of vacancy concentration on elastic properties of copper under high pressures (from 0GPa to 35 GPa) is studied by means of MD simulation. The embedded-atom model (EAM) is employed to describeinter-atomic interaction in face-centered cubic (FCC) copper. In order to avoid the influence of surface effect, the periodic boundary conditions is employed in.simulation, so that the defect can move in the infinite space. To control the constant temperature and stress, Nose-Hoover method and Parrinello-Rahman method are.used, respectively.
The main work and results of this part are as follows:
1). MD method with EAM potential were used to study the elastic constants.under pressures range from 0GPa to 35GPa in the cell with size of.8×8×8.The linear relation between the elastic constants and.pressure was obtained. The data were fitted to Murnagahan isothermal equation of.state (EOS) to get the bulk modulus. The P-V/Vo relation is compared with.experimental result.
2). Four cells with 5×5×5、6×6×6、7×7×7、8×8×8 chosen. Each cell has one correspond to different vacancy concentration. The simulation condition is at 0K and 0GPa. The relation between elastic constants and the vacancy concentration was calculated
3). The elastic constants of the cell, containing one vacancy, with dimensions of 8×8×8 under high pressures ranging from 0GPa to 35GPa were calculated. The comparison was made for the cell with one vacancy and the perfect cell with same size. Pressure effect on the elastic properties of imperfect crystal was obtained.
引文
[1] 周国清,徐军,周永宗,等.温梯法生长100mm蓝宝石晶体研制新进展[J].人工晶体学报,2000,29:93
[2] Urtiew P. A., J. Appl. Phys., 45 (1974) 3490.
[3] McQueen R. G. and Isaak D. G., J. Geophys. Res., 95(1990) 21753.
[4] Weir S. T., Mitchell A. C. and Nellis W. J., J. Appl. Phys.,80 (1996) 1522.
[5] Fat’pyanov O V, W ebb R L, Gup ta Y M, et al. Op tical Transm ission Through in elastically Deformed Shocked Sapphire: Stress and Crystal orientation Effects[ J ] . Journal of Applied Physics, 2005, 97, 123529.
[6] Hare D E, Holm sN C,W ebb D J, et al. Shock2wave2induced Op tical Em ission from Sapphire in the Stress Range 12 to 45 GPa: Images and Spectra [ J ]. Physical Review B , 2002, 66, 014108.
[7] Partouche-Sebbana D, Pe′lissiera J L, Anderson W W , et al. Investigation of Shock2induced L ight from Sapphire forU se in Pyrometry Studies [ J ]. Physica B , 2005, 364.
[8] U rtiew P A. Effect of Shock Loading on Transparency of Sapphire Crystals[ J ]. Journal of A pplied Physics, 1974, 45(8): 349023493.
[9] Mcqueen R G, Isaak I G. CharacterizingW indows for Shock W ave Radiation Studies[ J ]. Journal of Geophysical Research, 1990, 95(B13):217532-21765.
[10] 张岱宇 ,郝高宇 ,张明建 ,刘福生. 兆巴高压下 c向蓝宝石的冲击辐射研究[J] 人工晶体学报,2007,36:531
[11] Oganov A. R. and Ono S., Proc. Natl. Acad. Sci., 102(2005) 10828
[12] Ono S., Oganov A. R., Koyama T. and Shimizu H., Earth Planet. Sci. Lett., 246 (2006) 326.
[13] Hama J. and Suito K., High Temp. High Press., 34 (2002)323.
[14] Jing F. Q., Introduction to Experimental Equation of State (Science, Beijing) 1999,pp.302-303.
[15] Lin J. F., Degtyareva O., Prewitt C. T., Dera P., Sata N.,Gregoryanz E., Mao H.-K. and Hemley R., Nat. Mater., 3 (2004) 389
[16] Mashimo T., Tsumoto K., Nakamura K., Noguchi Y., Fukuoka K. and Syono, Y., Geophys. Res. Lett. 27 (2000) 2021.
[17] Holm.B, Ahuja.R, Yourdshahyan. Y et al. Elastic and optical properties of α ?and k ? AL2 O3, [J] Physical Review B, 1999-II 59(20): 12777-12787
[18] Tsuchiya J., Tsuchiya T. and Wentzcovitch R. M., Phys.Rev. B – Rapid Commun., 72 (2005) 020103.
[19] Caracas R. and Cohen R. E., Geophys. Res. Lett., 32(2005) L06303
[20] Holm B., Ahuja R., Yourdshahyan Y., Johansson B. and Lundqvist B. I., Phys. Rev. B, 59 (1999) 12777
[21] Boettger J. C., Phys. Rev. B, 55 (1997) 750
[22] R.H.French. Electronic band structure of Al2O3, with comparison to Alon and AIN. J.Am.Ceram.Soc. 73,477(1990)
[23] Zhu J. G., Zheng W. S., Zheng J. G., Sun X. S., and Wang H. T., Solid State Physics (Science, Beijing) 2005, pp. 166-170
[24] 刘恩科.半导体物理学 北京:电子工业出版社 2003 第327页
[25] 沈学础.半导体光谱和光学性质(第二版). 北京:科学出版社,1992, 20-28;76-91
[26] Duan, W., Wentzcovitch, R. M., and Thomson, K. T. (1998) First-Principles study of high-pressure alumina polymorphs. Physical Review B, 57,10363-10369
[27] Finger, L. W. and Hazen, R. M. (1978) Crystal structure and compression of ruby up to 46kba. Journal of Applied Physics, 49,5823-5826
[28] Mehl. M. J, Osburn. J. E, Papaconstantopoulos D A and Klein B M. Structural properties of ordered high-melting-temperature intermetallic alloys from first-principles total-energy calculations. Phys. Rev. B 1990, 41:10311 一10323
[29] Jean. E. Osburn, Michael J. Mehl, and Barry M. Klein. First-principles calculation of the elastic moduli of Ni3A1. Phys. Rev. B 1991, 43:1805-1807
[30] M. Alouani and R. C. Albers. Calculated elastic constants and structural properties of Mo and MoSiz. Phys. Rev. B 1991, 43: 6500-6509
[31] Per Soderlind, Olle Eriksson, J. M. Wills, and A. M .Boring. Theory of elastic constants of cubic transition metals and allow. Phys. Rev. B 1993, 48: 5844-5857
[32] Per Soderlind, Olle Eriksson, J. M. Wills, and A. M. Boring. Elastic constants of cubic f-electron elements: Theorv. Phys. Rev. B 1993, 48: 9306-9312
[33] Lars Fast, J. M. Wills, Borje Johansson and O. Eriksson. Elastic constants of hexagonal transition metals: Theorv. Phys. Rev. B 1995, 51:17431 一 17438
[34] Michael J. Mehl and Dimitrios A. Papaconstantopoulos. Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals. Phys. Rev. B 1996, 54: 4519-4530
[35] J. S. Tse, D. D. Klug, K. Uehara, and Z. Q. Li. Elastic properties of potential superhard phases of RuOz. Phys. Rev. B 2000, 61:10029-10034
[36] G Y. Guo and H. H. Wang. Calculated elastic constants and electronic and magnetic properties of bcc, fcc, and hcp Cr crystals and thin films. Phys.Rev. B 2000, 62: 5136-5143
[37] O. Beckstein, J. E. Klepeis, G L. W. Hart, and O. Pankratov. First-principles elastic constants and electronic structure of a-PtzSi and PtSi. Phys. Rev. B 2001, 63: 134112-1-134112-12
[38] H. J. F. Jansen and A. J. Freeman. Structural and electronic properties of graphite via an all-electron total-energy local-density approach. Phys. Rev. B 1987, 35:8207-8214
[39] Toshiaki Iitakaand Toshikazu Ebisuzaki. First-principles calculation of elastic properties of solid argon at high pressures. Phys. Rev. B 2002, 65: 012103-1-012103-4
[40] P. T. Jochym and K. Parlinski. Elastic properties and phase stability of Agar under pressure.Phys. Rev. B 2002, 65:024106-1-024106-6
[41] O. Gulseren and R. E. Cohen. High-pressure thermoelasticity of body-centered-cubic tantalum. Phys. Rev. B 2002, 65:064103-1-064103-5
[42] G V Sin'ko and N A Simrnov.Ab initio calculations of elastic constants and thermodynamic properties of bcc, fcc, and hcp Al crystals under pressure. J Phys.: Condens. Matter 2002, 14:6989-7005
[43] Woo C H, Rad. Effect Def. Solids, 1998, 144:145 一 169
[44] B.Henderson,晶体缺陷,高等教育出版社,1984
[45] H B Huntington and F Seitz. Mechanism for Self-Diffusion in Metallic Copper.Phys. Rev. B 1942, 61:315-325
[46] 玛端,金属物理学,第一卷,科学出版社,1987
[47] Warren B E. X-Ray Studies of Defermed Metals. Prog. Metal Phys.1959, 8:147
[48] Frenkel I. Z.Physik 1926, 35:652
[49] Chaki T K, Li J C M. Philos.Mag.1984, 557
[50] Audouard A, Balogh J, Dural J, Jousset J C. J.Nom Cryst. Sol. 1982, 50: 71
[51] Moser P, Hautojarvi P, Yli J, Van Zurk R et. a1.Proc. 4# Int. Con on Rapidly Quenched Metals 11 1981, 759
[52] Trifthaüser W, Kogel G, Amorphous and Liquid Materials, ed. Luscher E, Fritsch G and Jacucci G Eds., NATO ASI Series E,(Martinus Nijhoff Pub., 1987) n118
[53] Bennett C H, Chaudhari P, Moruzzi V and Steinhardt P. on the stability of vacancies and vacancy clusters in amorphous solid. Phil. Mag. 1979, 40: 485-495
[54] Emanuele Paci and Giovanni Ciccotti. Vacancy migration rates by molecular dynamics with constraints. J. Phys.: Condens. Matter. 1992, 4:2173-2184
[55] Inder P Batra and Farid F Abraham. Molecular dynamics study of self-interstitials in silicon. Phys. Rev. B 1986, 35:9552-9558
[56] Tomonori Kitashima, Koichi Kakimoto and Hiroyuki Ozoe. Molecular Dynamics Analysis of Diffusion of Point Defects in GaAs. J.Elec.Soci.2003150(3):G198-6202
[57] Murray S. Daw and M. I. Baskes. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals. Phy.Rev.Lett. 1983, 50:1285 一 1288
[58] Murray S. Daw and M. I. Baskes. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 1984, 29: 6443-6453
[59] M. I. Baskes. Atomistic potentials for the molybdenum-silicon system. Mater. Sci. Engin. A 1999, 261:165 一 168
[60] R Car and M Parrinello. Structural, Dymanical, and Electronic Properties of Amorphous Silicon: An Ab Initio Molecular-Dynamics Study.Phys. Rev. Lett. 1988, 60:204-207
[61] M J Gillan. Calculation of the vacancy formation energy in aluminium. J. Phys.: Condens. Matter. 1989, 1:689-711
[62] 朱梓忠.铝中空位形成能计算时的原胞尺寸等参数效应.物理学报 1998, 47 C 5: 0784-0790
[63] Y.Mishin,M. J. Mehl and D. A. Papaconstantopoulos. Structural stability and lattice defects in copper : Ab initio, tight-binding ,and embedded-atom calculations [J].Phys. Rev. B 2001,63:224106-1-16
[64] Alder B. J, Wainwright T. E. Phase Transition for a Hard Sphere System. J. Chem. Phys., 1957, 27: 1208-1209
[65] Alder B. J, wainwright T. E. Studies in Molecular Dynamics. I. General Method. J. Chem. Phys., 1959, 31:459-466
[66]J. B. Gibson,A. N. Goland and G. H. Vineyard. Dynamics of Radiation Damage. Phys. Rev. 1960, 120: 1229-1253
[67] Rahman A. Correlations in the Motion of Atoms in Liquid Argon. Phys. Rev., 1964, 136:A405-A411
[68] Gear C W. The Numerical integration of ordinary differential equations of various orders.Report ANL 7126, Argonne National Laboratory, 1966
[69] Gear C W. Numerical initial value problems in ordinary differential equations. Prentice-Hall, Englewood Cliffs, N.J., 1971
[70] Verlet L. Computer "Experiments" on Classical Fluids. I. Thermod ynamical Properties of Lennard-Jones Molecules. Phys.Rev. 1967, 159:98-103
[71] Hckney R. W. The potential calculation and some applications. Methods comput. Phys. 1970, 9: 136-211
[72] Potter D. Computational physics. Wiley, New York Chapter 5
[73] Swop W. C., Andersen H. C., Berens P. H., and Wilson K. R. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters. J. Chem.Phys. 1982, 76: 637-649
[74] Beeman D. Some multistep methods for use in molecular dynamics calculations. J. comput. Phys. 1976, 20: 130-139
[75] W. Deitz, W. O. Riede, and K. Heinzinger. Z. Naturforsch. 1982, 37(a): 1038-1048
[76] Berendsen H J C, Postma J P M, van Gunsteren W F, et al. Molecular dynamics with coupling to an external bath.1984 81:3684-3690
[77] Hoover W G Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A., 1985, 31:1695 一 1697
[78] Allen M P, Tildesley D J, Computer Simulation of Liquida. Clarendon Press, Pxford Science Publications, 1987
[79] Andersen H C. Molecular Dynamics simulations at constant pressure and/or temperature. J. Chem. Phys., 1980, 72:2384-2393
[80] Parrinello M, Rahman A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. App. Phys.1981, 52:7182-7190
[81] Parrinello M, Rahman A. Crystal Structure and Pair Potentials: A Molecular-Dynamics Study.Phys. Rev. Lett., 1980, 45:1196-1199
[82] S. M. Foiles, M. I. Baskes, and M. S. Daw. Embedded-atom-method functions for the metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 1986, 33: 7983-7991
[83] Jost W. Diffusion in Solids, Liquids and Gases. Academic Press, New York,1960
[84] Wallace D C. Solid State Physics. 1970, 25: 301 (New York: Academic)
[85] C.Kittel,Introduction to Solid State Physics 5th ed[M]. Wiley, New York, 1976
[86] Metal Reference Book, 5th ed., edited by C. J. Smith (Butterworth, London, 1976)
[87] G. Simmons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook[M]. MIT Press, Cambridge, MA, 1971
[88] T Hehenkamp. Absolute vacancy concentrations in noble metals and some of their alloys. [J]. J. Phys. Chem. Solids 1994,55: 907-915
[89] Murnagahan F D, Finite Deformations of an Elastic Solid. Am J Math, 1937, 49:235-260