摘要
二硼化锆(ZrB_2)具有陶瓷和金属的双重特性且具有高熔点(3245℃)、高硬度和优良的导电、导热和抗化学腐蚀性等性能,是一种性能优异的高温陶瓷材料,并且对熔融金属具有化学惰性。近年来,ZrB_2系复合材料由于独特的高强、高温、高导电、高稳定性等优良性能,使之在高温环境下的应用显示出强大的生命力,特别是能在许多领域起到金属和陶瓷难以胜任的独特作用。
虽然它在技术方面已得到广泛的应用,但是在高压下的某些性质没有得到研究,我们可以预言,由于二硼化锆独特的物理化学性质,在不久的将来,它在高压高温下的应用必定有长足的发展。但是目前在高压下的一些基本问题(包括其几何结构、电子结构及成键的机制等)还未获得解决。本文主要研究内容分为三个部分:
首先,利用平面波赝势密度泛函理论计算了ZrB_2的基本性质参数,包括晶格常数a和c、体弹模量B0、体弹模量对压强的一阶导数B0′,这些参数值分别为3.167A、3.544A、238.55 GPa、2.32,我们还计算了五个独立的弹性常数C_(11)、C_(12)、C_(13)、C_(33)、C_(44)。晶格常数的值与实验及其它理论值相符得比较好,很遗憾的是,弹性常数尚无实验值及其它理论值可比较。由弹性常数,我们推导出在零压、温度300 K时的德拜温度为908.787 K,这个结果与Wiley D.E.等人的结果ΘD= 910K比较接近。
其次,我们通过准谐德拜模型(Quasi-harmonic Debye Model)研究了ZrB_2热力学性质,给出了不同压强和不同温度下的热容和德拜温度的计算值,发现热容随着压强增加而减小,德拜温度随压强增加而增加。我们还拟合了不同压强(0 GPa、20 GPa、40 GPa)下热容和温度的关系,当温度低于1500 K时,热容随温度的增加而增加,但当温度高于1500 K时,热容几乎接近所有固体在高温条件下所要遵循的Dulong-Petit值,即9NA kB (≈74.85 J mol~(-1) K~(-1))。
最后,我们通过能带理论,利用CASTEP软件包,讨论了ZrB2在不同压强下的总体态密度,分态密度。我们注意到各部分态密度的相对强度都是随着压强的增加略有减小。而且,随着压强的逐渐增大,处于价带与导带部分的态密度都是向高能方向漂移(蓝移),导带和价带宽度略有增加。另外,我们还计算了电荷转移、键长、布局数。我们发现电荷转移随着压强的增大而增大,当压强从O GPa增加到40 GPa,电荷转移从1.16增加到1.27,键长分别从1.82847 A和2.54618A减少到1.75457A和2.43610A,电子云布局数分别从2.43和0.12变化到2.62和-0.26。随着压强的增加,它的导带和价带都展宽,而且都有向高能方向漂移的趋势,但导带漂移的幅度比价带明显要大,因此,导带和价带之间可能会出现带隙,极有可能从导体过渡到半导体。但是压强增大后,它的导带和价带间并没有出现带隙,这说明在我们所考虑到的压强范围内二硼化锆的电子结构和导电性并没有受到多大影响,这样也同样验证了二硼化锆能在一定的高温高压下保持良好的导电性。
Transition-metal borides ZrB_2 has several unique properties. For example, both metallic and ceramic property, high melting point 3245oC, high hardness, fine conductivity and thermal conduction, chemical stability and so on .They are excellent refractory ceramics material with chemical inertness for molten metal. Recently, because of its unique high strength, temperature, conductivity, stability, and other fine properties, it has demonstrated the formidable vitality.under the environment of high temperature. Especially it plays an unique role in many fields which metal and ceramics can not play.
Despite the technological developments of ZrB_2, some behaviors of ZrB_2 under the high pressure have not been paid enough attention. Many fundamental problems for ZrB_2 under high pressure condition, such as the structural, electronic and bonding mechanisms, has not been solved. The main contents studied in this thesis are divided into 3 parts, which are summarized below:
Firstly, we have employed ab initio plane-wave pseudopotential density functional theory to calculate the equilibrium lattice parameters, and the lattice constant a and c . The five independent elastic constants, the bulk modulus B0 and the first order pressure derivative of bulk modulus B0′has been obtained. The equilibrium lattice parameters obtained have been shown to be in good agreement with available experimental data and other theoretical results. No theoretical or experimental data for elastic constants are yet available for our comparison. At T=300K, P=0, using the single-crystal elastic constants of ZrB_2, we obtainΘ_D= 908.787K, which agrees well with the valueΘ_D= 910K by Wiley D.E.et al.
Secondly, the thermodynamic properties of the ZrB_2 have been obtained through the quasi-harmonic Debye model. We have calculated the heat capacities and the Debye temperatures at different temperatures and different pressures, it is found that as pressure increases, the heat capacity CV decreases and the Debye temperatureΘ_D increases. It is shown that when T < 1500 K, the heat capacity C_V is dependent on both the temperature T and the pressure P. However, at higher pressures and/or higher temperatures, the harmonic effect on C_V is suppressed, the calculated C_V is very close to the Dulong-Petit limit 9NA kB (≈74.85 J mol~(-1) K~(-1)), which is obeyed by to all solids at high temperature.
Finally, we have use the CASTEP package of Materials Studio to discuss total, valence band, and conduction band density of state of ZrB_2 at different pressures based on band theory. It has been noted that relative intensity of density of state on each section has a slight decrease when the pressure increases. Moreover, as pressure increases gradually, density of state of valence bands and conduction bands shift towards the high energy, the width of valence bands and conduction bands increase slightly. Furthermore, we have calculated Charge Transfer, Bond Length, Bond Population. We find that as pressure increases, the charge transfer increases, but the bond length decreases , and population has also changed .
引文
[1] P.H.Hohenberg.and W.Kohn, Phys.Rev.B ,1964,136:864
[2] W.Kohn and L.J.Sham, Phys.Rev.A,1965,140:1133
[3] D.R.Haltree, Proceedings of the Cambridge PhilosoPhical Society,1928, 24: 89-111
[4] V. Fock, Zeits.f, Physik,1930, 61:126
[5] R. M. Dreizler and E. K. U. Gross, Density functional theory, Berlin: Springer-Vertag, 1990.
[6] 王积方,高压下物质性质的研究,COLLEGE PHYSICS(大学物理),2001,20:11-14
[7] Cheng Y M, Gadalla A M. Materials and Manufacturing processes ,1996,11(4):575-587
[8] Martinez M.Rodriguez D.Journal of the European Ceramic Society,22:14-15 ,2543-2549
[9] Kim K H ,Materials Characterization,2003,50(1):31-37
[10] Tsuchida T, Journal of European Ceramic Society,2004,24(1):45-51
[11] R. M.Dreizler and E. K. U. Gross, Density functional theory, Berlin: Spri-nger-Vertag,1990
[12] R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules,New York : Oxford,1989
[13] 周世勋著,量子力学教程,北京:高等教育出版社,1992,p21
[14] 廖沐真,吴国是,刘洪霖著,量子化学从头计算方法,北京:清华大学出版社,1984,pl
[15] W. Kohn, Density functional theory, edited by E. K. U. Gross and R. M. Drei- zler,New York: Plenum Press,1995
[16] P.Ziesche, S.Kurth and J. P. Perew, Comput. Mater.Sci.1998,11:122
[17] 黄美纯,物理学进展,2000,20(3):199
[18] Hohenberg P and Kohn W.Phys.Rev.1964,136:B86
[19] Kohn W and Sham I ,J.Phys.RevA,1965,140:1133
[20] Thomas H.Proc.Camb,Phil,1927,23 :542
[21] Fermi E. Accad,Naz,Lincei ,1927,6:602
[22] J.C.Slater, Phys. Rev. ,1951,81:385
[23] J.C.Slater, The self-consistent field for molecules and solids, New York: Mcgraw-Hill, 1974
[24] R.O. Jones and O. Gunnarsson, Rev.Mod. Phys.1989, 61:689
[25] A.D. Becke, Phys. Rev.A,1988,38:3098
[26] J.P. Perdew, In Electronic structure of solids, eds. P. Ziesche and H. EscHr-ig, Berlin: Akademic Verlag,1991,p11
[27] C. Langreth and J.P.Perdew, Phys.Rev.B,1980,21:5469
[28] J. P. Perdew and Y. Wang, Phys. Rev.B,1992,45:13244
[29] J. P. Perdew, J. A. Chevary,S. H. Vosko, K.A. Jackson, M. R. Pederson, D .Singh and C. Foilhais, Phys.Rev.B,1992,46:6671
[30] J. P. Perdew, K. Burke and M. Emzerhof, Phys. Rev. Lett.1996,77:3865
[31] C. Lee, W. Yang and R. C. Parr, Phys. Rev.B,1988,37:785
[32] Y. Andersson, D. C. Langreth and B. L. Lundqvist, Phys. Rev. Lett. 1996,76:102
[33] W. Kohn, Y. Meir and D. E. Makarov, Phys. Rev. Lett.1998,80:4153
[34] D. R. Hamann, M. Schluter and C. Chiang, Phys. Rev. Lett.1977,3:1494
[35] G. B. Bachelet, D. R. Hamann and M. Schluter, Phys.Rev.B,1982,26:4199
[36] D. Vanderbilt, Phys.Rev.B,1990,41:7892
[37] M. A. Blanco, A. Martín Pendás,E. Francisco, J. M. Recio and R. Franco, J. Molec. Struct. (Theochem.)1996,368:245
[38] M. Flórez, J. M. Recio, E. Francisco, M. A. Blanco and A. M. Pendás, Phys.Rev. B,2002,66:144112
[39] M. A. Blanco, E .Francisco and V. Luana, Comput. Phys. Commun.2004,158:7
[40] J. P. Poirer, Introduction to the physics of the earth’s interior, England: Cambridge University Press,1991
[41] E. Francisco, J. M. Recio, M. A. Blanco and A. Martín Pendás, J. Phys. Chem.1998,102: 1595
[42] E. Francisco,M. A.Blanco and G.Sanjurjo, Phys.Rev.B ,2001,63:094107
[43] D. Vanderbilt,Phys.Rev.B,1990,41:7892
[44] Perdew, J. P.; Chevary, J. A.; Vosko,S. H.;Jackson, K. A.; Pederson, M. R.; Singh, D. J. Fiolhais, CPhys.Rev.B,1992,46:6671-6687
[45] M.C. Payne, M.P. Teter, D.C. Allen, T.A. Arias, J.D.Joannopoulos, Rev. Mod. Phys.,1992,64:1045
[46] V. Milman, B.Winkler, J.A.White, C.J. Packard, M.C.Payne, E.V. Akhmatskaya, R.H.Nobes, Int.J.QuantumChem.2000,77:895
[47] F. D. Murnaghan, Proc. Natl. Acad. Sci.USA,1944 30:244
[48] 章桥新, 中国有色金属学报,2000,vol.10,No.4 Sept.
[49] Prabhakar P.Singh Phys.Rev.B,2004,69:094519
[50] P. Vajeeston, P. Ravindran, C. Ravi1, and R. Asokamani1,Phys. Rev. B,2001,63: 045115
[51] 柴永泉 ,靳常青,刘邦贵 高压物理学报,2004 ,vol.18,No.3 Sept.
[52] William G.Fahrenholtz, and Gregory E. Hilmas, J.Am.Ceram.Soc.2007,90[5]: 1347–1364
[53] Hideo Ihara, Masayuki Hirabayashi, and Hiroshi Nakagawa ,Phys. Rev.B,1977,16 :2
[54] H.Y.Wang, X.R.Chen, W.J.Zhu, Y.Cheng, Phys.Rev.B ,2005,72:172502
[55] P.S.Spoor, J.D.Maynard, M.J.Pan, D.J.Green, J. R. Hellmann, T. Tanaka, Appl. Phys. Lett.1977,70:1959
[56] W. Voigt, Lehrbuch der Kristallphysik ,Leipzig: Taubner,1928
[57] A. Reuss, Z. Angew, Math. Mech.1929,9:55
[58] R . Hill, Proc. Soc. London,A,1952,65:350
[59] E. Schreiber, O. L Anderson and N. Soga, Elastic Constants and Their Measurements, New York: McGraw-Hill 1973
[60] O.L.Anderson, J. Phys. Chem. Solids,1963,24:909
[61] Wiley D.E., Manning W.R., Hunter O. Jr. JOURNAL OF THE LESS-COMMON METALS,1969,18: 149-157
[62] G.Grimvall, Thermophysical properties of materials, Elsevier/North-Holland, Amsterdam,1999
[63] M. A. Blanco, A. Martín Pendás,E. Francisco, J. M. Recio and R. Franco, J. Molec. Struct.(Theochem.)1996,368:245
[64] M. Flórez, J. M. Recio, E. Francisco, M. A. Blanco and A. M. Pendás, Phys.Rev. B 2002,66:144112
[65] J.P.Poirer, Introduction to the physics of the earth’s interior, England: Cambridge University Press,1991
[66] E.Francisco, J.M.Recio,M.A.Blanco and A.Martín Pendás, J.Phys.Chem.1998,102:1595
[67] E. Francisco, M. A. Blanco and G. Sanjurjo, Phys.Rev.B,2001, 63:094107
[68] M. A. Blanco, E .Francisco and V. Luana, Comput. Phys. Commun.2004,158:7
