结构材料中杂质复合缺陷的第一原理电子结构研究
摘要
杂质是材料中非常重要的一类缺陷。它的存在,不仅会影响材料的电子输运、磁学等方面的性质,同时也会与位错、晶界等其他结构缺陷构成复合缺陷,从而显著的影响材料的强度、韧性等力学性质,甚至决定了材料的基态结构。研究杂质在不同体系中的作用,并寻找微观层面上的解释,除了具有重要的科学意义之外,也会有力的促进高性能的材料设计以及现有材料性能上的改善,因而同时具有很强的应用价值和指导意义。在本篇论文中,利用精确的第一原理量子力学计算方法,我们系统的研究了杂质在不同类型的缺陷体系中的效用,并通过分析这些体系中电子结构和能量学上的变化,阐明了其中的微观机理。通过能量-原子位移曲线可知,当C、N及O处于α-Fe的{001}[110]裂纹前端时,前面二种元素可以阻碍裂纹沿原方向的进一步扩展,而O会加速裂纹的扩展,削弱α-Fe的韧性。进一步分析了掺杂体系的电荷密度、态密度以及给定原子对的原子间相互作用能等结果后,我们发现,起决定作用的是杂质原子与邻近铁原子成键的各向异性:C和N与Fe原子在垂直于裂纹面的方向上的成键强于平行于裂纹面方向的成键,而O原子并没有这种特点。根据Rice-Wang模型,Re偏聚于α-FeΣ5[001](010)晶界处时,可以强化晶界,增强晶界两侧的Fe原子之间的相互作用,通过分析杂质形成能以及不同元素的化学势发现,Re的作用可归因于其较大的化学势。同时,我们研究了多种杂质元素共偏聚于晶界处时的作用,发现对于两种致韧元素Ti和B而言,(Ti+B)共偏聚不会使得晶界进一步加强。而Ti和致脆元素O共存于晶界时,二者的效果相互抵消。我们定义了杂质偏聚能,发现Ti的存在可以非常有效的抑制O在α-FeΣ5[001](010)晶界处的偏聚,从而改善α-Fe的韧性。杂质偏聚能在研究杂质共偏聚的时候对于Rice-Wang模型是个很好的辅助分析手段。根据实验,Al取代MoSi2中的Si原子后形成Mo(Si1-x, Alx)_2,当x超过10 at.%后会导致Mo(Si_(1-x), Al_x)_2发生C11b→C40的相变。基于群论和晶体场理论,我们分析了不同浓度x下Mo(Si_(1-x), Al_x)_2体系的态密度,发现因为价电子浓度会随x变化,从而决定了费米能级的位置,因为C1 1b、C 40两种结构对称性的不同,体系的态密度会分裂为不同的子带,费米能级与这些子带的相对位置关系决定了两种结构的相对稳定性。基于这些讨论,我们提出了判断结构稳定性的判据,解释了大部分过渡金属二硅化物的基态结构,并讨论了通过第四元组分调控Mo(Si_(1-x), Al_x)_2基态结构的可行性。
Impurity is one important kind of defects in materials. The properties of electronic transmission and magnetism are affected by the presence of impurities in materials. Impurities also compose the complex with other defects, such as dislocations, grain boundaries, etc., and apparently affect the mechanical properties of materials, such as ductility, strength. It can even control the ground state structure of materials. Investigating the effects of impurities and finding the explanation at microscopic level has not only great scientific meanings, but also the worth on application and techniques, because these investigations can efficiently accelerate the design on high-performance alloys and improve the properties of widely-used materials. In this dissertation, by employing the state-of-art first principles quantum mechanical calculated methods, we systematically investigate the effects of impurities in kinds of defects systems, and explain the microscopic mechanism based on the analysis on the energy and electronic structures. According to the curve of binding energy verses displacements of atoms, it is found that C or N impede the propagation of {001}[110] crack inα-Fe when they lie at the front of the crack, while O accelerates the propagation, and has detrimental effects on the ductility ofα-Fe. According to the results of charge density distribution, density of states (DOS), and interatomic interaction, we also find that it is the anisotropic bonding character that controls the effects of the impurity on the crack propagation: the bonds of C (N)-Fe pair which is vertical to the crack plane is much larger than that of the C (N)-Fe pair which is parallel to the crack plane, while it is not the case of O. According to Rice-Wang model, when segregating toα-FeΣ5 [001] (010) grain boundary, Re is a cohesive enhancer, and strengthens the interaction of the Fe-Fe pairs which crosses the interface. The effect of Re can be attributed to the large value of chemical potential of Re based on the analysis on the formation energy and the chemical potential of both Re and Fe. We also investigate the effects of co-segregation of two kinds of impurities on the grain boundary, and find that though Ti and B are both cohesive enhancers, the co-segregation of (Ti+B) does not strengthen the grain boundary further. Ti can completely reduce the detrimental effect of O. Furthermore, based on the segregation energy, it is found that Ti can efficiently prohibit the segregation of O to the grain boundary, and thus improve the ductility ofα-Fe. The segregation energy is agood auxiliary method to Rice-Wang model. According to experiments, Al substitutes Si in MoSi2 to form Mo(Si_(1-x), Al_x)_2, when the x exceeds the 10 at.%, Mo(Si_(1-x), Al_x)_2 will performs C1 1b→C40phase transition, based on group theory and crystal field theory, we analyze the DOS of Mo(Si_(1-x), Al_x)_2 with different x, and find that the concentration of valence electrons is changed with x, and the Fermi level as well. DOS of C1 1band C 40structures will split into different sub-bands because of the different symmetry of structures. The stabilities of these two structures depend on the relative positions between the Fermi level and sub-bands. We provide a new criterion to judge the stabilities of different structures, and explain the ground-state structure of the most of the early transition metal disilicides. Furthermore, we predict the feasibility of controlling the microscopic structure by adding the quaternary component according to the criterion which is presented in the work.
Impurity is one important kind of defects in materials. The properties of electronic transmission and magnetism are affected by the presence of impurities in materials. Impurities also compose the complex with other defects, such as dislocations, grain boundaries, etc., and apparently affect the mechanical properties of materials, such as ductility, strength. It can even control the ground state structure of materials. Investigating the effects of impurities and finding the explanation at microscopic level has not only great scientific meanings, but also the worth on application and techniques, because these investigations can efficiently accelerate the design on high-performance alloys and improve the properties of widely-used materials. In this dissertation, by employing the state-of-art first principles quantum mechanical calculated methods, we systematically investigate the effects of impurities in kinds of defects systems, and explain the microscopic mechanism based on the analysis on the energy and electronic structures. According to the curve of binding energy verses displacements of atoms, it is found that C or N impede the propagation of {001}[110] crack inα-Fe when they lie at the front of the crack, while O accelerates the propagation, and has detrimental effects on the ductility ofα-Fe. According to the results of charge density distribution, density of states (DOS), and interatomic interaction, we also find that it is the anisotropic bonding character that controls the effects of the impurity on the crack propagation: the bonds of C (N)-Fe pair which is vertical to the crack plane is much larger than that of the C (N)-Fe pair which is parallel to the crack plane, while it is not the case of O. According to Rice-Wang model, when segregating toα-FeΣ5 [001] (010) grain boundary, Re is a cohesive enhancer, and strengthens the interaction of the Fe-Fe pairs which crosses the interface. The effect of Re can be attributed to the large value of chemical potential of Re based on the analysis on the formation energy and the chemical potential of both Re and Fe. We also investigate the effects of co-segregation of two kinds of impurities on the grain boundary, and find that though Ti and B are both cohesive enhancers, the co-segregation of (Ti+B) does not strengthen the grain boundary further. Ti can completely reduce the detrimental effect of O. Furthermore, based on the segregation energy, it is found that Ti can efficiently prohibit the segregation of O to the grain boundary, and thus improve the ductility ofα-Fe. The segregation energy is agood auxiliary method to Rice-Wang model. According to experiments, Al substitutes Si in MoSi2 to form Mo(Si_(1-x), Al_x)_2, when the x exceeds the 10 at.%, Mo(Si_(1-x), Al_x)_2 will performs C1 1b→C40phase transition, based on group theory and crystal field theory, we analyze the DOS of Mo(Si_(1-x), Al_x)_2 with different x, and find that the concentration of valence electrons is changed with x, and the Fermi level as well. DOS of C1 1band C 40structures will split into different sub-bands because of the different symmetry of structures. The stabilities of these two structures depend on the relative positions between the Fermi level and sub-bands. We provide a new criterion to judge the stabilities of different structures, and explain the ground-state structure of the most of the early transition metal disilicides. Furthermore, we predict the feasibility of controlling the microscopic structure by adding the quaternary component according to the criterion which is presented in the work.
引文
[1] 陈继勤,陈敏熊,赵敬世. 晶体缺陷. 浙江大学出版社,1992.
[2] 夏建白. 现代半导体物理. 北京大学出版社,2000.
[3] Ohno H. Making Nonmagnetic Semiconductors Ferromagnetic. Science, 1998, 281: 951-956.
[4] Ohno H, Shen A, Matsukura F, Oiwa A, Endo A, and Kutsumoto S. (Ga, Mn) As: A new diluted magnetic semiconductor based on GaAs. Appl. Phys. Lett. 1996, 69:363-365.
[5] Wert Ch A. Trapping of Hydrogen in Metals. Hydrogen in Metal II, edited by G. Alefeld and J. V?lkl, Springer-Verlag, Berlin, Heidelberg,New York, 1978, p.305-330.
[6] Lacornbe P, Aucouturier M, and Chere J. Hydrogen Trapping and Hydrogen Embrittlement. Hydrogen Embrittlement and Stress Corrosion Cracking, A Troiano Festschrift, edited by Gibala R and Hehemann R F, Ohio : American Society for Metals 1984, p.79-102.
[7] Ha K F, Zhang L W, and Liu B Z. A Research on Hydrogen Cracking in alpha-Iron. Metall. Trans., 1989, A20:2379-2384.
[8] Ha K F, Liu Y, An Z Z. Room-Temperature Aging of Hydrogen in alpha-Iron After Cathodic Charging. Metall. Trans., 1991, A22:261-264.
[9] Jagannadham K, Armstrong R W, and Hirth J P. Low Energy Cleavage Fracture Associated with the Hydrogen Embrittlement of Refractory Metal Alloys. Mater. Sci. Eng. A, 1989, 113:339-366.
[10] Fujita F E. Theory of Hydrogen Induced Delayed Fracture of Steel. Hydrogen in Metals, Paris, 1978, 2B10.
[11] Onodera R, Takaki S, Abiko K, and Kimura H. Effects of Oxygen and Substitutional Impurities on the Mechanical Properties of High Purity Iron. Mater. Sci. Eng. 1991, A2:261-267.
[12] Yoshino K, McMahon Jr. The cooperative relation between temper embrittlement and hydrogen embrittlement in a high strength steel. Metallurg. Trans, 1974, 5:363-370.
[13] Snavely C A. Hydrogen Embrittlement in Metal Finishing. Reinhold Pub., 1961.
[14] Rodriguez M V, and Ficaloca P J. The Mechanism of a Hydrogen-Dislocation Interaction in BCC Metals: Embrittlement and Dislocation Motion. Mat. Sci. Eng., 1987, 85:43-52.
[15] Hoke J H. Composition and Hydrogen Stress Cracking of Steels. Corrosion, 1970, 26:396-397.
[16] Whiteman H B, and Troiano A R. Hydrogen Embrittlement of Austenitic Stainless Steel. Corrosion, 21, 53-56, 1965.
[17] Kumnick A J, and Johnson H H. Deep Trapping States for Hydrogen in Deformed Iron. Acta. Met., 1980, 28:33-39.
[18] Zhang T, Chu W, and Hsiao C. Strain fields of hydrogen atoms in iron. Scripta. Met., 1984, 18:1421-1426.
[19] 哈宽富. 断裂物理基础. 科学出版社,2000.
[20] Zapffe C. Discussion of metal arc welding of steels by S. A. Herres. Trans. ASME, 1947, 191.
[21] Kazinczy F. A theory of hydrogen embrittlement. J. Iron. Steel. Inst., 1954, 177:85.
[22] Petch N J. The Lowering of Fracture-Stress due to Surface Adsorption. 1956, Phil. Mag. 1:331.
[23] Troiano A R. The role of hydrogen and other interstitials in the mechanical behavior of metals. Trans. ASME, 1960, 52:54.
[24] Tien J K, Nair S V, and Jensen R R. Hydrogen effects in Metals. edited by Bernstein I M, Thompson A W, Metallugical Society of AIME, 37, 1980.
[25] 张统一. 氢致钢铁开裂机理的研究. 北京钢铁学院博士论文,1985.
[26] Moliere M, Verdier Y, Leymonie C. Oxidation of copper in high purity water at 70 degree C: Application to electric generator operation. Corrosion Science, 1990, 30:183-188.
[27] Weins M, Gleiter H, and Chalmers B. Computer Calculations of the Structure and Energy of High-Angle Grain Boundaries. J. Appl. Phys., 1971, 42:2639-2645.
[28] Fisher J C. Calculation of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion J. Appl. Phys., 1951, 22:74-77.
[29] Young G, and Funderlic R E. On the grain boundary diffusion theory of Fisher and Whipple. J. Appl. Phys. 1973, 44:5151-5154.
[30] Aust A T, Hanneman R E, et al. Solute Induced Hardening near Grain Boundaries in Zone Refined Metals. Acta Metall., 1968, 16:291-302.
[31] Williams T M, Stoneham A M, and Harries D R. The segregation of boron to grain boundaries in solution-treated Type316 austenitic stainless steel. Metal. Science, 1976, 10:14-19.
[32] Edwards B C, and Eyre B L. Solute Effects on Intergranular Fracture. Dislocation Modeling of Physical System, edited by Ashby M F, Bullough R, Hartley C S, and Hirth J P, New York: Pergamon Press, 1981. p.28-44.
[33] Duscher G, Chisholm M, et al. Bismuth-induced embrittlement of copper grain boundaries. Nature Mater., 2004, 3:621-626.
[34] 王迪,邢文彬,解子章 等译. 钢中微量元素的偏析与晶界脆化. 北京:冶金工业出版社,1985.
[35] Yang R, Wang Y M, et al. First-principles study on the effect of Mn and N on the cohesion of a γ-iron grain boundary. Phys. Rev. B65, 094112, 2002.
[36] Stoloff N S. Fracture, An advanced Treatise. edited by Liebowitz H, VI, 1968, p.1.
[37] Bechtold J H, and Shaw B J. An advanced Treatise. edited by Liebowitz H, VI, p.371, 1968.
[38] Losch W. A New Model of Grain Boundary Failure in Temper Embrittled Steel. Acta Metall., 1979, 27:1885-1892.
[39] Seah M P, and Hondros E D. Atomistics of Fracture, 1981, 855-887.
[40] Cottrell A H. Effect of Solute Atoms on the Behaviour of Dislocations. In: Mott N F, eds. Report of a Conference on Strength of Solids. Bristol, 1947: 30-38. London: Physical Society, 1948; Cottrell A H and Bilby B A. Proc. Soc., London, Sect. A. 1949, 62: 49.
[41] Wilde J, Cerezo A, and Smith G D W. Three-dimensional atomic-scale mapping of a cottrell atmosphere around a dislocation in iron. Scripta Mater. 2000, 43: 39-48.
[42] Blavette D, Cadel E, Fraczkiewicz A, et al. Three-dimensional atomic-scale imaging of impurity segregation to line defects. Science, 1999, 286: 2317-2319.
[43] Banerjee D, Gogia A K, Nandi T K, and Joshi V A. A new ordered orthorhombic phase in a Ti3Al-Nb alloy. Acta Metall. 1988, 36:871-882.
[44] Ramanujan RV, Maziasz PJ and Liu CT. The thermal stability of the microstructure of gamma-based titanium aluminides Acta Metall. Mater. 1996, 44:2611-2642.
[45] Hagihara K, Nakano T, and Umakoshi Y. Mechanical properties of C40-Based ternary Mo(Si,Al)2 and quaternary (Mo,Zr)(Si,Al)2 silicides. Script. Mater. 1998, 38:471-476.
[46] Tabaru T, Shobu K, Sakamoto M and Hanada S. Effects of substitution of Al for Si on the lattice variations and thermal expansion of Mo(Si,Al)2. Intermetallics, 2004, 12:33-41.
[47] Grechnev A, Andersson P H, and Ahuja R. etc. H-H interaction and structural phase transition in Ti3SnHx. Phys. Rev. B 2002, 66:235104.
[48] Wright A F. Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN. J. Appl. Phys. 1997, 82:2833-2839.
[49] Stadler R, Wolf W, Podloucky, et al. Ab initio calculations of the cohesive, elastic, and dynamical properties of CoSi2 by pseudopotential and all-electron techniques. Phys. Rev. B 1996, 54:1729-1734.
[50] Fri?k M, ?ob M, and Vitek V. Ab initio study of the ideal tensile strength and mechanical stability of transition-metal disilicides. Phys. Rev. B, 2003, 68:184101.
[51] Daw M S and Baskes M I. Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys. Rev. Lett. 1983, 50: 1285-1288.
[52] Daw M S and Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B, 1984, 29: 6443-6453.
[53] Finnis M W and Sinclair J E. A simple empirical N-body potential for transition metals. Philos Mag A, 1984, 50: 45-55; Erratum. 1986, 53: 161.
[54] Ackland G J, Tichy G, Vitek V, and Finnis M W. Simple N-body potentials for the noble metals and nickel. Philos. Mag. A, 1987, 56: 735-756.
[55] Johnson R A. Analytic nearest-neighbor model for fcc metals. Phys. Rev. B, 1988, 37: 3924-3931.
[56] 张邦维,胡望宇,舒小林. 嵌入原子方法理论及其在材料科学中的应用-原子尺度材料设计理论. 长沙:湖南大学出版社,2003.
[57] Finnis M W and Sinclair J E. A simple empirical N-body potential for transition metals. Philos Mag A, 1984, 50: 45-55.
[58] Grujicic M, Zhao H, Krasko GL. International Journal of Refractory Metals & Hard Materials 1997, 15 (5-6): 341-355.
[59] Collins A, O’Handley R C, and Johnson K H. Bonding and magnetism in Fe-M (M=B,C,Si,N) alloys Phys. Rev. B, 1988, 38:3665-3670.
[60] Painter G S, Averill F W. Effects of segregation on grain-boundary cohesion: A density-functional cluster model of boron and sulfur in nickel. Phys. Rev. Lett. 1987, 58:234-237.
[61] Messmer R P. Local electronic structure of amorphous metal alloys using cluster models. Evidence for specific metalloid-metal interactions. Phys. Rev. B, 1981, 23:1616-1623.
[62] Tang S. Freeman A J, and Olson G B. Phosphorus-induced relaxation in a iron grain boundary: A cluster-model study. Phys. Rev. B, 1993, 47:2441-2445.
[63] Eberhart M E, Vvedensky D D. Localized Grain-Boundary Electronic States and Intergranular Fracture. Phys. Rev. Lett. 1987, 58:61-64.
[64] Rice J R, and Wang J S. Embrittlement of interfaces by solute segregation. Mater. Sci. Eng. A, 1989, 107:23-40.
[65] Wu R, Freeman A J, and Olson G B. First Principles Determination of the Effects of Phosphorus and Boron on Iron Grain Boundary Cohesion. Science, 1994, 265:376-380.
[66] Wu R, Freeman AJ, and Olson GB. Effects of carbon on Fe-grain-boundary cohesion: First-principles determination. Phys. Rev. B, 1996, 53:7504-7509.
[67] Geng W T, Freeman A J, Wu R, and Olson G B. Effect of Mo and Pd on the grain-boundary cohesion of Fe. Phys. Rev. B, 2000, 62:6208-6214.
[68] Geng W T, Freeman A J, and Olson G B. Influence of alloying additions on grain boundary cohesion of transition metals: First-principles determination and its phenomenological extension. Phys. Rev. B, 2001, 63:165415.
[69] Haydock R. The mobility of bonds at metal surfaces. J. Phys. C, 1981, 14:3807-3816.
[70] Messmer R and Briant C L. The role of chemical bonding in grain boundry embrittlement. Acta Metall. 1982, 30:457-467.
[71] Sutton A P and Vitek V. An atomistic study of tilt grain boundaries with substitutional impurities. Acta Metall. 1982, 30:2011-2033.
[72] Schweinfest R, Paxton A T, and Finnis M W. Bismuth embrittlement of copper is an atomic size effect. Nature, 2004, 432:1008-1011.
[73] Zhong L P, Wu R Q, Freeman A J, and Olson G B. Effects of Mn additions on the P embrittlement of the Fe grain boundary. Phys. Rev. B, 1997, 55:11133-11137.
[74] Hu Q M, Yang R, Xu D S, Hao Y L, and Li D. Energetics and electronic structure of grain boundaries and surfaces of B- and H-doped Ni3Al. Phys. Rev. B, 2003, 67:224203.
[75] Wang F H, Wang C Y, and Yang J L. The effect of boron on the electronic structure of grain boundaries in Ni3Al. J. Phys: Condens. Matter, 1996, 8:5527-5534.
[76] Wang F H, and Wang C Y. First-principles investigation of hydrogen embrittlement in polycrystalline Ni3Al. Phys. Rev. B, 1998, 57, 289-295.
[77] Wang F H, and Wang C Y. The effect of zirconium on the electronic structure of grain boundaries in Ni3Al. J. Phys: Condens. Matter, 1997, 9:4499-4508.
[78] Lu G, Kioussis N, Wu R, and Ciftan M. First-principles studies of the Σ5 tilt grain boundary in Ni3Al. Phys. Rev. B, 1999, 59:891-898.
[79] Djajaputra D, and Cooper B R. Systematic first-principles study of impurity hybridization in NiAl. Phys. Rev. B, 2002, 66:205108.
[80] Feng Y Q, Wang C Y. Electronic effects of light impurities on edge dislocation motion in iron at T=0 K. Journal of Alloys and Compounds, 2000, 312: 219–227.
[81] Yan J A, Wang C Y, Duan W H, and Wang S Y. Electronic states and doping effect of carbon in the edge-dislocation core of bcc iron. Phys. Rev. B, 2004, 69:214110.
[82] Song Y, Guo Z X, Yang R, and Li D. First Principles Study of Site Substitution of Ternary Elements in NiAl. Acta Materialia, 2001, 49:1647-1654.
[83] Hu Q M, Yang R, Xu D S, Hao Y L, and Li D. Geometric and electronic structure of Ti2AlX (X=V, Nb, or Ta). Phys. Rev. B, 2003, 68:054102.
[84] Medvedeva N I, Gornostyrev Y N, and Freeman A J. Carbon stabilized A15 Cr3Re precipitates and ductility enhancement of Cr-based alloys. Acta Mater., 2002, 50:2471-2476.
[85] Sun S N, Kioussis N, and Lim S P, et al. Impurity effects on atomic bonding in Ni3Al. Phys. Rev. B, 1995, 52:14421-14430.
[86] V. Fock. N?herungsmethode zur Losung des quanten-mechanischen Mehrk?rperprobleme. Z. Phys. 1930, 61:126-148.
[87] Born M, Oppenheimer J R. Zur Quqntentheorie der Molekeln. Ann. Physik, 1954, 84:457-480.
[88] Slater J C. Wave Functions in a Periodic Potential Phys. Rev. 1937, 51:846-851; An Augmented Plane Wave Method for the Periodic Potential Problem. ibid. 1953, 92:603-608.
[89] 李正中. 固体理论(第二版). 北京:高等教育出版,2002.
[90] 谢希德,陆栋,主编. 固体能带理论. 上海:复旦大学出版社,1998.
[91] Hohenberg P C and Kohn W. Inhomogeneous electron gas. Phys. Rev. B, 1964, 136: 864-871.
[92] Kohn W and Sham L J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140: A1133-A1138.
[93] Kohanoff J, and Gidopoulos N I. Handbook of Molecular Physics and Quantum Chemistry. Vol.5, p.532-568. edited by Wilson S. John Wiley & Sons, Ltd. Chichester, 2003.
[94] Kohn W. Nobel Lecture: Electronic structure of matter—wave functions and density functionals. Rev. Mod. Phys. 1999, 71: 1253-1266.
[95] Vosko S H, Wilk L, and Nusair M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys. 1980, 58: 1200-1211.
[96] Von Barth U, Hedin L. A local exchange-correlation potential for the spin polarized case. J. Phys. C, 1972, 5: 1629-1642.
[97] Perdew J P, Burke K, and Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77: 3865-3868; Erratum. Phys. Rev. Lett. 1997, 78: 1396.
[98] Becke A D. A multicenter numerical integration scheme for polyatomic molecules. J. Chem. Phys., 1988, 88: 2547-2553.
[99] Lee C, Yang W, Parr R G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B, 1988, 37: 785-789.
[100] Versluis L, Ziegler T. The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration. J. Chem. Phys. 1988, 88: 322-328.
[101] Andzelm J, Wimmer E, Salahub D R. Spin density functional approach to the chemistry of transition metal clusters: Gaussian-type orbital implementation. In: Salahub D R, Zerner M C, Eds. The Challenge of d-and f-Electrons: Theory and Computation. ACS Symposium ser. 1989, 394.
[102] Guenzburger D, and Ellis D E. Magnetism of Fe impurities in alkaline-earth metals and Al. Phys. Rev. B, 1992, 45:285-294.
[103] Ellis D E, Benesh G A, and Byrom E. Molecular cluster studies of binary alloys: LiAl. Phys. Rev. B, 1977, 16:3308-3313.
[104] Delley B, Ellis D E, Freeman A J, Baerends E J, and Post D. Phys. Rev. B, 1983, 27: 2132-2144.
[105] Delley B. An all-electron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 1990, 92:508-517.
[106] 肖慎修,王崇愚,陈天朗. 密度泛函理论的离散变分方法在化学和材料物理学中的应用. 北京:科学出版社,1998.
[107] DMol User Guide. Biosym/Molecular Simulations. 1995.
[108] Feynman R P. Forces in Molecules. Phys. Rev. 1939, 56:340-343.
[109] Martin R M. Electronic Structure-Basic Theory and Practical Methods. Cambridge University Press. 2004
[110] Payne M C, Teter M P, Allan D C, Arias T A, and Joannopoulos J D. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 1992, 64:1045–1097.
[111] 徐婉棠,喀兴林. 群论及其在固体物理中的应用. 北京:高等教育出版社,1999.
[112] Chadi D J, and Cohen M L. Special Points in the Brillouin Zone. Phys. Rev. B, 1973, 8:5747-5753.
[113] Monkhorst H J and Pack J D. Special points for Brillouin-zone integrations. Phys. Rev. B, 1976, 13: 5188-5192.
[114] Chadi D J. Special points for Brillouin-zone integrations. Phys. Rev. B, 1977, 16: 1746-1747.
[115] Pack J D, and Monkhorst H J. “Special points for Brillouin-zone intergrations”-a reply. Phys. Rev. B, 1977,16:1748-1749.
[116] Hamann D R, Schl ü ter M, and Chiang C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 1979, 43: 1494-1497.
[117] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B, 1990, 41: 7892–7895.
[118] Bl?chl P E. Projector augmented-wave method. Phys. Rev. B, 1994, 50: 17953-17979.
[119] Kresse G, and Joubert D. From ultrasoft pseudopotential to projecter augmented-wave method. Phys. Rev. B, 1999,59:1758-1775
[120] Resta R. Festk?rperprobleme: Advances in Solid-State Physics. edited by Grosse P. Vieweg, Braunschweig, 1985. Vol.25, p.183.
[121] Baroni S, de Gironcoli S, Dal Corso A, and Giannozzi P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 2001, 73:515-562.
[122] Frank W, Els?sser C, and F?hnle M. Ab initio Force-Constant Method for Phonon Dispersions in Alkali Metals. Phys. Rev. Lett. 1995, 74:1791-1794.
[123] Ye L H, Liu B G, Wang D S, and Han R S. Ab initio phonon dispersions of single-wall carbon nanotubes. Phys. Rev. B, 2004, 69:235409.
[124] 杨顺华. 晶体位错理论基础. 第一卷. 北京:科学出版社,1998.
[125] Griffith A A. The phenomenon of rupture and flow in solids. Phil. Trans. Royal Soc. 1920, A221:163-198.
[126] 郭雅芳. 铁中裂纹动力学研究及缺陷声子谱:[博士学位论文]. 北京:钢铁研究总院,2001.
[127] deCelis B, Argon A S, and Yip S. Molecular dynamics simulation of crack tip processes in alpha-iron and copper. I. J. Appl. Phys. 2003, 54: 4864-4878.
[128] Hirth J P and Lothe J. Theory of Dislocations (2nd ed.). New York: McGraw-Hill, 1982.
[129] McLean D. Grain boundaries in metals. Oxford: The Clarendon Press, 1957.
[130] Yang R, Wang Y M, Huang R Z, and Wang C Y. First-principles study on the effect of Mn and N on the cohesion of a γ-iron grain boundary. Phys. Rev. B, 2002, 65:094112.
[131] Lee D Y, Barrera E V, Stark J P, and Marcus H L. The Influence of Alloying Elements on Impurity-Induced Grain Boundary Embrittlement. Metall. Trans. A, 1984, 15:1415-1430.
[132] Venezuela P, Miwa R H, and Fazzio A. Carbon in SixGe1–x: An ab initio investigation. Phys. Rev. B, 2004, 69:115209.
[133] Kim S J, and Wayman C M. Strengthening behaviour and embrittlement phenomena in Fe-Ni-Mn- (Ti) maraging alloys. Mater. Sci. Eng. A, 1996, 207:22-29.
[134] Kittle C. Introduction to Solid State Physics, 4th edition. New York: Wiley, 1971, p.39.
[135] 张永刚,韩雅芳,陈国梁,郭建亭,万晓景,冯涤. 金属间化合物结构材料. 北京: 国防工业出版社, 2001, p.907.
[136] Fu M, and Sekhar J A. Processing, Microstructures, and Properties of Molybdenum Aluminosilicide. J. Am. Ceram. Soc. 1998, 81:3205-3219.
[137] Ramberg C E, and Worrell W L. Oxidation Kinetics and Composite Scale Formation in the System Mo(Al,Si)2. J. Am. Ceram. Soc. 2002, 85:444-452.
[138] Yanagihara K, Maruyama T, and Nugata K. High temperature oxidation of Mo-Si-X intermetallics (X = Al, Ti, Ta, Zr and Y). Intermetallics, 1995, 3:243-251.
[139] Liu Y, Shao G, and Tsakiropoulos P. Thermodynamic reassessment of the Mo–Si and Al–Mo–Si systems. Intermetallics, 2000, 8:953-962.
[140] Perdew J P, and Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B, 1992, 45:13244-13249.
[141] Tohei T, Kuwabara A, Yamamoto T, Oba F, and Tanaka I. General Rule for Displacive Phase Transitions in Perovskite Compounds Revisited by First Principles Calculations. Phys. Rev. Lett. 2005, 94:035502.
[142] Doland C M, and Nemanich R J. Phase formation during reactive molybdenum-silicide formation. J. Mater. Res. 1990, 5:2854-2864..
[143] Alouani M, Albers R C, and Methfessel M. Calculated elastic constants and structural properties of Mo and MoSi2. Phys. Rev. B. 1991, 43:6500-6509.
[144] 戴道生,钱昆明. 铁磁学(上册). 北京:科学出版社,1987.
[145] Zou J, and Fu C L. Structural, electronic, and magnetic properties of 3d transition-metal aluminides with equiatomic composition. Phys. Rev. B, 1995, 51:2115-2121.
[146] Nguyen-Manh, Paxton A T, Pettifor D G, and Pasturel A. On the phase stability of transition metal trialuminide compounds. Intermetallics, 1995, 3:9-14.
[147] Pankhurst D A, Nguyen-Manh D, and Pettifor D G. Electronic origin of structural trends across early transition-metal disilicides: Anomalous behavior of CrSi2. Phys. Rev. B, 2004, 69:075113.
[2] 夏建白. 现代半导体物理. 北京大学出版社,2000.
[3] Ohno H. Making Nonmagnetic Semiconductors Ferromagnetic. Science, 1998, 281: 951-956.
[4] Ohno H, Shen A, Matsukura F, Oiwa A, Endo A, and Kutsumoto S. (Ga, Mn) As: A new diluted magnetic semiconductor based on GaAs. Appl. Phys. Lett. 1996, 69:363-365.
[5] Wert Ch A. Trapping of Hydrogen in Metals. Hydrogen in Metal II, edited by G. Alefeld and J. V?lkl, Springer-Verlag, Berlin, Heidelberg,New York, 1978, p.305-330.
[6] Lacornbe P, Aucouturier M, and Chere J. Hydrogen Trapping and Hydrogen Embrittlement. Hydrogen Embrittlement and Stress Corrosion Cracking, A Troiano Festschrift, edited by Gibala R and Hehemann R F, Ohio : American Society for Metals 1984, p.79-102.
[7] Ha K F, Zhang L W, and Liu B Z. A Research on Hydrogen Cracking in alpha-Iron. Metall. Trans., 1989, A20:2379-2384.
[8] Ha K F, Liu Y, An Z Z. Room-Temperature Aging of Hydrogen in alpha-Iron After Cathodic Charging. Metall. Trans., 1991, A22:261-264.
[9] Jagannadham K, Armstrong R W, and Hirth J P. Low Energy Cleavage Fracture Associated with the Hydrogen Embrittlement of Refractory Metal Alloys. Mater. Sci. Eng. A, 1989, 113:339-366.
[10] Fujita F E. Theory of Hydrogen Induced Delayed Fracture of Steel. Hydrogen in Metals, Paris, 1978, 2B10.
[11] Onodera R, Takaki S, Abiko K, and Kimura H. Effects of Oxygen and Substitutional Impurities on the Mechanical Properties of High Purity Iron. Mater. Sci. Eng. 1991, A2:261-267.
[12] Yoshino K, McMahon Jr. The cooperative relation between temper embrittlement and hydrogen embrittlement in a high strength steel. Metallurg. Trans, 1974, 5:363-370.
[13] Snavely C A. Hydrogen Embrittlement in Metal Finishing. Reinhold Pub., 1961.
[14] Rodriguez M V, and Ficaloca P J. The Mechanism of a Hydrogen-Dislocation Interaction in BCC Metals: Embrittlement and Dislocation Motion. Mat. Sci. Eng., 1987, 85:43-52.
[15] Hoke J H. Composition and Hydrogen Stress Cracking of Steels. Corrosion, 1970, 26:396-397.
[16] Whiteman H B, and Troiano A R. Hydrogen Embrittlement of Austenitic Stainless Steel. Corrosion, 21, 53-56, 1965.
[17] Kumnick A J, and Johnson H H. Deep Trapping States for Hydrogen in Deformed Iron. Acta. Met., 1980, 28:33-39.
[18] Zhang T, Chu W, and Hsiao C. Strain fields of hydrogen atoms in iron. Scripta. Met., 1984, 18:1421-1426.
[19] 哈宽富. 断裂物理基础. 科学出版社,2000.
[20] Zapffe C. Discussion of metal arc welding of steels by S. A. Herres. Trans. ASME, 1947, 191.
[21] Kazinczy F. A theory of hydrogen embrittlement. J. Iron. Steel. Inst., 1954, 177:85.
[22] Petch N J. The Lowering of Fracture-Stress due to Surface Adsorption. 1956, Phil. Mag. 1:331.
[23] Troiano A R. The role of hydrogen and other interstitials in the mechanical behavior of metals. Trans. ASME, 1960, 52:54.
[24] Tien J K, Nair S V, and Jensen R R. Hydrogen effects in Metals. edited by Bernstein I M, Thompson A W, Metallugical Society of AIME, 37, 1980.
[25] 张统一. 氢致钢铁开裂机理的研究. 北京钢铁学院博士论文,1985.
[26] Moliere M, Verdier Y, Leymonie C. Oxidation of copper in high purity water at 70 degree C: Application to electric generator operation. Corrosion Science, 1990, 30:183-188.
[27] Weins M, Gleiter H, and Chalmers B. Computer Calculations of the Structure and Energy of High-Angle Grain Boundaries. J. Appl. Phys., 1971, 42:2639-2645.
[28] Fisher J C. Calculation of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion J. Appl. Phys., 1951, 22:74-77.
[29] Young G, and Funderlic R E. On the grain boundary diffusion theory of Fisher and Whipple. J. Appl. Phys. 1973, 44:5151-5154.
[30] Aust A T, Hanneman R E, et al. Solute Induced Hardening near Grain Boundaries in Zone Refined Metals. Acta Metall., 1968, 16:291-302.
[31] Williams T M, Stoneham A M, and Harries D R. The segregation of boron to grain boundaries in solution-treated Type316 austenitic stainless steel. Metal. Science, 1976, 10:14-19.
[32] Edwards B C, and Eyre B L. Solute Effects on Intergranular Fracture. Dislocation Modeling of Physical System, edited by Ashby M F, Bullough R, Hartley C S, and Hirth J P, New York: Pergamon Press, 1981. p.28-44.
[33] Duscher G, Chisholm M, et al. Bismuth-induced embrittlement of copper grain boundaries. Nature Mater., 2004, 3:621-626.
[34] 王迪,邢文彬,解子章 等译. 钢中微量元素的偏析与晶界脆化. 北京:冶金工业出版社,1985.
[35] Yang R, Wang Y M, et al. First-principles study on the effect of Mn and N on the cohesion of a γ-iron grain boundary. Phys. Rev. B65, 094112, 2002.
[36] Stoloff N S. Fracture, An advanced Treatise. edited by Liebowitz H, VI, 1968, p.1.
[37] Bechtold J H, and Shaw B J. An advanced Treatise. edited by Liebowitz H, VI, p.371, 1968.
[38] Losch W. A New Model of Grain Boundary Failure in Temper Embrittled Steel. Acta Metall., 1979, 27:1885-1892.
[39] Seah M P, and Hondros E D. Atomistics of Fracture, 1981, 855-887.
[40] Cottrell A H. Effect of Solute Atoms on the Behaviour of Dislocations. In: Mott N F, eds. Report of a Conference on Strength of Solids. Bristol, 1947: 30-38. London: Physical Society, 1948; Cottrell A H and Bilby B A. Proc. Soc., London, Sect. A. 1949, 62: 49.
[41] Wilde J, Cerezo A, and Smith G D W. Three-dimensional atomic-scale mapping of a cottrell atmosphere around a dislocation in iron. Scripta Mater. 2000, 43: 39-48.
[42] Blavette D, Cadel E, Fraczkiewicz A, et al. Three-dimensional atomic-scale imaging of impurity segregation to line defects. Science, 1999, 286: 2317-2319.
[43] Banerjee D, Gogia A K, Nandi T K, and Joshi V A. A new ordered orthorhombic phase in a Ti3Al-Nb alloy. Acta Metall. 1988, 36:871-882.
[44] Ramanujan RV, Maziasz PJ and Liu CT. The thermal stability of the microstructure of gamma-based titanium aluminides Acta Metall. Mater. 1996, 44:2611-2642.
[45] Hagihara K, Nakano T, and Umakoshi Y. Mechanical properties of C40-Based ternary Mo(Si,Al)2 and quaternary (Mo,Zr)(Si,Al)2 silicides. Script. Mater. 1998, 38:471-476.
[46] Tabaru T, Shobu K, Sakamoto M and Hanada S. Effects of substitution of Al for Si on the lattice variations and thermal expansion of Mo(Si,Al)2. Intermetallics, 2004, 12:33-41.
[47] Grechnev A, Andersson P H, and Ahuja R. etc. H-H interaction and structural phase transition in Ti3SnHx. Phys. Rev. B 2002, 66:235104.
[48] Wright A F. Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN. J. Appl. Phys. 1997, 82:2833-2839.
[49] Stadler R, Wolf W, Podloucky, et al. Ab initio calculations of the cohesive, elastic, and dynamical properties of CoSi2 by pseudopotential and all-electron techniques. Phys. Rev. B 1996, 54:1729-1734.
[50] Fri?k M, ?ob M, and Vitek V. Ab initio study of the ideal tensile strength and mechanical stability of transition-metal disilicides. Phys. Rev. B, 2003, 68:184101.
[51] Daw M S and Baskes M I. Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys. Rev. Lett. 1983, 50: 1285-1288.
[52] Daw M S and Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B, 1984, 29: 6443-6453.
[53] Finnis M W and Sinclair J E. A simple empirical N-body potential for transition metals. Philos Mag A, 1984, 50: 45-55; Erratum. 1986, 53: 161.
[54] Ackland G J, Tichy G, Vitek V, and Finnis M W. Simple N-body potentials for the noble metals and nickel. Philos. Mag. A, 1987, 56: 735-756.
[55] Johnson R A. Analytic nearest-neighbor model for fcc metals. Phys. Rev. B, 1988, 37: 3924-3931.
[56] 张邦维,胡望宇,舒小林. 嵌入原子方法理论及其在材料科学中的应用-原子尺度材料设计理论. 长沙:湖南大学出版社,2003.
[57] Finnis M W and Sinclair J E. A simple empirical N-body potential for transition metals. Philos Mag A, 1984, 50: 45-55.
[58] Grujicic M, Zhao H, Krasko GL. International Journal of Refractory Metals & Hard Materials 1997, 15 (5-6): 341-355.
[59] Collins A, O’Handley R C, and Johnson K H. Bonding and magnetism in Fe-M (M=B,C,Si,N) alloys Phys. Rev. B, 1988, 38:3665-3670.
[60] Painter G S, Averill F W. Effects of segregation on grain-boundary cohesion: A density-functional cluster model of boron and sulfur in nickel. Phys. Rev. Lett. 1987, 58:234-237.
[61] Messmer R P. Local electronic structure of amorphous metal alloys using cluster models. Evidence for specific metalloid-metal interactions. Phys. Rev. B, 1981, 23:1616-1623.
[62] Tang S. Freeman A J, and Olson G B. Phosphorus-induced relaxation in a iron grain boundary: A cluster-model study. Phys. Rev. B, 1993, 47:2441-2445.
[63] Eberhart M E, Vvedensky D D. Localized Grain-Boundary Electronic States and Intergranular Fracture. Phys. Rev. Lett. 1987, 58:61-64.
[64] Rice J R, and Wang J S. Embrittlement of interfaces by solute segregation. Mater. Sci. Eng. A, 1989, 107:23-40.
[65] Wu R, Freeman A J, and Olson G B. First Principles Determination of the Effects of Phosphorus and Boron on Iron Grain Boundary Cohesion. Science, 1994, 265:376-380.
[66] Wu R, Freeman AJ, and Olson GB. Effects of carbon on Fe-grain-boundary cohesion: First-principles determination. Phys. Rev. B, 1996, 53:7504-7509.
[67] Geng W T, Freeman A J, Wu R, and Olson G B. Effect of Mo and Pd on the grain-boundary cohesion of Fe. Phys. Rev. B, 2000, 62:6208-6214.
[68] Geng W T, Freeman A J, and Olson G B. Influence of alloying additions on grain boundary cohesion of transition metals: First-principles determination and its phenomenological extension. Phys. Rev. B, 2001, 63:165415.
[69] Haydock R. The mobility of bonds at metal surfaces. J. Phys. C, 1981, 14:3807-3816.
[70] Messmer R and Briant C L. The role of chemical bonding in grain boundry embrittlement. Acta Metall. 1982, 30:457-467.
[71] Sutton A P and Vitek V. An atomistic study of tilt grain boundaries with substitutional impurities. Acta Metall. 1982, 30:2011-2033.
[72] Schweinfest R, Paxton A T, and Finnis M W. Bismuth embrittlement of copper is an atomic size effect. Nature, 2004, 432:1008-1011.
[73] Zhong L P, Wu R Q, Freeman A J, and Olson G B. Effects of Mn additions on the P embrittlement of the Fe grain boundary. Phys. Rev. B, 1997, 55:11133-11137.
[74] Hu Q M, Yang R, Xu D S, Hao Y L, and Li D. Energetics and electronic structure of grain boundaries and surfaces of B- and H-doped Ni3Al. Phys. Rev. B, 2003, 67:224203.
[75] Wang F H, Wang C Y, and Yang J L. The effect of boron on the electronic structure of grain boundaries in Ni3Al. J. Phys: Condens. Matter, 1996, 8:5527-5534.
[76] Wang F H, and Wang C Y. First-principles investigation of hydrogen embrittlement in polycrystalline Ni3Al. Phys. Rev. B, 1998, 57, 289-295.
[77] Wang F H, and Wang C Y. The effect of zirconium on the electronic structure of grain boundaries in Ni3Al. J. Phys: Condens. Matter, 1997, 9:4499-4508.
[78] Lu G, Kioussis N, Wu R, and Ciftan M. First-principles studies of the Σ5 tilt grain boundary in Ni3Al. Phys. Rev. B, 1999, 59:891-898.
[79] Djajaputra D, and Cooper B R. Systematic first-principles study of impurity hybridization in NiAl. Phys. Rev. B, 2002, 66:205108.
[80] Feng Y Q, Wang C Y. Electronic effects of light impurities on edge dislocation motion in iron at T=0 K. Journal of Alloys and Compounds, 2000, 312: 219–227.
[81] Yan J A, Wang C Y, Duan W H, and Wang S Y. Electronic states and doping effect of carbon in the edge-dislocation core of bcc iron. Phys. Rev. B, 2004, 69:214110.
[82] Song Y, Guo Z X, Yang R, and Li D. First Principles Study of Site Substitution of Ternary Elements in NiAl. Acta Materialia, 2001, 49:1647-1654.
[83] Hu Q M, Yang R, Xu D S, Hao Y L, and Li D. Geometric and electronic structure of Ti2AlX (X=V, Nb, or Ta). Phys. Rev. B, 2003, 68:054102.
[84] Medvedeva N I, Gornostyrev Y N, and Freeman A J. Carbon stabilized A15 Cr3Re precipitates and ductility enhancement of Cr-based alloys. Acta Mater., 2002, 50:2471-2476.
[85] Sun S N, Kioussis N, and Lim S P, et al. Impurity effects on atomic bonding in Ni3Al. Phys. Rev. B, 1995, 52:14421-14430.
[86] V. Fock. N?herungsmethode zur Losung des quanten-mechanischen Mehrk?rperprobleme. Z. Phys. 1930, 61:126-148.
[87] Born M, Oppenheimer J R. Zur Quqntentheorie der Molekeln. Ann. Physik, 1954, 84:457-480.
[88] Slater J C. Wave Functions in a Periodic Potential Phys. Rev. 1937, 51:846-851; An Augmented Plane Wave Method for the Periodic Potential Problem. ibid. 1953, 92:603-608.
[89] 李正中. 固体理论(第二版). 北京:高等教育出版,2002.
[90] 谢希德,陆栋,主编. 固体能带理论. 上海:复旦大学出版社,1998.
[91] Hohenberg P C and Kohn W. Inhomogeneous electron gas. Phys. Rev. B, 1964, 136: 864-871.
[92] Kohn W and Sham L J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140: A1133-A1138.
[93] Kohanoff J, and Gidopoulos N I. Handbook of Molecular Physics and Quantum Chemistry. Vol.5, p.532-568. edited by Wilson S. John Wiley & Sons, Ltd. Chichester, 2003.
[94] Kohn W. Nobel Lecture: Electronic structure of matter—wave functions and density functionals. Rev. Mod. Phys. 1999, 71: 1253-1266.
[95] Vosko S H, Wilk L, and Nusair M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys. 1980, 58: 1200-1211.
[96] Von Barth U, Hedin L. A local exchange-correlation potential for the spin polarized case. J. Phys. C, 1972, 5: 1629-1642.
[97] Perdew J P, Burke K, and Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77: 3865-3868; Erratum. Phys. Rev. Lett. 1997, 78: 1396.
[98] Becke A D. A multicenter numerical integration scheme for polyatomic molecules. J. Chem. Phys., 1988, 88: 2547-2553.
[99] Lee C, Yang W, Parr R G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B, 1988, 37: 785-789.
[100] Versluis L, Ziegler T. The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration. J. Chem. Phys. 1988, 88: 322-328.
[101] Andzelm J, Wimmer E, Salahub D R. Spin density functional approach to the chemistry of transition metal clusters: Gaussian-type orbital implementation. In: Salahub D R, Zerner M C, Eds. The Challenge of d-and f-Electrons: Theory and Computation. ACS Symposium ser. 1989, 394.
[102] Guenzburger D, and Ellis D E. Magnetism of Fe impurities in alkaline-earth metals and Al. Phys. Rev. B, 1992, 45:285-294.
[103] Ellis D E, Benesh G A, and Byrom E. Molecular cluster studies of binary alloys: LiAl. Phys. Rev. B, 1977, 16:3308-3313.
[104] Delley B, Ellis D E, Freeman A J, Baerends E J, and Post D. Phys. Rev. B, 1983, 27: 2132-2144.
[105] Delley B. An all-electron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 1990, 92:508-517.
[106] 肖慎修,王崇愚,陈天朗. 密度泛函理论的离散变分方法在化学和材料物理学中的应用. 北京:科学出版社,1998.
[107] DMol User Guide. Biosym/Molecular Simulations. 1995.
[108] Feynman R P. Forces in Molecules. Phys. Rev. 1939, 56:340-343.
[109] Martin R M. Electronic Structure-Basic Theory and Practical Methods. Cambridge University Press. 2004
[110] Payne M C, Teter M P, Allan D C, Arias T A, and Joannopoulos J D. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 1992, 64:1045–1097.
[111] 徐婉棠,喀兴林. 群论及其在固体物理中的应用. 北京:高等教育出版社,1999.
[112] Chadi D J, and Cohen M L. Special Points in the Brillouin Zone. Phys. Rev. B, 1973, 8:5747-5753.
[113] Monkhorst H J and Pack J D. Special points for Brillouin-zone integrations. Phys. Rev. B, 1976, 13: 5188-5192.
[114] Chadi D J. Special points for Brillouin-zone integrations. Phys. Rev. B, 1977, 16: 1746-1747.
[115] Pack J D, and Monkhorst H J. “Special points for Brillouin-zone intergrations”-a reply. Phys. Rev. B, 1977,16:1748-1749.
[116] Hamann D R, Schl ü ter M, and Chiang C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 1979, 43: 1494-1497.
[117] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B, 1990, 41: 7892–7895.
[118] Bl?chl P E. Projector augmented-wave method. Phys. Rev. B, 1994, 50: 17953-17979.
[119] Kresse G, and Joubert D. From ultrasoft pseudopotential to projecter augmented-wave method. Phys. Rev. B, 1999,59:1758-1775
[120] Resta R. Festk?rperprobleme: Advances in Solid-State Physics. edited by Grosse P. Vieweg, Braunschweig, 1985. Vol.25, p.183.
[121] Baroni S, de Gironcoli S, Dal Corso A, and Giannozzi P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 2001, 73:515-562.
[122] Frank W, Els?sser C, and F?hnle M. Ab initio Force-Constant Method for Phonon Dispersions in Alkali Metals. Phys. Rev. Lett. 1995, 74:1791-1794.
[123] Ye L H, Liu B G, Wang D S, and Han R S. Ab initio phonon dispersions of single-wall carbon nanotubes. Phys. Rev. B, 2004, 69:235409.
[124] 杨顺华. 晶体位错理论基础. 第一卷. 北京:科学出版社,1998.
[125] Griffith A A. The phenomenon of rupture and flow in solids. Phil. Trans. Royal Soc. 1920, A221:163-198.
[126] 郭雅芳. 铁中裂纹动力学研究及缺陷声子谱:[博士学位论文]. 北京:钢铁研究总院,2001.
[127] deCelis B, Argon A S, and Yip S. Molecular dynamics simulation of crack tip processes in alpha-iron and copper. I. J. Appl. Phys. 2003, 54: 4864-4878.
[128] Hirth J P and Lothe J. Theory of Dislocations (2nd ed.). New York: McGraw-Hill, 1982.
[129] McLean D. Grain boundaries in metals. Oxford: The Clarendon Press, 1957.
[130] Yang R, Wang Y M, Huang R Z, and Wang C Y. First-principles study on the effect of Mn and N on the cohesion of a γ-iron grain boundary. Phys. Rev. B, 2002, 65:094112.
[131] Lee D Y, Barrera E V, Stark J P, and Marcus H L. The Influence of Alloying Elements on Impurity-Induced Grain Boundary Embrittlement. Metall. Trans. A, 1984, 15:1415-1430.
[132] Venezuela P, Miwa R H, and Fazzio A. Carbon in SixGe1–x: An ab initio investigation. Phys. Rev. B, 2004, 69:115209.
[133] Kim S J, and Wayman C M. Strengthening behaviour and embrittlement phenomena in Fe-Ni-Mn- (Ti) maraging alloys. Mater. Sci. Eng. A, 1996, 207:22-29.
[134] Kittle C. Introduction to Solid State Physics, 4th edition. New York: Wiley, 1971, p.39.
[135] 张永刚,韩雅芳,陈国梁,郭建亭,万晓景,冯涤. 金属间化合物结构材料. 北京: 国防工业出版社, 2001, p.907.
[136] Fu M, and Sekhar J A. Processing, Microstructures, and Properties of Molybdenum Aluminosilicide. J. Am. Ceram. Soc. 1998, 81:3205-3219.
[137] Ramberg C E, and Worrell W L. Oxidation Kinetics and Composite Scale Formation in the System Mo(Al,Si)2. J. Am. Ceram. Soc. 2002, 85:444-452.
[138] Yanagihara K, Maruyama T, and Nugata K. High temperature oxidation of Mo-Si-X intermetallics (X = Al, Ti, Ta, Zr and Y). Intermetallics, 1995, 3:243-251.
[139] Liu Y, Shao G, and Tsakiropoulos P. Thermodynamic reassessment of the Mo–Si and Al–Mo–Si systems. Intermetallics, 2000, 8:953-962.
[140] Perdew J P, and Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B, 1992, 45:13244-13249.
[141] Tohei T, Kuwabara A, Yamamoto T, Oba F, and Tanaka I. General Rule for Displacive Phase Transitions in Perovskite Compounds Revisited by First Principles Calculations. Phys. Rev. Lett. 2005, 94:035502.
[142] Doland C M, and Nemanich R J. Phase formation during reactive molybdenum-silicide formation. J. Mater. Res. 1990, 5:2854-2864..
[143] Alouani M, Albers R C, and Methfessel M. Calculated elastic constants and structural properties of Mo and MoSi2. Phys. Rev. B. 1991, 43:6500-6509.
[144] 戴道生,钱昆明. 铁磁学(上册). 北京:科学出版社,1987.
[145] Zou J, and Fu C L. Structural, electronic, and magnetic properties of 3d transition-metal aluminides with equiatomic composition. Phys. Rev. B, 1995, 51:2115-2121.
[146] Nguyen-Manh, Paxton A T, Pettifor D G, and Pasturel A. On the phase stability of transition metal trialuminide compounds. Intermetallics, 1995, 3:9-14.
[147] Pankhurst D A, Nguyen-Manh D, and Pettifor D G. Electronic origin of structural trends across early transition-metal disilicides: Anomalous behavior of CrSi2. Phys. Rev. B, 2004, 69:075113.