铝基金属间化合物电子结构和力学性质的第一性原理研究
|
摘要
铝基金属间化合物有诸多优异的性能如低密度、高的比强度、优异的抗氧化和耐腐蚀性,在航空航天、国防军工及日常生活用品中得到广泛的应用。近年来的大量研究表明,电子结构决定材料的力学性质。考虑实验条件的限制如实验方法上的缺陷、实验设备的昂贵,实验操作的复杂性,这些因素使得测试结果不准确,实验上对铝基金属间化合物的研究较少,从电子层次上对铝基金属间化合物的力学性质进行研究则更少。而在原子、电子尺度上基于密度泛函理论的第一性原理方法能准确地预测物质的各种性质。本论文运用了基于密度泛函理论的第一性原理计算方法研究了铝基金属间化合物的晶体结构、电子结构和力学性质。论文主要分为两部分:第一部分详细分析了Al-Cu金属间化合物的电子结构及力学性质之间的关系;第二部分研究了点缺陷对立方结构铝基金属间化合物电子结构和力学性质的影响。具体内容如下:
1.基于密度泛函理论的第一性原理方法研究了铝铜系列中几种重要金属间化合物(Al2Cu、Al3Cu2和AlCu3)的晶体结构和电子结构。通过计算它们的表面电子功函数、延展性、电子态密度和电荷密度,定性地解释了其延展性的差异。并进一步探讨了合金电子结构与延展性之间的关系,特别是电子功函数同合金材料脆性或延展性之间的关系。结果发现:延展性随着金属间化合物电子功函数的增加而减小,除了AlCu3。这主要归因于电荷的转移,一方面由于铜的电负性大于铝的电负性,在原子弛豫的时候,会使原子从电负性小向电负性大的铜原子移动,从而引起电荷分布的变化,电荷分布的变化又引起表面偶极子势的增加,因而使得电子功函数增加;另一方面材料的力学性能由电荷密度分布的均匀性和对称性来决定,对称性越好,说明材料的可塑性越好。
2.基于第一性原理研究点缺陷对立方结构铝基合金电子结构和力学性质的影响。计算了空位下的晶格常数和平衡体积,发现计算得到的平衡晶格常数与实验值吻合较好;点缺陷形成能的计算表明AlCu3比AlNi3更易形成空位;形成能和结合能的研究表明Al7Cu24和Al7Ni24具有较好的结构稳定性和延展性;杨氏模量、切变模量、泊松比和各向异性因子等力学参量的计算发现,对于空位结构计算得到的晶格常数和弹性常数与已报道的实验及计算值相吻合,Al7Cu24和Al7Ni24满足立方结构机械稳定性条件;态密度和电荷密度合理地解释了空位对合金的结构稳定性和力学性质的影响。
Al-based intermetallics have wide application,because of their low density, high mechanic strength, corrosion resistance, simple productionprocess, low costs in comparison with other alloys, particularly the significant advantages of easy-recycling. Recent theoretical investigations have revealed that the primary origin of brittleness in intermetallics should be attributed to their electronic structures or chemical bond nature. However, data are very limited due to the complications of sample preparation and the limitations of experimental testing techniques, and the electronic nature of the mechanical properties of Al-based intermetallics is also not clear. Therefore,it is crucial to investigate the electronic structures in detail in order to understand brittleness completely.In this paper, we use the first–principle calculation based on the density functional theory to investigate the crystal structure, electronic structure and mechanical properties of Al-based intermetallics. Firstly, we report the relationship between the electrical and mechanical properties of the Al-Cu intermetallics. Secondly, we carry out a systematic first-principles study on the electronic structure and mechanical properties of Al-based intermetallics with cubic structure and vacancy point defects. The main contents of our work are:
1. We use the first–principles calculation based on the density functional theory to investigate the crystal structure and electronic structure of Al-Cu intermetallic compounds (Al2Cu、Al3Cu2 and AlCu3). We calculate work function, ductility, density of states and charge density. The result shows that density of states and charge density can qualitatively affect the mechanical properties of material. And further explore the relationship between the electronic structure and ductility, that is, the relationship of work function and the brittleness. We find that the ductility decreases with increase of work function of intermetic compounds, except AlCu3. It mainly change charge distribution. When the atoms relax, atoms can move from aluminum to copper as the electronegativity of copper is greater than the electronegativity of aluminum. This can cause changes in charge distribution and form the surface dipole potential which can increase the electronic work function and lead to changes of mechanical properties. On the other hand, the electronic structure and mechanical properties is the charge density distribution of the material uniformity and symmetry; the better symmetry the better plasticity of materials which corresponds to the symmetry of charge distribution.
2. Electronic structure and mechanical properties of Al-based alloys with cubic structure and vacancy have been investigated by using the first–principles calculation based on the density functional theory. Equilibrium structural parameters were derived and agreed well with experimental value. AlNi3 is easier to form vacancy point defects than AlCu3; the heat of formation and cohesive energy were calculated and showed that Al7Cu24 and Al7Ni24 had the better alloying ability and structural stability. Elastic constants and mechanical parameters such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and anisotropy have also been calculated. There are a little difference between the imperfect crystal structures and perfect crystal structures from the calculated results and the experimental data. Investigation of the mechanical properties shows that cubic structures with vacancy point defects obey well the requirement of mechanical stability for cubic crystals. Cubic structure with vacancy point defects has a good alloying ability and structural stability due to an increase in the bonding electron numbers below the Fermi level. The effects of the alloying ability, structural stability and mechanical properties with vacancy point defects could be reasonably described and explained in terms of the electronic structure (the density of states and charge density distribution).
1.基于密度泛函理论的第一性原理方法研究了铝铜系列中几种重要金属间化合物(Al2Cu、Al3Cu2和AlCu3)的晶体结构和电子结构。通过计算它们的表面电子功函数、延展性、电子态密度和电荷密度,定性地解释了其延展性的差异。并进一步探讨了合金电子结构与延展性之间的关系,特别是电子功函数同合金材料脆性或延展性之间的关系。结果发现:延展性随着金属间化合物电子功函数的增加而减小,除了AlCu3。这主要归因于电荷的转移,一方面由于铜的电负性大于铝的电负性,在原子弛豫的时候,会使原子从电负性小向电负性大的铜原子移动,从而引起电荷分布的变化,电荷分布的变化又引起表面偶极子势的增加,因而使得电子功函数增加;另一方面材料的力学性能由电荷密度分布的均匀性和对称性来决定,对称性越好,说明材料的可塑性越好。
2.基于第一性原理研究点缺陷对立方结构铝基合金电子结构和力学性质的影响。计算了空位下的晶格常数和平衡体积,发现计算得到的平衡晶格常数与实验值吻合较好;点缺陷形成能的计算表明AlCu3比AlNi3更易形成空位;形成能和结合能的研究表明Al7Cu24和Al7Ni24具有较好的结构稳定性和延展性;杨氏模量、切变模量、泊松比和各向异性因子等力学参量的计算发现,对于空位结构计算得到的晶格常数和弹性常数与已报道的实验及计算值相吻合,Al7Cu24和Al7Ni24满足立方结构机械稳定性条件;态密度和电荷密度合理地解释了空位对合金的结构稳定性和力学性质的影响。
Al-based intermetallics have wide application,because of their low density, high mechanic strength, corrosion resistance, simple productionprocess, low costs in comparison with other alloys, particularly the significant advantages of easy-recycling. Recent theoretical investigations have revealed that the primary origin of brittleness in intermetallics should be attributed to their electronic structures or chemical bond nature. However, data are very limited due to the complications of sample preparation and the limitations of experimental testing techniques, and the electronic nature of the mechanical properties of Al-based intermetallics is also not clear. Therefore,it is crucial to investigate the electronic structures in detail in order to understand brittleness completely.In this paper, we use the first–principle calculation based on the density functional theory to investigate the crystal structure, electronic structure and mechanical properties of Al-based intermetallics. Firstly, we report the relationship between the electrical and mechanical properties of the Al-Cu intermetallics. Secondly, we carry out a systematic first-principles study on the electronic structure and mechanical properties of Al-based intermetallics with cubic structure and vacancy point defects. The main contents of our work are:
1. We use the first–principles calculation based on the density functional theory to investigate the crystal structure and electronic structure of Al-Cu intermetallic compounds (Al2Cu、Al3Cu2 and AlCu3). We calculate work function, ductility, density of states and charge density. The result shows that density of states and charge density can qualitatively affect the mechanical properties of material. And further explore the relationship between the electronic structure and ductility, that is, the relationship of work function and the brittleness. We find that the ductility decreases with increase of work function of intermetic compounds, except AlCu3. It mainly change charge distribution. When the atoms relax, atoms can move from aluminum to copper as the electronegativity of copper is greater than the electronegativity of aluminum. This can cause changes in charge distribution and form the surface dipole potential which can increase the electronic work function and lead to changes of mechanical properties. On the other hand, the electronic structure and mechanical properties is the charge density distribution of the material uniformity and symmetry; the better symmetry the better plasticity of materials which corresponds to the symmetry of charge distribution.
2. Electronic structure and mechanical properties of Al-based alloys with cubic structure and vacancy have been investigated by using the first–principles calculation based on the density functional theory. Equilibrium structural parameters were derived and agreed well with experimental value. AlNi3 is easier to form vacancy point defects than AlCu3; the heat of formation and cohesive energy were calculated and showed that Al7Cu24 and Al7Ni24 had the better alloying ability and structural stability. Elastic constants and mechanical parameters such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and anisotropy have also been calculated. There are a little difference between the imperfect crystal structures and perfect crystal structures from the calculated results and the experimental data. Investigation of the mechanical properties shows that cubic structures with vacancy point defects obey well the requirement of mechanical stability for cubic crystals. Cubic structure with vacancy point defects has a good alloying ability and structural stability due to an increase in the bonding electron numbers below the Fermi level. The effects of the alloying ability, structural stability and mechanical properties with vacancy point defects could be reasonably described and explained in terms of the electronic structure (the density of states and charge density distribution).
引文
[1] Nie J and Muddle B. Strengthening of an Al-Cu-Sn alloy by deformation-resistant precipitate plates [J]. Acta Materialia, 2008, 56(14): 3490-3501.
[2] Uyyuru R, Surappa M and Brusethaug S. Effect of reinforcement volume fraction and size distribution on the tribological behavior of Al-composite/brake pad tribo-couple [J]. Wear, 2006, 260(11-12): 1248-1255.
[3] Yanbin L, et al. Enhanced fatigue crack propagation resistance of an Al-Cu-Mg alloy by artificial aging [J]. Materials Science and Engineering: A, 2008, 492(1-2): 333-336.
[4] Zhang S and Wang F. Comparison of friction and wear performances of brake material drysliding against two aluminum matrix composites reinforced with different SiC particles [J].Journal of Materials Processing Technology, 2007, 182(1-3): 122-127.
[5]朴东学,齐笑冰,李惠玉,汽车轻量化用金属材料的现状与发展[J]. 1999, 6: 38-40.
[6] Bakavos D, et al.The effect of silver on microstructural evolution in two 2xxx series Al-alloyswith a high Cu:Mg ratio during ageing to a T8 temper [J]. Material Science and Engineering A,2008,492: 214-223.
[7] Guo J and Ohtera K. Microstructures and mechanical properties of rapidly solidified high strength Al-Ni based alloys [J]. Acta Materialia, 1998, 46(11): 3829-3838.
[8]李云凯.金属材料学[M].北京:北京理工大学出版社, 2006: 140-155.
[9]彭晓东,刘江.轻合金在汽车工业中的应用[J].汽车工艺与材料, 1999: 1-5.
[10]卢邦洪.贵金属材料的接触电阻及测量装置[J]. 1995,16(l): 30-33.
[11] Kurum E, Dong H and Hunt J. Microsegregation in Al-Cu Alloys [J]. Metallurgical and Materials Transactions A, 2005, 36(11): 3103-3110.
[12] Mu?oz-Morris M A, et al. Refinement of precipitates and deformation substructure in an Al-Cu-Li alloy during heavy rolling at elevated temperatures [J]. Materials Science and Engineering: A, 2008,492(1-2): 268-275.
[13] Xie F, et al. Microstructure and microsegregation in Al-rich Al-Cu-Mg alloys [J]. Acta Materialia, 1999, 47(2): 489-500.
[14] Zeren M. Effect of copper and silicon content on mechanical properties in Al-Cu-Si-Mg alloys [J]. Journal of Materials Processing Technology, 2005, 169(2): 292-298.
[15] Hutchinson C, et al. On the origin of the high coarsening resistance of [Omega] plates in Al-Cu-Mg-Ag Alloys [J]. Acta Materialia, 2001,49(14): 2827-2841.
[16] Lee C, Choi Y and Park I. Stress corrosion cracking behavior of Al- Cu- Li- Mg- Zr (- Ag) alloys [J]. Metals and Materials International, 2002, 8(2): 191-196.
[17] Olafsson P and Sandstrom R. Calculations of electrical resistivity for Al-Cu and Al-Mg-Si alloys [J]. Materials Science and Technology, 2001,17(6): 655-662.
[18] Weihony L, Xighng B and Haiyong L.Interaction between rare earth Ce and hydrogen in Al-Cu eutectic alloy melt [J]. Acta Metallrugica Sinica, 2001, 8.
[19] Wang J. Dislocation nucleation and the intrinsic fracture behavior of L12 intermetallic alloys [J]. Acta Materialia, 1998, 46(8): 2663-2674.
[20] Kioussis N, et al. Topology of electronic charge density and energetics of planar faults in fcc metals [J]. Physical Review Letters, 2002, 88(12): 125501.
[21] Fu C, et al. Phase stability, bonding mechanism, and elastic constants of Mo5Si3 by first-principles calculation [J]. Intermetallics, 1999, 7(2): 179-184.
[22] Lu G, et al. First-principles studies of the∑5 tilt grain boundary in Ni3Al [J]. Physical Review B, 1999, 59(2): 891-898.
[23]郭俊梅,邓德国,潘健生等.计算材料学与材料设计[J].贵金属, 1999,20(4): 62-68.
[24]邹卫东.从头计算的分子动力学的理论基础[J].咸宁师专学报, 2001, 21(6): 13-18.
[25] Gong H, Nishi Y, and Cho K. Effects of strain and interface on work function of a Nb¨CW metal gate system [J]. Applied Physics Letters, 2007, 91: 242105.
[26] Zhou W, et al. Structural, elastic, and electronic properties of Al-Cu intermetallics from first-principles calculations [J]. Journal of Electronic Materials, 2009,38(2): 356-364.
[27] Li W, et al., An electronic criterion for the intrinsic embrittlement of structural intermetallic compounds [J]. Journal of Applied Physics, 2005, 98: 083503.
[28]邢胜娣,余瑞璜.金属间化合物Ti3Al的价电子结构及其力学性能[J].吉林大学学报, 1985. 1.
[29]张建民,张瑞林,余瑞璜. Fe-Al系金属间化合物的环境脆性机理研究[J].中国科学, 1996, 26(2): 116-121.
[30]李文,关振中. Ti-Al系金属间化合物力学性能的电子理论[J].机械工程材料, 1996, 20(2): p. 9-12.
[31] Wang X, et al., First-principles calculations on the electronic structure and cohesive properties of titanium stannides [J]. Intermetallics, 2009, 17(9): 768-773.
[32]沈鹤年.晶体结构缺陷中的点缺陷[J].山东轻工业学院学报, 1987, (1): 13-16.
[33] Mattsson T and Mattsson A. Calculating the vacancy formation energy in metals: Pt, Pd, and Mo [J]. Physical Review B, 2002, 66(21): 214110.
[34]冯庆.锐钛矿型TiO2空位缺陷性质的第一性原理研究[J].重庆师范大学学报, 2009, 26(1): 78-81.
[35]陈律. L10-TiA1合金点缺陷结构的赝势平面波方法研究[J].中国材料科技与设备, 2009, 2: 63-66.
[36]胡文军,李建国,刘占芳,唐录成.介观尺度计算材料学研究进展[J].材料导报, 2004, 18: 12-18.
[37]熊家炬.介观尺度计算材料学研究进展[J].材料设计, 2000, 21: 10-19.
[38]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版社, 1998.
[39] Hohenberg P and Kohn W. Inhomogeneous electron gas [J]. Phys. Rev, 1964, 136(3B): B864-B871.
[40] Kohn W and Sham L. Self-consistent equations including exchange and correlation effects [J]. Phys. Rev, 1965, 140(4A): A1133-A1138.
[41] Markmaitree T, Ren R and Shaw L. Enhancement of lithium amide to lithium imide transition via mechanical activation [J]. J. Phys. Chem. B, 2006, 110(41): 20710-20718.
[42] Shaw L, et al., Effects of mechanical activation on dehydrogenation of the lithium amide and lithium hydride system [J]. Journal of Alloys and Compounds, 2008,448(1-2): 263-271.
[43] Payne M, et al. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients [J]. Reviews of Modern Physics, 1992, 64(4): 1045-1097.
[44] Perdew J and Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy [J]. Physical Review B, 1992,45(23): 13244-13249.
[45] Perdew J, et al. Applications of the generalized gradient approximation for exchange and correlation [J]. Phys Rev B, 1993, 46: 6671-6687.
[46] Slater J. A simplification of the Hartree-Fock method [J]. Physical Review, 1951, 81(3): 385-390.
[47] Slater J, T. Wilson and J. Wood. Comparison of several exchange potentials for electrons in cu ion [J]. Phys. Rev, 1969, 179(1): 28-38.
[48] Wigner E. On the interaction of electrons in metals [J]. Physical Review, 1934, 46(11): 1002-1011.
[49] Ceperley D and Alder B. Ground state of the electron gas by a stochastic method [J]. Physical Review Letters, 1980, 45(7): 566-569.
[50] Perdew J, Burke K and Ernzerhof M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996,77(18): 3865-3868.
[51] Liu C, Liu X and Borucki L. Defect generation and diffusion mechanisms in Al and Al-Cu [J]. Applied Physics Letters, 1999, 74: 34.
[52] Palasantzas G and Backx G. Self-affine roughness effects on the double-layer charge density and capacitance in the nonlinear regime [J]. The Journal of chemical physics, 2003, 118: 4631.
[53] Zilberman S and Persson B. Nanoadhesion of elastic bodies: roughness and temperature effects [J]. The Journal of chemical physics, 2003, 118: 6473.
[54] Li W and Li D Y. Effect of surface geometrical configurations induced by microcracks on the electron work function [J]. Acta Materialia, 2005,53(14): 3871-3878.
[55] Pugh S. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J]. Philosophical Magazine Series 7, 1954, 45(367): 823-843.
[56] Kresse G and Furthmuller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set [J]. Computational Materials Science, 1996, 6(1): 15-50.
[57] Kresse G and Hafner J. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium [J]. Physical Review B, 1994, 49: 14251.
[58] Bl?chl P E. Projector augmented-wave method [J]. Physical Review B, 1994, 50: 17953.
[59] Kresse G and Joubert D. From ultrasoft pseudopotentials to the projector augmented-wavemethod [J]. Physical Review B, 1999, 59: 1758.
[60] Sun S N, Kioussis N and Ciftan M. First-principles determination of the effects of boron and sulfur on the ideal cleavage fracture in Ni3Al [J]. Physical Review B, 1996,54: 3074.
[61] Perdew J P and Zunger A. Self-interaction correction to density-functional approximations for many-electron systems [J]. Physical Review B, 1981, 23: 5048.
[62] Monkhorst H J and Pack J D. Special points for Brillouin-zone integrations [J]. Physical Review B, 1976, 13: 5188.
[63] Debili M, Boukhris N and Lallouche M. Metastable ordered Cu3Al phase in sputter-deposited Al-Cu alloys system [J]. 2006, Wiley-VCH: 65.
[64] Meetsma A, De Boer J L and Van Smaalen S. Refinement of the crystal structure of tetragonal Al2Cu [J]. Journal of Solid State Chemistry, 1989,83(2): 370-372.
[65] Ramachandrarao P and Laridjani M. A metastable phase Al3Cu2 [J]. Journal of Materials Science, 1974, 9(3): 434-437.
[66]孙立忠,陈效双,郭旭光,等. CdTe和HgTe能带结构的第一性原理计算[J].红外与毫米波学报, 2004, 23(4): 271-275.
[67] Wolverton C and Ozoli?? V. Entropically favored ordering: the metallurgy of Al2Cu revisited [J]. Physical Review Letters, 2001, 86: 5518.
[68] Murray J. The aluminium-copper system [J]. International metals reviews, 1985, 30(5): 211-233.
[69] Leung T C, et al. Relationship between surface dipole, work function and charge transfer: Some exceptions to an established rule [J]. Physical Review B, 2003, 68(19): 195408.
[70] Wang X, Li W and Peng J. Correlation between ductility and work function in NiAl-Ce-Cr alloys [J]. Philosophical Magazine Letters, 2009, 89(2): 120-125.
[71] Nylén J, et al. Structural relationships, phase stability and bonding of compounds PdSnn (n=2, 3, 4) [J]. Solid State Sciences, 2004, 6(1): 147-155.
[72] Jordan J L, Deevi S C. Vacancy formation and effects in FeAl [J]. Intermetallics, 2003,11:507-528.
[73]陈丽娟,候柱峰,朱梓忠等. LiAl中空位形成能的第一原理计算[J].物理学报,2003,9: 2229-2234.
[74] Maeda T and Wada T. First-principles calculation of defect formation energy in chalcopyrite-type CuInSe2, CuGaSe2 and CuAlSe2 [J]. Journal of Physics and Chemistry of Solids, 2005, 66(11): 1924-1927.
[75] Ravindran P, et al. Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi [J]. Journal of Applied Physics, 1998, 84: 4891.
[76] Hill R. The elastic behaviour of a crystalline aggregate [J]. Proceedings of the Physical Society. Section A, 1952, 65: 349-354.
[77] Mattesini M, Ahuja R and Johansson B. Cubic Hf3N4 and Zr3N4: a class of hard materials [J]. Physical Review B, 2003, 68: 184108.
[78] Beckstein O, et al. First-principles elastic constants and electronic structure of alpha -Pt2Siand PtSi [J]. Physical Review B, 2001, 63: 134112.
[79] Ravindran P, et al. Detailed electronic structure studies on superconducting MgB2 and related compounds [J]. Physical Review B, 2001, 64: 224509.
[80] Born M and Huang K. Dynamical theory of crystal lattices [J]. 1988: Oxford University Press, USA.
[81] Rao P, et al. The high-temperature thermal expansion of Ni3Al measured by X-ray diffraction and dilation methods [J]. Journal of Physics: Condensed Matter, 1989, 1: 5357-5361.
[82] Zobov V, et al. Calculations of the thermal expansion,cohesive energy and thermodynamic stability of a Vander Waals crystal-fullerene C60 [J]. Phys. Lett.A, 1995,198:223-229.
[83] Karki B, et al. Structure and elasticity of MgO at high pressure [J]. American Mineralogist, 1997, 82(1): 51-60.
[2] Uyyuru R, Surappa M and Brusethaug S. Effect of reinforcement volume fraction and size distribution on the tribological behavior of Al-composite/brake pad tribo-couple [J]. Wear, 2006, 260(11-12): 1248-1255.
[3] Yanbin L, et al. Enhanced fatigue crack propagation resistance of an Al-Cu-Mg alloy by artificial aging [J]. Materials Science and Engineering: A, 2008, 492(1-2): 333-336.
[4] Zhang S and Wang F. Comparison of friction and wear performances of brake material drysliding against two aluminum matrix composites reinforced with different SiC particles [J].Journal of Materials Processing Technology, 2007, 182(1-3): 122-127.
[5]朴东学,齐笑冰,李惠玉,汽车轻量化用金属材料的现状与发展[J]. 1999, 6: 38-40.
[6] Bakavos D, et al.The effect of silver on microstructural evolution in two 2xxx series Al-alloyswith a high Cu:Mg ratio during ageing to a T8 temper [J]. Material Science and Engineering A,2008,492: 214-223.
[7] Guo J and Ohtera K. Microstructures and mechanical properties of rapidly solidified high strength Al-Ni based alloys [J]. Acta Materialia, 1998, 46(11): 3829-3838.
[8]李云凯.金属材料学[M].北京:北京理工大学出版社, 2006: 140-155.
[9]彭晓东,刘江.轻合金在汽车工业中的应用[J].汽车工艺与材料, 1999: 1-5.
[10]卢邦洪.贵金属材料的接触电阻及测量装置[J]. 1995,16(l): 30-33.
[11] Kurum E, Dong H and Hunt J. Microsegregation in Al-Cu Alloys [J]. Metallurgical and Materials Transactions A, 2005, 36(11): 3103-3110.
[12] Mu?oz-Morris M A, et al. Refinement of precipitates and deformation substructure in an Al-Cu-Li alloy during heavy rolling at elevated temperatures [J]. Materials Science and Engineering: A, 2008,492(1-2): 268-275.
[13] Xie F, et al. Microstructure and microsegregation in Al-rich Al-Cu-Mg alloys [J]. Acta Materialia, 1999, 47(2): 489-500.
[14] Zeren M. Effect of copper and silicon content on mechanical properties in Al-Cu-Si-Mg alloys [J]. Journal of Materials Processing Technology, 2005, 169(2): 292-298.
[15] Hutchinson C, et al. On the origin of the high coarsening resistance of [Omega] plates in Al-Cu-Mg-Ag Alloys [J]. Acta Materialia, 2001,49(14): 2827-2841.
[16] Lee C, Choi Y and Park I. Stress corrosion cracking behavior of Al- Cu- Li- Mg- Zr (- Ag) alloys [J]. Metals and Materials International, 2002, 8(2): 191-196.
[17] Olafsson P and Sandstrom R. Calculations of electrical resistivity for Al-Cu and Al-Mg-Si alloys [J]. Materials Science and Technology, 2001,17(6): 655-662.
[18] Weihony L, Xighng B and Haiyong L.Interaction between rare earth Ce and hydrogen in Al-Cu eutectic alloy melt [J]. Acta Metallrugica Sinica, 2001, 8.
[19] Wang J. Dislocation nucleation and the intrinsic fracture behavior of L12 intermetallic alloys [J]. Acta Materialia, 1998, 46(8): 2663-2674.
[20] Kioussis N, et al. Topology of electronic charge density and energetics of planar faults in fcc metals [J]. Physical Review Letters, 2002, 88(12): 125501.
[21] Fu C, et al. Phase stability, bonding mechanism, and elastic constants of Mo5Si3 by first-principles calculation [J]. Intermetallics, 1999, 7(2): 179-184.
[22] Lu G, et al. First-principles studies of the∑5 tilt grain boundary in Ni3Al [J]. Physical Review B, 1999, 59(2): 891-898.
[23]郭俊梅,邓德国,潘健生等.计算材料学与材料设计[J].贵金属, 1999,20(4): 62-68.
[24]邹卫东.从头计算的分子动力学的理论基础[J].咸宁师专学报, 2001, 21(6): 13-18.
[25] Gong H, Nishi Y, and Cho K. Effects of strain and interface on work function of a Nb¨CW metal gate system [J]. Applied Physics Letters, 2007, 91: 242105.
[26] Zhou W, et al. Structural, elastic, and electronic properties of Al-Cu intermetallics from first-principles calculations [J]. Journal of Electronic Materials, 2009,38(2): 356-364.
[27] Li W, et al., An electronic criterion for the intrinsic embrittlement of structural intermetallic compounds [J]. Journal of Applied Physics, 2005, 98: 083503.
[28]邢胜娣,余瑞璜.金属间化合物Ti3Al的价电子结构及其力学性能[J].吉林大学学报, 1985. 1.
[29]张建民,张瑞林,余瑞璜. Fe-Al系金属间化合物的环境脆性机理研究[J].中国科学, 1996, 26(2): 116-121.
[30]李文,关振中. Ti-Al系金属间化合物力学性能的电子理论[J].机械工程材料, 1996, 20(2): p. 9-12.
[31] Wang X, et al., First-principles calculations on the electronic structure and cohesive properties of titanium stannides [J]. Intermetallics, 2009, 17(9): 768-773.
[32]沈鹤年.晶体结构缺陷中的点缺陷[J].山东轻工业学院学报, 1987, (1): 13-16.
[33] Mattsson T and Mattsson A. Calculating the vacancy formation energy in metals: Pt, Pd, and Mo [J]. Physical Review B, 2002, 66(21): 214110.
[34]冯庆.锐钛矿型TiO2空位缺陷性质的第一性原理研究[J].重庆师范大学学报, 2009, 26(1): 78-81.
[35]陈律. L10-TiA1合金点缺陷结构的赝势平面波方法研究[J].中国材料科技与设备, 2009, 2: 63-66.
[36]胡文军,李建国,刘占芳,唐录成.介观尺度计算材料学研究进展[J].材料导报, 2004, 18: 12-18.
[37]熊家炬.介观尺度计算材料学研究进展[J].材料设计, 2000, 21: 10-19.
[38]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版社, 1998.
[39] Hohenberg P and Kohn W. Inhomogeneous electron gas [J]. Phys. Rev, 1964, 136(3B): B864-B871.
[40] Kohn W and Sham L. Self-consistent equations including exchange and correlation effects [J]. Phys. Rev, 1965, 140(4A): A1133-A1138.
[41] Markmaitree T, Ren R and Shaw L. Enhancement of lithium amide to lithium imide transition via mechanical activation [J]. J. Phys. Chem. B, 2006, 110(41): 20710-20718.
[42] Shaw L, et al., Effects of mechanical activation on dehydrogenation of the lithium amide and lithium hydride system [J]. Journal of Alloys and Compounds, 2008,448(1-2): 263-271.
[43] Payne M, et al. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients [J]. Reviews of Modern Physics, 1992, 64(4): 1045-1097.
[44] Perdew J and Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy [J]. Physical Review B, 1992,45(23): 13244-13249.
[45] Perdew J, et al. Applications of the generalized gradient approximation for exchange and correlation [J]. Phys Rev B, 1993, 46: 6671-6687.
[46] Slater J. A simplification of the Hartree-Fock method [J]. Physical Review, 1951, 81(3): 385-390.
[47] Slater J, T. Wilson and J. Wood. Comparison of several exchange potentials for electrons in cu ion [J]. Phys. Rev, 1969, 179(1): 28-38.
[48] Wigner E. On the interaction of electrons in metals [J]. Physical Review, 1934, 46(11): 1002-1011.
[49] Ceperley D and Alder B. Ground state of the electron gas by a stochastic method [J]. Physical Review Letters, 1980, 45(7): 566-569.
[50] Perdew J, Burke K and Ernzerhof M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996,77(18): 3865-3868.
[51] Liu C, Liu X and Borucki L. Defect generation and diffusion mechanisms in Al and Al-Cu [J]. Applied Physics Letters, 1999, 74: 34.
[52] Palasantzas G and Backx G. Self-affine roughness effects on the double-layer charge density and capacitance in the nonlinear regime [J]. The Journal of chemical physics, 2003, 118: 4631.
[53] Zilberman S and Persson B. Nanoadhesion of elastic bodies: roughness and temperature effects [J]. The Journal of chemical physics, 2003, 118: 6473.
[54] Li W and Li D Y. Effect of surface geometrical configurations induced by microcracks on the electron work function [J]. Acta Materialia, 2005,53(14): 3871-3878.
[55] Pugh S. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J]. Philosophical Magazine Series 7, 1954, 45(367): 823-843.
[56] Kresse G and Furthmuller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set [J]. Computational Materials Science, 1996, 6(1): 15-50.
[57] Kresse G and Hafner J. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium [J]. Physical Review B, 1994, 49: 14251.
[58] Bl?chl P E. Projector augmented-wave method [J]. Physical Review B, 1994, 50: 17953.
[59] Kresse G and Joubert D. From ultrasoft pseudopotentials to the projector augmented-wavemethod [J]. Physical Review B, 1999, 59: 1758.
[60] Sun S N, Kioussis N and Ciftan M. First-principles determination of the effects of boron and sulfur on the ideal cleavage fracture in Ni3Al [J]. Physical Review B, 1996,54: 3074.
[61] Perdew J P and Zunger A. Self-interaction correction to density-functional approximations for many-electron systems [J]. Physical Review B, 1981, 23: 5048.
[62] Monkhorst H J and Pack J D. Special points for Brillouin-zone integrations [J]. Physical Review B, 1976, 13: 5188.
[63] Debili M, Boukhris N and Lallouche M. Metastable ordered Cu3Al phase in sputter-deposited Al-Cu alloys system [J]. 2006, Wiley-VCH: 65.
[64] Meetsma A, De Boer J L and Van Smaalen S. Refinement of the crystal structure of tetragonal Al2Cu [J]. Journal of Solid State Chemistry, 1989,83(2): 370-372.
[65] Ramachandrarao P and Laridjani M. A metastable phase Al3Cu2 [J]. Journal of Materials Science, 1974, 9(3): 434-437.
[66]孙立忠,陈效双,郭旭光,等. CdTe和HgTe能带结构的第一性原理计算[J].红外与毫米波学报, 2004, 23(4): 271-275.
[67] Wolverton C and Ozoli?? V. Entropically favored ordering: the metallurgy of Al2Cu revisited [J]. Physical Review Letters, 2001, 86: 5518.
[68] Murray J. The aluminium-copper system [J]. International metals reviews, 1985, 30(5): 211-233.
[69] Leung T C, et al. Relationship between surface dipole, work function and charge transfer: Some exceptions to an established rule [J]. Physical Review B, 2003, 68(19): 195408.
[70] Wang X, Li W and Peng J. Correlation between ductility and work function in NiAl-Ce-Cr alloys [J]. Philosophical Magazine Letters, 2009, 89(2): 120-125.
[71] Nylén J, et al. Structural relationships, phase stability and bonding of compounds PdSnn (n=2, 3, 4) [J]. Solid State Sciences, 2004, 6(1): 147-155.
[72] Jordan J L, Deevi S C. Vacancy formation and effects in FeAl [J]. Intermetallics, 2003,11:507-528.
[73]陈丽娟,候柱峰,朱梓忠等. LiAl中空位形成能的第一原理计算[J].物理学报,2003,9: 2229-2234.
[74] Maeda T and Wada T. First-principles calculation of defect formation energy in chalcopyrite-type CuInSe2, CuGaSe2 and CuAlSe2 [J]. Journal of Physics and Chemistry of Solids, 2005, 66(11): 1924-1927.
[75] Ravindran P, et al. Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi [J]. Journal of Applied Physics, 1998, 84: 4891.
[76] Hill R. The elastic behaviour of a crystalline aggregate [J]. Proceedings of the Physical Society. Section A, 1952, 65: 349-354.
[77] Mattesini M, Ahuja R and Johansson B. Cubic Hf3N4 and Zr3N4: a class of hard materials [J]. Physical Review B, 2003, 68: 184108.
[78] Beckstein O, et al. First-principles elastic constants and electronic structure of alpha -Pt2Siand PtSi [J]. Physical Review B, 2001, 63: 134112.
[79] Ravindran P, et al. Detailed electronic structure studies on superconducting MgB2 and related compounds [J]. Physical Review B, 2001, 64: 224509.
[80] Born M and Huang K. Dynamical theory of crystal lattices [J]. 1988: Oxford University Press, USA.
[81] Rao P, et al. The high-temperature thermal expansion of Ni3Al measured by X-ray diffraction and dilation methods [J]. Journal of Physics: Condensed Matter, 1989, 1: 5357-5361.
[82] Zobov V, et al. Calculations of the thermal expansion,cohesive energy and thermodynamic stability of a Vander Waals crystal-fullerene C60 [J]. Phys. Lett.A, 1995,198:223-229.
[83] Karki B, et al. Structure and elasticity of MgO at high pressure [J]. American Mineralogist, 1997, 82(1): 51-60.