稀土镁合金β'和β"以及6HLPS相的第一性原理研究
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摘要
镁合金密度低、力学性能优异、电磁屏蔽能力强,在航空航天、交通运输、电子等领域具有重要的应用价值和应用前景。然而,镁合金绝对强度低、高温抗蠕变能力差,这些都大大限制了其应用。含稀土镁合金具有强度高、抗蠕变能力强和热稳定性好的优点,得到了材料研究者的广泛关注。本文利用基于密度泛函理论的第一性原理计算方法,研究了稀土镁合金部分中间相的结构、力学和电子属性。所得主要结果如下:
1.理论上确定了Mg–Gd系合金中β'相的晶格参数,并计算了正交晶体9个独立的弹性常数。Mg15Gd不符合正交晶体的力学稳定性准则,是一种力学不稳定结构。采用Voigt–Reuss–Hill(VRH)近似,得到了Mg7Gd的多晶体模量B,剪切模量G,杨氏模量E和泊松比ν。通过分析电子态密度和电荷密度,发现镁和钆之间形成了方向性的共价键。最后,还计算得到了Mg7Gd的密度、波速度和德拜温度。
2.通过理论计算,得到了Mg–Gd系合金中β"相的结构参数,从形成能的角度说明它是能够稳定存在的。计算的九个独立的弹性常数符合力学稳定性准则,并从单晶弹性常数得到了β"相的多晶体模量B,剪切模量G,杨氏模量E和泊松比ν。从这些参数可以看出,它的力学性能并不十分优异。它的延展性较好,弹性各项异性行为也比较显著。同β'相一样,体系内也存在较强的方向性共价键。
3.理论上调查了Mg_(97)Zn_1Y_2合金系统中6H型ABACAB长周期堆垛(LPS)结构的微结构、稳定性和电子属性特征。Y和Zn原子在浓度较低时主要分布于层错缺陷层,这个结果与实验观察一致。Y和Zn原子倾向于紧密排列,这样可以抵消原子半径不同带来的应变,使的6H型结构能量上更稳定。通过计算不同固溶原子含量时的结合能,发现Y元素增强了6H结构的稳定性,在改善合金的抗蠕变能力方面起到了重要作用。Zn原子位于两个不匹配的层错层时将导致晶格畸变,进一步的分析表明Y和Zn原子紧密排列将会削弱了畸变的幅度。通过分析电子态密度和电荷密度,发现Mg原子和Y原子之间形成了较强的共价键,这将增加合金强度。Mg原子与Zn原子之间的杂化作用广泛而均匀存在,这对改善合金延展性有帮助。
Magnesium alloys have important application value and prospect in the aerospace, transportation, electronics fields due to their low density, excellent mechanical properties, and electromagnetic shielding ability. However, the applications are still limited because of the lower strength, inferior fatigue and creep resistance at elevated temperature. Mg-rare earth alloys have received material researchers’great interest because of their high strength, good creep resistance and thermal stability. In this paper, we carried out first-principles calculations based on density functional theory to study on the structural, mechanical and electronic properties of the intermediate phase in Mg alloys. The obtained main results are as follows:
1. We determined the lattice parameters ofβ' phase in Mg–Gd alloy theoretically and calculated the nine independent elastic constants of the orthogonal crystal. The nine independent elastic constants did not meet the mechanical stability criteria, which suggest the reported Mg15Gd is a mechanically unstable structure. The polycrystalline bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratioνfor Mg7Gd are calculated within the scheme of Voigt–Reuss–Hill(VRH) approximation. We found the covalent bond was formed between the Mg and Gd atoms based on the analysis of the density of states and charge density. Finally, the density, wave velocity and Debye temperature of Mg7Gd are calculated.
2. The structural parameters ofβ" phase in Mg–Gd alloy are determined. The obtained formation enthalpy indicates that theβ" phase Mg3Gd could be formed energetically. The nine independent elastic constants are calculated, which suggest the Mg3Gd is mechanically stable. The polycrystalline bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratioνforβ" phase Mg3Gd are calculated from the elastic constants. It seems that the improvement of mechanical properties is limited after alloying from these parameters. Theβ" phase Mg3Gd is a ductile material and exhibits the elastic anisotropy apparently. Just as theβ' phase, the directional covalent bonding was formed in the system.
3. The microstructure, stability and electronic properties of the 6H-type ABACAB LPS phase in Mg_(97)Zn_1Y_2 are investigated theoretically. The enrichment of Y and Zn atoms occurs in the stacking fault defect layers, which is in accordance with the experimental observations. The present calculated results still show clearly that the Y and Zn atoms are preferably arranged closely. It is reasonable that the two atoms arrange closely to cancel strain due to the different atomic radii, and then lead the structure energetically more stable. The Y element enhances the structural stability from the calculated cohesive energy. It is clearly that the Y element would improve the creep property of alloy. The Zn atoms located in two different misfit fault layers would lead to lattice distortion. Further analysis shows that the intimate arrangement of Y and Zn atoms would weaken the distortion. Based on the analysis of the density of states, we found the covalent bonding exists between the Mg and Gd atoms which would enhance the strength of alloy. The hybridization between Mg and Zn is clear in entire region and the variation of hybridization is small. So this is helpful for improving the ductility of the 6H-type LPS structure.
1.理论上确定了Mg–Gd系合金中β'相的晶格参数,并计算了正交晶体9个独立的弹性常数。Mg15Gd不符合正交晶体的力学稳定性准则,是一种力学不稳定结构。采用Voigt–Reuss–Hill(VRH)近似,得到了Mg7Gd的多晶体模量B,剪切模量G,杨氏模量E和泊松比ν。通过分析电子态密度和电荷密度,发现镁和钆之间形成了方向性的共价键。最后,还计算得到了Mg7Gd的密度、波速度和德拜温度。
2.通过理论计算,得到了Mg–Gd系合金中β"相的结构参数,从形成能的角度说明它是能够稳定存在的。计算的九个独立的弹性常数符合力学稳定性准则,并从单晶弹性常数得到了β"相的多晶体模量B,剪切模量G,杨氏模量E和泊松比ν。从这些参数可以看出,它的力学性能并不十分优异。它的延展性较好,弹性各项异性行为也比较显著。同β'相一样,体系内也存在较强的方向性共价键。
3.理论上调查了Mg_(97)Zn_1Y_2合金系统中6H型ABACAB长周期堆垛(LPS)结构的微结构、稳定性和电子属性特征。Y和Zn原子在浓度较低时主要分布于层错缺陷层,这个结果与实验观察一致。Y和Zn原子倾向于紧密排列,这样可以抵消原子半径不同带来的应变,使的6H型结构能量上更稳定。通过计算不同固溶原子含量时的结合能,发现Y元素增强了6H结构的稳定性,在改善合金的抗蠕变能力方面起到了重要作用。Zn原子位于两个不匹配的层错层时将导致晶格畸变,进一步的分析表明Y和Zn原子紧密排列将会削弱了畸变的幅度。通过分析电子态密度和电荷密度,发现Mg原子和Y原子之间形成了较强的共价键,这将增加合金强度。Mg原子与Zn原子之间的杂化作用广泛而均匀存在,这对改善合金延展性有帮助。
Magnesium alloys have important application value and prospect in the aerospace, transportation, electronics fields due to their low density, excellent mechanical properties, and electromagnetic shielding ability. However, the applications are still limited because of the lower strength, inferior fatigue and creep resistance at elevated temperature. Mg-rare earth alloys have received material researchers’great interest because of their high strength, good creep resistance and thermal stability. In this paper, we carried out first-principles calculations based on density functional theory to study on the structural, mechanical and electronic properties of the intermediate phase in Mg alloys. The obtained main results are as follows:
1. We determined the lattice parameters ofβ' phase in Mg–Gd alloy theoretically and calculated the nine independent elastic constants of the orthogonal crystal. The nine independent elastic constants did not meet the mechanical stability criteria, which suggest the reported Mg15Gd is a mechanically unstable structure. The polycrystalline bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratioνfor Mg7Gd are calculated within the scheme of Voigt–Reuss–Hill(VRH) approximation. We found the covalent bond was formed between the Mg and Gd atoms based on the analysis of the density of states and charge density. Finally, the density, wave velocity and Debye temperature of Mg7Gd are calculated.
2. The structural parameters ofβ" phase in Mg–Gd alloy are determined. The obtained formation enthalpy indicates that theβ" phase Mg3Gd could be formed energetically. The nine independent elastic constants are calculated, which suggest the Mg3Gd is mechanically stable. The polycrystalline bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratioνforβ" phase Mg3Gd are calculated from the elastic constants. It seems that the improvement of mechanical properties is limited after alloying from these parameters. Theβ" phase Mg3Gd is a ductile material and exhibits the elastic anisotropy apparently. Just as theβ' phase, the directional covalent bonding was formed in the system.
3. The microstructure, stability and electronic properties of the 6H-type ABACAB LPS phase in Mg_(97)Zn_1Y_2 are investigated theoretically. The enrichment of Y and Zn atoms occurs in the stacking fault defect layers, which is in accordance with the experimental observations. The present calculated results still show clearly that the Y and Zn atoms are preferably arranged closely. It is reasonable that the two atoms arrange closely to cancel strain due to the different atomic radii, and then lead the structure energetically more stable. The Y element enhances the structural stability from the calculated cohesive energy. It is clearly that the Y element would improve the creep property of alloy. The Zn atoms located in two different misfit fault layers would lead to lattice distortion. Further analysis shows that the intimate arrangement of Y and Zn atoms would weaken the distortion. Based on the analysis of the density of states, we found the covalent bonding exists between the Mg and Gd atoms which would enhance the strength of alloy. The hybridization between Mg and Zn is clear in entire region and the variation of hybridization is small. So this is helpful for improving the ductility of the 6H-type LPS structure.
引文
[1] W. B. Pearson. A Handbook of Lattice Spacings and Structures of Metals and Alloys [M]. Pergamon Press, Oxford, 1967, 2:836.
[2] I. J. Polmear. ASM Specialty Handbook: Magnesium and Magnesium Alloys [M]. ASM International, Materials Park, Ohio, USA, 1999:12-25.
[3]丁文江.镁合金科学与技术[M].北京:科学出版社, 2007:12-14,
[4]张津,章宗和.镁合金及应用[M].北京:化学工业出版社, 2004:48-53.
[5]刘正,王越.镁基轻质材料的研究与应用[J].材料研究学报, 2000,14:449-456.
[6] D. Eliezer, E. Aghion, and F. H. Froes. Magnesium science, technology and applications [J]. Advanced Performance Materials, 1998, 5:201-212.
[7] K. U. Kainer and B. Von. Modern development of alloys for light weight components [J]. Materialwissenschaft und Werkstofftechnik, 1999, 30:159-167.
[8] Z. Chen and J. Chen. A review: Hot topics on magnesium technology in China [J]. Frontiers of Materials Science in China, 2008, 2:1-8.
[9] C. Potzies and K. U. Kainer. Fatigue of magnesium alloys [J]. Advanced Engineering Materials, 2004, 6:281-289.
[10] Y. Kawamura, K. Hayashi, A. Inoue, and T. Masumoto. Rapidly solidified powder metallurgy Mg_(97)Zn_1Y_2 alloys with excellent tensile yield strength above 600 MPa [J]. Mater Trans, 2001, 42:1172-1176.
[11] W. Hu, H. Xu, X. Shu, X. Yuan, B. Gao, and B. Zhang. Calculation of thermodynamic properties of Mg-RE (RE= Sc, Y, Pr, Nd, Gd, Tb, Dy, Ho or Er) alloys by an analytic modified embedded atom method [J]. Journal of Physics D: Applied Physics, 2000, 33:711-718.
[12] J. Zhang, W. A. Oates, F. Zhang, S. L. Chen, K. C. Chou, and Y. A. Chang. Cluster/site approximation calculation of the ordering phase diagram for Cd-Mg alloys [J]. Intermetallics, 2001, 9:5-8,.
[13] Y. Zhong, J. O. Sofo, A. A. Luo, and Z. K. Liu. Thermodynamics modeling of the Mg-Sr and Ca-Mg-Sr systems [J]. Journal of Alloys and Compounds, 2006, 421:172-178.
[14] S. Ganeshan, S. L. Shang, H. Zhang, Y. Wang, M. Mantina, and Z. K. Liu. Elastic constants of binary Mg compounds from first-principles calculations [J]. Intermetallics, 2009, 17:313-318.
[15] S. Ganeshan, S. L. Shang, Y. Wang, and Z. K. Liu. Effect of alloying elements on the elastic properties of Mg from first-principles calculations [J]. Acta Materialia, 2009, 57:3876-3884.
[16] W. A. Counts, M. Friák, D. Raabe, and J. Neugebauer. Using ab initio calculations in designing bcc Mg-Li alloys for ultra-lightweight applications [J]. Acta Materialia, 2009, 57:69-76.
[17] Y. Zhong, J. Liu, R. A. Witt, Y. Sohn, and Z. K. Liu. Al2 (Mg,Ca) phases in Mg-Al-Ca ternary system: First-principles prediction and experimental identification [J]. ScriptaMaterialia, 2006, 55: 573-576.
[18] J. Tani and H. Kido. Lattice dynamics of Mg_2Si and Mg_2Ge compounds from first-principles calculations [J]. Computational Materials Science, 2008, 42:531-536.
[19] B. L. Mordike. Creep-resistant magnesium alloys [J]. Materials Science and Engineering A, 2002, 324:103-112.
[20] T. B. Massalski, H. Okamoto, P. R. Subramanian, and L. Kacprzak, Binary Alloy Phase Diagrams [M]. ASM International, Materials Park, Ohio, USA, 1990.
[21] J. F. Nie, X. Gao, and S. M. Zhu. Enhanced age hardening response and creep resistance of Mg-Gd alloys containing Zn [J]. Scripta Materialia, 2005, 53:1049-1053.
[22] S. M. He, X. Q. Zeng, L. M. Peng, X. Gao, J. F. Nie, and W. J. Ding. Precipitation in a Mg-10Gd-3Y-0.4 Zr(wt.%) alloy during isothermal ageing at 250°C [J]. Journal of Alloys and Compounds, 2006, 421:309-313.
[23] X. Gao and J. F. Nie. Enhanced precipitation-hardening in Mg-Gd alloys containing Ag and Zn [J]. Scripta Materialia, 2008, 58:619-622.
[24] Z. Yang, J. P. Li, Y. C. Guo, T. Liu, F. Xia, Z. W. Zeng, and M. X. Liang. Precipitation process and effect on mechanical properties of Mg-9Gd-3Y-0.6Zn-0.5Zr alloy [J]. Materials Science and Engineering A, 2007, 454-455:274-280.
[25] Q. Peng, H. Dong, L. Wang, Y. Wu, and L. Wang. Aging behavior and mechanical properties of Mg-Gd-Ho alloys [J]. Materials Characterization, 2008, 59:983-986.
[26] J. Chang, X. Guo, S. He, P. Fu, L. Peng, and W. Ding. Investigation of the corrosion for Mg-xGd-3Y-0.4Zr alloys in a peak-aged condition [J]. Corrosion Science, 2008, 50:166-177.
[27] Z. Yang, Y. C. Guo, J. P. Li, F. He, F. Xia, and M. X. Liang. Plastic deformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-0.5Zn-0.5Zr alloy [J]. Materials Science and Engineering A, 2008, 485:487-491.
[28] P. Vostry, B. Smola, I. Stulikova, F. v. Buch, and B. L. Mordike. Microstructure evolution in isochronally heat treated Mg-Gd Alloys [J]. physica status solidi (a), 1999, 175:491-500.
[29] T. Kawabata, K. Matsuda, S. Kamado, Y. Kojima, and S. Ikeno. HRTEM observation of the precipitates in Mg-Gd-Y-Zr alloy [J]. Materials Science Forum, 2003, 419:303-306.
[30] T. Honma, T. Ohkubo, K. Hono, and S. Kamado. Chemistry of nanoscale precipitates in Mg-2.1 Gd-0.6 Y-0.2 Zr (at.%) alloy investigated by the atom probe technique [J]. Materials Science and Engineering A, 2005, 395:301-306.
[31] M. Nishijima, K. Hiraga, M. Yamasaki, and Y. Kawamura. Characterization of beta' phase precipitates in an Mg-5 at% Gd Alloy aged in a peak hardness condition: Studied by high-Angle annular detector dark-field scanning transmission electron microscopy [J]. Materials Transactions, 2006, 47:2109.
[32] T. Itoi, T. Seimiya, Y. Kawamura, and M. Hirohashi. Long period stacking structures observed in Mg_(97)Zn_1Y_2 alloy [J]. Scripta Materialia, 2004, 51:107-111.
[33] M. Nishida, Y. Kawamura, and T. Yamamuro. Formation process of unique microstructure in rapidly solidified Mg_(97)Zn_1Y_2 alloy [J]. Materials Science and Engineering A, 2004, 375: 1217-1223.
[34] M. Matsuda, S. Ii, Y. Kawamura, Y. Ikuhara, and M. Nishida. Variation of long-period stacking order structures in rapidly solidified Mg_(97)Zn_1Y_2 alloy [J]. Materials Science and Engineering A, 2005, 393:269-274.
[35] K. Amiya, T. Ohsuna, and A. Inoue. Long-period hexagonal structures in melt-spun Mg97Ln2Zn1 (Ln=Lanthanide Metal) alloys [J]. Materials Transactions, 2003, 44:2151-2156.
[36] E. Abe, Y. Kawamura, K. Hayashi, and A. Inoue. Long-period ordered structure in a high-strength nanocrystalline Mg-1 at% Zn-2 at% Y alloy studied by atomic-resolution Z-contrast STEM [J]. Acta Materialia, 2002, 50:3845-3857.
[37] D. H. Ping, K. Hono, Y. Kawamura, and A. Inoue. Local chemistry of a nanocrystalline high-strength Mg97Y2Zn1 alloy [J]. Philosophical Magazine Letters, 2002, 82:543-552.
[38] Y. F. Wang, Z. Z. Wang, N. Yu, X. Q. Zeng, W. J. Ding, and B. Y. Tang. Microstructure investigation of the 6H-type long-period stacking order phase in Mg97Y2Zn1 alloy [J]. Scripta Materialia, 2008, 58:807-810.
[39] W. Kohn and L. J. Sham. Self-consistent equations including exchange and correlation effects [J]. Physical Review, 1965, 140:A1133-A1138.
[40] P. Hohenberg and W. Kohn. Inhomogeneous electron gas [J]. Physical Review, 1964, 136: B864-B871.
[41]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版, 1998:8-9.
[42] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation [J]. Physical Review B, 1992, 46:6671-6687.
[43] D. R. Hamann, M. Schlüter, and C. Chiang. Norm-conserving pseudopotentials [J]. Physical Review Letters, 1979, 43:1494-1497.
[44] D. Vanderbilt. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Physical Review B, 1990, 41:7892-7895.
[45] P. E. Bl?chl. Projector augmented-wave method [J]. Physical Review B, 1994, 50:17953-17979.
[46] Y. Song, Z. X. Guo, R. Yang, and D. Li. First principles study of site substitution of ternary elements in NiAl [J]. Acta Materialia, 2001, 49:1647-1654.
[47] D. C. Wallace. Thermodynamics of crystals [M]. Wiley, New York, 1972.
[48] P. Ravindran, L. Fast, P. A. Korzhavyi, B. Johansson, J. Wills, and O. Eriksson. Density functional theory for calculation of elastic properties of orthorhombic crystals: application to TiSi [J]. Journal of Applied Physics, 1998, 84:4891.
[49] W. Voigt. Lehrbuch der Kristallphysik [M]. Teubner, Leipzig, 1928.
[50] A. Reuss. Calculation of the flow limits of mixed crystals on the basis of the plasticity of mono-crystals [J]. Z. Angew. Math. Mech, 1929, 9:49.
[51] R. Hill. The elastic behaviour of a crystalline aggregate [J]. Proceedings of the Physical Society. Section A, 1952, 65:349-354.
[52] O. L. Anderson. A simplified method for calculating the Debye temperature from elastic constants [J]. Journal of Physics and Chemistry of Solids, 1963, 24:909-917.
[53] E. Schreiber, O. L. Anderson, and N. Soga. Elastic Constants and their Measurements [M]. McGraw-Hill, New York, 1973.
[54] C. J. Bettles and M. A. Gibson. Microstructural design for dnhanced dlevated temperature properties in sand-castable Magnesium alloys [J] Advanced Engineering Materials 2003, 5: 859-865.
[55] M. O. Pekguleryuz and A. A. Kaya. Creep resistant magnesium alloys for powertrain applications [J]. Advanced Engineering Materials, 2003, 5:866-878.
[56] J. F. Nie and B. C. Muddle. Precipitation in magnesium alloy WE54 during isothermal ageing at 250°C [J]. Scripta Materialia, 1999, 40:1089-1094.
[57] J. F. Nie and B. C. Muddle. Characterisation of strengthening precipitate phases in a Mg-Y-Nd alloy [J]. Acta Materialia, 2000, 48:1691-1703.
[58] C. Antion, P. Donnadieu, F. Perrard, A. Deschamps, C. Tassin, and A. Pisch. Hardening precipitation in a Mg-4Y-3RE alloy [J]. Acta Materialia, 2003, 51:5335-5348.
[59] B. Smola and I. Stulikova. Equilibrium and transient phases in Mg-Y-Nd ternary alloys [J]. Journal of Alloys and Compounds, 2004, 381:L1-L2.
[60] B. Y. Tang, N. Wang, W. Y. Yu, X. Q. Zeng, and W. J. Ding. Theoretical investigation of typical fcc precipitates in Mg-based alloys [J]. Acta Materialia, 2008, 56:3353-3357.
[61] P. J. Apps, H. Karimzadeh, J. F. King, and G. W. Lorimer. Precipitation reactions in Magnesium-rare earth alloys containing Yttrium, Gadolinium or Dysprosium [J]. Scripta Materialia, 2003, 48:1023-1028.
[62] T. Honma, T. Ohkubo, S. Kamado, and K. Hono. Effect of Zn additions on the age-hardening of Mg-2.0Gd-1.2Y-0.2Zr alloys [J]. Acta Materialia, 2007, 55:4137-4150.
[63] G. Kresse and J. Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Physical Review B, 1996, 54:11169-11186.
[64] H. J. Monkhorst and J. D. Pack. Special points for Brillouin-zone integrations [J]. Physical Review B, 1976, 13:5188-5192.
[65] P. E. Bl?chl, O. Jepsen, and O. K. Andersen. Improved tetrahedron method for Brillouin-zone integrations [J]. Physical Review B, 1994, 49:16223-16233.
[66] A. F. Young, C. Sanloup, E. Gregoryanz, S. Scandolo, R. J. Hemley, and H. Mao. Synthesis of Novel Transition Metal Nitrides IrN2 and OsN2 [J]. Physical Review Letters, 2006, 96:155501.
[67] M. Mattesini, R. Ahuja, and B. Johansson. Cubic Hf3N4 and Zr3N4: A class of hard materials [J]. Physical Review B, 2003, 68:184108.
[68] F. Cardarelli. Materials Handbook [M]. Springer, London, 2000.
[69] S. F. Pugh. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J]. Philosophical Magazine Series 7, 1954, 45:823-843.
[70] V. Tvergaard and J. W. Hutchinson. Microcracking in ceramics induced by thermal expansion or elastic anisotropy [J]. Journal of the American Ceramic Society, 1988, 71:157-166.
[71] D. H. Chung, W. R. Buessem, and F. W. Vahldiek. Anisotropy in Single Crystal RefractoryCompounds [M]. Plenum Press, New York, 1968:217.
[72] J. F. Nye. Physical properties of crystals: their representation by tensors and matrices [M]. Oxford University Press, USA, 1985.
[73] W. Lin, J. Xu, and A. J. Freeman. Electronic structure, cohesive properties, and phase stability of Ni3(V, Co)3V, and Fe3V [J]. Physical Review B, 1992, 45:10863-10871.
[74] I. A. Anyanwu, S. Kamado, and Y. Kojima. Creep properties of Mg-Gd-Y-Zr alloys [J]. Materials Transactions, 2001, 42:1212-1218.
[75] M. Yamasaki, M. Sasaki, M. Nishijima, K. Hiraga, and Y. Kawamura. Formation of 14H long period stacking ordered structure and profuse stacking faults in Mg-Zn-Gd alloys during isothermal aging at high temperature [J]. Acta Materialia, 2007, 55:6798-6805.
[76] Q. M. Peng, Y. M. Wu, D. Q. Fang, J. Meng, and L. M. Wang. Microstructures and properties of Mg-7Gd alloy containing Y [J]. Journal of Alloys and Compounds, 2007, 430:252-256.
[77] J.íek, I. Procházka, B. Smola, I. Stulíková, R. Ku el, Z. Matěj, and V. Cherkaska. Thermal development of microstructure and precipitation effects in Mg–10wt%Gd alloy [J]. Phys. Stat. Sol.(a), 2006, 203:466-477.
[78] A. Inoue, M. Matsushita, Y. Kawamura, K. Amiya, K. Hayashi, and J. Koike. Novel hexagonal structure of ultra-high strength magnesium-based alloys [J]. Materials Transactions, 2002, 43:. 580-584.
[79] T. Itoi, K. Takahashi, H. Moriyama, and M. Hirohashi. A high-strength Mg-Ni-Y alloy sheet with a long-period ordered phase prepared by hot-rolling [J]. Scripta Materialia, 2008, 59:1155-1158.
[80] Y. Kawamura, T. Kasahara, S. Izumi, and M. Yamasaki. Elevated temperature Mg97Y2Cu1 alloy with long period ordered structure [J]. Scripta Materialia, 2006 , 55:453-456.
[81] D. J. Li, X. Q. Zeng, J. Dong, C. Q. Zhai, and W. J. Ding. Microstructure evolution of Mg-10Gd-3Y-1.2Zn-0.4Zr alloy during heat-treatment at 773°C [J]. Journal of Alloys and Compounds, 2009, 468: 164-169.
[82] A. Datta, U. Ramamurty, S. Ranganathan, and U. V. Waghmare. Crystal structures of a Mg-Zn-Y alloy: A first-principles study [J]. Computational Materials Science, 2006, 37:69-73.
[83] A. Datta, U. V. Waghmare, and U. Ramamurty. Structure and stacking faults in layered Mg-Zn-Y alloys: a first-principles study [J]. Acta Materialia, 2008, 56:2531-2539.
[84] M. Matsuura, M. Sakurai, K. Amiya, and A. Inoue. Local structures around Zn and Y in the melt-quenched Mg_(97)Zn_1Y_2 ribbon [J]. Journal of Alloys and Compounds, 2003, 353: 240-245.
[85] N. Hort, Y. Huang, and K. U. Kainer. Intermetallics in Magnesium Alloys [J]. Advanced Engineering Materials, 2006, 8:235-240.
[86] G. Garces, M. Maeso, I. Todd, P. Pérez, and P. Adeva. Deformation behaviour in rapidly solidified Mg97Y2Zn1(at.%) alloy [J]. Journal of Alloys and Compounds, 2007, 432:L10-L14.
[87] C. L. Fu, X. Wang, Y. Y. Ye, and K. M. Ho. Phase stability, bonding mechanism, and elasticconstants of Mo5Si3 by first-principles calculation [J]. Intermetallics, 1999, 7:179-184.
[2] I. J. Polmear. ASM Specialty Handbook: Magnesium and Magnesium Alloys [M]. ASM International, Materials Park, Ohio, USA, 1999:12-25.
[3]丁文江.镁合金科学与技术[M].北京:科学出版社, 2007:12-14,
[4]张津,章宗和.镁合金及应用[M].北京:化学工业出版社, 2004:48-53.
[5]刘正,王越.镁基轻质材料的研究与应用[J].材料研究学报, 2000,14:449-456.
[6] D. Eliezer, E. Aghion, and F. H. Froes. Magnesium science, technology and applications [J]. Advanced Performance Materials, 1998, 5:201-212.
[7] K. U. Kainer and B. Von. Modern development of alloys for light weight components [J]. Materialwissenschaft und Werkstofftechnik, 1999, 30:159-167.
[8] Z. Chen and J. Chen. A review: Hot topics on magnesium technology in China [J]. Frontiers of Materials Science in China, 2008, 2:1-8.
[9] C. Potzies and K. U. Kainer. Fatigue of magnesium alloys [J]. Advanced Engineering Materials, 2004, 6:281-289.
[10] Y. Kawamura, K. Hayashi, A. Inoue, and T. Masumoto. Rapidly solidified powder metallurgy Mg_(97)Zn_1Y_2 alloys with excellent tensile yield strength above 600 MPa [J]. Mater Trans, 2001, 42:1172-1176.
[11] W. Hu, H. Xu, X. Shu, X. Yuan, B. Gao, and B. Zhang. Calculation of thermodynamic properties of Mg-RE (RE= Sc, Y, Pr, Nd, Gd, Tb, Dy, Ho or Er) alloys by an analytic modified embedded atom method [J]. Journal of Physics D: Applied Physics, 2000, 33:711-718.
[12] J. Zhang, W. A. Oates, F. Zhang, S. L. Chen, K. C. Chou, and Y. A. Chang. Cluster/site approximation calculation of the ordering phase diagram for Cd-Mg alloys [J]. Intermetallics, 2001, 9:5-8,.
[13] Y. Zhong, J. O. Sofo, A. A. Luo, and Z. K. Liu. Thermodynamics modeling of the Mg-Sr and Ca-Mg-Sr systems [J]. Journal of Alloys and Compounds, 2006, 421:172-178.
[14] S. Ganeshan, S. L. Shang, H. Zhang, Y. Wang, M. Mantina, and Z. K. Liu. Elastic constants of binary Mg compounds from first-principles calculations [J]. Intermetallics, 2009, 17:313-318.
[15] S. Ganeshan, S. L. Shang, Y. Wang, and Z. K. Liu. Effect of alloying elements on the elastic properties of Mg from first-principles calculations [J]. Acta Materialia, 2009, 57:3876-3884.
[16] W. A. Counts, M. Friák, D. Raabe, and J. Neugebauer. Using ab initio calculations in designing bcc Mg-Li alloys for ultra-lightweight applications [J]. Acta Materialia, 2009, 57:69-76.
[17] Y. Zhong, J. Liu, R. A. Witt, Y. Sohn, and Z. K. Liu. Al2 (Mg,Ca) phases in Mg-Al-Ca ternary system: First-principles prediction and experimental identification [J]. ScriptaMaterialia, 2006, 55: 573-576.
[18] J. Tani and H. Kido. Lattice dynamics of Mg_2Si and Mg_2Ge compounds from first-principles calculations [J]. Computational Materials Science, 2008, 42:531-536.
[19] B. L. Mordike. Creep-resistant magnesium alloys [J]. Materials Science and Engineering A, 2002, 324:103-112.
[20] T. B. Massalski, H. Okamoto, P. R. Subramanian, and L. Kacprzak, Binary Alloy Phase Diagrams [M]. ASM International, Materials Park, Ohio, USA, 1990.
[21] J. F. Nie, X. Gao, and S. M. Zhu. Enhanced age hardening response and creep resistance of Mg-Gd alloys containing Zn [J]. Scripta Materialia, 2005, 53:1049-1053.
[22] S. M. He, X. Q. Zeng, L. M. Peng, X. Gao, J. F. Nie, and W. J. Ding. Precipitation in a Mg-10Gd-3Y-0.4 Zr(wt.%) alloy during isothermal ageing at 250°C [J]. Journal of Alloys and Compounds, 2006, 421:309-313.
[23] X. Gao and J. F. Nie. Enhanced precipitation-hardening in Mg-Gd alloys containing Ag and Zn [J]. Scripta Materialia, 2008, 58:619-622.
[24] Z. Yang, J. P. Li, Y. C. Guo, T. Liu, F. Xia, Z. W. Zeng, and M. X. Liang. Precipitation process and effect on mechanical properties of Mg-9Gd-3Y-0.6Zn-0.5Zr alloy [J]. Materials Science and Engineering A, 2007, 454-455:274-280.
[25] Q. Peng, H. Dong, L. Wang, Y. Wu, and L. Wang. Aging behavior and mechanical properties of Mg-Gd-Ho alloys [J]. Materials Characterization, 2008, 59:983-986.
[26] J. Chang, X. Guo, S. He, P. Fu, L. Peng, and W. Ding. Investigation of the corrosion for Mg-xGd-3Y-0.4Zr alloys in a peak-aged condition [J]. Corrosion Science, 2008, 50:166-177.
[27] Z. Yang, Y. C. Guo, J. P. Li, F. He, F. Xia, and M. X. Liang. Plastic deformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-0.5Zn-0.5Zr alloy [J]. Materials Science and Engineering A, 2008, 485:487-491.
[28] P. Vostry, B. Smola, I. Stulikova, F. v. Buch, and B. L. Mordike. Microstructure evolution in isochronally heat treated Mg-Gd Alloys [J]. physica status solidi (a), 1999, 175:491-500.
[29] T. Kawabata, K. Matsuda, S. Kamado, Y. Kojima, and S. Ikeno. HRTEM observation of the precipitates in Mg-Gd-Y-Zr alloy [J]. Materials Science Forum, 2003, 419:303-306.
[30] T. Honma, T. Ohkubo, K. Hono, and S. Kamado. Chemistry of nanoscale precipitates in Mg-2.1 Gd-0.6 Y-0.2 Zr (at.%) alloy investigated by the atom probe technique [J]. Materials Science and Engineering A, 2005, 395:301-306.
[31] M. Nishijima, K. Hiraga, M. Yamasaki, and Y. Kawamura. Characterization of beta' phase precipitates in an Mg-5 at% Gd Alloy aged in a peak hardness condition: Studied by high-Angle annular detector dark-field scanning transmission electron microscopy [J]. Materials Transactions, 2006, 47:2109.
[32] T. Itoi, T. Seimiya, Y. Kawamura, and M. Hirohashi. Long period stacking structures observed in Mg_(97)Zn_1Y_2 alloy [J]. Scripta Materialia, 2004, 51:107-111.
[33] M. Nishida, Y. Kawamura, and T. Yamamuro. Formation process of unique microstructure in rapidly solidified Mg_(97)Zn_1Y_2 alloy [J]. Materials Science and Engineering A, 2004, 375: 1217-1223.
[34] M. Matsuda, S. Ii, Y. Kawamura, Y. Ikuhara, and M. Nishida. Variation of long-period stacking order structures in rapidly solidified Mg_(97)Zn_1Y_2 alloy [J]. Materials Science and Engineering A, 2005, 393:269-274.
[35] K. Amiya, T. Ohsuna, and A. Inoue. Long-period hexagonal structures in melt-spun Mg97Ln2Zn1 (Ln=Lanthanide Metal) alloys [J]. Materials Transactions, 2003, 44:2151-2156.
[36] E. Abe, Y. Kawamura, K. Hayashi, and A. Inoue. Long-period ordered structure in a high-strength nanocrystalline Mg-1 at% Zn-2 at% Y alloy studied by atomic-resolution Z-contrast STEM [J]. Acta Materialia, 2002, 50:3845-3857.
[37] D. H. Ping, K. Hono, Y. Kawamura, and A. Inoue. Local chemistry of a nanocrystalline high-strength Mg97Y2Zn1 alloy [J]. Philosophical Magazine Letters, 2002, 82:543-552.
[38] Y. F. Wang, Z. Z. Wang, N. Yu, X. Q. Zeng, W. J. Ding, and B. Y. Tang. Microstructure investigation of the 6H-type long-period stacking order phase in Mg97Y2Zn1 alloy [J]. Scripta Materialia, 2008, 58:807-810.
[39] W. Kohn and L. J. Sham. Self-consistent equations including exchange and correlation effects [J]. Physical Review, 1965, 140:A1133-A1138.
[40] P. Hohenberg and W. Kohn. Inhomogeneous electron gas [J]. Physical Review, 1964, 136: B864-B871.
[41]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版, 1998:8-9.
[42] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation [J]. Physical Review B, 1992, 46:6671-6687.
[43] D. R. Hamann, M. Schlüter, and C. Chiang. Norm-conserving pseudopotentials [J]. Physical Review Letters, 1979, 43:1494-1497.
[44] D. Vanderbilt. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Physical Review B, 1990, 41:7892-7895.
[45] P. E. Bl?chl. Projector augmented-wave method [J]. Physical Review B, 1994, 50:17953-17979.
[46] Y. Song, Z. X. Guo, R. Yang, and D. Li. First principles study of site substitution of ternary elements in NiAl [J]. Acta Materialia, 2001, 49:1647-1654.
[47] D. C. Wallace. Thermodynamics of crystals [M]. Wiley, New York, 1972.
[48] P. Ravindran, L. Fast, P. A. Korzhavyi, B. Johansson, J. Wills, and O. Eriksson. Density functional theory for calculation of elastic properties of orthorhombic crystals: application to TiSi [J]. Journal of Applied Physics, 1998, 84:4891.
[49] W. Voigt. Lehrbuch der Kristallphysik [M]. Teubner, Leipzig, 1928.
[50] A. Reuss. Calculation of the flow limits of mixed crystals on the basis of the plasticity of mono-crystals [J]. Z. Angew. Math. Mech, 1929, 9:49.
[51] R. Hill. The elastic behaviour of a crystalline aggregate [J]. Proceedings of the Physical Society. Section A, 1952, 65:349-354.
[52] O. L. Anderson. A simplified method for calculating the Debye temperature from elastic constants [J]. Journal of Physics and Chemistry of Solids, 1963, 24:909-917.
[53] E. Schreiber, O. L. Anderson, and N. Soga. Elastic Constants and their Measurements [M]. McGraw-Hill, New York, 1973.
[54] C. J. Bettles and M. A. Gibson. Microstructural design for dnhanced dlevated temperature properties in sand-castable Magnesium alloys [J] Advanced Engineering Materials 2003, 5: 859-865.
[55] M. O. Pekguleryuz and A. A. Kaya. Creep resistant magnesium alloys for powertrain applications [J]. Advanced Engineering Materials, 2003, 5:866-878.
[56] J. F. Nie and B. C. Muddle. Precipitation in magnesium alloy WE54 during isothermal ageing at 250°C [J]. Scripta Materialia, 1999, 40:1089-1094.
[57] J. F. Nie and B. C. Muddle. Characterisation of strengthening precipitate phases in a Mg-Y-Nd alloy [J]. Acta Materialia, 2000, 48:1691-1703.
[58] C. Antion, P. Donnadieu, F. Perrard, A. Deschamps, C. Tassin, and A. Pisch. Hardening precipitation in a Mg-4Y-3RE alloy [J]. Acta Materialia, 2003, 51:5335-5348.
[59] B. Smola and I. Stulikova. Equilibrium and transient phases in Mg-Y-Nd ternary alloys [J]. Journal of Alloys and Compounds, 2004, 381:L1-L2.
[60] B. Y. Tang, N. Wang, W. Y. Yu, X. Q. Zeng, and W. J. Ding. Theoretical investigation of typical fcc precipitates in Mg-based alloys [J]. Acta Materialia, 2008, 56:3353-3357.
[61] P. J. Apps, H. Karimzadeh, J. F. King, and G. W. Lorimer. Precipitation reactions in Magnesium-rare earth alloys containing Yttrium, Gadolinium or Dysprosium [J]. Scripta Materialia, 2003, 48:1023-1028.
[62] T. Honma, T. Ohkubo, S. Kamado, and K. Hono. Effect of Zn additions on the age-hardening of Mg-2.0Gd-1.2Y-0.2Zr alloys [J]. Acta Materialia, 2007, 55:4137-4150.
[63] G. Kresse and J. Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Physical Review B, 1996, 54:11169-11186.
[64] H. J. Monkhorst and J. D. Pack. Special points for Brillouin-zone integrations [J]. Physical Review B, 1976, 13:5188-5192.
[65] P. E. Bl?chl, O. Jepsen, and O. K. Andersen. Improved tetrahedron method for Brillouin-zone integrations [J]. Physical Review B, 1994, 49:16223-16233.
[66] A. F. Young, C. Sanloup, E. Gregoryanz, S. Scandolo, R. J. Hemley, and H. Mao. Synthesis of Novel Transition Metal Nitrides IrN2 and OsN2 [J]. Physical Review Letters, 2006, 96:155501.
[67] M. Mattesini, R. Ahuja, and B. Johansson. Cubic Hf3N4 and Zr3N4: A class of hard materials [J]. Physical Review B, 2003, 68:184108.
[68] F. Cardarelli. Materials Handbook [M]. Springer, London, 2000.
[69] S. F. Pugh. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J]. Philosophical Magazine Series 7, 1954, 45:823-843.
[70] V. Tvergaard and J. W. Hutchinson. Microcracking in ceramics induced by thermal expansion or elastic anisotropy [J]. Journal of the American Ceramic Society, 1988, 71:157-166.
[71] D. H. Chung, W. R. Buessem, and F. W. Vahldiek. Anisotropy in Single Crystal RefractoryCompounds [M]. Plenum Press, New York, 1968:217.
[72] J. F. Nye. Physical properties of crystals: their representation by tensors and matrices [M]. Oxford University Press, USA, 1985.
[73] W. Lin, J. Xu, and A. J. Freeman. Electronic structure, cohesive properties, and phase stability of Ni3(V, Co)3V, and Fe3V [J]. Physical Review B, 1992, 45:10863-10871.
[74] I. A. Anyanwu, S. Kamado, and Y. Kojima. Creep properties of Mg-Gd-Y-Zr alloys [J]. Materials Transactions, 2001, 42:1212-1218.
[75] M. Yamasaki, M. Sasaki, M. Nishijima, K. Hiraga, and Y. Kawamura. Formation of 14H long period stacking ordered structure and profuse stacking faults in Mg-Zn-Gd alloys during isothermal aging at high temperature [J]. Acta Materialia, 2007, 55:6798-6805.
[76] Q. M. Peng, Y. M. Wu, D. Q. Fang, J. Meng, and L. M. Wang. Microstructures and properties of Mg-7Gd alloy containing Y [J]. Journal of Alloys and Compounds, 2007, 430:252-256.
[77] J.íek, I. Procházka, B. Smola, I. Stulíková, R. Ku el, Z. Matěj, and V. Cherkaska. Thermal development of microstructure and precipitation effects in Mg–10wt%Gd alloy [J]. Phys. Stat. Sol.(a), 2006, 203:466-477.
[78] A. Inoue, M. Matsushita, Y. Kawamura, K. Amiya, K. Hayashi, and J. Koike. Novel hexagonal structure of ultra-high strength magnesium-based alloys [J]. Materials Transactions, 2002, 43:. 580-584.
[79] T. Itoi, K. Takahashi, H. Moriyama, and M. Hirohashi. A high-strength Mg-Ni-Y alloy sheet with a long-period ordered phase prepared by hot-rolling [J]. Scripta Materialia, 2008, 59:1155-1158.
[80] Y. Kawamura, T. Kasahara, S. Izumi, and M. Yamasaki. Elevated temperature Mg97Y2Cu1 alloy with long period ordered structure [J]. Scripta Materialia, 2006 , 55:453-456.
[81] D. J. Li, X. Q. Zeng, J. Dong, C. Q. Zhai, and W. J. Ding. Microstructure evolution of Mg-10Gd-3Y-1.2Zn-0.4Zr alloy during heat-treatment at 773°C [J]. Journal of Alloys and Compounds, 2009, 468: 164-169.
[82] A. Datta, U. Ramamurty, S. Ranganathan, and U. V. Waghmare. Crystal structures of a Mg-Zn-Y alloy: A first-principles study [J]. Computational Materials Science, 2006, 37:69-73.
[83] A. Datta, U. V. Waghmare, and U. Ramamurty. Structure and stacking faults in layered Mg-Zn-Y alloys: a first-principles study [J]. Acta Materialia, 2008, 56:2531-2539.
[84] M. Matsuura, M. Sakurai, K. Amiya, and A. Inoue. Local structures around Zn and Y in the melt-quenched Mg_(97)Zn_1Y_2 ribbon [J]. Journal of Alloys and Compounds, 2003, 353: 240-245.
[85] N. Hort, Y. Huang, and K. U. Kainer. Intermetallics in Magnesium Alloys [J]. Advanced Engineering Materials, 2006, 8:235-240.
[86] G. Garces, M. Maeso, I. Todd, P. Pérez, and P. Adeva. Deformation behaviour in rapidly solidified Mg97Y2Zn1(at.%) alloy [J]. Journal of Alloys and Compounds, 2007, 432:L10-L14.
[87] C. L. Fu, X. Wang, Y. Y. Ye, and K. M. Ho. Phase stability, bonding mechanism, and elasticconstants of Mo5Si3 by first-principles calculation [J]. Intermetallics, 1999, 7:179-184.