Mo与Ni_3Al纳米丝单轴拉伸的分子动力学模拟
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摘要
纳米材料是当前国际材料科学研究的热点之一,纳米技术被认为是21世纪最有前途的研究领域。纳米技术在陶瓷、光电、微电子、生物工程等领域有着广泛的应用。纳米丝作为一种典型的一维纳米材料表现得尤为活跃,其表面原子多,比表面积大,力学性能备受关注。因此,本文对纳米丝力学性能的研究有着重要的实际意义。本文采用改进分析型(EAM)势模型计算原子间的相互作用,利用分子动力学模拟方法,模拟了单晶Mo及Ni3Al纳米丝的单轴拉伸过程,重点分析了纳米丝拉伸过程中的相转变机制以及力学性能,考虑了温度、尺寸等因素对纳米丝力学性能的影响。
在相变研究方面,Mo纳米丝在50K下的拉伸过程中共发生两次整体相转变,第一次相变整个纳米丝的构型由bcc结构变为fcc结构,第二次相变纳米丝的构型由fcc结构变为bcc结构。我们计算得到了bcc结构与fcc结构这两种晶格以沿[001]方向双倍层间距为变量的平均原子能量曲线,根据该能量曲线,结合径向分布函数,阐明了由应变驱动的相变机制。在高温下,相变过程更加复杂,相变过程中更多的hcp结构与fcc结构出现,我们的分析表明fcc结构与hcp结构有更好的抗高温性能与抗拉性能。在力学性能研究方面,Mo与Ni3Al纳米丝在不同温度下的模拟结果显示,纳米丝的杨氏模量与屈服强度均随温度的升高而降低。不同尺寸Ni3Al纳米丝的模拟情况表明,纳米丝的杨氏模量与屈服强度都随纳米丝尺寸的增加而增加。在Ni3Al纳米丝中,Re的加入对纳米丝力学性能有很大影响,不同的置换位置对纳米丝力学性能影响差异巨大。我们的研究表明,这种差异与新加入的Re原子和周围原子的结合强弱程度有关。
At present, nanomaterials are one of the hottest research points in international materials science. Nanotechnology is considered to be the most promising research area in the 21st century, which is widely used in ceramics, optoelectronics, microelectronics, biotechnology and so on. As a typical one-dimension nanomaterials, nanowires (NWs) which contain a lot of surface atoms and own large surface area to volume ratio is particularly active. The mechanical properties of NWs are the common concerns. Therefore, this article on the mechanical properties of NWs has important practical significance. In present paper, modified analysis embedded-atom method (EAM) is used to describe the interactions between atoms. Using molecular dynamics simulation, we studied the tensile behaviors of Mo and Ni3Al NWs under uniaxial tensile strain. It's analyzed that the mechanism of phase transitions and mechanical properties under uniaxial tension. The effects of temperature and size on the mechanical properties of NWs are also discussed.
The phase transition processes of a single crystal Mo NWs under uniaxial tensile strains were studied at 50K with molecular dynamics simulation. Two phase transitions have been observed during the uniaxial tensile processes. The first one is the configuration of Mo NWs transformed from body-centered cubic (bcc) structure to face-centered cubic (fee) structure and the second one is that transformed from fee structure to bcc structure. The phase structures have also been demonstrated with radial distribution function (RDF) analyses. Two average atom energy curves of bcc structure and fee structure as the function of the double layer space along [001] direction were obtained with the help of embedded-atom method potential calculations, by which the strain-driven bcc-to-fcc and fcc-to-bcc phase transition mechanisms have been clarified clearly for Mo NWs under uniaxial tensile strain. In high temperature, the phase transition processes became more complicated and much more hexagonal close-packed (hcp) structure and fcc structure were found. It's obvious that hcp and fcc structures are good at high temperature and high pull. At the aspect of mechanical properties, the young's modulus and yield strengths are decreased with increasing temperature in the tensile processes of Mo and Ni3Al NWs. The young's modulus and yield strengths are increased with increasing NWs size in the tensile processes of Ni3Al NWs. The mechanical properties of the Ni3Al NWs with Re are different from ones of the Ni3Al NWs. The location of Re in NWs has the obvious effect on the mechanical properties of Ni3Al NWs. According to our study, the difference of mechanical properties is caused by the difference of the bonding strength in Re atom and other atoms around Re atom.
在相变研究方面,Mo纳米丝在50K下的拉伸过程中共发生两次整体相转变,第一次相变整个纳米丝的构型由bcc结构变为fcc结构,第二次相变纳米丝的构型由fcc结构变为bcc结构。我们计算得到了bcc结构与fcc结构这两种晶格以沿[001]方向双倍层间距为变量的平均原子能量曲线,根据该能量曲线,结合径向分布函数,阐明了由应变驱动的相变机制。在高温下,相变过程更加复杂,相变过程中更多的hcp结构与fcc结构出现,我们的分析表明fcc结构与hcp结构有更好的抗高温性能与抗拉性能。在力学性能研究方面,Mo与Ni3Al纳米丝在不同温度下的模拟结果显示,纳米丝的杨氏模量与屈服强度均随温度的升高而降低。不同尺寸Ni3Al纳米丝的模拟情况表明,纳米丝的杨氏模量与屈服强度都随纳米丝尺寸的增加而增加。在Ni3Al纳米丝中,Re的加入对纳米丝力学性能有很大影响,不同的置换位置对纳米丝力学性能影响差异巨大。我们的研究表明,这种差异与新加入的Re原子和周围原子的结合强弱程度有关。
At present, nanomaterials are one of the hottest research points in international materials science. Nanotechnology is considered to be the most promising research area in the 21st century, which is widely used in ceramics, optoelectronics, microelectronics, biotechnology and so on. As a typical one-dimension nanomaterials, nanowires (NWs) which contain a lot of surface atoms and own large surface area to volume ratio is particularly active. The mechanical properties of NWs are the common concerns. Therefore, this article on the mechanical properties of NWs has important practical significance. In present paper, modified analysis embedded-atom method (EAM) is used to describe the interactions between atoms. Using molecular dynamics simulation, we studied the tensile behaviors of Mo and Ni3Al NWs under uniaxial tensile strain. It's analyzed that the mechanism of phase transitions and mechanical properties under uniaxial tension. The effects of temperature and size on the mechanical properties of NWs are also discussed.
The phase transition processes of a single crystal Mo NWs under uniaxial tensile strains were studied at 50K with molecular dynamics simulation. Two phase transitions have been observed during the uniaxial tensile processes. The first one is the configuration of Mo NWs transformed from body-centered cubic (bcc) structure to face-centered cubic (fee) structure and the second one is that transformed from fee structure to bcc structure. The phase structures have also been demonstrated with radial distribution function (RDF) analyses. Two average atom energy curves of bcc structure and fee structure as the function of the double layer space along [001] direction were obtained with the help of embedded-atom method potential calculations, by which the strain-driven bcc-to-fcc and fcc-to-bcc phase transition mechanisms have been clarified clearly for Mo NWs under uniaxial tensile strain. In high temperature, the phase transition processes became more complicated and much more hexagonal close-packed (hcp) structure and fcc structure were found. It's obvious that hcp and fcc structures are good at high temperature and high pull. At the aspect of mechanical properties, the young's modulus and yield strengths are decreased with increasing temperature in the tensile processes of Mo and Ni3Al NWs. The young's modulus and yield strengths are increased with increasing NWs size in the tensile processes of Ni3Al NWs. The mechanical properties of the Ni3Al NWs with Re are different from ones of the Ni3Al NWs. The location of Re in NWs has the obvious effect on the mechanical properties of Ni3Al NWs. According to our study, the difference of mechanical properties is caused by the difference of the bonding strength in Re atom and other atoms around Re atom.
引文
[1]Gleiter H. Nanostructured materials:basic concepts and microstructure. Acta Materialia,2000,48(1):1-29
[2]张立德,牟季美.纳米材料和纳米结构.北京：科学出版社,2001,1-45
[3]Siegel R W. Mechanical properties of nanophase materials. Materials Science Forum,1997,235-238:851-860
[4]Glener H. Nanocrystalline materials. Progress in Materials Science,1989,33(3): 223-315
[5]Andrievski R A. State-of-the-art and perspectives in particulate nanostructured materials. Materials Science Forum,1998,282-283:1-10
[6]卢柯,徐坚.纳米金属材料：进展和挑战.见：李桓德编98中国材料研讨会论文集.北京：化学工业出版社,1999,88-92
[7]卢柯,卢磊.金属纳米材料力学性能的研究进展.金属学报,2000,36(8)：785-789
[8]文玉华,周富信,刘曰武等.纳米材料的研究进展.力学进展,2001,31(1)：47-61
[9]Gusev A E. Effects of the nanocrystalline state in solids. Physics-Uspekhi,1998, 41(1):49-76
[10]Lu K. Nanocrystalline metals crystallized from amorphous solids: nanocrystalline, structure, and properties. Materials Science and Engineering Reports,1996,16(4):161-221
[11]吴恒安,王秀喜,梁海弋等.金属纳米丝力学行为研究进展.金属学报,2002,38(9)：903-907
[12]孙秀魁,丛洪涛,徐坚等.纳米晶Al的制备及拉伸性能(Ⅰ).材料研究学报,1998,12(6)：645-650
[13]丛洪涛,孙秀魁,徐坚等.纳米晶Al的制备及拉伸性能(Ⅱ).材料研究学报,1998,12(6)：651-654
[14]Hashimoto S, Kaneko Y, Kitagawa K, et al. On the cyclic behavior of ultra-fine grainedcopper produced by equi-channel angular pressing. Materials Science Forum,1999,312-314:593-598
[15]Zhu M, Fecht H J. Softening effect in nanocrystalline Fe-Cu supersaturated solid solutions. Nanostructured Materials,1995,6(5-8):921-924
[16]Wen B M, Sader J E, Boland J J. Mechanical properties of ZnO nanowires. Physical Review Letters,2008,101(17),175502-1-175502-4
[17]Sanders P G, Rittner M, Kiedaisch E, et al. Creep of nanocrystalline Cu, Pd, andAl-Zr. Nanostructured Materials,1997,9(1-8):433-440
[18]Honer H J, Tao R, Kim L, et al. Mechanical properties of single-phase and nano-compositemetals and ceramics. Nanostructured Materials,1995,6(5-8): 901-904
[19]Diao J, Gall K, Dunn M L. Surface-stress-induced phase transformation in metal nanowires. Nature Materials,2003,2(10):656-660
[20]Park H S. Stress-Induced martensitic phase transformation in intermetallic Nickel Aluminum nanowires. Nano Letters,2006,6(5):958-962
[21]Singh N. Effective pair potential and structural phase transitions of Cr, Mo, and W. Physical Review B,1992,46(1):90-97
[22]Luo W D, Roundy D, Cohen M L, et al. Ideal strength of bcc molybdenum and niobium. Physical Review B,2002,66(9):094110-1-094110-7
[23]Guo Y F, Wang Y S, Zhao D L, et al. Mechanisms of martensitic phase transformations in body-centered cubic structural metals and alloys:Molecular dynamics simulations. Acta Materialia,2007,55(19):6634-6641
[24]Li X F, Hu W Y, Xiao S F, et al. Molecular dynamics simulation of polycrystalline molybdenum nanowires under uniaxial tensile strain:Size effects. Physica E,2008,40(10):3030-3036
[25]Wong E W, Sheehan P E, Lieber C M. Nanobeam mechanics:elasticity, strength and toughness of nanorods and nanotubes. Science,1997,277(5334): 1971-1975
[26]Wu B, Heidelberg A, Boland J J. Mechanical properties of ultrahigh-strength gold nanowires. Nature Materials,2005,4(7),525-529
[27]Gonz'alez J C, Rodrigues V, Bettini J, et al. Indication of unusual pentagonal structures in atomic-Size Cu nanowires. Physical Review Letters,2004,93(12): 126103-1-126103-4
[28]Han X D, Zhang Y F, Zheng K, et al. Low-temperature in-situ large strain plasticity of ceramic SiC nanowires and its atomic-scale mechanism. Nano Letters,2007,7(2):452-457
[29]Brenner S S. Tensile strength of whiskers. Journal of Applied Physics,1956, 27(12):1484-1491
[30]Casady J B, Johnson R W. Status of silicon carbide (SiC) as a wide-bandgap semiconductor for high-temperature applications. Solid-State Electronics,1996, 39(10):1409-1422
[31]Nakamura D, Gunjishima I, Yamaguchi S, et al. Ultrahigh-quality silicon carbide single crystals. Nature,2004,430(7003):1009-1012
[32]Kizuka T. Atomistic visualization of deformation in gold. Physical Review B, 1998,57(18):11158-11163
[33]文玉华,周富信,刘日武.纳米晶铜单向拉伸变形的分子动力学模拟.力学学报,2002,34(1)：29-36
[34]Swygenhoven H V, Caro A. Molecular dynamics computer simulation of elastic and plajstic behavior of nanophase Ni. Materials Research Society Proceeding, 1997,457(1-2):193-198
[35]Swygenhoven H V, Caro A. Molecular dynamics computer simulation of nanophase Ni:structure and mechanicalproperties. Nanostructured Materials, 1997,9(1-8):669-672
[36]Lu L, Shen Y F, Chen X H, et al. Ultrahigh Strength and High Electrical Conductivity in Copper. Science,2004,304(5669):422-426
[37]Bahr D F, Kramer D E, Gerberich W W. Nonliner deformation mechanisms during nanoindentation. Acta Materialia,1998,46(10):3605-3617
[38]常明,孙伟,邢金华等.模拟纳米晶体原子分布及X射线散射理论图案.物理学报,1997,46(7)：1319-1325
[39]Thomas G J, Siegel R W, Eastman J A. Grain boundary in nanophase palladium: high resolution electronmicroscope and image simulation. Scripta Metalluryica et Materiallia,1990,24(1):201-206
[40]黄丹,陶伟明,郭乙木.分子动力学模拟单晶纳米铝丝的拉伸破坏.兵器材料科学与工程,2005,28(3)：1-4
[41]黄丹,章青,郭乙木.a-Fe和Ni纳米丝单向拉伸过程的分子动力学模拟.兵器材料科学与工程,2006,29(5)：12-15
[42]Nieman G W, Weertman J R, Siegel R W. Mechanical behavior of nanocrystalline Cu and Pd. Journal of Materials Research,1991,6(5): 1012-1027
[43]Sanders P G, Eastman J A, Weertman J R. Elastic and tensile behavior of nanocrystalline copper and palladium. Acta Materialia,1997,45(10): 4019-4025
[44]Shen T D, Koch C C, Tsui T Y, et al. On the elastic moduli of nanocrystalline Fe, Cu, Ni and Cu-Ni alloysprepared by mechanical milling/alloying. Journal of Materials Research,1995,10(11):2892-2896
[45]Schiotz J, Vegge T, Ditolla F D, et al. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Physical Review B,1999, 60(17):11971-11983
[46]Wang Z G, Zu X T, Yang L, et al. Weber W J. Atomistic simulations of the size, orientation, and temperature dependence of tensile behavior in GaN nanowires. Physical Review B,2007,76(4):045310-1-045310-9
[47]Chen D L, Chen T C. Mechanical properties of Au nanowires under uniaxial tension with high strain-rate by molecular dynamics. Nanotechnology,2005, 16(12):2972-2981
[48]Schiotz J, Tolla F D D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature,1998,391(6667):561-563
[49]Koh S J A, Lee H P, Lu C, et al. Molecular dynamics simulation of a solid platinum nanowire under uniaxial tensile strain:Temperature and strain-rate effects. Physical Review B,2005,72(8):085414-1-085414-11
[50]Sankaranarayanan S K R S, Bhethanabotla V R, Joseph B. Molecular dynamics simulation of temperature and strain rate effects on the elastic properties of bimetallic Pd-Pt nanowires. Physical Review B,2007,76(13): 134117-1-134117-13
[51]Seroodeh A R, Attariani H, Khosrownejad M. Nickel nanowires under uniaxial loads:A molecular dynamics simulation study. Computational Materials Science,2008,44(2):378-384
[52]Karch J, Birringer R, Gleiter H. Ceramics ductile at low temperature.Nature, 1987,330(6148):556-558
[53]Bohn R, Haubold T, Birringer R, et al.Nanocrystalline intermetallic compounds-An approach to ductility. Scripta Metallurgica et Materialia,1991, 25(4):811-816
[54]Koch C C, Morris D G, Lu K, et al. Ductility of nanostructured materials. MRS Buelltin,1999,24:54-58
[55]Mishra R S, Valley R Z, Mukherjee A K. The observation of tensile superplasticity in nanocrystalline materials. Nanostructured Materials,1997, 9(1-8):473-476
[56]Valley R Z. Superplasticity in nanocrystalline metallic materiajs. Materials Science Forum,1997,243-245:207-216
[57]Lu L, Sui M L, Lu K. Superplastic extensibility of nanocrystalline copper at room temperature. Science,2000,287(5457):1463-1466
[58]McFadden S X, Mishra R S, Valley R Z, et al. Low-temperature superplasticity innanostructured nickel and metal alloys. Nature,1999,398(6729):684-686
[59]Agostino G D, Swygenhoven H V. Structural and mechanical properties of a simulated nickel nanophase. Materials Research Society Proceeding,1996,400, 293-298
[60]Nieman G W, Weertman J R. Mechanical behavior of nanocrystalline copper and palladium. Journal of Materials Research,1991,6(15):1012-1027
[61]Diego G G, Eugenio Z S, Arturo D R, et al. Diffusion-driven superplasticity in ceramics:Modeling and comparison with available data. Physical Review B, 2009,80(21):214107-1-214107-8
[62]Liang W W, Zhou M. Atomistic simulations reveal shape memory of fcc metal nanowires. Physical Review B,2006,73(11):115409-1-115409-11
[63]Liang W W, Zhou M. Shape memory effect in Cu nanowires. Nano Letters,2005, 5(10):2039-2043
[64]Daw M S, Baskes M I. Embedded-atom method:Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B,1984, 29(12):6443-6453
[65]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,2003,1-20
[66]Daw M S, Foiles S M, BaskesM I. The embedded-atom method:a review of theory and applications. Materials Science Reports,1993,9(7):251-340
[67]Daw M S, Foiles S M. Calculations of the energetics and structure of Pt (110) using the embedded atom method. Journal of Vacuum Science and Technology A,1986,4(3):1412-1413
[68]Daw M S. Calculations of the energetics and structure of Pt (110) reconstruction using the embedded atom method. Surface Science,1986,166(2-3):L161-L169
[69]Foiles S M. Reconstruction of fcc (110) surface. Surface Science,1987, 191(1-2):L779-L784
[70]Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt and their alloys. Physical Review B,1986, 33(12):7983-7991
[71]Jacobsen K W, Norskov J K, Puska M J. Interatomtic interactions in the effective-medium theory. Physical Review B,1987,35(14):7423-7442
[72]Cleri F, Rosato V. Tight-binding potentials for transition metals and alloys. Physical Review B,1993,48(1):22-23
[73]Finnis M W, Sinclair J F. A simple empirical N-body potential for transition metals. Philosophical Magazine A,1984,50(1):45-55
[74]Johnson R A. Analytic nearest-neighbor model for fcc metals. Physical Review B,1989,37(12):3924-3931
[75]Norskov J K. Covalent effects in the effective-medium theory of chemical binding:hydrogen heats of solution in the 3d metals. Physical Review B,1982, 26 (6):2875-2885
[76]Daw M S, Baske M I. Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Physical Review B,1983,50(17):1285-1288
[77]Hu W Y, Zhang B W, Huang B Y, et al. Analytic Modified Embedded Atom Potentials for hcp Metals. Journal of Physics Condensed Matter,2001,13(6): 1193-1213
[78]Hu W Y, Masahiro F. The application of the analytic embedded atom potentials to alkali metals. Modelling and Simulation in Materials Science and Engineering,2002,10(6):707-726
[79]Wu Y, Hu W Y. Molecular Dynamic simulation of thermodynamics, elastic constants and solid solution strength for Mg-Gd alloys. The European Physical Journal B,2007,57(6):305-312
[80]Wu Y, Hu W Y, Yang S L, et al. Solid solution mechanism and thermodynamic properties of Ti-Re alloy system:Experiment and Theory. Intermetallics,2007, 15(1):1116-1121
[81]Villas P, Calvert L. Pearson's handbook of crystallographic data for intermetallic phases. Germany:ASM International, Materials Park, OH,1991, 456-458
[82]Hultgren R, Desai P D, Hawkins D T, et al. Selected values of thermodynamic properties of binary alloys. Germany:ASM. Matals Park, OH,1973,634-635
[83]Gear C W. Numerical initial value problems in ordinary differential equation. New Jersey:Prentice-Hall,1971,345-376
[84]肖时芳.纳米结构金属及合金热力学性能的原子模拟：[湖南大学博士学位论文].长沙：湖南大学材料科学与工程学院,2007,16-17
[85]吴玉蓉.稀土镁合金的热力学及固溶特性的理论模拟：[湖南大学博士学位论文].长沙：湖南大学材料科学与工程学院,2007,24-25
[86]Nose S. A Unifed formulation of the constant temperature molecular dynamics methods. Journal of Chemical Physics,1984,81(1):511-519
[87]Hoover W G. Canonical dynamics:equilibrium phase-space distributions. Physical Review A,1985,31(3):1695-1702
[88]Anderson H C. Molecular dynamics simulations at constant press and/or temperature. Journal of Chemical Physics,1980,72(4):2384-2393
[89]杨剑瑜.金属表面动力学性质的原子模拟研究：[湖南大学博士学位论文].长沙：湖南大学材料科学与工程学院,2006,20-22
[90]汤剑锋.B2-FeAl低指数表面动力学性质的分子动力学模拟：[湖南大学硕士学位论文].长沙：湖南大学物理与微电子科学学院,2008，16-18
[91]Hu W Y, Naka I M, Yamane T. Science and engineering in advanced materials. In:Proc of Int Conf on new frontiers of process. Japan,2004,7-14
[92]Yang J Y, Hu W Y, Deng H Q, et al. Temperature dependence of atomic relaxation and vibrations for the vicinal Ni (977) surface:a molecular dynamics study. Surface Science,2004,572(2-3):439-448
[93]Hu W Y, Shu X L, Zhang B W. Point-defect properties in body-centered cubic transition metals with analytic EAM interatomic potentials. Computational Materials Science,2002,23(1-4):175-189
[94]Xiao S F, Hu W Y, Yang J Y. Melting behaviors of nanocrystalline Ag. Journal of Physical Chemistry B,2005,109(43),20339-20342
[95]Hu W Y, Deng H Q, Yuan X J, et al. Point-defect properties in hcp rare earth metals with analytic modified embedded atom potentials. The European Physical Journal B,2003,34(4):429-440
[96]Hu W Y, Xiao S F, Yang J Y, et al. Melting evolution and diffusion behavior of vanadium nanoparticles. The European Physical Journal B,2005,45(4): 547-554
[97]Xiao S F, Hu W Y. Comparative study of microstructural evolution during melting and crystallization. Journal of Chemistry Physics,2006,125(1): 014503-014504
[98]Yang J Y, Hu W Y, Xiao S F. Anharmonic effects on Be(0001):a molecular dynamics study. Computational Materials Science,2006,37(4):607-612
[99]Luo W H, Hu W Y, Xiao S F. Melting temperature of Pb nanostructural materials from free energy calculation. Journal of Chemistry Physics,2008, 128(7):074710-074718
[100]Baskes M I. Modified embedded-atom potentials for cubic materials and impurities. Physical Review B,1992,46(5):2727-2742
[101]Honeycutt J D, Andersen H C. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. Journal of Chemistry Physics,1987, 91(19):4950-4963.
[102]Steiner R. ASM Handbook. New York:ASM International,1992,106-108
[103]Peng P, Soh A K, Yang R, et al. First-principles study of alloying effect of Re on properties of Ni/Ni3Al interface. Computational Materials Science,2006, 38(2):354-361
[104]Wang Y J, Wang C Y. The alloying mechanisms of Re, Ru in the quaternary Ni-based superalloys γ/γ' interface:A first principles calculation. Materials Science and Engineering,2008,490(1-2):242-249
[2]张立德,牟季美.纳米材料和纳米结构.北京：科学出版社,2001,1-45
[3]Siegel R W. Mechanical properties of nanophase materials. Materials Science Forum,1997,235-238:851-860
[4]Glener H. Nanocrystalline materials. Progress in Materials Science,1989,33(3): 223-315
[5]Andrievski R A. State-of-the-art and perspectives in particulate nanostructured materials. Materials Science Forum,1998,282-283:1-10
[6]卢柯,徐坚.纳米金属材料：进展和挑战.见：李桓德编98中国材料研讨会论文集.北京：化学工业出版社,1999,88-92
[7]卢柯,卢磊.金属纳米材料力学性能的研究进展.金属学报,2000,36(8)：785-789
[8]文玉华,周富信,刘曰武等.纳米材料的研究进展.力学进展,2001,31(1)：47-61
[9]Gusev A E. Effects of the nanocrystalline state in solids. Physics-Uspekhi,1998, 41(1):49-76
[10]Lu K. Nanocrystalline metals crystallized from amorphous solids: nanocrystalline, structure, and properties. Materials Science and Engineering Reports,1996,16(4):161-221
[11]吴恒安,王秀喜,梁海弋等.金属纳米丝力学行为研究进展.金属学报,2002,38(9)：903-907
[12]孙秀魁,丛洪涛,徐坚等.纳米晶Al的制备及拉伸性能(Ⅰ).材料研究学报,1998,12(6)：645-650
[13]丛洪涛,孙秀魁,徐坚等.纳米晶Al的制备及拉伸性能(Ⅱ).材料研究学报,1998,12(6)：651-654
[14]Hashimoto S, Kaneko Y, Kitagawa K, et al. On the cyclic behavior of ultra-fine grainedcopper produced by equi-channel angular pressing. Materials Science Forum,1999,312-314:593-598
[15]Zhu M, Fecht H J. Softening effect in nanocrystalline Fe-Cu supersaturated solid solutions. Nanostructured Materials,1995,6(5-8):921-924
[16]Wen B M, Sader J E, Boland J J. Mechanical properties of ZnO nanowires. Physical Review Letters,2008,101(17),175502-1-175502-4
[17]Sanders P G, Rittner M, Kiedaisch E, et al. Creep of nanocrystalline Cu, Pd, andAl-Zr. Nanostructured Materials,1997,9(1-8):433-440
[18]Honer H J, Tao R, Kim L, et al. Mechanical properties of single-phase and nano-compositemetals and ceramics. Nanostructured Materials,1995,6(5-8): 901-904
[19]Diao J, Gall K, Dunn M L. Surface-stress-induced phase transformation in metal nanowires. Nature Materials,2003,2(10):656-660
[20]Park H S. Stress-Induced martensitic phase transformation in intermetallic Nickel Aluminum nanowires. Nano Letters,2006,6(5):958-962
[21]Singh N. Effective pair potential and structural phase transitions of Cr, Mo, and W. Physical Review B,1992,46(1):90-97
[22]Luo W D, Roundy D, Cohen M L, et al. Ideal strength of bcc molybdenum and niobium. Physical Review B,2002,66(9):094110-1-094110-7
[23]Guo Y F, Wang Y S, Zhao D L, et al. Mechanisms of martensitic phase transformations in body-centered cubic structural metals and alloys:Molecular dynamics simulations. Acta Materialia,2007,55(19):6634-6641
[24]Li X F, Hu W Y, Xiao S F, et al. Molecular dynamics simulation of polycrystalline molybdenum nanowires under uniaxial tensile strain:Size effects. Physica E,2008,40(10):3030-3036
[25]Wong E W, Sheehan P E, Lieber C M. Nanobeam mechanics:elasticity, strength and toughness of nanorods and nanotubes. Science,1997,277(5334): 1971-1975
[26]Wu B, Heidelberg A, Boland J J. Mechanical properties of ultrahigh-strength gold nanowires. Nature Materials,2005,4(7),525-529
[27]Gonz'alez J C, Rodrigues V, Bettini J, et al. Indication of unusual pentagonal structures in atomic-Size Cu nanowires. Physical Review Letters,2004,93(12): 126103-1-126103-4
[28]Han X D, Zhang Y F, Zheng K, et al. Low-temperature in-situ large strain plasticity of ceramic SiC nanowires and its atomic-scale mechanism. Nano Letters,2007,7(2):452-457
[29]Brenner S S. Tensile strength of whiskers. Journal of Applied Physics,1956, 27(12):1484-1491
[30]Casady J B, Johnson R W. Status of silicon carbide (SiC) as a wide-bandgap semiconductor for high-temperature applications. Solid-State Electronics,1996, 39(10):1409-1422
[31]Nakamura D, Gunjishima I, Yamaguchi S, et al. Ultrahigh-quality silicon carbide single crystals. Nature,2004,430(7003):1009-1012
[32]Kizuka T. Atomistic visualization of deformation in gold. Physical Review B, 1998,57(18):11158-11163
[33]文玉华,周富信,刘日武.纳米晶铜单向拉伸变形的分子动力学模拟.力学学报,2002,34(1)：29-36
[34]Swygenhoven H V, Caro A. Molecular dynamics computer simulation of elastic and plajstic behavior of nanophase Ni. Materials Research Society Proceeding, 1997,457(1-2):193-198
[35]Swygenhoven H V, Caro A. Molecular dynamics computer simulation of nanophase Ni:structure and mechanicalproperties. Nanostructured Materials, 1997,9(1-8):669-672
[36]Lu L, Shen Y F, Chen X H, et al. Ultrahigh Strength and High Electrical Conductivity in Copper. Science,2004,304(5669):422-426
[37]Bahr D F, Kramer D E, Gerberich W W. Nonliner deformation mechanisms during nanoindentation. Acta Materialia,1998,46(10):3605-3617
[38]常明,孙伟,邢金华等.模拟纳米晶体原子分布及X射线散射理论图案.物理学报,1997,46(7)：1319-1325
[39]Thomas G J, Siegel R W, Eastman J A. Grain boundary in nanophase palladium: high resolution electronmicroscope and image simulation. Scripta Metalluryica et Materiallia,1990,24(1):201-206
[40]黄丹,陶伟明,郭乙木.分子动力学模拟单晶纳米铝丝的拉伸破坏.兵器材料科学与工程,2005,28(3)：1-4
[41]黄丹,章青,郭乙木.a-Fe和Ni纳米丝单向拉伸过程的分子动力学模拟.兵器材料科学与工程,2006,29(5)：12-15
[42]Nieman G W, Weertman J R, Siegel R W. Mechanical behavior of nanocrystalline Cu and Pd. Journal of Materials Research,1991,6(5): 1012-1027
[43]Sanders P G, Eastman J A, Weertman J R. Elastic and tensile behavior of nanocrystalline copper and palladium. Acta Materialia,1997,45(10): 4019-4025
[44]Shen T D, Koch C C, Tsui T Y, et al. On the elastic moduli of nanocrystalline Fe, Cu, Ni and Cu-Ni alloysprepared by mechanical milling/alloying. Journal of Materials Research,1995,10(11):2892-2896
[45]Schiotz J, Vegge T, Ditolla F D, et al. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Physical Review B,1999, 60(17):11971-11983
[46]Wang Z G, Zu X T, Yang L, et al. Weber W J. Atomistic simulations of the size, orientation, and temperature dependence of tensile behavior in GaN nanowires. Physical Review B,2007,76(4):045310-1-045310-9
[47]Chen D L, Chen T C. Mechanical properties of Au nanowires under uniaxial tension with high strain-rate by molecular dynamics. Nanotechnology,2005, 16(12):2972-2981
[48]Schiotz J, Tolla F D D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature,1998,391(6667):561-563
[49]Koh S J A, Lee H P, Lu C, et al. Molecular dynamics simulation of a solid platinum nanowire under uniaxial tensile strain:Temperature and strain-rate effects. Physical Review B,2005,72(8):085414-1-085414-11
[50]Sankaranarayanan S K R S, Bhethanabotla V R, Joseph B. Molecular dynamics simulation of temperature and strain rate effects on the elastic properties of bimetallic Pd-Pt nanowires. Physical Review B,2007,76(13): 134117-1-134117-13
[51]Seroodeh A R, Attariani H, Khosrownejad M. Nickel nanowires under uniaxial loads:A molecular dynamics simulation study. Computational Materials Science,2008,44(2):378-384
[52]Karch J, Birringer R, Gleiter H. Ceramics ductile at low temperature.Nature, 1987,330(6148):556-558
[53]Bohn R, Haubold T, Birringer R, et al.Nanocrystalline intermetallic compounds-An approach to ductility. Scripta Metallurgica et Materialia,1991, 25(4):811-816
[54]Koch C C, Morris D G, Lu K, et al. Ductility of nanostructured materials. MRS Buelltin,1999,24:54-58
[55]Mishra R S, Valley R Z, Mukherjee A K. The observation of tensile superplasticity in nanocrystalline materials. Nanostructured Materials,1997, 9(1-8):473-476
[56]Valley R Z. Superplasticity in nanocrystalline metallic materiajs. Materials Science Forum,1997,243-245:207-216
[57]Lu L, Sui M L, Lu K. Superplastic extensibility of nanocrystalline copper at room temperature. Science,2000,287(5457):1463-1466
[58]McFadden S X, Mishra R S, Valley R Z, et al. Low-temperature superplasticity innanostructured nickel and metal alloys. Nature,1999,398(6729):684-686
[59]Agostino G D, Swygenhoven H V. Structural and mechanical properties of a simulated nickel nanophase. Materials Research Society Proceeding,1996,400, 293-298
[60]Nieman G W, Weertman J R. Mechanical behavior of nanocrystalline copper and palladium. Journal of Materials Research,1991,6(15):1012-1027
[61]Diego G G, Eugenio Z S, Arturo D R, et al. Diffusion-driven superplasticity in ceramics:Modeling and comparison with available data. Physical Review B, 2009,80(21):214107-1-214107-8
[62]Liang W W, Zhou M. Atomistic simulations reveal shape memory of fcc metal nanowires. Physical Review B,2006,73(11):115409-1-115409-11
[63]Liang W W, Zhou M. Shape memory effect in Cu nanowires. Nano Letters,2005, 5(10):2039-2043
[64]Daw M S, Baskes M I. Embedded-atom method:Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B,1984, 29(12):6443-6453
[65]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,2003,1-20
[66]Daw M S, Foiles S M, BaskesM I. The embedded-atom method:a review of theory and applications. Materials Science Reports,1993,9(7):251-340
[67]Daw M S, Foiles S M. Calculations of the energetics and structure of Pt (110) using the embedded atom method. Journal of Vacuum Science and Technology A,1986,4(3):1412-1413
[68]Daw M S. Calculations of the energetics and structure of Pt (110) reconstruction using the embedded atom method. Surface Science,1986,166(2-3):L161-L169
[69]Foiles S M. Reconstruction of fcc (110) surface. Surface Science,1987, 191(1-2):L779-L784
[70]Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt and their alloys. Physical Review B,1986, 33(12):7983-7991
[71]Jacobsen K W, Norskov J K, Puska M J. Interatomtic interactions in the effective-medium theory. Physical Review B,1987,35(14):7423-7442
[72]Cleri F, Rosato V. Tight-binding potentials for transition metals and alloys. Physical Review B,1993,48(1):22-23
[73]Finnis M W, Sinclair J F. A simple empirical N-body potential for transition metals. Philosophical Magazine A,1984,50(1):45-55
[74]Johnson R A. Analytic nearest-neighbor model for fcc metals. Physical Review B,1989,37(12):3924-3931
[75]Norskov J K. Covalent effects in the effective-medium theory of chemical binding:hydrogen heats of solution in the 3d metals. Physical Review B,1982, 26 (6):2875-2885
[76]Daw M S, Baske M I. Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Physical Review B,1983,50(17):1285-1288
[77]Hu W Y, Zhang B W, Huang B Y, et al. Analytic Modified Embedded Atom Potentials for hcp Metals. Journal of Physics Condensed Matter,2001,13(6): 1193-1213
[78]Hu W Y, Masahiro F. The application of the analytic embedded atom potentials to alkali metals. Modelling and Simulation in Materials Science and Engineering,2002,10(6):707-726
[79]Wu Y, Hu W Y. Molecular Dynamic simulation of thermodynamics, elastic constants and solid solution strength for Mg-Gd alloys. The European Physical Journal B,2007,57(6):305-312
[80]Wu Y, Hu W Y, Yang S L, et al. Solid solution mechanism and thermodynamic properties of Ti-Re alloy system:Experiment and Theory. Intermetallics,2007, 15(1):1116-1121
[81]Villas P, Calvert L. Pearson's handbook of crystallographic data for intermetallic phases. Germany:ASM International, Materials Park, OH,1991, 456-458
[82]Hultgren R, Desai P D, Hawkins D T, et al. Selected values of thermodynamic properties of binary alloys. Germany:ASM. Matals Park, OH,1973,634-635
[83]Gear C W. Numerical initial value problems in ordinary differential equation. New Jersey:Prentice-Hall,1971,345-376
[84]肖时芳.纳米结构金属及合金热力学性能的原子模拟：[湖南大学博士学位论文].长沙：湖南大学材料科学与工程学院,2007,16-17
[85]吴玉蓉.稀土镁合金的热力学及固溶特性的理论模拟：[湖南大学博士学位论文].长沙：湖南大学材料科学与工程学院,2007,24-25
[86]Nose S. A Unifed formulation of the constant temperature molecular dynamics methods. Journal of Chemical Physics,1984,81(1):511-519
[87]Hoover W G. Canonical dynamics:equilibrium phase-space distributions. Physical Review A,1985,31(3):1695-1702
[88]Anderson H C. Molecular dynamics simulations at constant press and/or temperature. Journal of Chemical Physics,1980,72(4):2384-2393
[89]杨剑瑜.金属表面动力学性质的原子模拟研究：[湖南大学博士学位论文].长沙：湖南大学材料科学与工程学院,2006,20-22
[90]汤剑锋.B2-FeAl低指数表面动力学性质的分子动力学模拟：[湖南大学硕士学位论文].长沙：湖南大学物理与微电子科学学院,2008，16-18
[91]Hu W Y, Naka I M, Yamane T. Science and engineering in advanced materials. In:Proc of Int Conf on new frontiers of process. Japan,2004,7-14
[92]Yang J Y, Hu W Y, Deng H Q, et al. Temperature dependence of atomic relaxation and vibrations for the vicinal Ni (977) surface:a molecular dynamics study. Surface Science,2004,572(2-3):439-448
[93]Hu W Y, Shu X L, Zhang B W. Point-defect properties in body-centered cubic transition metals with analytic EAM interatomic potentials. Computational Materials Science,2002,23(1-4):175-189
[94]Xiao S F, Hu W Y, Yang J Y. Melting behaviors of nanocrystalline Ag. Journal of Physical Chemistry B,2005,109(43),20339-20342
[95]Hu W Y, Deng H Q, Yuan X J, et al. Point-defect properties in hcp rare earth metals with analytic modified embedded atom potentials. The European Physical Journal B,2003,34(4):429-440
[96]Hu W Y, Xiao S F, Yang J Y, et al. Melting evolution and diffusion behavior of vanadium nanoparticles. The European Physical Journal B,2005,45(4): 547-554
[97]Xiao S F, Hu W Y. Comparative study of microstructural evolution during melting and crystallization. Journal of Chemistry Physics,2006,125(1): 014503-014504
[98]Yang J Y, Hu W Y, Xiao S F. Anharmonic effects on Be(0001):a molecular dynamics study. Computational Materials Science,2006,37(4):607-612
[99]Luo W H, Hu W Y, Xiao S F. Melting temperature of Pb nanostructural materials from free energy calculation. Journal of Chemistry Physics,2008, 128(7):074710-074718
[100]Baskes M I. Modified embedded-atom potentials for cubic materials and impurities. Physical Review B,1992,46(5):2727-2742
[101]Honeycutt J D, Andersen H C. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. Journal of Chemistry Physics,1987, 91(19):4950-4963.
[102]Steiner R. ASM Handbook. New York:ASM International,1992,106-108
[103]Peng P, Soh A K, Yang R, et al. First-principles study of alloying effect of Re on properties of Ni/Ni3Al interface. Computational Materials Science,2006, 38(2):354-361
[104]Wang Y J, Wang C Y. The alloying mechanisms of Re, Ru in the quaternary Ni-based superalloys γ/γ' interface:A first principles calculation. Materials Science and Engineering,2008,490(1-2):242-249