Molecular dynamics (MD) simulation is a powerful tool in materials research. It has been widely used to provide an atomic description of the crystallization and glass forming processes during rapid solidification of alloys. Quantum mechanics based many-body Tight-Binding (TB) potential model has been utilized in our MD simulation to simulate structural and thermal properties of several metals and alloy systems.
Structure evolution was simulated for alloys consisting of two to eight equal-molar elements Ni, Al, Cu, Co, Ti, V, Zn, Zr as being molten, rapidly-solidified (at 2 x 1013 K/s), and annealed, respectively. We found that as the number of elements n < 4 the melt-quenched alloys tend to form amorphous structure; however when n is five and more, the alloys show a liquid-like solidified structure.
We propose to estimate the glass-forming-ability (GFA) criterion of alloys by simulation of reduced glass transition temperature (Trg). Trg of CuxZr100-x (x= 46, 50, 62) correspond well to experimental values in literature. We calculated GFA of TixCo100-x (x= 60 ~ 84) alloys and found potential glass-forming compositions, which were experimentally verified to be bulk metallic glasses. We succeeded for the first time in literature the prediction of BMG compositions before experimental trial-and-errors.
We tried to bring closer the mechanical melting to thermodynamic melting by incorporating into the TB-potential an extra lattice vibration energy in MD calculations. Calculated melting point of single elements was 0.5 to 9.8 % varied from the experimental ones instead of 20 to 30 % in conventional simulation. This method works well for elements with a low ratio between Debye temperature and melting temperature.

分子動力學模擬對材料研究而言為一有力的工具，且廣泛地應用於快速凝固合金之結晶化及玻璃形成程序上之研究。本研究利用以量子力學為基礎所簡化之緊束勢能模型來描述原子之運動行為，進行一連串之分子動力學相關之研究。
本研究包含三大主題，首先，以二元至八元等莫耳比例之鎳、鋁、銅、鈷、鈦、釩、鋅、鋯合金為題，探討這些合金經過熔融、固化(以 2 x 1013 K/s 之冷卻速度冷卻)與退火等程序，其結構及性質之變化。發現其結構變化與其元素多寡有絕對關係。當元素量為四元或更少時，合金固化後傾向成為非晶質結構；當合金組成元素為五元及以上時，固化之合金傾向形成類液體結構。
第二主題，以CuxZr100-x (x= 46, 50, 62) 及 TixCo100-x (x= 60, 70, 77 and 84)之合金系統，計算其約化玻璃轉化溫度(Trg= Tg/Tm，Tg為玻璃轉化溫度、Tm為熔點)，以探討其非晶形成能力。結果發現Cu-Zr系之Trg 計算值與文獻報導值吻合。計算亦得到Ti-Co系中具有高Trg之成分，並據以實驗驗證相吻合。本研究因而首先披露以MD模擬，定量預測高玻璃形成能力合金成分的方法。於開發新式塊狀非晶時，這將有助於以模擬方法先預測具有潛力的合金成份，可降低實驗嘗試錯誤的次數。
最後，為了縮短熔點計算值與實驗值之巨大差異，我們利用了調整勢能參數之方式，將無因次晶格振動能加進傳統緊束勢能參數中，計算單元素之熔點。結果發現可將原先計算之熔點（實為機械式熔融）誤差20∼30％降為0.5∼9.8％。我們成功地發展出使機械熔點逼近熱力學熔點的MD法，並發現特別適用於Debye溫度與熔點比值小於0.3之單元素。

[1] April L. Ulery, and Rattan Lal, Encyclopedia of Soil Science, 2nd ed. (Taylor & Francis, 2002).
[2] W. Klement, R.H. Wilens, P. Duwez, “Non-crystalline Structure in Solidified Gold–Silicon Alloys”, Nature 187 (1960) 869.
[3] W.L. Johnson, “Thermodynamic and kinetic aspects of the crystal to glass transformation in metallic materials”, Prog. Mater. Sci. 30 (1995) 81.
[4] A.L. Greer, “Metallic Glasses”, Science 267 (1995) 1947.
[5] H.A. Daveis, Amorphous Metallic alloys (Butterworth-Heinemann, 1993).
[6] S. Kavesh, Meatllic Glasses (ASM International, 1978).
[7] H.W. Kui, A.L. Greer, and D. Turbull, “Formation of bulk metallic glass by fluxing”, Appl. Phys. Lett. 45 (1984) 615.
[8] A. Inoue, N. Nishiyama, and H. Kimura, “Thermal stability and magnetic properties of bulk amorphous Fe-Al-Ga-P-C-B-Si alloys”, Mater. Trans., JIM 38 (1997) 179.
[9] H. Ma, L.L. Xu, Y. Li, and E. Ma, “Discovering inch-diameter metallic glasses in three-dimensional composition space”, Appl. Phys. Lett. 87 (2005) 181915.
[10] W.H. Wang, C. Dong, C.H. Shek, Mater. Sci. Eng. R 44 (2005) 45.
[11] K.L. Chopra, Thin film phenomena (McGraw-Hill, 1985).
[12] A. Inoue, “Stabilization of metallic supercooled liquid and bulk amorphous alloys”, Acta Mater. 48 (2000) 279.
[13] A. Inoue, “High strength bulk amorphous alloys with low critical cooling rates”, Mater. Trans., JIM 36 (1995) 866.
[14] T. Masumoto, Sci. Rep. RITU A39 (1994) 91.
[15] R. W. Cahn, Materials Science and Technology: A Comprehensive Treatment, Vol. 9, Glasses and Amorphous Materials (VCH Press, 1991).
[16] J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsai, and S. Y. Chang, “Nanostructured High-entropy Alloys with Multi-Principal Elements-Novel Alloy Design Concepts and Outcomes”, Adv. Eng. Mate. 6 (2004) 299.
[17] P. K. Huang, J. W. Yeh, T. T. Shun, and S. K. Chen, “Multi-principal-Element Alloys with Improved Oxidation and Wear Resistance for Thermal Spray Coating”, Adv. Eng. Mater. 6 (2004) 74.
[18] C. Y. Hsu, J. W. Yeh, S. K. Chen, and T. T. Shun, “Wear Resistance and High-Temperature Compression Strength of FCC CuCoNiCrAl0.5Fe Alloy with Boron Addition“, Met. and Mat. Trans. A 31 (2004) 1465.
[19] J.M. Haile, Molecular Dynamics Simulation: Elementary Methods (John Wiley & Sons, INC., 1997).
[20] B. J. Alder, and T. E. Wainwright, “Studies in Molecular Dynamics. I. General Method”, J. Chem. Phys. 31 (1959) 459.
[21] B. J. Alder and T. E. Wainwright, “Phase Transition for a Hard Sphere System”, J. Chem Phys. 27 (1957) 1208.
[22] J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, “Dynamics of Radiation Damage “, Phys. Rev. 120 (1960) 1229.
[23] L. Verlet, “Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules “, Phys. Rev. 159 (1967) 98.
[24] L. Verlet, “Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions “, Phys. Rev. 165 (1967) 201.
[25] A. Rahman, “Correlations in the Motion of Atoms in Liquid Argon“, Phys. Rev. 136 (1964) A405.
[26] T. Halicioğlu and G. M. Pound, “CALCULATION OF POTENTIAL ENERGY PARAMETERS FROM CRYSTALLINE STATE PROPERTIES”, Phys. Stat. Sol. (a) 30 (1975) 619.
[27] J. E. Lennard-Jones, “The determination of molecular fields. I. From the variation of the viscosity of a gas with temperature”, Proc. Roy. Soc. 106A (1924) 441.
[28] J. E. Lennard-Jones, “The determination of molecular fields. II. From the variation of the viscosity of a gas with temperature”, Proc. Roy. Soc. 106A (1924) 463.
[29] M. S. Daw and M. I. Baskes, “Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals”, Phys. Rev. B 29 (1984) 6443.
[30] D. Tomanek, A. A. Aliigia, and C. A. Balseiro, “Calculation of elastic strain and electronic effects on surface segregation”, Phys. Rev. B 32 (1985) 5051.
[31] F. Cleri, and V. Rosato, “Tight-binding potentials for transition metals and alloys”, Phys. Rev. B 48 (1993) 22.
[32] G. Duan, D. Xu, Q. Zhang, G. Zhang, T. Cagin, W. L. Johnson, and W. A. Goddard III, “Molecular dynamics study of the binary Cu46Zr54 metallic glass motivated by experiments: Glass formation and atomic-level structure”, Phys. Rev. B 71 (2005) 224208.
[33] R. Ferrando, G. Tréglia, “Tight-binding molecular dynamics study of diffusion on Au and Ag(111)”, Surface Science 331 (1995) 920.
[34] M. Guerdane and H. Teichler, “Structure of the amorphous, massive-metallic-glass forming Ni25Zr60Al15 alloy from molecular dynamics simulations”, Phys. Rev. B 65 (2001) 014203.
[35] K.L Chopra, Thin Film Phenomena (McGraw-Hill, 1985).
[36] C.Y. Lin, PhD thesis, “Fe-Based Bulk Amorphous and Bulk Nanocrstalline Soft Magnetic Alloys”, National Tschin-Hwa University (Tawain, 2006).
[37] F.X. Liu, P.K. Liaw, G.Y. Wang, C.L. Chiang, D.A. Smith, P.D. Rack, J.P. Chu, and R.A. Buchanan, “Specimen-geometry effects on mechanical behavior of metallic glasses“, Intermetallics 14 (2006) 1014.
[38] P.S. Gramt, ”SPRAY FORMING”, Prog. Mater. Sci. 39 (1995) 497.
[39] B. Lin, N. Nordstrom, and E.J. Lavernia, Mater. Sci. Eng. R A237 (1997) 141.
[40] R. Liu, J. Lin, K. Dong, C. Zheng, and H. Liu, Mater. Sci. Eng. R B94 (2002) 141.
[41] M. Ohring, and A. Haldipur, “Versatile arc melting apparatus for quenching molten metals and ceramics“, Rev. Sci. Instrum. 42 (1971) 530.
[42] R. Pond, and R. Maddin, “METHOD OF PRODUCING RAPIDLY SOLIDIFIED FILAMENTARY CASTINGS”, Trans. Met. Soc. AIME 245 (1969) 2475.
[43] M.S. El-Eskandarany, A. Inoue, “Solid-state crystalline-glassy cyclic phase transformations of mechanically alloyed Cu33Zr67 powders “, Metall.Mater. Trans. A 33 (2002) 135.
[44] C.C. Koch, O.B. Kavin, C.G. Mackamey, J.O. Scarbrough, “Preparation of ``amorphous'' Ni60Nb40 by mechanical alloying”, Appl. Phys. Lett. 43 (1983) 1017.
[45] J. Lee, F. Zhou, K.H. Chung, N.J. Kim, E.J. Lavernia, “Grain Growth of Nanocrystalline Ni Powders Prepared by Cryomilling”, Metall. Mater. Trans. A 32 (2001) 3109.
[46] A. Sagel, H. Sieber, H-J. Fecht, and J. H. Perepezko, “Synthesis of an amorphous Zr–Al–Ni–Cu alloy with large supercooled liquid region by cold-rolling of elemental foils”, Acta Mater. 46 (1998) 4233.
[47] Y. Saito, U. Utsunomiya, N. Tsuji, and T. Sakai, “Novel ultra-high straining process for bulk materials—development of the accumulative roll-bonding (ARB) process”, Acta Mater. 47 (1999) 579.
[48] Z.P. Xing, S.B. Kang, and H.W. Metall, “Microstructural Evolution and Mechanical Properties of the AA8011 Alloy during the Accumulative Roll-Bonding Process”, Mater. Trans. A 33 (2002) 1521.
[49] I.W. Donald, and H.A. Davies, “Prediction of glass-forming ability for metallic systems”, J. Non-Cryst. Solids 30 (1978) 77.
[50] A. Hruby, “Evaluation of glass-forming tendency by means of DTA”, Czech. J. Phys. 22 (1972) 1187.
[51] K. Mondal, and B.S. Murty, “On the parameters to assess the glass forming ability of liquids”, J. Non-Cryst. Solids 351 (2005) 1366.
[52] M. Saad, and M. Poulain, “GLASS FORMING ABILITY CRITERION”, M. Mater. Sci. Forum 19 (1987) 11.
[53] D. Turnbull, “Under what conditions can a glass be formed”, Contemp. Phys. 10 (1969) 473.
[54] T.H. Hung, J.C. Huang, J.S.C Jang, and S.C. Lu, “Improved Thermal Stability of Amorphous ZrAlCuNi Alloys with Si and B”, Mater. Trans. 48 (2007) 239.
[55] Z.P. Lu, C.T. Liu, and Y. Dong, “Effects of atomic bonding nature and size mismatch on thermal stability and glass-forming ability of bulk metallic glasses“, J. Non-Cryst. Solids 341 (2004) 93.
[56] O.N. Senkov, and D.B. Miracle, “Effect of the atomic size distribution on glass forming ability of amorphous metallic alloys“, Mater. Res. Bull 36 (2001) 2183.
[57] X. Xiao, S. Fang, G. Wang, Q. Hua, and Y. Dong, “Influence of beryllium on thermal stability and glass-forming ability of Zr–Al–Ni–Cu bulk amorphous alloys”, J. Alloys Compd. 376 (2004) 145.
[58] X. Xiao, S. Fang, L. Xia, W. H. Li, Q. Hua, and Y. Dong, “Thermal and mechanical properties of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass”, J. Alloys Compd. 351 (2003) 324.
[59] Z.J. Yan, J.F. Li, S.R. He, and Y.H. Zhou, “Evaluation of the optimum solute concentration for good glass forming ability in multicomponent metallic glasses“, Mater. Res. Bull 38 (2003) 681.
[60] T. Egami, “The atomic structure of aluminum based metallic glasses and universal criterion for glass formation“, J. Non-Cryst. Solids 205-207 (1996) 575.
[61] T. Egami, “Universal criterion for metallic glass formation“, Mater. Sci. Eng. A 226 (1997) 261.
[62] T. Egami, and Y. Waseda, “Atomic size effect on the formability of metallic glasses“, J. Non-Cryst. Solids 64 (1984) 113.
[63] D.B. Miracle, and O.N. Senkov, “A geometric model for atomic configurations in amorphous Al alloys“, J. Non-Cryst. Solids 319 (2003) 174.
[64] O.N. Senkov, and D.B. Miracle, “Topological criteria for amorphization based on a thermodynamic approach”, J. Appl. Phys. 97 (2005) 103502.
[65] S. Azad, A. Mandal, and R.K. Mandal, “On the parameters of glass formation in metallic systems”, Mater. Sci. Eng. A 458 (2007) 348.
[66] W. Chen, Y. Wang, J. Qiang, and C. Dong, “Bulk metallic glasses in the Zr-Al-Ni-Cu system”, Acta Mater. 51 (2003) 1899.
[67] M. Iqbal, W.S. Sun, H.F. Zhang, J.I. Akhter, and Z.Q Hu, “Effect of additional elements on mechanical properties of a specially constituted Zr-based alloy“, Mater. Sci. Eng. A 447 (2007) 167.
[68] Q. Wang, Y.M. Wang, J.B. Qiang, X.F. Zhang, C.H. Shek, and C. Dong, “Composition optimization of the Cu-based Cu–Zr–Al alloys”, Intermetallics 12 (2004) 1229.
[69] Y.M. Wang, C.H. Shek, J.B. Qiang, C.H. Wong, W.R. Chen, and C. Dong, “The e/a factor governing the formation and stability of (Zr76Ni24)1-xAlx bulk metallic glasses”, Script Mater. 48 (2003) 1525.
[70] Y.M. Wang, W.P. Xu, J.B. Qiang, C.H.Wong, C.H. Shek, and C. Dong, “The e/a criterion of Zr-based bulk metallic glasses”, Mater. Sci. Eng. A 375 (2004) 411.
[71] H.S. Chen, and D. Turnbull, “Formation, stability and structure of palladium-silicon based alloy glasses“, Acta Matall. 17 (1969) 1021.
[72] Z.P. Lu, H. Tan, Y. Li, and S.C. Ng, “The correlation between reduced glass transition temperature and glass forming ability of bulk metallic glasses”, Scripta Mater. 42 (2000) 667.
[73] B.S. Murty, and K. Hono, “Formation of Nanocrystalline Particles in Glassy Matrix in Melt-Spun Mg-Cu-Y based Alloys”, Mater. Trans. JIM 41 (2000) 1538.
[74] T.D. Shen, and R.B. Schwarz, “Bulk ferromagnetic glasses prepared by flux melting and water quenching”, Appl. Phys. Lett. 75 (1999) 49.
[75] T.A. Waniuk, J. Schroers, and W.L. Johnson, “Critical cooling rate and thermal stability of Zr–Ti–Cu–Ni–Be alloys”, Appl. Phys. Lett. 78 (2001) 1213.
[76] A. Inoue, W. Zhang, T. Zhang, and K. Kurosaka, “HIGH-STRENGTH Cu-BASED BULK GLASSY ALLOYS IN Cu–Zr–Ti AND Cu–Hf–Ti TERNARY SYSTEMS”, Acta Matall. 49 (2001) 2645.
[77] A. Inoue, W. Zhang, T. Zhang, and K. Kurosaka, “Formation and mechanical properties of Cu-Hf-Ti bulk glassy allo”, J. Mater. Res. 16 (2001) 2836.
[78] Z.P. Lu, and C.T. Liu, “A new glass-forming ability criterion for bulk metallic glasses”, Acta Mater. 50 (2002) 3501.
[79] Z.P. Lu, and C.T. Liu, “A new approach to understanding and measuring glass formation in bulk amorphous materials”, Intermeatllics 12 (2004) 1035.
[80] Z.P. Lu, and C.T. Liu, “Glass Formation Criterion for Various Glass-Forming Systems”, Phys. Rev. Lett. 91 (2003) 115505.
[81] X.H. Du, J.C. Huang, C.T. Liu, and Z.P. Lu, “New criterion of glass forming ability for bulk metallic glasses”, J. Appl. Phys. 101 (2007) 086108.
[82] R. Abbaschian and R.E. Reed-Hill, physical metallurgy principles 4th ed. (PWS, 1994).
[83] A. Inoue, T. Zhang, and T. Masumoto, “Glass-forming ability of alloys”, J. Non-cryst. Solids 156 (1993) 473.
[84] D. Ma, H. Tan, D. Wang, Y. Li, and E. Ma, ”Strategy for pinpointing the best glass-forming alloys”, Appl Phys Lett. 86 (2005) 191906.
[85] H. Tan, Y. Zhang, D. Ma, Y.P. Feng, and Y. Li, “Optimum glass formation at off-eutectic composition and its relation to skewed eutectic coupled zone in the La based La–Al–(Cu,Ni) pseudo ternary system”, Acta Mater. 51 (2003) 4551.
[86] D. Wang, Y. Li, B.B. Sun, M.L. Sui, K. Lu, E. Ma, “Bulk metallic glass formation in the binary Cu–Zr system”, Appl. Phys. Lett. 84 (2004) 4029.
[87] K.H. Huang, MS thesis, A Study on the Multi-component Alloy Systems Containing Equal-mole Elements, National Tsing-Hua University (Taiwan, 1995).
[88] J. W. Yeh, “Recent progress in high-entropy alloys”, Ann. Chim.-Sci. Mat. 31 (2006) 633.
[89] S. Ranganathan, “Alloyed pleasures: Multimetallic cocktails”, Curr. Sci. 85 (2003) 1404.
[90] J.W. Yeh, S.K. Chen, J.Y. Gan, S.J. Lin, T.S. Chin, T.T. Shun, C. H. Tsau, and S. Y. Chang, “Formation of simple crystal structures in Cu-Co-Ni-Cr-Al-Fe-Ti-V alloys with multiprincipal metallic elements”, Metall. Mater. Trans. A 35A (2004) 2533.
[91] T.K. Chen, T.T. Shun, J.W. Yeh, and M.S. Wong, “Nanostructured nitride films of multi-element high-entropy alloys by reactive DC sputtering“, Surf. Coat. Technol. 188 (2004) 193.
[92] Y.Y. Chen, T.Duval, U.D. Hung, J.W. Yeh, and H.C. Shih, “Microstructure and electrochemical properties of high entropy alloys—a comparison with type-304 stainless steel“, Corros. Sci. 47 (2005) 2257.
[93] Y.Y. Chen, U.T. Hong, J.W. Yeh, H.C. Shih, “Mechanical properties of a bulk Cu0.5NiAlCoCrFeSi glassy alloy in 288 °C high-purity water”, Appl. Phys. Lett. 87 (2005) 261918.
[94] C.J. Tong, Y.L. Chen, S.K Chen, J.W. Yeh, T.T. Shun, C.H. Tsau, S.J. Lin, and S.Y. Chang, “Microstructure characterization of AlxCoCrCuFeNi high-entropy alloy system with multiprincipal elements”, Metall. Mater. Trans. 36A (2005) 881.
[95] C.J. Tong, M.R. Chen, S.K Chen, J.W. Yeh, T.T. Shun, S.J. Lin, and S.Y. Chang, “Mechanical performance of the AlxCoCrCuFeNi high-entropy alloy system with multiprincipal elements”, Metall. Mater. Trans. 36A (2005) 1263.
[96] D.W. Heermann, Computer simulation methods, 2nd ed. (Springer, 1995).
[97] W.A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, 1966).
[98] J.K. Nørskov, and N.D. Lang, ” Effective-medium theory of chemical binding: Application to chemisorption”, Phys. Rev. B 21 (1980) 2131.
[99] M.S. Daw, and M.I. Baskes, “Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals”, Phys. Rev. Lett. 50 (1983) 1285.
[100] P. Hohenberg, and W. Kohn, “Inhomogeneous Electron Gas”, Phys. Rev. 136 (1964) B864.
[101] M.W. Finnis, and J.E. Sinclair, “A simple empirical N-body potential for transition metals “, Phil. Mag. A 50 (1984) 45.
[102] R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963).
[103] C.L. Brooks, M. Karplus, and B.M. Pettitt, Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, Vol.71 of Adv. Chem. Phys., (John Wiley & Sons, 1988).
[104] J. Broughton, W. Krakow, and S.T. Pantelides, Computer-based Microscopic Descripion of the Structure and Properties of Materials, (Materials Research Society, 1986).
[105] J.M. Haile, Molecular dynsmics simulation-Elementary methods (John Wiley & Sons, 1992).
[106] M.P. Allen, D.J. Tildesly, Computer simulation of liquids (Oxford, 1987).
[107] H. R. Wendt and F. F. Abraham, “Empirical Criterion for the Glass Transition Region Based on Monte Carlo Simulations”, Phys. Rev. Lett. 41 (1978) 1244.
[108] James R. Morris and Xueyu Song, “The melting lines of model systems calculated from coexistence simulations”, J. Chem. Phys., 116 (2002) 9352.
[109]G. Ciccotti and W.G. Hoover, Molecular dynamics simulation of statistical-mechanical systems (North-Holland, 1986).
[110] Y. Washea, The structure of metallic glasses (McGraw-HILL, 1980).
[111] S. R. Elliott, Physics of Amorphous materials, 2nd ed. (Langman Scientific & Technical, 1990).
[112] F. E. Luborsky, Amorphous Metallic Alloys, (Butterworths, 1983).
[113] K. Ding, and Hans C. Andersen, “Molecular-dynamics simulation of amorphous germanium”, Phys. Rev. B 34 (1986) 6987.
[114] D. Turnbull, “On the gram-atomic volumes of metal-metalloid glass forming alloys”, Scr. Mater. 11 (1977) 1131.
[115] D. Turnbull, “Metastable structures in metallurgy“, Metal. Trans. B, 12B (1981) 217.
[116] A. Lindsay Greer, “Confusion by design”, Nature 366 (1993) 303.
[117] H. W. Sheng, W. K. Luo, F. M. Alamgir, J. M. Bai, and E. Ma, “Atomic packing and short-to-medium-range order in metallic glasses“, Nature 439 (2006) 419.
[118] D. B. Miracle, E. A. Lord, S. Ranganathan, “Candidate Atomic Cluster Configurations in Metallic Glass Structures”, Mater. Trans. 47 (2006) 1737.
[119] D. B. Miracle, T. Egami, K. M. Flores, and K. F. Kelton, “Structural Aspects of Metallic Glasses”, MRS Bul. 32 (2007) 629.
[120] N.P. Lazarev, A.S. Bakai, C. Abromeit, “Molecular dynamics simulation of viscosity in supercooled liquid and glassy AgCu alloy“, J. Non-cryst. Solids 353, (2007) 3332.
[121] S. Kazanc, “Molecular dynamics study of pressure effect on glass formation and the crystallization in liquid CuNi alloy “, Comp. Mater. Sci. 38 (2006) 405.
[122] X. J. Han, and H. Teichler, “Liquid-to-glass transition in bulk glass-forming Cu60Ti20Zr20 alloy by molecular dynamics simulations“, Phys. Rev. E 75 (2007) 061501.
[123] H. Yang, Y.J. LÜ, M. Chen, and Z.Y. Guo, “A molecular dynamics study on melting point and specific heat of Ni3Al alloy”, Sci. China-Phys. Mech. Astron. 50 (2007) 407.
[124] H. Teichler, “Melting transition in molecular-dynamics simulations of the Ni0.5Zr0.5 intermetallic compound”,Phys. Rev. B 59 (1999) 8473.
[125] T. B. Massalski,and H. Okamoto, Binary Alloy Phase Diagrams, 2nd ed. (ASM International,1990).
[126] Janusz M. Holender, “Molecular-dynamics studies of the thermal properties of the solid and liquid fcc metals Ag, Au, Cu, and Ni using many-body interactions, Phys. Rev. B 41 (1990) 8054.
[127] J. Mei, J. W. Davenport, “Free-energy calculations and the melting point of Al”, Phys. Rev. B 46 (1992) 21.
[128] G. L. Chen, X. J. Liu, X. D. Hui, H. Y. Hou, K. F. Yao, C. T. Liu, and J. Wadsworth, “Molecular dynamic simulations and atomic structures of amorphous materials”, Appl. Phys. Lett. 88 (2006) 203115.
[129] W.N. Myung, H.G. Kim, T. Masumoto, “Glass transition behaviour of Zr- and Ti-based binary amorphous alloys”, Mater. Sci. Eng. A-Struct. 179 (1994) 252.
[130] A. Inoue, N. Nishiyama, K. Amiya, T. Zhang, T. Masumoto, “Ti-based amorphous alloys with a wide supercooled liquid region“, Mater. Lett. 61 (2007) 2851.
[131] A. Inoue, N. Nishiyama, K. Amiyam, T. Zhang, T. Masumoto, “Ti-based amorphous alloys with a wide supercooled liquid region”, Mater. Lett. 19 (1994) 131.
[132] D.V. Louzguine, A. Inoue, “Crystallization behavior of Ti50Ni25Cu25 amorphous alloy”, J. Mater. Sci. 35 (2000) 4159.
[133] L.E. Tanner, and R. Ray, “Physical properties of Ti50Be40Zr10 glass”, Scr. Metall. 11 (1977) 783.
[134] T. Zhang, A. Inoue, “Thermal and mechanical properties of Ti-Ni-Cu-Sn amorphous alloys with a wide supercooled liquid region before crystallization”, Mater Trans. JIM 39 (1998) 1001.
[135] Y. C. Kim, S. Yi, W. T. Kim, and D. H. Kim, “Glass Forming Ability and Crystallization Behaviors of the Ti-Cu-Ni-(Sn) Alloys with Large Supercooled Liquid Region”, Mater. Sci. Forum 67 (2001) 360.
[136] X.H. Lin and W.L. Johnson, “Formation of Ti–Zr–Cu–Ni bulk metallic glasses”, J. Appl. Phys. 78 (1995) 6514.
[137] T. Zhang, and A. Inoue, “Preparation of Ti-Cu-Ni-Si-B Amorphous Alloys with a Large Supercooled Liquid Region”, Mater. Trans. JIM 40 (1999) 301.
[138] W.B. Sheng, ”Correlations between critical section thickness and glass-forming ability criteria of Ti-based bulk amorphous alloys”, J. Non-Cryst. Solids 351 (2005) 3081.
[139] Y.C. Kim, W.T. Kim, and D.H. Kim, “A development of Ti-based bulk metallic glass”, Mater. Sci. Eng. A-Struct. 375 (2004) 127.
[140] F. Qin, X. Wang, S. Zhu, A. Kawashima, K. Asami, and A. Inoue, “Microstructure and Corrosion Resistance of Ti-Zr-Cu-Pd-Sn Glassy and Nanocrystalline Alloys”, Mater. Trans. JIM 48 (2007) 167.
[141] F. Q. Guo, H. J. Wang, S. J. Poon, and G. J. Shiflet, “Ductile titanium-based glassy alloy ingots”, Appl. Phys. Lett. 86 (2005) 091907.
[142] Y. C. Kim, H. J. Chang, D. H. Kim, W. T. Kim, and P. R. Cha, “Unusual glass-forming ability induced by changes in the local atomic structure in Ti-based bulk metallic glass”, J. Phys. Condens. Matter 19 (2007) 196104.
[143] Y. C. Kim, D. H. Bae, W. T. Kim, D. H. Kim,“Enthalpy recovery, creep and creep–recovery measurements during physical aging of amorphous selenium”, J. Non-Cryst. Solids 325 (2003) 242.
[144] Y. J. Huang, J. Shen, J. F. Sun, X. B. Yu, “A new Ti–Zr–Hf–Cu–Ni–Si–Sn bulk amorphous alloy with high glass-forming ability”, J. Alloys Compd. 427 (2007) 171.
[145] Jinghan Wang, Ju Li, Sidney Yip, Simon Phillpot and Dieter Wolf, “Mechanical instabilities of homogeneous crystals”, Phys. Rev. B 52 (1995) 12627.
[146] F. Ercolessi : A molecular dynamics primer (1997).
http://www.fisica.uniud.it/~ercolessi
[147] V. Sorkin, E. Polturak, and Joan Adler, “I. Mechanical Molecular dynamics study of melting of the bcc metal vanadium. Melting”, Phys. Rev. B 68 (2003) 174102.
[148] V. Sorkin, E. Polturak, and Joan Adler, “Molecular dynamics study of melting of the bcc metal vanadium. II. Thermodynamic melting”, Phys. Rev. B 68 (2003) 174103.
[149] X.J. Han, M. Chen, Z.Y. Guo, J. Phys. Condens. Matter 16 (2004) 705.
[150] J.F. Lutsko, D. Wolf, S.R. Philpot, and S. Yip, “Molecular-dynamics study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential”, Phys. Rev. B 40 (1989) 2841.
[151] W.L. Johnson, “Fundamental aspects of bulk metallic glass formation in multicomponent alloys”, Mater. Sci. Forum 225 (1996) 35.
[152] Z.P. Lu, C.T. Liu, J.R. Thompson, and W.D. Porter, “Structural Amorphous Steels”, Phys. Rev. Lett. 92 (2004) 245503.
[153] Donghua Xu, Gang Duan, and William L. Johnson, “Unusual Glass-Forming Ability of Bulk Amorphous Alloys Based on Ordinary Metal Copper”, Phys. Rev. Lett. 92 (2004) 245504.
[154] A.R. Ubbeldone, Melting and Crystal Structure (Oxford, 1965).
[155] F. A. Lindemann, “The Calculation of Molecular Vibration Frequencies “, Z. Phys. 11 (1910) 609.
[156] J.G. Dash, “History of the search for continuous melting”, Rev. Mod. Phys. 71 (1999) 1737.
[157] M.Born, “Thermodynamics of Crystals and Melting”, J. Chem. Phys. 7 (1939) 591.
[158] J.L. Tallon, “VOLUME DEPENDENCE OF ELASTIC MODULI AND THE BORN-DURAND MELTING HYPOTHESIS”, Philos. Mag. A 39 (1979) 151.
[159] D. Wolf, P.R. Okamoto, S. Yip, J.F. Lutsko, and M. Kluge, “Thermodynamic parallels between solid-state amorphization and melting”, J. Mater. Res. 5 (1990) 286.
[160] A.V. Granato, ”Interstitialcy model for condensed matter states of face-centered-cubic metals”, Phys. Rev. Lett. 68 (1992) 974.
[161] T.A. Weber and F.H. Stillinger, “Point defects in bcc crystals: Structures, transition kinetics, and melting implications”, J. Chem. Phys. 81 (1984) 5095.
[162] R.W. Cahn, ”Melting from within”, Nature 413 (2001) 582.
[163] A. Kanigel, J. Adler, and E. Polturak, ”Influence of point defects on the shear elastic coefficients and on the melting temperature of copper“, Int. J. Mod. Phys. C 12 (2001) 727.
[164] J.G. Dash, “Melting from one to two to three dimensions”, Contemp. Phys. 43 (2002) 427.
[165] R.W. Cahn, “Materials science: Melting and the surface”, Nature 323 (1986) 668.
[166] J.W.M. Frenken and J.F. van der Veen, “Observation of Surface Melting”, Phys. Rev. Lett. 54 (1985) 134.
[167] A. Trayanov and E. Tosatti, “Lattice theory of surface melting”, Phys. Rev. B 38 (1998) 6961.
[168] R.N. Barnett and U. Landman, “Surface premelting of Cu(110)”, Phys. Rev. B 44 (1991) 3226.
[169] J.F. van der Veen, Physe Transition in Surface Films 2 (Springer, 1991)
[170] R. Lipowsky, ”Critical Surface Phenomena at First-Order Bulk Transitions”, Phys. Rev. Lett. 49 (1982) 1575.
[171] R. Lipowsky, U. Breuer, K.C. Prince, and H.P. Bonzel, “Multicomponent Order Parameter for Surface Melting”, Phys. Rev. Lett. 62 (1989) 913.
[172] O.Tomagnini, F. Ercolessi, S. Iarlori, F.D. Di Tolla, and E. Tosatti, “Role of Layering Oscillations at Liquid Metal Surfaces in Bulk Recrystallization and Surface Melting”, Phys. Rev. Lett. 76 (1996) 1118.
[173] R. Ohnesorge, H. Lowen, and H. Wagner, “Density functional theory of crystal-fluid interfaces and surface melting”, Phys. Rev. E 50 (1994) 4801.
[174] H. Hakkinen and M. Manninen, “Computer simulation of disordering and premelting of low-index faces of copper”, Phys. Rev. B 46 (1992) 1725.
[175] H. Hakkinen and U. Landman, ”Superheating, melting, and annealing of copper surfaces”, Phys. Rev. Lett. 71 (1993) 1023.
[176] Y. Beaudet, L.J. Lewis, and M. Persson, “Surface anharmonicities and disordering on Ni(100) and Ni(110)”, Phys. Rev. B 50 (1994) 12084.
[177] E. T. Chen, R.N. Barnett, and U. Landman, “Surface melting of Ni(110)”, Phys. Rev. B 41 (1990) 439.
[178] E. T. Chen, R.N. Barnett, and U. Landman, “Crystal-melt and melt-vapor interfaces of nickel”, Phys. Rev. B 40 (1989) 924.
[179] H. Cox, R.L. Johnston, and J.N. Murrel, “Modelling of surface relaxation and melting of aluminium”, Surf. Sci. 373 (1997) 67.
[180] P.Stoltze, J.K. Norskov, and U. Landman, ”Disordering and Melting of Aluminum Surfaces”, Phys. Rev. Lett. 61 (1988) 440.
[181] http://en.wikipedia.org/wiki/Dulong%E2%80%93Petit_law