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Journal of Engineering Materials and Technology | Volume 131 | Issue 4 | PREDICTIVE SCIENCE AND TECHNOLOGY IN MECHANICS AND MATERIALS
PREDICTIVE SCIENCE AND TECHNOLOGY IN MECHANICS AND MATERIALS

Semi-Empirical Potential Methods for Atomistic Simulations of Metals and Their Construction Procedures

[+] Author and Article Information
Seong-Gon Kim1

Department of Physics and Astronomy, Center for Advanced Vehicular Systems, and Center for Computational Sciences, Mississippi State University, Mississippi State, MS 39762kimsg@hpc.msstate.edu

M. F. Horstemeyer

Center for Advanced Vehicular Systems, and Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762

M. I. Baskes

MST-8, MS G755, Los Alamos National Laboratory, Los Alamos, NM 87545

Masoud Rais-Rohani

Center for Advanced Vehicular Systems, and Department of Aerospace Engineering, Mississippi State University, Mississippi State, MS 39762

Sungho Kim, J. Houze, Amitava Moitra, Laalitha Liyanage

Department of Physics and Astronomy, and Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762

B. Jelinek

Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762

1

Corresponding author.

J. Eng. Mater. Technol 131(4), 041210 (Sep 01, 2009) (9 pages) doi:10.1115/1.3183784 History: Received March 10, 2009; Revised June 19, 2009; Published September 01, 2009
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General theory of semi-empirical potential methods including embedded-atom method and modified-embedded-atom method (MEAM) is reviewed. The procedures to construct these potentials are also reviewed. A multi-objective optimization (MOO) procedure has been developed to construct MEAM potentials with minimal manual fitting. This procedure has been applied successfully to develop a new MEAM potential for magnesium. The MOO procedure is designed to optimally reproduce multiple target values that consist of important material properties obtained from experiments and first-principle calculations based on density-functional theory. The optimized target quantities include elastic constants, cohesive energies, surface energies, vacancy-formation energies, and the forces on atoms in a variety of structures. The accuracy of the present potential is assessed by computing several material properties of Mg including their thermal properties. We found that the new MEAM potential shows a significant improvement over previously published potentials, especially for the atomic forces and melting temperature calculations.
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References

1
Shim, J.-H., Lee, B.-J., and Cho, Y. W., 2002, “Thermal Stability of Unsupported Gold Nanoparticle: A Molecular Dynamics Study,” Surf. Sci., 512 , pp. 262–268.  [CrossRef]
2
Kim, S. G., and Tománek, D., 1994, “Melting the Fullerenes: A Molecular Dynamics Study,” Phys. Rev. Lett., 72 , pp. 2418–2421.  [CrossRef]
3
Baskes, M. I., Nelson, J. S., and Wright, A. F., 1989, “Semiempirical Modified Embedded-Atom Potentials for Silicon and Germanium,” Phys. Rev. B, 40 (9), pp. 6085–6100.  [CrossRef]
4
Baskes, M. I., 1992, “Modified Embedded-Atom Potentials for Cubic Materials and Impurities,” Phys. Rev. B, 46 (5), pp. 2727–2742.  [CrossRef]
5
Baskes, M. I., and Johnson, R. A., 1994, “Modified Embedded Atom Potentials for HCP Metals,” Modell. Simul. Mater. Sci. Eng., 2 (1), pp. 147–163.  [CrossRef]
6
Daw, M. S., Foiles, S. M., and Baskes, M. I., 1993, “The Embedded Atom Method: A Review of Theory and Applications,” Mater. Sci. Rep., 9 , pp. 251–310.  [CrossRef]
7
Daw, M. S., and Baskes, M. I., 1983, “Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals,” Phys. Rev. Lett., 50 (17), pp. 1285–1288.  [CrossRef]
8
Daw, M. S., and Baskes, M. I., 1984, “Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals,” Phys. Rev. B, 29 (12), pp. 6443–6453.  [CrossRef]
9
Baskes, M. I., 1987, “Application of the Embedded-Atom Method to Covalent Materials: A Semiempirical Potential for Silicon,” Phys. Rev. Lett., 59 (23), pp. 2666–2669.  [CrossRef]
10
Daw, M. S., 1989, “Model of Metallic Cohesion: The Embedded-Atom Method,” Phys. Rev. B, 39 (11), pp. 7441–7452.  [CrossRef]
11
Cherne, F. J., Baskes, M. I., and Deymier, P. A., 2001, “Properties of Liquid Nickel: A Critical Comparison of EAM and MEAM Calculations,” Phys. Rev. B, 65 (2), p. 024209.  [CrossRef]
12
Baskes, M. I., Angelo, J. E., and Bisson, C. L., 1994, “Atomistic Calculations of Composite Interfaces,” Modell. Simul. Mater. Sci. Eng., 2 (3A), pp. 505–518.  [CrossRef]
13
Gall, K., Horstemeyer, M., Van Schilfgaarde, M., and Baskes, M., 2000, “Atomistic Simulations on the Tensile Debonding of an Aluminum-Silicon Interface,” J. Mech. Phys. Solids, 48 , pp. 2183–2212.  [CrossRef]
14
Lee, B. -J., and Baskes, M. I., 2000, “Second Nearest-Neighbor Modified Embedded-Atom-Method Potential,” Phys. Rev. B, 62 (13), pp. 8564–8567.  [CrossRef]
15
Wen, Y. -N., and Zhang, J. -M., 2008, “Surface Energy Calculation of the bcc Metals by Using the MAEAM,” Comput. Mater. Sci., 42 (2), pp. 281–285.  [CrossRef]
16
Zhang, J. -M., Wang, D. -D., and Xu, K. -W., 2006, “Calculation of the Surface Energy of bcc Transition Metals by Using the Second Nearest-Neighbor Modified Embedded Atom Method,” Appl. Surf. Sci., 252 (23), pp. 8217–8222.  [CrossRef]
17
Zhang, J. -M., Wang, D. -D., and Xu, K. -W., 2006, “Calculation of the Surface Energy of hcp Metals by Using the Modified Embedded Atom Method,” Appl. Surf. Sci., 253 (4), pp. 2018–2024.  [CrossRef]
18
Huang, H., Ghoniem, N. M., Wong, J. K., and Baskes, M. I., 1995, “Molecular Dynamics Determination of Defect Energetics in Beta-SiC Using Three Representative Empirical Potentials,” Modell. Simul. Mater. Sci. Eng., 3 (5), pp. 615–627.  [CrossRef]
19
Baskes, M. I., 1997, “Determination of Modified Embedded Atom Method Parameters for Nickel,” Mater. Chem. Phys., 50 , pp. 152–158.  [CrossRef]
20
Baskes, M. I., 1999, “Atomistic Potentials for the Molybdenum–Silicon System,” Mater. Sci. Eng., A, 261 (1–2), pp. 165–168.  [CrossRef]
21
Lee, B. -J., Shim, J. -H., and Baskes, M. I., 2003, “Semiempirical Atomic Potentials for the fcc Metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb Based on First and Second Nearest–Neighbor Modified Embedded Atom Method,” Phys. Rev. B, 68 (14), p. 144112.  [CrossRef]
22
Hu, W., Zhang, B., Huang, B., Gao, F., and Bacon, D. J., 2001, “Analytic Modified Embedded Atom Potentials for HCP Metals,” J. Phys.: Condens. Matter, 13 (6), pp. 1193–1213.  [CrossRef]
23
Hu, W., Deng, H., Yuan, X., and Fukumoto, M., 2003, “Point-Defect Properties in HCP Rare Earth Metals With Analytic Modified Embedded Atom Potentials,” Eur. Phys. J. B, 34 (4), pp. 429–440.  [CrossRef]
24
Liu, X. -Y., Ohotnicky, P., Adams, J., Rohrer, C., and Hyland, R., 1997, “Anisotropic Surface Segregation in Al–Mg Alloys,” Surf. Sci., 373 , pp. 357–370.  [CrossRef]
25
Lee, B. -J., and Lee, J. W., 2005, “A Modified Embedded Atom Method Interatomic Potential for Carbon,” CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 29 (1), pp. 7–16.  [CrossRef]
26
Potirniche, G. P., Horstemeyer, M. F., Wagner, G. J., and Gullett, P. M., 2006, “A Molecular Dynamics Study of Void Growth and Coalescence in Single Crystal Nickel,” Int. J. Plast., 22 (2), pp. 257–278.  [CrossRef]
27
Wang, G., Hove, M. V., Rossa, P., and Baskes, M., 1996, “Quantitative Prediction of Surface Segregation in Bimetallic PtM Alloy Nanoparticles (M=Ni,Re,Mo),” Surf. Sci., 79 (1), pp. 28–45.
28
Valone, S. M., Baskes, M. I., and Martin, R. L., 2006, “Atomistic Model of Helium Bubbles in Gallium-Stabilized Plutonium Alloys,” Phys. Rev. B, 73 (21), p. 214209.  [CrossRef]
29
Baskes, M. I., Lawson, A. C., and Valone, S. M., 2005, “Lattice Vibrations in δ-Plutonium: Molecular Dynamics Calculation,” Phys. Rev. B, 72 (1), p. 014129.  [CrossRef]
30
Baskes, M. I., Muralidharan, K., Stan, M., Valone, S. M., and Cherne, F., 2003, “Using the Modified Embedded-Atom Method to Calculate the Properties of Pu–Ga Alloys,” JOM, 55 (9), pp. 41–50.  [CrossRef]
31
Kim, J., Koo, Y., and Lee, B. -J., 2006, “Modified Embedded-Atom Method Interactomic Potential for the Fe–Pt Alloy System,” J. Mater. Res., 21 (1), pp. 199–208.  [CrossRef]
32
Lee, B. -J., and Shim, J. -H., 2004, “A Modified Embedded Atom Method Interatomic Potential for the Cu–Ni System,” CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 28 (2), pp. 125–132.
33
Kim, Y. -M., and Lee, B. -J., 2007, “A Semi-Empirical Interatomic Potential for the Cu–Ti Binary System,” Mater. Sci. Eng., A, 449-451 , pp. 733–736.  [CrossRef]
34
Zhang, J. -M., Xin, H., and Wei, X. -M., 2005, “Atomic-scale Calculation of Interface Energy for Ag/Ni,” Appl. Surf. Sci., 246 (1–3), pp. 14–22.  [CrossRef]
35
Ravelo, R., and Baskes, M., 1997, “Equilibrium and Thermodynamic Properties of Grey, White, and Liquid Tin,” Phys. Rev. Lett., 79 (13), pp. 2482–2485.  [CrossRef]
36
Weinberger, C. R., and Cai, W., 2008, “Surface-Controlled Dislocation Multiplication in Metal Micropillars,” Proc. Natl. Acad. Sci. U.S.A., 105 (38), pp. 14304–14307.  [CrossRef]
37
Tokumaru, K., Takahashi, K., Saito, S., and Yin, Y., 2007, “A Procedure of Determining Parameters to Expand Applicability of Modified Embedded Atom Method to Non-Bulk Systems,” Multiscale Modeling of Materials , "MRS Proceedings", Volume 978E , R.Devanathan, M.J.Caturla, A.Kubota, A.Chartier, and S.Phillpot, eds., Materials Research Society, Warrendale, PA, pp. 455–476.
38
Lenosky, T. J., Sadigh, B., Alonso, E., Bulatov, V. V., Diaz de la Rubia, T., Kim, J., Voter, A. F., and Kress, J. D., 2000, “Highly Optimized Empirical Potential Model of Silicon,” Modell. Simul. Mater. Sci. Eng., 8 , pp. 825–841.  [CrossRef]
39
Gracia-Pinilla, M. A., Perez-Tijerina, E., Garcia, J. A., Fernandez-Navarro, C., Tlahuice-Flores, A., Mejia-Rosales, S., Montejano-Carrizales, J. M., and Jose-Yacaman, M., 2008, “On the Structure and Properties of Silver Nanoparticles,” J. Phys. Chem. C, 112 (35), pp. 13492–13498.  [CrossRef]
40
Kuo, C. -L., and Clancy, P., 2005, “Development of Atomistic MEAM Potentials for the Silicon-Oxygen-Gold Ternary System,” Modell. Simul. Mater. Sci. Eng., 13 (8), pp. 1309–1329.  [CrossRef]
41
Ercolessi, F., and Adams, J., 1994, “Interatomic Potentials From First-Principles Calculations: The Force-Matching Method,” Europhys. Lett., 26 (8), pp. 583–588.  [CrossRef]
42
Liu, X. -Y., Adams, J. B., Ercolessi, F., and Moriarty, J. A., 1996, “EAM Potential for Magnesium From Quantum Mechanical Forces,” Modell. Simul. Mater. Sci. Eng., 4 (3), pp. 293–303.  [CrossRef]
43
Li, Y., Siegel, D. J., Adams, J. B., and Liu, X. -Y., 2003, “Embedded-Atom-Method Tantalum Potential Developed by the Force-Matching Method,” Phys. Rev. B, 67 (12), p. 125101.  [CrossRef]
44
Stadler, W., 1979, “A Survey of Multicriteria Optimization, or the Vector Maximum Problem,” J. Optim. Theory Appl., 29 , pp. 1–52.  [CrossRef]
45
Pareto, V., 1971, "Manuale di Economia Politica, Societa Editrice Libraria (Manual of Political Economy)", translated by A. S. Schwier, Macmillan, New York.
46
Andersson, J., 2001, “Multiobjective Optimization in Engineering Design—Applications to Fluid Power Systems,” Ph.D. thesis, Linköping University, Linköping, Sweden.
47
Han, Q., Kad, B. K., and Viswanathan, S., 2004, “Design Perspectives for Creep-Resistant Magnesium Die-Casting Alloys,” Philos. Mag., 84 (36), pp. 3843–3860.  [CrossRef]
48
Pettersen, G., Westengen, H., Høier, R., and Lohne, O., 1996, “Microstructure of a Pressure Die Cast Magnesium—4 wt % Aluminium Alloy Modified With Rare Earth Additions,” Mater. Sci. Eng., A, 207 , pp. 115–120.  [CrossRef]
49
Oh, D. J., and Johnson, R. A., 1988, “Simple Embedded Atom Method Model for fec and hcp Metals,” J. Mater. Res., 3 (3), pp. 471–478.  [CrossRef]
50
Igarashi, M., Khantha, M., and Vitek, V., 1991, “N-Body Interatomic Potentials for Hexagonal Close-Packed Metals,” Philos. Mag. B, 63 (3), pp. 603–627.  [CrossRef]
51
Finnis, M., and Sinclair, J., 1984, “A Simple Empirical N-Body Potential for Transition Metals,” Philos. Mag. A, 50 (1), pp. 45–55.  [CrossRef]
52
Pasianot, R., and Savino, E. J., 1992, “Embedded-Atom-Method Interatomic Potentials for hcp Metals,” Phys. Rev. B, 45 (22), pp. 12704–12710.  [CrossRef]
53
Jelinek, B., Houze, J., Kim, S., Horstemeyer, M. F., Baskes, M. I., and Kim, S. -G., 2007, “Modified Embedded-Atom Method Interatomic Potentials for the Mg–Al Alloy System,” Phys. Rev. B, 75 (5), pp. 054106.  [CrossRef]
54
Mendelev, M. I., Han, S., Son, W.-J., Ackland, G. J., and Srolovitz, D. J., 2007, “Simulation of the Interaction Between Fe Impurities and Point Defects in V,” Phys. Rev. B, 76 (21), p. 214105.  [CrossRef]
55
Rose, J. H., Smith, J. R., Guinea, F., and Ferrante, J., 1984, “Universal Features of the Equation of State of Metals,” Phys. Rev. B, 29 (6), pp. 2963–2969.  [CrossRef]
56
Kim, I. Y., and de Weck, O. L., 2006, “Adaptive Weighted Sum Method for Multiobjective Optimization: A New Method for Pareto Front Generation,” Struct. Multidiscip. Optim., 31 (2), pp. 105–116.  [CrossRef]
57
de Weck, O., 2004, "Multiobjective Optimization: History and Promise", The Third China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems , Kanazawa, Japan, October 30–November 2.
58
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1992, "Numerical Recipes in C: The Art of Scientific Computing", 2nd ed., Cambridge University Press, Cambridge.
59
Vanderbilt, D., 1990, “Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism,” Phys. Rev. B, 41 , pp. 7892–7895.  [CrossRef]
60
Kresse, G., and Hafner, J., 1994, “Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition Elements,” J. Phys.: Condens. Matter, 6 (40), pp. 8245–8257.  [CrossRef]
61
Kresse, G., and Furthmüller, J., 1996, “Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set,” Phys. Rev. B, 54 (16), pp. 11169–11186.  [CrossRef]
62
Ceperley, D. M., and Alder, B. J., 1980, “Ground State of the Electron Gas by a Stochastic Method,” Phys. Rev. Lett., 45 , pp. 566–569.  [CrossRef]
63
Perdew, J. P., and Zunger, A., 1981, “Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems,” Phys. Rev. B, 23 , pp. 5048–5079.  [CrossRef]
64
Kresse, G., and Hafner, J., 1993, “Ab Initio Molecular Dynamics for Liquid Metals,” Phys. Rev. B, 47 (1), pp. 558–561.  [CrossRef]
65
Monkhorst, H. J., and Pack, J. D., 1976, “Special Points for Brillouin-Zone Integrations,” Phys. Rev. B, 13 (12), pp. 5188–5192.  [CrossRef]
66
Methfessel, M., and Paxton, A. T., 1989, “High-Precision Sampling for Brillouin-Zone Integration in Metals,” Phys. Rev. B, 40 (6), pp. 3616–3621.  [CrossRef]
67
Emsley, J., 1998, "The Elements", 3rd ed., Oxford University Press, Oxford, UK.
68
Kittel, C., 1996, "Introduction to Solid State Physics", 7th ed., Wiley, Hoboken, NJ.
69
1976, "Metal Reference Book", 5th ed., C.J.Smith, ed., Butterworths, London, UK.
70
Althoff, J. D., Allen, P. B., Wentzcovitch, R. M., and Moriarty, J. A., 1993, “Phase Diagram and Thermodynamic Properties of Solid Magnesium in the Quasiharmonic Approximation,” Phys. Rev. B, 48 (18), pp. 13253–13260.  [CrossRef]
71
Ledbetter, H. M., 1977, “Elastic Properties of Zinc: A Compilation and a Review,” J. Phys. Chem. Ref. Data, 6 (4), pp. 1181–1203.
72
Mehl, M. J., Klein, B. M., and Papaconstantopoulos, D. A., 1994, “First-Principles Calculation of Elastic Properties of Metals,” "Intermetallic Compounds: Principles and Applications", J.H.Westbrook and R.L.Fleischer, eds., Wiley, London, Vol. 1 , pp. 195–210.
73
Hofmann, P., Pohl, K., Stumpf, R., and Plummer, E. W., 1996, “Geometric Structure of Be(101¯0),” Phys. Rev. B, 53 (20), pp. 13715–13719.  [CrossRef]
74
Staikov, P., and Rahman, T. S., 1999, “Multilayer Relaxations and Stresses on Mg Surfaces,” Phys. Rev. B, 60 (23), pp. 15613–15616.  [CrossRef]
75
Tyson, W. R., and Miller, W. A., 1977, “Surface Free Energies of Solid Metals: Estimation From Liquid Surface Tension Measurements,” Surf. Sci., 62 , pp. 267–276.  [CrossRef]
76
Chetty, N., and Weinert, M., 1997, “Stacking Faults in Magnesium,” Phys. Rev. B, 56 (17), pp. 10844–10851.  [CrossRef]
77
Mishin, Y., Farkas, D., Mehl, M. J., and Papaconstantopoulos, D. A., 1999, “Interatomic Potentials for Monoatomic Metals From Experimental Data and Ab Initio Calculations,” Phys. Rev. B, 59 (5), pp. 3393–3407.  [CrossRef]
78
Nosé, S., 1984, “A Unified Formulation of the Constant Temperature Molecular Dynamics Methods,” J. Chem. Phys., 81 (1), pp. 511–519.  [CrossRef]
79
Hoover, W. G., 1985, “Canonical Dynamics: Equilibrium Phase-Space Distributions,” Phys. Rev. A, 31 (3), pp. 1695–1697.  [CrossRef]
80
Luo, S. -N., Ahrens, T. J., Çağ ın, T., Strachan, A., Goddard, W. A., and Swift, D. C., 2003, “Maximum Superheating and Undercooling: Systematics, Molecular Dynamics Simulations, and Dynamic Experiments,” Phys. Rev. B, 68 (13), p. 134206.  [CrossRef]
81
Belonoshko, A. B., 2008, “Triple fcc-bcc-Liquid Point on the Xe Phase Diagram Determined by the N-Phase Method,” Phys. Rev. B, 78 (17), p. 174109.  [CrossRef]
82
Belonoshko, A. B., 1994, “Molecular Dynamics of MgSiO3 Perovskite at High Pressures: Equation of State, Structure, and Melting Transition,” Geochim. Cosmochim. Acta, 58 (19), pp. 4039–4047.  [CrossRef]
83
Morris, J. R., Wang, C. Z., Ho, K. M., and Chan, C. T., 1994, “Melting Line of Aluminum From Simulations of Coexisting Phases,” Phys. Rev. B, 49 (5), pp. 3109–3115.  [CrossRef]

Figures

Grahic Jump Location
+The cohesive energies as a function of the lattice constant a for Mg atoms in hcp crystal structure compared with the ones obtained from the Rose equation. The data points are computed with the present MEAM potential while the curve is obtained from the Rose equation.
View Large  |  Save Figure  |  Download Slide (.ppt)
The cohesive energies as a function of the lattice constant a for Mg atoms in hcp crystal structure compared with the ones obtained from the Rose equation. The data points are computed with the present MEAM potential while the curve is obtained from the Rose equation.
Figure 1

The cohesive energies as a function of the lattice constant a for Mg atoms in hcp crystal structure compared with the ones obtained from the Rose equation. The data points are computed with the present MEAM potential while the curve is obtained from the Rose equation.

Grahic Jump Location
+The internal energies of Mg crystal in hcp structure as a function of temperature. The energies are obtained from the ensemble average of the MD simulations of five structures containing 448 Mg atoms.
View Large  |  Save Figure  |  Download Slide (.ppt)
The internal energies of Mg crystal in hcp structure as a function of temperature. The energies are obtained from the ensemble average of the MD simulations of five structures containing 448 Mg atoms.
Figure 2

The internal energies of Mg crystal in hcp structure as a function of temperature. The energies are obtained from the ensemble average of the MD simulations of five structures containing 448 Mg atoms.

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