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.

1.
Shim
,
J.-H.
,
Lee
,
B.-J.
, and
Cho
,
Y. W.
, 2002, “
Thermal Stability of Unsupported Gold Nanoparticle: A Molecular Dynamics Study
,”
Surf. Sci.
0039-6028,
512
, pp.
262
268
.
2.
Kim
,
S. G.
, and
Tománek
,
D.
, 1994, “
Melting the Fullerenes: A Molecular Dynamics Study
,”
Phys. Rev. Lett.
0031-9007,
72
, pp.
2418
2421
.
3.
Baskes
,
M. I.
,
Nelson
,
J. S.
, and
Wright
,
A. F.
, 1989, “
Semiempirical Modified Embedded-Atom Potentials for Silicon and Germanium
,”
Phys. Rev. B
0163-1829,
40
(
9
), pp.
6085
6100
.
4.
Baskes
,
M. I.
, 1992, “
Modified Embedded-Atom Potentials for Cubic Materials and Impurities
,”
Phys. Rev. B
0163-1829,
46
(
5
), pp.
2727
2742
.
5.
Baskes
,
M. I.
, and
Johnson
,
R. A.
, 1994, “
Modified Embedded Atom Potentials for HCP Metals
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
2
(
1
), pp.
147
163
.
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.
0920-2307,
9
, pp.
251
310
.
7.
Daw
,
M. S.
, and
Baskes
,
M. I.
, 1983, “
Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals
,”
Phys. Rev. Lett.
0031-9007,
50
(
17
), pp.
1285
1288
.
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
0163-1829,
29
(
12
), pp.
6443
6453
.
9.
Baskes
,
M. I.
, 1987, “
Application of the Embedded-Atom Method to Covalent Materials: A Semiempirical Potential for Silicon
,”
Phys. Rev. Lett.
0031-9007,
59
(
23
), pp.
2666
2669
.
10.
Daw
,
M. S.
, 1989, “
Model of Metallic Cohesion: The Embedded-Atom Method
,”
Phys. Rev. B
0163-1829,
39
(
11
), pp.
7441
7452
.
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
0163-1829,
65
(
2
), p.
024209
.
12.
Baskes
,
M. I.
,
Angelo
,
J. E.
, and
Bisson
,
C. L.
, 1994, “
Atomistic Calculations of Composite Interfaces
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
2
(
3A
), pp.
505
518
.
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
0022-5096,
48
, pp.
2183
2212
.
14.
Lee
,
B. -J.
, and
Baskes
,
M. I.
, 2000, “
Second Nearest-Neighbor Modified Embedded-Atom-Method Potential
,”
Phys. Rev. B
0163-1829,
62
(
13
), pp.
8564
8567
.
15.
Wen
,
Y. -N.
, and
Zhang
,
J. -M.
, 2008, “
Surface Energy Calculation of the bcc Metals by Using the MAEAM
,”
Comput. Mater. Sci.
0927-0256,
42
(
2
), pp.
281
285
.
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.
0169-4332,
252
(
23
), pp.
8217
8222
.
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.
0169-4332,
253
(
4
), pp.
2018
2024
.
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.
0965-0393,
3
(
5
), pp.
615
627
.
19.
Baskes
,
M. I.
, 1997, “
Determination of Modified Embedded Atom Method Parameters for Nickel
,”
Mater. Chem. Phys.
0254-0584,
50
, pp.
152
158
.
20.
Baskes
,
M. I.
, 1999, “
Atomistic Potentials for the Molybdenum–Silicon System
,”
Mater. Sci. Eng., A
0921-5093,
261
(
1–2
), pp.
165
168
.
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
0163-1829,
68
(
14
), p.
144112
.
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
0953-8984,
13
(
6
), pp.
1193
1213
.
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
1434-6028,
34
(
4
), pp.
429
440
.
24.
Liu
,
X. -Y.
,
Ohotnicky
,
P.
,
Adams
,
J.
,
Rohrer
,
C.
, and
Hyland
,
R.
, 1997, “
Anisotropic Surface Segregation in Al–Mg Alloys
,”
Surf. Sci.
0039-6028,
373
, pp.
357
370
.
25.
Lee
,
B. -J.
, and
Lee
,
J. W.
, 2005, “
A Modified Embedded Atom Method Interatomic Potential for Carbon
,”
CALPHAD: Comput. Coupling Phase Diagrams Thermochem.
0364-5916,
29
(
1
), pp.
7
16
.
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.
0749-6419,
22
(
2
), pp.
257
278
.
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.
0039-6028,
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
0163-1829,
73
(
21
), p.
214209
.
29.
Baskes
,
M. I.
,
Lawson
,
A. C.
, and
Valone
,
S. M.
, 2005, “
Lattice Vibrations in δ-Plutonium: Molecular Dynamics Calculation
,”
Phys. Rev. B
0163-1829,
72
(
1
), p.
014129
.
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
1047-4838,
55
(
9
), pp.
41
50
.
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.
0884-2914,
21
(
1
), pp.
199
208
.
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.
0364-5916,
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
0921-5093,
449-451
, pp.
733
736
.
34.
Zhang
,
J. -M.
,
Xin
,
H.
, and
Wei
,
X. -M.
, 2005, “
Atomic-scale Calculation of Interface Energy for Ag/Ni
,”
Appl. Surf. Sci.
0169-4332,
246
(
1–3
), pp.
14
22
.
35.
Ravelo
,
R.
, and
Baskes
,
M.
, 1997, “
Equilibrium and Thermodynamic Properties of Grey, White, and Liquid Tin
,”
Phys. Rev. Lett.
0031-9007,
79
(
13
), pp.
2482
2485
.
36.
Weinberger
,
C. R.
, and
Cai
,
W.
, 2008, “
Surface-Controlled Dislocation Multiplication in Metal Micropillars
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
105
(
38
), pp.
14304
14307
.
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.
0965-0393,
8
, pp.
825
841
.
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
1932-7447,
112
(
35
), pp.
13492
13498
.
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.
0965-0393,
13
(
8
), pp.
1309
1329
.
41.
Ercolessi
,
F.
, and
Adams
,
J.
, 1994, “
Interatomic Potentials From First-Principles Calculations: The Force-Matching Method
,”
Europhys. Lett.
0295-5075,
26
(
8
), pp.
583
588
.
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.
0965-0393,
4
(
3
), pp.
293
303
.
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
0163-1829,
67
(
12
), p.
125101
.
44.
Stadler
,
W.
, 1979, “
A Survey of Multicriteria Optimization, or the Vector Maximum Problem
,”
J. Optim. Theory Appl.
0022-3239,
29
, pp.
1
52
.
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.
1478-6435,
84
(
36
), pp.
3843
3860
.
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
0921-5093,
207
, pp.
115
120
.
49.
Oh
,
D. J.
, and
Johnson
,
R. A.
, 1988, “
Simple Embedded Atom Method Model for fec and hcp Metals
,”
J. Mater. Res.
0884-2914,
3
(
3
), pp.
471
478
.
50.
Igarashi
,
M.
,
Khantha
,
M.
, and
Vitek
,
V.
, 1991, “
N-Body Interatomic Potentials for Hexagonal Close-Packed Metals
,”
Philos. Mag. B
1364-2812,
63
(
3
), pp.
603
627
.
51.
Finnis
,
M.
, and
Sinclair
,
J.
, 1984, “
A Simple Empirical N-Body Potential for Transition Metals
,”
Philos. Mag. A
0141-8610,
50
(
1
), pp.
45
55
.
52.
Pasianot
,
R.
, and
Savino
,
E. J.
, 1992, “
Embedded-Atom-Method Interatomic Potentials for hcp Metals
,”
Phys. Rev. B
0163-1829,
45
(
22
), pp.
12704
12710
.
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
0163-1829,
75
(
5
), pp.
054106
.
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
0163-1829,
76
(
21
), p.
214105
.
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
0163-1829,
29
(
6
), pp.
2963
2969
.
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.
1615-147X,
31
(
2
), pp.
105
116
.
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
0163-1829,
41
, pp.
7892
7895
.
60.
Kresse
,
G.
, and
Hafner
,
J.
, 1994, “
Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition Elements
,”
J. Phys.: Condens. Matter
0953-8984,
6
(
40
), pp.
8245
8257
.
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
0163-1829,
54
(
16
), pp.
11169
11186
.
62.
Ceperley
,
D. M.
, and
Alder
,
B. J.
, 1980, “
Ground State of the Electron Gas by a Stochastic Method
,”
Phys. Rev. Lett.
0031-9007,
45
, pp.
566
569
.
63.
Perdew
,
J. P.
, and
Zunger
,
A.
, 1981, “
Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems
,”
Phys. Rev. B
0163-1829,
23
, pp.
5048
5079
.
64.
Kresse
,
G.
, and
Hafner
,
J.
, 1993, “
Ab Initio Molecular Dynamics for Liquid Metals
,”
Phys. Rev. B
0163-1829,
47
(
1
), pp.
558
561
.
65.
Monkhorst
,
H. J.
, and
Pack
,
J. D.
, 1976, “
Special Points for Brillouin-Zone Integrations
,”
Phys. Rev. B
0556-2805,
13
(
12
), pp.
5188
5192
.
66.
Methfessel
,
M.
, and
Paxton
,
A. T.
, 1989, “
High-Precision Sampling for Brillouin-Zone Integration in Metals
,”
Phys. Rev. B
0163-1829,
40
(
6
), pp.
3616
3621
.
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
0163-1829,
48
(
18
), pp.
13253
13260
.
71.
Ledbetter
,
H. M.
, 1977, “
Elastic Properties of Zinc: A Compilation and a Review
,”
J. Phys. Chem. Ref. Data
0047-2689,
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
0163-1829,
53
(
20
), pp.
13715
13719
.
74.
Staikov
,
P.
, and
Rahman
,
T. S.
, 1999, “
Multilayer Relaxations and Stresses on Mg Surfaces
,”
Phys. Rev. B
0163-1829,
60
(
23
), pp.
15613
15616
.
75.
Tyson
,
W. R.
, and
Miller
,
W. A.
, 1977, “
Surface Free Energies of Solid Metals: Estimation From Liquid Surface Tension Measurements
,”
Surf. Sci.
0039-6028,
62
, pp.
267
276
.
76.
Chetty
,
N.
, and
Weinert
,
M.
, 1997, “
Stacking Faults in Magnesium
,”
Phys. Rev. B
0163-1829,
56
(
17
), pp.
10844
10851
.
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
0163-1829,
59
(
5
), pp.
3393
3407
.
78.
Nosé
,
S.
, 1984, “
A Unified Formulation of the Constant Temperature Molecular Dynamics Methods
,”
J. Chem. Phys.
0021-9606,
81
(
1
), pp.
511
519
.
79.
Hoover
,
W. G.
, 1985, “
Canonical Dynamics: Equilibrium Phase-Space Distributions
,”
Phys. Rev. A
1050-2947,
31
(
3
), pp.
1695
1697
.
80.
Luo
,
S. -N.
,
Ahrens
,
T. J.
,
Çağ ın
,
T.
,
Strachan
,
A.
,
Goddard
,
W. A.
, III
, and
Swift
,
D. C.
, 2003, “
Maximum Superheating and Undercooling: Systematics, Molecular Dynamics Simulations, and Dynamic Experiments
,”
Phys. Rev. B
0163-1829,
68
(
13
), p.
134206
.
81.
Belonoshko
,
A. B.
, 2008, “
Triple fcc-bcc-Liquid Point on the Xe Phase Diagram Determined by the N-Phase Method
,”
Phys. Rev. B
0163-1829,
78
(
17
), p.
174109
.
82.
Belonoshko
,
A. B.
, 1994, “
Molecular Dynamics of MgSiO3 Perovskite at High Pressures: Equation of State, Structure, and Melting Transition
,”
Geochim. Cosmochim. Acta
0016-7037,
58
(
19
), pp.
4039
4047
.
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
0163-1829,
49
(
5
), pp.
3109
3115
.
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