1. Interatomic Potentials
for Ionic Systems
Byeong-Joo Lee
POSTECH-CMSE

2. Background Importance of Ionic Materials
Sensor, Battery, Devices, Metal Surfaces, etc.
Need to handle “ionic + covalent + metallic” materials
Interfacial Reaction between metals and SiO2 substrate
Diffusion of metallic atoms in amorphous SiO2
Atomistic simulation on “ionic + covalent + metallic” materials
???

3. Purpose and Scope
Development of Interatomic Potential Model that covers
“ionic + covalent + metallic” materials, simultaneously.
Review interatomic potentials for ionic and hybrid materials
Propose possible form of an interatomic potential formalism

4. Outline Interatomic Potential for Ionic Materials Many-Body Potentials
Point Charge Model
Polarization (Shell Model)
Many-Body Potentials
Tersoff
EAM – MEAM – 2NN MEAM
Many-body potentials used for ionic systems
Many-Body Potentials for Ionic Materials
Charge Equilibration Model
EAM + Qeq
Tersoff + Qeq
Proposal of New Interatomic Potential Form

5. Interatomic Potential for Ionic Materials
Fixed Point Charge
Born-Mayer-Huggins
TTAM
BKS
Initially applied to liquid or glass, not crystals : probably, unable to reproduce crystal structures
1st MD on SiO2 glass Woodcock [5], 1976
More information available with upgraded measuring techniques for crystal structures and dynamics
1988: BMH + many-body interaction to reproduce O-Si-O bonding angle: (cosθjik - cosθojik)2 [6]
1988: BMH + modified Coulomb interaction considering excess charge distribution in oxygen
+ Ab Initio on SiO2 model clusters
→ α-quartz, α-cristobalite, Coesite, Stishovite, for the first time → TTAM [7]
1990: BMH + Ab Initio + Experimental Information on α-quartz
→ better description than TTAM → BKS [8]
TTAM&BKS: representative Point Charge Potential for SiO2 during 1990s. (qSi = +2.4, qO = -1.2)
Limitation: use of Point Charge, pair-wise potentials not applicable to pure Si or Si/SiO2
1994: Jiang & Brown: SW Si – BKS SiO2, ionization energy, charge variation, bond-softening function
→ behavior of O atom in Si [11]
2010: Soulairol & Cleri: SW Si – BKS SiO2 + different q for interface

6. Interatomic Potential for Ionic Materials
Fixed Point Charge + electronic polarization
Include dipole-charge, dipole-dipole interaction due to electronic polarization
Shell Model by Dick & Overhauser [13], 1958
Ion = core electron core + valence electron shell
Deviation of Center of mass of Shell causes a dipole
Shell connected to core by an artificial spring and interact through harmonic restoring force
Shell Model has been successful for diatomic molecule, alkali halides and also for Al2O3 [14]
BMH + polarization : representative approach during 1980s for alkali halides, binary, mixed oxides [15]
Shell model: leading model for ionic materials in GULP [19]
2002: Morse-Stretch pp + fixed point charge Coulomb + dipole polarization for Oxygen ions [17]
fitting (force-matching) on liquid SiO2 → better description for polymorphs than BKS
Limitation: not applicable to pure Si or Si/SiO2, not describing variable charge
Next Step: Many-body + variable charge

7. Many-Body Potential : EAM – 2NN MEAM
Embedding energy of impurity atoms is determined by the electron density of the host (from first-principles)
→ individual atoms are impurity atoms → EAM concept [29,30]
How to compute F and Ф ? No specific function form was given in initial EAM → reason for so many EAMs
Rose universal equation of state [23] gives a guide [31]
EAM : linear supposition for computation of electron density of a site → mainly for fcc
Introduction of bonding directionality → Modified EAM (1nn interaction only)
→ applied to Si [32], bcc [33] and hcp [34], but stability problem
Need to consider 2NN interactions to solve critical shortcomings in MEAM → 2NN MEAM [36,37]
→ applicable to both metallic and covalent systems: metals, carbides, nitrides, Si, Ge, etc. [38-40]

8. Many-Body Potential : Tersoff
1985 Abell : Close relation between Morse-type pair potential and Rose universal behavior
→ replacement of Born-Mayer by Morse-Stretch
Tersoff potential [24-26]
bij : bond order – 1nn interaction, bond length and angle, effect of local environments, etc.
applied to C [27] and SiC [28] and extended to Brenner-REBO [87-89]
for alloys : arithmetic mean to λ, μ and geometric mean to A, B, R, S

9. Many-Body Potential for Ionic Materials
Umeno [14] : using Tersoff for SiO2
Independent fitting to λ, μ, A, B instead of mean values
applicable to β-cristobalite, β-quartz which was difficult by BKS
Kuo [15] : using MEAM for SiO2
applicable to α, β-quartz, α, β-cristobalite, β-tridymite

10. Charge Equilibration Model
1991 Rappe & Goddard [48] : based on previous concepts on electronegativity, equilibration [49-57].
- equilibrium charge in molecules
considering Coulomb interaction and penalty energy for charged isolated atoms (atomic self-energy)
IP & EA : ionization potential과 electron affinity
χ0 : electronegativity
J0 : atomic hardness representing Coulomb repulsion between two electrons in an orbital
JAB : Coulomb interaction between A & B
computed by a Coulomb integral on atomic charge density expressed for a Slater-type orbital
Basic idea in Qeq model is to equalize the atomic chemical potential of all individual atoms (χ1 = χ2 = … = χN)
First applied to SiO2 in 1999 [58] : Morse-Stretch pair potential + charge equilibration
- Quartz-Stishovite phase transition & Silica glass
Swamy & Gale [59] in 2000 : Titanium oxide system
including rutile, anatase, brookite, TiO2-II, Ti2O3, monoclinic high- and low temp forms of Ti3O5,
TiO, ramsdellite-type TiO2, g-Ti3O5, two Magneli phases: Ti4O7 and Ti6O11

11. EAM + Charge Equilibration
1994 Streitz & Mintmire [60] : first Qeq approach for crystalline materials, EAM + Qeq for Al2O3
2004 Zhou [70] : solving charge stability problem,
- extened to multicomponent oxides, O-Al-Ni-Co-Fe system [71]
2007 Lazic [74] : MEAM (different from Baskes) + Qeq, not much is published
Oxidation of Al nano cluster [61,62]  

12. Tersoff + Charge Equilibration
1996 Yasukawa [76] : introduce atomic energy ΣiΦi & Coulomb energy ½ΣiΣjEIONij
- effective point charge with cutoff function in Coulomb potential, not with Ewald summation
- Considering changes in ionic radius and short range interaction due to charge
Crack propagation behavior of SiO2 with or without H2O
Adhesion strength on Al,Cu/TiN,W,SiO2 thin film interface [77]
Upgrade in parameter [78] & Formalism for Coulomb interaction [79]
2007 Sinnott & Phillpot group [80] : confirm application to α, β-quartz, α, β-cristobalite, but stability problem.
- atomic self-energy up to 4th order & introduction of bond-bending energy, (cosθOSiS - cosθoOSiO)2,
- COMB (Optimized Many-Body Potential), but cannot generate amorphous SiO2 & bad results for α-quartz
2010 modified version for SiO2 [81] : Slater 1s orbital type Coulomb integral & Ewald + another penalty term
- applicable to α, β-quartz, α, β-cristobalite, β-tridymite, Coesite, Stishovite, generally worse than TTAM
2010 Hf/HfO2, Cu/Cu2O [83,84] : different bond-bending form depending on cation element

13. Others : ReaxFF
Bond-Order : based on correlation between bond order & bond distance or bond energy
describe bond dissociation → chemical reaction
- including bonding angle, torsion, charge equilibration, van der Waals interaction, etc.
- mainly for hydrocarbon system [85], but also to oxides, Si/SiO2 system [86]
Most powerful : covering Hydrocarbon system like Brenner-REBO [87-89]
and charge equilibration like COMB
Number of parameters for Carbon, for example : 90s
- how to determine the parameter values ? → 10 ~ 15 systems during up to now
- retirement of Prof. Goddard → Dr. van Penn State

14. Summary
Up to now no interatomic potential for ionic + covalent + metallic alloy systems

15. Potential for Ionic+Covalent+Metallic Materials
Charge Effect ?
Correct physics : easy parameterization and good trasferability
Point Charge vs. Charge Distribution ?
TTAM that considered charge distribution could describe the SiO2 polymorphs for the first time
Shell Model ?
No publication for shell model + many-body potential
Variable charge can be superior to fixed charge, for bond dissociation, surface, interface, and other defects
Coulomb Integral ?
COMB10 [81] is generally worse than BKS or TTAM for SiO2 polymorphs
Coulomb intergral (COMB10 [81]) vs. effective point charge (Yasukawa 2010 [79]) ?
Summation of Long Range Potential (1/r radial behavior) ?
Ewald method [70], PPPM [75], direct summation method [82]
Charge Equilibration Method ?
Inverse matrix [60], Conjugate gradient method [70], Lagrangian dynamics [80]
Manybody Potential ?
- COMB had to change the functional form for bond-bending term, probably due to the limitation of Tersoff.
[Tersoff potential has never been applied to metallic alloy systems]
- MEAM is also a kind of bond order potential,
2NN MEAM has been applied to both covalent and metallic alloy systems
Conclusion
2NN MEAM + Qeq = Tersoff+Qeq + EAM+Qeq
Paying attention to charge stability and extension to multicomponent systems,
and searching for the best solution for Coulomb integral, long range potential and charge equilibraion

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17. Atomistic Simulations - MEAM & Applications
Byeong-Joo Lee
Dept. of MSE
Pohang University
of Science and Technology
(POSTECH)

18. Semi-Empirical Atomic Potentials - Historical Background
Pair Potentials (~1980)
▷ Elastic Constants are NOT correctly reproduced
Many Body Potentials (1980's)
▷ Embedded Atom Method (EAM: 1983)
▷ Finnis and Sinclair Potential (1984)
▷ Glue Model (1986)
▷ Equilivalent-Crystal Model (1987)

19. Semi-Empirical Atomic Potentials – History of Development
EAM Potentials (1983, M.S. Daw and M.I. Baskes)
▷ Successful mainly for FCC elements
- many other many-body potentials show similar performance
1NN MEAM Potentials (1987,1992, M.I. Baskes)
▷ Show Possibility for description of various structures
- important to be able to describe multi-component system
2NN MEAM Potentials (2000, B.-J. Lee & M.I. Baskes)
▷ Applicable to fcc, bcc, hcp, diamond structures and their alloys

20. EAM/MEAM – General
E : Total Potential Energy F : Embedding Energy  : Electron Density (Considering Bonding Directionality)  : Pair Interaction Energy

21. EAM/MEAM – Embedding Function
M.I. Baskes et al., Phys. Rev. B, 40, 6085 (1989)

22. EAM/MEAM – Universal EOS
J.H. Rose et al., Phys. Rev. B, 29, 2963 (1984)

23. EAM/MEAM – Electron Density for EAM

24. EAM/MEAM – Electron Density for MEAM
+ Angular contribution

25. EAM/MEAM – Electron Density for MEAM
+ Angular contribution
with ti(0) =1

26. EAM/MEAM – 1st Nearest Neighbor MEAM

27. 1NN MEAM vs. 2NN MEAM – Many-Body Screening
Xik=(Rik/Rij)2 and Xkj=(Rkj/Rij)2
Cmax
Cmin i j
fc(x) = x  1
0  x  1
x  0

28. 2NN MEAM – Computation of pair-wise potential

29. Evaluation of MEAM Potential Parameters for Elements
Ec, Re, B, A, d,  (0),  (1),  (2),  (3), t(1), t(2), t(3), Cmax, Cmin
▷ Cohesive Energy of Stable and Metastable Structure
▷ Nearest Neighbor Distance
▷ Bulk Modulus, Elastic Constants (C11, C12, C44)
▷ Stacking Fault Energy
▷ Vacancy Formation Energy
▷ Surface Energy

30. Semi-Empirical Atomic Potentials - Performance
Elastic Constants
▷ B, C11, C12, C44, ...
Defect Energy
▷ Surface Energy
▷ Heat of Vacancy Formation, …
Structural Energy
▷ Energy and Lattice Parameters in Different Structures
Thermal Property
▷ Specific Heat
▷ Thermal Expansion Coefficient
▷ Melting Temperature, ...

31. MEAM for BCC Transition Metals – B.-J. Lee et al., PRB, 2001
Elem. C11 C12 C E(100) E(110) E(111) Evf Ebcc/fcc Efcc/hcp Fe * Cr * Mo * W * V * Nb * Ta *

32. MEAM for FCC Transition Metals – B.-J. Lee et al., PRB, 2003
Elem. C11 C12 C E(100) E(110) E(111) Evf Ebcc/fcc Efcc/hcp ε (0-100oC)
Cu 1.762  1.249  0.818    1451        17.0
           1.249  0.818             1770          -0.04   
  Ag      0.973  0.511       983  1010   842    0.94         0.005  
           0.973  0.511             1320         1.1      -0.04     0.003   
  Au       1.697  0.454      1138  1179   928            0.009   
          1.697  0.454             1540         0.9          0.003   
  Ni      1.508  1.317      1943  2057  1606   1.51          0.02    
           1.508  1.317              2240        1.6          0.02    
Pd      1.761  0.712      1743  1786  1435    1.50          0.02    
          1.761  0.712             2043        1.4,1.7        0.02    
Pt       2.535  0.775      2288  2328  1710   1.50          0.02    
                         2691      ,1.5        0.03    
  Al       0.619  0.316       848   948   629          0.03    
           0.619  0.316             1085          0.68         0.06    
  Pb       0.454  0.194       426    440   375    0.58          0.003   
           0.454  0.194               534         0.58         0.003   

33. MEAM for Silicon
C11 C12 C44 E(100) E(110) E(111) Evf Edia/fcc Edia/hcp Edia/bcc ε
(1012dyne/cm2) (erg/cm2) (eV) (eV) (0-100oC) *

34. 2NN MEAM Interatomic Potentials – for Al and Fe
Property
MEAM-Al (exp.) MEAM-Fe (exp.)
C11 (1012 dyne/cm2)
C12 (1012 dyne/cm2)
C44 (1012 dyne/cm2)
Evf (eV)
QD (eV)
EIf (eV)
1.143 (1.143)
0.619 (0.619)
0.316 (0.316)
0.68 (0.68)
1.33 (1.33)
2.49 (-)
2.430 (2.431)
1.380 (1.381)
1.219 (1.219)
1.75 (1.79)
2.28 (2.5)
4.20 (-)
E(100) (mJ/m2)
E(110) (mJ/m2)
E(111) (mJ/m2)
d(100) (%)
d(110) (%)
d(111) (%)
848 (1085a)
948 (1085a)
629 (1085a)
+1.8 (+1.8)
-8.9 (-8.5±1.0)
+1.0 (0.9±0.5)
2510 (2360a)
2356 (2360a)
2668 (2360a)
-1.1 (-0.2, -1.5)
-1.5 (0)
-10.5 (-16.9)
Ebcc/fcc (eV/atom)
Efcc/hcp (eV/atom)
0.12 (0.10b)
0.03 (0.06b)
0.048 (0.082b)
(-0.023b)
(0-100oC) (10-6/K)
Cp (0-100oC) (J/mol·K)
m.p. (K)
Hm (KJ/mol)
Vm (%)
22.0 (23.5)
26.2 (24.7)
937 (933)
11.0 (10.7)
6.7 (6.5)
12.4 (12.1)
26.1 (25.5)
2000 (1811)
13.2 (13.8)
4.0 (3.5)

35. 2NN MEAM – 2NNMEAM for Alloy Systems

36. 2NN MEAM for Alloy Systems – Optimization of Potential Parameter, Fe-Pt
Selected value
Procedure for
the determination
ΔEc
Fitting to ΔH or Ttr re
2.7181
Fitting to lattice parameter B
2.6201
Fitting to bulk modulus d
0.25dFe+0.75dPt
Assumption
Cmin(Fe-Pt-Fe)
0.36 ( = CminFe)
Cmin(Pt-Fe-Pt)
1.53 ( = CminPt)
Cmin(Fe-Fe-Pt)
[0.5(CminFe)1/ (CminPt) 1/2 ]2
Cmin(Fe-Pt-Pt) ρ0
ρ0Fe = ρ0Pt = 1.0
A temporary assumption

37. 2NN MEAM for Fe-Cr Binary System – B.-J. Lee et al., CALPHAD, 2001
200K K K

38. MEAM for Cu-Ni Binary System – B.-J. Lee and J.-H. Shim, CALPHAD, 2004

39. MEAM for Ni-Si Binary System
Dilute Heat of Solution (eV/atom)
Si in (Ni) (-1.37)
Ni in (Si)
Ni3Si
(0.36)
3.504 (3.504)
2.64
3.67 ( )
2.13 ( )
1.54
1.96 ( )
5.3 (7.2)
NiSi2
(0.28)
5.391 (5.406)
(1.60)
2.39
1.69
(0.58)
0.32
8.0
Enthalpy of Formation (eV/atom)
Lattice constant (Å)
Bulk Modulus (100 GPa)
C11 (100 GPa)
C12 (100 GPa)
C11-C12 (100 GPa)
C44 (100 GPa)
(100) fracture energy (J·m-2)

40. MEAM for Co-Pt Binary System - S.I. Park et al., Scripta Mater., 2001.
Property Pt3Co PtCo PtCo3
Cohesive Energy
(eV/atom) ± ±0.005
Lattice Constant a= , c/a=
(Å) a= , c/a=
Transition
Temperature (K)

41. MEAM for Ni-W Binary System – J.-H. Shim et al., J. Mater. Res., 2003
Property fcc (XW=0.11) Ni4W
Cohesive Energy (fcc, 5.27)
(eV/atom)
Lattice Constant a= a=5.73, c=3.553
(Å) a= a=5.73, c=3.553

42. MEAM for Ni-W Binary System
a (Å) c (Å) Ec(eV) B(Gpa)
Ni4W (D1a)
Ni3W (L12)
Ni3W (D019)
NiW3 (L12)
NiW3 (D019)

43. Empirical Potentials for Multicomponent SystemsFe
▷ Finnis-Sinclair – modified by Calder and Bacon (1993)
Fe-Cu
▷ Osetsky (1996)
Fe: Pair-Potential, Osetsky (1995)
Cu: Pair-Potential, Osetsky (1995)
▷ Ackland, Bacon, Calder (1997)
Fe: F-S type, Ackland et al. (1997)
Cu: F-S type, Ackland, Tichy, Vitek, Finnis (1987)
▷ Ludwig, Farkas,.. (1998) → C.S. Becquart, C. Domain,
Fe: EAM, Simonelli, Pasianot, Savino (1993)
Cu: EAM, Voter (1993)

44. History of Fe-C Alloy Potential
R.A. Johnson, G.J. Dienes, A.C. Damask, Acta Metall. 12, 1215 (1964).
metal-metal: pairwise interaction
metal-carbon: pairwise interaction
can consider only one carbon atoms, not applicable to carbides
V. Rosato, Acta Metall. 37, 2759 (1989).
metal-metal: many-body interaction
M. Ruda, D. Farkas, and J. Abriata, Scr. Mater. 46, 349 (2002).
metal-metal: many-body interaction (EAM)
metal-carbon: many-body interaction (EAM)
carbon-carbon: many-body interaction (EAM)
unacceptable results

45. History of Carbon Potential
J. Tersoff, Phys. Rev. Lett. 61 (1988) 2879.
structural properties (cohesive energies, bond lengths of various polytypes)
elastic properties (elastic constants of diamond)
point defect properties (vacancy formation and migration energies,
and interstitial formation energies in diamond and graphite)
applicable to monolayer of graphite
applicable to only Diamond Structures (C, Si, Ge, SiC, …)
D.W. Brenner, Phys. Rev. B 42 (1990) 9458;
J. Phys.: Condens. Matter 14 (2002) 783.
modification of Tersoff formalism to better describe hydrocarbons
M.I. Heggie, J. Phys.: Condens. Matter 3 (1991) 3065.
E.P. Andribet et al., Nucl. Instr. & Meth. in Phys. Res. B 115 (1996) 501.
To better describe graphite structure than Tersoff
Only for graphite

46. (2NN) MEAM for Fe, C, N, Fe-C and Fe-N systems
Fe, Cr, Mo, W, V, Nb, Ta Second Nearest-Neighbor Modified Embedded Atom Method Potentials for BCC Transition Metals Byeong-Joo Lee, M.I. Baskes, Hanchul Kim and Yang Koo Cho,
Phys. Rev. B. 64, (2001).
C A Modified Embedded Atom Method Interatomic Potential for Carbon Byeong-Joo Lee and Jin Wook Lee, CALPHAD 29, 7-16 (2005).
Fe-C A Modified Embedded Atom Method Interatomic Potential for the Fe-C System Byeong-Joo Lee, Acta Materialia 54, (2006).
Fe-N A Modified Embedded-Atom Method Interatomic Potential for the Fe-N System: A Comparative Study with the Fe-C system
Byeong-Joo Lee, T-H Lee and S-J Kim, Acta Materialia (2006).

47. 2NN MEAM for pure Fe - PRB 64, 184102 (2001); 71, 184205 (2005)
MEAM F-S type EAM F-S type pair potential
expt This work Calder-Bacon Simonelli Ackland Osetsky
C11
C12
C44
Evf
∆Vvf/Ω
Evm
EIf
∆VIf/Ω
E(100)
E(110)
E(111)
∆d(100)
∆d(110)
∆d(111)
∆Ebcc/fcc
∆Ehcp/fcc
a(bcc)
a(fcc)
ε(0-100oC)
Cp (0-100oC)
m.p.
∆Hm
∆Vm
2.431a
1.381a
1.219a
< 2b
< -.4c
0.55d -
<110>due
2360f
-0.2, -1.5g 0g
-16.9g
-0.082h
-0.023h
2.8665i
12.1j
25.5j
1811h
13.8h
3.5j
2.430
1.380
1.219
1.75
-.41
0.53
4.20
<110>du
1.70
2510
2356
2668
-1.1
-1.5
-10.5
-0.048
-0.018
2.8637
3.611
12.5
26.1
2000
12.9
3.3
2.434k
1.381k
1.221k
1.83
-.21
0.91k
4.85
1.33
1920k
-0.054m
0.0m
2.866
2.42
1.47
1.12
1.63
0.66
3.54
<111>cr
-0.027
0.0
2.8664
2200
2.43
1.45
1.16
-.18
0.78
4.87
1.76
1812n
1585n
2269n
-0.054
2.8665
3.690
2358
21.0
1.19
2.05
-.29
3.92
0.69
-0.052
0.005
2.867
3.612
11.6

48. MEAM for Carbon – Physical Property of Diamond
MEAM Tersoff exp./calc.
C11
C12
C44
Evf
Evsplit
E I(T) f
E I(H) f
E I(110)db f
E I(100)db f
10.79
1.27
6.23
3.35
7.23
unstable
12.7
9.3
10.9a
1.2a
6.4a
4.3a
9.7a
19.6a
20.9a -
10.0a
10.80c
1.27c
5.77c
7.2d
9.1d
23.6d
16.7d
Eideal(100)
Eideal(110)
Eideal(111)
E1×1(100)
E2×1(100)
E1×1(111)
Δd1-2(111)
8811
5715
4666
7124
5720
2069
-17.9
+9.5
-52.5
+21.1
7565b
4949b
4040b
6639b
2772b
-15.9b
+2.0b
-39. 8b
+4.3b
9850e, 9250g
6540g
7960f, 5340g
9190e
5370e
6270f
-49f
+9f
ε ( K)
Cp ( K) 8
25.5
1~6h
5~22h

49. MEAM for Carbon – Physical Property of Graphite
MEAM + LJ Tersoff exp./calc.
Biso
C11
C12
C33
C44
C13
Evf
Evsplit
E InterLayer f
2.38
10.99
-0.45
0.38
0.0003
6.2
9.5
4.9 -
12.1a
-1.9a
7.1a
10.8a
2.86b
10.60c
1.80c
0.365c
0.04c
0.15c, -0.12d, e
7.6f
9.2f
7.0g
E (0001) 84
rhombohedral graphite simple graphite hexagonal graphite exp.
Egra/dia a
Lattice parameter, a ~2.47b
Lattice parameter, c ~6.93b

50. MEAM for Carbon – for several structures

51. MEAM for Carbon – Nanotubes and Fullerenes
MEAM (+ LJ) exp./calc.
ΔE of graphene
ΔE of (10,10) CNT
ΔE of (17,0) CNT
ΔE of C60 bucky ball
Young’s Modulus of (10,10) CNT
Vacancy formation energy in (8,0) CNT
0.037
0.05
0.59
10.4
5.71
0.02a, 0.045b
0.086a, 0.10b
0.088a, 0.10b
0.46a, 0.47b
10.02c
5.59d

52. MEAM for N2 N2 Re (Å) Ec (eV/atom) Exp. 1.10 -4.88 Bond-order 1.11
▪ Bond length and Cohesive energy for N2 N2
Re (Å)
Ec (eV/atom)
Exp.
1.10
-4.88
Bond-order
1.11
-4.96
2NN MEAM
▪ Bond length, Bond angle and cohesive Energy for N3 N3
Re (Å)
Angle (degree)
Ec (eV/atom)
Bond-order
1.272
180
-3.712
2NN MEAM
1.116
-3.45

53. 2NN MEAM for Fe-C & Fe-N – in BCC Fe
MEAM expt./calc.
Dilute Heat of Solution of Carbon (eV)
Migration Energy Barrier of Carbon (eV)
Vacancy-Carbon Binding Energy (eV)
Vacancy-Carbon Binding Distance (ao)
Dilute Heat of Solution of Nitrogen (eV)
Migration Energy Barrier of Nitrogen (eV)
Vacancy- Nitrogen Binding Energy (eV)
Vacancy- Nitrogen Binding Distance (ao)
1.22
0.82
0.90
0.43
0.33
0.78
0.64
0.42
1.1a
0.88b, 0.86c, d
0.41e, 0.85f, 1.05g, 1.1b, 0.44j
0.365k, 0.40j
0.32
0.76~0.80
0.67j
0.45j
Carbon in O site vacancy-carbon carbon-carbon SIA-carbon vacancy-two carbon

54. 2NN MEAM for Fe-C & Fe-N – in FCC Fe
MEAM expt./calc.
Dilute Heat of Solution of Carbon (eV)
Migration Energy Barrier of Carbon (eV)
Vacancy-Carbon Binding Energy (eV)
Carbon-Carbon Binding Energy (eV)
Dilute Heat of Solution of Nitrogen (eV)
Migration Energy Barrier of Nitrogen (eV)
Vacancy- Nitrogen Binding Energy (eV)
Nitrogen - Nitrogen Binding Energy (eV)
0.30
1.52
0.67
-0.12 <110>
-0.35 <100>
-0.48
1.36
0.23
-0.31 <110>
-0.10 <100>
0.36a, 0.12b
1.4c,1.53d
0.37 ~ 0.41e
<110> alignment
is less repulsive
-0.53
1.75
<100> alignment

55. 2NN MEAM for Fe-N – in Fe4N
ΔHf = +3.1 ~ -40 kJ/mol (-10.5) MEAM: -6.8 kJ/mol
a = 3.80 Å MEAM: 3.80 Å

56. 2NN MEAM for Fe-N – in Fe2N
Identification of the most stable atomic structure of Fe2N
ΔHf = kJ/mol MEAM: kJ/mol
a = 2.76 Å, c = 4.42 Å MEAM: a = 2.81 Å, c = 4.32 Å

57. Atomistic Simulation – Interatomic Potentials and Applications
Performance of 2NN MEAM for Elements and Alloys
Fundamental Properties of Structural Materials
Elastic Property
Defect (Point, Dislocation, Grain Bd./Interface) Property
Phase Transformations
Deformation/Fracture Mechanism
Fundamental Properties of Nano Materials
Thermodynamic Property
Atomic/Nano Structural Evolution
Fundamental Properties of Amorphous Materials
Irradiation Defects, etc.

58. Second Nearest Neighbor Modified EAM (2NN MEAM)
Pure Elements
Fe, Cr, Mo, W, V, Nb, Ta, Li Phys. Rev. B. 64, (2001); MSMSE 20, (2012) .
Cu, Ag, Au, Ni, Pd, Pt, Al, Pb Phys. Rev. B. 68, (2003).
Ti, Zr & Mg Phys. Rev. B. 74, (2006); CALPHAD 33, (2009).
Mn, P Acta Materialia 57, (2009).; J. Phys.: Condensed Matters (2012), in press.
C, Si, Ge, In CALPHAD 29, 7-16 (2005); 31, (2007); 32, (2008); 32, (2008)
Multicomponent Systems
Fe-C, Fe-N, Fe-H Acta Materialia 54, (2006); 54, (2006); 55, (2007).
Fe-Ti & Fe-Nb Scripta Materialia 59, (2008).
Fe-Ti-C & Fe-Ti-N Acta Materialia 56 , (2008); Acta Materialia 57 , (2009).
Fe-Nb-C & Fe-Nb-N J. Materials Research 25, (2010).
Al-H & Ni-H, V-H J. Materials Research 26, (2011); CALPHAD 35, (2011).
Fe-Mn Acta Materialia 57, (2009).
Fe-Cr CALPHAD 25, (2001).
Fe-Cu Phys. Rev. B. 71, (2005).
Fe-Pt J. Materials Research 21, (2006).
Fe-Al J. Phys.: Condensed Matters 22, (2010)
Fe-P J. Phys.: Condensed Matters (2012), in press.
Al-Ni CALPHAD 31, 53 (2007).
Co-Cu J. Materials Research 17, (2002).
Co-Pt Scripta Materialia 45, (2001).
Cu-Ni CALPHAD 28, (2004).
Ni-W J. Materials Research 18, (2003).
Cu-Ti Mater. Sci. and Eng. A , 733 (2007).
Cu-Zr J. Materials Research 23, 1095 (2008).
Cu-Zr-Ag Scripta Materialia 61, 801 (2009).
Mg-Al , Mg-Li CALPHAD 33, (2009); MSMSE 20, (2012) .
Ga-In-N J. Phys.: Condensed Matter 21, (2009).