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

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Interatomic Potentials for Ionic Systems

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Interatomic potentials for ionic systems

Interatomic Potentials

for Ionic Systems

Byeong-Joo Lee

POSTECH-CMSE


Interatomic potentials for ionic systems

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

    • ???


Interatomic potentials for ionic systems

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


Interatomic potentials for ionic systems

Outline

  • Interatomic Potential for Ionic Materials

    • 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


Interatomic potentials for ionic systems

Interatomic Potential for Ionic Materials

Fixed Point Charge

Born-Mayer-Huggins

TTAM

BKS

  • Initially applied to liquid orglass, 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 onα-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


Interatomic potentials for ionic systems

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 electroncore + valence electron shell

  • Deviation of Center of mass of Shell causes adipole

  • Shell connected to core by an artificial spring and interact throughharmonic restoring force

  • Shell Model has been successful for diatomic molecule, alkali halidesand 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


Interatomic potentials for ionic systems

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]


Interatomic potentials for ionic systems

Many-Body Potential : Tersoff

  • 1985Abell : Close relation between Morse-typepair 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


Interatomic potentials for ionic systems

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


Interatomic potentials for ionic systems

Charge Equilibration Model

  • 1991Rappe &Goddard [48] : based on previous concepts on electronegativity, equilibration [49-57].

  • - equilibrium charge in molecules

  • consideringCoulomb 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 onatomic charge density expressed for aSlater-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


Interatomic potentials for ionic systems

EAM + Charge Equilibration

  • 1994Streitz & 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]


Interatomic potentials for ionic systems

Tersoff + Charge Equilibration

  • 1996 Yasukawa [76] : introduce atomic energy ΣiΦi& Coulomb energy ½ΣiΣjEIONij

- effective point charge with cutoff functionin 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

  • 2010modified version for SiO2 [81] : Slater 1s orbital type Coulomb integral &Ewald + anotherpenalty term

  • - applicable to α, β-quartz, α, β-cristobalite, β-tridymite, Coesite, Stishovite, generally worse thanTTAM

  • 2010 Hf/HfO2, Cu/Cu2O [83,84] : different bond-bending form depending on cation element


Interatomic potentials for ionic systems

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 Duin @ Penn State


Interatomic potentials for ionic systems

Summary

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


Interatomic potentials for ionic systems

Potential for Ionic+Covalent+Metallic Materials

  • Charge Effect ?

  • Correct physics : easy parameterization and goodtrasferability

  • Point Charge vs. Charge Distribution ?

  • TTAM that considered charge distribution could describe the SiO2polymorphs 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 potentialhas 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


Interatomic potentials for ionic systems

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Atomistic simulations meam applications

Atomistic Simulations- MEAM & Applications

Byeong-Joo Lee

Dept. of MSE

Pohang University

of Science and Technology

(POSTECH)

[email protected]


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)

Semi-Empirical Atomic Potentials - Historical Background


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

Semi-Empirical Atomic Potentials – History of Development


Eam meam general

EAM/MEAM – General

E : Total Potential Energy F : Embedding Energy : Electron Density (Considering Bonding Directionality) : Pair Interaction Energy


Eam meam embedding function

EAM/MEAM – Embedding Function

M.I. Baskes et al., Phys. Rev. B, 40, 6085 (1989)


Eam meam universal eos

EAM/MEAM – Universal EOS

J.H. Rose et al., Phys. Rev. B, 29, 2963 (1984)


Eam meam electron density for eam

EAM/MEAM – Electron Density for EAM


Eam meam electron density for meam

EAM/MEAM – Electron Density for MEAM

+ Angular contribution


Eam meam electron density for meam1

EAM/MEAM – Electron Density for MEAM

+ Angular contribution

with ti(0) =1


Eam meam 1 st nearest neighbor meam

EAM/MEAM – 1st Nearest Neighbor MEAM


1nn meam vs 2nn meam many body screening

1NN MEAM vs. 2NN MEAM –Many-Body Screening

Xik=(Rik/Rij)2 and Xkj=(Rkj/Rij)2

Cmax

Cmin

j

i

fc(x) = 1 x 1

0  x  1

0x  0


2nn meam computation of pair wise potential

2NN MEAM – Computation of pair-wise potential


Evaluation of meam potential parameters for elements

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


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, ...

Semi-Empirical Atomic Potentials - Performance


Meam for bcc transition metals b j lee et al prb 2001

Elem. C11 C12 C44 E(100) E(110) E(111) Evf Ebcc/fcc Efcc/hcp

Fe 2.430 1.380 1.2192510 2356 2668 1.75 0.069 -0.023

2.431 1.381 1.219 2360* 1.79 0.082 -0.023

Cr 3.909 0.897 1.034 2300 2198 2501 1.91 0.070 -0.02

3.910 0.896 1.032 2200* 1.80 0.075 -0.029

Mo 4.649 1.655 1.088 3130 2885 3373 3.09 0.167 -0.038

4.647 1.615 1.089 2900* 3.10 0.158 -0.038

W 5.326 2.050 1.631 3900 3427 4341 3.95 0.263 -0.047

5.326 2.050 1.631 2990* 3.95 0.200 -0.047

V 2.323 1.194 0.460 2778 2636 2931 2.09 0.084 -0.011

2.324 1.194 0.460 2600* 2.10 0.078 -0.036

Nb 2.527 1.331 0.319 2715 2490 2923 2.75 0.176 -0.012

2.527 1.332 0.310 2300* 2.75 0.140 -0.036

Ta 2.664 1.581 0.875 3035 2778 3247 2.95 0.148 -0.023

2.663 1.582 0.874 2780* 2.95 0.166 -0.041

MEAM for BCC Transition Metals – B.-J. Lee et al., PRB, 2001


Meam for fcc transition metals b j lee et al prb 2003

Elem. C11 C12 C44 E(100) E(110) E(111) Evf Ebcc/fcc Efcc/hcp ε(0-100oC)

Cu1.762  1.249  0.818  1382  1451  11851.11-0.08    0.007   17.0

1.762  1.249  0.818             1770        1.03-1.30  -0.04    0.006 17.0

  Ag    1.315  0.973  0.511       983  1010   842    0.94    -0.08     0.005   18.9

         1.315  0.973  0.511             1320         1.1     -0.04     0.003    19.1

  Au     2.015  1.697  0.454      1138  1179   928   0.90    -0.06     0.009    14.2

        2.016  1.697  0.454             1540         0.9     -0.04     0.003    14.1

  Ni    2.612  1.508  1.317      1943  2057  1606   1.51     -0.16     0.02     12.6

         2.612  1.508  1.317              2240       1.6     -0.09     0.02     13.3

Pd    2.342  1.761  0.712      1743  1786  1435   1.50     -0.17     0.02     11.0

       2.341  1.761  0.712             2043        1.4,1.7   -0.11     0.02     11.0

Pt     3.581  2.535  0.775      2288  2328  1710  1.50     -0.28     0.02     9.2

         3.580  2.536 0.774              2691      1.35,1.5   -0.16     0.03     9.0

  Al     1.143  0.619  0.316       848   948   629  0.68   -0.12     0.03     22.0

         1.143  0.619  0.316             1085          0.68    -0.10     0.06     23.5

  Pb     0.556  0.454  0.194       426    440   375    0.58     -0.04     0.003    30.1

         0.555  0.454  0.194               534        0.58    -0.02     0.003    29.0

MEAM for FCC Transition Metals – B.-J. Lee et al., PRB, 2003


Meam for silicon

C11 C12 C44E(100)E(110)E(111)EvfEdia/fccEdia/hcpEdia/bcc ε

(1012dyne/cm2) (erg/cm2) (eV) (eV) (0-100oC)

1.67 0.65 0.80 2631 1766 1442 3.67 0.57 0.55 0.52 2.65

1.68 0.65 0.80 1135* 3.3-4.3 0.57 0.55 0.53 2.69

MEAM for Silicon


2nn meam interatomic potentials for al and fe

2NN MEAM Interatomic Potentials – for Al and Fe


2nn meam 2nnmeam for alloy systems

2NN MEAM – 2NNMEAM for Alloy Systems


2nn meam for alloy systems optimization of potential parameter fe pt

2NN MEAM for Alloy Systems – Optimization of Potential Parameter, Fe-Pt


Interatomic potentials for ionic systems

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

200K 850K 1000K


Meam for cu ni binary system b j lee and j h shim calphad 2004

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


Meam for ni si binary system

MEAM for Ni-Si Binary System

Dilute Heat of Solution (eV/atom)

Si in (Ni) -1.50 (-1.37)

Ni in (Si) +0.50

Ni3Si

0.36 (0.36)

3.504 (3.504)

2.64

3.67 (3.63-3.75)

2.13 (2.00-2.05)

1.54

1.96 (1.67-1.72)

5.3 (7.2)

NiSi2

0.28 (0.28)

5.391 (5.406)

1.93 (1.60)

2.39

1.69

0.70 (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)


Meam for co pt binary system s i park et al scripta mater 2001

MEAM for Co-Pt Binary System - S.I. Park et al., Scripta Mater., 2001.

Property Pt3Co PtCo PtCo3

Cohesive Energy 5.500 5.215 4.873

(eV/atom) 5.555±0.017 5.228±0.005

Lattice Constant a=3.833 3.754, c/a=.98 3.625

(Å) a=3.831 3.745, c/a=.98 3.668

Transition 1070-1080 970-980 760-770

Temperature (K) 1000 1100 840


Meam for ni w binary system j h shim et al j mater res 2003

MEAM for Ni-W Binary System –J.-H. Shim et al., J. Mater. Res., 2003

Property fcc (XW=0.11) Ni4W

Cohesive Energy 4.922 5.36 (fcc, 5.27)

(eV/atom) 4.925 5.40

Lattice Constant a=3.57 a=5.73, c=3.553

(Å) a=3.56 a=5.73, c=3.553


Interatomic potentials for ionic systems

MEAM for Ni-W Binary System

a (Å) c (Å) Ec(eV) B(Gpa)

Ni4W (D1a) 5.73 3.553 5.36 292

5.733.5535.40293

Ni3W (L12) 3.62 - 5.58 319

3.58 - 5.65287

Ni3W (D019) 2.56 4.05 5.59 316

2.53 - 5.42289

NiW3 (L12) 3.86 - 7.29 316

3.84 - 7.55283

NiW3 (D019) 2.76 4.44 7.36 321

2.76 - 7.70304


Empirical potentials for multicomponent systems

Fe

▷ 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)

Empirical Potentials for Multicomponent Systems


History of fe c alloy potential

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

    • metal-carbon:pairwise interaction

    • can consider only one carbon atoms, not applicable to carbides

  • 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


History of carbon potential

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


2nn meam for fe c n fe c and fe n systems

Fe, Cr, Mo, W, V, Nb, TaSecond Nearest-Neighbor Modified Embedded Atom Method Potentials for BCC Transition MetalsByeong-Joo Lee, M.I. Baskes, Hanchul Kim and Yang Koo Cho,

Phys. Rev. B. 64, 184102 (2001).

CA Modified Embedded Atom Method Interatomic Potential for CarbonByeong-Joo Lee and Jin Wook Lee, CALPHAD 29, 7-16 (2005).

Fe-CA Modified Embedded Atom Method Interatomic Potential for the Fe-C System Byeong-Joo Lee, Acta Materialia 54, 701-711 (2006).

Fe-NA 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 4597-4607 (2006).

(2NN) MEAM for Fe, C, N, Fe-C and Fe-N systems


2nn meam for pure fe prb 64 184102 2001 71 184205 2005

2NN MEAM for pure Fe- PRB 64, 184102 (2001); 71, 184205 (2005)


Meam for carbon physical property of diamond

MEAM for Carbon– Physical Property of Diamond


Interatomic potentials for ionic systems

MEAM for Carbon– Physical Property of Graphite


Interatomic potentials for ionic systems

MEAM for Carbon– for several structures


Interatomic potentials for ionic systems

MEAM for Carbon– Nanotubes and Fullerenes


Interatomic potentials for ionic systems

MEAM for N2

▪ Bond length and Cohesive energy for N2

▪ Bond length, Bond angle and cohesive Energy for N3


Interatomic potentials for ionic systems

2NN MEAM for Fe-C & Fe-N– in BCC Fe

Carbon in O site vacancy-carbon carbon-carbon SIA-carbon vacancy-two carbon


Interatomic potentials for ionic systems

2NN MEAM for Fe-C& Fe-N– in FCC Fe


Interatomic potentials for ionic systems

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


Interatomic potentials for ionic systems

2NN MEAM for Fe-N– in Fe2N

  • Identification of the most stable atomic structure of Fe2N

  • ΔHf = - 5.7 kJ/mol MEAM: -20.9 kJ/mol

  • a = 2.76 Å, c = 4.42 Å MEAM: a = 2.81 Å, c = 4.32 Å


Atomistic simulation interatomic potentials and applications

Atomistic Simulation – Interatomic Potentials and Applications

Interatomic Potential:

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.


Interatomic potentials for ionic systems

Second Nearest Neighbor Modified EAM (2NN MEAM)

  • Pure Elements

    • Fe, Cr, Mo, W, V, Nb, Ta, LiPhys. Rev. B. 64, 184102 (2001);MSMSE 20, 035005 (2012) .

    • Cu, Ag, Au, Ni, Pd, Pt, Al, PbPhys. Rev. B. 68, 144112 (2003).

    • Ti, Zr & MgPhys. Rev. B. 74, 014101 (2006); CALPHAD 33, 650-57 (2009).

    • Mn, PActa Materialia 57, 474-482 (2009).; J. Phys.: Condensed Matters (2012), in press.

    • C, Si, Ge, In CALPHAD 29, 7-16 (2005); 31, 95-104 (2007); 32, 34-42 (2008); 32, 82-88 (2008)

  • Multicomponent Systems

    • Fe-C, Fe-N, Fe-HActa Materialia 54, 701-711 (2006); 54, 4597-4607 (2006); 55, 6779-6788 (2007).

    • Fe-Ti & Fe-NbScripta Materialia 59, 595-598 (2008).

    • Fe-Ti-C & Fe-Ti-N Acta Materialia 56 , 3481-3489 (2008); Acta Materialia 57 , 3140-3147 (2009).

    • Fe-Nb-C & Fe-Nb-NJ. Materials Research 25, 1288-1297 (2010).

    • Al-H & Ni-H, V-HJ. Materials Research 26, 1552-1560 (2011); CALPHAD 35, 302-307 (2011).

    • Fe-MnActa Materialia 57, 474-482 (2009).

    • Fe-Cr CALPHAD 25, 527-534 (2001).

    • Fe-Cu Phys. Rev. B. 71, 184205 (2005).

    • Fe-Pt J. Materials Research 21, 199-208 (2006).

    • Fe-Al J. Phys.: Condensed Matters 22, 175702 (2010)

    • Fe-PJ. Phys.: Condensed Matters (2012), in press.

    • Al-Ni CALPHAD 31, 53 (2007).

    • Co-Cu J. Materials Research 17, 925-928 (2002).

    • Co-Pt Scripta Materialia 45, 495-502 (2001).

    • Cu-NiCALPHAD 28, 125-132 (2004).

    • Ni-WJ. Materials Research 18, 1863-1867 (2003).

    • Cu-TiMater. Sci. and Eng. A 449-451, 733 (2007).

    • Cu-ZrJ. Materials Research 23, 1095 (2008).

    • Cu-Zr-AgScripta Materialia 61, 801 (2009).

    • Mg-Al, Mg-LiCALPHAD 33, 650-57 (2009); MSMSE 20, 035005 (2012) .

    • Ga-In-N J. Phys.: Condensed Matter 21, 325801 (2009).


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