byeong-joo lee cmse.postech.ac.kr semi-empirical atomistic simulations in materials science and...

Byeong-Joo Lee cmse.postech.ac.kr

Semi-Empirical Atomistic Simulationsin Materials Science and Engineering

Byeong-Joo Lee Byeong-Joo Lee

Pohang University of Science and TechnologyPohang University of Science and Technologycmse.postech.ac.kr cmse.postech.ac.kr


Process Condition

(Atomic Level) Structure Evolution(Atomic Level) Structure Evolution

Materials Properties

R&D in Materials Science and EngineeringR&D in Materials Science and Engineering

Simulation

Simulation


Background & PurposeBackground & Purpose

Many materials properties originate from atomistic structure evolution

• Experimental Examination of Atomistic Structure is now Feasible

→ Need of Atomic Level Simulations


Semi-Empirical Atomic Potentials - PerformanceSemi-Empirical Atomic Potentials - Performance

• Elastic ConstantsElastic Constants ▷ ▷ B, C11, C12, C44, ... B, C11, C12, C44, ...

• Defect EnergyDefect Energy ▷ ▷ Surface EnergySurface Energy

▷ ▷ Heat of Vacancy Formation, …Heat of Vacancy Formation, …

• Structural EnergyStructural Energy ▷ ▷ Energy and Lattice Parameters in Different StructuresEnergy and Lattice Parameters in Different Structures

• Thermal PropertyThermal Property ▷ ▷ Specific HeatSpecific Heat

▷ ▷ Thermal Expansion CoefficientThermal Expansion Coefficient

▷ ▷ Melting Temperature, ...Melting Temperature, ...


Semi-Empirical Atomic Potentials – History of DevelopmentSemi-Empirical Atomic Potentials – History of Development

• EAM Potentials (1983, M.S. Daw and M.I. Baskes)EAM Potentials (1983, M.S. Daw and M.I. Baskes) ▷ ▷ Successful mainly for FCC elementsSuccessful mainly for FCC elements - many other many-body potentials show similar performance- many other many-body potentials show similar performance

• 1NN MEAM Potentials (1987,1992, M.I. Baskes)1NN MEAM Potentials (1987,1992, M.I. Baskes) ▷ ▷ Show Possibility for description of various structuresShow Possibility for description of various structures - important to be able to describe multi-component system- important to be able to describe multi-component system

• 2NN MEAM Potentials (2000, B.-J. Lee & M.I. Baskes)2NN MEAM Potentials (2000, B.-J. Lee & M.I. Baskes) ▷ ▷ Applicable to fcc, bcc, hcp, diamond structures and their alloysApplicable to fcc, bcc, hcp, diamond structures and their alloys


Second Nearest Neighbor Modified EAM (2NN MEAM)Second Nearest Neighbor Modified EAM (2NN MEAM)

• Second Nearest-Neighbor Modified Embedded-Atom Method Potential Byeong-Joo Lee and M.I. Baskes, Phys. Rev. B. 62, 8564-8567 (2000). Formalism of the 2NN MEAM

• Second Nearest-Neighbor Modified Embedded Atom Method Potentials for BCC Transition Metals

B.-J. Lee, M.I. Baskes, H. Kim and Y. K. Cho, Phys. Rev. B. 64, 184102 (2001). Potential for Fe, Cr, Mo, W, V, Nb, Ta

• Semi-Empirical 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

Byeong-Joo Lee, J.-H. Shim and M.I. Baskes, Phys. Rev. B. 68 144112 (2003). Potential for Cu, Ag, Au, Ni, Pd, Pt, Al, Pb

• Potential for other Elements: Ti, Zr, Si, Ge, C, O2

• Potential for Alloy Systems: Fe-Cr, Ni-W, Fe-Cu, Cu-Ni, Fe-Ni, Fe-Pt, Al2O3, SiO2


ContentsContents

• 2NN MEAM for Elements and Alloys2NN MEAM for Elements and Alloys

• ApplicationsApplications

▷ ▷ Phase Diagrams in Nano WorldPhase Diagrams in Nano World ▷ ▷ Computation of Grain Boundary EnergyComputation of Grain Boundary Energy ▷ ▷ Morphology Evolution of Nano StructuresMorphology Evolution of Nano Structures ▷ ▷ Mechanical Property of Nano Crystalline MaterialsMechanical Property of Nano Crystalline Materials ▷ ▷ Irradiation DefectsIrradiation Defects ▷ ▷ Quantum Dot/Wire Formation


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – EAM/MEAM : General– EAM/MEAM : General

i ijijijii rFE

)(

)(2

1)(

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


Evaluation of MEAM Potential ParametersEvaluation of MEAM Potential Parameters

• EEcc, R, Ree, B, A, d, , B, A, d, (0)(0), ,

(1)(1), , (2)(2), ,

(3)(3), t, t(1)(1), t, t(2)(2), t, t(3)(3), C, Cmaxmax, C, Cminmin

▷ ▷ Cohesive Energy of Stable and Metastable StructureCohesive Energy of Stable and Metastable Structure

▷ ▷ Nearest Neighbor Distance Nearest Neighbor Distance

▷ ▷ Bulk Modulus, Elastic Constants (C11, C12, C44)Bulk Modulus, Elastic Constants (C11, C12, C44)

▷ ▷ Stacking Fault EnergyStacking Fault Energy

▷ ▷ Vacancy Formation EnergyVacancy Formation Energy

▷ ▷ Surface EnergySurface Energy


MEAM for BCC Transition MetalsMEAM for BCC Transition Metals

Elem. C11 C12 C44Elem. C11 C12 C44 EE(100) (100) E E(110) (110) E E(111)(111) E Evvff E Ebcc/fccbcc/fcc E Efcc/hcpfcc/hcp

Fe 2.430 1.380 1.219 2510 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 - Defect PropertiesMEAM for BCC Transition Metals - Defect Properties

Elem. Elem. EEvvff QQ self-interstitial self-interstitial

MEAM exp. MEAM exp. MEAM exp. MEAM exp. EEII structure structure

Fe 1.75 1.79 2.28 2.5 4.23 [110] dumbbell

Cr 1.91 1.80 2.61 3.1 3.90 [110] dumbbell

Mo 3.09 3.10 4.22 4.5 5.97 [110] dumbbell

W 3.95 3.95 5.56 5.5 8.98 [110] dumbbell

V 2.09 2.10 2.47 3.2 2.49 [110] dumbbell

Nb 2.75 2.75 3.32 3.6 2.56 [110] dumbbell

Ta 2.95 2.95 3.71 4.3 4.88 [110] dumbbell


MEAM for BCC Transition Metals - Thermal PropertiesMEAM for BCC Transition Metals - Thermal Properties

Ele. ε (0-100oC) CP(0-100oC) Tm ΔHm ΔVm/Vsolid

MEAM exp. MEAM exp. MEAM exp. MEAM exp. MEAM exp.

Fe 12.4 12.1 26.1 25.5 2200 1811 13.2 13.8 3.4 3.5Cr 9.0 6.5 26.8 24.0 2050 2180 18.8 21.0 4.4 -Mo 5.3 5.1 25.9 24.1 3100 2896 20.1 37.5 3.0 -W 4.2 4.5 25.4 25.4 4600 3695 33.0 52.3 3.2 -V 8.7 8.3 26.1 25.4 1800 2183 11.7 21.5 1.3 -Nb 6.4 7.2 26.1 24.9 1900 2750 13.5 30.0 1.0 -Ta 5.8 6.5 25.7 25.7 3200 3290 22.3 36.6 2.1 -


MEAM for FCC Transition MetalsMEAM for FCC Transition Metals

Elem. C11 C12 C44Elem. C11 C12 C44 E E(100) (100) E E(110) (110) E E(111)(111) EEvvff E Ebcc/fccbcc/fcc E Efcc/hcp fcc/hcp εε (0-100(0-100ooC)C)

Cu 1.762 1.249 0.818 1382 1451 1185 1.11 -0.08 0.007 17.0 1.762 1.249 0.818 1770 1.03-1.30 -0.04 0.006 1

7.0 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 Silicon, Germanium, CarbonMEAM for Silicon, Germanium, Carbon

C11 C12 C44 E(100) E(110) E(111) Evf Edia/fcc Edia/hcp Edia/bcc ε

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

Si 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

Ge 1.31 0.50 0.68 2213 1580 1290 3.04 0.43 0.42 0.40 3.00 1.32 0.50 0.68 900 - 0.43 0.42 0.40 - C 10.8 1.27 5.81 4762 4082 3333 3.19 4.52 4.52 4.03 7.20 10.8 1.27 5.77 - 7.0 4.59 4.48 4.28 1.00


Semi-Empirical Potentials for pure Fe Semi-Empirical Potentials for pure Fe MEAM F-S type EAM F-S type pair potential expt. This work Calder-Bacon Simonelli Ackland Osetsky

C11C12C44Ev

f

∆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

2.4301.3801.2191.75-.410.534.20

<110>du1.70251023562668-1.1-1.5

-10.5-0.048-0.0182.86373.61112.526.1200012.93.3

2.434k

1.381k

1.221k

1.83-.210.91k

4.85<110>du

1.33

1920k

-0.054m

0.0m

2.866

2.421.471.121.63

0.663.54

<111>cr

-0.027 0.0

2.8664

2200

2.431.451.16 1.70-.180.784.87

<110>du1.76

1812n

1585n

2269n

--

2.8665

--

1.192.05-.290.533.92

<111>cr0.69

-0.0520.0052.8673.61211.6


2NN MEAM for Aluminum2NN MEAM for Aluminum

Property MEAM Experiment/FPProperty MEAM Experiment/FP

B 0.794 0.794B 0.794 0.794 ((B/ B/ P)P)0K 0K 4.59 4.72 4.59 4.72 C11 1.143 1.143C11 1.143 1.143 C12 0.619 0.619C12 0.619 0.619 C44 0.316 0.316C44 0.316 0.316 E_fcc/bcc 0.12 0.10E_fcc/bcc 0.12 0.10 H_vac 0.68 0.68H_vac 0.68 0.68 QQDD 1.33 1.28 1.33 1.28 E(100)/(110)/(111) 848/948/629 1085E(100)/(110)/(111) 848/948/629 1085 % relaxation 1.8/-8.9/1.0 1.8/ -8.5±1.0 / 0.9±0.5% relaxation 1.8/-8.9/1.0 1.8/ -8.5±1.0 / 0.9±0.5 E_E_SF(111) SF(111) 141 < 166 141 < 166 MP 937 933MP 937 933 H / H / V_f 11.0/6.7 10.7/6.5V_f 11.0/6.7 10.7/6.5 Cp/Cp/ (0-100°C) 26.2/22.0 24.7/23.5 (0-100°C) 26.2/22.0 24.7/23.5


200K 850K 1000K200K 850K 1000K

MEAM for Fe-Cr Binary SystemMEAM for Fe-Cr Binary System


MEAM for Cu-Ni Binary SystemMEAM for Cu-Ni Binary System


MEAM for Ni-Si Binary SystemMEAM for Ni-Si Binary System

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)

NiNi33SiSi 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)

NiSiNiSi22

0.28 (0.28) 5.391 (5.406) 1.93 (1.60) 2.39 1.69 0.70 (0.58) 0.32 8.0

Dilute Heat of Solution (eV/atom)

Si in (Ni)Si in (Ni) -1.50 (-1.37) Ni in (Si)Ni in (Si) +0.50


MEAM for Ni-W Binary System MEAM for Ni-W Binary System

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


Size Effect on the Phase Diagram Size Effect on the Phase Diagram – T. Tanaka et al., Z. Metallkd. 2001.– T. Tanaka et al., Z. Metallkd. 2001.


Size Effect on the Melting Point Size Effect on the Melting Point - J.-H. Shim et al., Surface Science, 2002.- J.-H. Shim et al., Surface Science, 2002.

Surface Facet, Au Size dependence of Melting pointSurface Facet, Au Size dependence of Melting point

0 2 4 6 8 10 12 14 16400

500

600

700

800

900

1000

1100

1200

1300

1400

Present simulation, MEAM Lewis et al. [10], EAM Buffat and Borel [25], Experiment Sambles [26], Experiment

Tem

pera

ture

(K

)

Diameter (nm)


Grain Boundary Energy Grain Boundary Energy – Degree of Freedom– Degree of Freedom

• Misorientation : Misorientation : ▷ ▷ Difference in Crystallographic Directions of two GrainsDifference in Crystallographic Directions of two Grains

- Two degrees of freedom (- Two degrees of freedom (φφ and and θθ))

• Inclination AngleInclination Angle ▷ ▷ Location of Grain Boundary and Direction of Grain Boundary Location of Grain Boundary and Direction of Grain Boundary Normal - Three degrees of freedom (Normal - Three degrees of freedom (hklhkl))


Computation of Grain Boundary Energy Computation of Grain Boundary Energy – Problem in Periodicity


Computation of Grain Boundary Energy Computation of Grain Boundary Energy


Precipitation of Co in a Cu-Co Nano Powder Precipitation of Co in a Cu-Co Nano Powder - J.-H. Shim et al., JMR, 2002.- J.-H. Shim et al., JMR, 2002.


Pure W W + 0.4wt% Ni

Vaccum Annealing

Surface Transition and Alloying Effect Surface Transition and Alloying Effect – N.M. Hwang et al., 2000.– N.M. Hwang et al., 2000.


Surface Transition and Alloying Effect Surface Transition and Alloying Effect

Pure W W-20at%NiPure W W-20at%Ni


Stress Induced Crystallization of Amorphous MaterialsStress Induced Crystallization of Amorphous Materials


Effect of Hydrostatic Pressure Effect of Hydrostatic Pressure


Stress Effect

Hydrostatic Compressive Pressure

Amorphous Crystalline

Hydrostatic Tensile Pressure

Mechanism of Stress Induced Crystallization of Amorphous MaterialsMechanism of Stress Induced Crystallization of Amorphous Materials


Atomistic Approach to Mechanical PropertiesAtomistic Approach to Mechanical Properties

J. Schiøtz et al.,J. Schiøtz et al.,Nature, 1998. Nature, 1998.


Response of pure Al to severe shear strainResponse of pure Al to severe shear strain


Irradiation Effect on Fe and Fe-Cu AlloysIrradiation Effect on Fe and Fe-Cu Alloys


Energetics of Dot Formation during Thin Film Growths : Ge on SiEnergetics of Dot Formation during Thin Film Growths : Ge on Si

Coverage (Dot-size) EII-EI EIII-EI

Double-Layer (5nm) 0.010 eV/atom 0.025 eV/atom Triple-Layer (5nm) 0.017 eV/atom 0.031 eV/atom Triple-Layer (10nm) 0.007 eV/atom 0.016 eV/atom

Double-Layer (10nm) 0.004 eV/atom : (100) side Double-Layer (10nm) 0.002 eV/atom : (110) side Double-Layer (12nm) 0.003 eV/atom : (100) side

I II III


SummarySummary

Performance of 2NN MEAM for Elements and Alloys

• Phase Diagrams in Nano World• Computation of Grain Boundary Energy• Morphology Evolution of Nano Structures• Mechanical Property of Nano Crystalline Materials• Irradiation Defects• Quantum Dot/Wire Formation


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – EAM/MEAM : General– EAM/MEAM : General

i ijijijii rFE

)(

)(2

1)(

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


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – EAM : Electron Density– EAM : Electron Density

i ijijijii rFE

)(

)(2

1)(


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – MEAM : Electron Density– MEAM : Electron Density

+ Angular contribution

( ) ( )( ) ( ) i ja

ijj i

R0 2 0

2

( ) ( )( ) ( )

iij

ijja

ijj i

R

RR1 2 1

2

( ) ( ) ( )( )

,

( ) ( )

iij ij

ijja

ijj i

ja

ijj i

R R

RR R2 2

22

2

2

21

3

( ) ( ) ( )( )

, ,

( ) ( )

iij ij ij

ijja

ijj i

ij

ijja

ijj i

R R R

RR

R

RR3 2

33

2

3

2

3

5


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – MEAM : Electron Density– MEAM : Electron Density

+ Angular contribution

with ti(0) =1

i i G ( ) ( )0

ti

h

h

ih

i

( )( )

( )1

3

0

2

Ge

( )

2

1

3

0

2)0(

)(3

1

)(2)0(2)()(2 )(1)()()(h i

hi

h

hii

hi

hii tt


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – MEAM : Embedding Function– MEAM : Embedding Function

i ijijijii rFE

)(

)(2

1)(

F AEc o o( ) ln

eea

eq

e n

n

r

rrr ln

)(

)'(2

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


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – MEAM : Universal EOS– MEAM : Universal EOS

i ijijijii rFE

)(

)(2

1)(

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

** )1()( ac

u eaErE

)1/(* erra

91 2

B

Ec

/


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – MEAM : Universal EOS– MEAM : Universal EOS

i ijijijii rFE

)(

)(2

1)(

*

)1()()())(( *21 a

cuo

eaErErrF

))](()([2

)(1

rFrEZ

rou


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

Cmax

Cmin

i j

xC

y Rij2 2

21 1

2

C

X X X X

X Xik kj ik kj

ik kj

2 1

1

2

2

( ) ( )

( )

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

S fC C

C Cikj c

min

max min

fc(x) = 1 x 1

1 1 4 2 ( )x

0 x 0

S Sij ikjk i j

,

0 x 1


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – 2NNMEAM – 2NNMEAM

i ijijijii rFE

)(

)(2

1)(

Eu (R) F(o(R))

Z1

2(R)

Z2 S

2(aR)

o

(R) Z1a(0) (R) Z 2S

a(0) (aR)

Eu (R) F(o(R))

Z1

2 (R)

(R) (R)Z2 S

Z1

(aR)

(R) (R) ( 1)n

n1 Z2S

Z1

n

(an R)


Semi-Empirical Atomic Potentials Semi-Empirical Atomic Potentials – 2NNMEAM for Alloy Systems– 2NNMEAM for Alloy Systems

i ijijijii rFE

)(

)(2

1)(


Evaluation of MEAM Potential ParametersEvaluation of MEAM Potential Parameters

• EEcc, R, Ree, B, A, d, , B, A, d, (0)(0), ,

(1)(1), , (2)(2), ,

(3)(3), t, t(1)(1), t, t(2)(2), t, t(3)(3), C, Cmaxmax, C, Cminmin

▷ ▷ Cohesive Energy of Stable and Metastable StructureCohesive Energy of Stable and Metastable Structure

▷ ▷ Nearest Neighbor Distance Nearest Neighbor Distance

▷ ▷ Bulk Modulus, Elastic Constants (C11, C12, C44)Bulk Modulus, Elastic Constants (C11, C12, C44)

▷ ▷ Stacking Fault EnergyStacking Fault Energy

▷ ▷ Vacancy Formation EnergyVacancy Formation Energy

▷ ▷ Surface EnergySurface Energy


MEAM for CopperMEAM for Copper


B 1.420 1.420B 1.420 1.420 ((B/ B/ P)P)0K 0K 4.95 5.25 4.95 5.25 C11 1.762 1.762C11 1.762 1.762 C12 1.249 1.249C12 1.249 1.249 C44 0.818 0.818C44 0.818 0.818 E_fcc/bcc 0.08 0.04E_fcc/bcc 0.08 0.04 H_vac 1.11 1.03-1.19H_vac 1.11 1.03-1.19 QQDD 2.19 2.09 2.19 2.09 E(100)/(110)/(111) 1382/1451/1185 1770E(100)/(110)/(111) 1382/1451/1185 1770

% relaxation -2.5/-9.3/-3.1 -1.1% relaxation -2.5/-9.3/-3.1 -1.1±±.4/-8.5.4/-8.5~-10~-10/-0.7±.5/-0.7±.5 E_E_SF(111) SF(111) 42 40 42 40~48, ~48, <80<80 MP 1602 1358MP 1602 1358 H / H / V_f 18.6/7.7 13.3/4.2V_f 18.6/7.7 13.3/4.2 Cp/Cp/ (0-100°C) 24.9/17.0 24.5/17.0 (0-100°C) 24.9/17.0 24.5/17.0


MEAM for TungstenMEAM for Tungsten


B 3.14 3.14B 3.14 3.14 ((B/ B/ P)P)0K 0K 4.79 4.50 4.79 4.50 C11 5.326 5.326C11 5.326 5.326 C12 2.050 2.050C12 2.050 2.050 C44 1.631 1.631C44 1.631 1.631 E_fcc/bcc 0.26 0.20E_fcc/bcc 0.26 0.20

E_hcp/fcc -0.047 -0.047E_hcp/fcc -0.047 -0.047 H_vac 3.95 3.95H_vac 3.95 3.95 QQDD 5.56 5.5 5.56 5.5 E(100)/(110)/(111) 3900/3427/4341 2990, 3468E(100)/(110)/(111) 3900/3427/4341 2990, 3468 % relaxation -3.2/-3.0/-13.2 -3.1/ -5.9/ -15.1% relaxation -3.2/-3.0/-13.2 -3.1/ -5.9/ -15.1 MP MP ∼∼4600 36954600 3695

H H //V_fV_f 33.0/3.2 52.3/ - 33.0/3.2 52.3/ - Cp/Cp/ (0-100°C) 25.4/4.2 25.4/4.5 (0-100°C) 25.4/4.2 25.4/4.5


2NN MEAM for Nickel2NN MEAM for Nickel


B 1.876 1.876B 1.876 1.876 ((B/ B/ P)P)0K 0K 4.90 4.89 4.90 4.89 C11 2.612 2.612C11 2.612 2.612 C12 1.508 1.508C12 1.508 1.508 C44 1.317 1.317C44 1.317 1.317 E_fcc/bcc 0.16 0.11E_fcc/bcc 0.16 0.11 H_vac 1.51 1.60H_vac 1.51 1.60 QQDD 2.98 2.87 2.98 2.87 E(100)/(110)/(111) 1943/2057/1606 2240E(100)/(110)/(111) 1943/2057/1606 2240 % relaxation -1.8/-6.0/-1.4 -3.2% relaxation -1.8/-6.0/-1.4 -3.21.1/ -8 ±1 / -1 ±11.1/ -8 ±1 / -1 ±1 E_E_SF(111) SF(111) 125 125 125 125 MP 2013 1728MP 2013 1728 H / H / V_f 24.6/9.1 17.5/4.5V_f 24.6/9.1 17.5/4.5 Cp/Cp/ (0-100°C) 25.4/12.6 26.5/13.3 (0-100°C) 25.4/12.6 26.5/13.3


2NN MEAM for Nickel2NN MEAM for Nickel


B 1.876 1.876B 1.876 1.876 ((B/ B/ P)P)0K 0K 4.90 4.89 4.90 4.89 C11 2.611 2.612C11 2.611 2.612 C12 1.508 1.508C12 1.508 1.508 C44 1.317 1.317C44 1.317 1.317 E_fcc/bcc 0.19 0.11E_fcc/bcc 0.19 0.11 H_vac 1.60 1.60H_vac 1.60 1.60 QQDD 2.92 2.90 2.92 2.90 E(100)/(110)/(111) 2715/2660/2238 2240E(100)/(110)/(111) 2715/2660/2238 2240 % relaxation -0.8/-6.3/+0.2 -3.2% relaxation -0.8/-6.3/+0.2 -3.21.1/ -8 ±1 / -1 ±11.1/ -8 ±1 / -1 ±1 E_E_SF(111) SF(111) 125 125 125 125 MP 1900 1728MP 1900 1728 H / H / V_f 16.5/7.4 17.5/4.5V_f 16.5/7.4 17.5/4.5 Cp/Cp/ (0-100°C) 25.6/12.7 26.5/13.3 (0-100°C) 25.6/12.7 26.5/13.3

byeong-joo lee cmse.postech.ac.kr semi-empirical atomistic simulations in materials science and...

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