Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomistic Simulations in Materials Science and Engineering Byeong-Joo Lee Pohang University of Science and Technology cmse.postech.ac.kr

Byeong-Joo Lee cmse.postech.ac.kr Process Condition (Atomic Level) Structure Evolution Materials Properties R&D in Materials Science and Engineering Simulation

Byeong-Joo Lee cmse.postech.ac.kr Background & Purpose Many materials properties originate from atomistic structure evolution Experimental Examination of Atomistic Structure is now Feasible → Need of Atomic Level Simulations

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials - Performance Elastic ConstantsElastic Constants ▷ B, C11, C12, C44,... ▷ B, C11, C12, C44,... Defect EnergyDefect Energy ▷ Surface Energy ▷ Surface Energy ▷ Heat of Vacancy Formation, … ▷ Heat of Vacancy Formation, … Structural EnergyStructural Energy ▷ Energy and Lattice Parameters in Different Structures ▷ Energy and Lattice Parameters in Different Structures Thermal PropertyThermal Property ▷ Specific Heat ▷ Specific Heat ▷ Thermal Expansion Coefficient ▷ Thermal Expansion Coefficient ▷ Melting Temperature,... ▷ Melting Temperature,...

Byeong-Joo Lee cmse.postech.ac.kr Semi-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 elements ▷ Successful 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 structures ▷ Show 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 alloys ▷ Applicable to fcc, bcc, hcp, diamond structures and their alloys

Byeong-Joo Lee cmse.postech.ac.kr 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, (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, (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 (2003). Potential for Cu, Ag, Au, Ni, Pd, Pt, Al, Pb Potential for other Elements: Ti, Zr, Si, Ge, C, O 2 Potential for Alloy Systems: Fe-Cr, Ni-W, Fe-Cu, Cu-Ni, Fe-Ni, Fe-Pt, Al 2 O 3, SiO 2

Byeong-Joo Lee cmse.postech.ac.kr Contents 2NN MEAM for Elements and Alloys2NN MEAM for Elements and Alloys ApplicationsApplications ▷ Phase Diagrams in Nano World ▷ Phase Diagrams in Nano World ▷ Computation of Grain Boundary Energy ▷ Computation of Grain Boundary Energy ▷ Morphology Evolution of Nano Structures ▷ Morphology Evolution of Nano Structures ▷ Mechanical Property of Nano Crystalline Materials ▷ Mechanical Property of Nano Crystalline Materials ▷ Irradiation Defects ▷ Irradiation Defects ▷ ▷ Quantum Dot/Wire Formation

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – EAM/MEAM : General E : Total Potential Energy F : Embedding Energy  : Electron Density (Considering Bonding Directionality)  : Pair Interaction Energy E : Total Potential Energy F : Embedding Energy  : Electron Density (Considering Bonding Directionality)  : Pair Interaction Energy

Byeong-Joo Lee cmse.postech.ac.kr Evaluation of MEAM Potential Parameters E c, R e, B, A, d,  (0),  (1),  (2),  (3), t (1), t (2), t (3), C max, C minE c, R e, B, A, d,  (0),  (1),  (2),  (3), t (1), t (2), t (3), C max, C min ▷ Cohesive Energy of Stable and Metastable Structure ▷ Cohesive 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 Energy ▷ Stacking Fault Energy ▷ Vacancy Formation Energy ▷ Vacancy Formation Energy ▷ Surface Energy ▷ Surface Energy

Byeong-Joo Lee cmse.postech.ac.kr MEAM for BCC Transition Metals Elem. C11 C12 C44 E (100) E (110) E (111) E v f E bcc/fcc E fcc/hcp Fe * Cr * Mo * W * V * Nb * Ta *

Byeong-Joo Lee cmse.postech.ac.kr MEAM for BCC Transition Metals - Defect Properties Elem. E v f Q self-interstitial MEAM exp. MEAM exp. E I structure MEAM exp. MEAM exp. E I structure Fe [110] dumbbell Cr [110] dumbbell Mo [110] dumbbell W [110] dumbbell V [110] dumbbell Nb [110] dumbbell Ta [110] dumbbell

Byeong-Joo Lee cmse.postech.ac.kr MEAM for BCC Transition Metals - Thermal Properties Ele. ε (0-100 o C) C P (0-100 o C) T m ΔH m ΔV m /V solid MEAM exp. MEAM exp. MEAM exp. MEAM exp. MEAM exp. Fe Cr Mo W V Nb Ta

Byeong-Joo Lee cmse.postech.ac.kr MEAM for FCC Transition Metals Elem. C11 C12 C44 E (100) E (110) E (111) E v f E bcc/fcc E fcc/hcp ε (0-100 o C) Cu Ag Au Ni Pd , Pt , Al Pb

Byeong-Joo Lee cmse.postech.ac.kr MEAM for Silicon, Germanium, Carbon C 11 C 12 C 44 E (100) E (110) E (111) E v f E dia/fcc E dia/hcp E dia/bcc ε (10 12 dyne/cm 2 ) (erg/cm 2 ) (eV) (eV) (0-100 o C) Si Ge C

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Potentials for pure Fe MEAM F-S type EAM F-S type pair potential expt. This work Calder-Bacon Simonelli Ackland Osetsky C11 C12 C44 E v f ∆V v f /Ω E v m E I f ∆V I f /Ω E(100) E(110) E(111) ∆d(100) ∆d(110) ∆d(111) ∆Ebcc/fcc ∆Ehcp/fcc a(bcc) a(fcc) ε(0-100 o C) Cp (0-100 o C) m.p. ∆H m ∆V m a a a < 2 b < -.4 c 0.55 d - du e f -0.2, -1.5 g 0 g g h h i j 25.5 j 1811 h 13.8 h 3.5 j du k k k k 4.85 du k m 0.0 m cr du n 1585 n 2269 n cr

Byeong-Joo Lee cmse.postech.ac.kr 2NN MEAM for Aluminum Property MEAM Experiment/FP Property MEAM Experiment/FP B B (  B/  P) 0K (  B/  P) 0K C C C C C C  E_fcc/bcc  E_fcc/bcc H_vac H_vac Q D Q D E(100)/(110)/(111) 848/948/ E(100)/(110)/(111) 848/948/ % relaxation 1.8/-8.9/ / -8.5±1.0 / 0.9±0.5 % relaxation 1.8/-8.9/ / -8.5±1.0 / 0.9±0.5 E_ SF(111) 141 < 166 E_ SF(111) 141 < 166 MP MP  H /  V_f 11.0/ /6.5  H /  V_f 11.0/ /6.5 Cp/  (0-100°C) 26.2/ /23.5 Cp/  (0-100°C) 26.2/ /23.5

Byeong-Joo Lee cmse.postech.ac.kr 200K 850K 1000K 200K 850K 1000K MEAM for Fe-Cr Binary System

Byeong-Joo Lee cmse.postech.ac.kr MEAM for Cu-Ni Binary System

Byeong-Joo Lee cmse.postech.ac.kr MEAM 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 ) Ni 3 Si 0.36 (0.36) (3.504) ( ) 2.13 ( ) ( ) 5.3 (7.2) NiSi (0.28) (5.406) 1.93 (1.60) (0.58) Dilute Heat of Solution (eV/atom) Si in (Ni) Si in (Ni) (-1.37) Ni in (Si) Ni in (Si) +0.50

Byeong-Joo Lee cmse.postech.ac.kr MEAM for Ni-W Binary System Property fcc (X W =0.11) Ni 4 W Cohesive Energy (fcc, 5.27) (eV/atom) Lattice Constant a=3.57 a=5.73, c=3.553 (Å) a=3.56 a=5.73, c=3.553

Byeong-Joo Lee cmse.postech.ac.kr Size Effect on the Phase Diagram – T. Tanaka et al., Z. Metallkd

Byeong-Joo Lee cmse.postech.ac.kr Size Effect on the Melting Point - J.-H. Shim et al., Surface Science, Surface Facet, Au Size dependence of Melting point Surface Facet, Au Size dependence of Melting point

Byeong-Joo Lee cmse.postech.ac.kr Grain Boundary Energy – Degree of Freedom Misorientation :Misorientation : ▷ Difference in Crystallographic Directions of two Grains ▷ Difference in Crystallographic Directions of two Grains - Two degrees of freedom (φ and θ) - Two degrees of freedom (φ and θ) 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 (hkl) Normal - Three degrees of freedom (hkl)

Byeong-Joo Lee cmse.postech.ac.kr Computation of Grain Boundary Energy Computation of Grain Boundary Energy – Problem in Periodicity

Byeong-Joo Lee cmse.postech.ac.kr Computation of Grain Boundary Energy

Byeong-Joo Lee cmse.postech.ac.kr Precipitation of Co in a Cu-Co Nano Powder - J.-H. Shim et al., JMR, 2002.

Byeong-Joo Lee cmse.postech.ac.kr Pure W W + 0.4wt% Ni Vaccum Annealing Surface Transition and Alloying Effect – N.M. Hwang et al., 2000.

Byeong-Joo Lee cmse.postech.ac.kr Surface Transition and Alloying Effect Pure W W-20at%Ni Pure W W-20at%Ni

Byeong-Joo Lee cmse.postech.ac.kr Stress Induced Crystallization of Amorphous Materials

Byeong-Joo Lee cmse.postech.ac.kr Effect of Hydrostatic Pressure

Byeong-Joo Lee cmse.postech.ac.kr Stress Effect Hydrostatic Compressive Pressure Amorphous Crystalline Hydrostatic Tensile Pressure Mechanism of Stress Induced Crystallization of Amorphous Materials

Byeong-Joo Lee cmse.postech.ac.kr Atomistic Approach to Mechanical Properties J. Schiøtz et al., Nature, 1998.

Byeong-Joo Lee cmse.postech.ac.kr Response of pure Al to severe shear strain

Byeong-Joo Lee cmse.postech.ac.kr Irradiation Effect on Fe and Fe-Cu Alloys

Byeong-Joo Lee cmse.postech.ac.kr Energetics of Dot Formation during Thin Film Growths : Ge on Si Coverage (Dot-size) E II -E I E III -E I Double-Layer (5nm) eV/atom eV/atom Triple-Layer (5nm) eV/atom eV/atom Triple-Layer (10nm) eV/atom eV/atom Double-Layer (10nm) eV/atom : (100) side Double-Layer (10nm) eV/atom : (110) side Double-Layer (12nm) eV/atom : (100) side I II III

Byeong-Joo Lee cmse.postech.ac.kr Summary 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

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – EAM/MEAM : General E : Total Potential Energy F : Embedding Energy  : Electron Density (Considering Bonding Directionality)  : Pair Interaction Energy E : Total Potential Energy F : Embedding Energy  : Electron Density (Considering Bonding Directionality)  : Pair Interaction Energy

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – EAM : Electron Density

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – MEAM : Electron Density + Angular contribution

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – MEAM : Electron Density + Angular contribution with t i (0) =1

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – MEAM : Embedding Function M.I. Baskes et al., Phys. Rev. B, 40, 6085 (1989)

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – MEAM : Universal EOS J.H. Rose et al., Phys. Rev. B, 29, 2963 (1984)

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – MEAM : Universal EOS

Byeong-Joo Lee cmse.postech.ac.kr 1NN MEAM vs. 2NN MEAM – Many-Body Screening C max C min i j X ik =(R ik /R ij ) 2 and X kj =(R kj /R ij ) 2 f c (x) = 1 x  1 0 x  0 0  x  1

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – 2NNMEAM

Byeong-Joo Lee cmse.postech.ac.kr Semi-Empirical Atomic Potentials – 2NNMEAM for Alloy Systems

Byeong-Joo Lee cmse.postech.ac.kr Evaluation of MEAM Potential Parameters E c, R e, B, A, d,  (0),  (1),  (2),  (3), t (1), t (2), t (3), C max, C minE c, R e, B, A, d,  (0),  (1),  (2),  (3), t (1), t (2), t (3), C max, C min ▷ Cohesive Energy of Stable and Metastable Structure ▷ Cohesive 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 Energy ▷ Stacking Fault Energy ▷ Vacancy Formation Energy ▷ Vacancy Formation Energy ▷ Surface Energy ▷ Surface Energy

Byeong-Joo Lee cmse.postech.ac.kr MEAM for Copper Property MEAM Experiment/FP Property MEAM Experiment/FP B B (  B/  P) 0K (  B/  P) 0K C C C C C C  E_fcc/bcc  E_fcc/bcc H_vac H_vac Q D Q D E(100)/(110)/(111) 1382/1451/ E(100)/(110)/(111) 1382/1451/ % relaxation -2.5/-9.3/ ±.4/-8.5~-10/-0.7±.5 % relaxation -2.5/-9.3/ ±.4/-8.5~-10/-0.7±.5 E_ SF(111) 42 40~48, <80 E_ SF(111) 42 40~48, <80 MP MP  H /  V_f 18.6/ /4.2  H /  V_f 18.6/ /4.2 Cp/  (0-100°C) 24.9/ /17.0 Cp/  (0-100°C) 24.9/ /17.0

Byeong-Joo Lee cmse.postech.ac.kr MEAM for Tungsten Property MEAM Experiment/FP Property MEAM Experiment/FP B B (  B/  P) 0K (  B/  P) 0K C C C C C C  E_fcc/bcc  E_fcc/bcc  E_hcp/fcc  E_hcp/fcc H_vac H_vac Q D Q D E(100)/(110)/(111) 3900/3427/ , 3468 E(100)/(110)/(111) 3900/3427/ , 3468 % relaxation -3.2/-3.0/ / -5.9/ % relaxation -3.2/-3.0/ / -5.9/ MP ∼ MP ∼  H /  V_f 33.0/ / -  H /  V_f 33.0/ / - Cp/  (0-100°C) 25.4/ /4.5 Cp/  (0-100°C) 25.4/ /4.5

Byeong-Joo Lee cmse.postech.ac.kr 2NN MEAM for Nickel Property MEAM Experiment/FP Property MEAM Experiment/FP B B (  B/  P) 0K (  B/  P) 0K C C C C C C  E_fcc/bcc  E_fcc/bcc H_vac H_vac Q D Q D E(100)/(110)/(111) 1943/2057/ E(100)/(110)/(111) 1943/2057/ % relaxation -1.8/-6.0/  1.1/ -8 ±1 / -1 ±1 % relaxation -1.8/-6.0/  1.1/ -8 ±1 / -1 ±1 E_ SF(111) E_ SF(111) MP MP  H /  V_f 24.6/ /4.5  H /  V_f 24.6/ /4.5 Cp/  (0-100°C) 25.4/ /13.3 Cp/  (0-100°C) 25.4/ /13.3

Byeong-Joo Lee cmse.postech.ac.kr 2NN MEAM for Nickel Property MEAM Experiment/FP Property MEAM Experiment/FP B B (  B/  P) 0K (  B/  P) 0K C C C C C C  E_fcc/bcc  E_fcc/bcc H_vac H_vac Q D Q D E(100)/(110)/(111) 2715/2660/ E(100)/(110)/(111) 2715/2660/ % relaxation -0.8/-6.3/  1.1/ -8 ±1 / -1 ±1 % relaxation -0.8/-6.3/  1.1/ -8 ±1 / -1 ±1 E_ SF(111) E_ SF(111) MP MP  H /  V_f 16.5/ /4.5  H /  V_f 16.5/ /4.5 Cp/  (0-100°C) 25.6/ /13.3 Cp/  (0-100°C) 25.6/ /13.3