Modeling and Simulations

1. Byeong-Joo Lee Department of Materials Science and Engineering Pohang University of Science and Technology (POSTECH) calphad@postech.ac.kr Modeling and Simulations

2. 모델링 : 대상이 되는 자연 현상을 지배하는 governing rule들을 찾아 Know-Why를 확립해 나가는 과정 시뮬레이션 : 주어진 조건에서 확립된 governing rule들이 작용하여 어떠한 결과를 만들어 내는지 가상적으로 재현해 내는 것 Introduction – Modeling과 Simulation의 개요

3. 모델링/시뮬레이션의 대상 · (금속,세라믹,반도체) 소재 내부 원자/나노/마이크로 수준의 구조 및 (상)조직 발현 활용 분야 · 상평형/반응 구동력의 계산 · 확산 반응 속도 및 경로, 계면 반응 · Defect (point defects and clusters, dislocations, surfaces) Chemistry · Atomic Structures at surfaces, grain boundaries, interfaces · Defects 간, 또는 defect와 interfaces 간의 상호작용 · Phase Transformations · Cracks and Mechanical behavior Introduction – Modeling 대상 및 Simulation 활용 분야

4. 강의 내용 및 평가 방법 I. Introduction 1 week II. Thermodynamic Calculation II-1. ThermoCalc - How to Do 2 weeks II-2. Modeling of Alloys 1 week II-3. Modeling of Pure Elements 1 week II-4. Calculation of Phase Equilibria 1 week II-5. Application to Multicomponent Diffusion Modelling 1 week III. Atomistic Simulation III-1. A Short Review of Statistical Mechanics 1 week III-2. Fundamentals of Molecular Dynamics 1 week III-3. Fundamentals of Monte Carlo Simulation 1 week III-4. KISSMD & KISSMC How to Do 2 weeks III-5. Semi-Empirical Atomic Potentials (EAM, MEAM) 1 week IV. Presentation of Final Report (Students) 2 weeks V. Evaluation - Mid. Report 30%, Term Paper 70%. CALPHAD/MD/MC 기법을 개별 연구 과제에 적용, 학기말 Report 제출

5. 열역학 계산, 확산 simulation, atomistic simulation (molecular dynamics, Monte Carlo) 기법 등을 실제 재료 연구 분야에 활용할 수 있도록 기본 modeling 및 계산/simulation 기법을 익히고, 기 개발된 컴퓨터 프로그램을 이용한 연습을 통해 경험을 쌓도록 한다. 강의목표

6. "용체모델 및 계산 열역학" 이병주, to be published (철강 공학). "합금계 확산 변태 Computer Simulation" 이병주 외, 한국표준과학연구원 연구보고서 KRISS-98-118-IR, 1998. "상평형 열역학" 이동녕, 이병주, 문운당, 1995. "Computer Calculation of Phase Diagrams" L. Kaufman and H. Bernstein, Academic Press, 1970. "CALPHAD: A Comprehensive Guide" N. Saunders and A.P. Miodownik, Pergamon Materials Series, vol.1, Pergamon, 1998. "Phase Equilibria, Phase Diagrams and Phase Transformations Their Thermodynamic Basis" M. Hillert, Cambridge University Press, 1998. "Diffusion in the Condensed State" J.S. Kirkaldy and D.J. Young, The Institute of Metals, 1987. "Molecular Dynamics Simulation - Elementary Methods" J.M. Haile, John Wiley & Sons, Inc., 1992. 참고문헌

7. 2004 세부 강의 진도 계획 3. 2 강의 소개 3. 4 Introduction 3. 9 Introduction 3. 11 ThermoCalc – Outline, (과제물 공고 – TC 계산) 3. 16 ThermoCalc – Calculation method 3. 18 ThermoCalc – Graphic & Management 3. 23,25 ThermoCalc – 연습 3. 30 과제물 제출, Computational Thermodynamics 4. 1 Computational Thermodynamics 4. 6 Computational Thermodynamics 4. 8 Computational Thermodynamics 4. 13 Computational Thermodynamics 4. 15 Computational Thermodynamics 4. 20 Thermodynamic Assessment, (학기말 과제물 공고 – Thermodynamic Assessment) 4. 22 학회 휴강 4. 27 Molecular Dynamics - Introduction 4. 29 Molecular Dynamics - Fundamentals 5. 4 Molecular Dynamics – Atomistic Analysis 5. 6 KISSMD – How to Do (과제물 공고 – Calculation of Fundamental Properties) 5. 11,13 KISSMD 연습 5. 18 과제물 제출, KISSMD 복습, Statistical Mechanics 5. 20 Micro & Atomistic Monte Carlo 5. 25 KISSMC How-to-do 5. 27 MEAM – assessment (학기말 과제물 공고 – Atomistic Simulation) 6. 1,3 학기말 과제물 질의 응답 6. 8 ~ 17 Student Presentation, Term Report 제출

8. Thermodynamic Calculations Diffusion Simulations Atomistic Simulations Introduction – Overview

9. Thermodynamic Equilibrium Why Gibbs Energy ? G = U + PV – ST For solutions, Thermodynamic Calculations – Modeling of Gibbs Energy

10. Gibbs-Duhem Equation - I

11. Gibbs-Duhem Equation - II

12. Introduction of α-function

13. Composition Dependence of α-function Fe-Ni Fe-Cu

14. Margules, 1895. Regular Solution Model • Hildebrade, 1929. (using van Laar Equation) • Quasi-Chemical Model (Guggenheim, 1935)

15. Quasi-Chemical Model - Guggenheim, 1935.

16. Regular Solution Model • Composition and temperature dependence of Ω • Extension into ternary and multi-component system • Sublattice Model • Inherent Inconsistency

17. Regular Solution Model Sn-In Sn-Bi

18. Sub-Regular Solution Model Sn-Zn Fe-Ni

19. Sub-Regular Solution Model - ex) Cr-Ni For fcc LCr,Ni = 8030 – 12.8801·T + (33080 – 16.0362·T)(1-2XNi) For bcc LCr,Ni = 17170 – 11.8199·T + (34418 – 11.8577·T)(1-2XNi)

20. Excess Energy in Ternary Systems

21. Ternary Extension

22. Sublattice Model • Interstitial Solid Solution • Intermediate Compounds • Ionic Liquid • Order/Disorder Transition

23. Subregular Solution Model - liquid Fe-C

24. Sublattice Model - fcc Fe-C

25. Limit of (Sub-)Regular Solution Model

26. Limit of (Sub-)Regular Solution Model

27. Ionic Solution Models • Modified Quasi-Chemical Model A.D. Pelton and M. Blander, Metall. Trans. 17B, 805 (1986) • Associate Model F. Sommer, Z. Metallkunde 73, 72 (1982); ibid. 73, 77 (1982). • Ionic Two-Sublattice Model M. Hillert, B. Jansson, B. Sundman and J. Ågren, Metall. Trans. 16A, 261 (1985)

28. Modified Quasi-Chemical Model • (A-A) + (B-B) = 2 (A-B) : ω-ηT

29. Associate Solution Model • iA + jB = AiBj : ω-ηT

30. Ionic Two-Sublattice Model

31. Gibbs Energy Expression for Pure Elements • Lattice Stability • Calculation of Lattice Stabilities using Cp data • Effect of Magnetic Transition • Effect of Pressure • Estimation of Lattice Stabilities for Metastable Phases - without Cp data

32. Lattice Stability

33. Lattice Stability • Available Experimental Data - Cp, H, V at 1atm and V(P)

34. Gibbs Energy Expression for Pure Elements

35. Temperature dependence of molar Enthalpy of Fe

36. Temperature and Pressure Dependence of Molar Volume of Fe

37. Lattice Stability from Cp Cv = 3RT/θ 0 < T < θ = 3R T > θ

38. Lattice Stability from Cp

39. Lattice Stability of hcp and bcc Ti - L. Kaufman, Acta Met. 7, 575 (1959). • γ(hcp-Ti) • θ(hcp-Ti) • γ(bcc-Ti) • θ(bcc-Ti) • ΔH(hcp→bcc: T=0K)

40. Lattice Stability of hcp and bcc Ti - L. Kaufman, Acta Met. 7, 575 (1959).

41. Lattice Stability from Cp T > Tm T < Tm

42. Model Calculation of Cp of pure Fe

43. Gibbs Energy Expression for Pure Elements

44. Effect of Magnetic Transition on the Temperature dependence of Cp

45. Modeling of Cp due to Magnetic Transition

46. Modeling of Gibbs Energy due to Magnetic Ordering

47. Modeling of Gibbs Energy due to Magnetic Ordering

48. Modeling of Gibbs Energy due to Magnetic Ordering

49. Modeling of pressure dependence of Gibbs Energy of pure Elements

50. Lattice Stability of pure Fe