Phase Transformations

1. PhaseTransformations Interfaces Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr

2. Scope • Fundamentals • Free Surfaces vs. Grain Boundaries vs. Interphase Interfaces • Concept of Surface Energy/Surface Tension • Origin of Surface Energy and its Anisotropy • Grain Boundary/Interfacial Energy • Interface Phenomena • 1. Curvature Effect • 2. Multi-component system • • Segregation • 3. General • • Grain Growth • • Morphological Evolution • 4. Interface Engineering

3. Surfaces

4. Concept of Surface Energy and Surface Tension for liquid film Generally,

5. Estimation of Solid Surface Energy -Origin of Surface Energy Pair approximation Necessary Work for Creation of (111) surface in fcc (/atom) For fcc (111): N/A = 4/(31/2a2) fcc (100): N/A = 2/a2 For Cu: a = 3.615 Å △Hs =337.7J/mol γ(111) = 2460 erg/cm2 (1700 by expt.) For fcc ※ Origin of Anisotropy

6. Estimation of Solid Surface Energy -Orientation dependence High Index Surface Energy Comparisons 1. W.R. Tyson and W.A. Miller, Surf. Sci. 62, 267 (1977). 2. L.Z. Mezey and J. Giber, Jpn. J. Appl. Phys., Part 1 21, 1569 (1982).

7. Equilibrium shape of a Crystal -Wulff construction

8. Equilibrium shape of a Crystal - Numerical Example

9. Note - Estimation of Surface Energy J. Park, J. Lee, Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 135–141

10. Atomistic Computation of Surface Energy Grain Boundary / Interface

11. Atomistic Computation of Surface Energy Grain Boundary / Interface

12. Grain • Boundaries

13. Grain boundaries in Solids - Misorientation Misorientation vs. Inclination

14. Grain boundaries in Solids - tilt vs. twist boundaries

15. [100] Twist Boundary Structure in pure Cu 3o 4o 7o 10o 15o 20o 30o 45o

16. [100] Twist Grain Boundary Energy of Copper

17. Special High-Angle Grain Boundaries

18. Special High-Angle Grain Boundaries · Incoherent boundary energy is insensitive to orientation.       ※ Special boundaries with low energy [100] and [110] tilt Boundary energy of Al

19. Equilibrium Microstructure - balance of GB tensions θ

20. Normal Grain Growth - the mechanism

21. Effect of particles on Grain Growth - Zener pinning effect Consider the balance between the dragging force (per unit area) and the pressure from the curvature effect • dragging force due to one particle of size r • number of ptl. per unit area of thickness 2r ⇒ drive it ! • total dragging force per unit area • Maximum grain size

22. Interphase • Interfaces

23. Interfaces in Solids – Coherent, Semi-Coherent & Incoherent Interfaces

24. Interfaces in Solids – Shape of Coherent Second-Phase from Y.S. Yoo KIMS ※ Equilibrium Shape

25. Strain Energy vs. Interfacial Energy - Mechanism of particle splitting Phase Field Method Simulation by P.R. Cha, KMU γ’ precipitates of Ni-Al alloy system, D.Y. Yoon et al. Metals and Materials

26. Morphological Evolution - from Y.S. Yoo, KIMS

27. Morphological Evolution - from Y.S. Yoo, KIMS

28. Interfaces • Phenomena

29. Question Interfacial Phenomena (Interface or Surface Segregation) • Thermodynamics of Surface or Grain Boundary Segregation • M. Guttmann, Surf. Sci., 53 (1975) 213-227; Metall. Trans. A, 8A (1977) 1383-1401. • T. Tanaka and T. Iida, Steel Research, 65, 21-28 (1994).

30. Interfacial Phenomena – Segregation (Guttmann) Assume a one atomic layer surface phase and consider equilibrium between bulk and surface where ωi is the molar surface area Assume ωi = ωj = … = ω

31. Interfacial Phenomena – Segregation (Physical Meaning of Quantities)

32. Interfacial Phenomena – Segregation (Butler/Tanaka)

33. Thermodynamic Calculation of Surface Tension of Liquid Alloys on the Web-board of this Lecture

34. Thermodynamic Calculation of Surface Segregation in Solid Alloys

35. Key Point Surface/Interface Energy of Crystalline Solids is Anisotropic

36. An issue for thinking - Surface Transition and Alloying Effect W + 0.4wt% Ni Pure W Vaccum Annealing

37. Abnormal Grain Growth – Mechanism ?

38. Abnormal Grain Growth – from N.M. Hwang

39. Phase Field Simulation of γ→α transformation in steels Wetting angle : 36o Wetting angle : 120o Fe - 0.5% Mn – 0.1% C, dT/dt = 1 oC/s from SG Kim, Kunsan University

40. Grain Boundary Identification Scheme H.-K. Kim et al., Scripta Mater. (2011) How to uniquely define misorientation and inclination between two neighboring grains

41. Grain Boundary Energy of BCC Fe H.-K. Kim et al., Scripta Mater. (2011)

42. Phase field simulation of grain growth H.-K. Kim et al. (2013) - Anisotropic GBE (realistic GBE DB) - Isotropic GBE • Isotropic GB mobility • Random crystallographic orientation vs. weakly-textured orientation • (LAGB = 1.4 % vs. 4.9 %)

43. Effect of Anisotropic GBE and Precipitates on Abnormal GG C.-S. Park et al., Scripta Mater. (2012)

44. Interface Engineering Case Study

45. {100} textured steel sheets • Widely used electrical steel: {110}<001> Goss texture • <001> is a “soft” magnetic direction ⇒ reduction of energy loss • Why {100} textured steel sheets? • Much improved magnetic properties (magnetic induction and core loss) are expected in {100}<001> cube textured electrical steels • Twenty-times high price compared to Goss texture

46. Atomistic Approach - surf segregation vs surf energy • Change of Surface Energy Anisotropy due to Surface Segregation

47. Phase Field Modeling - surface segregation & grain growth

48. Construction of Surface Energy Database • Isotropic grain boundaries (energy and segregation) is assumed to save computation time. • average phosphorus concentration on grain boundaries: 4.1 at% for a bulk concentration of 0.1 at% • the resultant average grain boundary energy: 0.666 J/m2 vs. for pure bcc Fe: 1.2 J/m2

49. Phase Field Simulation of Grain Growth – steel sheet

50. Experimental Verification – {100} texture on Steel Sheet Future work: Generation of {100}<001> cube texture