1. Fundamentals of Solidification Lecture 4: Nucleation and growth

4. Temperature vs. time in glass solidification and phase transition solidification

5. Viscosity vs. temperature in glass solidification and phase transition solidification (a) Glass solidification (b) Phase-transition solidification

6. Density vs. temperature in glass solidification and phase transition solidification

7. Heat capacity of Fe

9. Homogeneous nucleation r r

11. Local free energy change 1. Liquid to solid 2. Interface

12. Local free energy change Spherical nucleus:

13. Single nucleus

14. Critical radius

15. (G L -G S ) vs. supercooling Free energy density vs. temperature liquid solid temperature Free energy density

16. Parameters For FCC Copper, r*  1 nm, which contains 310 Cu atoms in each nucleus.

19. when Number of nuclei Boltzmann formula: Critical nuclei:

21. Heterogeneous nucleation Liquid Inclusion Nucleus   IL  NL  IN R r h a 

22. Force equilibrium where  IL ,  IN and  NL are the interface energies of inclusion-liquid, inclusion-nucleus and nucleus-liquid, respectively.  is the nucleus-inclusion wetting angle. The nucleus is a spherical cap of radius r. Heterogeneous nucleation

23. Free energy change

24. Free energy change Using

25. Thermodynamic barriers Heterogeneous nucleation barrier Homogeneous nucleation barrier

26. Thermodynamic barrier vs. wetting angle

28. Number of nuclei with critical radius where n s is the total number of atom around the incubating agents’ surface in liquid.

31. Growth and microstructure T. F. Brower and M.C. Flemings, Trans. AIME, 239, 1620 (1967)

32. Growth and microstructure H.B. Dong and P.D. Lee, Acta Mater. 53 (2005) 659

33. Outer chilled zones

34. Outer chilled zones

35. Outer chilled zones

36. Outer chilled zones Pure metals: Formation of shell because temperature gradient is the key factor in grain growth.

37. Outer chilled zones re-melted? Pouring temperature survived?

39. Intermediate columnar zone Columnar grains grows The grain is overtaken by neighbors.

40. Intermediate columnar zone Growth and overtaken

41. Intermediate columnar zone Columnar growth blocked