Published on

Published in: Technology, Business
  • Be the first to comment

  • Be the first to like this

No Downloads
Total views
On SlideShare
From Embeds
Number of Embeds
Embeds 0
No embeds

No notes for slide


  1. 1. Fundamentals of Solidification Lecture 4: Nucleation and growth
  2. 2. Outline <ul><li>Introduction </li></ul><ul><li>Homogeneous nucleation </li></ul><ul><li>Heterogeneous nucleation </li></ul><ul><li>Growth and microstructure </li></ul><ul><li>Summary </li></ul>
  3. 3. Introduction <ul><li>There are two types of solidification </li></ul><ul><ul><li>Glass formation </li></ul></ul><ul><ul><ul><li>Physical properties such as viscosity change smoothly across the solidifying region </li></ul></ul></ul><ul><ul><li>Phase transition </li></ul></ul><ul><ul><ul><li>Some physical properties change abruptly, such as viscosity, heat capacity </li></ul></ul></ul>
  4. 4. Temperature vs. time in glass solidification and phase transition solidification
  5. 5. Viscosity vs. temperature in glass solidification and phase transition solidification (a) Glass solidification (b) Phase-transition solidification
  6. 6. Density vs. temperature in glass solidification and phase transition solidification
  7. 7. Heat capacity of Fe
  8. 8. Introduction <ul><li>Solidification by phase transition is modelled as two stage </li></ul><ul><ul><li>Nucleation </li></ul></ul><ul><ul><ul><li>Homogeneous nucleation </li></ul></ul></ul><ul><ul><ul><li>Heterogeneous nucleation </li></ul></ul></ul><ul><ul><li>Growth </li></ul></ul>
  9. 9. Homogeneous nucleation r r
  10. 10. Homogeneous nucleation <ul><li>No preferred nucleation sites </li></ul><ul><ul><li>Spontaneous </li></ul></ul><ul><ul><li>Random </li></ul></ul><ul><li>Those of preferred sites </li></ul><ul><ul><li>Boundary </li></ul></ul><ul><ul><li>Surface </li></ul></ul><ul><ul><li>Inclusion, … </li></ul></ul>
  11. 11. Local free energy change 1. Liquid to solid 2. Interface
  12. 12. Local free energy change Spherical nucleus:
  13. 13. Single nucleus
  14. 14. Critical radius
  15. 15. (G L -G S ) vs. supercooling Free energy density vs. temperature liquid solid temperature Free energy density
  16. 16. Parameters For FCC Copper, r*  1 nm, which contains 310 Cu atoms in each nucleus.
  17. 17. System free energy <ul><li>Ideal solution: Particle of different sizes </li></ul><ul><li>n i particles with each contains i atoms </li></ul><ul><li>n particles with each contains 1 atom </li></ul>
  18. 18. Number of nuclei <ul><li>At equilibrium </li></ul>
  19. 19. when Number of nuclei Boltzmann formula: Critical nuclei:
  20. 20. Heterogeneous nucleation <ul><li>Nucleation site </li></ul><ul><ul><li>Mold walls </li></ul></ul><ul><ul><li>Inclusion </li></ul></ul><ul><ul><li>Interface </li></ul></ul><ul><ul><li>Surface </li></ul></ul><ul><ul><li>Impurity </li></ul></ul>
  21. 21. Heterogeneous nucleation Liquid Inclusion Nucleus   IL  NL  IN R r h a 
  22. 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. 23. Free energy change
  24. 24. Free energy change Using
  25. 25. Thermodynamic barriers Heterogeneous nucleation barrier Homogeneous nucleation barrier
  26. 26. Thermodynamic barrier vs. wetting angle
  27. 28. Number of nuclei with critical radius where n s is the total number of atom around the incubating agents’ surface in liquid.
  28. 29. Inoculating agents <ul><li>Small interface energy </li></ul><ul><ul><li>Similar crystal structure </li></ul></ul><ul><ul><li>Similar lattice distance </li></ul></ul><ul><ul><li>Same physical properties </li></ul></ul><ul><ul><li>Same chemical properties </li></ul></ul>
  29. 30. Casting refinement <ul><li>Adding inoculating agents </li></ul><ul><ul><li>Overheat might melt the agents </li></ul></ul><ul><li>Surface refinement </li></ul><ul><ul><li>Coat agents on mold walls </li></ul></ul><ul><li>Pattern induced solidification </li></ul>
  30. 31. Growth and microstructure T. F. Brower and M.C. Flemings, Trans. AIME, 239, 1620 (1967)
  31. 32. Growth and microstructure H.B. Dong and P.D. Lee, Acta Mater. 53 (2005) 659
  32. 33. Outer chilled zones
  33. 34. Outer chilled zones
  34. 35. Outer chilled zones
  35. 36. Outer chilled zones Pure metals: Formation of shell because temperature gradient is the key factor in grain growth.
  36. 37. Outer chilled zones re-melted? Pouring temperature survived?
  37. 38. Microstructure of ingot <ul><li>Chilled zone </li></ul><ul><ul><li>Fine equiaxed grains. </li></ul></ul><ul><ul><li>Pure substance: Continuous shell. </li></ul></ul><ul><ul><li>Solution: Particles </li></ul></ul><ul><ul><li>Particles flushed away from wall into the central </li></ul></ul><ul><ul><ul><li>Re-melted </li></ul></ul></ul><ul><ul><ul><li>Survived – nucleus </li></ul></ul></ul>
  38. 39. Intermediate columnar zone Columnar grains grows The grain is overtaken by neighbors.
  39. 40. Intermediate columnar zone Growth and overtaken
  40. 41. Intermediate columnar zone Columnar growth blocked
  41. 42. Central equiaxed zone <ul><li>Equiaxed grain </li></ul><ul><ul><li>Nucleation: </li></ul></ul><ul><ul><ul><li>Supercooling </li></ul></ul></ul><ul><ul><ul><li>Falling particles </li></ul></ul></ul><ul><ul><ul><li>Dendrite fragments </li></ul></ul></ul><ul><ul><li>Elevated pouring temperature: </li></ul></ul><ul><ul><ul><li>Larger equiaxed grains </li></ul></ul></ul>
  42. 43. <ul><li>More columnar zone </li></ul><ul><ul><li>Anisotropic properties </li></ul></ul><ul><ul><ul><li>Magnetic materials </li></ul></ul></ul><ul><ul><ul><li>Turbo blade. </li></ul></ul></ul><ul><li>More equiaxed zone </li></ul><ul><ul><li>Isotropic properties </li></ul></ul><ul><ul><li>Less segregation </li></ul></ul>Structure and properties
  43. 44. Summary <ul><li>Casting </li></ul><ul><li>Heat management </li></ul><ul><li>Thermodynamics </li></ul><ul><li>Nucleation and growth </li></ul>