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Basics of Phases and Phase Transformations

Basics of Phases and Phase Transformations. W. Püschl University of Vienna. Content 1. Historical context 2. Classification of phase transformations 3. Graphical thermodynamics – Phase diagrams 4. Miscibility Gap – Precipitation nucleation vs. spinodal decomposition

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Basics of Phases and Phase Transformations

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  1. Basics of Phases and Phase Transformations W. Püschl University of Vienna

  2. Content 1. Historical context 2. Classification of phase transformations 3. Graphical thermodynamics – Phase diagrams 4. Miscibility Gap – Precipitation nucleation vs. spinodal decomposition 5. Order 6. Ising model: atomic and magnetic spin configuration 7. Martensitic transformations

  3. Early technological application of poly-phase systems: Damascus Steel

  4. Aloys v. Widmannstätten 1808 Iron meteorite cut, polished, and etched: Intricate pattern appears

  5. Oldest age hardening curve: Wilms Al-Cu(Mg,Mn,Fe, Si) alloy Retarded precipitation of a disperse phase.

  6. A scientific understanding of phases and phase transformation begins to develop end 19th / beginning 20th centuries physical metallurgy Experimental: Gustav Tammann (Göttingen) Theoretical: Josiah Willard Gibbs

  7. What is a phase? Region where intrinsic parameters have (more or less) the same value lattice structure, composition x, degree of order , density ,… Need not be simply (singly) connected. Expreme example: disperse phase and matrix phase where it is embedded (like Swiss cheese) When is a phase thermodynamically stable? How can we determine wihich phase is stable at a certain composition, temperature (and pressure, magnetic field…) What happens if this is not the case  metastability or phase transition How can a phase transition take place?

  8. Ehrenfest (1933) 1st oder phase transition 2nd order (generally: higher order)

  9. Free energy vs. order parameter according to Landau Higher-order phase transition 1st oder phase transition

  10. Chemical potentials gi of the components

  11. Gibbs phase rule f =  (n - 1) – n ( - 1) + 2 = n -  + 2

  12. Liquid-solid transition of a two-component System (Ge-Si)

  13. Excess enthalpy and miscibility gap

  14. Excess enthalpy and miscibility gap

  15. Precipitation: alternative mechanisms

  16. Heterophase fluctuation corresponds to nucleation Homophase fluctuation corresponds to spinodal decomposition

  17. Free energy of a spherical precipitate particle

  18. Precipitation by nucleation and growth: NV particle number, c supersaturation, mean particle radius Ni36Cu9Al55

  19. Spinodal Decomposition

  20. Excess enthalpy Positive: like atoms preferred: Phase separation Negative: unlike atoms preferred: ordering Short range order: there is (local) pair correlation Cowley- Warren SRO parameter Decay with distance from reference atom If they do not decay  long range order

  21. Long range order out of the fcc structure: L12

  22. Long range order out of the fcc structure: L12 ordered state L12 disordered state (fcc)

  23. fcc  L10 stoichiometry 1:1

  24. Different long range ordered structures in the Cu-Au phase diagram L10 L12 L12 L12 L10

  25. Different long range ordered structures in the Cu-Au phase diagram L10 CuAu II (long period.) L12 L12 L12 L10

  26. Statistical physics of ordered alloys Partition function Possibly different vibration spectrum for every atom configuration Does it really matter?

  27. FePd: Density of phonon states g() Mehaddene et al. 2004 L10 - ordered fccdisordered

  28. Simplifying almost everything: Bragg – Williams model: only nn pair interactions, disregard pair correlations R long range order parameter <1 >1 tanh R/

  29. Different levels of approximation in calculating internal interaction energy Experiment Bragg-Williams Quasi-chemical Experiment quasi-chemical Bragg-Williams

  30. Ising model (Lenz + Ising 1925) Hamiltonian for alloy (pair interaction model) pin atom occupation function Can be brought to Ising form by identifying (for nn interaction)

  31. Idea of mean field model: treat a few local interactions explicitly, environment of similar cells is averaged and exerts a mean field of interaction

  32. Local interaction only 1 atom  Bragg- Williams – model Correspondences: Phase-separating ----- ferromagnetic Long range ordering ----- antiferromagnetic ferromagnetic

  33. Structure on polished surface after martensitic transformation: roof-like, but no steps. A scratched line remains continuous

  34. Martensite morphologies

  35. Homogeneous distorsion by a martensitic transformation

  36. First step :Transformation into a new lattice type: Bain transformation

  37. Second step: Misfit is accomodated by a complementary transformation: twinning or dislocation glide

  38. Thermoelastic Martensites: Four symmetric variants per glide plane: Can be transformed into one another by twinning

  39. Shape Memory effect

  40. Final remarks: As the number of components grows and interaction mechanisma are added, phase transformations can gain considerable complexity For instance: Phase separation and ordering (opposites in simple systems) may happen at the same time. I have completely omitted many interesting topics, for instance Gas-to-liquid or liquid-to-liquid transformations The role of quantum phenomena at low-temperature phases Dynamical phase transformations, self-organized phases far from equilibrium

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