Download presentation

Presentation is loading. Please wait.

Published byIsaias Pickles Modified about 1 year ago

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 transition2nd order (generally: higher order)

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

10

11
Chemical potentials g i of the components

12
Gibbs phase rule f = (n - 1) – n ( - 1) + 2 = n - + 2

13
Liquid-solid transition of a two-component System (Ge-Si)

14
Excess enthalpy and miscibility gap

15
Excess enthalpy and miscibility gap

16
Precipitation: alternative mechanisms

17
Heterophase fluctuation corresponds to nucleation Homophase fluctuation corresponds to spinodal decomposition

18
Free energy of a spherical precipitate particle

19
Ni 36 Cu 9 Al 55 Precipitation by nucleation and growth: N V particle number, c supersaturation, mean particle radius

20
Spinodal Decomposition

21
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

22
disordered state (bcc) Long range order: out of bcc structure the B2 (CsCl) structure arises ordered state (B2) disordered state (bcc)

23
Long range order: B2 (CsCl) representatives

24
D0 3 stoichiometry 3:1 Out of the same bcc structure:

25
L1 2 Long range order out of the fcc structure:

26
L1 2 ordered state L1 2 disordered state (fcc)

27
L1 2 representatives

28
fcc L1 0 stoichiometry 1:1

29
representatives fcc L1 0 stoichiometry 1:1

30
Different long range ordered structures in the Cu-Au phase diagram L1 2 L1 0 L1 2 L1 0

31
L1 2 L1 0 CuAu II (long period.) L1 2 L1 0 Different long range ordered structures in the Cu-Au phase diagram

32
Fcc L1 1 stoichiometry 1:1

33
Statistical physics of ordered alloys Partition function Possibly different vibration spectrum for every atom configuration Does it really matter?

34
FePd: Density of phonon states g( ) L1 0 - ordered fcc disordered Mehaddene et al. 2004

35
Bragg – Williams model: only nn pair interactions, disregard pair correlations R long range order parameter tanh R/ <1 >1 Simplifying almost everything:

36
Different levels of approximation in calculating internal interaction energy Bragg-Williams Experiment Quasi-chemical quasi-chemical Experiment Bragg-Williams

37
Ising model (Lenz + Ising 1925) Can be brought to Ising form by identifying (for nn interaction) Hamiltonian for alloy (pair interaction model) p i n atom occupation function

38
Idea of mean field model: treat a few local interactions explicitly, environment of similar cells is averaged and exerts a mean field of interaction

39
Local interaction only 1 atom Bragg- Williams – model Correspondences: Phase-separating ferromagnetic Long range ordering antiferromagnetic ferromagnetic

40
Structure on polished surface after martensitic transformation: roof-like, but no steps. A scratched line remains continuous

41
Martensite morphologies

42
Homogeneous distorsion by a martensitic transformation

43
First step :Transformation into a new lattice type: Bain transformation

44
Second step: Misfit is accomodated by a complementary transformation: twinning or dislocation glide

45
Thermoelastic Martensites: Four symmetric variants per glide plane: Can be transformed into one another by twinning

46
Shape Memory effect

47
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

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google