Download presentation

Presentation is loading. Please wait.

Published byIsaias Pickles Modified over 2 years 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

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

OK

1 U N C L A S S I F I E D LANS Company Sensitive — unauthorized release or dissemination prohibited Operated by Los Alamos National Security, LLC for NNSA.

1 U N C L A S S I F I E D LANS Company Sensitive — unauthorized release or dissemination prohibited Operated by Los Alamos National Security, LLC for NNSA.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sea level rise data Ppt on world war 2 Ppt on central administrative tribunal judgements Gallbladder anatomy and physiology ppt on cells Maths ppt on exponents and powers Ppt on business environment nature concept and significance of ash Seminar ppt on brain computer interface Ppt on hotel management software Ppt on water resources class 10 download Ppt on indian constitution for class 9