1. MLB - Core Courses -3.21- Kinetic processes in materials
Jean-Philippe Péraud
Course 2
May 4th, 2012

2. Phase Transformations
Mass Diffusion in general
-Mathematical concepts
-Diffusion equation and associated phenomena
-Solution methods
3 main parts
Diffusion processes
-relate microscopic effects to macroscopic equations and parameters
Phase Transformations
-continuous
-discontinuous
-kinetics of transformation
-stability problems

3. Forces and fluxes Force-flux relations force=-grad(potential) Onsager
Constraint on quantities merges potentials. network constraint, electrochemical, elastochemical potential…

4. Diffusivities and frames1 *1
Self-diffusivity *D
Intrinsic diffusivity
Interdiffusivity, Darken equation

5. Interdiffusion & KirkendallJA
C-Frame JV JB A B v
Vacancy sinks
Dislocation shrink
Vacancy sources
Dislocation climb

6. Solution of diffusion equation: Toolbox
Point source
Step function
Fourier series
+ superposition principle
+method of images

7. Typical problems
C=0
J=0

8. Diffusivity and random walks
Sequence of random jumps
Average displacement = 0
Average squared displacement proportional to D

9. Diffusivity and random walks
Simple models for frequency of jumps
More or less complicated depending on diffusion mechanism
Correlation factor

10. Diffusion in ionic crystals
Kröger-Vink notation, Schottky, Frenkel defects
Be able to write the equation of incorporation of impurities
Use equation of equilibrium (Keq)+balance of charges
Identify diffusion regimes D
Position depends on PO2
1/T

11. Other diffusion mechanisms. In brief.
In grain boundaries
In amorphous materials
Polymers (by reptation)

12. Capillary phenomena: surface smoothing
By surface diffusion
By vapor transport
+ + +
- - -

13. Capillary phenomena: anisotropic surface tension

14. Capillary phenomena: coarsening and grain growth
Diffusion limited
Source-limited
N-6 rule
grows
shrinks
Fluxes of atoms joining or leaving the particle

15. Continuous transformations: spinodal decomposition
Due to concave free energy profile in miscibility gap
Be able to explain Cahn-Hilliard equation
Kinetics: use perturbation to derive critical and thermodynamic wavelength+amplification factor
Credit: Balluffi, Allen, Carter, Kinetics of Materials

16. Continuous transformations: order-disorder transformation
No energy barrier in concave up regions
Be able to explain Allen-Cahn equation
Kinetics: use perturbation to derive critical and thermodynamic wavelength+amplification factor
Credit: Balluffi, Allen, Carter, Kinetics of Materials

17. Nucleation Curve-to-curve and tangent to curve construction
Calculate Rc and ΔGc
Determine steady state rate.
Heterogeneous nucleation: almost the same thing

18. Not covered: stability of moving interfaces

19. Advice Get some sleep Don’t panic
Always try to answer (partial credit)

20. Questions