Transcript MLB - Core Courses -3.21- Kinetic processes in materials
MLB - Core Courses -3.21 Kinetic processes in materials
Jean-Philippe Péraud Course 2 May 4th, 2012 1
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 2
Forces and fluxes
• Force-flux relations force=-grad(potential) • Onsager • Constraint on quantities merges potentials. network constraint, electrochemical, elastochemical potential… 3
*1 1
Diffusivities and frames
• Self-diffusivity *D 1 • Intrinsic diffusivity • Interdiffusivity, Darken equation 4
Interdiffusion & Kirkendall
J A J V J B A B
C-Frame
v Vacancy sinks Dislocation shrink Vacancy sources Dislocation climb 5
Solution of diffusion equation: Toolbox Step function Point source Fourier series + superposition principle +method of images 6
C=0
Typical problems
J=0 7
Diffusivity and random walks
• Sequence of random jumps • Average displacement = 0 • Average squared displacement proportional to D 8
Diffusivity and random walks
• Simple models for frequency of jumps • More or less complicated depending on diffusion mechanism • Correlation factor 9
D
Diffusion in ionic crystals
Position depends on P O2 1/T • • • • Kröger-Vink notation, Schottky, Frenkel defects Be able to write the equation of incorporation of impurities Use equation of equilibrium (K eq )+balance of charges Identify diffusion regimes 10
Other diffusion mechanisms. In brief.
• In grain boundaries • In amorphous materials • Polymers (by reptation) 11
Capillary phenomena: surface smoothing • By surface diffusion + + + - - • By vapor transport 12
Capillary phenomena: anisotropic surface tension 13
Capillary phenomena: coarsening and grain growth • Diffusion limited Fluxes of atoms joining or leaving the particle • Source-limited • N-6 rule shrinks grows 14
Continuous transformations: spinodal decomposition • Due to concave free energy profile in miscibility gap • Be able to explain Cahn Hilliard equation Credit: Balluffi, Allen, Carter, Kinetics of
Materials
• Kinetics: use perturbation to derive critical and thermodynamic wavelength+amplification factor 15
Continuous transformations: order disorder transformation • No energy barrier in concave up regions Credit: Balluffi, Allen, Carter, Kinetics of
Materials
• Be able to explain Allen Cahn equation • Kinetics: use perturbation to derive critical and thermodynamic wavelength+amplification factor 16
Nucleation
• Curve-to-curve and tangent to curve construction • • Calculate R c and ΔG c Determine steady state rate.
• Heterogeneous nucleation: almost the same thing 17
• Not covered: stability of moving interfaces 18
Advice
• • • Get some sleep Don’t panic Always try to answer (partial credit) 19
Questions
20