MLB - Core Courses -3.21- Kinetic processes in materials Jean-Philippe Péraud Course 2 May 4th, 2012
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
Forces and fluxes Force-flux relations force=-grad(potential) Onsager Constraint on quantities merges potentials. network constraint, electrochemical, elastochemical potential…
Diffusivities and frames 1 *1 Self-diffusivity *D Intrinsic diffusivity Interdiffusivity, Darken equation
Interdiffusion & Kirkendall JA C-Frame JV JB A B v Vacancy sinks Dislocation shrink Vacancy sources Dislocation climb
Solution of diffusion equation: Toolbox Point source Step function Fourier series + superposition principle +method of images
Typical problems C=0 J=0
Diffusivity and random walks Sequence of random jumps Average displacement = 0 Average squared displacement proportional to D
Diffusivity and random walks Simple models for frequency of jumps More or less complicated depending on diffusion mechanism Correlation factor
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
Other diffusion mechanisms. In brief. In grain boundaries In amorphous materials Polymers (by reptation)
Capillary phenomena: surface smoothing By surface diffusion By vapor transport + + + - - -
Capillary phenomena: anisotropic surface tension
Capillary phenomena: coarsening and grain growth Diffusion limited Source-limited N-6 rule grows shrinks Fluxes of atoms joining or leaving the particle
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
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
Nucleation Curve-to-curve and tangent to curve construction Calculate Rc and ΔGc Determine steady state rate. Heterogeneous nucleation: almost the same thing
Not covered: stability of moving interfaces
Advice Get some sleep Don’t panic Always try to answer (partial credit)
Questions