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Sintering
- 1. Matls 3F03 Lecture 6 Sintering
- 2. Local Driving Force • Gibbs Thompson Effect ∆µ = µ curve − µ flat = γ sv Ω MX κ • For Spheres κ = 2/ ρ
- 3. Local Driving Force µ = RT ln p pcurve ∆µ = RT ln p flat Ω MX γ sv pcurve κ = ln RT p flat
- 4. Local Driving Force µ = RT ln p pcurve ∆µ = RT ln p flat Ω MX γ sv pcurve κ = ln RT p flat
- 5. Local Driving Force Ω MX γ sv pcurve κ = ln RT p flat Ω MX γ sv ∆p pcurve − p flat κ = = RT p flat p flat 2Ω MX γ sv pcurve = p flat (1 + ) ρRT
- 6. Local Driving Force 2Ω MX γ sv pcurve = p flat (1 + ) ρRT Concave ----ρ =−ve Convex ----ρ =+ve
- 7. 2Ω MX γ sv pcurve = p flat (1 + ) ρRT pore pore Pore Grows Pore shrinks
- 8. Critical Coordination Number for Given Dihedral Angle Dihedral Angle 1.4 1.2 Pores 1 Shrink 0.8 0.6 Pores 0.4 Grow 0.2 0 0 5 10 15 20 25 number of grains
- 9. Densification • Favoured by small number of grain boundaries intersecting pore • Large pores with many grains difficult to fill
- 10. Sintering Kinetics • Densification vs Coarsening • Coarsening – Material source surface – Material sink neck – No shrinkage – Increase in strength • Densification – Source of material has to be grain boundary or region between particles
- 11. Coarsening • Surface diffusion • Evaporation Condensation Mechanism
- 12. Densification • Higher vacancy concentration in the neck ----driving force for vacancy diffusion into the bulk----atoms diffuse in opposite direction
- 13. Sintering • Promote Densification over Coarsening – High GB diffusion – High bulk diffusion – Low surface diffusion • Depends on – Particle size and packing – Atmosphere – Degree of Agglomeration – Temperature – Impurities
- 14. Sintering Stages • Initial Stage – Interparticle contact increases by neck growth – Relative density increases from~60 to ~65% • Intermediate Stage – Continuous pore channels coincident with three grain edges – Increase from ~65 to ~90% density
- 15. Sintering Stages • Final Stage – Pore pinched off – Increase in pore and GB mobilities – Must keep pores in contact with grain boundaries to eliminate pores completely.
- 16. What Have We Learned • Surface Energy Driving Force – Particle Growth – Sintering • Balance Between Coarsening and Densification – Depends on mechanism – Role of Dihedral angle – Coordination number of pores
- 17. What Have We Learned • Three Stages of Sintering
- 18. What Next? • Models of Sintering • Liquid Versus Solid State