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