This document discusses sintering, which is the process where solid materials are bonded together below their melting point due to heat or pressure. It covers three key topics: 1) The Gibbs-Thompson effect and how it relates the local driving force for sintering to factors like surface energy and curvature. 2) The different stages of sintering (initial, intermediate, final) and how they impact density and pore structure. 3) The balance between densification, which reduces porosity, and coarsening, which increases grain size, and how this depends on factors like diffusion mechanisms and dihedral angle.

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