sintering - course notescoursenotes.mcmaster.ca/3f03/lecture_notes/module_8.pdf · learning...
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Matls 3F03 High Temperature Materials
Production Sintering
Learning Objectives
• Be able to discuss characteristics of non-reactive sintering
• Be able to discuss the fundamental thermodynamics and kinetics of sintering.
Basic Characteristics of Sintering
• Manufacturing of Ceramics • Agglomeration step in pyrometallurgy • Powder Metallurgy
Classifications
• Reactive or non-reactive • Solid-state or liquid phase
– Liquid phase- one liquid is formed and fill in crevasses, enhances diffusion of other species.
– Solid state- particles coarsen through diffusion.
– Liquid phase-higher density
Ceramic Manufacture
• Forming a hard dense material from fine powder
• Grinding/Forming/Firing/surface finish • Non-reactive, solid state sintering is
common.
Ceramic Manufacture
• Starting Materials – Particle size and distribution – Particle packing – Void fraction and distribution – Volatile content.
Ceramic Manufacture
• Starting Materials – Particle size and distribution – Particle packing – Void fraction and distribution – Volatile content.
• Caution! – The more you heat it up the more chance of
blowing it up, watch out for volatiles
Brief Description of Process
• Heating – Function of drying rate and limitations of the furnace
• Holding at Sintering Temperature – Manipulate temperature and time to control grain size,
density and even crystal structure of product. • Cooling rate
– Function of properties of ceramic body (thermal shock resistance) and limitations of furnace.
Firing Ceramics
• Increase Density • Reducing porosity
– Critical flaw size for fracture – Size distribution of pores may be more
important than size. Why? • Controlling grain structure
– desire small – How does this fit with density and porosity
objectives?
Desired Microstructure Property Desired Microstructure
High Strength Small Grain size, uniform, flaw free
High Toughness Duplex microstructure with high aspect ratio
High creep resistance Large grains, no amorphous GB phase
Optical Transparency Pore free, grains>>or<< than wavelength of light
Low dielectric loss Small uniform grains
Good Varistor Controlled GB chemistry
Catalyst Large surface area
Many Microstructure Effects on Properties
• Often conflicting • Must understand the processes involved in
controlling microstructure – Thermodynamics – Kinetics
Thermodynamics of Sintering
• Lower Energy (Surface) • Small Pores Shrink, Large Pores Grow
– Why? – Is this good news? – How do we make this work for us?
• Read Sintering section in course pack.
Thermodynamics of Sintering
• Lower Energy (Surface)
• No reaction change in volume or internal energy
• dS must be positive for spontaneous change--- dA must be negative
∑++−= iisv dndAPdVTdSdU µγ
dATdS svγ−=
Thermodynamics of Sintering
• Applies to decrease in total surface area
• What about two particles (2 surfaces) becoming two grains(1 grain boundary) ?
dATdS svγ−=
Two Particles Sintering
• Equilibrium Dihedral Angle
2cos2 φ
γγ svgb =
Worked Example 10.1
• A) Calculate the enthalpy change for an oxide during sintering as the average particle diameter increases from 0.5 to 10µ– Assume the molar volume of the oxide is 10
cm3/mol and surface energy 1J/m2
Worked Example 10.1
• B) Recalculate the enthalpy change if, instead of coarsening, the 0.5µ spheres are sintered together as cubes. – The dihedral angle for this system was
measured to be 100o
Summary
• Microstructure dominates properties in sintered ceramics
• Microstructure development during sintering dominated by surface energy.
Local Driving Force
• Gibbs Thompson Effect
• For Spheres
κγµµµ MXsvflatcurve Ω=−=Δ
ρκ /2=
Local Driving Force
pRT ln=µ
flat
curve
ppRT ln=Δµ
flat
curvesvMX
pp
RTln=
Ω γκ
Local Driving Force
pRT ln=µ
flat
curve
ppRT ln=Δµ
flat
curvesvMX
pp
RTln=
Ω γκ
Local Driving Force
flat
curvesvMX
pp
RTln=
Ω γκ
flat
flatcurve
flat
svMX
ppp
pp
RT−
=Δ
=Ω γ
κ
)21(RT
pp svMXflatcurve ρ
γΩ+=
Local Driving Force
)21(RT
pp svMXflatcurve ρ
γΩ+=
Convex ----ρ =+ve
Concave ----ρ =-ve
)21(RT
pp svMXflatcurve ρ
γΩ+=
pore
Pore Grows
pore
Pore shrinks
Critical Coordination Number for Given Dihedral Angle
00.20.40.60.81
1.21.4
0 5 10 15 20 25
number of grains
Dih
edra
l Ang
le
Pores Shrink
Pores Grow
Densification
• Favoured by small number of grain boundaries intersecting pore
• Large pores with many grains difficult to fill
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
Coarsening
• Surface diffusion • Evaporation Condensation Mechanism
Densification
• Higher vacancy concentration in the neck ----driving force for vacancy diffusion into the bulk----atoms diffuse in opposite direction
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
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