Sintering - Course Notescoursenotes.mcmaster.ca/3F03/Lecture_Notes/Module_8.pdf · Learning...

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