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Mass Transport Review and

Kinetics of Sintering

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Transport Mechanisms determine how mass flows in reponse to the driving

force for sintering

There are 2 mechanism, both contribute to neck growth

Remember neck growth calculation using neck diameter X via surface transport does

not produce shrinkage i.e., it does not help density increases or densification. Here

Mass just gets repositioned on the pore surface to lower surface area and to remove

curvature.

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Bulk Transport helps densification. See below the mass is moved between

two internal positions. i.e, mass that grows the sinter neck comes from

inside the body

Plastic flow is important during heating before dislocation population anneals out of the

material.

Surface energy is generally insufficient to generate new dislocations, so sintering

corresponds to declining dislocation density and declining role from plastic flow.

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Viscous flow Sintering – Application in glasses and polymers

Here particle coalesce at a rate which depends on particle size and material

viscosity

Viscous flow is also seen in Metals. Here liquid phase form on the grain

boundary

The junction of 2 grains is a grain boundary (see bonding is not there or

negligible) hence provides path for rapid diffusion.

With sufficient grain boundary area, grain boundary diffusion dominates

sintering. Example: Powdery substances (metals) melt faster than a solid metal

piece.

Grain growth and gain boundary elimination is bad for sintering.

Note: Amorphous material lack grain boundaries.

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See Hightemperature

decreases

viscosity

hence neck

growth

should

progress with

high

temperature

This plot is a characteristic plot for viscous

flow sintering

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A very linear decrease in

volume is expected with

increase holding time for a

specific material exhibiting

viscous flow.

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Temperature is a Kinetic Parameter which decides

sintering rate

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Surface Diffusion

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The 3 Steps of Surface Diffusion

1. Atom breaks the existing bonds typically surface kink(defective site), which is on the surface

2. The atom now tumbles (Motion) across or jumps

3. Atom finally finds a vacancy or a atomic sink thus

repositioning itself. Hence there is no shrinkage

The product of population of defective sites Pdefect and

probability of motion Pmotion

 between sites gives net diffusion

mobility M. Here both probabilities are thermally activated ,

hence

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VOLUME DIFFUSION

Atom exchange with vacancies, hence also

known aslattice diffusion

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Bulk Transport helps densification. See below the mass is moved between

two internal positions. i.e, mass that grows the sinter neck comes from

inside the body

Plastic flow is important during heating before dislocation population anneals out of the

material.

Surface energy is generally insufficient to generate new dislocations, so sintering

corresponds to declining dislocation density and declining role from plastic flow.

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Two dimensional

representation of a atom

vacancy exchange

During sintering each atom

changes position 6 times per

second

Volume diffusion

sintering involves the

motion of vacancies

along these paths

Volume diffusion adhesionVacancy flow tothe

inter-particle

grain boundary

Vacancy interactwith dislocations

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Dislocation Motion- Climb and Slip

Dislocation climb is due to vacancy absorption

Dislocation glide is due to surface stresses

Densification rate ( here is defined as the change of porosity ε divided by

change of time t) improves since dislocation climb occurs with pore

elimination

Σ is surface stress from pore curvature, Ω is atomic volume, Dv is diffusivity, R

is gas constant, T is absolute temperature and λ is dislocation spacing.

Volume diffusion rate is increases 100 folds by dislocations in the neck

region.

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Initial Stage Sintering Equations