Solid state sintering

Question 1

How do you calculate shrinkage?

Answer 1

~ assume a part is made up of cube elements
~ assume the sintered part is theoretically dense

~ Ai = green body dimension
~ Af = sintered dimension
~ Fp = volume fraction pores in the green body

Question 2

Fp =

Answer 2

~ Vi - Vf / Vt = 1 - Vf/Vi = 1 - Af^3/Ai^3

~ Vi - Vf: volume taken up by pores
~ Vt: total volume

Question 3

What is Xl?

Answer 3

~ Xl = linear shrinkage fraction

~ Xl = Ai-Af/Ai
~ Ai-Af: change in length
~ Ai: original length

Question 4

What is Fp knowing that Af = Ai(1-Xl)?

Answer 4

~ Fp = 1 - Ai^3(1-Xl)^3 / Ai^3

~ Fp = 1-(1-Xl)^3

Question 5

What is the final Xl equation?

Answer 5

~ because 1 - Xl = (1 - Fp)^1/3

~ Xl = 1 - Fs^1/3
~ Fs = fraction solid in the green body = 1 - Fp

Question 6

What is the driving force for sintering?

Answer 6

~ the elimination of solid-vapor interfaces (many un-sataisfied bonds), replacing them with solid-solid interfaces (grain boundary, fewer unsatisfied bonds)

Question 7

What is the average particle size for a good sinter?

Answer 7

~ avg particle size of 0.5-1 μm

~ green relative densities generally sinter well

Question 7

What occurs during the initial stages of sintering?

Answer 7

~ atoms show net migration to points of particle contact, filling them in to form early grain boundaries in the form of necks

~ atoms supplied by surface diffusion or evaporation condensation if the solid has a high vapor pressure

~ atoms diffusing to this neck location satisfy more dangling surface bonds-surface atoms are more stable at this location

Question 8

What occurs during the intermediate stage of sintering?

Answer 8

~ most macroscopic shrinkage

~ atomic source is predominately from interior sources: grain boundaries and particle interiors

~ GB diffusion dominates because of high conc. of vacancies from lattice mismatch

~ bulk diffusion has an increasing role with increasing temp because of an exponential increase in vacancy concentration

~ gaps between particles sinter to near-cylinders. these are interconnected and the network extends to the part surface: open porosity

Question 9

What happens during the final stage of solid state sintering?

Answer 9

~ starts at 90% relative density

~ cylindrical pores close off to isolated spherical pores along 3-grain intersection curves and at four grain intersection points