If you consider that sintering is isotropic process change of length is also change of diameter and of volume as a result so if you know the mass of green compact and its dimensions the change of length can be related to the change of density.

During the dilatometric experiment there is also thermal expansion which needs to be taken into account. If you do fast heating and isothermal holding experiments the thermal expansion will happen during fast heating up and most of the sintering (shrinkage) will happen during the hold time.

I. Let us suppose that the powder compact is heated from a reference temperature Tº to T, exceeding Tº by ΔT = T-Tº. Let us also accept that the powder compact volumetric thermal expansion coefficient, defined as α = -(1/ρ)·[dρ/d(ΔT)], can be taken as approximately constant (α ≈ αº).

II. For the temperature T, we may write: ρ = ρº·exp(-αº·ΔT), where ρº is the density for the reference temperature. After differentiation (in order to ΔT), ΔT dependency can be conveniently eliminated for small ΔT: dρ/d(ΔT) = ρº·exp(-αº·ΔT)·d(-αº·ΔT)/d(ΔT) = - αº·ρº·exp(-αº·ΔT) = -αº·ρ.

III. Note that as long as expansion can be considered isotropic, the volumetric thermal expansion coefficient is three times the linear coefficient (β).

I Let us suppose that the powder compact is heated from a reference temperature Tº to T, exceeding Tº by ΔT = T-Tº. Let us also accept that the powder compact volumetric thermal expansion coefficient or parentage.

Thanks a lot, Grzegorz Cios , Carlos Araújo Queiroz , Ravinaik Banoth, for your valuable answers. I managed to find the relative density by going through some literature, which I have attached below. But the graph between sintered relative density and Temperature is not so good as the density decreases when it reaches the sintering temperature, but it should increase. I don't know why ?. Is there any way to correct this? Any feedback would be valuable? I am also attaching the graph with it.

Dsr8= Drel*(1/1+Ed+alpha*(Temp - Troom)).^3;

where Dsr8 is the relative density, Drel is the relative green density; Ed is the change in length upon original length that is the shrinkage data from the dilatometer experiment, alpha is the thermal expansion coefficient of bulk iron

Temp is the temperature obtained from the dilatometer experiment data.

Regards,

Prateek