Abstract
The shrinkage rate of solid state sintering has been theoretically derived by combining the rate equation of material transport and the net free energy change resulting from the decrease of solid-vapor interface and the increase of grain boundary during sintering. For a sinteing model an idealized situation of the spherical particles with BCC packing was taken as the initial condition and the shrinkage was assumed to occur by forming the flat circualr grain boundaries on each particle. The plotted shrinkage rates as a function of grain boundary to surface energy ratio $(gamma_g/gamma_s)$ have shown that the relative density increases linearly at the initial stage of sintering but the shrinkage rate is decreased upon further sintering due to a decrease in driving force for densificaton. It has been also shown that the densification is critically affected by the $gamma_g/gamma_s$ ratio. In order to get the complete densificatin the ratio should be less than $sqrt{3}$. Any additive or atmospheric condition causing the decrease of$_g/gamma_s$ ratio will enhance sintering.
