An indirect model for sintering thermodynamics

A model was proposed and used to calculated the changes in enthalpy $(\Delta H^{o})$, entropy $(\Delta S^{o}),$ and Gibbs energy $(\Delta G^{o})$, as well as equilibrium constant $(K)$ relating to the sintering of alumina compacts. Specific nanopore volume $(V)$ of the compacts was assumed as a thermodynamic variable. A hypothetical equilibrium constant $(K_{h})$ and corresponding Gibbs energy $(\Delta G_{h}^{o})$ were calculated depending on the $V$ value measured after each sintering. The thermodynamic relationships with the SI units were respectively evaluated for the initial-stage $(i)$ sintering between 1000 and 1200 $^{\circ}$C and final-stage $(f)$ sintering between 1200 and 1600 $^{\circ}$C in the following form: $\, \Delta G_{i}^{o}=-RT\ln K_{i}=\Delta H_{i}^{o}-T\Delta S_{i}^{o}=$161,042$-$110.5$T$ and $\Delta G_{f}^{o}=-RT\ln K_{f}=\Delta H_{f}^{o}-T\Delta S_{f}^{o}=$39,000$-$47.5$T$.