Applications of the zero-order reaction rate model and transition state theory on the intra-particle sintering of an alumina powder by using surface area measurements

The cylindrical compacts with the diameter of 14 mm were prepared under 32 MPa of an alumina powder having agglomeration degree of 80% and maximum surface area of 81 m2 g−1 after calcination at 900 °C for 2 h. Each compact was fired isothermally at a different temperature between 950 and 1150 °C for 2 h. The rate constant for each temperature was obtained from the application of the zero-order reaction rate model on the surface area measurements after sintering. Arrhenius equation for the sintering was obtained in the form: k = (8.09 × 106 m2 mol−1 s−1) exp (−187 643 J mol−1/RT). Transition state theory was applied to the sintering and thermodynamic parameters of the activation were calculated. The relation of these parameters in SI units can be summarized in the forms: ΔH# = 178 643 − 8.314T, ΔS# = −73.6 − 8.314 ln T, and ln K# = −ΔG#/RT = −(ΔH# − TΔS#)/RT = −21 487/T − ln T  − 7.853, where ΔG#, ΔH#, ΔS# and K# are the Gibbs free energy, enthalpy, entropy, and equilibrium constant of activation.