Non-extensive treatment of surface nucleation on glass particles

Experimental data of phase transformation kinetics was used to fit a new model based on a non-extensive formalism derived from Tsallis thermostatistics and another based on the Johnson–Mehl–Avrami–Yerofeyev–Kolmogorov (JMAYK) theory. For this we considered the same experimental parameters such as crystal geometric factor g, the density of nucleation sites, NS and crystal growth rates U on glass powders. The kinetics of nucleation and growth of diopside crystals (MgO⋅CaO⋅2SiO2) on the glass surface at 825 °C (Tg∼727°C) were studied. Treatments for sinter-crystallization were performed in compacts of diopside glass particles by varying the treatment time. The crystallized fraction of the samples subjected to such treatments, which develop from the particles’ surface toward their volume, was characterized by means of optical microscopy and X-ray diffraction. The two models were then fitted to the measured crystallized fraction data and compared to each other. It was found that surface nucleation occurs very rapidly from a random number of active sites. The JMAYK theory describes the case of fast heterogeneous nucleation from a constant number of sites on the glass surface. The Tsallis approach is better than the JMAYK model considering that the q factor equals 1.268±0.062 and does not require taking into account the change in crystallization mode from three dimensional to one dimensional as JMAYK predicts, and this is advantageous. Furthermore, Tsallis thermostatistics contains the Austin–Rickett model as a special and limiting case study for this system. A generalized Avrami plot is also presented.