A model of growth of titanium dioxide crystals with simultaneous transformation from anatase to rutile

摘要

This study simulates the combination of crystal growth by evaporation-condensation with the potential for a phase change once the crystals have reached a critical size. Crystal growth has been simulated as a two-dimensional Monte Carlo process in which the probability of accepting or rejecting an individual evaporation-condensation step is given by the Metropolis algorithm. Crystals, taken to be of the anatase form of TiO_2, which have grown larger than a specified critical size may transform irreversibly to a second phase, taken to be rutile. The probability of conversion increases with increasing crystal size. For each critical size there exists a limited range over which the transformation kinetics follow the familiar relationship alpha = 1 - exp(-kt~n) (where alpha is the fractional conversion at time, t). The dependence of the mean size of the two polymorphs and of the rutile size-spread (rms) on critical size have been investigated. The most significant aspect of the plots of the normalized size-spread, rms/mean-size, is its gradual increase as the rutile fraction increases from 0.75 to 0.98.