Journal of Chemical Physics, Vol.117, No.23, 10739-10743, 2002
Effects of nucleation transience on crystallization kinetics under strongly nonequilibrium conditions
An approach to quantitatively assess the effects of nucleation transience on the kinetics of crystallization under static and dynamic conditions is proposed. The approach is based on an order of magnitude analysis that involves time scales characterizing the rates of nucleation relaxation and processing. The method is implemented to evaluate the effects of nucleation transience on kinetic computations performed in the tungsten-carbon system. The assessment is verified by contrasting the kinetics computed by means of a cluster dynamics simulation that implicitly accounts for transience to those evaluated using a quasi-steady-state model. When interpreting the kinetics of tungsten carbide surface crystallization, the proposed scaling method predicts that under static conditions transient effects need to be accounted for when annealing below 2600 K, while under dynamic conditions transient effects become important when quenching at ultrahigh cooling rates such as 10(8) K/s. Accordingly, in the case of isothermal annealing the steady-state kinetics appears to be in good agreement with those computed dynamically above 2600 K, but gradually deviates at lower temperatures. Consequently, the steady-state model underestimates the transformation time by more than an order of magnitude at the nose of the TTT curve (similar to2200 K). In the case of continuous cooling, the kinetic rate is well approximated by the quasi-steady-state model for processing rates of 10(4) and 10(6) K/s; however, for ultrahigh cooling rates of order 10(8) K/s, the kinetics computed by the quasistatic model deviates substantially from that computed using cluster dynamics. As a consequence, the crystallized fraction computed from the quasistatic model is overestimated by at least an order of magnitude at every undercooling temperature. The results from the two kinetic models appear to validate the assessment of transience based on the proposed scaling method.