Kinetic simulation of thermally induced metastability in the tungsten-carbon system

A dynamic computational model is developed within the context of classical nucleation theory for thermally induced non-equilibrium phase transitions. The conditions for this model are those encountered in rapid thermal processing of invariantly nucleating compound phases. The kinetic variables used in the model were directly obtained from the free energy formulations that characterize the stable and metastable equilibria amongst participating phases. The isothermal as well as non-isothermal kinetics were simulated by means of stochastic equations which model the fluctuational process of crystal nucleation along with the deterministic process of crystal growth. A strategy to evaluate the static (isothermal) and dynamic (non-isothermal) effects of nucleation transience based on time scale analogy is outlined and validated by contrasting the results of the dynamic model against those obtained from a steady state model. The developed model was applied to the W-C compound-forming binary system. The stable phase equilibria were reproduced using free energy data obtained from literature, while the metastable ones were obtained by extrapolating the stable equilibria into regions of metastability. The model was utilized to simulate the kinetics of graphitization during non-equilibrium peritectic melting of WC. The isothermal kinetic analysis suggests that graphitization becomes extremely rapid when annealing at large superheatings, while the highest crystallization rate was found to occur at the metastable congruent melting point of WC (∼3107 K) where 1-ppm crystallize in ∼2 nanoseconds. The non-isothermal kinetic analysis suggests that increasing the heating rate suppresses graphitization, while graphitization may be completely bypassed by the rapidly forming metastable liquid when processing under extreme rapid heating (∼10₈ K/s) beyond the metastable congruent melting point of WC. The model was also utilized to simulate the kinetics of phase selection during non-equilibrium solidification at 50%-C between the thermodynamically stable WC and the metastable WC _1−x and W₂C. The isothermal kinetic analysis suggests that thermodynamic stability prevails at low to moderate undercoolings, while at deep undercoolings (∼1000 K) the crystallization of W₂C completes faster than the more thermodynamically stable WC_1−x and almost as fast as WC. The non-isothermal kinetic analysis suggests that thermodynamic stability prevails under moderate (∼104 K/s) to high (∼10 6 K/s) cooling rates, however under ultra-high (∼108 K/s) cooling rates all three phases crystallize at nearly the same undercooling. Based on the model results it was therefore concluded that under extreme non equilibrium conditions such as those encountered in splat quenching nucleation-controlled kinetics constitute the limiting factor in the phase selection process and consequently in the microstructural evolution.