On the Effect of Nucleation Undercooling on Phase Transformation Kinetics

We carry out an extensive comparison between Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory of first-order phase transformation kinetics and phase-field (PF) results a benchmark problem on nucleation. To address the stochasticity problem, several hundreds simulations are performed to establish comprehensive, statistically significant analysis coincidences discrepancies PF JMAK kinetics. find that predictions in excellent agreement with both classical nucleation theory, as long original assumptions latter appropriately reproduced—in particular, constant growth rates infinite domain. When deviating from these assumptions, at odds theory. In we observe size initial particle radius \(r_0\) relative critical \(r^*\) has effect rate transformation. While agree when is sufficiently higher than \(r^*\), duration transient stage particle, before it reaches steady velocity, increases \(r_0/r^*\rightarrow 1\). This incubation time overall kinetics, e.g., Avrami exponent multi-particle simulations. contrast, for considered conditions parameters, interface curvature upon kinetics—in particular negative regions appearing during impingement, present but absent theory—appears be minor compared \(r_0/r^*\). argue rigorous benchmarking models stochastic processes (e.g., nucleation) needs sufficient statistical data order make comparisons against ground truth theories. problems, probability distributions clearly preferable deterministic approach.