Activation energies for nucleation and growth and critical cluster size dependence in JMAK analyses of kinetic Monte-Carlo simulations of precipitation

Kinetic Monte-Carlo (KMC) methods are used as an approach to simulate precipitation in Cu-alloyed bcc Fe. In order to characterize the process, transformed fractions, that is, the precipitated atoms, are related to Johnson-Mehl-Avrami-Kolmogorov theory. However, simulated data often deviate from corresponding fit curves and so does the resulting growth exponent when compared to theoretical expectations. Furthermore, some data may suggest the development of a metastable phase. In our study, we show that the characteristics of the transformed fraction and, as a consequence, the derived growth exponents sensitively depend on the number of atoms that are considered to form a particle and hence contribute to the transformed fraction. With a temperature dependence of the critical cluster size and additionally accounting for severe impingement of the particles, we obtain growth exponents which lie close to the expected range between n = 1.5 and n = 2.5 for pre-existing nuclei or continuous nucleation, respectively. From these, we obtain activation energies for nucleation and growth of precipitates. In this way, atomistic KMC simulations yield thermodynamical quantities, which can be valuable input parameters for larger length scale simulation methods, for example, for Phase Field Method simulations.