Johnson–Mehl–Avrami–Kolmogorov model applied to describe the site blocking effect in interstitial solid solution

Interstitial solid solutions, such as carbon in steels or hydrogen in metal and alloys, are important materials for many applications. Thermodynamic models that accurately predict the behavior of interstitial solid solution are essential for designing new materials and to improve computational materials tools. In this work, we revisited the problem of calculating the configurational entropy of interstitial solid solutions when site blocking effect occurs. Using an unprecedented approach, we propose a new site blocking model that uses the Johson-Mehl-Avrami-Kolmogorov (JMAK) equation to calculate the fraction of blocked sites. Since the occupation of interstitial sites in solid solutions is random, the blocking of neighbor sites can also be assumed to be random. Thus, the blocking site effect can be described as a Poisson process and the JMAK equation can derived from Poisson statistics. The proposed model (to be called JMAK model) allows to estimate the number of blocked sites considering the site blocking overlapping phenomenon in a simple and direct way. The JMAK model was validated by comparing the calculated values of configurational entropy with both numerical simulation and experimental data.