Extending cluster dynamics to concentrated and disordered alloys: The linear-chain case

Cluster dynamics is often used in the multi-scale procedure to link atomistic and macroscopic approaches, in particular when modelling precipitation processes. To extend its use to concentrated alloys, it is necessary to take into account accurately the exclusion zones and their overlap. By investigating the one-dimensional case, one obtains an exact formula for these zones, and its generalization to higher dimensions is proposed. By integrating cluster fragmentation/coagulation processes into cluster dynamics equations, a perfect agreement between atomistic simulations (Kinetic Monte Carlo) and cluster dynamics is reached on the whole range of concentrations for kinetics which govern microstructure in one dimension.