Theory and practice of “shape spectroscopy” of local FCC structures in computer simulations of nucleation and crystallization

Starting from the previously developed probabilistic method for recognition of structures of small clusters of atoms undergoing thermal fluctuations, we derive simple algorithms for the very detailed study of local face-centered-cubic (FCC) arrangements of the atoms, directly in a configuration of atoms when it is being simulated. This includes (i) an algorithm for a local identification of FCC-like clusters, with the discussion of its reliability, and (ii) an algorithm for the calculation of the relative orientational correlations between the clusters. As an illustration, the method is used for studying nucleation and growth of an FCC phase in a rapidly quenched melt of 4000 Lennard-Jones atoms. On the basis of this analysis, we propose two trial hypotheses about (i) the existence of “slow” and “quick” regimes during the nucleation and growth and (ii) that in the intermediate stages of nucleation and crystallization the FCC-like local order appears rather in two-, than in three-dimensional aggregates.