Simulation study of size distributions and magic number sequences of clusters during the solidification process in liquid metal Na

To investigate the size distributions of various clusters formed during solidification processes, a molecular dynamics (MD) simulation study has been performed for a system consisting of 10⁶ liquid metal Na atoms. With the cluster-type index method (CTIM), it is demonstrated that the basic clusters of (13 3 6 4), (13 1 10 2), (14 2 8 4), (14 4 4 6) and (12 0 12 0) and their combinations play a critical role in the microstructure transitions. Also, using a new method to classify all the clusters in the system, the size distributions of various clusters clearly reveal magic number characteristics. The total magic number sequence can be regarded as the superposition of all partial magic numbers corresponding to the related group levels of clusters. The first 10 magic numbers are present in order 14, 22, 28, 34, 41(43), 46(48), 52(54), 57(59), 61(66), 70(74),... (the numbers in the parentheses are the second magic numbers corresponding to the same group level of clusters). This magic number sequence is compared with the experimental and computational results of other authors.