**5. Conclusions**

In this chapter, for deeply understanding the formation and evolution characteristics of various clusters, especial of nano-clusters formed during solidification processes, molecular dynamic simulation studies have been performed for a large-sized system consisting of 106 liquid metal for Al and Na atoms, respectively. Several microstructure analysis methods, especial the cluster-type index method (CTIM) have been adopted to describe various types of cluster, especial of nano-cluster by basic clusters. It is demonstrated that the icosahedral cluster (12 0 12 0) is the most important basic cluster, and plays a critical role in the microstructure transition. The nano-clusters are formed by connecting various middle and small clusters with different cluster-types or sizes, and their structures are different from those obtained by gaseous deposition, ionic spray and so on.

For the evolution processes of the nano-clusters, at different temperatures, it is demanstrated clearly that the central atoms of basic clusters in the nano-clusters are bonded each other with different ways, some central atoms are multi-bonded, and others singlebonded. A new statistical method has been proposed to classify the clusters (from basic cluster to nano-cluster) formed in the system by the number of basic cluster contained in them, and the clusters consisting of the same number of basic cluster but not the same number of atoms can be classified as a group level of clusters. It can be clearly seen that the size distribution characteristics of various clusters in the system is related to the magic number of each group level of clusters. The total magic number sequence of the system can be obtained for metal Al as 13, 19, 25(27), 31(33), 38(40), 42(45), 48(51), 55(59), 61(65) , 67, ... the numbers in the brackets are the second magic numbers corresponding to the same group level of clusters. This magic number sequence is in good agreement with the experimental results obtained by Schriver and Harris et al (for Al). For metal Na, the magic number sequence are in the order of 14, 22, 28, 34, 41(43), 46(48), 52(54), 57(59), 61(66), 70(74), …This magic number sequence is in good agreement with the experimental results obtained by Knight et al and the calculating results obtained by Noya et al (containing the primary and secondary magic numbers) (for Na). Highly interesting, these simulation results can be used to provide a reasonable explanation for those experimental results.
