**7. References**

Alexander, V. M. & Moshe, B. Z., (2001). Temporal evolution of an argon cluster during the process of its evaporation, *Chemical Physics*, Vol. 264: 135-143.

connecting bonds, respectively, at 223K (the gray spheres are the center atoms of basic clusters). From the diagrams of their center atoms with multi-bonded or single-bonded each other, it can be clearly seen that the cluster consisting of 43 atoms has a dense connecting of all atoms and would possess better stability and higher heredity than other two clusters

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

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

This work was supported by the National Natural Science foundation of China (Grant No

Alexander, V. M. & Moshe, B. Z., (2001). Temporal evolution of an argon cluster during the

process of its evaporation, *Chemical Physics*, Vol. 264: 135-143.

consisting of 53 and 69 atoms, respectively, in turn.

those obtained by gaseous deposition, ionic spray and so on.

to provide a reasonable explanation for those experimental results.

**5. Conclusions** 

**6. Acknowledgment**

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**10** 

*Turkey* 

**A Molecular Dynamics Study on Au** 

*1Gazi University; Science Faculty, Physics Department, Ankara* 

Yasemin Öztekin Çiftci1, Kemal Çolakoğlu1 and Soner Özgen2

*2Firat University; Faculty of Art and Science, Physics Department, Elaziğ* 

Theoretical and computational modeling is becoming increasingly important in the devolopment of advanced high performance materials for industrial applications.[1] Computer simulations on various metallic systems usually use simple pairwise potentials. However, the interactions in real metallic materials can not be represented by simple pairwise interactions only. A pure pairwise potential model gives the Cauchy relation, *C12*=*C44,* between the elastic constants, which is not the case in real metals. Therefore, manybody interactions should be taken into account in any studies of metals and metal alloys.

It is very important to calculate the phase diagrams of metallic systems and their alloys in order to achieve technological improvements. The phase diagrams are still obtained by using experimental techniques because there are no available methods for entirely theoretical predictions of all of the phase diagrams of any pure metal. Therefore, in the calculations of the phase diagrams some expressions have been formed by using theoretical or semi-empirical approach and their validity have been investigated in a selected portion of the phase diagrams. The expressions suggested in semi-empirical approaches generally contain some factors depending on temperature and pressure. Therefore, the calculated phase region is restricted by experimental limits. Today, the free energy concepts, such as Gibbs and Helmholtz, on the other hand, have been widely used to calculate the macroscopic phase diagrams [2, 3] in which thermodynamics parameters are dominant. In microscopic scale, their calculations require some vibrational properties which can be derived from elastic constants of the material. So, the correct calculations of the elastic

MD simulations can be utilized to compute the thermodynamic parameters and the results of the external effects, such as temperature and pressure or stress acted on a physical system [4, 5]. In the MD simulations, the interatomic interactions are modeled with a suitable mathematical function, and its gradient gives the forces between atoms. Hence, Newton's equations of motion of the system are solved numerically and the system is forced to be in a state of minimum energy, an equilibrium point of its phase space. Although many properties of the system, such as enthalpy, cohesive energy and internal pressure, have been directly calculated in the MD simulations, the entropy which is required for the free energy calculations has not been directly obtained and it is possible to obtain it by some approaches involved harmonic and anhormonic assumptions. There are some investigations related to

constants are important as well as the calculations of phase diagrams.

**1. Introduction** 
