Determination of the coordination number of liquid metals near the melting point
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I.
INTRODUCTION
THE coordination
number of a solid is defined as the number of atoms bonded to a central atom. The concept of the coordination number for the liquid state can be related to solid state theory since solids and liquids have comparable densities and intermolecular separation distances. The coordination number is useful in making first-order approximations to the macroscopic behavior of fluids and in predicting transport properties, e.g., liquid diffusion coefficients.~'2 On a microscopic scale the coordination number has been useful in estimating the nonadditive contribution to the effective intermolecular pair potential function of nonpolar liquids. 3 Short range order for simple liquids has been observed from available radial distribution curves, particularly for the first and second coordination shells. Bernal 4 pointed out that the short range order exhibited by a liquid is of a different nature than the short range order present in the crystalline state. According to Bernal 4 the structure of simple liquids can be characterized as a homogeneous, coherent, and essentially irregular assemblage of particles. The coordination number for the liquid state typically has been computed from the radial distribution function (RDF), g(r). This function represents the relative probability of finding two atoms or molecules separated by the distance r averaged over time and over all possible configurations of the remaining atoms or molecules in the liquid. Locations of maxima in the RDF curve represent the mean interatomic distances, and areas under the peaks of the function 47rr2pg(r) (p is the average number density) represent the mean number of neighbors within various distances. The number of nearest neighbors is generally referred to as the coordination number. There is no unique value for the number of nearest neighbors in an irregular liquid, but a range within which the coordination number of any liquid can be found. Bernal and King 5 used models to show that a random close packed structure, which represents a simple liquid closely, is characterized by a certain coordination number distribution function. The available data 6-1~from X-ray and neutron diffraction experiments indicate that the average coordination number ANTHONY L. HINES, Associate Dean and Professor, and KANHAIYALAL R. JETHANI, Graduate Student, are with The Oklahoma State University, Stillwater. OK 74078. HUGH. A. WALLS is Director of Planning and Analysis and Professor, The University of Texas at Austin, Austin, TX 78712. Manuscript submitted January 24, 1983. METALLURGICALTRANSACTIONS A
for most liquid metals falls in the range of 8 to 11. This range of values is higher than the values obtained by Bernal and Mason" and Scott ~2 who used random close packed and random loose packed models of hard spheres to represent the structure of simple liquids. Four methods have been used to compute the coordination number from the radial distribution function. These are: (1) the method of symmetrical peaks using the function rg (r) about a radiu
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