Prediction of the coordination numbers of liquid metals
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For liquids, a coordination number is defined as the average number of nearest neighbors about a given atom or molecule and the positions of neighbors are only statistically describable. So far, a number of experimental data concerned with the coordination numbers of liquid metals near the melting point have been reported due to the importance of understanding the local structure of liquid metals.[1,2,3] Some macroscopic properties of liquid metals and alloys such as activity,[4,5] diffusion, viscosity,[6,7] and the nucleation phenomena of supercooled liquid could be correlated with their structural information.[8] Usually, the physical scene of shortrange order can be observed from the measured curves of the radial distribution function (RDF) from which the coordination number may be obtained. Recently, experimental studies on the dynamical structure of liquid metals have been actively carried out by the inelastic X-ray scattering technique using the synchrotron radiation, which has stimulated theoretical studies. Hoshino[9] described the recent progress in theoretical studies on the dynamical structure of liquid metals in two approaches, i.e., the theoretical approach based on the memory function formalism and the various kinds of computer simulations. Hines et al.[10] concluded that the variation in the number of nearest neighbors computed from the RDF curves for simple liquids has been estimated to be about 20 to 30 pct, depending on the method of determination, and the coordination numbers were predicted for 39 liquid metals with average deviations of 13 to 23 pct from the literature values, depending on their graphical correlation method. Cahoon[11] presented a simple and absolute method for the calculation of the first coordination number for any pure, isotropic liquid element, which required only the liquid density and the position for the first peak of the radial distribution function, assumed to be the atomic diameter, which was based on the plot of coordina-
tion number vs packing fraction. Using this method, Cahoon concluded that the coordination number for liquid metals that exhibit a body-centered-cubic solid structure averages 7.4, while the first coordination number for liquid metals with a face-centered-cubic or close-packed-hexagonal solid structure averages 7.1. The modified coordination equation[12] supposed by the author contained a mistake and was short of being systematically verified. Therefore, it is necessary to clarify the modified coordination equation so as to propose a more accurate and convenient method for predicting the coordination number of a metal in its temperature range of liquid state. Based on the pair distribution function, the coordination number of a liquid metal i can be expressed as rmi
Z i 2 ∫ 4pr2ri gi (r,T)dr
where i Ni/Vi 0.6022/Vmi is the molecular number density; Vmi the molar volume in cm3 mol1; gi(r,T) the pair distribution function; 4r2 igi(r,T) the radial distribution function; and r0i and rmi the beginning and first peak values of radial distance
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