Development of a Non-Integral Form of Coordination Number Equation Based on Pair Distribution Function and Gaussian Function

Abstract

The coordination number (CN) is an important structure property of liquid metals. A simple yet extremely precise method for calculating CN is proposed, the classical CN methods are evaluated systematically, and the mathematical forms of the symmetry method are corrected. Using the Gaussian function construct, the first coordination shell of the pair distribution function (PDF), the right-hand side of the first peak of the pair distribution function is extrapolated, and the CN expression is simplified with a Gaussian function to obtain its non-integral form. The first coordination shell is used to explain the Tao coordination number model (Tao CN) and obtain a Modified Tao CN. The Gaussian function is combined with the Tao CN, obtaining the function expression for the peak with peak position. These are important for the structural research of liquid metals. The CN of 27 liquid metals is calculated by these methods. The average relative deviation of the Gaussian function extrapolation method is ±6.46%, of the Modified Tao CN is ± 18.51%; those of the four classical methods range from ±15% to ±42%. The Modified Tao CN and extrapolation methods to calculate CN are more accurate for calculating CN than the classical method; they are more suitable for use in quantitative applications of CN. The equations derived in this work can be applied to the problem of integration of distribution functions to obtain simple mathematical models.