MATHEMATICAL MODEL FOR CALCULATING THE STRUCTURE OF A LIQUID (MELT) USING DISTRIBUTION FUNCTIONS

Abstract

This article considers a spatio-temporal study of the structure of melts using the correlation functions of the distribution of physical and chemical analysis. The authors consider the properties of metallic melts and their dependence on the physical state of the melt. The dynamic structure of the melt is considered, the numerical description is given. The binary distribution function is distinguished as the one that best corresponds to the structure of the fluid. With the help of the atomic distribution function, if the interaction potentials are known, it is possible to find the equation of state of a system fluid, to determine its energy, compression, and a number of other kinetic and thermodynamic quantities. The atomic distribution function allows you to quantify the parameters of the short order in a liquid. The authors indicate two approaches for the theoretical calculation of the atomic distribution function to quantify short-range parameters in a fluid based on integro-differential equations that relate correlation functions to interaction potentials.

For real systems, the most common methods of finding the radial distribution function are the method of diffraction of X-rays, neurons or electrons. This paper presents the results of X-ray diffraction by Pb-Cd melts, calculated functions of radial distribution of atomic density, presents the main parameters of the radial distribution function and the results of model interpretation.

The article proves that the implementation of the mathematical model is possible through the theoretical calculation of distribution functions. The authors took as a basis the solutions of integro-differential equations, which include both the equation of the complete and correlation functions, and the equation that connects the distribution functions with the even interaction potential. The proposed mathematical model is implemented using the function of radial distribution of atomic density on the basis of physicochemical analysis. As a result of realization, the dependences of the percentage of atoms on the coordination numbers calculated in two ways in the graphical results are obtained.