The use of a cluster-associate pattern for calculation of melt viscosity

Abstract

The liquid state of the substance is the most complex for theoretical description. Modern ideas about the liquid and its viscosity are reduced to the following: in the structure of the liquid, the spatial arrangement of atoms is not fixed, as in a crystal, and is not in a free state, as in a gas. Therefore, liquid may approach its properties to gas near the boiling point or the solid state near the melting point. Thus, the structure of the liquid is characterized by the short-range order of the bond. The properties of liquid metals are obtained mainly from experimental studies. This article provides mathematical justification for the cluster-associate pattern. The purpose of the study is to show the possibility of applying a semi-empirical model to calculate the viscosity of liquid metals. The proposed model is developed using the concept of chaotized particles, which is based on the Boltzmann distribution. This model is developed based on the association degree of clusters of their crystal- moving particles. For many years, the viscosity of liquid metals has been studied only by experimental methods. The model enables to find melt viscosity values analytically. The calculated viscosity values of some metals are compared to experimental values in this model. It is established that in all cases the obtained values coincide with the experimental values. The correctness of the proposed model is confirmed by the correlation coefficient. The application of the proposed model has been shown previously on some metals. In this work, we also show the applicability of the cluster-associate pattern using the example of beryllium, since it can be correlated with semimetals by many physicochemical properties. The degree of novelty of the scientific results lies in the fact that the obtained high correlation coefficients for the analysed metals indicate their functionality.