Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

Abstract

The Arrhenius crossover temperature, T A , corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below T A . The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates.In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T . The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature T A and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature T A was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature T g , the melting temperature T m , the ratio of these temperatures T g /T m and the fragility index m were applied as input parameters. It has been established that the temperatures T g and T m are significant parameters, whereas their ratio T g /T m and the fragility index m do not correlate much with the temperature T A . An important result of the present work is the analytical equation relating the temperatures T g , T m and T A , and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature T A for a large class of materials, regardless of their compositions and glass-forming abilities.