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

Abstract

The Arrhenius crossover temperature, (Formula presented.), 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 (Formula presented.). 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 (Formula presented.) and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature (Formula presented.) was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature (Formula presented.), the melting temperature (Formula presented.), the ratio of these temperatures (Formula presented.) and the fragility index m were applied as input parameters. It has been established that the temperatures (Formula presented.) and (Formula presented.) are significant parameters, whereas their ratio (Formula presented.) and the fragility index m do not correlate much with the temperature (Formula presented.). An important result of the present work is the analytical equation relating the temperatures (Formula presented.), (Formula presented.) and (Formula presented.), 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 (Formula presented.) for a large class of materials, regardless of their compositions and glass-forming abilities.