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

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.