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.