A neural network will help control the process of solidification of melts

Russian scientists have developed a neural network-based method that will help quickly and accurately determine the Arrhenius temperature, an indicator on which the process of melt solidification depends. The proposed approach allowed the authors to determine this parameter with an accuracy of more than 90% for various types of materials — metallic, silicate, borate, and organic. The new algorithm will help speed up the production of materials such as glass and metal alloys, as well as more accurately control their quality. The results of the study, supported by a grant from the Russian Science Foundation (RSF), are published in the journal Materials.


Many solid materials used in everyday life and in technology, such as glass, metals and plastics, initially have the form of so-called melts – viscous liquids that solidify at a certain temperature, turning into a solid state. The point at which a change in the state of aggregation begins is called the Arrhenius temperature. If the temperature is above this value, the atoms in the liquid are mobile, making the material flowable; when approaching the Arrhenius temperature, the atoms begin to move in bundles – in groups – and more slowly than before, which is a sign that the liquid is preparing to solidify.

Knowing the Arrhenius temperature is important in the production of any solid materials, as it helps to predict the viscosity and atomic structure of the final material. However, it is difficult to accurately determine the Arrhenius temperature for silicate and borate materials, such as glasses, because in them the slow movement of atoms in groups continues even after reaching the temperature corresponding to solidification. Silicate glasses are perhaps the most common type of this material, as they are used in the manufacture of dishes, aquariums, windows and many other things. Borate glasses are mainly used in optics, for example, in lasers and various detectors.


Scientists from Kazan Federal University (Kazan) have developed a computer algorithm based on a neural network that allows you to accurately calculate the Arrhenius temperature from just a few physical parameters of the material. Prior to this, specialists could not determine those characteristics that unambiguously affect the value of the Arrhenius temperature and which can be used in its assessment.

As the initial data with which the algorithm worked, the authors used only four physical characteristics of materials that are easy to measure in the laboratory or, if necessary, to find in the literature. These indicators, which included, for example, the melting point, glass transition temperature, and brittleness value, are used by physicists to describe phase transitions and structural changes in liquids upon cooling. The researchers tested the algorithm on metallic, silicate, borate and organic glasses, for which all four parameters were known. The entire data set was divided by the authors into three groups: the first group was used to train the algorithm, the second was used to test it, and the third was used to calculate the Arrhenius temperature.


Calculations have shown that for the created neural network, the melting and glass transition temperatures of the material are significant and sufficient characteristics for estimating the Arrhenius temperature. From these two values, the algorithm determined the Arrhenius temperature for all analyzed liquids with an accuracy of more than 90%. Moreover, the scientists obtained a mathematical equation that relates the Arrhenius temperature to the melting and glass transition temperatures. It will make it possible to estimate the Arrhenius temperature without resorting to expensive experimental measurements.

“Melting and glass transition temperatures are easily determined in the laboratory. Moreover, they can be found in the relevant literature. Therefore, the calculation of the Arrhenius temperature from them becomes a very fast procedure. This will help to simplify the analysis of the properties of liquids and more accurately evaluate the characteristics of the final solid materials. In the future, we plan to adapt the developed algorithm to materials with a more complex composition and structure, such as polymers,” says Bulat Galimzyanov, Ph.D.

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