Linear Modeling of the Glass Transition Temperature of the system $SiO_2-Na_2O-CaO$

TL;DR

This paper develops a new mathematical model, called P Model, to predict the glass transition temperature of the SiO2-Na2O-CaO system using data-driven methods, outperforming existing equations.

Contribution

The paper introduces the P Model, a novel equation for predicting Tg in the SiO2-Na2O-CaO system, with improved accuracy over previous models.

Findings

P Model has lower mean absolute error than existing equations.

P Model shows lower standard deviation of errors.

Model is valid within the data limits used.

Abstract

This work aimed to mathematically model the glass transition temperature (Tg), one of the most important parameters regarding the behavior of slag, responsible for the sudden change in thermomechanical properties of non-crystalline materials, by the chemical composition of the SiO2-Na2O-CaO system, widely applicable in the production of glasses and constituent of iron, magnesium and aluminum metallurgy slags. The SciGlass database was used to provide data for mathematical modeling through the Python programming language, using the method of least squares. A new equation was established, called P Model, and it presented a lower mean absolute error and lower standard deviation of absolute errors in relation to 3 equations in the literature. The raised equation provides significant results in the mathematical modeling of Tg by the chemical system SiO2-Na2O-CaO, valid for the limits of the data used in the mathematical modeling.