The melting point is one of the most important material properties, which determines the potential of its application in various fields. Experimental measurement of the melting point is complex and expensive, while computational methods will help achieve an equally accurate result faster and easier.

A research group from Skoltech conducted a study to calculate the maximum melting point of a high-entropy carbonitrides — a compound of titanium, zirconium, tantalum, hafnium, and niobium with carbon and nitrogen. The results published in the Scientific Reports journal indicate that high-entropy carbonitrides can be used as promising materials for protective coatings of equipment operating under extreme conditions — high temperature, thermal shock, and chemical corrosion.

“In the new study, we used deep neural network-based potentials of interatomic interaction to model the structure of high-entropy carbonitride (TiZrTaHfNb)CxN1−x in both solid and liquid states. This allowed us to predict the heating and cooling temperatures depending on the nitrogen content, determine the melting point, and analyze the structure-property relationship in terms of interatomic interactions. An increase in the nitrogen content leads to an increase in the melting point, which is associated with a change in the relative stability of the liquid phase compared to the solid phase when nitrogen is added,” commented Professor Alexander Kvashnin from the Skoltech Energy Transition Center and the study supervisor.  

The team has created a new approach for training the DeepMD potential to mimic the melting and crystallization processes of the TiZrTaHfNbCxN1-x, which enabled them to calculate its melting point. The potential was trained on atomic trajectories obtained by ab initio molecular dynamics, which ensured high accuracy of predictions in atomic forces and energies. The approach aimed at expanding the capabilities of classical molecular dynamics modeling, which allows for accurate modeling and analysis of the melting process with prediction of the melting temperature not only of high-entropy carbonitrides, but also of other complex multicomponent materials.

The authors identified the maximum melting point for the composition (TiZrTaHfNb)C0.75N0.25 — 3580±30 K. By adding nitrogen, the melting characteristics of high-entropy compounds can be improved, while the thermophysical properties of functional and structural materials will change.