Boosting the melting point record to 4431 K: Simulated with machine learning potential at SCAN accuracy

Carbides or carbonitrides in the Hf-Ta-C-N system are believed to exhibit the highest melting point, attracting significant interest for both scientific and engineering means. In this study, we developed a machine learning potential model for Hf-Ta-C-N carbonitrides at Strongly Constrained and Appropriately Normed (SCAN) semi-local density functional accuracy. In addition, we proposed a novel critical equilibrium method for simulating melting points. Utilizing these two advancements, we successfully simulated solidus and liquidus lines in phase diagrams of HfC_1−x and TaC_1−x, demonstrating excellent agreement with experimental results. We then discovered new compounds with even higher melting points by employing Bayesian global optimization. The compound with the highest melting point found is Hf_0.956Ta_0.044C_0.600N_0.338, which has a melting point of 4431 K, surpassing the experimental record by approximately 150 K. We conducted an in-depth thermodynamic analysis in the HfC–HfN pseudo-binary system and found that the addition of N has a dual effect: on the one hand, it increases the enthalpy change due to melting ($\Delta H\uparrow$) with a maximum value at ∼15 at% N in the anion site; on the other hand, it reduces the entropy of the liquid phase and increases the entropy of the solid phase ($\Delta S\downarrow$). This results in a maximum melting point at a specific N content. Furthermore, we discussed the effects of N alloying on thermal expansion and mechanical properties, which are invaluable for the ongoing development of carbonitrides. This research not only advances our understanding of Hf-Ta-C-N carbonitrides but also provides a promising framework for future materials research and the development of materials with exceptional properties.