First-principles insights into the stability and mechanical properties of four typical tantalum carbides

From a first-principles perspective, the four typical tantalum carbides, TaC, Ta₂C, Ta₃C₂, and Ta₄C₃ are comprehensively investigated by calculating their formation energies, phase diagrams, Ta-C bonding strength, and mechanical properties, such as elastic modulus, ductile, and Vickers hardness. The Vickers hardnesses at finite temperatures were also predicted. Our calculations clearly show that the stabilities of the four tantalum carbides are highly temperature-dependent. Although Ta₃C₂ is slightly metastable at lower temperatures, it becomes stable above 1200 °C and lies ∼0.003 kJ/mol below convex hull. This may explain why it has been hardly reported in experiments. The calculations further indicate that the relative stability ranking of the four tantalum carbides significantly changes across four distinct temperature regions defined by three temperatures of ∼415 K, ∼855 K, and ∼1165 K. Below ∼1165 K, Ta₄C₃ is the most stable phase. Although TaC is least stable below ∼415 K, its stability step-wisely increases in the four temperature regions and becomes the most stable phase above ∼1165 K. The Ta₂C, which seems to be ductile in our calculations, is least stable above ∼415 K due to its weaker Ta-C bonding. Our calculations provide comprehensive insights into the stability and mechanical properties of the four tantalum carbides.