Zirconium Carbide as a High-Temperature Benchmark for the Beyond Quasi-Harmonic Method
Christopher M. Stanley
Molar heat capacity at constant pressure, C_p (T), is a central thermodynamic quantity in materials science, but it remains difficult to calculate accurately from first principles when anharmonic vibrational effects become important. In this work, rocksalt ZrC is used as a high-temperature benchmark for the Beyond Quasi-Harmonic (BQH) method, a prepared-supercell first-principles approach that extracts anharmonic vibrational energy directly from density-functional-theory energy evaluations. The calculated BQH molar heat capacity is compared with CALPHAD reference values, a fully anharmonic thermodynamic-integration calculation, a calculated C_v (T) curve from the present work, and a quasi-harmonic calculation. The BQH curve gives a substantial improvement beyond C_v (T) and beyond the quasi-harmonic approximation. Because ZrC is electronically conductive, an electronic heat-capacity correction was also estimated from the density of states at the Fermi level and added to the vibrational BQH result. This correction brings the calculated molar heat capacity into close agreement with the fully anharmonic theoretical benchmark through approximately 1200 K. These results show that the BQH method fully captures important anharmonic phonon contributions missing from ordinary quasi-harmonic calculations.
cond-mat.mtrl-sciCross-listedarXiv:2609.08913•Sep 9, 2026