In this paper, the vibrational and lattice thermal behaviors of ThC are investigated through the density functional theory. Thermal characteristics of ThC are studied under the novel models based on the Debye-Grϋneisen and full quasi-harmonic approximation (FQHA). The Gibbs free energy, thermal Grϋneisen ratio, adiabatic bulk moduli, vibrational contributions of Helmholtz free energy, internal energy, and entropy of ThC are studied for the first time. The structural properties including lattice constant (a0), bulk modulus (B0), and the first derivative of the bulk modulus (B0'), are calculated and compared to other theoretical and experimental works that revealed a good agreement. Phonon band structure was calculated using density functional perturbation theory along the several high symmetry directions in the first Brillouin zone. The absence of imaginary phonon frequencies in the whole Brillouin zone is characteristic of the dynamical stability of the crystalline structure. Thermodynamic computations show that the vibrational Helmholtz free energy, Gibbs free energy, and adiabatic bulk modulus decreased with increasing the temperature at a given pressure.
