In this study, the lattice dynamics and thermal characteristics of thorium dioxide are calculated using the first principle calculations based on the density functional theory (DFT). The Gibbs free energy, isothermal bulk moduli,Debye temperature, thermal Grüneisen parameter as well as vibrational contributions of Helmholtz free energy, internal energy and entropy of thorium dioxide are studied for the first time under high temperatures and pressures. Thermal properties are compared using generalized gradient approximation (GGA) and local density approximation (LDA) under a novel model based on the quasi-harmonic Debye–Einstein method. The results of the simulation reveal that the lattice constant calculated by LDA is less than the one calculated by GGA, while the Gibbs free energy, Debye temperature, adiabatic and isothermal bulk modulus obtained from LDA are greater than ones obtained from GGA. The volumetric thermal expansion coefficient and vibrational contribution of entropy obtained from GGA and LDA increase with rise in temperature.

In this study, the vibrational and lattice thermal behaviours of ThC are investigated through the density functional theory. Thermal characteristics of ThC are studied under the novel models based on the Debye–Grüneisen andfull quasi-harmonic approximation. The Gibbs free energy, thermal Grüneisen 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 (a$_0$), bulk modulus (B$_0$) and the first derivative of the bulk modulus (B$'$$_0$) are calculated and compared with 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 increase in the temperature at a given pressure.