First-principles investigations of isotope effects in thermodynamic properties of TiX2 (X = H, D, and T) system

As hydrogen, deuterium and tritium storage materials, a series of investigations of mechanical and thermal properties of titanium hydrides, deuterides and tritides have been performed, however, very limited theoretical studies of thermodynamic properties for them can be found. Based on density-functional theory (DFT) and density-functional perturbation theory (DFPT) we have discussed systematically the hydrogen isotope effects on the thermodynamic properties of TiX₂ (X = H, D, and T) system. Our calculations indicate that for evaluating accurately their physical properties at absolute zero temperature, such as the equilibrium lattice constants, bulk modulus, and heat of formation, the zero-point energy correction must be taken into account. By performing the phonon calculation within quasiharmonic approximation (QHA), we obtain their vibrational free energies, vibrational entropies, and temperature dependence of specific heat, thermal expansion, and bulk modulus. Those results demonstrate that comparing with TiH₂, TiT₂ and TiD₂ are more stable and the zero-point effects play an important role in their thermal expansion. The increase in the force constant between Ti and H causes the higher value of specific heat of TiH₂ during the phase transition from FCC to FCT. In addition, comparing with available experimental values, we can conclude that QHA is feasible for describing the thermal properties of TiX₂.