Investigation of thermodynamic, electrochemical properties, and optoelectronic devices of Na_xTi₂O₄ (x = 1 and 2) anode material for Na-ion battery: an ab initio calculations

In this work, the structural, electronic, and thermodynamic properties of NaTi₂O₄ were studied through first-principle calculations based on density functional theory (DFT) using generalized gradient approximation (GGA). The calculated lattice constant for NaTi₂O₄ and Na₂Ti₂O₄ equals 8.22 Å and 8.35 Å, respectively. Characteristics of the battery, such as average voltage (0.816 V vs. Na⁺/Na) and energy density (122.4 Wh/kg), were extracted. The thermodynamic properties of NaTi₂O₄, such as Debye temperature, bulk modulus (B), and heat capacity (C_v), are obtained by the quasi-harmonic Debye model. The heat capacity (C_v) of NaTi₂O₄ is 325 J/molK approximately. The bulk modulus (B) increases with pressure and decreases with temperature. The Debye stiffness of NaTi₂O₄ increases as the pressure increases. According to all results, the NaTi₂O₄ compound is suitable for use as an anode for Na-ion batteries. According to the electronic structures, we can derive the optical properties of both NTOs in the infrared and visible regions from the electronic transition between the O_2p and Ti_3d states. On the other hand, the optical properties in the ultraviolet region depend on the transition from the O_2p valence band states to the Ti_3d conduction band states. Therefore, these differences were due to various electronic distributions that determine the Ti–O hybridization. Furthermore, the outcomes open horizons for the use of NaTi₂O₄ and Na₂Ti₂O₄ compounds as optical devices.