Solving Static and Dynamic Disorder in Cu₄TiTe₄: Crystal Structure and Thermodynamic Properties

Cu₄TiTe₄ shows positional disorder because one of the copper atoms does not occupy a precise position in the unit cell. This fact complicates the development of simple and reliable crystalline models capable of capturing the promising thermodynamic and optical properties of Cu₄TiTe₄. Here, we select practical supercells accounting for the different Cu atomic environments in the crystal and identify nonequivalent structural configurations. Their electronic energies and thermodynamic properties are calculated by coupling DFT and the quasi-harmonic approximations. Average values corresponding to the experimentally observed Cu₄TiTe₄ structure are obtained introducing Boltzmann weights based on the total energy of these configurations. For Cu₄TiTe₄, differences in the calculated properties among the 16 nonequivalent configurations of its 2 × 2 × 1 supercell demonstrate the inadequacy of focusing just on a single configuration. After calculating the energy barriers associated with the diffusion of the disordered copper atoms among its four equivalent positions (lower than 0.5 eV), we evidence the importance of taking into account this dynamic disorder, which reveals a negative thermal expansion for this telluride at low temperatures, not found under the static disorder approach.