Bipolaron effects on the lattice energy of Ti 4O 7

Abstract

Taking into account the electron-phonon interactions proposed by Anderson, the lattice energy in semiconducting Ti 4O 7, below the metal-to-semiconductor transition temperature, in which bipolarons are formed, is calculated, using the polarizable point ion shell model developed by Dienes et al. The electron-phonon coupling constants (λ) which represent the strengths of the electron-phonon interactions are estimated by fitting the ionic spacings calculated theoretically to the experimental ones. The coupling constant between the electron trapped at a Ti 3+ site and the phonon of the nearest cation (λ +) and that due to the phonon of the nearest anion (λ −) are found to have values of −107.0 eV nm −1 and 14.0 eV nm −1, respectively where these constants have the dimension of the change in the energy per the change in the ionic spacing induced by electron-phonon interactions. Using these values, the lattice energies are calculated. Then, the Ti 4O 7 structure is found to be stabilized by formation of bipolarons. In addition, the electrons trapped at Ti 3+ sites are also found to be stabilized because their potential energies reduce by 1.615eV per bipolaron due to electron-phonon interactions. The deformation energy of a bipolaron in Ti 4O 7 is calculated to be 2.41 eV per bipolaron, as well.