Lattice energy calculations for Ti 4O 7 using a shell model

Abstract

The lattice energies of Ti 4O 7 containing Ti 3+-Ti 3+ pairs at temperatures below 120 K have been calculated by the polarizable point ion shell model. The positions of ions which minimize the total energy of the crystal have first been determined and then the lattice energies have been obtained using these ion positions. The defect energy is found to be 65.79 eV per eliminated oxygen ion. The ion positions determined in the calculation are, in general, found to move toward the positions in the real structure from their initial positions in the ideal structure. The lattice energies of the Ti 4O 7 structure in which the Ti 3+ ions are redistributed hypothetically at the sites adjacent to the crystallographic shear planes have been also calculated. This was found to have a defect energy lower than the Ti 4O 7 structure with the distribution of valences observed experimentally. This result is discussed in terms of the quantum effect due to the nonmagnetic bond formed by electrons trapped on the Ti 3+-Ti 3+ pairs.