Pressure and temperature dependences of the ionic conductivities of the thallous halides TlCl, TlBr, and TlI

Detailed studies of the pressure and temperature dependences of the ionic conductivities of TlCl and TlBr have allowed determination of the lattice volume relaxations and energies associated with the formation and motion of Schottky defects in these crystals. The volume relaxations deduced from the conductivity are found to be comparable in magnitude with values calculated from the strain energy model and a dynamical model. The association energy of ${\mathrm{Tl}}^{+}$ vacancies and divalent impurities was also determined for TlBr. A particularly important result is the finding that for these CsCl-type crystals the relaxation of the lattice associated with vacancy formation is outward. Earlier studies on ionic crystals having the NaCl structure have yielded a similar result. This outward relaxation thus appears to be a general result for ionic crystals of both the NaCl and CsCl types (and possibly other ionic lattice types), in disagreement with earlier theoretical calculations which show that the relaxation should be inward for all models of ionic vacancies investigated. The conductivity of TlI was studied in both the (low temperature and pressure) orthorhombic phase as well as in the cubic CsCl-type phase. There is a large electronic contribution to the conductivity in the orthorhombic phase. An interesting result for all three materials is the observation in the cubic phase of a pressure-induced transition from ionic to electronic conduction. This is in qualitative agreement with what is known about the pressure dependences of the electronic structure of these materials.