Temperature and Pressure Dependence of the Dielectric Constants of the Thallous Halides

The effects of temperature (76-400°K) and hydrostatic pressure (up to 20 kbar) on the static dielectric constants of single crystal TlCl and TlBr and polycrystalline TlI were investigated. TlCl and TlBr have the CsCl structure, whereas TlI transforms from an orthorhombic structure to the CsCl structure at 4.8 kbar and 300°K. In all cases, the dielectric constant $\epsilon$ decreases with both increasing temperature (at low temperatures) and increasing pressure. At 1 bar and 293°K, ${\left(\frac{\partial \ln \epsilon }{\partial T}\right)}_P$ and ${\left(\frac{\partial \ln \epsilon }{\partial P}\right)}_T$ (in units of ${10}^{-4\mathrm{}}$°${\mathrm{K}}^{-1\mathrm{}}$ and ${10}^{-2\mathrm{}}$ ${\mathrm{kbar}}^{-1\mathrm{}}$) are -3.94 and -1.81, -3.70 and -1.77, -0.68 and -0.65 for TlCl, TlBr, and TlI (orthorhombic), respectively. For TlI (cubic) the corresponding values at 3 kbar and 293°K are -4.04 and -1.47. At the orthorhombic → cubic transition, $\epsilon$ of TlI increases by 35%, but this change is found to be entirely due to the change in volume, the total polarizability per molecule being independent of crystal structure. The temperature dependence of $\epsilon$ is separated into volume-dependent and volume-independent contributions. For the thallous halides the latter contribution, which is determined by anharmonic lattice effects, is large and determines the sign of ${\left(\frac{\partial \ln \epsilon }{\partial T}\right)}_P$. On the basis of Szigeti's theory and the assumption that the optical dielectric constant ${\epsilon }_{\mathrm{op}}$ is a unique function of volume, it is found that anharmonicities in the potential energy and nonlinearities in the dipole moment account for 30-40% of the lattice contribution to $\epsilon$ of the thallous halides. The effective charge ratio $\frac{e^{*}}{e}$ at room temperature is 0.96 for TlCl and 0.95 for TlBr. At low temperatures, $\epsilon$ of TlCl and TlBr obeys a Curie-Weiss law $\epsilon =\frac{c}{(T-T_0)}$ with $T_0$ negative. At high temperatures (>300°K) the dielectric constant and dielectric loss are predominantly determined by the formation and transport of lattice defects. The activation energies calculated from the results agree well with values obtained from ionic-conductivity measurements.