Thermal Expansion of Bismuth Telluride

The results of X-ray and dilatometric measurements of the thermal expansion of bismuth telluride in the temperature range of $4.2$–$850$ K have been critically analyzed. The joint statistical processing of the experimental data has been performed by the least squares method and the most reliable temperature dependences of the linear thermal expansion coefficients along the principal crystallographic axes $\alpha_a$ and $\alpha_c$ and the average linear coefficient $\overline{\alpha}_L$, as well as the density of $\mathrm{Bi}_2$$\mathrm{Te}_3$, have been recommended. The results indicate that the linear thermal expansion coefficients along the directions parallel and perpendicular to the cleavage planes decrease with an increase in the temperature in a narrow temperature range. At temperatures below $298$~K, the character of the temperature dependences of the linear thermal expansion coefficients of $\mathrm{Bi}_2
$$\mathrm{Te}_3$ has been analyzed in terms of the anharmonicity of the chemical bonding forces in the layer structure and anisotropy of the elastic constants. In terms of the deviations of the composition of the $\mathrm{Bi}_2$$
\mathrm{Te}_3$ compound from the stoichiometric one and the real (defect) structure of the compound, a model has been proposed to explain the minimum in the $\alpha_a(T)$ dependence of $\mathrm{Bi}_2$$\mathrm{Te}_3$ near the melting temperature of bismuth. A method for calculating the temperature dependence of the linear thermal expansion coefficients of the anisotropic layer crystals using the data on the specific heat has been discussed, which provides good agreement of the calculated linear thermal expansion coefficients with the experimental data within the accuracy of the measurements of the linear thermal expansion coefficients.