Elastic Moduli and Phonon Properties ofBi2Te3

Abstract

The six independent elastic moduli of ${\mathrm{Bi}}_2$ ${\mathrm{Te}}_3$ have been measured from 4.2 to 300 K using a continuous-wave resonance technique. Extrapolation of the measurements to absolute zero gives $C_{11}=7.436\mathrm{}$, $C_{66}=2.619\mathrm{}$, $C_{33}=5.160\mathrm{}$, $C_{44}=3.135\mathrm{}$, $C_{13}=2.917\mathrm{}$, and $C_{14}=1.541\mathrm{}$ in units of ${10}^{11}$ ${\mathrm{d}\mathrm{y}\mathrm{n}/\mathrm{c}\mathrm{m}}^2$. These values correspond to a limiting Debye temperature of 164.9 ± 0.2 K, which agrees with the calorimetric value of 165 ± 2 K. A Born—von Kármán lattice model providing for central and angular forces between first and second neighbors is constructed to fit the moduli. Using the model, the frequencies of infrared absorption and Raman scattering are predicted and the density of phonon states and lattice specific heat are found. The calculated specific heat differs appreciably from the calorimetric measurements, indicating the possible importance of third- and fourth-neighbor interactions.