Splitting of the TO Mode in Calcite by the Polarization Field

This paper describes an investigation of the behavior of an infrared-active $E_u$ mode of the internal vibrations in a calcite crystal when a wave vector is inclined at an angle $\theta$ to the crystallographic $c$ axis. It has been deduced through theoretical consideration that the polarization field splits the $E_u$ mode into two components which have dipole moments with orthogonal polarizations $P_{\parallel }$ and $P_{\perp }$, and that the value of ${\omega }_{\mathrm{TO}}\left(P_{\parallel }\right)$ changes with $\theta$, while the values of ${\omega }_{\mathrm{LO}}\left(P_{\parallel }\right)$, ${\omega }_{\mathrm{TO}}\left(P_{\perp }\right)$, and ${\omega }_{\mathrm{LO}}\left(P_{\perp }\right)$ remain unchanged. In order to see whether or not this prediction is valid, the values of the above frequencies for various values of $\theta$ were obtained by analyzing the reststrahlen bands observed in five specimens with reflecting surfaces of $\theta$ equal to 0°, 24.5°, 44.5°, 65.5°, and 90°, which were found to be in accordance with the curves given by theoretical calculation.