Knowledge Bank

The frequencies of the symmetry allowed $k\approx 0$ transverse and longitudinal modes were obtained from a Kramers-Kronig analysis of far infrared reflectance data taken between $80-800\circ K$. Above the Curie temperature $(760\circ K),PbTiO3$ exhibits a broad second order Raman spectrum. For a strong first-order spectrum is superimposed which sharpens considerably with decreasing temperature. The $\Delta \nu /\Delta T$ of several modes is quite marked; bands observed at $760\circ K$ at about 60, 120, 182, 280 and $495cm-1$ increase in frequency by about 4, 6, 8, 2 and $3.5cm-1$ respectively for each $100\circ$ drop in temperature. The lowest frequency mode $(60cm-1)$ is relatively the ``softest'' but the 120 and $182cm-1$ modes contribute significantly to the temperature dependence of $ϵ0$ and may also approach instability.