The frequency dependence of the transverse optical mode in the long-wavelength limit on the density of conduction electrons is calculated. This dependence is a consequence of the dielectric properties of the free electron gas which gives a change of the effective ion-ion interaction. By putting the limiting frequency equal to zero one finds an equation for the ferroelectric Curie temperature.
Hallers, J. J., & Caspers, W. J. (1969). On the Influence of Conduction Electrons on the Ferroelectric Curie Temperature. Physica status solidi B, 36(2), 587-592. https://doi.org/10.1002/pssb.19690360221