Temperature Dependence of the Dielectric Constant of Paraelectric Materials

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Abstract
An expression is obtained for the dielectric constant of a displacive ferroelectric in its unpolarized phase. This has been derived with the use of a Hamiltonian treated by Szigeti in connection with the temperature-dependent dielectric constant of the alkali halides. In the present work, however, it is assumed that the "soft ferroelectric mode" is unstable in the harmonic approximation, i.e., has an imaginary frequency associated with it. The linear response can be obtained exactly for this Hamiltonian. It is shown that the lowest order anharmonic interaction that can stabilize this mode is of fourth order. In the classical limit, the potential energy terms and the term linear in the electronic moment lead to a Curie-Weiss behavior of the dielectric constant. The most significant effect arising from the presence of terms of higher order than linear in the electric moment is to make the Curie constant temperature dependent. It is suggested that an observed temperature-independent contribution to the dielectric constant cannot be unambiguously attributed to the electronic polarization or temperature-independent infrared active modes of the system.

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