Atomic Displacement Relationship to Curie Temperature and Spontaneous Polarization in Displacive Ferroelectrics

Abstract

The phase transition from nonpolar to polar in displacive ferroelectric crystals is accompanied by the displacement $\ensuremath{\Delta}z$ of certain atoms from their higher-temperature symmetry positions. A study of all displacive ferroelectrics in which atomic positions have been determined has shown that a fundamental relationship exists between $\ensuremath{\Delta}z$ and the Curie temperature ${T}_{C}$. This relation has been form ${T}_{C}=(\frac{\mathcal{K}}{2k}){(\ensuremath{\Delta}z)}^{2}$, where $\mathcal{K}$ has the dimensions of a force constant, $k$ is Boltzmann's constant, and ${T}_{C}$ is in absolute units. A least-squares fit, based on $\ensuremath{\Delta}z$ and ${T}_{C}$ for ten different ferroelectrics, gives $\frac{\mathcal{K}}{2k}=(2.00\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{4}\ifmmode^\circ\else\textdegree\fi{}$K ${\mathrm{\AA{}}}^{\ensuremath{-}2}$. In addition, the spontaneous polarization ${P}_{s}$ is found to be related to $\ensuremath{\Delta}z$ by the equation ${P}_{s}=(258\ifmmode\pm\else\textpm\fi{}9)\ensuremath{\Delta}z$ \ensuremath{\mu}C ${\mathrm{cm}}^{\ensuremath{-}2}$. $\mathcal{K}$ is discussed in terms of the interatomic force constant along the polar axis.