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 $\Delta z$ 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 $\Delta z$ and the Curie temperature $T_C$. This relation has been form $T_C=\left(\frac{\mathcal{K}}{2k}\right){\left(\Delta z\right)}^2$, 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 $\Delta z$ and $T_C$ for ten different ferroelectrics, gives $\frac{\mathcal{K}}{2k}=(2.00\mathrm{}\pm 0.09)\times {10}^4°$K ${\mathrm{\AA }}^{-2\mathrm{}}$. In addition, the spontaneous polarization $P_s$ is found to be related to $\Delta z$ by the equation $P_s=(258\mathrm{}\pm 9)\Delta z$ μC ${\mathrm{cm}}^{-2\mathrm{}}$. $\mathcal{K}$ is discussed in terms of the interatomic force constant along the polar axis.