2.1 Instabilities in Crystals with a Centrosymmetric Prototype

Temperature and/or pressure determine the structure (structural phase) of crystals. At high temperature the materials usually show highest symmetry. This phase is called the prototype phase.

Ferroelectricity is one of the possible effects caused by asymmetry of a material where the prototype phase is centrosymmetric. In the following an overview is given on the different types of asymmetry that evolve if the temperature drops beyond a certain level, the Curie Temperature $T_C$.

Typically, asymmetric structures show two or more states with the same energy, and depending on the energy barrier between them, one of these states can transform easily into the other, thus forming an instability in the lattice structure. If there are only two possible positions for the center ion, and both of them are situated at one of the symmetry axes of the lattice, the instability is called uniaxial.

An overview of the different types of uniaxial instabilities is given in Fig. 2.1.

Figure 2.1: Fundamental types of uniaxial instabilities of centrosymmetric crystals (after Lines and Glass [LG96])

If the material is biaxial, any combination of the phase transitions outlined above is possible. This means that a material can show e.g. ferroelectric properties in one direction and antipolar ones into the other. Some of these possible transitions are outlined in Fig. 2.2

Figure 2.2: Fundamental types of biaxial instabilities of centrosymmetric crystals (after Lines and Glass [LG96])