Thermodynamics of Ferroelectricity

This chapter is about the macroscopic theory of ferroelectrics, which is based on the Landau theory of phase transformations. It was first proposed by Landau in the 1930s to study a wide range of complex problems in solid-state phase transformations in general, and ordering phenomena in metallic alloys in particular (Landau and Lifshitz 1980). It was further developed and brought to the realm of ferroelectrics by Devonshire (1949, 1951). It has since then proven to be a very versatile tool in analyzing ferroelectric phenomena, and has become a de facto tool of analysis among ferroelectricians.

At the heart of the Landau theory of phase transformations is the concept of order parameter, which was first proposed in the context of order–disorder transformation involving a change in the crystal symmetry. In such systems, the material of interest transforms from a high-symmetry disordered phase to a low-symmetry ordered phase (de Fontaine 1979; Ziman 1979). The so-called broken symmetry of the crystal due to ordering is represented by an order parameter. Landau has shown that the (Helmholtz) free energy of an order–disorder transformation can be expressed very simply as a Taylor series expansion of the order parameter describing the degree of order (or disorder). Generally, the order parameter can be any variable of the system that appears at the phase transition point. In the case of ferroelectrics, it is the spontaneous polarization. Originally, the Taylor expansion of the order parameter was intended to be limited to temperatures close to the phase transformation temperature, as any mathematical series has a radius of convergence. However, quite oddly, it is a well-established fact that the free energy functional provides a very good approximation even at temperatures far below the transition temperature once higher-order expansion terms are included.