Microscopic theory of the lattice dynamics and the nature of the ferroelectric instability in crystals

A brief review is given of model theories of the displacive structural instability in ferroelectrics. Particular attention is paid to the idea of compensation of the contributions of the short-range forces and the long-range internal field dipole forces to the square of the frequency of critical lattice vibrations. A vibronic theory of ferroelectricity is also discussed and its shortcomings are identified. A detailed analysis is made of the modern microscopic theory of lattice dynamics and exact expressions are derived for the force matrix governing the phonon spectrum of a crystal. The theory is discussed in the specific case of polar nonmetallic crystals. The example of semiconducting ferroelectrics from the group of IV–VI compounds is used to formulate rigorously the microscopic problem of the causes of the structural instability of such compounds on the basis of the exact expressions for the matrix of the force constants.