The self-consistent phonon theory (SCPT) is formulated using Green's function method to describe both the dynamical and thermodynamical properties of highly anharmonic crystals and to investigate the dynamical stability of anharmonic lattices. The rcsults of calculations for the phonon spectrum, elastic constants, PV-diagrams, etc., ate presented for a simple model of the fcc lattice. The phenomenon of lattice instability due to the volume fluctuations at sufficicntly high temperatures oras a consequence of a high zero-point energy is investigated. An application of the SCPT to structural (or ferroeleetric) phase transitions (PT) is also discussed. In that case taking into account the fluetuations of the order parameter by the SCPT results in the renormalization of the Landau expansion and in a first order PT. A unified model for ferroelectric PT, where both the statistical disorder and the instability of latticc in the PT are taken into account, is shortly reviewed.

The properties of the f.c.c. lattice with central nearest neighbour interaction are investigated on the basis of the dynamical theory of the anharmonic crystal developed in [l]. It is shown that in the case of constant external pressure the lattice becomes unstable a t sufficiently high zero point energy or temperature. The behaviour of the physical quantities in the vicinity of the unstability point is investigated.Ha ocnoBe jmHaMmecKofi Teopm aHrapMoHHsecHofi pemeTm, p a 3 s~~o i i paHee [ 11, HCCJIeHymTCR CBOfiCTBa rpaHe~eHTpHpOBaHHOfi HYGHY~CKOZ~ PelueTKH C napHbIM 4eHTpanhHhIM B3aMMOAefiCTBHeM 6 n~x a i i m~x COCenefi. nOKa3aH0, YTO IIpH no-CTOHHHOM BHeUIHeM HaBJIeHMM PeIIIeTKa HeyCTOfiYHBa npH HOCTaTOYHO 60~1hmofi 3HeprllH HyJIeBbIX K0~1e6aHElfi MJIH J&OCTaTOYHO BbICOKOfi TeMnepaType. PaCCMO-TpeHO IlOBeHeHHe @H3HYeCKHX BeJIMYMH B~J I H~H OT T 0 9 K H HeYCTOfi YHBOCTM peIueTIEM.

The theory of lattice dynamics of an anharmonic crystal is developed without using the harmonic approximation as starting point. On the basis of the double-time Green's function method the self-consistent system of equations determining the equilibrium parameters of the lattice, the vibrational frequency and their damping is obtained. The free energy and the internal energy of an anharmonic crystal are calculated.

A possible unified theory which would describe both "order-disorder" and "displacive" type ferroelectrics is proposed. The ferroelectric phase transitions are considered as a consequence of the dynamical instability of the lattice as well as of the statistical disorder of active (tunnelling) atoms between several equilibrium positions insthe lattice. The self-consistent equations for both order parameters (average displacement and average localization) is obtained and solved numerically. The order of the phase transition depends on the two particle potential by single particle potential ratio, while the actual type of ferroelectricity is a consequence of the mutual competition between the two order parameters.

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