On a possible unified theory of ferroelectricity

Abstract

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.

The Unified Model Description of Order-Disorder and Displacive Structural Phase Transitions

“…For a complete description of SPT one has to take into account the both above mentioned mechanisms simultaneously -within the framework of a universal model -as was originally proposed and done in [1,2]. In the next section we are going to present the main features and results of such a description.…”

“…The nature of the SPT described within such a model was examined by applying both the Curie-Weiss (molecular-field) and the self-consistent phonon approximations ([cf. [1,2,7]). By comparing the results of the both approximations it has been shown that for a weak lattice coupling (f 0 ≪ 1) the character of the SPT is of the order-disorder type, which is more consistently described by the molecular-field approximation; for a strong lattice coupling (f 0 ≫ 1) the SPT has to be related to the displacive type, which can be reasonably described by the self-consistent phonon approximation.…”

“…Among numerous attempts to develop a unified microscopic theory of both displacive and order-disorder structural phase transitions (SPTs), on the occasion of the 60th anniversary of Prof. Stasyuk's birthday, our modest contribution [1][2][3][4][5][6][7] to the same problem in ferroelectric phase transitions is reviewed and partly innovated. To expose as clear as possible the basic proposals for a unified description of SPT-systems and to better comprehend this peculiar problem in connection with its prospective development, we shall try to keep mostly to the original studies of the co-authors' group, with reference to other similar approaches cited in the co-authors' publications.…”

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A series of co-authors' studies [1][2][3][4][5][6][7] devoted to the unified model description of structural phase transitions (SPT) in ferroelectrics and related materials are reviewed and partly innovated.Starting from a general Hamiltonian of pair-coupled anharmonic (quartic) oscillators, together with the concept of local normal coordinates, a unified model description of both order-disorder and displacive types of SPT-systems is proposed. Within the framework of the standard variational procedure, a hybridized pseudospin-phonon Hamiltonian is formulated by introducing variables corresponding to phonon, magnon-like(flipping) and nonlinear(domain-wall-like) displacements of atoms participating in SPT.

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“…A series of co-authors' studies [1][2][3][4][5][6][7] devoted to the unified model description of structural phase transitions (SPT) in ferroelectrics and related materials are reviewed and partly innovated.…”