Green's-function theory of ferroelectric phase transitions in hydrogen-bonded triglycine sulfate with the pseudospin-lattice coupled-mode model: A unified theory of structural phase transitions. I. Static and dynamic properties.

Abstract

A pseudospin-lattice coupled-mode (PLCM) model and the statistical Green's-function theory have been used to explain the static as well as the dynamic properties of ferroelectric phase transitions in triglycine sulfate (TGS) and in its deuterated and undeuterated families. An attempt to settle the long-standing controversy over the coexistence of both order-disorder and displacive phase transitions in TGS and in many other H-bonded crystals (as observed from the studies of different static and dynamic properties) has been made by expressing the transition mechanism in these crystals as a ``mixed'' type rather than a purely order-disorder or a purely displacive type. This mixed behavior is due to the importance of the pseudospin-phonon and the higher-order anharmonic phonon-phonon interaction terms. The pseudospins are considered to be associated with the local ordering (rotation, displacements, etc.) of some ions or groups in the lattice. This makes the mechanism of structural phase transitions, in general, very complicated.As a consequence, the calculated expression for the total phonon self-energy is found to contain an extra term in addition to that which appears in the existing theoretical calculations by Cowley and others describing purely displacive phase transitions with phonon-phonon interaction only. This additional self-energy term is found, in principle, to be responsible for the observed deviations of some thermal and dielectric properties of TGS from the Landau theory, the existence of the ``double peak'' in the NMR or NQR relaxation times in TGS and in other crystals, and the appearance of both order-disorder and the displacive type of behavior in many crystals. This additional part of the self-energy is also found to be related to the ``central peak'' phenomenon. Depending on the strengths of the pseudospin-phonon interaction terms, this part of the self-energy might also be responsible for the crossover from order-disorder to displacive behavior observed in some structural transitions. This is also supported by recent EPR and other experimental observations made by M\"uller. The theoretical expressions derived for the transition temperature (${T}_{c}$), dielectric constant (\ensuremath{\epsilon}'), spontaneous polarization (${P}_{s}$), Curie-Weiss constant (C), renormalized phonon frequency, etc., have been fitted with the corresponding experimental data to find a single set of Blinc--de Gennes model parameters for the TGS family. Finally, the unified character of the PLCM model in explaining various salient features of structural phase transitions in crystals has been discussed, and supports the conclusion of our previous work.