To explain the large isotope effect on the transition temperature in KH2P04, the tunnel­ ing motion of the protons in hydrogen bonds is considered and a theory of the phase transi­ tion is developed under the assumption that the ferroelectric behavior of this substance is due to cooperation of the ionic displacements, the interactions between ions and protons and the tunneling motion of protons. The relation between the present theory and the Slater model or the Blinc model is discussed. § I. Introduction In spite of the considerable amount of investigation made from the theo­ retical as well as the experimental side, the microscopic mechanism of the phase transition in KH2P04 and isomorphous crystals does not seem to be clearly un­ derstood. If . we classify the ferroelectric substances roughly into two groups, displacive and order-disorder type ferroelectrics, then KH2P04 will certainly belong to the latter group. However, the experimental data accumulated so far do not really give us a definite molecular picture of the phase transition, but sometimes reveals obvious inconsistencies among observed quantities. The main object of the present paper and a forthcoming one is to organize the somewhat divergent observed facts from the theoretical point of view and to suggest some experiments which might be helpful in attaining a full understanding of the phenomena. The crystal structure of KH2P04 (which will be abbreviated as KDP here­ after) is the so-called tetragonal diamond type. A characteristic feature of this structure is the existence of hydrogen bonds connecting two P04 tetrahedra, which run almost perpendicularly to the direction of the ferroelectric c axis. In the ferroelectric phase, the magnitude of the saturated polarization Ps is well accounted for by making use of the observed values for the displacements of ions K+I, p+ 5 and o- 2 along the c axis relative to their symmetric positions. 2 ),s) Therefore the hydrogen bonds do not contribute any appreciable dipole moments to the saturated polarization, and hence the essential unit of the dielectric prop­ erties in this crystal is the dipole moment of the complex [K-P04] as shown in Fig. 1. If KDP is of an " order-disorder " type of ferroelectric, that is, if the phase transition is caused by order-disorder arrangements of the dipole moments, the two configurations of the complex [K-P04] denoted as (A) and

Theory of Ferroelectric Phase Transition in KHzP04 Type Crystals. I

In this paper, we investigated the newly found order-disorder ferroelectrics PbHPO4 along with its deuterated analogue PbDPO4. Because the major contribution of the spontaneous polarization is the dipoles forming by the proton (or deuteron) ordering, not the displacements of heavy atoms as in the case of KDP-type crystals. Therefore in the Hamiltonian, the influence of the lattice vibration may not be considered, but the 4th order interaction of pseudo-spin is included. By introducing the undetermined-constant into the Green's function method, we carried out the spontaneous polarization of PbHPO4 and PbDPO4 crystals, the results are good agreement with the experimental data.

Green's function theory of phase transition in PbHPO4 and PbDPO4 ferroelectrics

The concentration dependence of the ferroelectric transition temperature Tc of single crystals of the solid solution Tris-sarcosine calcium chloride1-x bromidex is studied experimentally by measurement of the static dielectric constant eb and described by the empirical relation Tc(x) = Tc(0) (1 x/xcc)1/2. The Ising model with transverse field and the model of coupled anharmonic oscillators are used to explain the concentration dependence of the transition temperature Tc. The influence of quantum fluctuations is discussed.

Ferroelectric properties of single crystals of solid solutions of tris-sarcosine calcium chloride-bromide

The infrared reflectivity spectra polarised in a direction perpendicular to the c axis of potassium dihydrogen phosphate were studied for both the ferro- and paraelectric phase, over a wide temperature range: 10 to 420K. The reflectivity spectra are fitted to the factorised form of the dielectric function. The temperature dependences of the optical mode parameters (frequencies, dampings and oscillator strengths) are reported for both phases. The analysis shows the activity of a low-frequency heavily damped mode in addition to the five observed lattice modes in the paraelectric phase. The parameters of the low-frequency mode, assigned to the proton collective motion, are studied in detail.

Temperature dependence of the lattice modes polarised in a direction perpendicular to the c axis of potassium dihydrogen phosphate

A pseudospin-phonon coupled model in double-time Green's function theory has been developed to investigate the dielectric susceptibility of the ferroelectric-dielectric superlattice BaTiO3/SrTiO3 (BTO/STO). As the pseudospin-pseudospin and pseudospin-phonon interactions increase, the dielectric susceptibility changes from a narrow shape into the strong and broad shape with the peak shifting to a higher temperature region. With increasing pseudospin-phonon interaction in the BTO layer and at small pseudospin-pseudospin interaction in BTO layer, the dielectric susceptibility was sensitively adjusted around the transition temperature of strontium titanate, and at large pseudospin-pseudospin interaction in the BTO layer, the dielectric susceptibility was increased in the high-temperature region covering the tetragonal-cubic transition temperature of barium titanate. A critical period of 10/10 in the BTO/STO superlattice has been obtained, which is in good agreement with the experimental data of 40 A, for ten unit cells.

Dielectric Characteristics and Layer Periodic Effects of Ferroelectric Superlattice BaTiO3/SrTiO3

Green's-function theory of phase transitions in hydrogen-bonded ferroelectric crystals with pseudo-spin-lattice coupled mode model

Green's-function theory of phase transitions in the hydrogen-bonded PbHPO 4 -type ferroelectrics with pseudospin model

Statistical Green's function theory has been successfully applied to study the ferroelectric phase transitions in the Rochelle Salt and its deuterated form with two sub-lattice pseudo-spin model containing spin-phonon interaction terms. The Blinc-de Gennes model parameters have been calculated for both of the salts. A phenomenological explanation of the isotope and the impurity dependence of the transition temperatures has also been sought from our calculations. The origin of non-logarithmic behaviour of the heat capacity has been attributed to the strong proton-phonon and anharmonic interactions. Finally, renormalized phonon frequency and the temperature dependence of the soft mode frequency have been studied theoretically. The present study suggests that phase transitions for the Rochelle Salt and its deuterated variety can be understood by a displacive mechanism.

Suvra Ganguli

Papers

Green's-function theory of phase transitions in hydrogen-bonded ferroelectric crystals with pseudo-spin-lattice coupled mode model

Green's-function theory of phase transitions in the hydrogen-bonded PbHPO 4 -type ferroelectrics with pseudospin model

Study of Ferroelectric Phase Transitions in the Rochelle Salt with the Pseudo-Spin-Lattice Coupled Mode Model

On the transverse electrical susceptibilities of KDP type crystals