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

Sodium-potassium niobate [Na 0.5 K 0.5 NbO 3 ] powders were prepared following the conventional mixed oxide method. An orthorhombic XRD pattern, consistent with single-phase Na 0.5 K 0 . 5 NbO 3 , was obtained after calcination at 900°C for 6 h. Introducing 5 mol% excess Na 2 CO 3 and K 2 CO 3 into the starting mixture allowed milder calcination conditions to be used, for example 800°C for 2 h. Primary particles in 5 mol% excess samples were cuboid, with maximum sizes of ∼2.5 μm. Equiaxed 0.3-0.4-μm particles were formed for non-excess powders, and also for powders prepared with 1 and 3 mol% excess alkali carbonates. The results suggest liquid formation during calcination of the excess 5-mol% starting powders.

Effect of Calcination Conditions and Excess Alkali Carbonate on the Phase Formation and Particle Morphology of Na0.5K0.5NbO3 Powders

Magnetoelectric composites with composition x BaTiO 3 +(1− x )MnFe 1.8 Cr 0.2 O 4 in which x varies as 1, 0.85, 0.7, 0.55 and 0 were prepared by a standard ceramic technique. X-Ray analysis confirms single-phase formation in x =1 and x =0 compositions whereas the presence of both phases in x =0.85, 0.7 and 0.55 compositions. The dielectric constant (e′), loss tangent (tan δ) and AC conductivity ( σ AC ) of the composites have been investigated in the frequency range 100 Hz–1 MHz and also in the temperature range 30–400 °C. The results obtained are interpreted in terms of a polaron hopping mechanism. Static magnetoelectric conversion factor (d E /d H ) as a function of magnetic field was measured in x =0.85, 0.70 and 0.55 compositions. The maximum value of d E /d H obtained was 150 μV/(cm −1 ×Oe) for x =0.85 composition.

AC conductivity and magnetoelectric effect in MnFe1.8Cr0.2O4-BaTiO3 composites

The sol-gel processing of lead-free (Na,K) NbO3 ferroelectric films was studied. Sodium ethoxide (NaOC2H5) and potassium ethoxide (KOC2H5) were prepared by reacting solid Na and K with ethanol (99.7%) in a solvent of 2-methoxyethanol. 0.5-μm-thick (Na,K)NbO3 thin films with orthorhombic perovskite structure were obtained by pyrolyzing at 400°C and annealing at 800–900°C. The films had relatively dense and uniform microstructure with grain size of about 50 nm, whose ferroelectricity was proved by the P-E hysteresis loop measurement. It was found that excess K was effective to reduce the annealing temperature for the crystallization of sol-gel-derived (Na,K)NbO3 thin films.

Sol-gel processing of lead-free (Na,K)NbO3 ferroelectric films

Pellets of ceramic Na1−xKxNbO3 (x = 0, 0.2 and 0.5), were prepared by conventional solid-state reaction method. Prepared samples were characterized using XRD and SEM. The frequency and temperature variation of dielectric constant, loss tangent and dielectric conductivity of prepared samples were measured in the frequency range from 10 KHz-1 MHz, and in the temperature range from 50–250°C for x = 0.2 and 0.5, and between 50 and 480°C for x = 0 compositions. It was observed that the dielectric constant and loss tangent decrease, and conductivity increases with increasing frequency. Near the transition temperature the material shows anomalous behaviour for the observed properties, and the peaks of dielectric constant and loss tangent were observed shifting towards lower temperature with increasing frequency.

/pdf/dielectric-properties-of-na1-xkxnbo3-in-orthorhombic-phase-1mq9z2fnzk.pdf

Dielectric properties of Na1-xKxNbO3 in orthorhombic phase

The soft mode dynamical model has been used to study the dielectric properties of Perovskite-type crystals. The model Hamiltonian proposed by Pytte has been modified and designed in terms of creation and annihilation operators. The correlations appearing in the dynamical equation have been evaluated using double time thermal retarded Green’s function and Dyson’s equation. Without any decoupling the higher order correlations have been evaluated using the renormalized Hamiltonian and thus, all possible interactions among phonons have been taken into account. The expressions for phonon frequencies and widths have beenMcalculated. Using appropriate parameters the softening of different modes at different transition temperatures give rise to a series of transitions from cubic to tetragonal, orthorhombic or trigonal phases. The significantly temperature-dependent modes are considered responsible for damping constant, dielectric constant, tangent loss and attenuation constant for these crystals. The dielectric properties are directly related to the optical phonon frequencies and widths and acoustic attenuation to the acoustic and optical phonon widths. Using suitable approximations, the model explains the experimental results on dielectric properties and acoustic attenuation reported for LiNbO3, SrTiO3, BaTiO3 and LaAlO3.

/pdf/dielectric-properties-of-perovskite-crystals-3a1epgkd9k.pdf

N. S. Panwar

Papers

Dielectric properties of Na1-xKxNbO3 in orthorhombic phase

Dielectric properties of perovskite crystals