Theory of Ferroelectric Phase Transitions in Pure and Mixed Perovskites.
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Theory of Ferroelectric Phase Transitions in Pure and Mixed Perovskites. Yizhak Yacoby and Yakov Girshberg Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem Israel. ABSTRACT We present a comprehensive model of ferroelectricity in oxygen perovskite crystals that account quantitatively for both displacive like and order-disorder like properties. The model assumes that in the paraelectric phase, the system has a soft mode, interacting with spontaneous disordered off-center displacements. The resulting theory is shown to quantitatively explain the properties of two representative perovskites: KNbO3 and PbTiO3. We have further extended this theory to explain the properties of mixed incipient ferroelectrics with small concentrations of ferroelectricity inducing ions such as KTa1-xNbxO3. The model quantitatively reproduces the basic experimental data in the quantum regime: the temperature dependence of the inverse dielectric function, the impurity and temperature dependence of the renormalized soft mode vibrational frequency and the impurity concentration dependence of the transition temperature Tc. In particular we show that, the critical concentration for Tc=0 is determined by the ion tunneling frequency, the bare soft mode parameters and the pseudospin - phonon coupling constant. INTRODUCTION Numerous models have been proposed to explain the properties of ferroelectric oxygen perovskite crystals[1-4]. The problem is that each model accounts for some properties but not for many others. The difficulty to explain all the important properties simultaneously is a result of the fact that these systems display both displacive like and order-disorder like properties(see reference [5] and references therein). On the one hand, the systems display soft mode behavior as expected from displacive like models but the frequency of the soft mode does not extrapolate to zero at the extrapolated second order phase transition temperature, Tc. In some cases as in KNbO3 for example the soft mode frequency squared extrapolates to zero at about 100K[6] but the transition temperature Tc=620K[1]. The temperature dependence of the dielectric constant obeys the Curie – Weiss law with a large Curie – Weiss constant of the order of 105K[1]. This is typical of displacive type models. On the other hand, these systems display a central peak[7, 8] with an integrated intensity that grows critically and a width that goes to zero as the system approaches Tc. Attempts to explain this behavior within a displacive model have failed. Raman experiments have shown that the Raman selection rules in the paraelectric phase break down[9]. Diffuse x-ray scattering[10] experiments have detected scattering in planes in reciprocal space perpendicular to the main crystallographic axes. All these suggest an order-disorder like behavior. Ferroelectric phase transition of incipient ferroelectric crystals, doped with ions, that drive them into the ferroelectric phase are particularly interesting because at small concentrations Tc is close to 0K and quantu
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