A Study on Effective Charge in the Dipole Theory of Ferroelectrics

Abstract

The effective charge used in dipole theory of ferroelectrics has been investigated theoretically. Particular emphasis is placed on its temperature dependence. Employing the concept of the statistical theory of ferroelectricity, it is shown that in the dipole theory the effective charge corresponds to the temperature, and the relation between them has been established in a statistical way within the framework of dipole theory. The temperature dependence of the effective charge has been determined in detail by carrying out the numerical calculations and the results obtained have been discussed. As a result, it is found that in the ferroelectric phase the effective charge depends strongly on temperature as the long-range dipole interaction becomes large and this inclination is more remarkable in the vicinity of the transition point, whereas in the paraelectric phase the effective charge is nearly independent of temperature over a wide range of it, except near the transition point.Es wird die in der Dipoltheorie der Ferroelektrika benutzte effektive Ladung theoretisch untersucht. Besonderes Gewicht wird auf ihre Temperaturabhangigkeit gelegt. Mit dem Konzept der statistischen Theorie der Ferroelektrizitat wird gezeigt, daD in der Dipoltheorie die effektive Ladung der Temperatur entspricht, und es wird die Beziehung zwischen ihnen in einer statistischen Weise im Rahmen der Dipoltheorie aufgestellt. Die Temperaturabhangigkeit der effektiven Ladung wird ausfiihrlich durch numerische Rechnungen bestimmt, und die erhaltenen Ergebnisse werden diskutiert. Als Ergebnis wird gefunden, daD in der ferroelektrischen Phase die effektive Ladung stark von der Temperatur abhangt, da die langreichweitige Dipolwechselwirkung groD wird und dieser EinfluD in der Niihe des tfbergangspunktes starker ist, wahrend in der paraelektrischen Phase die effektive Ladung nahezu unabhingig von der Temperatur in einem grol3en Bereich mit Ausnahme der Nahe des tfbergangspunktes ist.

Effects of Ba2+/Sr2+ ratio on the microstructure, dielectric and ferroelectric properties of BaxSr(1−x)TiO3 films prepared by micro-arc oxidation

“…It can also be seen that the dielectric constant of the BST films increased with the increase in Ba 2+ content in all the measured frequency ranges, shown in Figure 7. This is because the spontaneous polarizability of Ba 2 + is larger than that of Sr 2+ , and the displacement of Ba 2+ to Ti 4+ is larger than that of Sr 2+ to Ti 4+ in a local field [39,40]. In addition, it can be seen from Figure 5 that the thickness of the BST film derived from the electrolyte with a Ba 2+ concentration of 0.8 M is more than twice that from 0.6 and 0.7 M. According to Equation (1), the dielectric constant is proportional to the thickness of the film.…”