Dielectric and Piezoelectric Properties in the Ternary System of Pb(Zn_1/3Nb_2/3)O₃-Ba(Zn_1/3Nb_2/3)O₃-PbTiO₃

Abstract

The semiclassical nuclear properties have been studied in the framework of the energy density formalism by choosing two energy densities, one containing derivative terms up to second order and the other also containing fourlh-order derivative terms. The surface energy density in each of the two cases can be suitably approximated so that the Euler-Lagrange (EL) equations in a semi-infinite nuclear medium (SINM) lead to a pure Fermi distribution (F-1) for the density. The importance of the inclusion of the fourth-order derivative terms in the energy density to reproduce the correct surface energy and the correct behaviour of the density in the outer part of the surface has been shown explicitly. The variations of lhe central density pa and lhe surface thickness (I with the sue of the nucleus have been studied under the assumption that the departures E and A of these quantities from their respective SINM values are small. The restricted simple nature of the surface energy density resulting from the imposition of an F-1 distribution of density in a SMM has the advantage of describing the variations E and A in terms of the small ratio ( I between the surface thickness and the half-density radius in a general way, independent of the charactefistics of the energy density used. This study shows that the correct behaviour oi the variations of E and h cannot be reproduced in an expansion in powers of ( I and retaining the first few terms. It is further observed that the lower-order terms in the energy in an expansion in powers of ( I are quite important for a correct description of the departures E and A, at least in the region ( I aO.1, although these lower-order terms are not so important as far as the total energy is concerned. A comparison of the variations of the surface thickness with the size of the nucleus for the two different energy densities shows that the variation h is much smaller for the fourth-order case, in conformity with the fact that the surlace thickness is almost independent of the sue of the nucleus and thereby favours an energy density containing derivative terms up to fourth order over an energy density having only second-order derivative terms.A-"'. In the work of Brack el a/ (1985), the energy density lunctional resulting from the semiclassical expansion upto A4 t e r m has been used for the leptodermous expansion of the total energy. However, in their work, they have not considered the variation of a and v , and have taken fixed values for them. On the other hand, the B Behera and T R Routray

Heterovalent andA-atom effects inA(B′B″)Bellaïche1, Padilla2, Vanderbilt3 1999Phys. Rev. B613290View full textAdd to dashboardCite

“…This points to the importance of lattice relaxation in heterovalent alloys. As usual in LDA calculations, the calculated lattice constants agree within 1-2% with the experimental lattice constants of 4.096 Å for BZN 39,40 and 4.04 Å for PZN 41 , the experimental values having been measured at room temperature in the cubic paraelectric phase.…”

Study of structural phase transitions in solid-solution (1 −x)PZN-xPT relaxor ferroelectric using Raman scattering

“…21 The sample of PZN-5%PT was poled in the (001) direction with a d.c. bias of 20 kV cm 1 from 200°C T × T m to room temperature and was therefore denoted poled compared with the unpoled specimen PZN-2%PT. The samples were prepared by the molten flux method with excess lead oxide (PbO) as described.…”

Effects of addition of BT on structural phase formation and electrical properties of relaxor ferroelectric Pb(In0.5Nb0.5)(1−x)Ti(x)O3 ceramics

“…However, the average lattice parameter decreases with increasing PT concentration for both of PINT and PBINT ceramic systems. It is expected that diffusion of the smaller Ti cation into B-site results in a decrease in lattice constant and the partial substitution of the larger Ba cation into Asite causes an increase in the average lattice parameters [19][20][21]. From the results of the XRD patterns and the lattice parameters, it is believed that the MPB of the PBINT system lies between the compositions x = 0.2 and 0.3.…”