Grain-size effect on ferroelectricPb(Zr1−xTi

Synthesis of nano-structured Bi1−xBaxFeO3 ceramics with enhanced magnetic and electrical properties

“…This could be interpreted by high resistivity of synthesized BaBFO samples under very large electric field region. Enhancing of spontaneous polarization with increasing calcination temperature can be a consequence of either larger particle size [48] or induced strain to the lattice by introducing of the Ba 2+ in BFO structure. The variation of permittivity () and dielectric loss (tan ) with temperature for BaBFO-850 sample are shown in Fig.…”

Size dependence of nanostructures: Impact of bond order deficiency

“…After that, Jiang and Bursill [377] assumed the phenomenological LandaueGinzburgeDevonshire (LGD) coefficients in the Gibbs energy to change with particle size to solve this problem. Huang et al [378] combined the LGD phenomenological theory and the BOLS correlation to study the size effect of ferroelectrics. The model assumes that the surface bond contraction occurs only within three outermost nanoferroelectric layers whereas the core interior remains ferroelectric [379].…”

General approach for the description of size effects in ferroelectric nanosystems

“…It should be noted, that strain fields (23b) and (24b) satisfies compatibility conditions (20) for the case of onedimensional distribution of polarization in the form P 3 (x 3 ) and P 3 (x 1 ) respectively, since conditions (20) for onedimensional distributions is reduced to more simple forms, q 2 u 11 /qx 3 2 = q 2 u 22 /qx 3 2 = 0 and q 2 u 33 /qx 1 2 = q 2 u 22 /qx 1 2 = 0 respectively. The nontrivial stress components for different boundary conditions are summarized in Table 3.…”

“…It is worth to note the enormous achievements of both the phenomenological [14] and microscopic [15] theories, their recent advances in different fields like the description of nanorods [16,17], size effects in thin films [18,19], ferroelectric nanoparticles [20][21][22]; flexoelectric effect influence on the intrinsic properties [23,24] and response [25][26][27] of the nanosystems; the developed analytical model accounting for depolarization field as well as the formation of misfit dislocations [28][29][30]. However, despite this progress, the phenomenological theory lacks a general method, suitable for the solution of vast variety of different problems of ferroics description.…”