Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics

As the grain size decreases to the nanometer range, the characteristics of the ferroelectric nanoceramic can be ultimately determined by the competition between two effects: the intrinsic effect that is associated with the local properties of the grain boundary and the extrinsic effect that arises from the dynamics of domain structure which is highly influenced by the depolarization field caused by the grain boundary. In this work we investigate such a competition with a phase-field simulation based on the time-dependent Ginzburg-Landau kinetic equation. The study is performed on poled/unpoled nanoceramics under high- and low-amplitude bipolar alternating electric field with selected grain size and loading frequency. Our calculations for poled $\mathrm{BaTi}{\mathrm{O}}_3$ at 100 Hz show that, for the grain size from 170 to 50 nm, its properties are dominated by the extrinsic effect, and from 50 to 10 nm, they are dominated by the intrinsic one. As the grain size decreases, the dielectric and piezoelectric constants at the remnant state continuously rise in the extrinsic-dominated region and then drop sharply in the intrinsic-dominated region. Our frequency calculations from 10 to 2500 Hz at the grain size of 100 nm indicate that the high-frequency behavior is very similar to that of the small grain-size, intrinsic-dominated one, whereas the low-frequency behavior is closely related to that of the large grain-size, extrinsic-dominated part, with the demarcation line occurring around 400 Hz. For the unpoled ceramics under small-signal loading, the intrinsic effect is dominant over the entire range of grain size and frequency.

Figure 1

The schematic of the polycrystalline model.

Figure 2

The computed grain-size dependence of (a) the hysteresis loop and (b) the butterfly loop of the poled nanoceramics with varied grain size.

Figure 3

The grain-size dependence of remnant polarization, coercive field, and actuation strain of the poled nanoceramics.

Figure 4

The grain-size dependence of the differential dielectric constant at the remnant state and coercive state, and the remnant piezoelectric constant for poled nanoceramics.

Figure 5

The grain-size dependence of the remnant dielectric constant for unpoled nanoceramics.

Figure 6

The remnant-state polarization distribution of poled $\mathrm{BaTi}{\mathrm{O}}_3$ nanoceramic with the grain size of (a) 15 nm and (b) 110 nm.

Figure 7

The computed frequency dependence of (a) the hysteresis loop and (b) the butterfly loop.

Figure 8

The frequency dependence of the coercive field and remnant polarization for poled nanoceramics

Figure 9

The frequency dependence of the differential dielectric constant at the remnant state and coercive state, and the remnant piezoelectric constant for poled nanoceramics.

Figure 10

The frequency dependence of the remnant dielectric constant of the unpoled $\mathrm{BaTi}{\mathrm{O}}_3$ nanoceramic.

Figure 11

The remnant-state polarization distribution of poled $\mathrm{BaTi}{\mathrm{O}}_3$ nanoceramic with the low frequency of 10 Hz with 100 nm grain size.

Figure 12

The remnant-state polarization distribution of poled $\mathrm{BaTi}{\mathrm{O}}_3$ nanoceramic with the high frequency of 1000 Hz with 100 nm grain size.