Relaxor-ferroelectric crossover in $(\mathrm{B}{\mathrm{i}}_{1/2}{\mathrm{K}}_{1/2})\mathrm{Ti}{\mathrm{O}}_3$: Origin of the spontaneous phase transition and the effect of an applied external field

The temperature evolution of polar order in an $A$-site complex perovskite $(\mathrm{B}{\mathrm{i}}_{1/2}{\mathrm{K}}_{1/2})\mathrm{Ti}{\mathrm{O}}_3$ (BKT) has been investigated by measurements of dielectric permittivity, depolarization current, and stress-stain curves at elevated temperatures. Upon cooling from high temperatures, BKT first enters a relaxor state and then spontaneously transforms into a ferroelectric state. The analyses of temperature and frequency dependence of permittivity have revealed that polar nanoregions of the relaxor phase appear at temperatures higher than $560{}^{\circ }\mathrm{C}$, and also that their freezing at $296{}^{\circ }\mathrm{C}$ triggers the spontaneous relaxor-ferroelectric transition. We discuss the key factors determining the development of long-range polar order in $A$-site complex perovskites through a comparison with the relaxor $(\mathrm{B}{\mathrm{i}}_{1/2}\mathrm{N}{\mathrm{a}}_{1/2})\mathrm{Ti}{\mathrm{O}}_3$. We also show that application of biasing electric fields and compressive stresses to BKT favors its ferroelectric phase, resulting in a significant shift of the relaxor-ferroelectric transition temperature towards higher temperatures. Based on the obtained results, electric field-temperature and stress-temperature phase diagrams are firstly determined for BKT.

Figure 1

Temperature dependence of (a) real part ε′ and (b) imaginary part ε″ of dielectric permittivity of BKT measured at varying frequencies from ${10}^3$ to ${10}^6\mathrm{Hz}$.

Figure 2

Inverse of dielectric permittivity as a function of temperature at ${10}^6\mathrm{Hz}$ for the relaxor state of BKT. Solid line is the fittings to the $\mathrm{C}\text{−}\mathrm{W}$ law [Eq. (2)]. The inset shows the squared residual of the fitting to the $\mathrm{C}\text{−}\mathrm{W}$ law as a function of temperature. The arrow in the inset presents the temperature for the onset of deviation from the $\mathrm{C}\text{−}\mathrm{W}$ low.

Figure 3

Relationship between the inverse of the temperature of the dielectric maximum of BKT and the measurement frequency. The solid line is the fittings to the V-F law [Eq. (3)].

Figure 4

Stress-strain behavior of BKT measured at varying temperatures. Arrows indicate the loading direction.

Figure 5

Remanent strain of BKT as a function of temperature.

Figure 6

Remanent polarization of BKT as a function of temperature.

Figure 7

Temperature dependence of dielectric permittivity of BKT measured at ${10}^6\mathrm{Hz}$ under the application of varying electric fields.

Figure 8

Temperature dependence of dielectric permittivity of BKT measured at ${10}^6\mathrm{Hz}$ under the application of varying stresses.

Figure 9

$E\text{−}T$ and $\sigma \text{−}T$ phase diagrams for BKT. The microstructure models for the corresponding phases are also shown.