Broadband dielectric spectroscopy of phonons and polar nanoclusters inPbMg1/3Nb2/3O3−35%PbTiO3ceramics: Grain size effects

Abstract

The dielectric response of ${\text{PbMg}}_{1/3}{\text{Nb}}_{2/3}{\text{O}}_{3}\text{\ensuremath{-}}35%{\text{PbTiO}}_{3}$ ceramics (close to the morphotropic phase boundary) from 100 Hz up to 100 THz was determined in a broad temperature range of 5--900 K. Two ceramics were studied and compared: coarse grain ceramics (CGC) (grain size $\ensuremath{\sim}4\text{ }\ensuremath{\mu}\text{m}$) and fine grain ceramics (FGC) (grain size $\ensuremath{\sim}150\text{ }\text{nm}$). Both ceramics showed similar polar-phonon response and the ferroelectric transition near ${T}_{C}=440\text{ }\text{K}$ that was manifested by partial softening of the overdamped lowest-frequency phonon using the time-domain THz spectroscopy. However, the dielectric response was dominated by a complex relaxational dispersion in the microwave range due to relaxorlike dynamics of the polar nanoclusters, which strongly differed in both the ceramics. Whereas the CGC undergoes a well-defined ferroelectric transition such as a single crystal, FGC exhibits a relaxor behavior with substantially smaller permittivity showing partial clamping of the polar nanocluster dynamics by grain boundaries. The pronounced difference was also revealed in a second-harmonic generation showing much larger paraelectric signal in the FGC with a much smeared ferroelectric transition only. Due to contributions of both the soft phonon mode and dielectric relaxations into the dielectric constant near its maximum even in the paraelectric phase, the ferroelectric transition corresponds to a percolation threshold of the polar nanoclusters into macroscopic domains. Such a type of phase transition can be considered as a special case of crossover between the displacive and order-disorder types, where the ordering process concerns a mesoscopic range.