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The temporal evolution of domain structure and its piezoelectric behavior of ferroelectric material BaTiO₃ during the transition process from rhombohedral to tetragonal phase under an applied electric field have been studied by employing Landau–Ginzburg theory and the phase-field method. The results obtained show that, during the transformation process, the intermediate phase was monoclinic M_A phase, and several peak values of piezoelectric coefficient appeared at the stage where obvious change of domain pattern occurred. In addition, by comparing the cases of applied electric field with different frequencies, it was found that the maximum piezoelectric coefficient obtained decreased with increasing frequency value. These results are of great significance in tuning the properties of engineering domains in ferroelectrics, and could provide more fundamentals to the design of ferroelectric devices.

A model of a heterophase sample with interlayers is proposed to describe coexistence of tetragonal and orthorhombic phases in lead-free perovskite-type ferroelectric solid solutions. Versions of phase coexistence are analyzed at variations of unit-cell parameters of (Ba, Ca)(Ti, Zr)${\mathrm{\text{O}}}_3$ and (K, Na)(Nb, Sb)${\mathrm{\text{O}}}_3$-(Ba, Ca)${\mathrm{\text{ZrO}}}_3$ with compositions near morphotropic phase boundaries. Large regions of the tetragonal and orthorhombic phases are split into $90^{\circ }$ and $120^{\circ }$ domains, respectively. The interlayer of the orthorhombic phase is either single-domain or split into $90^{\circ }$ domains. A complete stress relief can be achieved at an elastic matching of the polydomain/single-domain or polydomain/polydomain phases. It is shown that different phase contents in (${\mathrm{\text{Ba}}}_{0.85}{\mathrm{\text{Ca}}}_{0.15}$)$\cdot \cdot$(${\mathrm{\text{Ti}}}_{0.9}{\mathrm{\text{Zr}}}_{0.1}$)${\mathrm{\text{O}}}_3$ powder and ceramic are caused by different non-${180}^{\circ }$ domain structures in the phases. The interlayer of the orthorhombic phase plays an important role in forming the phase content in solid solutions. Agreement is shown when comparing the evaluated volume fractions of the orthorhombic phase to experimental data.

A novel lead zinc titanate tungsten oxide (PbZn${}_{1∕3}$Ti${}_{1∕3}$W${}_{1∕3}$O${}_3)$ single perovskite was synthesized employing a cost-effective solid-state reaction technique. A phase transition occurs from tetragonal (P4mm) to monoclinic (C2/m) after substituting zinc (Zn) and tungsten (W) into the B-site of the pure lead titanate. The average crystallite size and micro-lattice strain are 66.2nm and 0.159%, respectively, calculated by the Williamson–Hall method. The grains are uniformly distributed through well-defined grain boundaries and the average grain size is about 17.8$\mu$m analyzed from the SEM micrograph. Raman spectrum suggests the presence of all constituent elements in the sample. The UV–Visible study suggests that the sample is suitable for photovoltaic applications because of high bandgap energy $E_g=4.17$eV. The dielectric study confirms the negative temperature coefficient resistance (NTCR) behavior of the sample. The activation energy increases from 13.9meV to 142meV with a rise of temperature suggesting that ac conductivity is thermally activated. The thermally activated relaxation process was managed by immobile charge carriers at low temperatures while defects and oxygen vacancies at higher temperatures. The presence of the asymmetrical curves in modulus plots confirms the non-Debye-type behavior. Both Nyquist and Cole–Cole semi-circular arcs confirm the semiconductor nature of the sample.

In the present investigation, the synthesis of the strontium copper titanate $({\mathrm{\text{Sr}}}_3{\mathrm{\text{CuTi}}}_4{\mathrm{\text{O}}}_{12},\mathrm{\text{SCTO}})$ ceramic by the cost-effective solid-state reaction was reported. The structural analysis suggests a single-phase tetragonal crystal symmetry with space group P4/mmm. The average crystallite size and mechanical compressive microlattice strain are found to be 65.8nm and 0.000594, respectively. The study of the field emission scanning electron microscope (FESEM) micrograph suggests that grains and grain boundaries are uniformly distributed on the sample surface with less porosity. The study of Raman lines suggests the presence of all constituent elements, which is well supported by EDAX analysis. The UV–Vis spectroscopy analysis shows that the bandgap of SCTO is about 3.2eV suitable for photovoltaic and other higher-temperature sensor applications. The decrease of dielectric constant with frequency supports the reduction of space charge polarization. The modulus analysis suggests that the immobile charge carriers at lower and defects and oxygen vacancies at higher temperatures are responsible for the thermally activated conduction process. The calculated activation energies are 4.54meV, 4.40meV, 3.39meV and 3.29meV at 1kHz, 10kHz, 100kHz and 1MHz; the decrease with the rise of the frequency confirms a thermally activated conduction process. Thermistor constant $(\beta )$, sensitivity factor $(\alpha )$ and stability factor of the sample were calculated, which confirms the characteristics of the NTC thermistor. The Nyquist and Cole–Cole semicircular arcs confirm NTCR character and are found to be suitable applications for energy storage devices and thermistors.