In the present work, the structure and microwave dielectric properties of (Ba,Sr,Ca)HfO₃ ceramics were systematically investigated to understand the general mechanism of tuning the temperature coefficient of resonant frequency, τ_f in perovskite ceramics. Ba_1-xSr_xHfO₃ and Sr_1-yCa_yHfO₃ could form continuous solid solutions while the solid solubility of Ca in Ba_1-yCa_yHfO₃ was about 20% (in mole). τ_f changed nonlinearly with increasing tolerance factor as the result of competition between the increase in the restoring force on the ions and the increase in polarizability. Under the guidance of three microscopic mechanisms affecting τ_f, a preliminary attempt was made to explore the suitable parameters to predict the variation trend of τ_f. Normalized ionic radii and the τ_f values of the end members were selected as independent variables, and τ_f was calculated by using multiple linear regression method. For Ba_1-xSr_xHfO₃ and Sr_1-yCa_yHfO₃ with orthorhombic structures, the root mean square error between the calculated and measured τ_f was only 6.8 × 10⁻⁶ ℃⁻¹. The good agreement between the calculated τ_f values and the measured ones in Ba_1-x-ySr_xCa_yHfO₃ ceramics confirmed its validity where three elements jointly occupy A-site, but it only works when there is no structural phase transition. Progresses in this research field would not only deepen our understanding of mechanism of regulating properties in multi-ion solid solutions, but also boost the developments of closely related fields such as machine learning-assisted design and high-entropy ceramics. Finally, a good combination of microwave dielectric properties was achieved in Sr_0.15Ca_0.85Hf_0.96Ti_0.040O₃: ε_r = 27.8, Qf = 36,470 GHz, τ_f = +5 × 10⁻⁶ ℃⁻¹.

Ba(Ti_0.25Zr_0.25Hf_0.25Sn_0.25)O₃ high-entropy ceramics were prepared by a standard solid state reaction process, and the dielectric and ferroelectric characteristics were investigated together with the structures. Both X-ray diffraction (XRD) and energy dispersive spectroscopy (EDS) analysis demonstrated a single-phase perovskite structure in the present ceramics. A broad dielectric peak with strong frequency dispersion feature was determined, which indicated the typical relaxor nature originating from the nanoscale ferroelectric domain structures. These resulted from the structural distortion and chemical disorder due to high-entropy, where the long-range order of ferroelectric domains was destroyed. The homogeneous microstructure led to the reduced leakage current density and significantly improved dielectric strength, which was desired for the practical applications. Compared with the similar systems of Ba(TiZr)O₃ & Ba(TiSn)O₃, the present high-entropy ceramics indicated better relaxor ferroelectric characteristics.

Ordered domain engineering has been further developed for modifying and improving physical properties in complex perovskite ceramics. In the present work, Ba(Ni_1/3Nb_2/3)O₃ ceramic is taken as a typical example for ordered domain engineering, in which the sintering temperature lies above the order-disorder transition temperature. Though the well-ordered structure could not be obtained in as-sintered samples, high ordering degree could be achieved together with preferred ordered domain structures in Ba(Ni_1/3Nb_2/3)O₃ ceramics through long-time annealing, and subsequently the physical properties such as electrical resistivity, thermal conductivity, dielectric strength and energy storage density are significantly enhanced, where the ordering degree, ordered domain structure and ordered domain boundary play the critical rules. The present work provides an effective approach for developing complex perovskite dielectric ceramics with superior physical properties.

BiFeO₃ has been recognized as one of the most important room-temperature single-phase multiferroic materials, but it still suffers from several drawbacks especially the weak magnetoelectric coupling. In the present work, the electric-field-controlled magnetism is achieved in Bi_1-xGd_xFeO₃ system, which involves a field-induced transition of Pna2₁/R3c at the morphotropic phase boundary region, and the magnetic state is switched between cycloidal state and canted antiferromagnetic state. The electric-field-controlled magnetism becomes reversible with the help of annealing, which is confirmed by magnetic hysteresis loops and the quantitative ratio of the involved phases for the as-sintered, as-poled and as-annealed samples. Compared with the systems of Bi_1-xNd_xFeO₃ and Bi_1-xSm_xFeO₃, it is easier to tune the symmetry from R3c to Pna2₁ with lower rare earth-content, and the field-induced transition is more apparent and subsequently leads to more significant electric-field-controlled magnetism in a wider composition range.

The variation of dielectric, ferroelectric and piezoelectric characteristics of BaZrO₃–modified (Ba_0.85Ca_0.15)TiO₃ ceramics, (1-x)(Ba_0.85Ca_0.15)TiO₃-xBaZrO₃, have been investigated together with the structure evolution. The crystal structure at room-temperature varies from tetragonal to metrically cubic through orthorhombic and rhombohedral, and the morphotropic phase boundary (MPB) is determined around x = 0.12 where the significantly enhanced dielectric, ferroelectric and piezoelectric characteristics are achieved. With increasing x, the present ceramics indicate the crossover from normal to diffused and relaxor ferroelectric, and the evolution process is explored systematically.