Ba 0.85 Sr 0.15 ) 1−x Pb x TiO 3 ), along with various compositions (x(mol %) = 0, 2, 4, and 8), was synthesized through the conventional sol−gel reaction method. Following this, the resultant powders underwent a carefully controlled calcination process at 1000 °C for a period of 4 h. The examination of the crystalline phase of the calcined ceramics was conducted at room temperature using X-ray diffraction. Rietveld refinement of the XRD data, performed using FullProf, revealed that the samples exhibited a tetragonal structure within the space group P4mm. The impact of Pb doping on the lattice structure of BaSr 1−x TiO 3 was explored by analyzing the charge density distribution. The FTIR analysis unveiled a distinct absorptive band within the 450−600 cm −1 range, indicative of the stretching and bending vibrations associated with TiO 6 octahedra. Notably, sintering the material at 1150 °C for 4 h resulted in improved densification, as observed in scanning electron microscopy images showcasing a nearly uniform distribution of densely packed grains. Through the utilization of Williamson−Hall plots derived from XRD data, the average particle diameter was estimated to fall within the range of 131.87−141 nm, with an associated uncertainty ranging from 5 to 10%. Additionally, the dielectric characteristics unveiled the presence of a negative dielectric constant (ε r ) spanning the frequency range from 1 kHz to 2 MHz. The (Ba 0.85 Sr 0.15 ) 1−x Pb x TiO 3 ceramic displayed a widespread occurrence of negative permittivity, emphasizing the influence of dielectric resonance. The investigation revealed that the sintered ceramic with the formula (Ba 0.85 Sr 0.15 ) 1−x Pb x TiO 3 exhibited exceptional piezoelectric properties, achieving the highest piezoelectric constant (d 33 = 137 pC/N) and electromechanical coupling factor (k p = 0.49).
