^aDepartment of Physics / CCET / Federal University of São Carlos, CEP 13565-

905, São Carlos-SP, Brazil

^bDepartment of Physics, Koneru Lakshmaiah Education Foundation, Bowrampet, Hyderabad, 500043, Telangana, India

^cDepartment of Zoology, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

^dDepartment of Physics, College of Science, P.O. BOX 2455, King Saud

University, Riyadh 11451, Saudi Arabia

An investigation examined the impact of co-doping BaTiO3 ceramics with La3+ and Nd3+ on their microstructural, dielectric, and phase transition properties. The synthesis of BaTiO3 with co-doping of La3+ and Nd3+, using the general formula Ba1-x(La1/3, Nd1/3)xTiO3 (BLNdTx) with varying concentrations of x (0%, 2%, 4%, and 8%), is achieved by the solid-state reaction technique. A temperature-dependent dielectric permittivity investigation was conducted at four distinct frequencies (1 kHz, 10 kHz, 100 kHz, 500 kHz, and 1 MHz) within the 30–200 °C temperature range. The findings indicate that the samples show a diffuse phase transition and a noticeable divergence from the typical Curie-Weiss equation. The diffuseness parameters γ for phase transition rose from

1.15 to 1.75 as x grew from 0 to 8%, respectively. The concurrent impact of surface phenomena, mechanical stress phenomena, and the external effect of grain boundaries might explain the substantial size reduction. An in-depth understanding of the grain size effect and its underlying mechanism would be advantageous for advancing and practically using BaTiO3-based ceramics and other ferroelectrics.