The structural, electronic, and optical properties of pure and Ce-doped BaTiO₃ were investigated based on first-principle calculation. Here, we concentrate on understanding the effect of the substitution of Ce for Ba and Ti sites in the equilibrium lattice parameters, DOS, electronic band structure, and optical performance of the materials. The crystal structures with a 12.5% doping ratio at different sites were constructed by superseding an atom of Ba (or Ti) site with a Ce atom and investigating the optimized crystal structure parameters. The substitution of Ce leads to a reduction in the band gap by inducing the movement of the conduction band minimum (CBM) and valence band maximum (VBM). The reduction in the band gap has been shown to be beneficial in increasing electrical conductivity. The density of states of the materials was calculated to gain insight into the valence band, conduction band, and contribution of each orbital to the total density of states in the electronic structure. The charge density, Mulliken charges, and bond overlap populations of pristine and Ce-doped BaTiO₃ were calculated to understand the nature of chemical bonds before and after doping. In addition, the optical properties of the materials were calculated, and the substitution of Ce for Ba site increased the static dielectric constant. In contrast, it decreased when Ce was doped into the Ti site. The substitution of Ce for different sites reduced the reflectivity of the material, while the transparency of the materials before and after doping was almost the same. The materials were transparent to incident light when the photon energy was below 10 eV, whereas opacity was in the ultraviolet range of 10–13 eV and beyond 20 eV. The theoretical calculation of different properties provides a new idea for the theoretical study of the BaTiO₃-based system.

Materials with perovskite phases are widely used in solar cells and ferroelectric, piezoelectric, dielectric and superconducting devices due to their various notable functions. However, structural instability limits some compositions in forming robust perovskite phases for device applications. The analytical approach using the tolerance factor (t) can only guarantee prediction accuracy within a limited range, ascribed to its nature of overlooking the atomic interaction. Hence, here we establish a prediction model using formation energy as the target parameter for its reflection of the reaction of atoms and apply machine learning as the analysis method since it has been successfully employed in plenty of material property prediction studies. Machine learning employs statistical methodologies to identify correlative patterns within large-scale datasets, enabling accurate predictions with robust generalization. In this work, we built a model to predict the formation energy of ABX₃ perovskite using machine learning and achieved a model with an R-squared value of 0.928 and a root mean square error of 0.301 eV/atom, validated by first-principles computations. In total, 75% of the values were correctly predicted within an error lower than 0.06. This work could contribute to accelerating the study of solving perovskites’ instability.

Due to their remarkable piezoelectric characteristics, (BaCa)(ZrTi)O₃ (BCZT) ceramics exhibit vast potential for being employed in cutting-edge electromechanical apparatus. Extensive experimental studies have been conducted to better meet the practical needs of BCZT-based materials, focusing on their mechanical performance. However, there is a serious lack of research on the theoretical computational aspects. Here, first-principles calculations were utilized to evaluate the mechanical properties of BCZT-xGd ceramics. The structural models were established using the virtual crystal approximation (VCA) method. The investigated compounds demonstrate structural and mechanical strength, as evidenced by their negative formation energies and adherence to the Born stability criteria. Compared to pure BCZT, the substitution of Gd leads to a significant enhancement in the system’s elasticity and stiffness. The BCZT-0.05Gd with B-site doping demonstrates the highest level of Vicker’s hardness ($H_V$), with the noteworthy observation that the inclusion of Gd concomitantly augments its machinability performance. Upon the incorporation of the Gd element, the anisotropic elasticity in the systems gradually transitions into isotropic elasticity, which favors a more uniform stress distribution and consequently reduces sensitivity to the formation and propagation of microcracks. These results indicate that BCZT-xGd exhibits potential for application in electromechanical systems.