The effect of internal stress on the physical properties (the temperature dependence of the dielectric constant and the lattice constant, and the diffuseness (gamma)) of solid solutions of 0.97BaTiO(3)-0.03Gd(2)O(3):1.5TiO(2) and 0.97BaTiO(3)-0.03CeO(2):1.5TiO(2) was investigated using various particle sizes of the starting BaTiO3, pressure-dielectric spectroscopy, and high-pressure X-ray analysis. The grain size was almost proportional to the particle size of the starting BaTiO3 and was inversely proportional to the internal stress. A sudden change in internal stress occurred at grain sizes of similar to 2 mu m for cerium-doped BaTiO3 and similar to 3 mu m for gadolinium-doped BaTiO3. With an increase in external pressure and a decrease in grain size, the lattice anomalies of the cubic-to-tetragonal transformation and two other factors (the tetragonal-to-orthorhombic and orthorhombic-to-rhombohedral transformations) shifted to lower and higher temperatures, respectively. The temperature dependencies of the dielectric constant and the lattice constant were less sensitive to external pressure in cerium-doped core-shell-grained BaTiO3 than in gadolinium-doped homogeneous-grained BaTiO3; this difference was attributable to internal stress, In cerium-doped BaTiO3, gamma was related to internal stress.