Quantitative analysis of the solution energy of alkaline-earth metal elements to perovskite-type BaTiO 3 was carried out by a first-principles calculation combined with thermodynamics theory. The solution energies of neutral solute and a compensated solute with an oxygen vacancy were systematically calculated. They were obtained for two cation sites and four thermodynamical conditions with different chemical potentials of constituent atoms. Both Ca and Sr preferably occupy the Ba site of BaTiO 3 . On the other hand, Mg occupies the Ti site. This corresponds well to the widely accepted experimental findings regarding site preference. Moreover, under the condition of coexising BaO, CaO and BaTiO 3 , energy difference between the Ba-site solution and O-vacancy compensated Ti-site solution of Ca ions has been found to be smaller than that of Sr. Under this condition, the O-vacancy compensated Ti-site solution of Ca should be favorable compared with that of Sr. The same number of oxygen vacancies as Ca ions occupying Ti sites can be introduced. This also explains well experimental feature of the Ca-doped BaTiO 3 -based nonreducible multilayer ceramics capacitor (MLCC) materials regarding solution site of the Ca ion and abundance of O-vacancy.
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Moriwake et al. (2007) studied this question.
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