Corrigendum to “Abnormal Curie temperature behavior and enhanced strain property by controlling substitution site of Ce ions in BaTiO₃ ceramics” (Ceramics International (2017) 43(1) (10683–10690)(S0272884217307800)(10.1016/j.ceramint.2017.04.164))

The authors regret unfortunately two equations were missing from the main text of this article. The authors would like to apologise for any inconvenience caused, and the full correct text is reproduced below. Section 3.6. The adjusting factors of the T_c As mentioned above, though compared with the pure BaTiO₃, the T_c for the BT-xCe-A and the BT-xCe-B ceramics is decreased, different doping sites have a distinct phase transition behavior. Compared with the BT-xCe-A ceramics, the BT-xCe-B ceramics shows a higher T_c leading to an enhanced P_max. And the T_c shows an abnormal increasing behavior with the increase of the Ce content. In previous reports, most dopants decrease the T_c. Little attention is about the abnormal T_c increasing behavior and its reason. Some researchers have studied the influence factors of T_c from three aspects [4,45–47]: (1) average size effect produced by partial replacement, here we call it “<R>effect”,<R>=(1-x)R_Ba,Ti+xR_M, where R_Ba,Ti is the extrapolated Shannon ionic radius [48] of A-site Ba²⁺ ions for 12-fold coordination or the extrapolated Shannon ionic radius of B-site Ti⁴⁺ ions for 6-fold coordination; R_M is the extrapolated Shannon ionic radius of the doping ions; (2) local strain field produced by size mismatch in the ionic radius of the matrix ions and the doped ions, described by the statistical variance in the distribution of the radii σ². Here we call it “σ² effect”, σ²=x(1-x)(R_Ba,Ti-R_M)²; (3) local electric field produced by the electrovalence mismatch between the doped ions and the matrix ions.