Semi-empirical estimation for enhancing negative thermal expansion in PbTiO₃-based perovskites

Generally, most materials expand when heated and contract when cooled, whereas negative thermal expansion (NTE) materials are very rare. As a typical NTE material, PbTiO₃ and related compounds have drawn particular interest in recent years. The discovery of an enhanced NTE system in PbTiO₃ is beneficial to deepen our understanding of its mechanism and regulate its properties. At present, the method of discriminating an enhanced NTE material based on PbTiO₃ is not universal. Here, we propose a semi-empirical method through evaluating the average lattice distortion in related systems to estimate the relative coefficient of thermal expansion conveniently. The rationality of the method was verified by the analysis of the 0.6PbTiO₃–0.4Bi(Ga_xFe_1−x)O₃ system. So far, all PbTiO₃-based compounds with enhanced NTE conform well to this method. This method provides the possibility to find more enhanced NTE PbTiO₃-based materials.