Physics-embedded machine learning search for Sm-doped PMN-PT piezoelectric ceramics with high performance

Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ (PMN-PT) piezoelectric ceramics have excellent piezoelectric properties and are used in a wide range of applications. Adjusting the solid solution ratios of PMN/PT and different concentrations of elemental doping are the main methods to modulate their piezoelectric coefficients. The combination of these controllable conditions leads to an exponential increase of possible compositions in ceramics, which makes it not easy to extend the sample data by additional experimental or theoretical calculations. In this paper, a physics-embedded machine learning method is proposed to overcome the difficulties in obtaining piezoelectric coefficients and Curie temperatures of Sm-doped PMN-PT ceramics with different components. In contrast to all-data-driven model, physics-embedded machine learning is able to learn nonlinear variation rules based on small datasets through potential correlation between ferroelectric properties. Based on the model outputs, the positions of morphotropic phase boundary (MPB) with different Sm doping amounts are explored. We also find the components with the best piezoelectric property and comprehensive performance. Moreover, we set up a database according to the obtained results, through which we can quickly find the optimal components of Sm-doped PMN-PT ceramics according to our specific needs.