fig5

Figure 5. Machine learning-guided examination of elemental substitution effects on the electronic structure and functional properties of BiFeO₃: (A) Orbital electron distributions and net spin variations induced by elemental substitution at the A and B sites; (B) Correlations between the 5d-electron fraction and the predicted band gap, piezoelectric tensor, and spin polarization; (C) Correlations between the net spin and the predicted band gap, piezoelectric tensor, and spin polarization; (D) Three-dimensional relationship among the predicted band gap, piezoelectric tensor, and spin polarization for elemental substitutions at the A and B sites.