Fig. 6: Phase transition mechanism.

a, c Evolution of SAED patterns during decreasing temperature for PZTN98/2 and PZTN97/3, respectively. The M-type and R-type superlattice reflections are marked by yellow circles and red arrows, respectively. The M-points in IP are magnified and inserted in upper-right corners. b Evolution of structural instabilities. The symbols of blue color refer to dominant structural instabilities while those of gray color represent the very small or disappeared structural instabilities. d The energy difference as function of volume for AFE, FE and IP phases, where the minimum for AFE phase is set as 0 eV. e, f The frozen-phonon potential of soft modes driving PE into FE or AFE state, respectively, under different strains. g Comparison of two possible pathways for phase transition between AFE and FE by using NEB method.