Fig. 3: Stress in the BCTZ–xAlN ceramic.

Finite-element simulation of internal stress distribution within (a) BCTZ and (b) BCTZ–xAlN ceramics. c1 HRTEM image of BCTZ and corresponding strain maps obtained by GPA along the (c2) xx direction and (c3) yy direction. d1 HRTEM image of BCTZ–1.75AlN–300 and corresponding strain maps obtained by GPA along the (d2) xx direction and (d3) yy direction. Raman mapping images of ceramic integrating with the bands of 523 cm⁻¹: (e1) BCTZ, (f1) BCTZ–1.75AlN–300, (g1) BCTZ–1.75AlN–3000, and (h1) BCTZ–1.75AlN–50 ceramics. Raman mapping images of ceramic integrating with the bands of 390 cm⁻¹: (f2) BCTZ–1.75AlN–300, (g2) BCTZ–1.75AlN–3000, and (h2) BCTZ–1.75AlN–50 ceramics. Corresponding contour plots of specific Raman spectra from points A to B in the bands range of 100–1000 cm⁻¹ and 450–650 cm⁻¹, respectively: (e2–e3) BCTZ, (f3–f4) BCTZ–1.75AlN–300, (g3–g4) BCTZ–1.75AlN–3000, and (h3–h4) BCTZ–1.75AlN–50 ceramics. i Schematic of unit cell of pristine and strained BaTiO₃ bulk with (1 × 1) periodicities. j The total energies of the R, O, T, and C phases of BaTiO₃ as a function of strain. k The difference in the total energies of O, T, and C phases of BaTiO₃ and its R phase as a function of strain.