Investigation of ferroelectric Ba_1-xCa_xZr_yTi_1-yO₃ single crystal by in situ temperature-dependent x-ray diffraction and first-principles calculations

In situ temperature-dependent crystal structure of lead-free ferroelectric perovskite Ba0.798Ca0.202Zr0.006Ti0.994O3 single crystal was characterized using x-ray diffraction from 170 to 380 K. Three phases were identified at different temperatures of 170, 220, and 298 K, revealing rhombohedral (R3m), orthorhombic (Pmm2), and tetragonal (P4mm) crystal structures, respectively. The change in the bond length and its distortion are reported for both AO(12) and BO6 polyhedrons, allowing for the estimation of the spontaneous polarization. The Debye-Waller factor is reported as a function of temperature for A and B-sites. Density-functional theory calculations on the tetragonal phase were performed to obtain information on the distribution of the Ca ions, the local atomic displacements, and the ideal value of the spontaneous polarization of a defect-free crystal at 0 K. We find that Ca prefers to arrange in columnar 2D plates oriented along the tetragonal axis. The Ca ions avoid being next neighbors of Zr; however, the specific arrangement of Ca has only a minor impact on the spontaneous polarization.