Structural instability in BaZrO$_3$ crystals: Calculations and experiment

The phonon spectrum of cubic barium zirconate is calculated from first principles using the density functional theory. An unstable $R_{25}$ phonon mode observed in the phonon spectrum indicates an instability of the BaZrO$_3$ structure with respect to the oxygen octahedra rotations. It is shown that the symmetry of the ground-state structure of the crystal is $I4/mcm$. The local structure of BaZrO$_3$ is studied by the EXAFS spectroscopy at the Ba$L_{\mathrm{III}}$ absorption edge at 300 K to search for the instability predicted by calculations. Anomalously high values of the Debye–Waller factor for the Ba–O atomic pairs ($\sigma^2_1\sim$ 0.015 $\mathring{\mathrm{A}}^2$) are attributed to the appearance of this structural instability. The average amplitude of the octahedra rotations caused by thermal vibrations is estimated from the measured $\sigma^2_1$ value to be $\sim$4$^\circ$ at 300 K. The closeness of the calculated energies of various distorted phases resulting from the condensation of the $R_{25}$ mode suggests a possible formation of the structural glass state in BaZrO$_3$ as the temperature is lowered. It explains the origin of the disagreement between the results of calculations and diffraction experiments.