Giant thermal vibrations in the framework compoundsBa1−xSrxAl2O4

Synchrotron x-ray diffraction experiments were performed on the network compounds ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_x{\mathrm{Al}}₂{\mathrm{O}}₄$ at temperatures between 15 and 800 K. The ferroelectric phase of the parent ${\mathrm{BaAl}}₂{\mathrm{O}}₄$ is largely suppressed by substituting a small amount of Sr for Ba and disappears for $x\ensuremath{\ge}0.1$. Structural refinements reveal that the isotropic atomic displacement parameter ${B}_{\mathrm{iso}}$ in the bridging oxygen atom is largely independent of temperature and retains an anomalously large value in the adjacent paraelectric phase even at the lowest temperature. The ${B}_{\mathrm{iso}}$ systematically increases as $x$ increases, exhibiting an especially large value for $x=0.5$. According to previous electron diffraction experiments for ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_x{\mathrm{Al}}₂{\mathrm{O}}₄$ with $x\ensuremath{\ge}0.1$, strong thermal diffuse scattering occurs at two reciprocal points relating to two distinct soft modes at the $M$ and $K$ points over a wide range of temperatures below 800 K [Y. Ishii et al., Sci. Rep. 6, 19154 (2016)]. Although the latter mode disappears at approximately 200 K, the former does not condense, at least down to 100 K. The anomalously large ${B}_{\mathrm{iso}}$ observed in this study is ascribed to these soft modes existing in a wide temperature range.