The structure and dynamics of a mixed cadmium-sodium β-alumina crystal, with composition (Cd0.79Na0.42O)1.22⋅11Al2O3, was investigated by x-ray diffraction and Raman spectroscopy. The conventional crystal-structure determination was carried out at room temperature, attaining R=0.043 in the least-squares refinement. Cadmium ions are close to mid-oxygen sites, but displaced by 0.168(5) Å from the conduction plane. Sodium ions are located in 6h sites near the Beevers-Ross positions, and the bridging oxygen atoms are disorderly distributed slightly off the threefold axes. Al interstitial-vacancy pairs correlated with oxygen interstitials were detected. Polarized Raman spectra, obtained in the low-frequency region at some temperatures from 300 K down to liquid-helium temperature region, are analyzed. The results of the analysis of features connected with cadmium-ion vibrational dynamics in room-temperature spectra are consistent with the model of ionic distribution obtained by refining x-ray-diffraction data. The temperature evolution of some Raman bands is discussed in terms of cadmium-ion rearrangement.
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