SODIUM-ION DISTRIBUTION IN NA+ BETA-ALUMINA - A CRYSTALLOGRAPHIC CHALLENGE

The Na+-ion distribution in Na+ beta-alumina has been reinvestigated at 295 K by conventional single-crystal X-ray diffraction techniques (Mo K-alphaBAR radiation, lambda = 0.71073 angstrom). The structure [idealized formula: Na1 + (x)Al11O17 + x/2 for x = 0.22, M(r) = 598.6, F(000) = 586.6] comprises spinel-type blocks interleaving two-dimensional conduction planes with a spacing of approximately 11 angstrom. The atoms in the spinel framework have the centrosymmetric hexagonal space group P6(3)/mmc with a = 5.5929 (4), c = 22.526 (3) angstrom, V = 610.22 angstrom-3, Z = 2, D(x) = 3.25 g cm-3, mu-0 = 10.3, mu-c = 10.3 cm-1. The Na+-ion distribution within the conduction plane is described using three different models: the best fit is obtained for a model in which the Na+ ions occupy Beevers-Ross and interstitial sites near mid-oxygen, Na(1) and Na(2), respectively, wR(F2) = 0.0436 for 2036 observed reflections. Thermal vibration and/or displacement is described with beta-ij and gamma-ijk tensors for Na(1), and beta-ij tensors only for Na(2). Neither the inclusion of additional Na+ sites, nor the removal of the mirror-plane constraint on the conduction plane (to test for local ordering) could be shown to bring about significant improvement to the model. Attempts to refine local ordering within the Frenkel defect were also made with negative results. The crystallographic result is discussed in terms of possible conduction mechanisms.