Cristobalite-Related Phases in the NaAlO 2 –NaAlSiO 4 System. II. A Commensurately Modulated Cubic Structure

The crystal structure of a new cubic cristobalite-related sodium aluminosilicate Na 1.45 Al 1.45 Si 0.55 O 4 [ P 2 1 3, a = 14.553 (1) Å] has been modelled using a modulation wave approach and the model tested against X-ray powder diffraction data using the Rietveld method. Owing to there being 64 independent positional parameters and eight independent Na sites, refinement of the tetrahedral framework atom positions and Na occupancies was not possible. The framework was modelled successfully in terms of q 1 = 1\over 4〈020〉_p^*-type ( p = parent) modulation waves with the requirement that the M O 4 ( M = Al 0.725 Si 0.275 ) tetrahedra be as close to regular as possible. Na/vacancy ordering was modelled successfully in terms of q 2 = 1\over 4〈220〉_p^* modulation waves. Only the Na-atom positions were refined. The significance of this unique modulated cubic cristobalite-related structure and the possible insight it provides to understanding β-cristobalite are discussed.