Cristobalite‐Related Phases in the NaAlO2–NaAlSiO4 System. II. A Commensurately Modulated Cubic Structure

The crystal structure of a new cubic cristobalite-related sodium aluminosilicate Na1.45Al1.45Si0.55O4 [P213, a = 14.553 (1) A] 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 q1 = 1\over 4〈020〉_p^*-type (p = parent) modulation waves with the requirement that the MO4 (M = Al0.725Si0.275) tetrahedra be as close to regular as possible. Na/vacancy ordering was modelled successfully in terms of q2 = 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.