Crystallographic parameterisation of distortions in the SOD framework in the sodalite and helvine groups: An analysis in condensed normal modes of an aristotype phase

Abstract Crystallographic distortions in the alternating aluminium and silicon tetrahedral framework of sodalite (Na 8 Al 6 Si O 24 Cl 2 ), beryllium helvine (Mn Be S (framework designated SOD) are described terms a set condensed normal mode amplitudes phases derived from an ideal tetrahedron theoretical aristotype phase. For sodalite-structured hettotype phase space group $P{\overline 4} 3n$ , these modes transform as irreducible representations A 1 E (α) T (z) point-group ${\overline 3m$ where to good approximation acts pure breathing mode, polyhedral distortive rigid unit rotation about unique 4}$ axis T-site under consideration. Parameterisation low-order polynomials function thermodynamic variable permits crystal structure be accurately interpolated at intermediate values variable. Published data for high-temperature behaviour have been re-analysed which reproduce temperature dependence bond lengths, angles Al–O–Si inter-polyhedral angle. Full expressions structural parameters lattice parameter tabulated agree with experimental results within one estimated standard deviation parameter. The potential decomposition lower symmetry SOD structures is illustrated by deriving tugtupite ) room $I{\overline .