Cation-vacancy ordering in dehydrated Na6†AlSiO4‡6

The low-temperature cation-ordered superstructure of anhydrous sodium sodalite, a zeolite with composition Na 6 ͓AlSiO 4 ] 6 , has been determined through the use of both density functional theory ͑DFT͒ and classical force-field lattice energy minimizations. The charge-balancing Na ϩ cations are assumed to occupy their characteristic locations within the cubic alumino–silicate framework near the centers of the 6-ring windows. Within the constraints of the volume-doubled pseudotetragonal supercell reported in a previous x-ray diffraction study ͓B. all possible arrangements of cations and vacancies amongst the 6-ring window sites were considered. Force-field calculations employing the ab initio based potential energy function derived by Blake, Weakliem, and Metiu ͓J. were used to perform full lattice-energy minimizations of each configuration, and to assess their relative stabilities both before and after minimization. The most stable configurations were then examined in more detail via ab initio density functional calculations in the generalized gradient approximation. The lowest-energy supercell ordering proved more stable than the lowest-energy parent cell ordering, and also yielded a pseudotetragonal distortion ͑space group Pnc2͒ and a calculated diffraction pattern that qualitatively match experimental results. The structural influences that contribute to the low energy of the correct vacancy ordering are described in detail.