The crystal structures of aluminosilicate-sodalites: X-ray diffraction studies and computer modelling

X-ray powder methods have been used to study the room-temperature structures of the synthetic sodalites: Li8(AI6Si6024)CI2, KT.6Nao.4(A16Si6Oz4)CI2, and Nas(A16Si6024)I ~. Natural sodalite was also studied and the atomic coordinates show satisfactory agreement with those determined from the single-crystal data of L6ns and Schulz (1967). The LiC1and KCIas well as the NaCl-sodalites refined in the expected sodalite space group PTl3n, but the NaI-sodalite fitted 1713m better. The resulting structural data reveal shortcomings in the previous computer models for sodalite structures and an improved computer modelling procedure is devised which successfully predicts atomic coordinates, starting from the experimental a value and an estimate of the cation anion distance. The method incorporates the experimental result that the average T O distance (T = A1, Si) throughout the samples is ~ 1.678 A, and Si-O and AI-O are set at 1.618 and 1.738A, respectively. Although T-O remains little changed throughout the samples, the data confirm the inverse relationship between /_ T-O T and the tetrahedron tilt angle ~b, in which I_T-O-T approaches ~ 160 ~ as ~b ~ 0 ~ and the sodalite cage becomes fully expanded. P R E V I O U S work on members of the sodalite family (Henderson and Taylor, 1977, 1979a; Taylor and Henderson, 1978; Dempsey and Taylor, 1980) has been directed towards: (i) understanding the nature of the bonding in framework structures, particularly in respect of T O distances and T O T a n g l e s (T = A1, Si); (ii) interpreting the infra-red spectra of framework structures and; (iii) interpreting the thermal expansion behaviour of framework structures. However, each of the studies, to which reference has been made, encountered problems which could not be resolved without more structural data for sodalites, particularly aluminosilicatesodalites. * Present address: 15 Leigh Road, Congleton, Cheshire CW12 2EG. 9 Copyright the Mineralogical Society The structural data required include T O distances, T O T angles and tilt angles ff for aluminosilicate-sodalites showing a wide range of cell edge and hence a wide degree of structural collapse (for nomenclature see Taylor, 1972, and Dempsey and Taylor, 1980). Such a range of aluminosilicatesodalites is available, in powder form, from earlier studies (Henderson and Taylor, 1977). F rom these powder samples, Li8(A168i6024)C12, Na8(A16 Si6024)C12, KT.6Nao.4(A16Si6024)C12, and Nas(A16Si6024)I 2 were selected for the present X-ray structural study. The structure of natural sodalite, Nas(AI6Si6024)C12, has already been determined by Pauling (1930) and refined by L6ns and Schulz (1967) who used single-crystal data, but this mineral was included in the present study to check the correspondence of powder and single crystal results. Once the powder studies were complete, it proved possible to develop a computer model enabling structural details to be calculated for each sodalite simply from its unit-cell parameter a. Experimental procedure. The specimen of Naa(A16Si6Oz4)C12 was a natural one, No. 19 of Taylor (1967); the remaining specimens were the synthetic sodalites used in an earlier infra-red study (Henderson and Taylor, 1977). Each powdered specimen was packed into a glass capillary, 0.3 mm internal diameter, and a powder X-ray diffraction film produced using Cu-K, radiation and a Philips 114 mm diameter powder camera (IevinsStraumanis film mounting). To obtain intensity measurements each film was scanned at 0.05 mm intervals along the axis of the diffraction pattern using an automated Joyce-Loebl microdensitometer. Digitized data obtained on punched paper tape were loaded into computer files on the joint ICL 1906A/CDC 7600 computer system of the University of Manchester Regional Computer Centre and processed by programmes in our MOLecular structure programme LibrarY(MOLLY) to optical density read460 B. B E A G L E Y ET AL. ings at each step. Reflection peak areas were determined by integration from the computer output and an average taken of corresponding reflections on the two halves of the X-ray pattern. The reflections were divided into unique and non-unique sets. The intensity of each nonunique reflection (a composite made up of components with different Miller indices hkl) was split into the intensities of its components in proportion to the ratios of the intensities of the components calculated from an initial estimate of the crystal structure (Beagley et al., 1982). At stages through the structure refinement, the ratios of the intensities of the components of the nonunique reflections were redetermined from the partiallyrefined parameters and used to re-divide the intensities of the non-unique reflections into their component reflections. Because of the difficulty of determining space groups from powder diffraction data, in preliminary least-squares refinements of structural parameters it was initially assumed that all the structures had the space group of the mineral sodalite, PT~3n. The atomic scattering factors used were for Si 2+, A1 § O, Na § Li § K § CI-, and I (International Tables, 1974). Factors for partially ionized Si, A1, and O were used to make some allowance for covalency in the tetrahedral framework. Each unique reflection was given unit weight. The weight given to each component of a non-unique reflection was the reciprocal of the number of components making up that non-unique reflection, thereby giving unit weight, in total, to each non-unique reflection. The calculated linear absorption coefficients for the specimens were reduced by 30 % to make an approximate allowance for the pore space present in the specimen in the capillary. Isotropic temperature factors were employed for each atom. Initially, separate scale factors were used for the unique and non-unique reflections, although if the method of processing the latter succeeds they should be equal. In fact, the individual scale factors were not significantly different so that ultimately a single factor was used. The structural determinations and refinement were carried out using the X-ray Systems, Version of June 1972 (Technical Report TR-192 of the Computer Science Center, University of Maryland, USA, June 1972). Because of correlation effects the isotropic temperature factors of the Si and AI atoms could not be refined separately and so were refined together. Nas(A16Si6024)I 2 did not refine coherently in space group P~3n. During refinement, the coordinates of the oxygen atom moved to x, x, z rather than x, y, z and the F0 map in the region of the oxygen atom supported this relationship. The equality of x and y shows that the A1, Si-O bond lengths are equal suggesting that the Si and AI sites are disordered and that the space group is I713m. The structure refined more smoothly in I~3m and the agreement with experiment remained the same as for PT13n. The criteria of Hamilton (1965) support the adoption of I7~3m because no reduction in the appropriate residual is observed in the p743n refinement although there is one extra variable. The isotropic temperature factors for all the atoms in the I-sodalite structure were much higher than those for the other sodalites with ordered frameworks. The single-crystal structural data of Ltns and Schulz (1967) for natural sodalite were also refined using the X-ray System 1972, for comparison with our own structural analysis of powdered Nas(A16Si6024)C12. Results. Bond distances and angles for the sodalites studied are given in Table I. Un i t cell parameters a, a tomic coordinates , isotropic tempera ture factors, etc., are given in Table II. We have chosen to present the da ta in this order so as to facilitate compar i son of measured a tomic parameters with those es t imated using the model. For na tura l sodali te [Nas(A16Si6024)C12], the a tomic parameters of L t n s and Schulz (1967) are no t significantly different f rom those of our own refinement (Table II) us ing their da ta except for the x-coordinate of the oxygen a t o m (z of L6ns and Schulz, 1967; note tha t x, y, z here are a cyclic pe rmuta t ion of those of L t n s and Schulz). This slight difference, which results in shor ter S i -O and longer A1-O distances, may result from the use of a different set of scat ter ing factors and a different ref inement programme. The results of the refinemen t using our powder da ta for na tu ra l sodali te are in fair agreement (generally slightly greater t han 2~r) with the results for the single crystal de te rmina t ion (Table IIb and Table I, columns 2 and 3). These refinements demons t ra te tha t the powder studies are reasonably reliable. The structures of Lis(A16Si6024)C12, KT.6Nao.4 (A16Si6024)C12 and Nas(A16Si6024)I2 have no t been determined previouslY a l though they have been modelled by Taylor and Hender son (1978) and Dempsey and Taylor (1980). The C A and C O distances calculated by the lat ter authors are given in Table I for compar i son with the observed values (C = cavity cation, A = cavity anion). In all cases (except tha t of the single crystal data, which had been used as a cons t ra in t on the model) the model C O distances are smaller t han the corresponding observed values, and the model C -A distances are greater than observed, part icular ly for the l i thium sodalite. This suggests tha t the model calculat ions give poor cat ion coordinates. The model C O distances which fix the ca t ion coordinates , had been calculated as the sum of ionic radii, and it is clear tha t this is a feature of the earlier model l ing which is unsatisfactory. Fur thermore , the model calculat ions recognized only three oxygen near -ne ighbours (and one anion) for each cation, whereas there are actually six oxygen near-neighbours: three (for example in sodali te itself) with C O ~ 2 .36A and three more with C O ' ~ 3 .08A (Table I). According to the criteria of Brown and S h a n n o n (1973) bo th types of C O distance have significant b o n d s t rengths s(C-O) and s(C-O') which can be calculated from A L U M I N O S I L I C A T E S O D A L I T E S 461 T~tble======~I. Bo~d d i s t ~ n c ~ and ~gles for Rlumin~ili~te sodalZtes _C8r ( E s t t ~ t e d s tandard d e v m t l ~ s in pa ren thes~) . CA LICI NaCI NaCI KC~ Nal sample powder pOWder single p~der p~der