A. sample synthesis

Rb₂X ²⁺Si₅O₁₂ and Cs₂X ²⁺Si₅O₁₂ were prepared from appropriate stoichiometric mixtures of Rb₂CO₃, Cs₂CO₃, SiO₂, and XO (X = Mg, Ni, Cd; Bell et al., Reference Bell, Redfern, Henderson and Kohn1994b; Bell and Henderson, Reference Bell and Henderson1996, Reference Bell and Henderson2009, Reference Bell and Henderson2016) and then 50:50 mixtures of the Rb and Cs samples were made for each of the three pairs of samples with the same X ²⁺ cation. For X = Ni the starting materials were both glasses, the mixture was sealed in a gold capsule and heated in a furnace at 1173 K for 7 days. For X = Cd and Mg the starting materials were both crystalline, the mixtures were sealed in a gold capsule (X = Cd) or a Pd-Ag alloy capsule (X = Mg) and these were heated in a furnace at 1173 K for 6 h.

B. X-ray powder diffraction data collection

After heating the samples were removed from the metal capsules, ground with a mortar and pestle and then mounted on low-background silicon wafers with a drop of acetone prior to ambient temperature X-ray powder diffraction. Data were collected for the X = Mg and Cd samples with a PANalytical X'Pert Pro MPD using CuKα X-rays, a graphite monochromator and a 2.122°2θ wide 100 channel X'Celerator area detector. For X = Mg data were collected in eight scans lasting 61 h in total which were summed together. These data were collected over the range 10°–100°2θ with a step width of 0.0167°2θ and an effective counting time of 5150 s per point. The beam size was defined with a 20 mm mask, fixed antiscatter (¼°) and divergence (⅛°) slits. For X = Cd data were collected in eight scans lasting 64 h in total which were summed together. These data were collected over the range 10°–100°2θ with a step width of 0.0167°2θ and an effective counting time of 5570 s per point. The beam size was defined with a 15 mm mask, fixed antiscatter (¼°) and divergence (⅛°) slits. For the X = Ni sample data were collected with a PANalytical Empyrean diffractometer using Co Kα X-rays with an iron β-filter and a 3.3473°2θ wide 255 channel PIXCEL-3D area detector. Data were collected in two scans over 28 h. These data were collected over the range 15°–100°2θ with a step width of 0.0131°2θ and an effective counting time of 2487 s per point, the beam size was defined with a 20 mm mask, fixed divergence antiscatter (¼°) slit and automatic divergence slit with a 20 mm long beam footprint. These diffracted intensities for the X = Ni sample were summed and then converted from automatic divergence slit mode to fixed divergence slit mode in High Score Plus (PANalytical, 2009) prior to data analysis. No smoothing or α ₂ stripping was done on any of these data. Both diffractometers were calibrated with an external NIST 640e silicon standard.

C. X-ray powder diffraction data analysis

Analyses of the summed powder diffraction data for each sample showed that all samples were single-phase and isostructural with the Pbca structure of Cs₂CdSi₅O₁₂ (Bell et al., Reference Bell, Redfern, Henderson and Kohn1994b). Rietveld refinements were done using FULLPROF (Rodríguez-Carvajal, Reference Rodríguez-Carvajal1993), using the structures of Rb₂XSi₅O₁₂ (Bell and Henderson, Reference Bell and Henderson1996, Reference Bell and Henderson2009, Reference Bell and Henderson2016) as starting models but with half the Rb replaced by Cs. Backgrounds were fitted by linear interpolation between a set of background points with refinable heights. The Thompson-Cox-Hastings Pseudo-Voigt function (van Laar and Yelon, Reference van Laar and Yelon1984), convoluted with asymmetry because of axial divergence (Finger et al., Reference Finger, Cox and Jephcoat1994), was used to model the profile shape. For X = Mg data over the range 10°–71.5°2θ were used for data analysis as there were no visible Bragg reflections above 71.5°2θ. For X = Cd the whole 10°– 100°2θ range was used and for X = Ni the whole 15°–100°2θ range was used. Soft distance restraints were used on the Si-O and X-O distances. Si-O distances were restrained at 1.61 ± 0.01 Å; this distance is intermediate over the typical distance for tetrahedrally coordinated Si-O in framework silicates (1.59–1.63 Å; International Tables for X-ray Crystallography, 1985, Vol. III). Ni-O and Mg-O distances were restrained at 1.89 ± 0.01 Å; these distances are similar to those determined for X = Ni (Bell and Henderson, Reference Bell and Henderson1996, Reference Bell and Henderson2016), K₂MgSi₅O₁₂ (Bell et al., Reference Bell, Henderson, Redfern, Cernik, Champness, Fitch and Kohn1994a) and Cs₂MgSi₅O₁₂ (Bell and Henderson, Reference Bell and Henderson2009) leucites. Cd-O distances were restrained at 2.23 ± 0.01 Å; these distances are similar to those determined for X = Cd (Bell et al., Reference Bell, Redfern, Henderson and Kohn1994b; Bell and Henderson, Reference Bell and Henderson2009, Reference Bell and Henderson2012) leucites.

In these Rietveld refinements all atoms were located on the Pbca 8c Wyckoff general position. There are two distinct extraframework alkali metal cation sites for Rb and Cs. There are six T-sites, one for divalent X ²⁺ cations and five for silicon cations, there are also twelve oxygen anion sites. Isotropic atomic displacement parameters were constrained to be the same for all sites occupied by silicon. Isotropic atomic displacement parameters were also constrained to be the same for all sites occupied by oxygen. As there is only one X ²⁺ cation site then this site had no constraint on the isotropic atomic displacement parameter. Initial refinements had 50% Rb and 50% Cs on each of the two extraframework alkali metal cation sites, these site occupancies were allowed to refine but were constrained so that the sum of the occupancies for each element over the two sites was 100%. Isotropic atomic displacement parameters were constrained to be the same for Rb and Cs on the same alkali metal cation site but different to the isotropic atomic displacement parameters for Rb and Cs on the other alkali metal cation site. VESTA (Momma and Izumi, Reference Momma and Izumi2011) was used to plot crystal structures.

A. RbCsMg²⁺Si₅O₁₂ structure

Figures 1 and 2, respectively, show the Rietveld difference and the VESTA crystal structure plots for the refined crystal structure of RbCsMg²⁺Si₅O₁₂, in Figure 2 light blue (Cs⁺) and pink (Rb⁺) shadings show the occupancies of the two A cation sites. Table I shows that this crystal structure has a unit cell volume which is approximately intermediate between those for Rb₂Mg²⁺Si₅O₁₂ and Cs₂Mg²⁺Si₅O₁₂. The refined occupancies of the two extraframework A sites are: Rb1 0.63(3), Cs1 0.37(3); Rb2 0.37(3), Cs2 0.63(3); there is some partial, but not complete, ordering of these occupancies. The greater occupancy of the larger Cs⁺ cation on the extraframework A2 cation site is reflected in the larger A2-O distance compared to A1-O (see Table II). Table II also shows that the mean Si-O-Si and Si-O-X angles are similar for all X = Mg structures. Table III shows that the MgO₄ tetrahedron in the silicate framework structure for RbCsMg²⁺Si₅O₁₂ is less distorted than those for Rb₂Mg²⁺Si₅O₁₂ and Cs₂Mg²⁺Si₅O₁₂.

Figure 1. (color online) Rietveld difference plot for RbCsMg²⁺Si₅O₁₂. Blue circles represent observed data points, red line represents calculated data points, green line represents difference curve and purple crosses represent positions of Bragg reflections. R-factors for this refinement were:- R _p = 1.2305, Rwp = 1.5794, R _exp = 1.6182, χ ² = 0.9526. Miller indices are shown for some of the stronger peaks in the powder diffraction plot.

Figure 2. (color online) VESTA structure plot for RbCsMg²⁺Si₅O₁₂, viewed down [111] showing a channel for extraframework Rb⁺ and Cs⁺ cations. SiO₄ tetrahedra are shown in blue, MgO₄ tetrahedra are shown in orange with O²⁻ anions are shown in red. Pink (Rb⁺) and light blue (Cs⁺) shadings show the occupancies of the two A cation sites.

B. RbCsNi²⁺Si₅O₁₂ structure

Figures 3 and 4, respectively, show the Rietveld difference and the VESTA crystal structure plots for the refined crystal structure of RbCsNi²⁺Si₅O₁₂, in Figure 4 light blue (Cs⁺) and pink (Rb⁺) shadings show the occupancies of the two A cation sites. Table I shows that this crystal structure also has a unit cell volume which is approximately intermediate between those for Rb₂Ni²⁺Si₅O₁₂ and Cs₂Ni²⁺Si₅O₁₂. The refined occupancies of the two extraframework A sites are: Rb1 0.49(6), Cs1 0.51(6); Rb2 0.51(6), Cs2 0.49(6). Within error limits there is complete disorder of these occupancies. For X = Ni the A-O distances for each of the two extraframework A cation sites are the same within error limits reflecting the disorder of Rb and Cs over these two sites. Table II also shows that the mean Si-O-Si angles are similar for all X = Ni structures but the corresponding Si-O-X angles are all smaller. The Si-O-X angle for Rb₂Ni²⁺Si₅O₁₂ is smaller than those for RbCsNi²⁺Si₅O₁₂ and Cs₂Ni²⁺Si₅O₁₂. Table III shows that the NiO₄ tetrahedron in the silicate framework structure for RbCsNi²⁺Si₅O₁₂ is slightly less distorted than those for Rb₂Ni²⁺Si₅O₁₂ and Cs₂Ni²⁺Si₅O₁₂.

Figure 3. (Color online) Rietveld difference plot for RbCsNi²⁺Si₅O₁₂. Blue circles represent observed data points, red line represents calculated data points, green line represents difference curve and purple crosses represent positions of Bragg reflections. R-factors for this refinement were:- R _p = 1.6058, Rwp = 2.7720, R _exp = 0.8916, χ ² = 9.6659. Miller indices are shown for some of the stronger peaks in the powder diffraction plot.

Figure 4. (color online) VESTA structure plot for RbCsNi²⁺Si₅O₁₂, viewed down [111] showing a channel for extraframework Rb⁺ and Cs⁺ cations. SiO₄ tetrahedra are shown in blue, NiO₄ tetrahedra are shown in grey with O²⁻ anions are shown in red. Pink (Rb⁺) and light blue (Cs⁺) shadings show the occupancies of the two A cation sites.

C. RbCsCd²⁺Si₅O₁₂ structure

Figures 5 and 6, respectively, show the Rietveld difference and the VESTA crystal structure plots for the refined crystal structure of RbCsCd²⁺Si₅O₁₂, in Figure 6 light blue (Cs⁺) and pink (Rb⁺) shadings show the occupancies of the two A cation sites. Table I shows that this crystal structure has a unit cell volume larger than that for Rb₂Cd²⁺Si₅O₁₂ (Bell and Henderson, Reference Bell and Henderson1996) and smaller than that for Cs₂Cd²⁺Si₅O₁₂ (Bell et al., Reference Bell, Henderson, Redfern, Cernik, Champness, Fitch and Kohn1994a,Reference Bell, Redfern, Henderson and Kohnb). However, Table I shows that this crystal structure has a unit cell volume much closer to (but still smaller) than that for Cs₂Cd²⁺Si₅O₁₂ than that for Rb₂Cd²⁺Si₅O₁₂. The refined occupancies of the two extraframework A sites are: Rb1 0.52(2), Cs1 0.48(2); Rb2 0.48(2), Cs2 0.52(2). Within error limits there is complete disorder of these occupancies, similar to RbCsNi²⁺Si₅O₁₂. For X = Cd the A-O distances for each of the two extraframework A cation sites are also the same within error limits reflecting the disorder of Rb and Cs over these two sites. Table III shows that the CdO₄ tetrahedra in the silicate framework structure for RbCsCd²⁺Si₅O₁₂ is less distorted than those for Rb₂Cd²⁺Si₅O₁₂ and Cs₂Cd²⁺Si₅O₁₂. As was also seen for X = Ni, all X = Cd structures have larger mean Si-O-Si angles than the corresponding mean Si-O-X angles.

Figure 5. (color online) Rietveld difference plot for RbCsCd²⁺Si₅O₁₂. Blue circles represent observed data points, red line represents calculated data points, green line represents difference curve and purple crosses represent positions of Bragg reflections. R-factors for this refinement were:- R _p = 3.5399, Rwp = 4.5294, R _exp = 3.0185, χ ² = 2.2516. Miller indices are shown for some of the stronger peaks in the powder diffraction plot.

Figure 6. (color onlinr) VESTA structure plot for RbCsCd²⁺Si₅O₁₂, viewed down [111] showing a channel for extraframework Rb⁺ and Cs⁺ cations. SiO₄ tetrahedra are shown in blue, CdO₄ tetrahedra are shown in green with O²⁻ anions are shown in red. Pink (Rb⁺) and light blue (Cs⁺) shadings show the occupancies of the two A cation sites.

D. comparison of RbCsX ²⁺Si₅O₁₂ structures

The refined structure for X = Mg shows that having two different extraframework cation species results in structural changes compared to the structures with only one type extraframework cation. There are different mean A-O distances for the two A sites and partial A site cation ordering. For all X = Mg structures (with both one and two different extraframework cation species) the mean Si-O-Si and Si-O-X angles are similar.

However the refined structures for both X = Ni and Cd have similar mean A-O distances for the two A sites and no A site cation ordering. For all X = Ni and Cd structures (with both one and two different extraframework cation species) the mean Si-O-Si angles are larger than the corresponding Si-O-X angles. We have reported (Bell and Henderson, Reference Bell and Henderson2018) that this is the usual relationship for ordered P2 ₁/c leucites and reflects the presence of weaker X-O bonds in the tetrahedral framework leading to greater degrees of framework collapse about the cavity cation sites.

The refined unit cell volumes for the X = Mg and X = Ni (see Table I) are approximately intermediate between the unit cell volumes for the corresponding structures with only one extraframework cation species. The unit cell volumes for the Rb₂X ²⁺Si₅O₁₂ structures are smaller than the volumes for the RbCsX ²⁺Si₅O₁₂ structures by approximately the same amount that the corresponding unit cell volumes are larger for Cs₂X ²⁺Si₅O₁₂ structures. However, for X = Cd (see Table I) the unit cell volume for the Rb₂Cd²⁺Si₅O₁₂ structure is much smaller than that for the RbCsCd²⁺Si₅O₁₂ structure, and the unit cell volume for the RbCsCd²⁺Si₅O₁₂ structure is almost as large as the volume for the Cs₂Cd²⁺Si₅O₁₂ structure. This relationship might suggest that the framework is close to being fully expanded for a mean cavity cation radius slightly lower than that for Cs.