Crystal structures and X-ray powder diffraction data for AAlGe₂O₆ synthetic leucite analogs (A = K, Rb, Cs)

Abstract

Leucites are tetrahedrally coordinated silicate framework structures with some of the silicon framework cations that are partially replaced by divalent or trivalent cations. These structures have general formulae A₂BSi₅O₁₂ and ACSi₂O₆, where A is a monovalent alkali metal cation, B is a divalent cation, and C is a trivalent cation. There are also leucite analogs with analogous tetrahedrally coordinated germanate framework structures. These have general formulae A₂BGe₅O₁₂ and ACGe₂O₆. In this paper, the Rietveld refinements of three synthetic Ge-leucite analogs with stoichiometries of AAlGe₂O₆ (A = K, Rb, Cs) are discussed. KAlGe₂O₆ is I4₁/a tetragonal and is isostructural with KAlSi₂O₆. RbAlGe₂O₆ and CsAlGe₂O₆ are $I\bar{4}3d$ cubic and are isostructural with KBSi₂O₆.

I. INTRODUCTION

Synthetic anhydrous analogs of the silicate framework minerals such as leucite (KAlSi₂O₆) and pollucite (CsAlSi₂O₆) can be prepared with the general formulae A ₂BSi₅O₁₂ and ACSi₂O₆, where A is a monovalent alkali metal cation, B is a divalent cation, and C is a trivalent cation. These structures have the same topology, with B and C cations partially substituting onto tetrahedrally coordinated sites (T-sites) in the silicate framework, and charge-balancing A cations sitting in extraframework channels. The A cations can be replaced by ion exchange, and Cs-containing silicate framework minerals are of potential technological interest as storage media for radioactive Cs from nuclear waste (Gatta et al., 2008, 2009).

Many ambient temperature leucite analogs are known with different crystal structures and different A, B, and C cations (Bell, 2024). These structures all have the same topology, CsAlSi₂O₆ is $Ia\bar{3}d$ cubic (Beger, 1969), KBSi₂O₆ is $I\bar{4}3d$ cubic (Millini et al., 1993), and KAlSi₂O₆ is I4₁/a tetragonal (Mazzi et al., 1976). All these high symmetry structures have disordered T-site cations. However, lower symmetry structures are also known with ordered T-site cations. Examples of these cation-ordered structures are Eu²⁺-doped CsZnSi₂O₆ (Hariyani et al., 2020, $Pa\bar{3}$ cubic), Cs₂CdSi₅O₁₂ (Bell et al., 1994b, Pbca orthorhombic), and K₂MgSi₅O₁₂ (Bell et al., 1994a, P2₁/c monoclinic).

However, it is also possible to synthesize analogs of leucite and pollucite in which silicon is replaced with germanium. These Ge-leucites have germanate framework structures with the same topology as the leucite structure. In these cases, A ₂BGe₅O₁₂ and ACGe₂O₆ leucite analogs can be synthesized where B and C cations partially substitute onto tetrahedrally coordinated sites (T-sites) in the germanate framework, and charge-balancing A cations sit in extraframework channels.

Lattice parameters have been reported for A ₂BGe₅O₁₂ analogs (A = Rb, Cs; B = Be, Mg, Zn, Co, Fe, Ni, Cu, Cd) (Richerson and Hummel, 1972; Torres-Martinez et al., 1984; Torres-Martinez and West, 1989). Lattice parameters have also been reported for analogs ACGe₂O₆ (A = K, Rb, Cs, NH₄; C = B, Al, Ga, Cr, Fe) (Torres-Martinez et al., 1984; Torres-Martinez and West, 1989). Additionally, lattice parameters have been reported for K_0.8Rb_0.2AlGe₂O₆ (Klaska, 1978).

This paper reports the Rietveld refinements (Rietveld, 1969) of three Ge-leucites with stoichiometries of AAlGe₂O₆ (A = K, Rb, Cs). A crystal structure has been reported for CsAlGe₂O₆ (Tripathi and Parise, 2002), but no crystal structures have yet been reported for the K and Rb analogs. Powder Diffraction File (Gates-Rector and Blanton, 2019) data have been reported for these three Ge-leucite analogs. The PDF numbers are 00-37-1349 (KAlGe₂O₆), 00-37-348 (RbAlGe₂O₆), 00-37-347, and 04-012-2039 (CsAlGe₂O₆).

II. EXPERIMENTAL

A. Sample synthesis

All three samples were prepared from appropriate stoichiometric mixtures of K₂CO₃, Rb₂CO₃, Cs₂CO_3.3H₂O, GeO₂, and Al₂O₃. These mixtures were loaded into Pt crucibles and heated in air in a furnace. For all three samples, the mixtures were heated for 12 h at 1073 K (to decompose carbonates). For A = K, the crucible was air quenched, but for A = Rb and Cs the crucibles were quenched by dipping the bottom of the crucible in the bucket of cold water. For A = K, the mixture was then heated for 3 days at 1373 K. The sample was then removed from the furnace, reground, and then reheated for 4 days at 1373 K. For A = Rb, the mixture was then reground before further heating for 4 days at 1373 K. For A = Cs, the mixture was then reground before further heating for 50 h at 1373 K. The sample was then ground again before heating for 1 more day at 1373 K.

B. X-ray powder diffraction data collection

After heating, the samples were removed from the Pt crucibles, 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.

For A = K, data were collected on a PANalytical X'Pert Pro MPD using Cu Kα X-rays, with a nickel β-filter and a 3.3473° 2θ wide 255 channel PIXCEL-1D area detector. Data were collected in two scans using Data Collector 5.5a (PANalytical, 2017), scan 1 lasted 1 h, and scan 2 lasted 7 h and 30 min. These data were collected over the range of 5–100° 2θ with a step width of 0.0131° 2θ and an effective counting times of 118 s per point (scan 1) and 919 s per point (scan 2). For both scans, the beam size was defined with a 20 mm mask, fixed antiscatter (¼°), and divergence (⅛°) slits. These two scans were summed together after data collection.

For A = Rb, data were also collected on a PANalytical X'Pert Pro MPD using Cu Kα X-rays, with a nickel β-filter and a 3.3473° 2θ wide 255 channel PIXCEL-1D area detector. Data were collected in a single scan over 22 h using Data Collector 5.5a (PANalytical, 2017). These data were collected over the range of 10–100° 2θ with a step width of 0.0131° 2θ and an effective counting time of 2838 s per point. The beam size was defined with a 20 mm mask, fixed antiscatter (¼°), and divergence (⅛°) slits.

For A = Cs, data were collected on 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 a single scan over 19 h using Data Collector 5.1a (PANalytical, 2014). These data were collected over the range of 15–100° 2θ with a step width of 0.0131° 2θ and an effective counting time of 2592 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 were converted from an automatic divergence slit mode to a fixed divergence slit mode in HighScore 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 SRM640e silicon standard.

C. X-ray powder diffraction data analysis

All powder diffraction data were analyzed using HighScore Plus and the ICDD Powder Diffraction File. For A = K, analysis of the powder diffraction data showed that this sample was mostly KAlGe₂O₆ (PDF# 00-37-1349) with GeO₂ (PDF# 00-43-1016) and KAlGeO₄ (PDF# 01-78-1173) present as minor phases. For A = Rb, analysis of the powder diffraction data showed that this sample was mostly RbAlGe₂O₆ (PDF# 00-37-0348) with GeO₂ (PDF# 04-03-0650) and Al₂O₃ (PDF# 01-73-5928) present as minor phases. For A = Cs, analysis of the powder diffraction data showed that this sample was single-phase CsAlGe₂O₆ (PDF# 00-37-0347), apart from an unassigned Bragg reflection at about 17.8° 2θ.

All Rietveld refinements (Rietveld, 1969) for these data were done using GSAS-II (Toby and von Dreele, 2013). Table I shows details of the refinements, including the number of observed and calculated reflections, the number of structural parameters and profile parameters, and the R factors.

TABLE I. Details of Rietveld refinements.

For A = K, the crystal structure of KAlGe₂O₆ was refined using the I4₁/a tetragonal structure of KAlSi₂O₆ (Mazzi et al., 1976) as a starting model. The lattice parameters from PDF# 00-37-1349 were used and Ge atoms were put on the Si sites. The crystal structures of GeO₂ (Haines et al., 2002) and KAlGeO₄ (Sun et al., 2019) were used for the minor phases. Rietveld refinement showed that for A = K, the sample consisted of 98.1(5) wt% KAlGe₂O₆, 0.32(31) wt% GeO₂, and 1.57(7) wt% KAlGeO₄. In this KAlGe₂O₆ crystal structure, all atoms were located on the I4₁/a 16f Wyckoff general position. There is one 16f position for K, three 16f positions for T-sites (disordered 1/3^rd Al and 2/3^rd Ge), and six 16f positions for O. The isotropic temperature factors of the T-site atoms Al and Ge were constrained to be the same on each T-site but were allowed to vary between different T-sites. All isotropic temperature factors for the six O sites were constrained to have the same value. The T–O interatomic distances were soft-constrained to be 1.74 ± 0.02 Å (average bond distance for tetrahedral Al–O and Ge–O). This assumption is made due to complete T-site disorder (1/3^rd Al and 2/3^rd Ge on each T-site) as it was not possible to refine chemically sensible T-site occupancies. This constraint distance was determined from the differences between the ionic radii for Si⁴⁺ and Ge⁴⁺ (Shannon, 1976) and then added the difference to the KAlSi₂O₆ T–O soft constraint distance of 1.68 ± 0.02 Å.

For A = Cs, the crystal structure of CsAlGe₂O₆ was refined using the $I\bar{4}3d$ cubic structure of CsAlGe₂O₆ (Tripathi and Parise, 2002) as a starting model. Due to the presence of the unassigned Bragg reflection at about 17.8° 2θ, the data from 15 to 18° 2θ were excluded from the Rietveld refinement, which was then done assuming a single phase of CsAlGe₂O₆. For A = Rb, the crystal structure of CsAlGe₂O₆ was used as a starting model, the lattice parameters from PDF# 00-37-0348 were used, and Rb was replaced Cs in the extraframework cation site. The crystal structures of GeO₂ (Haines et al., 2002) and Al₂O₃ (Finger and Hazen, 1978) were used for the minor phases. Rietveld refinement showed that for A = Rb, the sample consisted of 88.80(24) wt% RbAlGe₂O₆, 0.24(7) wt% GeO₂, and 10.96(23) wt% Al₂O₃. For both A = Cs and A = Rb, the T–O interatomic distances were also soft-constrained to be 1.74 ± 0.02 Å.

VESTA (Momma and Izumi, 2011) was used to plot crystal structures.

III. RESULTS AND DISCUSSION

Crystal structures have been refined for AAlGe₂O₆ (A = K, Rb, Cs) synthetic leucite analogs from X-ray powder diffraction data. The crystal structure of KAlGe₂O₆ is isostructural with the I4₁/a tetragonal structure of KAlSi₂O₆. The crystal structures of RbAlGe₂O₆ and CsAlGe₂O₆ are both isostructural with the $I\bar{4}3d$ cubic structure of CsAlGe₂O₆ (Tripathi and Parise, 2002). All refined structures have disordered T-site cations.

Table II shows the comparison of the refined lattice parameters for AAlGe₂O₆ (A = K, Rb, Cs) with the starting structures used for Rietveld refinement. Table III, Table IV, and Table V similarly show refined interatomic distances and angles. Table VI shows the tetrahedral angle variances for the T-sites (Robinson et al., 1971) in these germanate framework structures.

TABLE II. Refined lattice parameters compared with those for starting structures.

^a Mazzi et al. (1976)

^b This work.

^c Tripathi and Parise (2002).

TABLE III. Refined interatomic A–O distances (Å) (A = K, Rb, Cs).

TABLE IV. Refined interatomic T–O distances (Å) (T = Al/Ge).

TABLE V. Refined interatomic angles (°) (T = Al/Ge).

TABLE VI. Tetrahedral angle variance [σ ², deg²]: σ ² = Σ(θ–109.47)²/5 (Robinson et al., 1971) where θ is the O–T–O tetrahedral angle.

Mean variance and standard deviation are given for the three tetrahedral sites in the A = K I4 ₁/a structure. Variance is given for the single tetrahedral site in the A = Rb and Cs $I\bar{4}3d$structures.

A. KAlGe₂O₆ structure

Figures 1 and 2, respectively, show the Rietveld difference and the VESTA crystal structure plots for the refined crystal structure of KAlGe₂O₆. Table II shows that this crystal structure has a unit cell volume that is larger than the isostructural KAlSi₂O₆, which was used as a starting model for Rietveld refinement, reflecting the difference between the ionic radii for Si⁴⁺ and Ge⁴⁺ (Shannon, 1976).

Figure 1. Rietveld difference plot for KAlGe₂O₆. Red circles represent observed data points, blue line represents calculated data points, and the green line represents difference curves. The upper line of black crosses represents positions of Bragg reflections for KAlGe₂O₆, the middle line of black crosses represents positions of Bragg reflections for GeO₂, and the lower line of black crosses represents positions of Bragg reflections for KAlGeO₄.

Figure 2. VESTA I4₁/a tetragonal structure plot for KAlGe₂O₆, viewed down [1–11] showing a channel for extraframework purple K⁺ cations. Disordered (Al/Ge)O₄ tetrahedra are shown in light purple, and O²⁻ anions are shown in red.

B. RbAlGe₂O₆ structure

Figures 3 and 4, respectively, show the Rietveld difference and the VESTA crystal structure plots for the refined crystal structure of RbAlGe₂O₆. Table II shows that the crystal structure of RbGaSi₂O₆ has a smaller unit cell volume than that of CsGaSi₂O₆, which was used as a starting model for Rietveld refinement. This also reflects the difference in the ionic radii for Rb⁺ and Cs⁺ cations (Shannon, 1976).

Figure 3. Rietveld difference plot for RbAlGe₂O₆. Red circles represent observed data points, blue line represents calculated data points, and the green line represents difference curves. The upper line of black crosses represents positions of Bragg reflections for RbAlGe₂O₆, the middle line of black crosses represents positions of Bragg reflections for Al₂O₃, and the lower line of black crosses represents positions of Bragg reflections for GeO₂.

Figure 4. VESTA $I\bar{4}3d$ cubic structure plot for RbAlGe₂O₆, viewed down [111] showing a channel for extraframework pink Rb⁺ cations. Disordered (Al/Ge)O₄ tetrahedra are shown in light purple, and O²⁻ anions are shown in red.

C. CsAlGe₂O₆ structure

Figures 5 and 6, respectively, show the Rietveld difference and the VESTA crystal structure plots for the refined crystal structure of CsAlGe₂O₆. Table II shows that the crystal structure of CsAlGe₂O₆ has a slightly smaller unit cell volume than that of the CsAlGe₂O₆ structure (Tripathi and Parise, 2002), which was used as a starting model for Rietveld refinement.

Figure 5. Rietveld difference plot for CsAlGe₂O₆. Red circles represent observed data points, blue line represents calculated data points, and the green line represents difference curves. The line of black crosses represents positions of Bragg reflections for CsAlGe₂O₆.

Figure 6. VESTA $I\bar{4}3d$ cubic structure plot for CsAlGe₂O₆, viewed down [111] showing a channel for extraframework light blue Cs⁺ cations. Disordered (Al/Ge)O₄ tetrahedra are shown in light purple, and O²⁻ anions are shown in red.

D. Comparisons between AAlGe₂O₆ structures

Figures 2, 4, and 6 show plots of the AAlGe₂O₆ crystal structures. Figure 2 (A = K) shows that the central channel for the I4₁/a tetragonal structure shows greater framework collapse (Taylor and Henderson, 1968) compared to the corresponding channels for the $I\bar{4}3d$ cubic structures for A = Rb and Cs, reflecting the differences in the sizes of the extraframework alkali metal cations (Shannon, 1976).

Table III shows that the mean A–O distances are smallest for A = K and largest for A = Cs, also reflecting the differences in the sizes of the extraframework alkali metal cations (Shannon, 1976). Table IV shows that there are some significant differences between the mean T–O distances in these crystal structures. All refinements were done assuming stoichiometries of AAlGe₂O₆, with Ge and Al in a 2:1 ratio. However, the presence of impurity phases in the A = K and Rb samples could mean that the Ge and Al may not be in an exact 2:1 ratio. This could change the mean size of the T-site cation and consequently change the mean T–O distances.

Table V shows the intratetrahedral (O–T–O) and intertetrahedral (T–O–T) angles for the three crystal structures. The mean O–T–O angles are close to the ideal tetrahedral angle of 109.47°, and the mean T–O–T angles for the three structures are similar. Table VI shows that the greatest tetrahedral distortion is for the A = Cs structure.

E. Future work on the KAlGe₂O₆ structure

The crystal structure of KAlGe₂O₆ is isostructural with the I4₁/a tetragonal structure of KAlSi₂O₆ (Mazzi et al., 1976) and KGaSi₂O₆ (Bell and Henderson, 2020). Both I4₁/a silicate structures undergo high temperature-phase transitions to $Ia\bar{3}d$ cubic structures, which was isostructural with CsAlSi₂O₆ (Beger, 1969). The phase transition temperatures were 943 K (KAlSi₂O₆, Palmer et al., 1997) and 673–970 K (KGaSi₂O₆, Bell and Henderson, 2020). It would be interesting to see if KAlGe₂O₆ would undergo a similar phase transition on heating, would there be a phase transition to an $Ia\bar{3}d$ or $I\bar{4}3d$ cubic structure?

IV. CONCLUSIONS

Crystal structures have been refined for AAlGe₂O₆ synthetic leucite analogs (A = K, Rb, Cs). All refined structures have disordered T-site cations. KAlGe₂O₆ is isostructural with I4₁/a tetragonal KAlSi₂O₆ leucite. However, CsAlGe₂O₆ has the $I\bar{4}3d$ cubic space group and is isostructural with a previously published structure for CsAlGe₂O₆. RbAlGe₂O₆ also has the $I\bar{4}3d$ cubic space group and is isostructural with CsAlGe₂O₆.

V. DEPOSITED DATA

CIF files with information related to crystal structure, interatomic distances and angles, and powder diffraction data for KAlGe₂O₆, RbAlGe₂O₆, and CsAlGe₂O₆ synthetic leucite analogs were deposited with the ICDD. You may request these data from ICDD at [email protected].