Concerning the incorporation of potassium in the crystal structure of combeite (Na2Ca2Si3O9)

Potassium incorporation in the structure of combeite has been studied in detail. Since natural combeites are known to contain only small amounts of potassium focus was laid on the Na-rich part of a hypothetical solid-solution series with composition Na2-xKxCa2Si3O9. Samples were prepared from mixtures of silica and the corresponding carbonates for nominal compositions with x = 0.2, 0.3 and 0.5, heated from ambient temperature to 1350 °C and slowly cooled to 1000 °C. After disintegration of the carbonates, the platinum capsules used as sample containers were welded shut in order to avoid losses of the volatile K2O and Na2O components. From all three batches potassium containing combeite crystals could be retrieved. Single-crystal diffraction experiments revealed the following compositions: Na2.10(1)K0.11(1)Ca1.90(1)Si3O9, Na2.09(1)K0.18(1)Ca1.91(1)Si3O9 and Na2.13(1)K0.18(1)Ca1.87(1)Si3O9. Consistently, the trigonal crystals (space group P 31 2 1) contained (i) (K + Na):Ca ratios larger than 1:1 and (ii) potassium concentrations lower than those in the starting mixtures. Since the K-contents of the samples obtained from the runs with x = 0.3 and 0.5 were almost identical, the solid-solution seems to be rather limited with an upper boundary of about one potassium atom per unit cell. The structure of the K-containing combeites is very close to the K-free structures reported in the literature. It can be described as a mixed tetrahedral-octahedral network in which additional K, Na and Ca cations are incorporated for charge compensation. A detailed analysis of the topological features of the net is presented. From the six observed extra-framework sites only the M22 position showing a coordination environment with ten next oxygen neighbours is involved in the K-substitution. Potassium uptake is also reflected in increasing values for the lattice parameters a and c as well as the unit-cell volumes. Actually, the c-axis is more affected from the incorporation of the comparatively large K+-cations.


Introduction
Combeite (idealized formula Na 2 Ca 2 Si 3 O 9 ) is a rare highlyalkaline silicate mineral, whose formation requires very special petrological settings. It has been observed, for example, in lapilli and ashes of the only active carbonatite volcano on Earth, Ol Doinyo Lengai (Tanzania) (Dawson et al. 1989;Keller et al. 2010;Mitchell and Dawson 2012), in lavas and pyroclastic rocks from the Nyiragongo volcano range (Democratic Republic of the Congo) (Andersen et al. 2012), in the Ettringer Bellerberg volcano in the Eifel district (Germany) (Fischer and Tillmanns 1983) or in foidites occuring as porphyric dikes (Brava Island, Cape Verde) (Weidendorfer et al. 2016). According to the articles cited above, combeite is associated with minerals such as götzenite, wollastonite, clinopyroxene, nepheline, melilite, titanium-rich garnet, sodalite or aegirine.
The corresponding synthetic analogue with composition Na 2 O × 2CaO × 3SiO 2 or NC 2 S 3 (using the nomenclature of technical mineralogy) has been first mentioned by Morey and Bowen (1925). Köppen and Padurow (1958) suggested a rhombohedral unit cell, consistent with its optically uniaxial properties. About ten years later, indexed X-ray powder diffraction data of this phase have been published (Dent Glasser and Mileson 1968). At the same time there were also first indications that the chemical composition of the so-called "1:2:3-phase" is more complex involving a solid-solution  (Maki and Sugimura 1968). Furthermore, the same authors reported that Na 2 Ca 2 Si 3 O 9 shows a reversible phase transition at about 485 °C. The existence of a continuous solid-solution series Na 3-x Ca 1.5+0.5x Si 3 O 9 (0 ≤ x ≤ 1) was suggested by Moir and Glasser (1974). Finally, the crystal structures of both, the ambient and the high-temperature polymorph, have been studied using single-crystal diffraction (Ohsato and Takéuchi 1986;Ohsato et al. 1990;Fischer and Tillmanns 1987).
In the field of materials science, Na 2 Ca 2 Si 3 O 9 has been intensively investigated as a crystalline phase in so-called 45S5 bioactive glass ceramics (Siqueira and Zanotto 2011;Xie et al. 2015;Blaeß et al. 2019;Karimi et al. 2018;Nawaz et al. 2020). Furthermore, the compound has been of interest as a potential host material for the preparation of red-emitting phosphors (Zhu et al. 2018), in the context of crystal nucleation and growth kinetics in soda-lime-glasses (Strnad and Douglas 1973;Macena et al. 2020) or as a phase occurring in steel slag glass-ceramics (Luo et al. 2020).
Data on the incorporation of alkali ions other than sodium into the crystal structure of combeite are rare. Natural samples from the Ol Doinyo Lengai locality, for example, contain only 0.13-0.50 wt.-% K 2 O which is equivalent to 0.010 to 0.037 potassium atoms per formula unit. By contrast, whole rock analysis of the corresponding lavas resulted in K 2 O-contents between 3.84 and 5.64 wt.-% (Klaudius and Keller 2006). Actually, mineral chemistry of the different species in the mineral assemblages indicates that nepheline is the primary potassium sink. A similar situation is observed when comparing combeites from the Nyiragongo area with the bulk chemistry of the nephelinite host rocks (Klaudius and Keller 2006). This leaves the question whether potassium cations can be incorporated into the combeite structure and, if so, to what extent. The aim of the present contribution was to bridge this gap in crystal-chemical knowledge. It is part of a wider ongoing research project on the phase relationships in the system Na 2 O-K 2 O-CaO-SiO 2 .

Experimental details
In order to study the Na ↔ K substitution in the combeite structure, samples corresponding to a hypothetical solidsolution series Na 2-x K x Ca 2 Si 3 O 9 with x = 0.2, 0.3 and 0.5 have been prepared. For easy reference, these mixtures will be denoted K-Comb-n with n = 2, 3, 5, respectively. Starting materials were Na 2 CO 3 (Merck, 99.9%), CaCO 3 (Merck, > 99.9%), K 2 CO 3 (Alfa Aesar, 99.997%) and SiO 2 (AlfaAesar, 99.995%) which were dried for 24 h at 400 °C before weighing on an analytical balance. Subsequently, stoichiometric batches of 0.5 g each were thoroughly mixed in a planetary ball mill for 45 min at 600 rpm using ethanol as a milling fluid. After careful evaporation of the alcohol at 60 °C in a hot-air cabinet the educts were stored in a desiccator. Synthesis experiments were performed in small platinum capsules having an inner diameter of 5 mm and a length of approximately 35 mm. After closing the lower ends of each capsule using a welding apparatus, about 100 mg of the corresponding educts were charged into the Pt-tubes. The capsules were placed vertically in corundum combustion boats filled with alumina hollow spheres, transferred to a chamber furnace, heated slowly to 700 °C and annealed for 12 h for complete disintegration of the carbonates. After removing from the furnace, the solid material inside the tubes was carefully compacted with a fitting plastic bar. The upper open ends of the capsules were pinched and welded shut. Actually, sealing was performed in order to prevent K 2 O and Na 2 O losses which are likely to occur at elevated temperatures. Subsequently, the containers were placed back into the combustion boats and heated from 25 °C to 1350 °C with a ramp of 5 °C/min. After holding the target temperature for 1.5 h, the samples were cooled down to 1000 °C with a rate of 0.1 °C/min and, finally, quenched to ambient conditions by removing the alumina boats from the furnace. Weighing the closed capsules before and after the hightemperature treatment indicated that they had not leaked during the synthesis runs.
After opening the capsules, the solidified melt cakes were mechanically separated from the container, further crushed in an agate mortar and transferred to glass slides under a polarizing binocular. A first inspection revealed the presence of transparent, colorless-birefringent single crystals up to 250 μm in size embedded in a glassy matrix. The crystals showed sharp extinction between crossed polarizers. For each composition, between 5 and 8 crystals were fixed on glass fibers using nail hardener as glue. Preliminary X-ray diffraction data were collected on an Oxford Diffraction Gemini R Ultra single-crystal diffractometer equipped with a four-circle kappa-goniometer and a Ruby CCD detector. Measurements were conducted with Mo-K α radiation. Initial diffraction experiments aiming on the determination of the unit-cell parameters proved the presence of combeiterelated compounds. Within a single batch, only very minor variations concerning lattice parameters and cell volumes were observed pointing to a homogenous composition of the samples. Finally, the crystal with the best overall diffraction quality from each batch was selected for further structural investigations (see Table 1). The CrysAlisPRO software package (Rigaku Oxford Diffraction 2015) was employed to process the data. After indexing, the diffraction patterns were integrated. Further data reduction included Lorentz and polarization as well as an analytical numeric absorption correction using multifaceted crystal models.
Diffraction symmetry of all crystals conformed to the trigonal Laue group 3 2∕m.
Initial coordinates for the structure refinements were taken from Fischer and Tillmanns (1987) using the same site nomenclature. Full-matrix least-squares refinements for all samples were performed with the program SHELXL (Sheldrick 2008) embedded in the software suite WinGX (Farrugia 1999). X-ray scattering factors were taken from the International Tables for Crystallography, Vol. C (Wilson 1995). The optimization calculations included fractional atomic coordinates and anisotropic displacement parameters. Allocation of the different cation species to the various nontetrahedral cation sites was performed using a combination of site occupancy refinements and bond distance considerations. No constraints concerning the bulk chemistry of the crystals were applied. The refinements converged to residual values for R(|F|) between 3.10 and 4.80%. The largest shifts/ esd in the final cycles were < 0.001. Notably, the resulting compositions were almost charge neutral. In comparison with the required six positive charges per formula unit that have to be contributed by the (Na + K + Ca)-cations the following values have been obtained: K-Comb-2: 6.01(2), K-Comb-3: 6.13(2) and K-Comb-5: 6.05(2). However, the formulas depart somewhat from ideal Na 2-x K x Ca 2 Si 3 O 9 and consistently exhibit less than two Ca-and more than two (Na + K)-atoms per formula unit (see Table 1). Due to the acentric character of the combeite structure, racemic twinning was taken into consideration. Actually, all samples represented inversion twins with volume ratios of the two individuals close to 1:1. Final coordinates, site occupancies as well as equivalent isotropic displacement parameters are given in Table 2. Anisotropic displacement parameters are listed in Table 3. Selected interatomic distances are summarized in Table 4
Charge compensation within the structure is realized by the incorporation of Na-, K-and Ca-atoms which are distributed among a total of six different non-tetrahedral cation positions showing six (M1, M4), seven (M32, M31), eight (M21) and ten (M22) next oxygen neighbors.
Based on the previous investigation of Fischer and Tillmanns (1987), most of the M-sites were considered as mixed Na-Ca positions and the corresponding percentages were obtained from site population refinements. In summary, the M4-site is exclusively occupied with calcium, whereas M21 contains only sodium cations. M32 is Ca-dominated, while M1 and M31 show significant amounts of both sodium and calcium, respectively. Since the M22-O bond lengths (see Table 4) were considerably longer when compared with the other M-O distances, it was assumed that potassium is restricted to this position. A refinement of the corresponding site population, however, revealed that M22 is only partially occupied. Notably, our approach for allocating the different cation species to specific M-positions resulted in almost charge neutral chemical compositions without the need for the introduction of additional restraints in the refinements.
While the polyhedra around M1 and M4 can be described as distorted octahedra, the coordination environments of the remaining M-positions are more complex. For the present study, the M22-position is of special interest. Actually, it represents the barycenter of the largest void. The corresponding polyhedral volumes for the three samples vary between 47.4 and 47.9 Å 3 . A projection of the whole structure parallel to [001] is given in Fig. 2.
Finally, the polyhedral microensembles or PME's have been constructed. On the lowest sublevel they are formed for each octahedron and tetrahedron in the asymmetric unit by considering all directly bonded [M4O 6 ]-and [SiO 4 ]-groups. They represent a geometrical interpretation of the coordination sequences up to the index k = 3. The PME's of the first sublevel observed for the M4 nodes can be described as follows: each [M4O 6 ]-octahedron is immediately linked to six tetrahedra. Using the classification based on the calculation of the coordination sequences up to k = 3 (Ilyushin and Blatov 2002) the PME's of M4 can be denoted as {6,6,18}. The PME's of all three crystallographically independent tetrahedral Si nodes conforms to {4,3,11} (see Fig. 3a and b).

Discussion
From a mineralogical point of view, combeite belongs to the so-called lovozerite-group of minerals (Pekov et al. 2009). The authors gave a comprehensive summary of the different members of the group including a detailed description of their structural characteristics. According to their analysis the lovozerite structure type is based on pseudo-cubic modules with edge lengths of about 7.5 Å. They distinguished non-tetrahedrally coordinated M, A and B cations which are located at the corners (M), the edge-centers (A) and the face-centers (B) of a single cube. Furthermore, so-called C-cations are mentioned which reside on one of the bodydiagonals of a single cube. For the K-containing samples of this study the following allocations can be made: M = M4, A = M32/M31, B = M21/M22, C = M1 (see Fig. 4a). Notably, the barycenter of the smaller cube formed by the six Siatoms of a single puckered ring and two additional M1-sites (see Fig. 1b) is located exactly in the center of the abovementioned larger cube (see Fig. 4b).
So far, two other structure refinements of the ambient temperature polymorph of combeites have been published (Ohsato and Takéuchi 1986;Fischer and Tillmanns 1987). Though the samples employed in the previous investigations did not contain potassium, it is interesting to compare the results of the refinements in more detail. Ohsato and Takéuchi (1986) used a synthetic sample retrieved from a starting composition with a Na:Ca ratio of 1:1. Notably, for the refinement of the site-populations the bulk composition  (2) -5(1) -8(2) 6(2) 23 (2) 14(2) 29(2) -5(2) -6(2) 4(2) 26 (2) 18 (2) 28 (2) -4(2) -5(2) 7(2) O10 11(1) 20(2) 24(2) 1(2) 3(1) 7(1) 10(2) 32(3) 24(2) 1(2) 5(1) 8(2) 12 (2) 32 (2) 26 (2) -1(2) 3(1) 9 (2) The anisotropic displacement factor exponent takes the form: -2π 2 [h 2 a* 2 U 11 + … + 2 h k a* b* U 12 ]. Lines one, two and three for each specific entry refer to the data of the samples K-Comb-2, K-Comb-3 and K-Comb-5, respectively  (6) 2.572(7) 2.502 (6) 2.569(7)  (7) 2.683(4) 2.680 (7) 2.685(4) M21-O7 2.663(5) M21-O4 2.784(4) 2.688 (7) 2.771(5) 2.680 (7) 2.764 (5)   was constrained to be Na 2 Ca 2 Si 3 O 9 . Fischer and Tillmanns' study from 1987 was based on a natural crystal where microprobe analysis indicated a chemical composition of Na 2.2 Ca 1.9 Si 3 O 9 . With respect of the composition, the K-containing samples also show less than two Ca-and more than two (Na + K)-atoms per formula unit. Differences between the refinements can be also found concerning the sites into which the Na, Ca and K cations are incorporated. For example, Ohsato and Takéuchi (1986) did not observe any scattering density on the M22 site. For the samples studied in the present contribution as well as for the crystal characterized by Fischer and Tillmanns (1987), this position is partially occupied with K-or Na-ions, respectively. Consistently, all three investigations report the existence of more or less pronounced maxima in the difference Fourier maps close to some of the extra-framework M-sites. In the present study, the two highest peaks of residual scattering density for all three samples were observed about 0.8 Å away from the M1-and the M31-position, respectively. Due to their comparatively low absolute values of about 1.5 e/Å 3 it was decided not to include them into the refinements. Notably, Ohsato and Takéuchi (1986) preferred to split the M1 position, while Fischer and Tillmanns (1987) did not model any scattering density on their most significant maximum of 2.0 e/Å 3 in the vicinity the M1-position. In summary one can say, that the combeite structure type offers a quite large number of extra-framework positions which can be fully or partially occupied providing a large flexibility concerning the uptake of the sodium and calcium ions and, therefore, an appreciable range of stoichiometry.
The incorporation of potassium is also reflected in the unit-cell volumes. With respect to the lattice parameters given by Ohsato and Takéuchi (1986)  Distortion parameters for the tetrahedral units (quadratic elongation, bond angle variance) and average bond distances are also listed. Lines one, two and three for a specific entry refer to the data of the samples K-Comb-2, K-Comb-3 and K-Comb-5, respectively  , sodium (yellow) and additional calcium (light blue) cations occupy voids between the tetrahedra and octahedra. Bi-colored spheres indicate mixed populations. The sizes of the bi-colored segments refer to the percentages determined from the site-occupancy refinements from 1248.7 Å 3 (K-free) to 1250.2 Å 3 (K-Comb-2) to 1262.8 Å 3 (K-Comb-3), that is-as might be expected-an increasing K-content leads to an increase in the unit-cell volumes. On the other hand, the two samples K-Comb-3 and K-Comb-5 having almost identical potassium contents exhibit a difference of about 2 Å 3 in the cell volumes (1262.8 as well as 1260.7 Å 3 ). By comparing the lattice parameters of a K-free combeite with one of the samples in this study, the so-called compositional strain (Ohasi and Burnham 1973) due to the potassium incorporation can be derived.

the volume increases
Using the data sets of Ohsato and Takéuchi (1986) (a 0 , c 0 ) as well as the sample K-Comb-3 (a 1 , c 1 ) as reference points the following strain components can be derived: Actually, the potassium induced expansion of the combeite structure parallel to [001] is about 1.56 times larger than perpendicular to the c-axis.