Occurrence and associated minerals

Letnikovite-(Ce) was found in the moraine of the Darai-Pioz glacier in the upper reaches of the Darai-Pioz River, Tien-Shan mountains, near the junction of the Turkestansky, Zeravshansky and Alaisky ranges (39°30′N 70°40′E). This area is in the Rasht (formerly Garm) district, Central Tajikistan. The alkaline Darai-Pioz massif belongs to the Upper Paleozoic Alaysky (Matchaisky) intrusive complex. Information on the geology of the Darai-Pioz massif can be found in Pautov et al. (Reference Pautov, Agakhanov, Karpenko, Uvarova, Sokolova and Hawthorne2019) with reference to relevant earlier publications.

Letnikovite-(Се) was found in boulders (up to 2 m) of quartz rock, 90–95% medium- to coarse-grained quartz of ice-like appearance (quartz grains vary from 2 mm to 2 cm) characteristic for moraine deposits of the Darai-Pioz glacier. The following subordinate and accessory minerals are present: large (up to 10 cm across) golden-brown tabular and lamellar crystals of polylithionite, pink plates of sogdianite–sugilite, pale-yellow to orange aggregates and tabular crystals of reedmergnerite, black crystals of aegirine, orange–brown semi-transparent lentil-like crystals of stillwellite-(Се), grass-green or yellowish-green semi-transparent and transparent crystals of leucosphenite, dark-green crystals of turkestanite and aggregates of large white grains of microcline. Also common are fine-grained brown or greyish-brown aggregates of Mn-bearing pectolite, quartz, Sr-bearing fluorite, aegirine and a variety of rare minerals; letnikovite-(Ce) occurs in these pectolite-rich aggregates (Fig. 1a). Associated minerals are quartz, fluorite, pectolite, baratovite, aegirine, leucosphenite, neptunite, reedmergnerite, orlovite, sokolovaite, mendeleevite-(Ce), odigitriaite, pekovite, zeravshanite, kirchhoffite and garmite. Letnikovite-(Ce) occurs in a peralkaline pegmatite oversaturated with silica (silexite-like) and was formed at a late, probably hydrothermal, stage of the pegmatite.

Figure 1. Back-scatter electron images of polished sections with letnikovite-(Ce) [Lkv-Ce] in association with mendeleevite-(Ce) [Mdl-Ce], pectolite [Pct], fluorite [Fl] and quartz [Qz]: (a) the grain used for Raman spectroscopy, determination of micro-indentation hardness and reflectance spectra; (b) a microprobe mount with a grain that was deposited as holotype material (#98145) at the Fersman Mineralogical Museum.

Physical properties

Letnikovite-(Ce) occurs as isolated prismatic grains up to 0.1 mm long and up to 0.03 mm thick in a quartz–pectolite aggregate (Fig. 1a,b). The mineral is colourless and has a white streak and a vitreous lustre. Letnikovite-(Ce) does not fluoresce under cathode rays or ultraviolet light. The mineral is brittle, cleavage is {001} perfect, the fracture is stepped along the cleavage plane and uneven across this direction; no parting was observed. The average micro-indentation hardness is VHN50 = 239 kg/mm² (with a range of 193–266). Although micro-indentation and Mohs hardness are different hardness measurements (Broz et al., Reference Broz, Cook and Whitney2006), the first representing the resistance to indentation and the second one the resistance to scratch, the present value of micro-indentation hardness corresponds roughly to a Mohs hardness of ~4. Measurements were done on the PMT-3 instrument, calibrated on NaCl at a loading of 50 g. The calculated density, D _calc., is 2.847 g/cm³.

Macroscopically, the crystals do not show twinning. However, because of the microscopic twinning, the 2V value and optic sign could not be determined. Letnikovite-(Ce) is nonpleochroic. In reflected light, letnikovite-(Ce) is grey. Bireflectance is weak, ΔR = 0.8% (589 nm). When observed in air, internal reflections were not seen, and anisotropy is not visible. Reflectance values were measured with a UMSP-50 Opton microspectrophotometer using the Opton SiC standard 474251 (with a spectral slot width of 10 nm) and are given in Table 1.

Table 1. Reflectance values (%) for letnikovite-(Ce).*

* The values required by the COM are given in bold.

Raman spectroscopy

The Raman spectrum of letnikovite-(Ce) (Fig. 2a,b) was obtained at room temperature from a randomly oriented crystal (polished section, 70 × 30 μm size) using a Thermo DXR2xi Raman imaging confocal microscope with a green laser (532 nm). The output power of the laser beam was 5 mW (at 50% power), holographic diffraction grating with 4000 lines per cm, spectral resolution was 2 cm^–1, and the range was from 50 to 6000 cm^–1. The diameter of the focal spot on the sample was 2 μm. The back-scattered Raman signal was collected with a 100× objective; the signal acquisition time for a single scan from 50–6000 cm^–1 was 0.5 s and the signal was averaged over 1000 scans. For the range 50–1800 cm^–1 the signal acquisition time was 2.0 s and the signal was averaged over 30 scans. The spectrum was processed using Omnic software (Thermo Scientific™). Letnikovite-(Ce) shows intensive luminescence from 100 to 3500 cm^–1, and background subtraction was applied.

Figure 2. Background-subtracted Raman spectrum of letnikovite-(Ce): (a) the ‘fingerprint’ region from 50–1800 cm^–1; and (b) the principal O–H stretching region from 3000–3800 cm^–1.

On the basis of data for some ring silicates with Na, Ca and rare earth elements (REE) (Sitarz et al., Reference Sitarz, Mozgawa and Handke1998; Frost and Xi, Reference Frost and Xi2012; Tobbens et al., Reference Tobbens, Kahlenberg, Kaindl, Sartory and Konzett2008), we assign the bands at 1107 and 952 cm^–1 to Si–O stretching vibrations, and those at 667 and 693 cm^–1 are attributed to O–Si–O bending modes. Raman bands of lower frequency (500–100 cm^–1, Fig. 2a) are assigned to Me–O stretching vibrations and collective lattice vibrations and translational and deformation modes, including the intense band at 464 cm^–1 which probably corresponds to a Ca–O stretching mode (Frost and Xi, Reference Frost and Xi2012).

From 3000–3700 cm^–1 (Fig. 2b), there are several broad peaks (3233, 3402 and 3553 cm^–1) corresponding to stretching modes of H₂O and OH groups.

Chemical composition

The chemical composition of letnikovite-(Ce) was determined using a JEOL 773 electron-microprobe (EDS mode, an accelerating voltage of 20 kV, a beam current of 2 nA and a beam diameter of 5 μm; Fersman Mineralogical Museum). The following standards were used: microcline USNM 143966 (Si; K); albite 107 (Na); SrTiO₃ (Sr); CsTbP₄O₁₂ (Cs); ilmenite USNM 96189 (Fe); anorthite USNM 137041 (Ca); diopside USNM 11773 (Mg); LaPO₄ (La); CePO₄ (Ce); PrPO₄ (Pr); NdPO₄ (Nd); SmPO₄ (Sm); EuPO₄ (Eu); GdPO₄ (Gd); and MgF₂ (F).

The data (5 analyses) were reduced and corrected by the PAP method of Pouchou and Pichoir (Reference Pouchou, Pichoir and Armstrong1985). The chemical composition of letnikovite-(Ce) is the mean of five determinations and is given in Table 2. The empirical formula calculated on 7 Si atoms per formula unit (apfu) is Na_0.72K_0.14Cs_0.04Ca_2.10Sr_0.55Mg_0.28Pb_0.05Fe_0.04(Ce_0.71Nd_0.33La_0.14Pr_0.10Eu_0.02Gd_0.01)_Σ1.31Si₇O_21.84F_3.81H_8.58, Z = 4. The structural formula based on refined site-occupancies (see below) is (Na_0.72Ca_0.16□_1.12)_Σ2(Cs_0.04□_0.96)_Σ1(Ca_1.83□_0.17)_Σ2(Mg_0.28Fe_0.04□_0.68)_Σ1(Ln ³⁺_1.31Sr_0.55Ca_0.09Pb_0.05)_Σ2[Si₇O₁₇(OH)]F_3.81(H₂O)_3.79, where Ln ³⁺_1.31 = (Ce_0.71Nd_0.33La_0.14Pr_0.10Eu_0.02Gd_0.01)_Σ1.31. The simplified formula is (Na,□)₂Ca₂(Ln ³⁺,Sr)₂[Si₇O₁₇(OH)]F₄(H₂O)₄, where Ce is the dominant lanthanoid and (□,Cs) and (□,Mg) are omitted as □ > 70%. The ideal formula of letnikovite-(Ce), (Na□)Ca₂Ce₂[Si₇O₁₇(OH)]F₄(H₂O)₄ (see below), requires (wt.%) Na₂O 3.04, CaO 11.03, Ce₂O₃ 32.28, SiO₂ 41.36, F 7.47, H₂O 7.97, O ≡ F –3.15, total 100.00.

Table 2. Chemical composition and unit formula for letnikovite-(Ce).

* Formula calculated on 7 Si apfu; Esd = estimated standard deviation.

** H₂O calculated from structure-refinement results: H₂O = 3.79 pfu and OH = 1.0 pfu.

Powder X-ray diffraction

Powder X-ray diffraction data were obtained by collapsing single-crystal experimental data into two dimensions. Data (in Å for MoKα) are listed in Table 3. Unit-cell parameters are therefore the same as from the single-crystal data (Table 4).

Table 3. Simulated powder X-ray diffraction data (d in Å) * for letnikovite-(Ce).

* Powder data were obtained by collapsing single-crystal X-ray diffraction data into two dimensions.

Intensities are listed for reflections with I _est. ≥ 20; the eight strongest peaks are marked in bold.

Table 4. Miscellaneous structure-refinement data for letnikovite-(Ce).

*Twin components are related by the transformation matrix ($\bar{1}$ 0 0, 0 $\bar{1}$ 0, 1 0 1).

X-ray single-crystal data collection and structure solution and refinement

X-ray single-crystal data for letnikovite-(Ce) were collected from a twinned crystal with a Rigaku Oxford Diffraction diffractometer equipped with a Mo micro-source X-ray tube and a Dectris Pilatus-200 K detector, controlled by the Crysalis-Pro™ software (Rigaku Oxford Diffraction, 2018). The intensities of reflections with –13 ≤ h ≤ 13, –41 ≤ k ≤ 41 and –25 ≤ l ≤ 25 were collected with a frame width of 0.5° and a frame time of 40 s up to 2θ ≤ 81.34°, and an empirical absorption correction (SCALE3 ABSPACK, Rigaku Oxford Diffraction, 2018) was applied. There were few observed reflections at high 2θ, and refinement of the structure was done for 2θ ≤ 54°, –9 ≤ h ≤ 9, –29 ≤ k ≤ 29 and –17 ≤ l ≤ 17. The observed lattice is metrically orthorhombic F with the following cell parameters obtained from the monoclinic cell via the transformation matrix $\bar{1}$00/102/010: a = 7.473, b = 26.852 and c = 22.920 Å. However, a tentative structure solution in space group F222 yielded wrong coordination geometries as well as ill-defined anisotropic displacement parameters. The monoclinic cell with half-cell volume led to a much more satisfactory solution. The crystal-structure solution by direct methods and refinement were done with the Bruker SHELXTL Version 5.1 software (Sheldrick, Reference Sheldrick2015) in space group C2/m. We refined the structure as two components related by the TWIN matrix ($\bar{1}$ 0 0, 0 $\bar{1}$ 0, 1 0 1). The crystal structure of letnikovite-(Ce) was refined to R ₁ = 4.20%, the twin ratio being 0.502(5):0.498(5) (Table 4). Details of data collection and structure refinement are given in Table 4. The occupancies of six cation sites were refined with the following scattering curves: M1 site: Ce; M(2,3) sites: Ca; M4 site: Mg; A1 and A2 sites: Na and Cs, respectively. The occupancies of the X(1–4) and W(1–5) anion sites were refined with the scattering curves of F and O, respectively. Refinement of the X2 and W1 site-occupancies converged to integer values (within 3 e.s.d.) and were subsequently fixed at full occupancy. Scattering curves for neutral atoms were taken from the International Tables for Crystallography (Wilson, Reference Wilson1992). Final atom coordinates and equivalent displacement parameters are given in Table 5, selected interatomic distances and angles in Table 6, refined site-scattering values and assigned site-populations in Table 7, and bond-valence values in Tables 8 and 9. A list of observed and calculated structure factors and a Crystallographic Information File (CIF) have been deposited with the Principal Editor of Mineralogical Magazine and are available as Supplementary Material (see below). The sturcture diagrams were drawn using Atoms 6.4 software (Dowty, Reference Dowty2016).

Table 5. Atom coordinates, site occupancies (Site occ., %) and anisotropic displacement parameters (Ų) for letnikovite-(Ce).

* For composition of the M(1–4) and A(1,2) sites see Table 7; X1 = [(H₂O),F]; X2 = F, X(3,4) = [F,(H₂O)]; W(1–5) = O atoms of H₂O groups; **U _iso.

Table 6. Selected interatomic distances (Å) and angles (°) in letnikovite-(Ce).

φ = O, F, H₂O and OH.

Symmetry codes: a: –x, y, –z + 1; b: –x + 1, y, –z + 1; c: x+½, y–½, z; d: x+½, –y+½, z; e: –x+½, –y+½, –z + 1; f: –x+½, y–½, –z + 1; g: –x+³/₂, –y+½, –z + 1; h: –x+³/₂, y–½, –z + 1; i: x–½, y+½, z; j: x+½, y+½, z + 1; k: x, –y + 1, z; l: x, y, z; m: –x, y, –z; n: x, y, z–1; o: x–½, y+½, z–1; p: –x+½, y+½, –z + 1; q: x, –y + 1, z–1; r: –x, –y + 1, –z + 1; s: x–½, –y–½, z; t: –x + 2, –y, –z + 1; u: –x + 1, –y, –z.

Table 7. Refined site-scattering and assigned site-populations for letnikovite-(Ce).

φ = O, F, OH and H₂O.

* Ln ³⁺_1.31 = Ce_0.71Nd_0.33La_0.14Pr_0.10Eu_0.02Gd_0.01 [76.76 epfu]; f_av = 58.60 el. (f_av = average scattering curve for Ln³⁺_1.31).

** Site scattering was refined, adjusted in accord with chemical analysis (Table 2), and then fixed at the last stages of the refinement.

Table 8. Bond-valence values (vu) for anions in letnikovite-(Ce).

*Bond-valence parameters (vu) are from Brown (Reference Brown, O'Keeffe and Navrotsky1981); bonds to oxygen were used for O(1–10), X1 and W(1,2); bonds to fluorine were used for X(2–4); occupancies of cation sites were taken into account for all calculations; the last row gives bond-valence sums for M2, M4 and A1 where the corresponding sites are 100% occupied.

**See discussion in the text on the contribution of hydrogen bonding to the bond-valence sum at O10.

Table 9. Bond-valence values (vu) for the O2 and X(1,3,4) anions involved in short-range order in letnikovite-(Ce)*.

* Bond-valence parameters (vu) are from Brown (Reference Brown, O'Keeffe and Navrotsky1981); anion curves are shown in square brackets for each atom.

** There are O–O distances [O2–W1 and O2–W3, Table 6] suitable for possible hydrogen bonding which can add ~0.3 vu in total to the bond-valence sum of 1.38 vu at O2. With the bond-valence sum of 1.68 vu, O2 = O atom.

Site-population assignment

Firstly, we assign Si to four tetrahedrally coordinated Si sites, with <Si–O> = 1.619 Å (Tables 5, 6).

Next considered are the four M sites in the heteropolyhedral sheet (Table 5). At the [9]-coordinated M1 site, the refined scattering is 104.5 electrons per formula unit (epfu), the highest value for the M sites; the mean bond length <M1–φ> = 2.539 Å (φ = O, F and H₂O). In accord with the grand mean bond length <^[9]Ce³⁺–O> = 2.553 Å observed in inorganic structures (Gagné, Reference Gagné2018), we assign heavy scatters: REE = Ln ³⁺_1.31, where Ce is the dominant lanthanoid (Ln = lanthanoids) and minor Pb: 0.05 apfu, plus Sr: 0.55 apfu and minor Ca: 0.09 apfu, to the M1 site [^[9]Ce³⁺: r = 1.196 Å, ^[9]Sr: r = 1.31, ^[9]Pb: r = 1.35 Å, ^[9]Ca²⁺: r = 1.18 Å, Shannon (Reference Shannon1976)] (Tables 5–7). There is a good agreement between refined and calculated site-scattering for the M1 site: 104.5 and 103.56 epfu, respectively (Table 7). On the basis of the refined site-scattering values and observed bond distances, we assign Ca_0.83□_0.17 and Ca_1.0 apfu to the M2 and M3 sites, respectively (Table 7). The remaining M4 octahedron is the smallest polyhedron, and the refined scattering at the M4 site is 4.4 epfu, the lowest value for the M sites. Therefore, we allocate all the available Mg and Fe²⁺ to the M4 site, and the composition of the site is Mg_0.28Fe²⁺_0.04□_0.68 apfu.

The interstitial A1 and A2 sites have refined site-scattering values of 11.0 and 2.2 epfu, respectively, with a sum of 13.2 epfu (Table 7). The cations to be assigned to these sites are Na, Ca and Cs, with a total scattering of 13.32 epfu (Table 2). The A1 polyhedron is smaller (mean bond distance of 2.546 Å), whereas the A2 polyhedron is larger, with <A2–φ> = 3.65 Å. Therefore, we assign all the available Na and Ca to the A1 site, which yields 11.12 epfu, in good agreement with the refined value of 11.0(4) epfu. Cs is the largest cation left to be assigned, and we allocate it to the A2 site. Hence a vacancy is dominant at the A2 site (Table 7).

Description of the structure

Cation sites

The crystal structure contains three groups of cation sites: M sites of the heteropolyhedral sheet, Si sites of the Si–O–OH sheet, and interstitial A1 and A2 sites.

Heteropolyhedral sheet

There are four cation sites in the heteropolyhedral sheet: the Ce-dominant M1 site, the Ca-dominant M(2,3) sites, and the □-dominant M4 site (Fig. 3a,b). The M1 site is occupied by Ln _1.31Sr_0.55Ca_0.09Pb_0.05 apfu, where Ce is the dominant lanthanoid. The M1 atom is coordinated by nine anions: five O atoms and four X(1–4) anions where X = F and H₂O (Tables 5–7) (see discussion on short-range order below). The ideal composition of the M1 site is Ce₂ apfu. The M2 site is occupied by Ca at 83%, its composition is Ca_0.83□_0.17 pfu, ideally Ca_1.0 apfu. The M2 atom is coordinated by seven anions: two O atoms, four X(3,4) anions and an H₂O group at the W1 site (Tables 6, 7). The M3 site is fully occupied by Ca, its ideal composition is Ca_1.0 apfu. The M3 atom is coordinated by seven anions: three O atoms and four X(2,4) anions (Tables 6, 7). The M4 site is occupied by Mg_0.28Fe²⁺_0.04□_0.68 pfu, its ideal composition is □_1.0 pfu. Ideally, cations of the heteropolyhedral sheet, ^{M 2}Ca +^{M 3}Ca + ^{M 1}Ce₂ + ^{M 4}□, sum to [Ca₂Ce₂]¹⁰⁺ apfu (Table 7).

Figure 3. Short-range order (SRO) arrangements in the heteropolyhedral sheet, ideally [Ca₂Ce₂F₄(H₂O)₂]⁷⁺: (a) SRO-68%, the M4 site is vacant, and the X1 site is occupied by an H₂O group; (b) SRO-32%, the M4 site is occupied by Mg plus minor Fe²⁺, the X1 site is occupied by F, and M4 octahedra share edges and vertices with M1 and M2 polyhedra. The [9]-coordinated Ce-dominant M1 polyhedra are green, [7]-coordinated Ca-dominant M(1,2) polyhedra are pink, Mg-dominant M4 octahedra are purple, the vacant M4 site is shown as a white circle with a purple rim; H₂O groups and F atoms are shown as large red and small yellow spheres, respectively.

Si–O–OH sheet

In the Si–O–OH sheet (Fig. 4a,b), there are four Si(1–4) tetrahedrally coordinated sites occupied by Si with a <Si–O> distance of 1.619 Å (Tables 5, 6). We consider the Si–O–OH sheet as a complex anion (see below).

Figure 4. A single [Si₇O₁₇(OH)]^7– sheet of five-membered and ten-membered rings of SiO₄ and SiO₃(OH) tetrahedra parallel to (001): (a) in the lower sheet at z ≈ 0.69, SiO₃(OH) tetrahedra are oriented upward along c; (b) in the upper sheet at z ≈ 1.21, SiO₃(OH) tetrahedra of the upper sheet are oriented downward along c; upward looking SiO₃(OH) tetrahedra belong to the lower sheet and indicate the relative orientations of the two sheets. Si tetrahedra are orange, OH groups are shown as small turquoise spheres.

Interstitial sites

In letnikovite-(Ce), there are two interstitial sites: A1 and A2. They occur in the large channels between two Si–O–OH sheets (Fig. 5a,b). The A1 site is coordinated by three basal O atoms of Si tetrahedra, two H₂O groups at the W(1,2) sites and an X4 anion (Table 6, Fig. 6a,b). It is ~50% occupied by Na_0.72Ca_0.16□_1.12 pfu, and <A1–φ> = 2.546 Å (Table 7). We write the ideal composition of the A1 site as (Na□) pfu. The A2 site occurs in the centre of the channel (Fig. 5a) and is dominantly vacant. The A2 site is coordinated by eight basal oxygen atoms of Si tetrahedra on both sides of the channel and three H₂O groups at the W(2,4) sites in the centre of the channel (Table 6, Fig. 7). It is occupied at 4% by Cs: Cs_0.04□_0.96 pfu, and <A2–φ> = 3.65 Å (Table 7). We write the ideal composition of the A2 site as □ pfu. Ideally, interstitial cations, ^{A 1}(Na□) +^{A 2}□, sum to (Na□)¹⁺ pfu.

Figure 5. Letnikovite-(Ce): (a) general view of the crystal structure; (b) linkage of a heteropolyhedral sheet and a single Si–O–OH sheet. Inset on the right from (a) shows possible hydrogen bonds between OH groups of two Si4 tetrahedra in the upper and lower Si–O–OH sheets along c. Legend as in Fig. 3, Si tetrahedra are orange, OH groups are shown as small turquoise spheres; interstitial cations, ^[7]Na at the A1 site (44% occupancy) and ^[11]Cs at the A2 site (4% occupancy) are shown as blue and pale-orange spheres; H₂O groups at partly occupied W(2–5) sites in between two Si–O–OH sheets are shown as large red spheres.

Figure 6. Short-range order arrangements related to the A1 site occupied by Na at 44% and W2 site occupied by H₂O at 44%: (a) SRO-44%, the A1 site is 100% occupied by Na and the [7]-coordinated A1 polyhedra link via vertices occupied by H₂O groups at the W1 and W2 sites; (b) SRO-56%, the A1 and W2 sites are vacant. Legend as in Fig. 5, the O atom at the O2 site is shown as a small white sphere.

Figure 7. The ^[11]Cs at the A2 site. Legend as in Fig. 5.

Cations of the heteropolyhedral sheet and interstitial complex ideally sum to (Ca₂Ce₂)¹⁰⁺ + (Na□)⁺ = [(Na□)Ca₂Ce₂]¹¹⁺.

General topology of the crystal structure

In the crystal structure of letnikovite-(Ce), the main structural unit is a layer of the central heteropolyhedral Ca–Ce sheet and two adjacent identical Si–O–OH sheets. The heteropolyhedral sheet parallel to (001) is composed of [9]-coordinated Ce-dominant M1 polyhedra, [7]-coordinated Ca-dominant M(2,3) polyhedra and vacancy-dominant M4 octahedra which share common edges and common vertices (Fig. 3a,b). We sum the cation and anion parts of the heteropolyhedral sheet to derive its ideal composition: [Ca₂Ce₂]¹⁰⁺ + [F₄(H₂O)₂]^4– = [Ca₂Ce₂F₄(H₂O)₂]⁶⁺. The Si–O–OH sheet is composed of SiO₄ and SiO₃(OH) tetrahedra in the ratio 6:1, Si tetrahedra form five-membered [Si₅O₁₅]^10– and ten-membered [Si₁₀O₃₃(OH)₂]^28– rings in the ratio 2:1 (Fig. 4a,b). In a sheet, ribbons of ten-membered and five-membered rings extend along [100]. Rings of tetrahedra share common vertices to form a single [Si₇O₁₇(OH)]^7– sheet parallel to (001). This is the first occurrence of a single [Si₇O₁₇(OH)]^7– sheet with a new topology that has not been found in any mineral (Hawthorne et al., Reference Hawthorne, Uvarova and Sokolova2019) and we call it the ‘letnikovite’ sheet. Two equivalent single sheets related by a mirror plane occur at z ≈ 0.69 and z ≈ 1.21 and connect via hydrogen bonding between OH groups of the two SiO₃(OH) tetrahedra (Fig. 5a, inset). Polyhedra of the central Ca–Ce sheet share common vertices with two adjacent Si–O–OH sheets to form a layer of composition {Ca₂Ce₂[Si₇O₁₇(OH)]F₄(H₂O)₂}^1– (Fig. 5a,b). The layers are stacked along [001] and link via (1) cations at the interstitial A(1,2) sites and H₂O groups, and (2) hydrogen bonding between OH groups of the Si–O–OH sheets and H₂O groups of the Ca–Ce sheets. This type of linkage yields wide channels along [100] (Fig. 5a). Along [100], the interstitial A1 and A2 sites (Figs. 6, 7) are partly occupied by Na (44%) and Cs (4%), respectively. We sum cation and anion parts of the interstitial complex to derive its ideal composition: (Na□)¹⁺ + (H₂O)₂ = [(Na□)(H₂O)₂]¹⁺.

The general structural formula of letnikovite-(Ce)

On the basis of the SREF results and bond-valence calculations, we write the ideal formula of letnikovite-(Ce) as the sum of the cation and anion components: [(Na□)Ca₂Ce₂]¹¹⁺ + {[Si₇O₁₇(OH)]F₄(H₂O)₄}^11– = (Na□)Ca₂Ce₂[Si₇O₁₇(OH)]F₄(H₂O)₄, Z = 4. The simplified formula is (Na,□)₂Ca₂(Ln ³⁺,Sr)₂[Si₇O₁₇(OH)]F₄(H₂O)₄, where Ce is the dominant lanthanoid. The validity of the ideal formula is supported by the good agreement between the total charges for cations in the ideal and empirical formulae: 1⁺ (Na□) + 10⁺ (Ca₂Ce₂) = 11⁺ versus 1.08⁺ (□_2.08Na_0.72Ca_0.16Cs_0.04) + 9.61⁺ (Ca_1.92Ln _1.31Sr_0.55Mg_0.28Pb_0.05Fe²⁺_0.04□_0.85) = 10.69⁺.

Above, we wrote the ideal formulae of letnikovite-(Ce) on the basis of the sum of the cation and anion components. Here, we write the ideal structural formula and ideal formula of letnikovite-(Ce) (Z = 4) on the basis of ideal compositions of cation and anion sites, ^{A 1}(Na□), ^{A 2}□, ^{M 2}Ca, ^{M 3}Ca, ^{M 1}Ce₂, ^{M 4}□, [Si₇O₁₇(OH)], ^{X 2}F, ^{X 3}F, ^{X 4}F₂, ^{X 1}H₂O,^{W 1}H₂O, ^{W (2–5)}(H₂O)₂, as (Na□)□Ca₂Ce₂□[Si₇O₁₇(OH)][F₄(H₂O)](H₂O)(H₂O)₂ and (Na□)Ca₂Ce₂[Si₇O₁₇(OH)]F₄(H₂O)₄, respectively.

Relation to other sheet silicates

We can remotely relate letnikovite-(Ce) to nekoite, Ca₃Si₆O₁₅⋅7H₂O (Alberti and Galli, Reference Alberti and Galli1980), okenite, Ca₁₀Si₁₈O₄₆⋅18H₂O (Merlino, Reference Merlino1983), and zeravshanite, Cs₄Na₂Zr₃[Si₁₈O₄₅](H₂O)₂ (Uvarova et al., Reference Uvarova, Sokolova, Hawthorne, Pautov and Agakhanov2004; Pautov et al., Reference Pautov, Agakhanov, Uvarova, Sokolova and Hawthorne2004), silicate minerals with a single sheet of five-membered rings and eight-membered rings of SiO₄ tetrahedra; the composition of this sheet is (Si₆O₁₅)^6–. In zeravshanite, the Si–O sheet is folded, hence Uvarova et al. (Reference Uvarova, Sokolova, Hawthorne, Pautov and Agakhanov2004) wrote its composition as (Si₁₈O₄₅)^18–. In a Si–O–OH sheet in letnikovite-(Ce), ribbons of ten-membered rings and five-membered rings are parallel to [100], a = 7.4726(3) Å. In nekoite, okenite and zeravshanite, ribbons of eight-membered rings and five-membered rings are parallel to: [001], c = 7.339 Å (nekoite); [010], b = 7.28 Å (okenite) and [010], b = 7.5464 Å (zeravshanite).