Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O, a New Member of the OD-Family of Natural and Synthetic Layered Silicates: Topology-Symmetry Analysis and Structure Prediction

Abstract

Crystals of new silicate-germanate Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O have been synthesized hydrothermally in a multi-component system TbCl₃:GeO₂:SiO₂ = 1:1:5 at T = 280 °C and P = 100 atm. K₂CO₃, Rb₂CO₃ and Cs₂CO₃ were added to the solution as mineralizers. The crystal structure was solved using single crystal X-ray data: a = 15.9429(3), b = 14.8407(3), c = 7.2781(1) Å, sp. gr. Pbam. New Rb,Cs,Tb-silicate-germanate consists of a [Si₅.₄₃Ge₀.₅₇O₁₅]_∞∞ corrugated tetrahedral layer combined by isolated TbO₆ octahedra into the mixed microporous framework as in synthetic K₃Nd[Si₆O₁₅]·2H₂O, K₃Nd[Si₆O₁₅] and K₃Eu[Si₆O₁₅]·2H₂O with the cavities occupied by Cs, Rb atoms and water molecules. Luminescence spectrum on new crystals was obtained and analysed. A comparison with the other representatives of related layered natural and synthetic silicates was carried out based on the topology-symmetry analysis by the OD (order-disorder) approach. The wollastonite chain was selected as the initial structural unit. Three symmetrical ways of forming ribbon from such a chain and three ways of further connecting ribbons to each other into the layer were revealed and described with symmetry groupoids. Hypothetical structural variants of the layers and ribbons in this family were predicted.

1. Introduction

Si and Ge elements have equal formal charge 4+ and tetrahedral coordination. In the crystal structures, Si and Ge occur together only as the isomorphic substitution Si-Ge in tetrahedra. Both elements are present isomorphically in the minerals sanbornite, milarite, albite, perrierite, farmakosiderite, garnet, titanite, and zeolite analogues [1]. Lone pair heavy metals act together with different anionic units containing mixing components. Such an approach is actually used in materials design to result in promising properties. There are no silicate-germanates with Tb in the nature or synthetic compounds according to [1,2]. However, there are a lot of original synthetic Tb-silicates with different anionic radicals [2,3]: ortho- NaTb₉(SiO₄)₆O₂ [4], KTb₉(SiO₄)₆O₂ and Cd₂Tb₈(SiO₄)₆O₂ [5] (structural type of apatite), Na₅Tb₄(OH)[SiO₄]₄ [6]; diortho- Tb₂Si₂O₇ [7], K₃TbSi₂O₇ [8], Tb₄S₃Si₂O₇ [9]; triortho- K₃TbSi₃O₈(OH)₂ [10]; tetraortho-groups Ba₂Tb₂Si₄O₁₃ [11]; six-membered rings Na₃Tb₃Si₆O₁₈·H₂O (synthetic gerenite) [12]; chains—unbranched Rb₂TbGaSi₄O₁₂ [13], wollastonite Na₂Tb_1.08Ca_2.92Si₆O₁₈H_0.8 [14] and spiral Na₃TbSi₃O₉·3H₂O [15]; layers in Cs₃TbSi₄O₁₀F₂ [16] and K_7.04Tb₃Si₁₂O_32.02·1.36H₂O [17]; sheets in Cs₃TbSi₈O₁₉·2H₂O [18] and Na₄K₂Tb₂Si₁₆O₃₈·10H₂O [19]. For some of these compounds, the luminescence properties were investigated [6,10,13,14,15,18,19].

Silicate crystal structures with the layers are presented [20,21] as a result of condensation of various chains. The formation of chains, layers, or frameworks by linking tetrahedra by the symmetry elements are partially addressed in a monograph [20], where the chains of Ba-silicates and symmetry elements responsible for their formation are identified. Important aspects of the modular approach and OD description of crystal structures were analyzed in [22]. For careful analysis of the similarities and differences in crystal structures, it is necessary to separate building units or modules which may be similar in different minerals, for example, layers in micas. The use of symmetry, a fundamental concept in crystallography, is a key tool for the description of structural families and for the construction of anionic radicals. Such an approach was suggested in [23] for layered ordered crystal structures in which a significant disorder component may be presented (OD theory). The local symmetry of layers or rods leads to structural variants of their conjugation and allows to predict new crystal structures. In the OD family, sursassite-pumpellyite-ardennite, the fourth member, was predicted and confirmed by high-resolution electron microscopy [24]. Strict symmetric rules dictate all possibilities in real or hypothetical crystal structures. The symmetry approach, based on the principles of OD theory [23], was developed for the borates [25] at all levels of condensation from the initial isolated tetrahedron to the chain, layer, and framework anionic units and described by groupoids of different ranks. As mentioned in the investigation of the crystal structure of the chain diborate GdH[B₂O₅] [26], the results are the same for borates, silicates, and other tetrahedral radicals. Thus, the borate chain in vimsite Ca[B₂O₂(OH)₄] is identical to the pyroxene chain. The formation of ribbons, layers, and frameworks in the well-known silicates are considered in [26]. The letters U (upward) and D (downward), which are commonly used in the literature for the description of tetrahedral anionic groups (chains, layers, and frameworks) actually reflects the absence or presence of inversion symmetry elements [27]. Two-chain ribbons are present in palygorskite Mg₅[Si₄O₁₀]₂(OH)₂·8H₂O, and three-chain ribbons in sepiolite Mg₄[Si₆O₁₅](OH)₂·6H₂O. In both minerals, pyroxene chains are related by the symmetry elements m_y, −1, m_y, −1… (palygorskite) or m_y, m_y, 2_x, m_y, m_y, 2_x… (sepiolite) [26]. The crystal structure of α-celsian Ba[Al₂Si₂O₈] demonstrates next step of condensation: nonpolar double-decker sheets are formed of polar mica-like layers multiplied by the mirror plane m_z via sharing of the apical vertices of the tetrahedra.

Synthesis of a new Rb,Cs,Tb-silicate-germanate, its structure solution and crystal chemical comparison with known related natural and synthetic silicates led us to using topology-symmetry analysis of OD theory. The following rubricating of known and predicted layered crystal structures is presented in this work. Luminescence properties are also characterized.

2. Materials and Methods

2.1. Synthesis of Crystals

The crystals of a new Rb,Cs,Tb-silicate-germanate were synthesized by a hydrothermal method in the system, containing oxide and chloride components in the mass ratio TbCl₃:GeO₂:SiO₂ = 1:1:5 that corresponds to 1.0 g (0.003 mol) TbCl₃, 1.0 g (0.001 mol) GeO₂ and 5.0 g (0.017 mol) SiO₂. All the reagents were of analytical grade. The mass ratio of solid and liquid phases was 1:5. K₂CO₃, Rb₂CO₃ and Cs₂CO₃ were added at the solution as mineralizers. The phase formation occurred at a pH 3 (measured after the completion of the reaction). The synthesis was carried out at the temperature of 280 °C and pressure of 100 atm. A standard autoclave (capacity 5 to 6 cm³) lined with Teflon was used. The characteristics of experiment were limited by the kinetics of the hydrothermal reactions and the instrumental capabilities. The reaction went to completion during heating for 18 to 20 days; followed by cooling to room temperature for over 24 h. The grown crystals were isolated by filtering the stock solution, washed with water and finally dried at room temperature. The small colorless transparent prismatic crystals, splices and brushes of crystals were found in the reaction products. The yield of the crystals was about 50 vol.%. Determination of the unit cell parameters on single crystals was performed using pre-experiment on Xcalibur S diffractometer (CCD area detector; graphite-monochromated Mo-K_α radiation). The chemical composition was determined using a Jeol JSM-6480LV scanning electronic microscope combined with WDX analysis (Jeol, Osaka, Japan). The qualitative test revealed the presence of Tb, Cs, Rb, Si, Ge and O.

2.2. Luminescence Study

Photoluminescence emission (PL) and excitation (PLE) spectra were recorded on an Agilent Cary Eclipse fluorescence spectrometer (Agilent Technology, Malaysia) with a 75 kW xenon light source (pulse length τ = 2 μs, pulse frequency ν = 80 Hz, wavelength resolution 0.5 nm; PMT Hamamatsu R928). For correct determination of photoluminescent properties, the measurements were performed on three portions of the crystals. The photoluminescence spectra of all samples were obtained under similar experimental conditions to compare the relative emission intensities and reduce the error. The experiment showed complete reproduction of the photoluminescence data for these three portions. The obtained spectra were corrected for the sensitivity of the spectrometer.

In Figure 1a, the PLE spectrum of Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O is shown. According to the results, the Tb³⁺ ion can be excited in different ways: within intraconfigural 4f⁸ transitions, and by interconfigural 4f^8–4f⁷5d¹ transition [28]. Several bands at 300 to 500 nm are attributed to f-f transitions of Tb³⁺ ions from the ⁷F₆ ground state to the ⁵H₆ (303 nm), ⁵H₇ (320 nm), ⁵L₉ (360 nm), ⁵D₃ (378 nm) and ⁵D₄ (480 nm). The most intensive ⁵D₃ transition was not split.

In Figure 1b, the PL spectrum of Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O controlled at λ_exc = 378 nm is shown. The spectrum consists of ⁵D₄ → ⁷F_J (J = 3–6) optical transitions of Tb³⁺ ion. The emission from the hypersensitive ⁵D₄–⁷F₅ transition at 540 nm is predominant. There was no emission from the higher lying ⁵D₃ level to ⁷F_J states (Figure 1b). Generally, the absence of these transitions is due to the presence of efficient cross-relaxation processes [29]. The deactivation in the ⁵D₃ emitting state such as ⁵D₃ → ⁵D₄ and ⁷F₆ → ⁷F₀ or ⁵D₃ → ⁷F₀ and ⁷F₆ → ⁵D₄ [30,31] is observed since the concentration of Tb³⁺ is relatively high. The main peak is split into two Stark components. This, apparently, is due to the presence of two non-equivalent positions occupied by Tb³⁺ in the crystal structure. Only the ⁵D₄–⁷F_J (J = 3–6) transition lines have a measurable intensity. It was noted that the luminescence intensity of the ⁵D₄ → ⁷F₃ transition could become comparable to that of the main green ⁵D₄ → ⁷F₅ transition of Tb³⁺, when the crystal field is strong [32]. In Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O the ⁵D₄ → ⁷F₃ compared to ⁵D₄ → ⁷F₅ is less, by approximately 10 times. So, the studied crystal has a low crystal field strength. In addition, the ratio between the ⁵D₄ → ⁷F₅ transition (green band at 490 nm) to the ⁵D₄ → ⁷F₆ transition (blue band at 540 nm) is known as green-to-blue fluorescence factor (G/B) [33]. The G/B (Tb³⁺) determines the asymmetry of the local environment around the Tb³⁺ ions and character bonding (covalent/ionic) between Tb³⁺ and O²⁻. The G/B factor for Tb³⁺ ions in Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O is 5.01 has been calculated. The obtained value is rather high, which suggests more covalent character of the bonding between terbium and oxygen ions. This is due to the presence of heavy rubidium and cesium atoms in the crystal composition.

3. Results

Structure Solving and Description

A small colorless transparent short-prismatic crystal with a size of 0.10 × 0.05 × 0.04 mm was selected for the single-crystal X-ray study. The diffraction experiment was carried out on an Xcalibur-S diffractometer (Oxford Diffraction, Oxford, UK) with a graphite-monochromatized Mo-K_α radiation source (λ = 0.71073 Å) and a CCD detector (ω scanning mode). The data were integrated using the CrysAlis Pro Agilent Technologies (v.1.1713735. 2014) software [34] and corrected for the Lorentz and polarization factors. The refined orthorhombic unit-cell parameters are a = 15.9429(3), b = 14.8407(3), c = 7.2781(1) Å, V = 1722.03(6) ų. A structural model was found by the direct method determination using SHELXS [35] within the WinGX v2018.3 [36] software in the suggested space group Pbam in agreement with the systematically absent reflections. At the first step, Tb1, Tb2, Rb1, Rb2, Cs1, Si and several of O sites were found. The remaining O sites were detected in different Fourier syntheses and were introduced in the model. As the temperature displacement parameters for all Si sites and Rb2 site were decreased, a small amount of Ge was isomorphically added in the Si sites ((Si_0.93Ge_0.07)1, (Si_0.88Ge_0.12)2, (Si_0.91Ge_0.09)3, (Si_0.92Ge_0.08)4) and Cs—in Rb2 site (Rb_0.66Cs_0.34)2 which significantly improved the R-factor. The occupations of these sites were found first by changing them step by step in a search for the minimum R-factor with the control of the temperature displacement parameters. After that, we applied the procedure of the refinement of tetrahedral position occupations and (Rs,Cs)2 position occupations, which made it possible to improve the result. The O11 atom was identified as the oxygen of a water molecule based on Pauling’s bond valence distribution [37] (

Table 1. Pauling’s balance of valences for Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O.

	Tb13+ C.N. = 6 0.25*	Tb23+ C.N. = 6 0.25*	Cs1+ C.N. = 11 0.5*	Rb1+ C.N. = 9 0.5*	(Rb,Cs2)+ C.N. = 7 0.5*	T14+ C.N. = 4 0.5*	T24+ C.N. = 4 1.0*	T34+ C.N. = 4 1.0*	T44+ C.N. = 4 0.5*	Σexp	Σtheor
O12− 0.5 *			0.045	0.056				1.0		−1.1	−1.0
O22− 0.5 *					0.071	0.5			0.5	−1.071	−1.0
O32− 1.0 *		0.125 × 4	0.045 × 4		0.071 × 2			1.0		−1.825	−2.0
O42− 1.0 *	0.125 × 4			0.056 × 4			1.0			−1.722	−2.0
O52− 1.0 *				0.056 × 2		0.5 × 2		1.0		−2.111	−2.0
O62− 1.0 *					0.071 × 2		1.0	1.0		−2.143	−2.0
O72− 0.5 *		0.125 × 2	0.045 × 2		0.071				0.5	−0.912	−1.0
O82− 1.0 *			0.045 × 2				1.0		0.5 × 2	−2.091	−2.0
O92− 0.5 *	0.125 × 2				0.071	0.5				−0.821	−1.0
O102− 0.5 *			0.045	0.056			1.0			−1.1	−1.0
O11w2− 0.5 *			0.045	0.056						−0.1	0
Σ	+0.75	+0.75	+0.5	+0.5	+0.5	+2	+4	+4	+2	15	15

* These values correspond to multiplicities scaled to common position multiplicity equal to 1.0.

). The resulting chemical formula is Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O, Z = 4. The structural model in a space group Pbam was refined using the least squares procedure in anisotropic approximation of the atomic displacements and with the refinement of the weighting scheme using SHELXL [38]. The absorption of crystal was not corrected because it was negligible µr_max = 0.63 and did not influence the result. Crystallographic data, atomic coordinates and selected bonds are presented in

Table 2. Crystal data and structure refinement for Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O.

Formula	Rb1.66Cs1.34Tb[Si5.43Ge0.57O15]·H2O
formula weight (g/mol)	930.48
T (K)	293(2)
crystal system	Orthorhombic
space group, Z	Pbam, 4
a (Å)	15.9429(3)
b (Å)	14.8407(3)
c (Å)	7.2781(1)
V (Å 3)	1722.03(6)
crystal size (mm)	0.10 × 0.05 × 0.04
ρcalc (g/cm 3)	3.532
μ (mm−1)	12.610
F(000)	1677
wavelength (Å)	0.71073
θ range/deg.	2.75–30.78
limiting indices	−22 ≤ h ≤ 22, −21≤ k ≤ 20, −10 ≤ l ≤ 10
refl. collected/unique	28316/2756 [Rint = 0.0695]
completeness to theta	99.9
data/restraints/parameters	2756/0/143
GOF	1.187
R1, wR21 [I > 2σ(I)]	0.0541, 0.0885
R1, wR2 (all data) 1	0.0670, 0.0926
Δρmax and Δρmin (e Å−3)	1.726 and −2.318

¹R(F) = ∑||F_o| − |F_c||/∑|F_o| and wR₂ = [∑w(F_o² − F_c ²)²/∑w(F_o²)²]^1/2 for F_o² > 2σ(F_o²).

,

Table 3. Atomic coordinates and atomic displacement parameters (U, Ų) for Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O_. U_eq is defined as one third of the trace of the orthogonalized U_ij tensor.

Atoms	Wyckoff Position, Point Symm.	S.o.f.	X	Y	Z	Ueq
Cs1	4g, m	1.0	0.1306(1)	0.5459(1)	0	0.0255(2)
Rb1	4h, m	1.0	0.2830(1)	0.8920(1)	0.5	0.0408(4)
(Rb, Cs)2	4g, m	0.66, 0.34	0.4222(1)	0.4033(1)	0	0.0250(2)
Tb1	2b, 2/m	1.0	0.5	0.5	0.5	0.00832(14)
Tb2	2d, 2/m	1.0	0	0.5	0.5	0.00750(14)
(Si, Ge)1	4h, m	0.93, 0.07	0.0874(1)	0.7829(2)	0.5	0.0083(7)
(Si, Ge)2	8i, 1	0.88, 0.12	0.3535(1)	0.6345(1)	0.7838(2)	0.0077(5)
(Si, Ge)3	8i, 1	0.91, 0.09	0.0395(1)	0.3024(1)	0.2181(2)	0.0087(5)
(Si, Ge)4	4h, m	0.92, 0.08	0.2068(1)	0.6291(2)	0.5	0.0060(7)
O(1)	4g, m	1.0	0.0165(5)	0.2918(5)	0	0.0192(16)
O(2)	4h, m	1.0	0.1804(4)	0.7355(4)	0.5	0.0139(15)
O(3)	8i,1	1.0	0.0526(3)	0.4042(3)	0.2791(7)	0.0150(10)
O(4)	8i,1	1.0	0.4291(3)	0.5701(4)	0.7326(8)	0.0176(11)
O(5)	8i, 1	1.0	0.0392(3)	0.7465(4)	0.3168(7)	0.0184(11)
O(6)	8i, 1	1.0	0.1258(3)	0.2425(3)	0.2554(7)	0.0141(10)
O(7)	4h, m	1.0	0.1292(4)	0.5630(5)	0.5	0.0134(14)
O(8)	8i, 1	1.0	0.2653(3)	0.6115(4)	0.6809(7)	0.0189(11)
O(9)	4h, m	1.0	0.0990(4)	0.8882(5)	0.5	0.0142(15)
O(10)	4g, m	1.0	0.3262(5)	0.6260(6)	0	0.0187(16)
O(11)w	4g, m	1.0	0.2446(9)	0.3400(10)	0	0.079(4)

and

Table 4. Selected interatomic distances for Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O.

Atoms	Bonds (Å)	Atoms	Bonds (Å)
Tb1O6 Octahedron		Tb2O6 Octahedron
Tb1-O4 x4	2.286(5)	Tb2-O7 ×2	2.262(7)
Tb1-O9 ×2	2.290(7)	Tb2-O3 ×4	2.304(5)
Average	2.287	Average	2.290
(Si,Ge)1O4 Tetrahedron		(Si,Ge)2O4 Tetrahedron
(Si,Ge)1-O9	1.573(7)	(Si,Ge)2-O4	1.582(5)
(Si,Ge)1-O5 ×2	1.632(5)	(Si,Ge)2-O8	1.629(5)
(Si,Ge)1-O2	1.640(7)	(Si,Ge)2-O10	1.637(3)
Average	1.619	(Si,Ge)2-O6	1.662(5)
(Si,Ge)3O4 Tetrahedron		Average	1.628
(Si,Ge)3-O3	1.588(5)	(Si,Ge)4O4 Tetrahedron
(Si,Ge)3-O5	1.617(5)	(Si,Ge)4-O7	1.579(7)
(Si,Ge)3-O1	1.637(3)	(Si,Ge)4-O8 x2	1.634(5)
(Si,Ge)3-O6	1.660(5)	(Si,Ge)4-O2	1.635(7)
Average	1.626	Average	1.621

. CCDC CSD 2,062,486 contains crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif (accessed on 24 March 2021). Illustrations were produced using ATOMS (v. 5.1) [39] and CORELDRAW (v. 21.0.0.593, 2019) programs.

The new crystal structure of Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O consists of mixed (Si, Ge) tetrahedra (Table 3) which are combined into the corrugated layer [Si_5.68Ge_0.32O₁₅]_∞∞ parallel to ac containing four-, six- and eight-membered rings. The isolated TbO₆ centro-symmetric octahedra (Table 4) connected with (Si, Ge) tetrahedral layers into the mixed microporous framework. Rb, Cs atoms and water molecules fill the channels of the framework (Figure 2a,b).

4. Discussion

4.1. Structural Comparison with the Related Layered Silicates

Polytypic relations between isochemical alkali-REE layer silicates and sazhinite were analyzed in [40]. Multiring tetrahedral sheets for four crystal structures: sazhinite Na₂Ce[Si₆O₁₄(OH)₂]·nH₂O [41], Na_2.74K_0.26Ce[Si₆O₁₅]·2H₂O [42], Na_2.4Ce[Si₆O₁₅]·2H₂O [43], K₃Nd[Si₆O₁₅]·2H₂O [44] were analyzed, emphasizing the presence of a xonotlite-like ribbon. Polytypic relations were derived for the compounds and the crucial role of large K cations was found in forming crystal structures. Some symmetry elements were described: m mirror plane for sazhinite structure type, a glide for Na_2.4Ce[Si₆O₁₅]·2H₂O. Diffraction features, which present some diffusion effects and spurious reflections, were fixed on reciprocal lattice h0l and h1l.

The crystal structure of a new member of the family, Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O, is close to the layered K₃Nd[Si₆O₁₅]·2H₂O [44], K₃Nd[Si₆O₁₅] [45] and K₃Eu[Si₆O₁₅]·2H₂O (symmetry decrease is caused by the displacement of some atoms from the m-plane) [46] (

Table 5. The main crystallographic characteristics of the family structures.

Chemical Formula	Space Group	Unit CellParameters, Å	Reference
Rb1.66Cs1.34Tb[Si5.43Ge0.57O15]· H2O	Pbam	a = 15.943 b = 14.841 c = 7.278	[this work]
K3Nd[Si6O15]·2H2O	Pbam	a = 16.008 b = 15.004 c = 7.279	[44]
K3Nd[Si6O15]	Pbam	a = 16.011 b = 14.984 c = 7.276	[45]
K3Eu[Si6O15]·2H2O	P21212	a = 14.852 b = 15.902 c = 7.243	[46]
Na2Ce[Si6O14(OH)2]·nH2O Ce-sazhinite	Pmm2	a = 7.500 b = 15.620 c = 7.350	[41]
Na3La[Si6O15]·2H2O La-sazhinite	Pmm2	a = 7.415 b = 15.515 c = 7.164	[47]
β-K3Nd[Si6O15]	Bb21m	a = 14.370 b = 15.518 c = 14.265	[44]
Na2.4Ce[Si6O15]·2H2O	Pman	a = 7.309 b = 14.971 c = 7.135	[43]
NaNd[Si6O13(OH)2]·H2O	Cmm2	a = 30.870 b = 7.387 c = 7.120	[48]
NaNd[Si6O15]·2H2O	Cmm2	a = 7.385 b = 30.831 c = 7.117	[49]
Na2.74K0.26Ce[Si6O15]·2H2O	Cmm2	a = 7.413 b = 30.965 c = 7.167	[42]
Na3La[Si6O15]·2.25H2O	Cmm2	a = 7.415 b = 31.008 c = 7.153	[42]
Na2.72K0.25LaSi6O15·2.25H2O	Cmm2	a = 7.422 b = 31.039 c = 7.196	[42]

). All the compounds have identical mixed frameworks consisting of Si-O tetrahedral layers combined with isolated REEO₆-octahedra. The new crystal structure differs from these only by the substitution of Rb, Cs for K and the amount of water molecules. Different filling of voids is a characteristic feature of this structural family up to differences in individual crystals of the same mineral sample. Silicate K₃Eu[Si₆O₁₃(OH)₄]·2H₂O [46] contains ribbon [Si₆O₁₃(OH)₄]_∞ instead of layer (Figure 3a). The similar ribbon as in the latter crystal structure is presented in the layers of all former silicates including the new member. Ribbons are multiplied into the layer along the a-axis by inversion center (Figure 3b).

The crystal structure of sazhinite Na₂Ce[Si₆O₁₄(OH)₂]·nH₂O [41] (Na₃La[Si₆O₁₅]·2H₂O [47]) (Table 5) is similar to the Rb,Cs,Tb-silicate-germanate mixed framework and configuration of the corrugated tetrahedral layer with four-, six- and eight-membered rings (Figure 2a and Figure 4a, side projections). However, these layers have a different topology and symmetry visible in frontal projections (Figure 2b and Figure 4b). In sazhinite, the wollastonite chain multiplies into the ribbon by the mirror plane m_y (Figure 4b) and then into the layer by inversion centers valid only for the layer pairs and not for the whole structure. That corresponds to local symmetry operation used in OD theory. A flat ribbon is formed in sazhinite in contrast to a double-decker ribbon in new silicate and in K₃Eu[Si₆O₁₃(OH)₄]·2H₂O because of influence of large K atoms [40]. The β-K₃Nd[Si₆O₁₅] [44] (Table 5) is a distorted variety of the sazhinite crystal structure (Figure 4a–d).

The original crystal structure Na_2.4Ce[Si₆O₁₅]·2H₂O [43] (Table 5, Figure 5) discussed in [40] has a new variant multiplication of wollastonite chains into the ribbon by a_z glide which are further multiplied by the inversion center in the layer.

In the NaNd[Si₆O₁₃(OH)₂]·H₂O [48] (equal to Na₃Nd[Si₆O₁₅]·2H₂O [49]), Na_2.74K_0.26Ce[Si₆O₁₅]·2H₂O, Na₃La[Si₆O₁₅]·2.25H₂O and Na_2.72K_0.25LaSi₆O₁₅·2.25H₂O [42] crystal structures (Table 5, Figure 6a,b), two variants of ribbon-forming are observed: by m_x as in sazhinite, and by the b_x operation in accordance with the unit cell selection. Ribbons are connected into the layer by local operation or pseudo-inversion centers $\overline{1}$ (Figure 6b). As a result, the a parameter (b in sazhinite) is doubled (Table 5).

4.2. Topology-Symmetry Analysis and Structure Prediction

Based on the topology-symmetry analysis of this family of layered crystal structures and the wollastonite chain with m_x symmetry, we can identify the ribbon from the chain by three variants of symmetry operations: m_y, $\overline{1}$ (equal to 2_x) and a_y. This first step is illustrated at the top of the Figure 7. The ribbons can be connected into the layers in several ways using the same operations: m_y, $\overline{1}$ and a_y left to right, shown on the next line marked as “layers”. The first case is when the ribbon with the symmetry Pm_y is multiplied by the mirror plane m_y giving the layer with the polar symmetry group Pmm2. Multiplication of the same ribbon by the inversion center gives the layer of idealized sazhinite with symmetry group Pmmb. The second case is when a centro-symmetric ribbon with symmetry P$\overline{1}$ is multiplied by m_y, giving the Pmmb space group or by the inversion center giving the P2/m space group. The third case describes multiplying of the ribbon with another symmetry group Pa by m_y or inversion center giving the Cmm2 or Pman space groups, correspondingly. The latter variant presents known structure Na_2.4Ce[Si₆O₁₅]·2H₂O (space group setting Pmna) [43]. In all drawings, the resulting unit cells are shown.

Structural diversity has an OD character described by a symmetry groupoid. The chain, which has a one-dimensional periodicity, is multiplied in the ribbon in different ways; thus, a groupoid family symbol of lower rank is used as it was in [25] for borates:

$$P\left(m_x\right)1\mathsf{\lambda }-\mathrm{PO},$$

$$\overline{1}\left|\right|m_y\left|\right|a_y\mathsf{\sigma }-\mathrm{PO}.$$

Different ribbons are joined by different symmetrical operations in different layers, and that corresponds to the groupoid family symbol:

$$\left(Pmm2\right||P2/m|\left|Pma2\right)1\mathsf{\lambda }-\mathrm{PO},$$

$$\overline{1}\left|\right|m_y\left|\right|a_y\mathsf{\sigma }-\mathrm{PO}.$$

All variants are shown in Figure 7 and belong to the members of the unify OD family with the maximum degree of order (MDO) because the λ-PO and σ-PO operations are the same for every layer, and all the ribbon pairs in the layer are equal.

Periodic crystal structures with the alternation of λ-PO and σ-PO may exist in the family up to disordered members if no order will be in initial λ-PO or σ-PO.

It is possible to predict not only layers but also different ribbons containing crystal structures, if we use a_y as σ-PO. They are shown in the next row in Figure 7 for different initial ribbon λ-PO (see arrows) with the different σ-PO multiplication and resulting space groups and unit cells. Hypothetic crystal structures with double ribbons are shown at the bottom of Figure 7 as an intermediate case between ribbon and layered crystal structures.

The specific diffraction effects described in [40] were explained by the polytypic nature of the compounds. This is consistent with the order–disorder (OD) nature of the crystal structures belonging to the OD family described using topology-symmetry analysis.

5. Conclusions

Crystals of Rb_1.66Cs_1.34Tb[Si_5.43Ge_0.57O₁₅]·H₂O have been synthesized hydrothermally in a multi-component system at T = 280 °C and P = 100 atm and luminescence properties on the crystals were investigated. The crystal structure of new Rb,Cs,Tb-silicate-germanate with the isomorphic substitution in tetrahedra consists of corrugated layers [Si_5.43Ge_0.57O₁₅]_∞∞ which are connected with isolated TbO₆-octahedra into the mixed microporous framework. Larger than Na,K-atoms, Rb, Cs atoms and water molecules fill the channels of the framework. The substitution of larger Nd, Eu REE by smaller Tb REE does not changes the dimensions of voids. Structural comparison with the related layered silicates was carried out. Modular description added with the symmetry analysis of the OD approach allows to systematically describe the structural families or to predict new members. Topology-symmetry analysis of this silicates family was performed based on consideration of the wollastonite chain and symmetry variants of chain combination into the ribbons and then into the layers. The structural representatives of minerals and synthetic compounds are potentially extended. One example of “hypothetical structure” with the space group Pman corresponds to real Na_2.4Ce[Si₆O₁₅]·2H₂O being in a systematically derived position in the field of structural variants. Most of the hypothetical layered and ribbon crystal structures are not yet discovered. Their description will help to recognize new crystal structures of minerals in nature or in synthetic experiments and to confirm the predicted models.