The Na2-Nhn[Zr(Si2o7)]Mh2o Minerals and Related Compounds (N = 0–0.5; M = 0.1): Structure Refinement, Framework Topology

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Article The Na2−nHn[Zr(Si2O7)]·mH2O Minerals and Related Compounds (n = 0–0.5; m = 0.1): Structure Reﬁnement, Framework Topology, and Possible Na+-Ion Migration Paths

Natalya A. Kabanova 1,2, Taras L. Panikorovskii 1,3,* , Vladimir V. Shilovskikh 4 , Natalya S. Vlasenko 4, Victor N. Yakovenchuk 5, Sergey M. Aksenov 1 , Vladimir N. Bocharov 4 and Sergey V. Krivovichev 3,6

1 Laboratory of Nature-Inspired Technologies and Environmental Safety of the Arctic, Kola Science Centre, Russian Academy of Sciences, Fersmana str. 14, 184209 Apatity, Russia; [email protected] (N.A.K.); [email protected] (S.M.A.) 2 Samara Center for Theoretical Materials Science, Samara State Technical University, Molodogvardeyskaya Str. 244, 443100 Samara, Russia 3 Crystallography Department, Institute of Earth Sciences, St. Petersburg State University, University emb. 7/9, 199034 Petersburg, Russia; [email protected] 4 Geo Environmental Centre “Geomodel”, Saint–Petersburg State University, Ul’yanovskaya Str. 1, 198504 Petersburg, Russia; [email protected] (V.V.S.); [email protected] (N.S.V.); [email protected] (V.N.B.) 5 Geological Institute, Kola Science Centre, Russian Academy of Sciences, Fersmana str. 14, 184209 Apatity, Russia; [email protected] 6 Nanomaterials Research Centre, Kola Science Centre, Russian Academy of Sciences, Fersmana str. 14, 184209 Apatity, Russia * Correspondence: [email protected]; Tel.: +7-8155-579-628

Received: 26 October 2020; Accepted: 6 November 2020; Published: 9 November 2020

Abstract: The Na2 nHn[Zr(Si2O7)] mH2O family of minerals and related compounds (n = 0–0.5; m − · = 0.1) consist of keldyshite, Na3H[Zr2(Si2O7)2], and parakeldyshite, Na2[Zr(Si2O7)], and synthetic Na [Zr(Si O )] H O. The crystal structures of these materials are based upon microporous 2 2 7 · 2 heteropolyhedral frameworks formed by linkage of Si2O7 groups and ZrO6 octahedra with internal + channels occupied by Na cations and H2O molecules. The members of the family have been studied by the combination of theoretical (geometrical–topological analysis, Voronoi migration map calculation, structural complexity calculation), and empirical methods (single-crystal X-ray diﬀraction, microprobe analysis, and Raman spectroscopy for parakeldyshite). It was found that keldyshite and parakeldyshite have the same fsh topology, while Na ZrSi O H O is diﬀerent and has the xat 2 2 7· 2 topology. The microporous heteropolyhedral frameworks in these materials have a 2-D system of channels suitable for the Na+-ion migration. The crystal structure of keldyshite can be derived from that of parakeldyshite by the Na+ + O2 OH + substitution mechanism, widespread in the − ↔ − postcrystallization processes in hyperagpaitic rocks.

Keywords: keldyshite; parakeldyshite; crystal structure; ion migration; transformation; Raman spectroscopy; Voronoi analysis; topology

1. Introduction Microporous zirconosilicates attract considerable interest as ionic conductors, molecular sieves, and ion exchangers [1–3]. Among them, compounds with the NASICON-type structures are considered

Crystals 2020, 10, 1016; doi:10.3390/cryst10111016 www.mdpi.com/journal/crystals Crystals 2020, 10, 1016 2 of 14 as ionic conductors, while sodium amphoterosilicates (e.g., ETS-4) are of interest as selective adsorbents for 137Cs and 90Sr radioactive isotopes [2,4–10]. The beginning of the study of zirconium silicate was stimulated by the discovery of keldyshite-group minerals in the Lovozero alkaline massif, Kola peninsula, Russia [11–15]. Keldyshite, (Na,H)2[Zr(Si2O7)], was discovered in 1962 and the further detailed study of its holotype material indicated the existence in the mineral sample of polysynthetic intergrowths of two phases Na3HZr2(Si2O7)2 and Na2[Zr(Si2O7)] (renamed as keldyshite and parakeldyshite, respectively) [16]. The crystal-structure model for parakeldyshite was proposed in 1970 [17] and confirmed in 1974 [18]. The crystal structure of keldyshite was determined in 1978 [19], when the similarity between the crystal structures of keldyshite and parakeldyshite was demonstrated. The “M-34 phase” with the idealized chemical formula NaH[Zr (Si O )] H O was discovered in the samples of 2 2 7 · 2 parakeldyshite from Khibiny alkaline massif, but its crystal structure remains unknown [16]. General mineralogical and structural relationships between keldyshite, parakeldyshite, and the “M-34 phase” allowed establishment of the ‘parakeldyshite keldyshite “M-34 phase”’ → → transformational group of minerals (similar to the ‘kazakovite tisinalite’ [20], ‘zirsinalite → → lovozerite’ [21], etc. series). Within each group, transformation of the minerals is induced by ion-exchange reactions under natural conditions [22–26]. Synthetic zirconium silicates related to keldyshite are known [5,6] and can be obtained by different methods: (i) by crystallization from a melt at the temperature range 1000–1250 ◦C or (ii) by the hydrothermal technique at the temperatures of 450–500 ◦C[1,3]. Recently, an alternative model of the arrangement of Na cations in parakeldyshite was obtained [27] and the phase Na ZrSi O H O 2 2 7· 2 was discovered, which is close in composition to the M-34 phase [28]. Keldyshite-related compounds have serious potential for their use in the purification of gases from sulfur dioxide in the production of sulfuric acid and heavy non-ferrous metals from sulfide ores [29]. Further work determined the presence of ion-exchange properties in the new zirconosilicate minerals discovered on the territory of the Kola alkaline province [27,30–32]. In this paper, we report the results of the theoretical analysis of the Na+-ion migration paths in the crystal structures of keldyshite, parakeldyshite, and zirconium silicate Na [Zr(Si O )] H O using 2 2 7 · 2 a geometrical and topological approach [33,34]. The crystal structure of parakeldyshite was refined using the sample from albitized pegmatite at Takhtarvumchorr Mt., Khibiny alkaline massif, Russia. The transformational nature of keldyshite-related minerals is discussed.

2. Materials and Methods

2.1. Sample A sample of parakeldyshite was collected from albitized pegmatites at the Takhtarvumchorr Mt. (Khibiny massif). Albitites are composed of a fine-fine-grained aggregate of lamellar albite with lenses (up to 1 0.5 m) of sugar-like apatite. The mass contains flattened prismatic crystals of enigmatite, × flakes and radial-radiant aggregates of molybdenite, plates of ilmenite and pyrrhotite, and dark-orange prismatic spherulites of pale cream fibrous сhirvinskyite. Parakeldyshite was found as transparent barley-like crystals up to 2 mm long, with the marginal zones replaced by powdery precipitates of the “M-34 phase” [22] with the chemical composition NaH[Zr(Si2O7)] (Figure1). In association with parakeldyshite, spherulites of сhirvinskyite, lemon-yellow radial-radial aggregates, and individual prismatic crystals of titanite (partially replaced by lorenzenite, eudialyte, and zircon grains) have been observed. Crystals 2020, 10, 1016 3 of 14 Crystals 2020, 10, x FOR PEER REVIEW 3 of 15

Figure 1. PowderedPowdered aggregates aggregates of of parakeldyshite/keldysh parakeldyshite/keldyshiteite (1) (1) in in association association with with eudialyte eudialyte (2), (2), aegirine (3), albite (4), and låvenite (5) in albitizedalbitized pegmatite in foyaites at Takhtarvumchorr Mt.Mt.

2.2. Composition Composition The chemical composition of parakeldyshite wa wass determined at the ‘Geomodel’ resource center of St. Petersburg Petersburg State State University University using the scan scanningning electron microscope Hitachi S-3400N equipped by INCA 500 WDS detector operating at 20–30 nA nA an andd 20 20 kV. kV. The analyses were performed with the beam sizesize ofof 5 5µ mμm and and the the counting counting time time of 10–20 of 10–20/10/10 s on peakss on /backgroundpeaks/background for each for chemical each chemical element. element.Quartz (Si), Quartz corundum (Si), corundum (Al), calcite (Al), (Ca), calcite halite (Ca), (Na), ha zirconlite (Na), (Zr), zircon rutile (Ti), (Zr), hematite rutile (Ti), (Fe), hematite celestine (Fe), (Sr), celestineand rhodonite (Sr), and (Mn) rhodonite were used (Mn) as standards.were used Anas standards. average chemical An average composition chemical based composition on 5 analyzes based (inon wt.%):5 analyzes ZrO2 (in39.95, wt.%): Na2O ZrO 20.022 39.95, SiO2 39.41, Na2O sum 20.02 99.38 SiO The2 39.41, empirical sum formula 99.38 The calculated empirical per 5formula cations calculatedcan be written per 5 as: cations Na1.99 canZr0.99 beSi written2.02O7.015 as:. Na1.99Zr0.99Si2.02O7.015. 2.3. Single-Crystal X-ray Diffraction 2.3. Single-Crystal X-Ray Diffraction The crystal-structure studies of parakeldyshite were carried out at the X-ray Diffraction Resource The crystal-structure studies of parakeldyshite were carried out at the X-ray Diffraction Centre of St. Petersburg State University on an Agilent Technologies Xcalibur EOS diffractometer Resource Centre of St. Petersburg State University on an Agilent Technologies Xcalibur EOS equipped with the CCD detector using monochromatic MoKα radiation (λ = 0.71069 Å) at room diffractometer equipped with the CCD detector using monochromatic MoKα radiation (λ = 0.71069 temperature. More than a hemisphere of diffraction data was collected (scanning step 1 , exposure Å) at room temperature. More than a hemisphere of diffraction data was collected (scanning◦ step 1°, time 10 s). The absorption correction was done empirically using spherical harmonics implemented in exposure time 10 s). The absorption correction was done empirically using spherical harmonics the SCALE ABSPACK calibration algorithm in the CrysAlysPro software package [35]. The unit-cell implemented in the SCALE ABSPACK calibration algorithm in the CrysAlysPro software package parameters were determined and refined by the least squares method using 1364 independent reflections. [35]. The unit-cell parameters were determined and refined by the least squares method using 1364 The structure was refined using the SHELXL software package [36]. The data are deposited in CCDC independent reflections. The structure was refined using the SHELXL software package [36]. The under Entry No. 22040710. The coordination number of Na determined by number bonds with data are deposited in CCDC under Entry No. 22040710. The coordination number of Na determined maximal length constrained 3.10 Å. Crystal data, data collection information, and refinement details by number bonds with maximal length constrained 3.10 Å. Crystal data, data collection information, are given in Table1. Atom coordinates and isotropic parameters of atomic displacements are given in and refinement details are given in Table 1. Atom coordinates and isotropic parameters of atomic Table S1, interatomic distances in Table S2, and the anisotropic parameters of atomic displacements are displacements are given in Table S1, interatomic distances in Table S2, and the anisotropic parameters given in Table S3. of atomic displacements are given in Table S3.

Crystals 2020, 10, 1016 4 of 14

Table 1. Crystal data, data collection information, and reﬁnement details for parakeldyshite from Takhtarvumchorr Mt., Khibiny, Russia.

Parameter Data Temperature/K 293(2) Crystal system triclinic Space group P1 a/Å 5.4243(6) b/Å 6.5923(5) c/Å 8.8083(6) α/◦ 71.309(7) β/◦ 87.162(8) γ/◦ 85.497(8) Volume/Å3 297.34(5) Z 2 –3 ρcalc/g cm 3.411 µ/mm-1 2.388 F(000) 292.0 Crystal size/mm3 0.17 0.12 0.11 × × Radiation Mo Kα (λ = 0.71073) 2θ range for data collection/◦ 6.538 to 54.986 Index ranges 5 h 7, 8 k 8, 11 l 10 − ≤ ≤ − ≤ ≤ − ≤ ≤ Reflections collected 2296 Independent reflections 1364 [Rint = 0.0221, Rσ = 0.0362] Data/restraints/parameters 1364/0/109 Goodness-of-fit on F2 1.120 Final R indexes [I 2σ(I)] R = 0.0237, wR = 0.0602 ≥ 1 2 Final R indexes [all data] R1 = 0.0256, wR2 = 0.0616 Largest diff. peak/hole/e Å 3 0.79/ 0.69 − −

2.4. Geometrical–Topological Analysis Geometrical–topological analysis of the crystal structures of keldyshite-related compounds was carried out using algorithms implemented in the ToposPro software package (https://topospro.com/)[33]. Maps of the migration of Na+-ions were constructed by the Voronoi method, which was shown to be efficient for various types of ionic conductors [34,37,38]. The radius of an elementary channel (Rchan) suitable for Na+-ion migration was chosen as 2.0 Å, similar to that reported previously [38,39]. Topological analysis of the crystal structures of keldyshite-related compounds also included the determination of the type basic grid, the construction of tiling, and the search for topologically similar inorganic compounds. The base grid is a graph whose vertices are the centers of gravity of the structural units, i.e., SiO4 tetrahedra and ZrO6 octahedra [40]. After contraction of doubly connected nodes (“bridging” oxygen atoms), a 4,6-coordinated grid was obtained (Figure2). The topological classification of the atomic nets in crystal structures was carried out in accordance with the following basic principle [41]: atomic nets with the same set of topological indices (coordination sequence, vertex symbols) belong to the same topological type [42]. In the case of the presence of stable polyhedral units in the crystal structure, the classification was carried out according to the basic grid [40]. Determination of the topological mesh type was performed using the ToposPro complex of the TopCryst web service (http://topcryst.com), which contains data on about 190,000 topological types of the nets. The tiling theory, which is actively used to study and analyze the crystal structures of zeolites [43] and zeolite-related materials with heteropolyhedral frameworks [44–46], was introduced and developed by M. O’Keeffe [47]. This approach allows study of the smallest cavities in inorganic frameworks that can be used to fill the entire crystal space [47]. Since the grids in the crystal structures of keldyshite and parakeldyshite have the same topology, the set of tilings in these structures is the same. Crystals 2020, 10, x FOR PEER REVIEW 5 of 15

Crystals 2020, 10, 1016 5 of 14 Crystals 2020, 10, x FOR PEER REVIEW 5 of 15

Figure 2. Basic net representation for the crystal structure of keldyshite.

The tiling theory, which is actively used to study and analyze the crystal structures of zeolites [43] and zeolite-related materials with heteropolyhedral frameworks [44–46], was introduced and developed by M. O’Keeffe [47]. This approach allows study of the smallest cavities in inorganic frameworks that can be used to fill the entire crystal space [47]. Since the grids in the crystal structures of keldyshite and parakeldyshite have the same topology, the set of tilings in these structures is the same.

2.5. Raman SpectroscopyFigure 2.2. Basic net representation for the crystal structurestructure ofof keldyshite.keldyshite. 2.5. RamanThe Raman Spectroscopy spectrum (RS) was obtained using a Horiba Jobin-Yvon LabRam HR 800 The tiling theory, which is actively used to study and analyze the crystal structures of zeolites spectrometer (Geomodel Resource Center, St. Petersburg State University) from the surface of a [43] Theand Ramanzeolite-related spectrum materials (RS) was with obtained heteropo usinglyhedral a Horiba frameworks Jobin-Yvon LabRam[44–46], HRwas 800 introduced spectrometer and parakeldyshite crystal at room temperature and a wavelength of 514 nm in the range from 4000 to 80 (Geomodeldeveloped by Resource M. O’Keeffe Center, [47]. St. PetersburgThis approach State allows University) study fromof the the smallest surface cavities of a parakeldyshite in inorganic cm−1. The baseline correction was carried out using the algorithms implemented in the OriginPro 8.1 crystalframeworks at room that temperature can be used and to afill wavelength the entire crystal of 514 nmspace in the[47]. range Since from the grids 4000 to in 80 the cm crystal1. The structures baseline software package. − correctionof keldyshite was and carried parakeldyshite out using the have algorithms the same implemented topology, the in set the of OriginPro tilings in 8.1these software structures package. is the same. 3.3. ResultsResults 2.5. Raman Spectroscopy 3.1.3.1. Single-CrystalSingle-Crystal X-rayX-Ray Di Diffractionﬀraction The Raman spectrum (RS) was obtained using a Horiba Jobin-Yvon LabRam HR 800 TheThe crystalcrystal structuresstructures ofof microporousmicroporous zirconiumzirconium silicatessilicates areare basedbased uponupon frameworksframeworks consistingconsisting spectrometer (Geomodel Resource Center, St. Petersburg State University) from the surface of a ofof ZrOZrO6 octahedraoctahedra andand SiOSiO4 tetrahedratetrahedra linkedlinked viavia commoncommon OO atoms.atoms. AccordingAccording toto thethe structuralstructural parakeldyshite6 crystal at room4 temperature and a wavelength of 514 nm in the range from 4000 to 80 classiﬁcationclassification proposed proposed by Ilyushinby Ilyushin and Blatov and [40Blatov], the crystal[40], structuresthe crystal of keldyshite,structures NaH[Zr(Siof keldyshite,O )], cm−1. The baseline correction was carried out using the algorithms implemented in the OriginPro2 78.1 parakeldyshite,NaH[Zr(Si2O7)], Na parakeldyshite,[Zr(Si O )], and Na Na2[Zr(Si[Zr(Si2OO7)],)] HandO containNa2[Zr(Si polyhedral2O7)]∙H2O microensembles contain polyhedral (PME) software package. 2 2 7 2 2 7 2 6 · MTmicroensembles6 of the A-1 type (PME) (Figure MT3 ).of the A-1 type (Figure 3). 3. Results

3.1. Single-Crystal X-Ray Diffraction The crystal structures of microporous zirconium silicates are based upon frameworks consisting of ZrO6 octahedra and SiO4 tetrahedra linked via common O atoms. According to the structural classification proposed by Ilyushin and Blatov [40], the crystal structures of keldyshite, NaH[Zr(Si2O7)], parakeldyshite, Na2[Zr(Si2O7)], and Na2[Zr(Si2O7)]∙H2O contain polyhedral microensembles (PME) MT6 of the A-1 type (Figure 3).

Figure 3. Polyhedral microensemble of MT6-type forms the frameworks in the crystal structures of Figure 3. Polyhedral microensemble of MT6-type forms the frameworks in the crystal structures of parakeldyshite, keldyshite, and the phase Na2[Zr(Si2O7)] H2O. parakeldyshite, keldyshite, and the phase Na2[Zr(Si2O7)]∙·H2O. In the terms proposed in [5], the crystal structure of parakeldyshite can be described as a framework consisting of the M2T4-type secondary building units (SBUs) with Na atoms in adjacent cavities (Figure4a). Each ZrO 6 octahedron is linked to six SiO4 tetrahedra, which in turn are linked to two Zr octahedra each.

Figure 3. Polyhedral microensemble of MT6-type forms the frameworks in the crystal structures of

parakeldyshite, keldyshite, and the phase Na2[Zr(Si2O7)]∙H2O.

CrystalsCrystals 2020 2020, 10, ,10 x ,FOR x FOR PEER PEER REVIEW REVIEW 6 of6 of15 15

InIn the the terms terms proposed proposed in in [5], [5], the the crystal crystal struct structureure of of parakeldyshite parakeldyshite can can be be described described as as a a frameworkframework consisting consisting of of the the M M2T24T-type4-type secondary secondary building building units units (SBUs) (SBUs) with with Na Na atoms atoms in in adjacent adjacent cavities (Figure 4a). Each ZrO6 octahedron is linked to six SiO4 tetrahedra, which in turn are linked to Crystalscavities2020 ,(Figure10, 1016 4a). Each ZrO6 octahedron is linked to six SiO4 tetrahedra, which in turn are linked6 of 14 to twotwo Zr Zr octahedra octahedra each. each.

(a)( a) (b()b ) (c)( c)

FigureFigureFigure 4.4. Secondary 4.Secondary Secondary building building building units units (SBUs)units (SBUs) (SBUs) in Na-zirconosilicates: in inNa-zirconosilicates: Na-zirconosilicates: (a) M2 T(4a -block)( aM) M2T in42-blockT4 the-block crystal in inthe structurethe crystal crystal

ofstructure parakeldyshite;structure of ofparakeldyshite; parakeldyshite; (b) M2T4-block (b ()b M) M2 inT42-blockT the4-block crystal in inthe structurethe crystal crystal structure of structure keldyshite; of ofkeldyshite; keldyshite; (c) M2T6 (-blockc )( cM) M2T in62-blockT the6-block crystal in inthe the

structurecrystalcrystal structure ofstructure the Na of2 ofZrSithe the Na2O Na27ZrSiH2ZrSi2O2O phase.27O H7 2HO2 Ophase. phase.

TheTheThe crystalcrystal crystal structure structure structure of parakeldyshiteof of parakeldyshite parakeldyshite from from albitizedfrom albitized albitized pegmatite pegmatite pegmatite of Takhtarvumvorr of of Takhtarvumvorr Takhtarvumvorr Mt., Khibiny, Mt., Mt., 2 2 Russia was solved in the space group P1 and refined to final R = 0.024 [for 1364 F > 4σ(F )]. In2 general,2 Khibiny,Khibiny, Russia Russia was was solved solved in in the the space space group group P1 P 1 and and refined refined1 to to final final R 1R =1 0.024= 0.024 [for [for 1364 1364 F F >2 4>σ 4(σF(F)].2)]. theInIn general, structure general, the modelthe structure structure proposed model model in proposed [17 proposed] was confirmed. in in [17] [17] was was The confirmed. confirmed. bond lengths The The bond in bond polyhedra lengths lengths in vary in polyhedra polyhedra significantly vary vary andsignificantlysignificantly are equal and to and 2.047-2.139(2), are are equal equal to to 2.047 1.601-1.672(2),2.047‒2.139(2),‒2.139(2), 1.601 1.600-1.669(2),1.601‒1.672(2),‒1.672(2), 1.600 2.443-2.913(3),1.600‒1.669(2),‒1.669(2), 2.443 and2.443‒ 2.384-2.913(3)2.913(3),‒2.913(3), and and 2.384 Å 2.384 for‒ ‒ the ZrO , Si1O , Si2O , Na1O , and Na2O polyhedra, respectively. The degrees of distortion of 2.913(3)2.913(3)6 Å Åfor for 4the the ZrO ZrO4 6, 6Si1O, Si1O48, 4Si2O, Si2O4, 4Na1O, Na1O7 8, 8and, and Na2O Na2O7 polyhedra,7 polyhedra, respectively. respectively. The The degrees degrees of of polyhedra (based on bond lengths) calculated according to Baur [48] for the Si1O , Si2O , ZrO , distortiondistortion of of polyhedra polyhedra (based (based on on bond bond lengths) lengths) calculated calculated according according to to Baur Baur [48] [48] for for the4 the Si1O Si1O44, Si2O4, Si2O64, 4, Na1O , and Na2O polyhedra are equal to 0.01369, 0.01171, 0.01626, 0.04376, and 0.07001, respectively. ZrOZrO6,8 6Na1O, Na1O8, 8and, and7 Na2O Na2O7 polyhedra7 polyhedra are are equal equal to to 0.01369, 0.01369, 0.01171, 0.01171, 0.01626, 0.01626, 0.04376, 0.04376, and and 0.07001, 0.07001, Accordingrespectively.respectively. to ourAccording According data, there to to our are our nodata, data, additional there there are are Na no sitesno addi addi describedtionaltional Na Na in sites [sites27]. described Indescribed contrast in toin [27]. keldyshite,[27]. In In contrast contrast there to to arekeldyshite,keldyshite, two independent there there are are two positions two independent independent of Na1 positions and positions Na2 withof of N Na1 aa1 coordinationand and Na2 Na2 with with number a coordinationa coordination (CN) of number 8, number respectively, (CN) (CN) of of in8, 8, therespectively, respectively, crystal structure in in the the crystal of crystal parakeldyshite stru structurecture of (Figureofparakeldyshite parakeldyshite5a). (Figure (Figure 5a). 5a).

(a)( a) (b()b ) (c)( c)

FigureFigureFigure 5. 5. Projections 5.Projections Projections of the of crystal ofthe the structurescrystal crystal ofstructures (structuresa) parakeldyshite; of of( a)( a)parakeldyshite; (bparakeldyshite;) keldyshite (c) Na( b()b [Zr(Si)keldyshite keldyshiteO )] H (O. c)( c) 2 2 7 · 2 Na2[Zr(Si2O7)]∙H2O. The SiO4 tetrahedra are blue, the ZrO6 octahedra are green, the Na atoms are TheNa SiO2[Zr(Si4 tetrahedra2O7)]∙H2O. are The blue, SiO the4 tetrahedra ZrO6 octahedra are blue, are green, the ZrO the6 Naoctahedra atoms are are yellow, green, and the theNa Oatoms atoms are areyellow,yellow, red. and and the the O Oatoms atoms are are red. red.

TheTheThe crystalcrystal crystal structure structure structure of of keldyshite of keldyshite keldyshite (Figure (Figure (Figure5b) 5b) di 5b)ff differsers differs from from thatfrom that of that parakeldyshite of of parakeldyshite parakeldyshite and containsand and contains contains only oneonlyonly independent one one independent independent Na site Na withNa site sevenfoldsite with with sevenfold sevenfold coordination. co coordination.ordination. The uneven The The distribution uneven uneven distribution distribution of Na in keldyshite of of Na Na in in resultskeldyshitekeldyshite in the results slightresults in framework in the the slight slight framework deformation framework deformation manifested deformation bymanifested manifested the change by by of the the change Si–O–Sichange of of anglethe the Si–O–Si Si–O–Si of 126.7(9) angle angle◦ comparedofof 126.7(9)° 126.7(9)° to compared 127.7(8)compared◦ toin to 127.7(8)° parakeldyshite. 127.7(8)° in in parakeldyshi parakeldyshi At the samete.te. At At time,the the same thesame shapetime, time, the of the theshape shape channels of of the the channels changes channels significantlychangeschanges significantly significantly as can be as clearly as can can be seen be clea clea inrly therly seen seen projection in in the the projection ofprojection the MT oflayer of the the MT (Figure MT layer layer6b). (Figure (Figure 6b). 6b). TheTheThe crystalcrystal crystal structurestructure structure of of Naof Na Na2[Zr(Si2[Zr(Si2[Zr(Si22OO727O)])]7∙H)]H∙22HO2 O is is based based onon on thethe the MM 2M2TT626T type6 type of of SBUsSBUs SBUs (Figure(Figure (Figure4 4c).c). 4c). As As As in in in · thethethe structuresstructures structures of of keldyshite of keldyshite keldyshite and and parakeldyshite,and parakeldyshite, parakeldyshite, the ZrO the the6 ZrOoctahedron ZrO6 octahedron6 octahedron is linked is is throughlinked linked throughcommon through commonvertices common toverticesvertices six SiO to4 tetrahedra,to six six SiO SiO4 tetrahedra,4 each tetrahedra, connected each each to connectedthree connected Zr-centered to to three three octahedra. Zr-centered Zr-centered The topologicaloctahedra. octahedra. diThe ffTheerence topological topological of the MTdifferencedifference-framework of of the the (Figure MT MT-framework-framework5c) from those (Figure (Figure observed 5c) 5c) from from in keldyshitethose those observed observed and parakeldyshitein in keldyshite keldyshite and isand confirmed parakeldyshite parakeldyshite by the is is di ff erent value of the Si-О-Si angle equal to 156.96(9)◦. The increasing Si-O-Si angle corresponds to the increasing size of the structure channels (Figure6c,f). Crystals 2020, 10, x FOR PEER REVIEW 7 of 15

Crystals 2020confirmed, 10, 1016 by the different value of the Si‒О‒Si angle equal to 156.96(9)°. The increasing Si-O-Si angle 7 of 14 corresponds to the increasing size of the structure channels (Figure 6c,f).

(a) (b) (c)

(d) (e) (f)

FigureFigure 6. Projections 6. Projections of the of MTthe MTlayers layers in in the the crystal crystal structuresstructures of of (a (,ad,)d parakeldyshite;) parakeldyshite; (b,e) ( bkeldyshite;,e) keldyshite; (c,f) Na(c[Zr(Si,f) Na2[Zr(SiO )]2OH7)]O.∙H2O. 2 2 7 · 2 3.2. Topological3.2. Topological Analysis Analysis The topologicalThe topological type type of the of the base base grid grid in in the the crystal crystal structuresstructures of of keldyshite keldyshite and and parakeldyshite parakeldyshite is fsh, while that in Na2[Zr(Si2O7)]∙H2O is xat (Figure 7). Table 2 shows data on related inorganic is fsh, while that in Na [Zr(Si O )] H O is xat (Figure7). Table2 shows data on related inorganic compounds of the fsh2 and 2xat7 topological· 2 types. Keldyshite and parakeldyshite consists of one type compoundsof the [4 of3.6 the3] tilesfsh formedand xat bytopological three four-membered types. Keldyshite rings and three and parakeldyshitesix-membered rings consists (Figure of 8). one In type 3 3 of the [4the.6 case] tilesof Na formed2[Zr(Si2O by7)]∙H three2O, there four-membered are two types of rings tiles: and [63] t-kah three and six-membered [46.63] t-afo (Figure rings 8). (Figure Na 8). 3 6 3 In the caseatoms of are Na located2[Zr(Si inside2O7)] Hall2 O,[43.6 there3] tiles are in twoparakeldyshite types of tiles: and only [6 ] t-kahhalf ofand these [4 tiles.6 ] aret-afo filled(Figure in 8). · 3 3 Na atomskeldyshite. are located In the insidecrystal allstructure [4 .6 ]of tiles Na2 in[Zr(Si parakeldyshite2O7)]∙H2O, one andNa site only is located half of in these the t-kah tiles aretile, ﬁlled in keldyshite.whereas Inanother the crystal one is within structure the t-afo of Na tile.[Zr(Si O )] H O, one Na site is located in the t-kah tile, 2 2 7 · 2 whereasCrystals another 2020, 10, onex FOR is PEER within REVIEW the t-afo tile. 8 of 15

(a) (b)

FigureFigure 7. Tiling 7. Tiling representation representation of of the the crystalcrystal structuresstructures of: of: (a ()a parakeldyshite/keldyshite) parakeldyshite/keldyshite (the fsh (the fsh 3 3 topology);topology); (b) phase(b) phase Na Na[Zr(Si2[Zr(SiO2O)]7)]H∙H2O (the xatxat topology).topology). The The [4 [4.63].6 tiles3] tiles are shown are shown as light-blue, as light-blue, 2 2 7 · 2 the t-afothe t-afoand andt-kah t-kahtiles tiles in in (b )(b are) are yellow yellow and and violet,violet, respectively.

Table 2. Examples of inorganic compounds with the grids of the fsh or xat topological type.

Formula Space group Topology ICSD code Ref. NaH[Zr(Si2O7)] keldyshite P1 fsh 20186 [47] Na2[Zr(Si2O7)] parakeldyshite P1 fsh – This work K2[Zr(Si2O7)] khibinskite P21/b fsh 20100 [49] K2[Zr(Ge2O7)] C2/c fsh 88843 [50] K2[Cd(P2O7)] C2/c fsh 12117 [51] Na[Ti(P2O7)] P21/c fsh 202751 [52] Na2[SiVI(SiIV2O7) C2/c fsh 81134 [53] Na2[Zr(Si2O7)]∙H2O C2/c xat 419420 [28] K[Y(P2O7)] Cmcm xat 75171 [54] Ba6Dy2Al4O15 Cmcm xat 85071 [55] Si(P2O7) P63 xat 75116 [56] Tm(BO3) P6c2 xat 27942 [57] Na3[Sc(Si2O7)] Pbnm xat 20120 [58]

Figure 8. Fragments of the crystal structures and the corresponding tiles. The [43.63] tile is present in the crystal structures of keldyshite and parakeldyshite, while the t-kah and t-afo tiles are present in

Na2[Zr(Si2O7)]∙H2O.

Crystals 2020, 10, x FOR PEER REVIEW 8 of 15

(a) (b)

Figure 7. Tiling representation of the crystal structures of: (a) parakeldyshite/keldyshite (the fsh Crystals 2020, 10, 1016 8 of 14 topology); (b) phase Na2[Zr(Si2O7)]∙H2O (the xat topology). The [43.63] tiles are shown as light-blue, the t-afo and t-kah tiles in (b) are yellow and violet, respectively. Table 2. Examples of inorganic compounds with the grids of the fsh or xat topological type. Table 2. Examples of inorganic compounds with the grids of the fsh or xat topological type. Formula Space Group Topology ICSD Code Ref. Formula Space group Topology ICSD code Ref. NaH[Zr(Si O )] 2 7 P1 fsh 20186 [47] keldyshiteNaH[Zr(Si2O7)] keldyshite P1 fsh 20186 [47] NaNa[Zr(Si2[Zr(SiO2O)]7)] parakeldyshite P1 fsh – This work 2 2 7 P1 fsh – This work parakeldyshiteK2[Zr(Si2O7)] khibinskite P21/b fsh 20100 [49] K2[Zr(Si2O7)] K2[Zr(Ge2O7)] P2 /b C2/c fsh fsh 2010088843 [50] [49] khibinskite 1 K2[Cd(P2O7)] C2/c fsh 12117 [51] K2[Zr(Ge2O7)] C2/c fsh 88843 [50] K2[Cd(P2ONa[Ti(P7)] 2O7)] C2/c P21/c fsh fsh 12117202751 [52] [51] Na[Ti(P2NaO72)][SiVI(SiIV2O7) P21/c C2/c fsh fsh 20275181134 [53] [52] VI IV C c fsh Na2[Si Na(Si 2[Zr(Si2O7) 2O7)]∙H2O 2/ C2/c xat 81134419420 [28] [53] Na2[Zr(Si2O7)] H2O C2/c xat 419420 [28] K[Y(P· 2O7)] Cmcm xat 75171 [54] K[Y(P2O7)] Cmcm xat 75171 [54] Ba6Dy2Al4O15 Cmcm xat 85071 [55] Ba6Dy2Al4O15 Cmcm xat 85071 [55] Si(P2O7) Si(P2O7) P63 P63 xat xat 7511675116 [56] [56] Tm(BO3) Tm(BO3) P6c2 P6c2 xat xat 2794227942 [57] [57] Pbnm xat Na3[Sc(Si2NaO73)][Sc(Si2O7)] Pbnm xat 2012020120 [58] [58]

Figure 8. Fragments of the crystal structures and the corresponding tiles. The [43.63] tile is present in Figure 8. Fragments of the crystal structures and the corresponding tiles. The [43.63] tile is present in the crystal structures of keldyshite and parakeldyshite, while the t-kah and t-afo tiles are present in the crystal structures of keldyshite and parakeldyshite, while the t-kah and t-afo tiles are present in Na2[Zr(Si2O7)] H2O. Na2[Zr(Si2O7)]∙H· 2O. 3.3. Raman Spectroscopy

The Raman spectrum of parakeldyshite from the albitites of Takhtarvumchorr Mt. is shown in (Figure 9). The most intense spectral lines are similar to those for parakeldyshite from the Alluaiv Mt., 1 Lovozero alkaline massif [52], RRUF, 120048 [59]. The bands in the range 850–1020 cm− correspond to 1 stretching vibrations of Si-O bonds. Two intense absorption bands at 968 and 1017 cm− are attributed 1 to asymmetric stretching vibrations of Si-O-Si bonds, while three bands at 850, 905, and 941 cm− are 1 attributed to symmetric vibration modes of similar bonds [60–62]. The non-typical band at 718 cm− can be associated with symmetric stretching vibrations of the Si-O-Si bridging oxygen in sorosilicate 1 groups [63]. The bands in the range 450–600 cm− correspond to asymmetric bending vibrations of 1 Si-O bonds in tetrahedra [62]. Bands of diﬀerent intensities in the region 350–450 cm− belong to symmetric deformation vibration modes in SiO4 tetrahedra [63]. The most intense absorption band at 1 331 cm− is attributed to bending vibration modes of the Zr-O bonds in octahedra, and the bands in the 1 range 90–300 cm− correspond to symmetric bending vibrations of bonds in octahedra or translational Crystals 2020, 10, x FOR PEER REVIEW 9 of 15

3.3. Raman Spectroscopy The Raman spectrum of parakeldyshite from the albitites of Takhtarvumchorr Mt. is shown in (Figure 9). The most intense spectral lines are similar to those for parakeldyshite from the Alluaiv Mt., Lovozero alkaline massif [52], RRUF, 120048 [59]. The bands in the range 850‒1020 cm−1 correspond to stretching vibrations of Si‒O bonds. Two intense absorption bands at 968 and 1017 cm‒ 1 are attributed to asymmetric stretching vibrations of Si‒O‒Si bonds, while three bands at 850, 905, and 941 cm−1 are attributed to symmetric vibration modes of similar bonds [60–62]. The non-typical band at 718 cm−1 can be associated with symmetric stretching vibrations of the Si‒O‒Si bridging oxygen in sorosilicate groups [63]. The bands in the range 450‒600 cm−1 correspond to asymmetric bending vibrations of Si‒O bonds in tetrahedra [62]. Bands of different intensities in the region 350‒ 450 cm−1 belong to symmetric deformation vibration modes in SiO4 tetrahedra [63]. The most intense absorption band at 331 cm−1 is attributed to bending vibration modes of the Zr‒O bonds in octahedra, Crystals 2020, 10, 1016 9 of 14 and the bands in the range 90‒300 cm−1 correspond to symmetric bending vibrations of bonds in octahedra or translational vibrations [64]. The absence of bands in the region 3000–3800 cm−1 (Figure 1 vibrationsS1) indicates [64 the]. The absence absence of ofOH bands groups in thein the region structure 3000–3800 of parakeldyshite, cm− (Figure S1) confirming indicates its the unchanged absence of OHnature. groups in the structure of parakeldyshite, conﬁrming its unchanged nature.

Figure 9. RamanRaman spectrum spectrum of of parakeldyshite parakeldyshite from Takhtarvumchorr Mt., Khibiny, Russia.Russia.

4. Discussion According to the approach of matrix (self)assemb (self)assemblyly of the crystal structures from SBUs proposed by Ilyushin for sodium zirconium silicates, all possible SBUs variants are defined as М2Тn (n = 2, by Ilyushin for sodium zirconium silicates, all possible SBUs variants are defined as М2Тn (n = 2, 4, 6) 4, 6) [5]. The crystal structure of keldyshite/parakeldyshite is based upon the M T blocks, while [5]. The crystal structure of keldyshite/parakeldyshite is based upon the M2T4 2blocks,4 while the the structure of Na2[Zr(Si2O7)] H2O is based upon the M2T6 blocks. This fact indicates different structure of Na2[Zr(Si2O7)]∙H2O is· based upon the M2T6 blocks. This fact indicates different formation formationconditions conditionsand the impossibility and the impossibility of the transformation of the transformation of one structure of one type structure into another type intothrough another the through the rearrangement of Na+-ions. Indeed, the conditions of the formation of phases in the rearrangement of Na+-ions. Indeed, the conditions of the formation of phases in the Na2CO3-ZrO2- Na CO -ZrO -SiO -H O hydrothermal system are different: parakeldyshite crystallizes at 450 ◦C[5], SiO22-H23O hydrothermal2 2 2 system are different: parakeldyshite crystallizes at 450 °C [5], while the while the Na2[Zr(Si2O7)] H2O phase appears at a temperature of about 200 ◦C[28]. According to [65], Na2[Zr(Si2O7)]∙H2O phase· appears at a temperature of about 200 °C [28]. According to [65], keldyshite keldyshiteis a product is of a productthe sequential of the sequentialtransformation transformation of parakeldyshite of parakeldyshite under hypergenic under hypergenic conditions conditions with the withpreservation the preservation of the overall of the framework overall framework topology. topology. According According to our data to on our the data migration on the migration of Na+-ions, of + Nasuch-ions, transition such transitionis possible. is possible. The unit-cell parameters (Table3) of keldyshite and parakeldeshite are close to each other and differ from those of Na [Zr(Si O )] H O. 2 2 7 · 2

Table 3. Unit cell parameters of Na-zirconosilicates chemically close to keldyshite.

Unit Cell Parameters Compound Sp. Gr., Z V,Å3 Citation a, Å, α, ◦ b, Å, β ◦ c, Å, γ, ◦ Keldyshite 9.01 5.34 6.96 P1, 2 300.39 [19] NaH[Zr(Si2O7)] 92.1 116.1 88.1 Parakeldyshite 8.8083 5.4243 6.5923 Current P1, 2 297.34 Na2[Zr(Si2O7)] 87.162 85.497 71.309 work 10.422 8.247 9.205 Na [Zr(Si O )] H O C2/c, 4 672.2 [27] 2 2 7 · 2 90 116.55 90 Note. For parakeldyshite, the same setting as in the initial study of keldyshite was used (associated with that given in this work by the transition matrix 0 1 0/0 0 1/1 0 0). Crystals 2020, 10, x FOR PEER REVIEW 10 of 15

The unit-cell parameters (Table 3) of keldyshite and parakeldeshite are close to each other and differ from those of Na2[Zr(Si2O7)]∙H2O.

Table 3. Unit cell parameters of Na-zirconosilicates chemically close to keldyshite.

Unit Cell Parameters Compound Sp. Gr., Z V, Å3 Citation a, Å, α, ° b, Å, β ° c, Å, γ, ° Keldyshite 9.01 5.34 6.96 P1, 2 300.39 [19] NaH[Zr(Si2O7)] 92.1 116.1 88.1 Parakeldyshite 8.8083 5.4243 6.5923 Current P1, 2 297.34 Na2[Zr(Si2O7)] 87.162 85.497 71.309 work 10.422 8.247 9.205 Na2[Zr(Si2O7)]∙H2O C2/c, 4 672.2 [27] 90 116.55 90 Note. For parakeldyshite, the same setting as in the initial study of keldyshite was used (associated with that given in this work by the transition matrix 0 1 0/0 0 1/1 0 0).

The paths of the Na+-ion migration obtained using the Voronoi method are two-dimensional, running through all the crystallographic positions of Na (Figure 10). Thus, the migration of Na+-ions in the keldyshite-related zirconium silicates occurs along a two-periodic network of channels. Diffusion is possible when Na+-ions move from cavity to cavity (from one tile to another) through four-membered and six-membered rings. Calculating the radius of these rings (Table 4) and + comparingCrystals 2020, 10it ,with 1016 the threshold value of 2.0 Å, we can conclude that free migration of Na in10 these of 14 structures will occur only through six-membered rings. Moreover, in the case of parakeldyshite, there is one six-membered ring that is too narrow (marked in red in Table 4) for sodium to move along. + However,The paths the migration of the Na paths-ion through migration the obtainedremainin usingg six-membered the Voronoi rings method form area 2-D two-dimensional, migration map, + whichrunning is throughconsistent all with the crystallographic the result obtained positions by the of Voronoi Na (Figure method. 10). Thus, the migration of Na -ions in the keldyshite-relatedThe refinement of zirconium the crystal silicates structure occurs of para alongkeldyshite a two-periodic from the network Takhtarvumchorr of channels. Di pegmatiteﬀusion is + demonstratespossible when the Na absence-ions move of splitting from cavity of the to cavity Na sites. (from According one tile to to another) the chemical through data four-membered and Raman spectroscopy,and six-membered the studied rings. Calculatingsample of theparakeldys radius ofhite these is the rings extreme (Table 4Na-member) and comparing of the it withpossible the + keldyshite-parakeldyshitethreshold value of 2.0 Å, we series. can conclude The migration that free paths migration analysis of Naby thein theseVoronoi structures method will showed occur onlythat allthrough three six-memberedstudied phases rings. have Moreover, a 2-D system in the caseof channels of parakeldyshite, (Figures 10 there and is one11), six-memberedwithin which ringthe migrationthat is too narrowof Na+ (marked cations inis red possible. in Table 4These) for sodium data toconfirm move along.the possibility However, theof migrationtransition pathsfrom parakeldyshitethrough the remaining to keldyshite six-membered by the Na rings+ + O2 form‒ ↔ OH a 2-D‒ + □ migration substitution map, scheme, which iswhich consistent is widespread with the inresult postcrystallization obtained by the processes Voronoi method. in peralkaline rocks.

(a) (b)

Figure 10. Migration paths of Na + cationscations obtained obtained using using the the Voronoi Voronoi method method for for the structures: ( (aa)) parakeldyshite; ( b) keldyshite.

Table 4. The radii of the rings for the possible migration of Na+ cations in the structures of keldyshite,

parakeldyshite, and Na ZrSi O H O calculated using the geometric-topological approach. 2 2 7· 2 Number of Number of Radius of Radius of Compound Nodes in the Compound Nodes in the Ring, Å Ring, Å Ring Ring 6 2.12 6 2.09 6 2.06 6 2.00 6 1.75 6 2.05 6 2.14 6 2.12 Parakeldyshite 6 2.06Keldyshite 6 2.10 Na2ZrSi2O7 4 1.53NaZr(Si2O6OH) 4 1.77 4 1.54 4 1.37 4 1.80 4 1.65 4 1.66 4 1.84 4 1.64 4 1.17 6 2.36 4 1.77 Na ZrSi O H O 6 2.37 4 1.78 2 2 7· 2 4 1.75

The reﬁnement of the crystal structure of parakeldyshite from the Takhtarvumchorr pegmatite demonstrates the absence of splitting of the Na sites. According to the chemical data and Raman spectroscopy, the studied sample of parakeldyshite is the extreme Na-member of the possible keldyshite-parakeldyshite series. The migration paths analysis by the Voronoi method showed that all three studied phases have a 2-D system of channels (Figures 10 and 11), within which the migration of Na+ cations is possible. These data conﬁrm the possibility of transition from Crystals 2020, 10, x FOR PEER REVIEW 11 of 15

Table 4. The radii of the rings for the possible migration of Na+ cations in the structures of keldyshite,

parakeldyshite, and Na2ZrSi2O7∙H2O calculated using the geometric-topological approach.

Number of Nodes Radius of Number of Nodes Radius of Compound Compound in the Ring Ring, Å in the Ring Ring, Å 6 2.12 6 2.09 6 2.06 6 2.00 6 1.75 6 2.05 6 2.14 6 2.12 Parakeldyshite 6 2.06 Keldyshite 6 2.10 Na2ZrSi2O7 4 1.53 NaZr(Si2O6OH) 4 1.77 4 1.54 4 1.37 4 1.80 4 1.65 Crystals 2020, 10, 1016 4 1.66 4 1.8411 of 14 4 1.64 4 1.17 6 2.36 4 1.77 parakeldyshite to keldyshite by the Na+ + O2 OH + substitution scheme, which is widespread Na2ZrSi2O7∙H2O 6 2.37− ↔ − 4 1.78 in postcrystallization processes4 in peralkaline1.75 rocks.

FigureFigure 11.11. Migration paths of Na+ cationscations obtained obtained using using the the Voronoi Voronoi method for the crystal structure ofof NaNa2[Zr(Si2O7)])]∙HH2O.O. 2 2 7 · 2

TheThe structural complexity complexity IG,totalIG,total waswas calculated calculated according according to th toe themethod method proposed proposed in [66]. in [The66]. Thecalculated calculated values values for keldyshite/parakeldyshite for keldyshite/parakeldyshite and Na and2ZrSi Na2O7ZrSi∙H2O Oare H76.107O are and 76.107 86.606 and (bits/u.c.), 86.606 2 2 7· 2 (bitsrespectively./u.c.), respectively. The identity Theof the identity structural of the comp structurallexity values complexity for keldyshite values forand keldyshiteparakeldyshite and parakeldyshiteemphasizes their emphasizes structural theirsimilarity. structural The similarity.increase in Thestructural increase complexity in structural with complexity the decreasing with thecrystallization decreasing temperature crystallization is temperaturein agreement is with in agreement the general with tendency the general observed tendency for hydrothermal observed for hydrothermalsystems [66,67]. systems [66,67].

SupplementarySupplementary Materials:Materials: TheThe followingfollowing materialsmaterials are are available available online online at at http: www.mdpi.com/xxx/s1,//www.mdpi.com/2073-4352 Figure/ 10S1:/ 4 11title,/1016 Table/s1, FigureS1: Fractional S1: title, atomic Table S1:coordinates Fractional (×10 atomic4) and coordinates equivalent ( isotropic10 ) and displacement equivalent isotropic parameters displacement (Å2 × 103) 2 3 × parametersfor parakeldyshite. (Å 10 Table) for S2: parakeldyshite. selected interatomic Table S2: distances selected in interatomic parakeldyshite. distances Table in S3: parakeldyshite. anisotropic parameters Table S3: anisotropic parameters× of atomic displacements in parakeldyshite. of atomic displacements in parakeldyshite. Author Contributions: N.A.K. and T.L.P. designed the study. V.V.S. and N.S.V. performed microprobe analyses, V.N.Y.Author provide Contributions: samples forN.A.K. investigation. and T.L.P. V.N.B. designed performed the study. Raman V.V.S. spectroscopy and N.S.V. performed measurements, microprobe T.L.P. performed analyses, andV.N.Y. interpreted provide Single-crystal samples for X-ray investigation. diﬀraction experiments.V.N.B. performed N.A.K., Raman T.L.P. and spectroscopy S.M.A. wrote measurements, the draft paper. T.L.P. S.V.K. supervising,performed and review interpreted and editing. Single-cryst All authorsal X-ray have diffraction read and agreed experiments. to the published N.A.K., T.L.P. version and of S.M.A. the manuscript. wrote the Funding:draft paper.This S.V.K. work supervising, was supported review by and the editing. Kola ScienceAll authors Center have of read Russian and agreed Academy to the of published Sciences (Projectversion 0226-2019-0011)of the manuscript. and funded by the Russian Foundation for Basic Research (Grant 18-29-12039). N.A.K. thanks the Ministry of Education and Science of the Russian Federation for ﬁnancial support within grant No. 0778-2020-0005.

Acknowledgments: Technical support by the SPbSU X-ray Diffraction and ‘Geomodel’ Resource Centers is gratefully acknowledged. There are two anonymous reviewers are thanked for fruitful remarks and corrections. Conflicts of Interest: The authors declare no conflict of interest.

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