New Data on the Isomorphism in Eudialyte-Group Minerals. 1. Crystal Chemistry of Eudialyte-Group Members with Na Incorporated into the Framework as a Marker of Hyperagpaitic Conditions

A review of the crystal chemistry of Fe-deficient eudialyte-group minerals is given. Specific features of cation distribution over key sites in the crystal structure, including partial substitution of Fe2+ with Na, Mn and Zr at the M2 site are discussed. It is concluded that Na-dominant (at the M2 site) eudialyte-group members (M2Na-EGMs) are markers of specific kinds of specific peralkaline (hyperagpaitic) igneous rocks and pegmatites. New data are obtained on the chemical composition, IR spectra and crystal chemistry for two samples of M2Na-EGMs with disordered M1 cations, which are a potentially new mineral species with the simplified formula (Na,H2O)15Ca6Zr3[Na2(Fe,Zr)][Si26O72](OH)2Cl·nH2O.


Introduction
Eudialyte, ideally Na 15 Ca 6 3 (Cl,OH) 2 (Z = 3), is the most important zirconosilicate mineral. It was discovered two hundred years ago in the Ilímaussaq alkaline complex, South Greenland [1], and later, numerous other finds of eudialyte and related mineral species defined as eudialyte-group members were described. Eudialyte-bearing rocks are considered as a potential source of different rare elements (Zr, Hf, Nb, Y, lanthanides, etc.); the largest reserves of such rocks with potential industrial significance are in the Lovozero alkaline complex, Kola Peninsula, Russia, and in the Ilímaussaq complex.
This paper summarizes structural data on EGMs in which Na prevails at the M2 site (below -M2 Na-EGMs). To date, the crystal structures of 23 samples of M2 Na-EGMs have been published. In this paper, we discuss the crystal chemical features of these minerals and provide some additional (chemical, IR spectroscopic and detailed crystal chemical) data on two samples of Fe-deficient EGMs whose crystal structures were reported elsewhere [24,31]. In addition, the significance of M2 Na-EGMs as markers of hyperagpaitic rocks is discussed.

Materials and Methods
Sample 1 (sample Kdk-6626) was collected from the Kedykverpakhk area of the Karnasurt underground loparite mine at Mt. Kedykverpakhk in the northwest part of the Lovozero alkaline massif. The studied EGM occurs as transparent, reddish, equant grains up to 1.5 mm across in a peralkaline (hyperagpaitic) foyaite near the contact point with the loparite malignite layer. This rock mainly consists of potassic feldspar, nepheline, sodalite and aegirine, and contains accessory EGM, lamprophyllite, lomonosovite, loparite and interstitial villiaumite. Sample 2 originates from the Kvanefjeld area, Ilímaussaq alkaline complex. It comprises brownish yellow grains and imperfect equant crystals up to 2 mm across in an agpaitic rock composed of potassic feldspar, albite, nepheline, aegirine and arfvedsonite.
Electron microprobe analyses (three spot analyses for each sample) were carried out using a Tescan VEGA-II XMU electronic microscope (EDS mode, 20 kV, 400 pA, Oxford Instruments plc, London, UK) housed at the Institute of Experimental Mineralogy RAS. Data reduction was carried out by means of a modified INCA Energy 450 software package (Oxford Instruments, Oxfordshire, UK). The size of the electron beam was 157-180 nm. The beam was rastered on an area 20 µm × 20 µm in order to minimize sample damage. The time of data acquisition was 50 s. The sample-to-detector distance was 25 mm. The standards used were: albite for Na and Si, sanidine for K, wollastonite for Ca, BaSO 4 for S, SrF 2 for Sr, individual REE(PO 4 ) for rare-earth elements, metallic Fe, Mn, Ti, Zr, Hf and Nb for corresponding elements, and NaCl for Cl. The contents of other elements with atomic numbers >8 were below detection limits. H 2 O was not determined directly because of the paucity of material.
In order to obtain infrared (IR) absorption spectra, powdered samples were mixed with dried KBr, pelletized and analyzed using an ALPHA FTIR spectrometer (Bruker Optics, Karlsruhe, Germany) in the range 360-4000 cm −1 with a resolution of 4 cm −1 and 16 scans. An IR spectrum of an analogous pellet prepared from pure KBr was used as a reference.

Chemical Composition of Samples 1 and 2
The chemical data of Samples 1 and 2 are presented in Table 2. The empirical formulae calculated on 25.48 and 25.80 Si atoms per formula unit, respectively (in accordance with structural data, Z = 3, see below) are as follows.   Note: bdl = below detection limit; EGM = eudialyte-group minerals.

Infrared Spectroscopy of Samples 1 and 2
The IR spectra of Samples 1 and 2 ( Bands below 500 cm −1 are due to lattice mode involving predominantly bending vibrations of rings of tetrahedra, and stretching vibrations of M1-centered octahedra. Bands of CO 3 2− are absent in both spectra. The assignment of IR bands was made based on analyses of the IR spectra of several dozen structurally investigated eudialyte-group minerals, in accordance with [2]. Note: bdl = below detection limit; EGM = eudialyte-group minerals.

Infrared Spectroscopy of Samples 1 and 2
The IR spectra of Samples 1 and 2 ( Figure 2) contain bands of O-H stretching vibrations (in the range 3200-3700 cm −1 ), H-O-H bending vibrations (at 1650 and 1635 cm −1 ), stretching vibrations of the rings of tetrahedra (in the range 1000-1100 cm −1 ) and SiO4 tetrahedra at the M3 and M4 sites (at the centers of 9-membered rings of tetrahedra) at 933 and 936 cm −1 . Broad absorption in the range 2600-3300 cm −1 indicates the presence of H3O + groups. Bands in the range 650-750 cm −1 correspond to mixed vibrations of the rings of tetrahedra ("ring bands"). Weak absorptions in the region 510-530 cm −1 are related to Zr-O and Fe-O stretching modes of the M2-centered polyhedra. Bands below 500 cm −1 are due to lattice mode involving predominantly bending vibrations of rings of tetrahedra, and stretching vibrations of M1-centered octahedra. Bands of CO3 2-are absent in both spectra. The assignment of IR bands was made based on analyses of the IR spectra of several dozen structurally investigated eudialyte-group minerals, in accordance with [2].
The number of observed absorption maxima and shoulders in the IR spectrum of Sample 2 is less than in the IR spectrum of Sample 1. This is due to a high content of H2O molecules and H3O + groups in Sample 2. The disordering of Na + , H2O and H3O + , as well as hydrogen bonding, result in the broadening of individual bands, their poor resolution and changes of peak intensities which are most significant for narrow bands. The number of observed absorption maxima and shoulders in the IR spectrum of Sample 2 is less than in the IR spectrum of Sample 1. This is due to a high content of H 2 O molecules and H 3 O + groups in Sample 2. The disordering of Na + , H 2 O and H 3 O + , as well as hydrogen bonding, result in the broadening of individual bands, their poor resolution and changes of peak intensities which are most significant for narrow bands.

Crystal Chemistry of Samples 1 and 2
The crystal structures of Samples 1 and 2 are published elsewhere [24,31]. In this subsection, we discuss only the crystal-chemical features in the microregions around the key sites M2-M4 (see Table 3). Sample 1 is trigonal, space group R3m; the unit cell parameters are a = 14.198(1) Å, c = 30.380(1) Å, and V = 5303.9(1) Å 3 . The crystal structure was refined to a final reliability factor value R = 4.2% in the anisotropic approximation of atomic displacements using 3174 reflections with F > 3σ(F) [22]. All features of the distribution of cations between different sites in the structure of Sample 1 are reflected in its crystal chemical formula (Z = An excess of Zr (0.87 atoms per formula unit) was located at the M2a site in the square base pyramid with apical OH group and average Zr-O distance of 2.204 Å. This vertex also belongs to the NbO 6 octahedron located on the threefold axis, which results in the formation of a cluster [NbZr 3 O 3 ] whose occupancy factor is equal to 0.21.
A large, elongated, Na-centered, seven-fold M2b polyhedron is characterized by the average Na-O distance of 2.754 Å. One base of this prism-like polyhedron is square, and another is a triangle involving two O atoms in the framework and one Cl atom located on the threefold axis. These two M2 polyhedra are turned in opposite directions and are only partially occupied, since the distance between the cations centering them is short, amounting to 1.781 Å.
The key sites M3 and M4 on the threefold axis are statistically occupied by Si-centered tetrahedra of two orientations with a common triangular base, and subordinate Ti and Nb atoms in octahedral coordination.
Large extra-framework cations are located at the sites N1-N4, which are split and mainly occupied by sodium atoms coordinated by 7-and 8-fold polyhedra with average distances within the range of 2.56-2.64 Å. Based on the number of refined electrons, one may suppose that the group of closely spaced N5 sites is occupied by hydronium groups and water molecules.

Discussion
About 150 years have passed since the description of eudialyte by Stromeyer in 1819 [1], but the structure of this mineral remained unknown for a long time, since it has a volume of more than 5000 Å 3 . Another cause of this situation was unique crystal-chemical complexity and variability of eudialyte and related minerals (Tables 1 and 4).   [10] Note: Roman numerals denote coordination numbers. A part of the data corresponds to holotype samples of EGMs: raslakite (12), sergevanite (13), aqualite (14), alluaivite (17), dualite (19), labirinthite (20) and rastsvetaevite (21).
Only in the early 1970s was the structural motive of eudialyte characterized in general terms by a group of researchers led by academician N.V. Belov [52,53], and almost simultaneously by G. Giuseppetti et al. [54]. Further studies of the structure of eudialyte revealed its complexity and variety of structural fragments.
Mineral species belonging to the eudialyte group are distinguished by symmetry (representatives with the space groups R3m, R-3m and R3 are known) and different combinations of predominant components at the key sites [2][3][4][5][6][7]. In addition, there is a subgroup of EGMs with modular structures and doubled c parameter of the unit cell. The distribution of cations among key sites is the result of a combination of two factors: the competition of their activities in the mineral-forming medium, and their affinity to different sites in the structures of EGMs.
Additional key sites M3 and M4 are located at the centers of the Si9O27 rings, and can be vacant or occupied by different components, including [4] Si, [4] Al, [6] Nb, [6] W, Na. Large cations (Na + , K + , H3O + , Ca 2+ , Sr 2+ , REE 3+ , etc.) occupy extra-framework sites N1-N5, which are typically split. Additional anions (Cl -, F -, OH -, S 2-, SO4 2-, CO3 2-) and water molecules occur at two sites on the threefold axis.  The crystallochemical diversity of EGMs is determined by complex mechanisms of isomorphism accompanied by the splitting of positions and variations in their coordination numbers [2]. The most complex isomorphism schemes are realized at the group of the M2 sites in the microregion between two neighboring M1 6 O 24 octahedra. Eudialyte s.s. is a Na-and Si-rich EGM in which the M2 site is occupied by Fe 2+ with flat-square coordination. However, different Fe-deficient members of the eudialyte group are known. In these minerals, the deficiency of iron at the M2 site is compensated for by other cations (Fe 2+ , Fe 3+ , Ti 4+ , Hf 4+ , Zr 4+ , Ta 5+ , Mn 2+ , and Mg 2+ ). The agpaitic and, especially, hyperagpaitic rocks of some alkaline massifs are characterized by the prevalence of M2 Na-dominant minerals over other EGMs.
The substitution of Fe 2+ by Na + (usually accompanied by the change of the coordination number from 4 to 5, 6 or 7) is a specific crystal-chemical feature of these EGMs. Additional O atoms coordinating M2 Na belong to H 2 O molecules or to OH groups of the M3(O,OH) 6 (Figures 4 and 5). Table 4 contains data on the distribution of Na atoms at the M2-key site in the structurally studied M2 Na-dominant EGMs, most of which were found in the Lovozero massif. The exceptions are Sample 2 (Table 4), from Ilímaussaq, Greenland, labyrinthite and rastsvetaevite (Samples 20 and 21 in Table 4, respectively) which originate from the Khibiny massif and two hydrated samples from the Inagli massif, Eastern Siberia (Samples 5 and 6 in Table 4). It is to be noted that Lovozero is characterized by manganese specificity and differs from the Khibiny massif in its significantly lower iron content.
Minerals 2020, 3, x 9 of 16 [2]. The most complex isomorphism schemes are realized at the group of the M2 sites in the microregion between two neighboring M16O24 octahedra. Eudialyte s.s. is a Na-and Si-rich EGM in which the M2 site is occupied by Fe 2+ with flat-square coordination. However, different Fe-deficient members of the eudialyte group are known. In these minerals, the deficiency of iron at the M2 site is compensated for by other cations (Fe 2+ , Fe 3+ , Ti 4+ , Hf 4+ , Zr 4+ , Ta 5+ , Mn 2+ , and Mg 2+ ). The agpaitic and, especially, hyperagpaitic rocks of some alkaline massifs are characterized by the prevalence of M2 Na-dominant minerals over other EGMs. The substitution of Fe 2+ by Na + (usually accompanied by the change of the coordination number from 4 to 5, 6 or 7) is a specific crystal-chemical feature of these EGMs. Additional O atoms coordinating M2 Na belong to H2O molecules or to OH groups of the M3(O,OH)6 and M4(O,OH)6 octahedra or SiO3(OH) tetrahedra occurring on the threefold axes at the centers of the Si9O27 rings. The 5-, 6-and 7-fold Na-centered M2 polyhedra are based on the square formed by four O atoms of the neighboring M16O24 rings (Figures 4 and 5). Table 4 contains data on the distribution of Na atoms at the M2-key site in the structurally studied M2 Na-dominant EGMs, most of which were found in the Lovozero massif. The exceptions are Sample 2 (Table 4), from Ilímaussaq, Greenland, labyrinthite and rastsvetaevite (Samples 20 and 21 in Table 4, respectively) which originate from the Khibiny massif and two hydrated samples from the Inagli massif, Eastern Siberia (Samples 5 and 6 in Table 4). It is to be noted that Lovozero is characterized by manganese specificity and differs from the Khibiny massif in its significantly lower iron content.  The M2 site can be split into two or more subsites. Usually, the M2O4 square (Figures 5a and 6) is filled with Fe 2+ ; less often, it contains Na. Zr, Hf and Ta may also be present as subordinate and impurity components in this position. The four-fold coordination of M2 Na is a specific feature of  (Table 4) [29].
Minerals 2020, 3, x 9 of 16 [2]. The most complex isomorphism schemes are realized at the group of the M2 sites in the microregion between two neighboring M16O24 octahedra. Eudialyte s.s. is a Na-and Si-rich EGM in which the M2 site is occupied by Fe 2+ with flat-square coordination. However, different Fe-deficient members of the eudialyte group are known. In these minerals, the deficiency of iron at the M2 site is compensated for by other cations (Fe 2+ , Fe 3+ , Ti 4+ , Hf 4+ , Zr 4+ , Ta 5+ , Mn 2+ , and Mg 2+ ). The agpaitic and, especially, hyperagpaitic rocks of some alkaline massifs are characterized by the prevalence of M2 Na-dominant minerals over other EGMs. The substitution of Fe 2+ by Na + (usually accompanied by the change of the coordination number from 4 to 5, 6 or 7) is a specific crystal-chemical feature of these EGMs. Additional O atoms coordinating M2 Na belong to H2O molecules or to OH groups of the M3(O,OH)6 and M4(O,OH)6 octahedra or SiO3(OH) tetrahedra occurring on the threefold axes at the centers of the Si9O27 rings. The 5-, 6-and 7-fold Na-centered M2 polyhedra are based on the square formed by four O atoms of the neighboring M16O24 rings (Figures 4 and 5). Table 4 contains data on the distribution of Na atoms at the M2-key site in the structurally studied M2 Na-dominant EGMs, most of which were found in the Lovozero massif. The exceptions are Sample 2 (Table 4), from Ilímaussaq, Greenland, labyrinthite and rastsvetaevite (Samples 20 and 21 in Table 4, respectively) which originate from the Khibiny massif and two hydrated samples from the Inagli massif, Eastern Siberia (Samples 5 and 6 in Table 4). It is to be noted that Lovozero is characterized by manganese specificity and differs from the Khibiny massif in its significantly lower iron content.  The M2 site can be split into two or more subsites. Usually, the M2O4 square (Figures 5a and 6) is filled with Fe 2+ ; less often, it contains Na. Zr, Hf and Ta may also be present as subordinate and impurity components in this position. The four-fold coordination of M2 Na is a specific feature of alluaivite [44]. The M2 site can be split into two or more subsites. Usually, the M2O 4 square (Figures 5a and 6) is filled with Fe 2+ ; less often, it contains Na. Zr, Hf and Ta may also be present as subordinate and impurity components in this position. The four-fold coordination of M2 Na is a specific feature of alluaivite [44].
The M2 semioctahedron or square pyramid is a pentahedron formed on the basis of a square with the addition of an OH-group belonging to the M3 or M4 octahedron (Figures 5b and 7). This polyhedron can be occupied by Na + , Fe 2+ , Fe 3+ , or Mn 2+ .
The M2 octahedron is formed when the square coordination is supplemented by the two OH groups of the axial M3 and M4 octahedra, or by water molecules (Figures 5c and 8). Besides Na + , the cations Fe 2+ , Fe 3+ and Mn 2+ may enter the M2 octahedron.
The largest seven-fold M2 polyhedra are built on the basis of the square involving O atoms of the framework (Figure 9), additional anions and/or water molecules occurring on the threefold axis. Such coordination is known for M2 Na + , M2 Mn 2+ and M2 Zr 4+ . M2 NaO 7 polyhedra are dominant in the structures described in [32,34]. As subordinate components, such polyhedra (with the Na-O distances in the ranges of 2.23(4)-2.96(3) and 2.33(1)-3.01(1) Å) occur in the structures of intermediate members of the manganoeudialyte-ilyukhinite [25] and eudialyte-sergevanite [27] series, respectively. The largest seven-fold M2 polyhedra are built on the basis of the square involving O atoms of the framework (Figure 9), additional anions and/or water molecules occurring on the threefold axis. Such coordination is known for M2 Na + , M2 Mn 2+ and M2 Zr 4+ . M2 NaO7 polyhedra are dominant in the structures described in [32,34]. As subordinate components, such polyhedra (with the Na-O distances in the ranges of 2.23(4)-2.96(3) and 2.33(1)-3.01(1) Å) occur in the structures of intermediate members of the manganoeudialyte-ilyukhinite [25] and eudialyte-sergevanite [27] series, respectively.    (Table 4) [30]. The largest seven-fold M2 polyhedra are built on the basis of the square involving O atoms of the framework (Figure 9), additional anions and/or water molecules occurring on the threefold axis. Such coordination is known for M2 Na + , M2 Mn 2+ and M2 Zr 4+ . M2 NaO7 polyhedra are dominant in the structures described in [32,34]. As subordinate components, such polyhedra (with the Na-O distances in the ranges of 2.23(4)-2.96(3) and 2.33(1)-3.01(1) Å) occur in the structures of intermediate members of the manganoeudialyte-ilyukhinite [25] and eudialyte-sergevanite [27] series, respectively.   The diagnostic signs of M2 Na-EGMs are the specific features of their chemical composition (low total content of Fe + Mn + Ca, i.e., usually less than 7 atoms per formula unit, Z = 3, at relatively high Si contents) and reduced intensities of the IR bands in the range 515-545 cm -1 , corresponding to M2 Fe-O and M2 Mn-O stretching vibrations. Until recently, these minerals were known exclusively in hyperagpaitic igneous rocks and pegmatites of the Lovozero alkaline massif, which are indicated by highly alkaline titano-, zircono-and niobo-silicates (with atomic ratios Na:Si ≥ 1) such as lomonosovite, vuonnemite, zirsinalite, kazakovite, etc. [55]. Unlike the neighboring Khibiny alkaline massif, where even high-sodium EGMs typically do not contain M2 Na and mainly occur in pegmatites, in the Lovozero complex, these minerals are common components of specific igneous rocks (hyperagpaitic varieties of foyaite), and are often M2 Na-dominant. Figure 7. The local situation around M2 Na-centered semioctahedra (square pyramids) in the structure of Sample 9 (Table 4) [2].  (Table 4) [29].  (Table 4) [29].  (Table 4) [32].
The diagnostic signs of M2 Na-EGMs are the specific features of their chemical composition (low total content of Fe + Mn + Ca, i.e., usually less than 7 atoms per formula unit, Z = 3, at relatively high Si contents) and reduced intensities of the IR bands in the range 515-545 cm -1 , corresponding to M2 Fe-O and M2 Mn-O stretching vibrations. Until recently, these minerals were known exclusively in hyperagpaitic igneous rocks and pegmatites of the Lovozero alkaline massif, which are indicated by highly alkaline titano-, zircono-and niobo-silicates (with atomic ratios Na:Si ≥ 1) such as lomonosovite, vuonnemite, zirsinalite, kazakovite, etc. [55]. Unlike the neighboring Khibiny alkaline massif, where even high-sodium EGMs typically do not contain M2 Na and mainly occur in pegmatites, in the Lovozero complex, these minerals are common components of specific igneous rocks (hyperagpaitic varieties of foyaite), and are often M2 Na-dominant.
M2 Na-EGMs belong to three structure types: eudialyte (with disordered population of the M1 octahedra, space groups R3m or R-3m), raslakite (with ordering of Ca and smaller cations, Fe 2+ in raslakite and Mn 2+ in sergevanite; space group R3) and alluaivite (EGMs with doubled c parameter including alluaivite, dualite, rastsvetaevite and labyrinthite). M2 Na-EGMs 1, 3 and 7 in Table 4 belong to the eudialyte structure type and are Fe-deficient, with a strong predominance of Na over Fe at M2. Consequently, these samples can be considered as representatives of a potentially new mineral species.
In the structure of the Mn-rich alluaivite-type Sample 22 (Table 4), M2 Na-dominant modules alternate with kentbrooksite ( Figure 10). In rastsvetaevite (Figure 11), labyrinthite and a centrosymmetric analogue of labyrinthite (Samples 21, 20 and 23 in Table 4, respectively) M2 Na-dominant modules alternate with eudialyte. The alternation of modules with different populations at the M2 site is one of the main causes of the unit-cell doubling in these minerals.  (Table 4) [32].
M2 Na-EGMs belong to three structure types: eudialyte (with disordered population of the M1 octahedra, space groups R3m or R-3m), raslakite (with ordering of Ca and smaller cations, Fe 2+ in raslakite and Mn 2+ in sergevanite; space group R3) and alluaivite (EGMs with doubled c parameter including alluaivite, dualite, rastsvetaevite and labyrinthite). M2 Na-EGMs 1, 3 and 7 in Table 4 belong to the eudialyte structure type and are Fe-deficient, with a strong predominance of Na over Fe at M2. Consequently, these samples can be considered as representatives of a potentially new mineral species.
In the structure of the Mn-rich alluaivite-type Sample 22 (Table 4), M2 Na-dominant modules alternate with kentbrooksite ( Figure 10). In rastsvetaevite (Figure 11), labyrinthite and a centrosymmetric analogue of labyrinthite (Samples 21, 20 and 23 in Table 4, respectively) M2 Na-dominant modules alternate with eudialyte. The alternation of modules with different populations at the M2 site is one of the main causes of the unit-cell doubling in these minerals.   (Table 4) [51].
Author Contributions: R.K.R., N.V.C. and I.V.P. wrote the paper. N.V.C. obtained and interpreted the IR spectra. K.V.V. obtained chemical data. R.K.R. carried out the crystal-chemical analysis. I.V.P. and C.S. provided Samples 1 and 2, respectively. All authors have read and agreed to the published version of the manuscript.
Funding: This work was supported by the Ministry of Science and Higher Education within the State assignment FSRC «Crystallography and Photonics» RAS and state task, state registration number Figure 11. Alternation of Na-and Fe-centered squares in rastsvetaevite [49,50].