Who Is Who in the Eudialyte Group: A New Algorithm for the Express Allocation of a Mineral Name Based on the Chemical Composition

: Eudialyte-group minerals (EGMs) are Na-Ca zirconosilicates typical for peralkaline plutonic rocks. In the zeolite-like crystal structure of these minerals, there are many sites of different volumes and conﬁgurations, and therefore EGMs can include up to one-third of the periodic table. Although there are preferred sites for many elements in the crystal structure of eudialyte-group minerals, the same element can appear in several sites. In addition, many sites may be partially or fully vacant. Currently, 30 mineral species are established in the eudialyte group. However, this diversity is, in fact, limited to holotype specimens. To name any mineral from the eudialyte group, you need to solve its crystal structure and compare it with holotypes. Meanwhile, the composition (and, therefore, the name) of any mineral of the eudialyte group is an excellent indicator of the composition of the mineral-forming media, which is very important to petrological and mineralogical studies. In this article, we propose a diagnostic scheme for minerals of the eudialyte group, based only on the chemical composition. The scheme includes ﬁve consecutive steps, each of which evaluates the content of a species-forming element (or the sum of such elements). This scheme can be supplemented by new members without changing its hierarchical structure.

The eudialyte group combines 30 mineral species and a wide range of their varieties have been described. The crystal chemical formula of EGMs (derived from the IMA approved formula [2]) can be written as (Z = 3): {N (1) (4) sites are located at the centers of the (Si9O27) rings and are predominantly occupied by Si, Nb, W, and some other components or can be partly vacant. In addition, the M(2) site is located at M(2)O4Øn-polyhedra (n = 0-2) between the octahedral six-membered rings. The M(2-4) sites form microregions of split "subsites" with close distance to each other. These "subsites" can differ by their chemical composition and/or The M(3) and M(4) sites are located at the centers of the (Si 9 O 27 ) rings and are predominantly occupied by Si, Nb, W, and some other components or can be partly vacant. In addition, the M(2) site is located at M(2)O 4 Ø n -polyhedra (n = 0-2) between the octahedral six-membered rings. The M(2-4) sites form microregions of split "subsites" with close distance to each other. These "subsites" can differ by their chemical composition and/or coordinational environment [6]. The large cavities of the zeolite-like framework are filled by extraframework cations and water molecules located at N(1)-N(5) sites.
The principles of nomenclature of the eudialyte-group minerals have been developed by the Eudialyte Nomenclature Subcommittee established by the Commission on New Minerals and Mineral Names of the International Mineralogical Association [2]. The following nomenclature schemes have been tested: (1) Linnean biological principle; (2) Hierarchical system with root names modified by using the modifiers and Levinson suffixes; (3) A unique-name system using the modifiers.
Conventional unique names with a maximum of one cation prefix are recommended for the eudialyte-group minerals, and this prefix should refer to the M(2) site. As in other groups of minerals, a new mineral in the eudialyte group is considered to be one in which at least one structural position is occupied by a different chemical element than in other minerals with a similar structure. Empirical and CNMNC formulas of the IMA-approved members of the eudialyte group are presented in Table 1, and site occupancies are shown in Table 2.    RREGMs are widely used in petrological studies. Together with other Na-Ca-HFSE minerals (i.e., rinkite, wöhlerite, aenigmatite, astrophyllite, catapleiite, etc.) they are considered as mineralogical markers of agpaitic rocks [33] which attract economic interest as the most promising sources for future high-field-strength elements (HFSE) and rare earth elements (REE) supply [34,35]. Moreover, the highly variable composition of EGMs may be used to study the compositional and/or physical-chemical changes during the evolution of magmatic and hydrothermal systems [36][37][38][39].
In this case, because of the great economic, petrological, and mineralogical significance of the EGMs, an express diagnostic based on microprobe data is especially important. However, the large number of framework and extraframework sites in the crystal structure (which can be partial or completely vacant), the different types of cation distributions, and the presence and predominance of the same element at one or more sites make it difficult to give a name to a sample of EGMs based only on the chemical composition (without additional single-crystal X-ray diffraction analysis, IR-and Mössbauer spectroscopy). Originally. a possible way to determine the mineral species based on the empirical formula was proposed by Johnsen and Grice [1]. Pfaff with coauthors [40] presented an extended and improved scheme for site assignment using IMA-approved end-members also based on microprobe analyses (however, the different valence states of Fe and Mn and undetermined H 2 O-contents were ignored in these studies).
Later, Rastsvetaeva and Chukanov [3] proposed a hierarchical crystal chemical scheme for the classification of EGMs (without formal approval by the CNMNC IMA) which contains the following features steps: 1.
Cation ordering in octahedral six-membered [M(1) 6  Based on this classification scheme and taking into account the data on the site occupancy in the crystal structures of different EGMs (Table 2), we propose a new algorithm that makes it possible to determine minerals based on chemical data only without a direct site assignment procedure. Our diagnostic scheme consists of the following steps:

Methods
The diagnostic scheme has been developed in accordance with the principles and rules of the Commission on New Minerals and Mineral Names of the International Mineralogical Association. The list of eudialyte-group minerals was taken from IMA list of minerals 2021 (http://cnmnc.main.jp/imalist.htm accessed on 20 November 2021).

Diagnostic Scheme of EGMs
The proposed diagnostic scheme is based on the values of the formula coefficients of the elements, which must be normalized on Si+Al+Ti+Zr+Hf+Nb+Ta+W = 29 [1]. After that, the apfu values of species-forming elements are considered step-by-step.

Framework Cations: Zirconium or Titanium in Z Site (Step 1)
In all "12-layer" minerals, as well as "24-layer" rastsvetaevite and labyrintite, ZO 6 octahedra are occupied by zirconium and there are no other structural sites in which zirconium dominates. In the crystal structure of "24-layer" dualite, a half of the zirconium is replaced by titanium, while in the "24-layer" alluaivite, titanium fully occupies the ZO 6 octahedra. To establish the corresponding values of apfu for Zr and Ti at Z site, the following case should be considered: (1) Zirconium fully occupies Z site; (2) Titanium fully occupies Z site; (3) Half of zirconium is replaced by titanium.
Let us assume that Z = Zr 3 Ti 3 in dualite (=Zr 1.5 Ti 1.5 in comparison with "12-layer"), Z = Ti 6 in alluaivite (=Ti 3 in comparison with "12-layer"), and Z = Zr 3 in other minerals (as well as in "24-layer" rastsvetaevite and labyrintite). In accordance with IMA-CNMNC dominant-constituent rule [41], the content of Zr in Z site should be: is 0.75 < Zr < 2.25 apfu in dualite; Zr < 0.75 apfu in alluaivite; Zr > 2.25 apfu in other minerals. Thus, at the first step, all members of the eudialyte group are divided into zirconium-titanium eudialytes (represented only by "24-layer" dualite and alluaivite), and zirconium eudialytes (all "12-layer" minerals and "24-layer" rastsvetaevite and labyrintite). It should also be noted that in the holotype samples of kentbrooksite and ikranite, the M(1) site is not fully occupied by calcium, but the corresponding split of this site (due to the symmetry reducing like in oneillite, raslakite, and voronkovite) has not been observed. In holotype kentbrooksite, the composition of the M(1) site is (Ca 0.545 Mn 0.297 REE 0.103 Na 0.05 ) or (Ca 3.27 Mn 1.78 REE 0.62 Na 0.33 ) Σ6 for the whole [M(1) 6 O 24 ] ring). The IMA-formula of kentbrooksite is approved without specification of the amount of calcium, therefore, kentbrooksite should be attributed to the Ca-rich zirconium eudialytes. The ikranite holotype sample also contains a low amount of calcium without split of the M(1) site due to symmetry reducing. Ikranite will be attributed to Ca-poor zirconium eudialytes.
For T + T members, the following conditions are required: Nb ≤ 0.5 apfu 3. W ≤ 0.5 apfu For T + M members, the following condition is required: 24.5 < Si ≤ 25.5 apfu.
Minerals T + M with a predominance of niobium must additionally meet the condition Nb > 0.5 ≥ W. Tungsten is the species-forming element if the following conditions are met: 24.5 < Si ≤ 25.5; W > 0.5 ≥ Nb. It should also be noted that in the holotype samples of kentbrooksite and ikranite, the M(1) site is not fully occupied by calcium, but the corresponding split of this site (due to the symmetry reducing like in oneillite, raslakite, and voronkovite) has not been observed. In holotype kentbrooksite, the composition of the M(1) site is (Ca0.545Mn0.297REE0.103Na0.05) or (Ca3.27Mn1.78REE0.62Na0.33)Σ6 for the whole [M(1)6O24] ring). The IMA-formula of kentbrooksite is approved without specification of the amount of calcium, therefore, kentbrooksite should be attributed to the Ca-rich zirconium eudialytes. The ikranite holotype sample also contains a low amount of calcium without split of the M(1) site due to symmetry reducing. Ikranite will be attributed to Ca-poor zirconium eudialytes.

Framework Cations: Occupation of the M(3) and M(4) Sites (Step 3)
The  It should be noted that the normalization Si + Al + Ti + Zr + Hf + Nb + Ta + W = 29 implies complete filling of the positions Z 3 M(3)M(4)Si 24 [1]. However, in the case of the presence of vacancies in either the M(3) or the M(4) sites, such a calculation may lead to unreliable results.
The presence of vacancies can only be accurately established using additional methods, for example, spectroscopic ones. In the IR spectra of EGMs with additional SiO 4 tetrahedra located at the centers of nine-membered rings, there are bands in the range 905-940 cm −1 . Bands in the range 676-689 cm −1 indicate additional NbO 6 and WO 6 octahedra at the centers of the nine-membered rings. Figure 3 shows for comparison the IR spectra of holotype samples of manganoeudialyte, oneillite, mogovidite, and ikranite. Obviously, IR spectroscopy data increase the accuracy of diagnostics of EGMs.
Let us consider different options for calculating the formula for holotype samples of mogovidite (vacancy in M(3) site) and ikranite (vacancies in M(3) and M(4) sites) ( Table 3).
As can be seen from Table 3 It should be noted that the normalization Si + Al + Ti + Zr + Hf + Nb + Ta + W = 29 implies complete filling of the positions Z3M(3)M(4)Si24 [1]. However, in the case of the presence of vacancies in either the M(3) or the M(4) sites, such a calculation may lead to unreliable results.
The presence of vacancies can only be accurately established using additional methods, for example, spectroscopic ones. In the IR spectra of EGMs with additional SiO4 tetrahedra located at the centers of nine-membered rings, there are bands in the range 905-940 cm −1 . Bands in the range 676-689 cm −1 indicate additional NbO6 and WO6 octahedra at the centers of the nine-membered rings. Figure 3 shows for comparison the IR spectra of holotype samples of manganoeudialyte, oneillite, mogovidite, and ikranite. Obviously, IR spectroscopy data increase the accuracy of diagnostics of EGMs. Figure 3. IR spectra of holotype samples of manganoeudialyte [25] (a), oneillite [27] (b), mogovidite [18] (c), and ikranite [19] (d). The spectra of manganоeudialite, oneillite, and mogovidite contain bands corresponding to additional SiO4 tetrahedra located at the centers of nine-membered rings (933, 925, 928 cm −1 , respectively).     EGMs can be enriched by calcium (Ca > 6 apfu) and in addition to M(1) site the excess of Ca can occupy the extraframework N(3) and N(4) sites. The excess calcium ( N Ca = Total Ca − 6 apfu) will then be considered together with the elements assigned the N sites: Sr, REE, and K. In feklichevite, golyshevite, and mogovidite, N Ca > 1.5 apfu, since calcium in these minerals not only fills the six-membered [M(1) 6 O 24 ] rings, but also predominates in N(3) site (feklichevite, golyshevite) or N(3) and N(4) sites (mogovidite).
Schematically, variants for filling positions in the structure of EGMs with iron and/or manganese are shown in Figure 4.  For T + M and T + T Ca-poor eudialytes, the sequence of calculations is as follows: 1. An estimate of the sum Ca + Mn + Fe, i.e., the total content of cations in the M(1a), For T + M and T + T Ca-poor eudialytes, the sequence of calculations is as follows: 1.
An estimate of the sum Ca + Mn + Fe, i.e., the total content of cations in the M(1a), M(1b), and M(2) sites. If only Ca, Mn, or Fe prevail in the listed sites, then the sum will be from 7.5 to 10.5 apfu. If the listed positions contain other species-forming elements (for example, sodium in the M(2) site in raslakite and sergevanite), then the Ca + Mn + Fe sum will be in the range from 7.5 to 4.5 apfu.

2.
Assessment of the calcium content. If calcium dominates in one of the positions, for example, M(1a), then the condition Ca > 1.5 apfu must be satisfied. In voronkovite, calcium is not a species-forming element and in this mineral Ca < 1.5 apfu.

Extraframework Cations (N Sites)
Further separation of EGMs should be performed in accordance with the filling of N sites, namely, according to values of N Na, N Ca, K, Sr, N REE apfu. If potassium predominates in one of the N sites (for example, andrianovite), the conditions N Na > 10.5; K > 1.5; N Ca < 1.5; N REE < 1.5; Sr < 1.5 must be satisfied simultaneously. If strontium predominates, as in odikhinchaite, then the conditions N Na > 7.5; K < 1.5; N Ca < 1.5; N REE < 1.5; Sr > 1.5 must be met. At this step, in some subgroups, it is possible to select series.

Synthesizing the Diagnostic Scheme
The general diagnostic scheme of minerals of the eudialyte group minerals is shown in Table 4. It can be supplemented by new members without changing its hierarchical structure. This scheme does not require writing the complete empirical formula of the mineral, but uses some rules for writing it, for example, the sequence of filling the M(1) position with different elements when the calcium content is below 6 pfu. It is important to note that many positions in the crystal structure of EGMs (for example, M3 and M4) are filled statistically and therefore an empirical formula can only be obtained by solving the structure of the mineral. The approach we propose makes it possible, in conditions of limited data (only on chemical composition), to navigate in the virtually infinite variety of minerals of the eudialyte group.

Conclusions
We propose a diagnostic scheme for the eudialyte-group minerals based on their chemical composition (and, in four cases, by using IR spectroscopy, for detection manganoeudialyte, oneillite, mogovidite and ikranite). The scheme includes five consecutive steps, each of which evaluates the content of a species-forming element (or the sum of such elements). So, it is possible name any eudialyte-group mineral sample without applying a time-consuming crystallographic investigation.

Conflicts of Interest:
The authors declare no conflict of interest.