Further on the Choice of Space Group for Scapolite Group Members and Genetic Considerations about the Si-Al Ordering in Their Framework Construction

Abstract

This paper poses a major question regarding the choice of space group for scapolite mineral group members. An artificial boundary is typically drawn between space groups I4/m and P4₂/n when solving the structures of scapolites within the marialite–meionite series. The authors debate if solving the crystal structure in lower symmetries is justified. The choice of space group here is attributed to Si-Al ordering of the framework, and it is shown that the interstitial framework cations and anions have an accompanying role in that decision. Some answers on the ranges and limits of distribution of space groups of scapolite members in the marialite–meionite series, and the manifestations of violation of the Lowenstein rule or the so-called aluminum avoidance rule are presented. Modern physical methods (SEM-EDS and SXDA) are employed in the study to properly analyze the solid solution series in detail. New crystal–chemical data are reported for scapolite samples from different localities. An analysis was made for the types of possible Al-O-Al bonds that can occur in the structures at different Al:Si ratios and their influence on Al-Si ordering. Finally, genetic considerations about Al-Si ordering in the framework construction during the mineral formation processes are proposed.

1. Introduction

Recently, results of crystal–chemical studies of scapolites from two Bulgarian localities—Samurski dol, Chepelare region, Central Rhodopes and Urdini lakes, Northwestern Rila—were published [1,2]. Their goal was to use modern and local analytical methods (Single-crystal X-ray diffraction analysis (SXDA), Scanning Electron Microscopy (SEM), and Energy-Dispersive Spectroscopy (EDS)) to make a more precise determination of the meionite content (Me) than those previously made for samples from these localities. A preliminary literature review on the results of previous investigations on representatives of the scapolite group has testified that these are compounds with well-pronounced crystal–chemical complexity and that some questions related to their study have not yet found an unequivocal answer. Among the important questions in this regard are those related to the elucidation of possible isomorphic substitutions in scapolite solid solutions, the relationship between chemical composition and crystal structure characteristics (choice of space group, presence or absence of phase transitions, and antiphase domains), and classification of the members of this group. Over the years, when studying the structure of scapolites of various compositions, several tetragonal space groups were established, as two of them are considered the most probable—I4/m and P4₂/n [3,4,5,6]. For scapolite members close to the ideal compositions of marialite (Na₄Al₃Si₉O₂₄Cl) and meionite (Ca₄Al₆Si₆O₂₄(CO₃)), the more highly symmetric space group of I4/m is characteristic, while for intermediate compositions, the space group P4₂/n is preferred.

The present study attempts to shed more light on the issues related to the choice of space group for scapolite minerals. Questions posed in this work are as follows: (i) where is it correct to draw a boundary between scapolites falling compositionally within the marialite–meionite series whose structures should be solved in space group I4/m and those ones with P4₂/n space group structures? (ii) Is the use of space groups of lower symmetries justified in solving the crystal structures of these compounds? A supported thesis is that these issues are closely related to the Si-Al ordering in the framework construction, and the interstitial framework cations and anion species play and have a rather accompanying role. Genetic considerations for the mechanism of Si-Al ordering in scapolite structures during the mineralization process are presented. Data from structural X-ray diffraction experiments reported previously by other authors as well as data from our own structural investigations are used in this study.

2. Materials and Methods

2.1. Scapolites from Urdini Lakes (Northwestern Rila, Bulgaria), Samurski Dol (Chepelare Region, Central Rhodopes, Bulgaria), Sluydyanka (Urals, Russia), and Madagascar (Unknown Locality)

Scapolite samples from four localities were studied mainly by single crystal investigations. Details on the crystal structures of the scapolites from Bulgaria are given elsewhere [1,2].

The specimen from the Sludyanka deposit was taken from a museum exhibit currently preserved in the National Museum of Natural History at the Bulgarian Academy of Sciences, Sofia under number 3123, provided with the courtesy of museum associate Iliya Dimitrov.

The specimen from Madagascar was taken from the private collection of Dimitar Stoyanov. This is a pale-yellow transparent crystal of gem quality, 2.4 × 1.0 cm in size; however, no other information for its exact locality is available.

2.2. Scanning Electron Microscopy (SEM) and Energy-Dispersive Spectroscopy (EDS)

SEM and EDS analyses were performed on polished, carbon-coated sections of scapolite-containing samples using an X-MaxN 50 mm² EDS detector by Oxford Instruments (20 kV accelerating voltage) mounted on a Tescan Vega 3 XMU electron microscope at the Research and Development Department of Aurubis Bulgaria AD, Pirdop. Aztec Energy software was used for data collection, integration, and corrections using integrated factory standards. The chemical formulas of the studied scapolites were calculated based on 13 analyses per each one of the studied samples, with the exception of that of the Madagascar locality, under the following assumptions: (i) Al + Si = 12 apfu (Z = 2); (ii) CO₃ = 1–Cl–SO₄; conversion factors S → SO₄(3), Cl → Cl(1); (iii) negligible amounts of detected di- and monovalent interstitial framework cations (IFC) together with possible vacancies are treated as a monovalent fictive cation M⁺; (iv) Me% = 100 × Ca/4.

2.3. Single-Crystal X-ray Diffraction Analysis (SXDA)

Single crystals with appropriate sizes from the studied compounds were mounted on a glass capillary without grinding and analyzed by a single-crystal diffraction method. The data collection was performed on Bruker D8 Venture diffractometer. The determination of unit cell parameters, data integration, and scaling and absorption corrections were performed by APEX4 program package [7]. The crystal structures were solved by direct methods using the ShelxS program and refined with the ShelxL program [8] using full-matrix least-squares method of F². All atom positions were assigned successfully from the produced Fourier electron density map. The tetrahedral positions were assumed to be mixed Si/Al with occupancy parameters of Al and Si fixed accordingly to the deviations from the standard Si/Al-O distances and then compared to those obtained by EDS analyses. Only Ca and Na were refined, and the overall occupancies of these IFCs sharing a common crystallographic position were fixed to 98% for all used structural models to better match the chemical analysis data. The occupancy parameters of the anion groups in the structure were refined with a constraint to maintain 100% occupancy of the common anion position. Chlorine was omitted in the refinement of the Urdini Lakes sample due to its very low content. The differences between the theoretical and analytical structural factors were first conducted with isotropic temperature displacement parameters and then for the anisotropic refinement including all atoms. The obtained structural models are optimal with respect to the reliability factors and the chemical analysis data. Most important experimental and structure refinement parameters are given in

Table 1. Crystal data and structure refinement parameters for the scapolites from Madagascar, Urdini Lakes, Samurski Dol, and Sluydyanka localities.

	Space Group	Madagascar, Unknown Locality		Urdini Lakes, Northwestern Rila, Bulgaria
Data		P 42/n	I 4/m	P 42/n	I 4/m
		1	2	3	4
Chemical formula/Z		Ca0.69Na1.27Al1.88Si4.12O12.57 C0.18Cl0.29S0.02/4	Ca0.62Na1.38Al1.92Si4.08O12.55 C0.18Cl0.31 S0.01/4	Ca1.36Na0.59Al2.39Si3.629O13.58 C0.42S0.08/4	Ca1.38Na0.58Al2.32Si3.68O13.58 C0.42S0.08/4
Formula weight		437.78	437.20	459.18	459.46
a,b/Å		12.0600(4)	12.0595(5)	12.1350(7)	12.1293(9)
c/Å		7.5779(4)	7.5781(4)	7.5560(5)	7.5552(7)
Volume/Å3		1102.16(9)	1102.09(11)	1112.68(15)	1111.52(19)
ρcalc (g/cm3)		2.638	2.635	2.741	2.746
Crystal size/mm3		0.025 × 0.02 × 0.02	0.025 × 0.02 × 0.02	0.15 × 0.1 × 0.1	0.15 × 0.1 × 0.1
Temperature/K		273.15 K	273.15 K	273.15 K	273.15 K
Radiation, λ [Å]		0.71073	0.71073	0.71073	0.71073
2Θ range for data collection/°		4.776 to 51.366	4.76 to 52.6	4.74 to 56.528	4.75 to 56.592
Reflections collected/unique		9812/1057[R(int) = 0.0810]	4908/610[R(int) = 0.0591]	13,464/1372[R(int) = 0.1130]	7245/745[R(int) = 0.0602]
Data/restraints/para-meters		1057/0/99	610/0/59	1372/0/106	745/0/66
Goodness-of-fit on F2		1.083	1.103	1.044	1.074
Final R indexes [I ≥ 2σ (I)]		R1 = 0.0449, wR2 = 0.09	R1 = 0.0362, wR2 = 0.0709	R1 = 0.0461, wR2 = 0.0858	R1 = 0.0319, wR2 = 0.0728
Final R indexes [all data]		R1 = 0.0726, wR2 = 0.1020	R1 = 0.0435, wR2 = 0.0733	R1 = 0.1002, wR2 = 0.1053	R1 = 0.0430, wR2 = 0.0787
Largest diff. peak/hole/e Å−3		0.52/−0.37	0.447/−0.445	0.69/−0.55	0.93/−0.46
	Space Group	Samurski dol Central Rhodopes, Bulgaria		Sluydyanka (Urals, Russia)
Data		P 42/n	I 4/m	P 42/n	I 4/m
		5	6	7	8
Chemical formula/Z		Ca1.44Na0.52Al2.49Si3.51O13.47 C0.49Cl0.010S0.002/4	Ca1.43Na0.53Al2.41Si3.59O13.48 C0.49Cl0.007 S0.002/4	Ca1.63Na0.33Al2.62Si3.38O13.63 C0.36Cl0.007 S0.129/4	Ca1.63Na0.33Al2.61Si3.39O13.63 C0.36Cl0.008 S0.127/4
Formula weight		457.24	457.17	465.48	465.31
a,b/Å		12.1450(2)	12.1445(3))	12.1604(2)	12.1613(2)
c/Å		7.5572(2)	7.5572(2)	7.5689(2)	7.5688(2)
Volume/Å3		1114.69(4))	1114.60(5)	1119.25(4)	1119.40(4)
ρcalc (g/cm3)		2.725	2.724	2.762	2.761
Crystal size/mm3		0.02 × 0.02 × 0.01	0.02 × 0.02 × 0.01	0.02 × 0.01 × 0.01	0.02 × 0.01 × 0.01
Temperature/K		273.15 K	273.15 K	273.15 K	273.15 K
Radiation, λ [Å]		0.71073	0.71073	0.71073	0.71073
2Θ range for data collection/°		4.74 to 52.6	4.74 to 52.6	4.74 to 52.64	4.74 to 56.64
Reflections collected/unique		14573/1380[R(int) = 0.0354]	6533/605[R(int) = 0.0247]	14690/1398[R(int) = 0.0393]	7344/752[R(int) = 0.0342]
Data/restraints/para-meters		1380/0/103	605/0/63	1398/0/111	752/0/67
Goodness-of-fit on F2		1.03	1.055	1.035	1.062
Final R indexes [I ≥ 2σ (I)]		R1 = 0.0380, wR2 = 0.0836	R1 = 0.0280, wR2 = 0.0651	R1 = 0.0331, wR2 = 0.852	R1 = 0.0261, wR2 = 0.0653
Final R indexes [all data]		R1 = 0.0511, wR2 = 0.0914	R1 = 0.0288, wR2 = 0.0660	R1 = 0.0499, wR2 = 0.0979	R1 = 0.0284, wR2 = 0.0671
Largest diff. peak/hole/e Å−3		1.08/−0.67	1.08/−0.51	1.36/−0.63	1.24/−0.49

.

Information about the structural data is available in the Cambridge Structural Database: CSD 2354350, 2354351, 2354352, 2354353, 2354354, 2354355, 2354356, and 2354357 for RV34.4 (I4/m), RV34.4 (P4₂/n), RV72 (I4/m), RV70 (P4₂/n), RV70 (I4/m), RV82 (I4/m), RV72 (P4₂/n), and RV82 (P4₂/n), respectively. The following Supporting Information can be found as Supplementary Materials at the end of this article: Madagascar_I4m.cif, Madagascar_P42n.cif, Samurski dol_I4m.cif, Samurski dol_P42n.cif, Sluydyanka_I4m.cif, Sluydyanka_P42n.cif, Urdini Lakes_I4m.cif, Urdini Lakes_P42n.cif.

3. Results

Information on the geological setting of the two Bulgarian localities, wherefrom the scapolites for the present study were selected, are given elsewhere [1,2]. Images of scapolite from the Sluydyanka deposit are presented in Figure 1.

The chemical composition of unaltered scapolite from this locality as determined by EDS; its crystal–chemical formula is (Ca_3.22–3.30Na_0.67–0.71K_0.03–0.04Fe_{0.005–0.012} Mn_0.00–0.008Mg_0.00–0.03)_3.98–4.10(Al_5.20–5.25Si_6.50–6.80)₁₂O₂₄(0.66–0.68CO₃,0.31–0.32SO₄,0.01–0.02Cl). The variations in the extra framework cations contents imply the following suggestions: (i) part of the iron form of Fe³⁺ may enter the framework in the tetrahedrally coordinated cation positions where the sum of IFCs exceeds 4 apfu; (ii) there are vacancies in this position in cases when the IFCs sum falls below 4 apfu. The overall effect of the very low content and not-always-constant presence of the minor IFCs, as well as the possible presence of vacancies in these positions, can be presented as a fictive monovalent cation M⁺ whose occupancy does not exceed 0.05 apfu. Thus, the average (from 13 analyses) crystal–chemical formula can be presented as (Ca_3.26Na_0.70,M_0.04)(Al_5.22Si_6.78O₂₄(0.67CO₃, 0.31SO₄, 0.02Cl), where M ⁺ =K⁺, Fe²⁺, Mn²⁺, Mg²⁺, and □; Ca/Na = 4.66; Me% = 81.5. This is also the reason why only Ca²⁺ and Na⁺ have been refined in the extra framework sites of all used structural models during the single-crystal X-ray experiments and their overall occupancy has been fixed to 98%.

Single-crystal X-ray diffraction investigations were performed for the sample applying the abovementioned methodic. The contents of interstitial framework cations (calcium and sodium) were determined solely by the single-crystal experiment and were not compared with other results, e.g., from chemical analyses. Thus, its meionite component has been defined as Me34.4.

Attempts to solve some of the structures presented here in lower symmetry were successful in terms of the obtained structure refinement parameters [2] but proved unreliable in terms of the methodological platform adopted in this work (see Section 5.2).

4. Comparative Study of Scapolites from the Marialite–Meionite Series

4.1. Previous Investigations

4.1.1. General Notes

Minerals of the scapolite group are common rock-forming aluminosilicates that occur in a wide variety of metamorphic and altered igneous rocks. Their wide distribution in metamorphic terrains, as well as high stability over a wide range of pressures and temperatures, turn scapolites into potential geothermometers and geobarometers, and provides the opportunity to obtain information on the Eh (from Fe valence) and pH (from anion speciation) of their formation [9]. Scapolites store volatiles in the lower crust and upper mantle and are indicators of the activities of the volatile components [10]. The volatile components in scapolite indicate that they may play a natural role in the capture and storage of greenhouse gases. It is also of general interest to note that some scapolite representatives exhibit gem-quality features.

The general formula of this group of minerals is M₄[T₁₂O₂₄]A. The M position is represented predominantly by Ca²⁺ and Na⁺ but may also contain K⁺, Sr²⁺, Ba²⁺, and Fe²⁺. The T position is occupied by Si⁴⁺ and Al³⁺; Fe³⁺ may also be present there; and the A position stands for Cl⁻, (CO₃)²⁻, (SO₄)²⁻, and rarely F⁻. Quite often, H₂O is also detected in scapolite analyses. As established by spectroscopic studies, hydrogen can be present in the structure in various forms (H₂O, HCO³⁻, HC1, OH⁻, etc.) [11]. In the second half of the 20th century, it was widely accepted that natural scapolites form a solid-solution series between the two theoretical end-members, Na₄Al₃Si₉O₂₄Cl (marialite) and Ca₄A1₆Si₆O₂₄CO₃ (meionite). In 1998, a third end-member of this group of minerals was approved under the name silvialite (Ca₄Al₆Si₆O₂₄SO₄) [12].

Three main forms of isomorphous substitution were recognized for the scapolite-group minerals: Si⁴⁺ for Al³⁺ in the T site, Na⁺ for Ca²⁺ in the M site, and Cl⁻ for CO₃^2– or SO₄^2– in the A site. These substitutions are interrelated in a complex way, as expressed by the nonlinear variation in chemical composition, variation in Al–Si order, discontinuities of composition and structure parameters, and changes in space group across the scapolite solid solutions established so far [6,10,13] and the references therein.

Over the years, the level and quality of research, as well as the specific results obtained by various researchers, have had a significant impact on the classification schemes through which they describe the representatives of the scapolites. Inevitably, these schemes reflect ambiguities on the contentious topics listed in the Introduction part [6,13,14,15,16,17,18]. One of the earliest divisions concerning the marialite–meionite series is based on the introduction of the index of chemical composition, presenting the meionite (Me) content in at. %. It has been defined as 100(Ca + Sr + Fe + Mn + Mg)/(Na + K + Ca + Sr + Fe + Mn + Mg) or as its short form—Me% = 100 × Ca/(Na + Ca). It was first introduced by Shaw in 1960 [14] but is still in active use by researchers of the group.

4.1.2. Framework Topology

The scapolite framework can be described as consisting of two types of four-membered rings (4MRs), each of which is made up of AlO₄ and SiO₄ tetrahedra, together designated also as T [4,19,20,21]. The type 1 ring consists of tetrahedra with vertices that do not belong to tetrahedron bases forming the ring point in the same direction. These rings are designated as T1 in Figure 2. Their equipoint rank is 8 when the structure is described in both tetragonal space groups. The type 2 ring consists of tetrahedra that point alternately up and down, designated as T2 (in SG I4/m; equipoint rank 16). Symmetry lowering leads to splitting of T2 into two tetrahedra designated as T2 and T3 (in SG P4₂/n; each with an equipoint rank of 8) (Figure 2). Both type rings outline continuous oval-shaped channels that run parallel to the c axis. These contain the interstitial framework cations (IFCs), predominantly Ca²⁺, Na⁺, and K⁺. In the same direction, both type rings also form large cages that contain clusters composed of the IFCs and the interstitial framework anions (IFAs), presented predominantly by Cl⁻, CO₃^2–, and SO₄^2– species (Figure 2 and Figure 3). Additionally, the two types of rings are connected in a way to form five-membered rings, each composed of one T1 (apple green) and four T2 (muted purple) (in SG I4/m) or composed of one T1 (apple green), two T2 (red), and two T3 (blue) tetrahedra in SG P4₂/n. Figure 3 presents only the P4₂/n case.

4.1.3. Determination of Framework Aluminum from X-ray Data

Since the scattering factors of Si (Z = 14) and Al (Z = 13) are not very different, the XRD method cannot be used directly to refine the occupancies of T-sites. Instead, the ionic radii difference of tetrahedrally coordinated aluminum and silicon is used, which directly affects the <T–O> bond-lengths and, hence, the Si and Al occupancies to each tetrahedral site are evaluated and assigned. In 1963, Smith and Bailey proposed corrected values of earlier examined measured (Si,A1)-O distances and suggested standard values for estimating the substitution of aluminum and silicon atoms in tetrahedra [22]. For framework compounds, these are Si-O = 1.61 Å and Al-O = 1.75 Å, correspondingly. In 1965, Papike and Zoltan reported their own data obtained for the crystal structure of marialite scapolite—Si-O = 1.608 Å and Al-O = 1.732 Å [19]. Later, all these data or curves prepared on them were used by other researchers to determine T-site occupancies in scapolite structures [20,23,24]. Other authors used Si-O and Al-O distances values of 1.6100 and 1.7435 Å, respectively, as observed in a structure related to the scapolite series compound—the mineral sodalite Na₈(Al₆Si₆O₂₄)Cl₂ [25,26,27]. Sokolova and Hawthorne, based on single crystal data, collected a representative set of T-site distances for scapolite samples; these were selected in such a way as to cover the widest possible compositional range for this group’s members [6]. These authors established that the grand <T–O> distance is a linear function of Al content in apfu and further divided this trend into three parts, corresponding to the different space-group symmetries found by them within the studied range. They used linear regression to develop equations for prediction of Al site occupancies in each particular group.

Despite the subtle differences in reference data and approaches used, application of such geometrical relations proved to be an efficient tool for evaluation and assignment of Al in the T-sites of the studied structures, and the obtained results are often dully supported by electron probe microanalysis (EPMA) data. Researchers mostly use these to meet the important question for Al-Si ordering within the scapolite members that is closely related to the aluminum avoidance rule.

4.1.4. Si-Al Ordering in Scapolite Group Members and Its Relations with the Intensity of Peaks Violating the Body-Centered Symmetry (Odd Peaks)

The experimental data received so far clearly give evidence that with the increase in its content, Al first enters the type 2 tetrahedra (T2, T2, and T3 in Figure 2). A plausible explanation for such preference is the proximity of these type 4MRs framework cations to the IFCs in this part of the structure. With further increases in aluminum content in the structure, a change in symmetry from I4/m to P4₂/n occurs, and the T2 site splits into two sites—T2 and T3—with Al slightly to strongly ordered there [6] (Figure 2 and Figure 3). The results show that in the Me52, Al atoms already start to enter T1 sites, because this will decrease the probability of formation of unstable A1-O-A1 linkages in type 2-rings [20] (Figure 2).

NMR investigations of scapolite members of various Me number [28,29,30] indicate an obvious violation of Lowenstein’s rule in almost the entire compositional range of this group apart from those samples of scapolite with 4 apfu Al [30]. Although not seemingly caused by the quantitative ratio of the two framework cations, the presence of single Al–O–Al moieties has been detected within the type 2 four-membered rings and reported for scapolite samples of predominantly marialitic content by Sokolova et al. in 1996 [28].

In 2008, Antao and Hassan published results for the crystal–chemical behavior of two scapolite samples upon thermal treatment up to 900 °C: Me79.6, with structure modeled and refined in space group I4/m [25], and Me32.9—P4₂/n [26]. What is common in both cases is that as the temperature increases, the dimensions (central atom–ligand distance) of the tetrahedra in type 2 4MRs increase, while those ones in type 1 decrease (shrinkage). For the more highly symmetric sample, the authors interpret the high temperature results as follows: “At 900 °C, the T1 site becomes fully ordered with only Si atoms while the T2 site contains Al_0.511Si_0.49 and, therefore, is fully disordered“. The following explanation is given for the Me32.9 sample: “At 902 °C, the T1 site remains fully occupied by Si atoms, whereas the disorder at the T2 and T3 sites is close to being complete”. In addition, the authors noted that, upon cooling, both samples’ <T–O> distances “do not fully revert back to their initial values”.

In 1973, Lin and Burley reported results of X-ray diffraction studies of 10 scapolite samples covering the compositional range between Me20 and Me93 [31,32]. It was concluded that the space group of all the scapolite specimens is P4₂/n. By plotting the ratio r = ∑I_0+k+l=odd/∑I_0+k+l=even, they built an r–Me% curve and first reported reaching the maximum intensity for the weak peaks violating the body-centered symmetry in the region around 37% meionite [31].

In 2011, Antao and Hassan experimentally confirmed the validity of such conclusions and the prediction for complete Si-Al order for the ideal Me37 on the example of the crystal structure of an intermediate scapolite Me36.6 from Lake Clear, Ontario [27]. Based on the average distances of <T1–O> = 1.617(1) Å, <T2–O> = 1.744(1) Å, and <T3–O> = 1.601(1) Å, they concluded that the T1 and T3 sites contain only Si atoms and the T2 site contains only Al atoms, so the Al and Si atoms are completely ordered.

4.1.5. Violations of Löwenstein’s (Lowenstein’s) Rule

Lowenstein’s rule, known also as “aluminum avoidance”, was formulated more than seventy years ago [33]. It states that –Al–O–Al– bond formation in three-dimensional aluminosilicate frameworks is forbidden and that a maximum substitution of 50% of the tetrahedrally coordinated silicon by aluminum is only possible in suchlike compounds, hence restricting the minimum Si/Al ratio to unity. Lowenstein had to build his empirical finding on the rather small set of structural data that was at his disposal at that time. Since then, the enormously increased knowledge on new aluminosilicate structures, both natural and synthetic, and the advances in supercomputing services supporting involvement of quantum mechanical approaches, have allowed more well-founded statements on the validity of Lowenstein’s rule to be made [34,35]. Many exceptions and violations of this rule have been reported, which calls into question, if not its validity as a whole, then at least the value of the minimal limit ratio Si/Al = 1, after which local deformations in the structure are expected to occur. Thus, based on the general idea for coupled substitution, in 2008, Peters et al. [34] attempted a successful synthesis to prepare members of the sodalite family in which the Al:Si ratio is >2.

Some of the representatives of the scapolite group are among the aluminosilicate minerals known to exhibit violation of Lowenstein’s rule. Several researchers of these compounds reported their considerations and explanations on this issue [4,9,21,23,24,28,29,30,31,36,37,38].

4.1.6. The Choice of Space Group and Boundaries of Transitions I4/m↔P4₂/n↔ I4/m

The highest symmetry space group used in crystal structure refinement in the marialite–meionite series is the tetragonal I4/m. Typically, it is applicable to the representatives falling within the compositional ranges in the vicinities of the two end-members. In the middle region, however, additional reflections are observed in the diffraction patterns, which require the use of the primitive P4₂/n of the tetragonal syngony. Drawing boundaries between the representatives of the two space groups, especially those with high calcium content, is still controversial. The range of P4₂/n scapolites, as defined by various authors, may comprise group members as follows: from Me6 to Me93, and even from Me0 to Me100 [31,39]; from Me12.8 to approx. Me66.7 [9,16]; from Me18 to Me90 [5]; from Me21 to Me77 [6] (Figure 4).

Things get further complicated by the registration of antiphase boundaries (APB) and crystal–chemical discontinuities of varying nature and manifestation among the members of the group. Theses about their origin are varied and controversial. Phase transitions and their presence in general in the border areas between I4/m and P4₂/n scapolites are greatly debated. More information on these issues can be found in the following works: [6,10,13,27,39] and the references therein.

4.2. Choice of Scapolites for the Comparative Study

The present study comprises scapolite samples covering as wide a compositional range as possible in the marialite–meionite series, whose crystal structures have been solved in the P4₂/n space group by X-ray diffraction methods. Seventeen specimens have been chosen. They can be divided into three groups, according to the research teams dealing with them, as follows: nine specimens, designated hereinafter as SH were studied by Sokolova and Hawthorne [6]; four pieces, denoted AH, were studied by Antao and Hassan [26,27,39]; and four samples whose structures have been determined and refined in the present work and are denoted as RV.

Table 2. Provenance of scapolite group representatives whose crystal structural data have been processed in this work.

Me%	Sample Code This Work	Sample Code Original Work	Locality	Reference
1	2	3	4	5
6.2	AH6.2	Me6	Badakhshan, Afghanistan	Antao and Hassan, 2011 [39]
26.4	SH26.4	S(7)	Tanzania	Sokolova and Hawthorne, 2008 [6]
28.7	SH28.7	S(8)	Madagascar	Sokolova and Hawthorne, 2008 [6]
32.3	SH32.3	S(9)	Pamir, Tajikistan	Sokolova and Hawthorne, 2008 [6]
32.9	AH32.9	Me32.9	Monmouth Township, Ontario	Antao and Hassan, (2008) [26]
34.4	RV34.4	-	Madagascar, unknown locality	This work
36.6	AH36.6	Me36.6	Lake Clear, Ontario	Antao and Hassan, 2011 [27]
42.0	SH42.0	S(10)	Monte Somma, Italy	Sokolova and Hawthorne, 2008 [6]
45.7	SH45.7	S(11)	Madagascar	Sokolova and Hawthorne, 2008 [6]
57.7	SH57.7	S(12)	Minden, Canada	Sokolova and Hawthorne, 2008 [6]
66.7	SH66.7	S(13)	Pargas, Finland	Sokolova and Hawthorne, 2008 [6]
69.6	SH69.6	S(14)	Bolton, USA	Sokolova and Hawthorne, 2008 [6]
70	RV70	-	Urdini lakes, Bulgaria	This work
72	RV72	-	Samurski dol, Bulgaria	This work
76.9	SH76.9	S(15)	Sluydyanka, Russia	Sokolova and Hawthorne, 2008 [6]
82	RV82	-	Sluydyanka, Russia	This work
92.9	AH92.9	Me93	Mt. Vesuvius, Italy	Antao and Hassan, 2011b [39]

provides data for the final selection of scapolites, outlining which Crystallographic Information Files (CIF) were used for this comparative study.

4.3. Methodological Platform of Research

The starting point in this study is the understandings of Lin and Burley, Antao and Hassan, and to some extent Sherriff et al. [23,24,27,29,31,32], presented in Section 4.1.4, Section 4.1.5 and Section 4.1.6 and summarized and supplemented below as follows:

(i) The use of space group P4₂/n is justified for the entire range of compositions in the marialite–meionite series except for small areas around the two end-members.

(ii) The intensity of weak h + k + l odd reflections violating the body-centered symmetry is primarily proportional to the degree of ordering of Al and Si in the tetrahedra of type 2. It reaches maximum values at compositions around Me37, where the difference in Al occupancy between the two crystallographic sites is greatest and extrapolates almost to zero at the pure end-members. It is precisely in this area that the largest absolute values of the difference between <T2-O> and <T3-O> from type 2 tetrahedra are observed.

(iii) Al-Si ordering in the scapolite structure allows the formation of single Al-O-Al linkages, even in the region of low meionite number compositions. With increasing Al in the composition, the mechanism of Al-Si ordering works in the direction of minimizing the violation of the aluminum avoidance rule to the extent that the formation of longer than single unstable fragments of the type …-Al-O-Al-O-Al-…. is prevented.

An important prerequisite for the selection of space group P4₂/n is the registration in the experimental file of even weak intensities of reflections that violate the body centering of the unit cell of the studied structure. Their values should be meaningful in terms of their sign and magnitude of standard deviations.

With such a platform, the research focus is on Al-Si ordering in the scapolite structure as the main prerequisite for the degree of manifestation of h + k + l odd reflections in terms of their intensity and, therefore, for the correct choice of space group.

4.4. CIF Data Processing

VESTA software ver. 3.3.2 [40] was used for graphic presentations as well as to derive certain important parameters for the subsequent studies. Among them are the average bond lengths of the framework constituent (Al,Si)-tetrahedra. Thus, the absolute values of the difference between <T2-O> and <T3-O> from type 2 4MRs in the crystal structures of the investigated samples have been obtained (Figure 2b). In the graphs and text below, the difference ΔT = ǀ<T2-O> − <T3-O>ǀ is referred to as DELTA for brevity. Furthermore, the facilities of the VESTA software to calculate intensities (I) and structure factors (|F|) for any chosen reflection based on the structural model were utilized. Attention was focused on the (h + k + l = odd) reflections. The following reflections were initially selected from the small-angle region preferably chosen for their relatively high intensities: (111); (201); (221); and (3-11). The crystal structure atoms were divided into three groups as follows: framework atoms (FRA), including Al and Si, and the oxygen atoms of their polyhedral environment; the interstitial framework cations (IFC) presented predominantly by Ca²⁺ and Na⁺, sometimes containing K⁺, Mg²⁺, etc.; the interstitial framework anions (IFA) presented mainly by Cl⁻, CO₃^2–, and SO₄^2– species. The structure factors |F_FRA|, |F_IFC|, and |F_IFA| were calculated (

Table 3. Selected geometrical and crystal structural data for the studied scapolite samples.

Me, %	Sample Code	<T1-O>, Å	<T2-O>, Å	<T3-O>, Å	DELTA	(111)					(201)
						I, rel. int.	ǀFǀ	ǀFFMAǀ	ǀFIFCǀ	ǀFIFAǀ	I, rel	ǀFǀ	ǀFFMAǀ	ǀFIFCǀ	ǀFIFAǀ
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
6.2	AH6.2	1.5996	1.6545	1.6633	0.0088	0.0091	1.17	1.46	2.63	0	0.0694	3.91	2.43	1.48	0
26.4	SH26.4	1.6066	1.7189	1.6265	0.0924	0.0632	3.14	8.28	5.08	0.0548	0.4582	10.20	7.99	2.60	0.3843
28.7	SH28.7	1.6079	1.7261	1.6214	0.1047	0.0784	3.48	9.38	5.86	0.03628	0.6120	11.76	9.06	2.96	0.2635
32.3	SH32.3	1.6091	1.7241	1.6247	0.0994	0.0742	3.41	8.90	5.48	0.0111	0.5395	11.11	8.79	2.73	0.4081
32.9	AH32.9	1.6059	1.7256	1.6117	0.1139	0.1169	4.27	9.40	5.09	0.0428	0.7411	12.98	10.41	2.86	0.2798
34.4	RV34.4	1.6071	1.7316	1.6120	0.1196	0.1641	5.05	11.26	6.16	0.0430	0.7737	13.25	10.60	3.02	0.3646
36.6	AH36.6	1.6172	1.7439	1.6014	0.1425	0.1770	5.22	12.13	5.93	0.9742	0.9335	14.47	12.91	2.98	1.4143
42	SH42.0	1.6133	1.7377	1.6158	0.1219	0.1160	4.29	11.21	6.84	0.0921	0.7412	13.09	10.87	3.29	1.0647
45.7	SH45.7	1.6165	1.7364	1.6176	0.1188	0.0999	3.96	10.83	6.89	0.0187	0.7320	12.94	10.52	3.25	0.8292
57.7	SH57.7	1.6283	1.7310	1.6220	0.1090	0.0654	3.24	9.99	6.51	0.2428	0.5336	11.17	9.78	2.97	1.5794
66.7	SH66.7	1.6348	1.7194	1.6327	0.0867	0.0292	2.18	7.85	5.75	0.0748	0.4107	9.85	7.48	2.56	0.1861
69.6	SH69.6	1.6378	1.7241	1.6295	0.0946	0.0301	2.21	8.42	6.27	0.0410	0.5021	10.87	8.28	2.76	0.1728
70	RV70	1.6358	1.7203	1.6285	0.0918	0.0544	2.98	8.82	5.47	0.3805	0.3750	9.42	8.77	2.42	1.8019
72	RV72	1.6388	1.6957	1.6529	0.0427	0.0091	1.22	4.04	2.85	0.0086	0.1165	5.25	4.14	1.27	0.1728
76.9	SH76.9	1.6431	1.6908	1.6662	0.0246	0.0089	1.21	2.80	1.66	0.0694	0.0303	2.69	2.15	0.74	0.1975
82	RV82	1.6451	1.6904	1.6650	0.0236	0.0036	0.77	2.47	1.65	0.0501	0.0402	3.09	2.53	0.69	0.0982
92.9	AH92.9	1.6615	1.6755	1.6637	0.0118	0.1033	4.09	1.34	5.58	0.1566	0.0251	2.43	1.14	2.45	1.1123
Me, %	Sample code	<T1-O>, Å	<T2-O>, Å	<T3-O>, Å	DELTA	(221)					(3-11)
						I, rel. int	ǀFǀ	ǀFFMAǀ	ǀFIFCǀ	ǀFIFAǀ	I, rel	ǀFǀ	ǀFFMAǀ	ǀFIFCǀ	ǀFIFAǀ
1	2	3	4	5	6	17	18	19	20	21	22	23	24	25	26
6.2	AH6.2	1.5996	1.6545	1.6633	0.0088	0	0.13	1.69	1.82	0	0.0016	0.85	0.07	0.79	0
26.4	SH26.4	1.6066	1.7189	1.6265	0.0924	0.5416	14.26	11.20	2.85	0.2074	0.2592	10.82	11.04	0.70	0.4793
28.7	SH28.7	1.6079	1.7261	1.6214	0.1047	0.6780	15.91	12.57	3.24	0.0951	0.3152	11.90	12.41	0.75	0.2356
32.3	SH32.3	1.6091	1.7241	1.6247	0.0994	0.5651	14.61	11.59	2.98	0.0431	0.3041	11.76	11.81	0.61	0.5634
32.9	AH32.9	1.6059	1.7256	1.6117	0.1139	0.7223	16.47	13.49	2.86	0.1141	0.4290	13.93	14.64	1.01	0.2994
34.4	RV34.4	1.6071	1.7316	1.6120	0.1196	0.8281	17.62	14.19	3.32	0.1153	0.4085	13.58	13.78	0.60	0.4091
36.6	AH36.6	1.6172	1.7439	1.6014	0.1425	1.2012	21.10	15.30	3.11	2.6855	0.5876	16.19	16.61	0.58	0.1674
42	SH42.0	1.6133	1.7377	1.6158	0.1219	0.8271	17.76	13.96	3.54	0.2644	0.4906	15.01	14.20	0.50	1.3112
45.7	SH45.7	1.6165	1.7364	1.6176	0.1188	0.7893	17.27	13.81	3.48	0.0310	0.4756	14.71	13.89	0.37	1.1792
57.7	SH57.7	1.6283	1.7310	1.6220	0.1090	0.6772	16.14	12.28	3.19	0.6771	0.4348	14.20	12.63	0.16	1.7326
66.7	SH66.7	1.6348	1.7194	1.6327	0.0867	0.4370	13.04	10.50	2.75	0.2146	0.2401	10.60	10.23	0.03	0.3967
69.6	SH69.6	1.6378	1.7241	1.6295	0.0946	0.5256	14.27	11.45	2.94	0.1138	0.2776	11.38	11.03	0.04	0.3086
70	RV70	1.6358	1.7203	1.6285	0.0918	0.4916	13.85	10.05	2.72	1.0918	0.3072	12.01	10.33	0.07	1.7872
72	RV72	1.6388	1.6957	1.6529	0.0427	0.1131	6.63	5.25	1.42	0.0210	0.0712	0.57	5.57	0.06	0.2207
76.9	SH76.9	1.6431	1.6908	1.6662	0.0246	0.0228	2.99	2.42	0.77	0.1911	0.0193	3.02	2.58	0.02	0.4206
82	RV82	1.6451	1.6892	1.6656	0.0236	0.0295	3.39	2.38	0.84	0.1770	0.0142	2.59	2.48	0.01	0.3101
92.9	AH92.9	1.6615	1.6755	1.6637	0.0118	0.0206	2.82	4.86	2.47	0.4192	0.0076	1.88	0.81	0.14	1.2107

), and the values of some of them were subsequently used to evaluate the studied dependencies.

The following comparisons were made: I; I_FMA; I_IFC; I_IFA; |F|; |F_FMA|; |F_IFC|; |F_IFA| vs. DELTA. The resulting dependencies were considered linear and were evaluated by their R-squared values (

Table 4. Averaged results for selected R2 values and F-fractions of the studied marialite–meionite representatives for each of the considered crystallographic directions.

Crystall. Direction	R2 ǀFǀ vs. DELTA	R2 ǀFFMAǀ vs. DELTA	R2 ǀFIFCǀ vs. DELTA	R2 ǀFIFAǀ vs. DELTA	∑ǀFFMAǀ/∑ǀFabsǀ × 100	∑ǀFIFCǀ/∑ǀFabsǀ × 100	∑ǀFIFAǀ/∑ǀFabsǀ × 100
	1	2	3	4	5	6	7
(111)	0.5529	0.9914	0.6320	0.1318	59.07	39.86	1.07
(201)	0.9758	0.9879	0.7107	0.1479	71.10	23.09	5.81
(221)	0.9938	0.9648	0.7072	0.1303	76.45	20.55	3.00
(3-11)	0.9505	0.9931	0.1493	0.0390	89.50	4.19	6.31

, columns 1–4; see next subsection). In addition, an estimate of the fraction of structure factors and amplitudes for each of the distinct atom groups (FMA, IFC, and IFA) from the sum of their absolute values for a given reflection have been calculated and expressed as a percentage for each of the samples, e.g., ǀF_{FMA,AH6.2,111}ǀ/∑(ǀF_{FMA,AH6.2,111}ǀ + ǀF_{IFC,AH6.2,111}ǀ + ǀF_{IFA,AH6.2,111}ǀ) × 100 = ǀF_{FMA,AH6,2,111}ǀ/∑ǀF_{abs,AH6.2,111}ǀ×100. Finally, averaged results for the studied representatives of the marialite–meionite series for each of the considered reflections, e.g., ∑ǀF_FMA,hklǀ/17/∑(ǀF_FMA,hklǀ + ǀF_IFC,hklǀ + ǀF_IFA,hklǀ)/17×100 = ∑ǀF_FMA,hklǀ/∑ǀF_abs,hklǀ × 100, are presented and expressed as a percentage in Table 4 (columns 5–7).

4.5. Crystal–Chemical Investigations and Space Group Selection Considerations for Scapolites

Table 3 summarizes data from the processing of CIFs of all investigated samples, some of which have been used to compile Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9.

It can be seen from Figure 5 that the odd reflections are of low intensity. The highest value observed for (221) does not exceed 1.2%. The graphs in Figure 5 with few exceptions show a nearly bell shape with a maximum around Me37, which supports Lin and Burley’s observations [31]. It can also be seen that the intensity of the odd peaks extrapolates almost to zero towards the pure end-members.

In Figure 6, for each of the investigated samples, the calculated odd peak intensities for the respective reflections are compared against the absolute value of the difference between the average values of the central atom–ligand bond lengths for the tetrahedra in type 2 4MRs., i.e., ǀ<T2-O> − <T3-O>ǀ (Figure 2b) or DELTA.

There is a varying degree, but a well-expressed linear dependence for (201), (221), and (3-11), and a not so good one for (111) (see the dot line presenting the trend line and the corresponding R² value).

The data from Table 4 (columns 1–4) show a strong, positive, linear relationship between ǀFǀ and DELTA for (201), (221), and (3-11), and a moderate one for (111). The linear dependence between ǀF_FMAǀ and DELTA is very strong for all reflections. The relationship between ǀF_IFCǀ and DELTA is moderate for all reflections with the exception of (3-11), which exhibits a very low R² value. ǀF_IFAǀ vs. DELTA exhibits none or a very weak linear relationship for all reflections. The relative shares for each of the groups of atoms defined above in the formation of the intensity of the corresponding Bragg reflection are presented in columns 5–7 in Table 4. For each reflection, the share of ǀF_FMAǀ is the highest, and that of ǀF_IFAǀ is the lowest with the exception of (3-11), for which the ǀF_IFCǀ exhibits the lowest value.

Among the groups of structural factors thus distinguished, the most suitable for the comparative studies in the present work is the one obtained from the group of framework atoms (FMA). The reasons for this are as follows:

(i) The constant, equal number of atoms that participate in the formation of ǀF_FMAǀ for each member of the marialite–meionite series for a given reflection. These are all of the silicon and aluminum cations distributed in three crystallographically distinct positions and all the oxygen atoms of their tetrahedral surroundings distributed in six non-equivalent sites.

(ii) Full occupancy of all atomic positions.

(iii) Very small difference between Si (Z = 14) and Al (Z = 13) X-ray scattering factors, which minimizes the effect of their mutual isomorphic substitution along the studied series.

Under these conditions, the values of ǀF_FMAǀ are primarily determined by the positions of the atoms (fractional coordinates x_j, y_j, z_j) that compose it. These, in turn, are determined by the lengths of the central cation–ligand bond for the three types of tetrahedra that make up the framework construction. The latter depend on the statistically averaged size of the central cation, which depends on the ratio of silicon and aluminum occupying the corresponding position. The two end-cases are those of pure silicon or pure aluminum. Based on Shannon’s data—^IVSi⁴⁺ = 0.26 Å, ^IVAl³⁺ = 0.39 Å; ^IIO²⁻ = 1.35 Å—we obtain Si-O = 1.61 Å and Al-O = 1.74 Å [41]. Hence, this is a very good premise for a strong linear correlation of ǀF_FMAǀ with another purely geometric indicator such as DELTA.

For the other two groups of structural factors, ǀF_IFCǀ and ǀF_IFAǀ, there are additional reasons that influence the values obtained for them within the studied series:

(i) The different number of atoms involved in making up the structure factor, especially for the group of interstitial framework anions (IFA). The operation of the substitution mechanism Cl⁻ ↔ CO₃^2– ↔ SO₄²⁻ leads to a different number of (oxygen) atoms for each member of the marialite–meionite series.

(ii) Occupancies, often different from unity, both for the representatives of interstitial framework cations (IFC) and for those of interstitial framework anions (IFA).

(iii) Different values of atomic scattering factors for the substituted cations in each of these two groups.

From what has been stated so far, it follows that the strongest, positive, linear relationship between the intensity of the odd peaks (respectively, the value of the overall structure factor) for a considered reflection will be registered where the R²-value and the relative share of ǀF_FMAǀ for the respective reflection are highest. According to the data in Table 4, such will be the linear dependencies for (201), (221), and (3-11) and to a lesser extent for (111).

An additional degree of uncertainty and discrepancy in the determination of the linear dependencies are introduced by the specificity and quality of the X-ray experiments and chemical analyses applied by the three groups of researchers, as well as the differences in the methodologies for solving the crystal structures [1,2,6,26,27,39].

Apart from (3-11) in Figure 9, a moderate to strong linear dependence of the compared quantities is observed everywhere. For the data in Figure 8, it can be said that the dependencies are very strong. Certain deviations from the linear trend are due to the objective and subjective factors as listed above. In many of the cases presented, the R²-value could be increased if the data were grouped according to the research teams from which they were obtained (see Table 2). For example, R² values for the linear dependence of ǀF_FMAǀ on DELTA for (111) obtained only for the samples of Sokolova and Hawthorne (nine SH-samples), only for the samples of Antao and Hassan (four AH-samples), and only for those four of the RV-samples are 0.9952, 0.9982, and 0.9994, respectively, vs. 0.9914 for the whole series. This is interpreted here as impact of the specificity of technique and methodology used by the respective teams for solving the crystal structures.

The linear relationships shown in Figure 7, Figure 8 and Figure 9 occur over the entire range of the marialite–meionite series from Me6 to Me93. A certain discontinuity is observed in the DELTA interval 0.43–0.9, where scapolites with meionite numbers between 6 and 26 would fall, as well as those between Me82 and Me93. So far, no data for representatives with similar compositions whose structures have been solved in the P4₂/n space group have been found in the literature.

In 2008, Sokolova and Hawthorne assessed the statistical significance of the difference between the mean values of the central atom–ligand distances—i.e., type 2 4MRs ǀ<T2-O> − <T3-O>ǀ (Figure 2b)—at the 95% confidence limit to determine the correct space group (I4/m or P4₂/n) for one of their samples, S(15) [6]. In the present work, the same approach was applied for representatives of scapolites that remained outside the range of the P4₂/n space group members determined in their study (from Me21 to Me77). These are samples RV82, AH93, and AH6.2 (Table 2). The <T2-O> and <T3-O> bond lengths in the RV82 crystal structure are 1.6445(3) and 1.6904(3) Å with a difference of 0.04565(3) Å. This difference is significant at the 95% confidence limit; hence, it is justified to assign the space group P4₂/n to this sample. The relevant distances for the AH93 sample are 1.6755(35) and 1.66375(325) Å, with a difference of 0.01175 Å, correspondingly, and the difference is significant at the 95% confidence limit. For the AH6.2 sample from the range of compositions with low meionite number, these values are 1.6545(55) and 1.6635(55) Å with a difference of 0.009(55). The difference between <T2-O> and <T3-O> is not significant at the 95% confidence limit; however, it is significant at the 90% confidence limit.

Therefore, to unambiguously assign the space group P4₂/n to representatives of the scapolites in the region nearby the end members of the marialite–meionite series, the following are necessary:

(i) To analyze the intensities of reflections that violate the body-centering of the studied structure. They should be meaningful in terms of their sign and magnitude of their standard deviations.

(ii) To indicate the confidence limits for the statistical significance of the differences found between the mean values of the tetrahedral bond lengths in type 2 4MRs. In this regard, the accuracy and precision of X-ray measurements play an important role, along with the preliminary preparation of the samples (grinding to spheres or spheroids), as well as their compositional uniformity.

5. Discussion

5.1. Further on the Si-Al Ordering in the Scapolite Framework Construction

Among the scapolites studied in the present work, the highest degree of Al-Si ordering is observed in sample AH36.6 [27]. In its structure, the T1 and T3 sites contain only Si atoms, and the T2 site contains only Al atoms, so the Al and Si atoms are completely ordered. Thus, in its composition, the Al:Si ratio tends to the ideal value 1:2. This is characteristic of Me37.5, ideally Ca₃Na₅[Al₈Si₁₆O₄₈]Cl(CO₃), predicted earlier by Lin and Burley [31], in which there is no violation of Lowenstein’s rule (Figure 10a). This P4₂/n space group sample is also characterized by the highest value for the DELTA parameter (Table 3, column 6) and, accordingly, by the highest measured and calculated values for I, ǀFǀ, ǀF_FMAǀ, and ǀF_IFCǀ for reflections (111), (201), (221), and (3-11) (Figure 5; Table 3). When the amount of aluminum increases, this element begins to enter the positions of type 1 4MRs, which, as explained by previous researchers, leads to a decrease in the possibility of formation of unstable -Al-O-A1- linkages in type 2 rings (Figure 2 and Figure 3). Its presence in the tetrahedra of type 1 is easily established by the increasing average distance <T1-O> with the increase in its amount in the studied samples (Table 3, column 3). The compositions of the scapolites in the vicinity of the Me100 end member—ideally Ca₄A1₆Si₆O₂₄CO₃ (meionite)—are characterized by an Al:Si ratio tending to 1:1. In their structures, complete or almost complete Al-Si disorder is observed in both types of 4MRs (Figure 10b). The DELTA parameter values as well as those of the calculated intensities of the odd reflections tend to zero (Figure 5; Table 3), and it becomes more and more justified to use the space group I4/m in order to describe the crystal structures.

It is worth paying attention to the behavior of the DELTA parameter with the increasing aluminum content in the studied compositions. The graphs in Figure 11 are constructed from Table 3 data (column 4 vs. column 1 and column 5 vs. column 1). They illustrate the gradual increase in DELTA with the increasing amount of aluminum in type 2 tetrahedra, reflecting its arrangement in the structure according to Lowenstein’s rule. DELTA reaches its maximum value at Al:Si tending to 1:2 (Me37.5). Then, and simultaneously with the entry of Al into type 1 4MRs, DELTA begins to smoothly decrease almost to a merger of <T2-O> and <T3-O> values in the vicinity of the Me100 end-member.

The plots in Figure 11 are similar in form to those presented by Teertstra and Sherriff in 1996 (compare to Figure 6 in [9]). The interpretation of the results is identical. The differences arise from the determination of range limits of the P4₂/n space group for the studied compositions: approx. Me21–66.7 [9] and Me6.2–92.9 (this work).

Previous NMR investigations of scapolite members of various Me numbers [28,29,30] indicate obvious violation of Lowenstein’s rule in almost the entire compositional range of the group. In the region up to Me37.5, where Al:Si < 1:2, the formation of single Al–O–Al moieties is obviously not forcedly caused by the quantitative ratio of the two framework cations. Their presence does not appear unusual and seems to be stabilized by the proximity of IFCs. Further on and up to Me100, where 1:1 > Al:Si > 1:2, the appearance of unstable –Al–O–Al– bonds is forced by the quantitative relations in favor of aluminum. It would be interesting to understand in what form, where, and how the unstable -Al-O-Al- bonds occur and in what way their presence affects the Al-Si ordering in the scapolite structures within the whole studied compositional range.

For this purpose, a careful inspection of the scapolite’s framework topology has been carried out. Potentials for occurrence of four types of single Al-O-Al linkages have been established in it as follows: between type 1 and type 2 4MRs tetrahedra; between the type 2 4MRs; within the type 1 4MRs; and within the type 2 4MRs, denoted hereinafter as bt1-t2, bt2, wt1, and wt2, respectively (Figure 12a).

According to Sokolova et al., up to 80% of the Al atoms in the T2 site are involved in one Al-O-Al bond for scapolite samples of predominantly marialitic content, i.e., Me4.6, Me7.5, and Me7.6 (I4/m) [28]. The authors suggest that these bonds occur within the four-membered type 2 rings (wt2 linkages in Figure 12a) and not between them (bt2 in Figure 12a) as their arguments are that in this part of the structure, the distances from Na to O between the type 2 4MRs are longer than those between sodium and oxygen atoms within the same rings and, therefore, “the stabilizing influence would be greater within the four-membered rings, where the Na-O bond is the shortest” [28].

Figure 13, Figure 14 and Figure 15 show idealized schemes of Si-Al arrangement in the crystal structure of Me100 as the guiding principle in their composition is the smallest possible number of Al-O-Al linkages within a single unit cell while avoiding moieties with a length of larger than a single bond, Al-O-Al. The color designations are as follows: dark green color—type 1 Si tetrahedra, yellow—Al type 1 tetrahedra, blue—Si type 2 tetrahedra, and red—Al type 2 tetrahedra. With such a marking, it is not always possible to adequately trace the symmetry operations characteristic of the two tetragonal groups of symmetries considered for the representatives of the scapolites. The reliability of the arrangement can be judged by imposing the colors of tetrahedra with the same coordinates of the atoms that make them up from two neighboring cells, for example, green + yellow = apple green and blue + red = muted purple, which indicate complete Al-Si disorder in type 1 and type 2 4MRs, respectively; or red + red = red and blue + blue = blue, indicating complete Al-Si order in type 2 4MRs.

Figure 13 presents four possible schemes of Si-Al arrangement, in which only Al-O-Al linkages of type bt1-t2 (indicated by black arrows) are allowed. In each of the structures, four unstable A1-O-A1 single bonds are found within a single unit cell. Figure 13a shows a case where aluminum insertion into type 1 tetrahedra continues without changing its arrangement in type 2 4MRs. Type 1 tetrahedra reach complete disorder (green + yellow = apple green), but type 2 tetrahedra retain an arrangement identical to that of Me37.5 (Figure 10a). In this case, the maximum difference DELTA = ǀ<T2-O> − <T3-O>ǀ would also be preserved, which, however, is not found in the measurements performed (Figure 11, Table 3, columns 3 and 4). Options 13b, c, and d, however, are suitable for the purpose and correspond to the experimental observations. There, the respective color impositions lead to obtaining a picture as in Figure 10b, with a general increase in the size of the tetrahedra of type 1 4MRs and with increasing aluminum in the composition of the scapolites.

Figure 14 illustrates variants of an alternative mechanism for Si-Al arrangement in the framework structure of Me100, in which only type wt2 bonds are present (Figure 14a,b) or combinations of wt2 and bt1-t2 linkages (Figure 14c,d). In the first case, it is possible to distinguish a minimum of four unstable linkages of wt2 type in a single unit cell. Their length is single, i.e., it does not exceed that of the indicated inter-atomic distances in a moiety consisting of A1-O-A1. The results are similar to those shown in Figure 13. In the second case, the preservation of complete Si-Al disorder in type 2 4MRs forces the appearance of bt1-t2 linkages and, along with this, longer A1-O-A1 moieties are observed (Figure 14d).

From a crystal–chemical point of view, the two mechanisms of Si-Al ordering presented in Figure 13 and Figure 14 would “ease” the structure because both work in the direction of minimizing the violation of the aluminum avoidance rule. The realization of such arrangements of the framework cations would lead to such a statistical distribution of them where, with the increase of aluminum in the composition of the scapolites, it begins to enter alternately into the tetrahedra of type 1 but simultaneously also into the smaller (in terms of size; provisionally designated here as T3) tetrahedra of type 2 at the expense of silicon, which in turn increases its content in position T2.

Such a mechanism for ordering of the framework cations can work both in the direction of reducing the number of unstable A1-O-A1 bonds in the unit cell as well as their separation into shorter (single) fragments (Figure 13 and Figure 14). As a result, the distance <T2-O> should start to decrease after reaching its maximum value at the highest degree of Si-Al ordering, and <T3-O> should start to increase accordingly. On the other hand, it follows that the differences between <T2-O> and <T3-O> (DELTA values) after reaching a maximum value in the region of Me37.5 will gradually decrease almost to a merger, as previously noted by Teertstra and Sherriff in 1996 ([9]; Figure 11).

Figure 15 presents idealized models of the framework construction of Me100, in which Al-O-Al linkages of the bt2 type are shown (indicated by blue arrows). Their introduction, however, inevitably leads to the appearance of bt1-t2 type bonds (black arrows). Thus, the number of unstable moieties in the unit cell reaches at least eight. There are also fragments with double bond lengths, i.e., Al-O-Al-O-Al. Figure 15a,b differ only in the arrangement of the dark green (Si) and the yellow (Al) tetrahedra in the type 1 4MRs that however does not affect the overall effect, which is hardly energetically advantageous for the structure as a whole.

Attempts to build an idealized scheme of the structure of Me100, based only on wt1-linkages, always lead to the appearance of other types of unstable Al-O-Al linkages. Thus, their total number in the unit cell exceeds four, their length often exceeds that of a single moiety, and branching of the chain has also been observed. For this reason, these schemes are not presented here.

Obviously, from the point of view of the concept adopted here to minimize the effect of the violation of the Lowenstein’s rule, the most favorable for the framework structure of scapolite Me100 are the linkages of the type wt2 and bt1-t2. Separately, for each of them, a minimum of four unstable moieties—whose lengths do not exceed the length of a single bond of the Al-O-Al type—can be formed within a single unit cell. Which of the two types is preferred is difficult to say or evidence experimentally, at least for now.

Following the assumptions of Sokolova et al. [28] for the stabilizing influence of the IFCs on the bridging oxygens “within the four-membered type 2 rings and not between them”—i.e., wt2 and bt2 (after this work notations)—analogous measurements were carried out for the bridging oxygens of each of the two bonds, wt2 and bt1-t2, for the structures of selected scapolites in the studied compositional range. The results are presented in

Table 5. Selected shortest interatomic distances within the structures of the studied scapolites.

Me, %	Sample Code	O3-IFC, Å	O4-IFC, Å	O5-IFC, Å	O6-IFC, Å	O3-IFA, Å	O4-IFA, Å	O5-IFA, Å	O6-IFA, Å
1	2	3	4	5	6	7	8	9	10
6.2	AH6.2	2.5390	2.5880	2.9580	2.8950	4.5750	4.5580	3.9710	4.0660
26.4	SH26.4	2.5289	2.4972	2.7891	2.8944	4.5650	4.5452	4.0443	4.0242
45.7	SH45.7	2.5188	2.4882	2.7063	2.8499	4.5700	4.5367	4.0709	4.0291
70	RV70	2.5190	2.4940	2.6530	2.7870	4.5830	4.5430	4.1110	4.0480
82	RV82	2.5000	2.5020	2.6680	2.7080	4.5650	4.5720	4.1160	4.0950
92.9	AH92.9	2.4910	2.5530	2.7680	2.6220	4.6000	4.5820	4.0570	4.1670
average		2.5161	2.5204	2.7571	2.7927	4.5763	4.5562	4.0617	4.0716

.

The distances between IFCs on the one hand and O3 and O4 (bridging oxygen atoms in wt2 bonds) on the other hand are shorter than those between IFCs and O5 and O6 (bridging oxygen atoms in bt1-t2 bonds). The opposite is observed for the distances of IFAs to O3 and O4 and IFAs to O5 and O6 (Table 5, last row; Figure 12b). It is concluded that in the corresponding parts of the structures, Al-O3-Al and Al-O4-Al linkages experience a stronger stabilizing effect coming from the relative proximity of the IFCs and the remoteness of the IFAs compared to Al-O5-Al and Al-O6-Al and should, therefore, be more stable for the considered structures.

5.2. Regarding the Possibilities of Lowering the Symmetry of the Scapolites

Over the years, cases have been reported in which, for various reasons, the crystal structure of the same scapolite sample was solved in both space groups I4/m and P4₂/n [12,23,30,39]. The same approach was used for the samples from the RV-series considered in the present study (Table 2). The I4/m → P4₂/n transition “splits” the cationic position of the T2 tetrahedra of type 2 four-membered rings into two crystallographically non-equivalent positions (Figure 2). Their tetrahedral environments differ in size, which is determined by the degree of occupancy of aluminum in the positions of the cations from the two tetrahedra (<T2-O> and <T3-O>) and generally gives information about the degree of Al-Si ordering in this type of 4MRs. Despite the subtle differences in the reference data and the approaches used, the application of such relations between certain geometrical parameters and the framework cations arrangement has proven to be an efficient tool for evaluation and assignment of Al in all T-sites of the studied structures. The obtained results are often fully supported by accompanying chemical analyses data. However, the question reasonably arises as to whether it is possible for a Si-Al arrangement like that recorded in type 2 4MRs to also be found in type 1 4MRs. If this is the case, differences in the mean central atom (Si, Al)—ligand (O) distances in the tetrahedra of this type of ring will appear, and a change in the space group, probably to a lower symmetry, will be necessary. The two tetragonal space groups traditionally used to describe the structures of scapolites—I4/m or P4₂/n—however, do not allow for the distinction of tetrahedra from this type of rings, because when applied these are all symmetry-equivalent and, therefore, identical in size. An examination of the group–subgroup relations for I4/m or P4₂/n shows that only one of them, space group I2/m (C2/m), enables splitting of the T1 positions of type 1 4MRs into T1′ and T1″ (Figure 16a). However, the following considerations should be taken into account when using it:

(i) Space group I2/m (C2/m) is body-centered; therefore, it is inapplicable where reflections violating body-centered symmetry have been registered in the X-ray experiment. In the compositional range of the marialite–meionite series with a low Me number, i.e., Me0–Me26, there are no prerequisites for splitting at the T1 positions because the amount of aluminum in the structure is too low and this element still only populates Type 2 4MRs without necessarily violating Lowenstein’s rule. This can easily be verified by measuring <T1-O> for the available samples. It has been found in the present study that for all of the investigated samples in the region Me6~Me40, the average sizes of bond lengths T1-O do not substantially exceed the value 1.61 Å, i.e., they are populated only by Si atoms and there are no prerequisites for splitting of this framework cation site (Table 3, column 3). The area between Me82 and Me93 remains to be checked. For sample AH92.9, the space group P4₂/n has already been tested to be applicable by Antao and Hassan in 2011 [39]. In addition, the tetrahedral ǀ<T2-O> − <T3-O>ǀ difference for this sample has been found to be of statistical significance at the 95% confidence limit (see Section 4.5). The same applies to the RV82 sample, in which the experimental file contains additional unequivocal evidence for the presence of meaningful odd peaks.

(ii) Strict application of C2/m in structure description leads to the conclusion of preferential aluminum occupancy in either of the two tetrahedra of type 1 4MRs. However, this leads not only to the formation of unstable A1-O-A1 linkages in the scapolite structure as a whole but also to the emergence of chains of similar fragments (Figure 16b).

Figure 16b illustrates a violation of Lowenstein’s rule that occurs where yellow and red tetrahedra (populated with aluminum) are in contact (corner-sharing). The formation of three consecutive bonds (…A1-O-A1-O-A1-O-A1…) among the tetrahedra of both types of four-membered rings is shown when using the monoclinic space group to describe the structure. Such an atomic configuration is hardly favorable for the stability of the structure. Again, we come to the conclusion of no preferred position for aluminum in this type of rings; a logical absence of a difference in the mean distances of its tetrahedra; and, therefore, a justified use of P4₂/n to describe the structure (symmetry-equivalent = equal in size to type 1 tetrahedra).

5.3. Genetic Consideration about the Mechanisms of Si-Al Ordering in Scapolites’ Framework

In 1960, Shaw gave a comprehensive review of the scapolite literature, chemical analyses, and occurrence [14]. According to him, “Scapolite is one of the less common rock-forming minerals, but is widely distributed in metamorphic rocks, especially those rich in Ca. It may occur in pegmatites but is otherwise unknown as a primary igneous mineral: it is not known to form in sedimentary environments”. Today, most of the scapolite researchers agree with the thesis that “Common to metasomatic environments and to many metamorphic terrains, scapolite is stable over a wide range of pressure and temperature” [16].

In the following lines, an idealized scenario of the arrangement and rearrangement of framework and interstitial framework cations in the structure of representatives from the scapolite group with different initial Al:Si ratios is considered. The processes start at high temperatures, with gradual cooling and at a rate allowing coupled CaAl-NaSi interdiffusion similar to that observed in plagioclase feldspars [42]. The results of Antao and Hassan’s thermal studies presented in Section 4.1.4 [25,26] show that, at temperatures around 900 °C, the available aluminum in the scapolite proto-structure is more likely to occupy positions in type 2 4MRs because of the larger sizes of the tetrahedra there. Upon cooling, the following developments are possible depending on the Al:Si ratio:

(i)

Al:Si < 1:2

Aluminum does not leave the confines of Type 2 4MRs. Single Al-O-Al bonds are not prohibited, although the aluminum content in this compositional range is low enough to cause forced formation of this type of bond. Their presence is stabilized by the proximity of interstitial framework cations, which in the considered compositional range are mainly represented by sodium, and their type is predominantly of the wt2 type ([28]; Figure 12 and Figure 14). As the starting aluminum increases, the probability of forming double and triple unstable Al-O-Al bonds increases, which is disadvantageous for the structure. To prevent their occurrence, a mechanism works for the selective occupancy of aluminum in one of the tetrahedrally coordinated positions (conditionally denoted here as T2). It is more pronounced in terms of the size of the tetrahedron and, accordingly, the greater the intensity of odd reflections, the more aluminum there is in the described compositional interval.

(ii)

Al:Si > 1:2

Aluminum is starting to make its way into Type 1 4MRs. Its amount there is greater and more noticeable the greater the Al:Si ratio is in the scapolite proto-structure. In the process of cationic diffusion, the formation of all types of aluminum–oxygen linkages is possible (Figure 12). However, the occurrence of some of them, e.g., bt2 and wt1, in the structure during the mineral formation process is unfavorable because this is a prerequisite for the creation of chains consisting of double and/or triple Al-O-Al bonds (Figure 15 and Figure 16). Therefore, their appearance is considered here as an intermediate stage, tracing the cation interdiffusion route to the formation at lower temperatures of the final structure in which the more stable bt1-t2 and wt2 bonds predominate. The arrangement mechanism of Al and Si in type 1 4MRs corresponds to complete Si-Al disorder for the entire considered compositional interval. As the starting aluminum decreases, its quantitative presence in type 1 tetrahedra also decreases. Simultaneously, the selective occupancy of aluminum in one of the tetrahedrally coordinated positions in type 2 4MRs increases as a counteracting mechanism for the formation of longer chains of unstable Al-O-Al bonds in the structure.

The presented scenario is simplified and idealized. In it, Al-Si ordering mechanisms play a leading role, which generally follow Lowenstein’s rule without prohibiting the occurrence and presence of single Al-O-Al bonds, but rather avoiding the formation of longer fragments of them in the final structure. The movement of the IFCs generally follows that of FMAs, probably by the mechanism of coupled CaAl-NaS interdiffusion, but together with IFA species they rather have an accompanying role in the final scapolite structure formation.

In fact, several syn- and post-genetic processes can have a significant influence on the final Al-Si arrangement in the scapolite structure. Such can be fluctuations in temperatures, the type and concentration of the starting reagents, the rate of mineral formation, and various types of reactions with minerals in direct contact and/or fluids in later stage alteration, e.g., [43]. Their manifestation leads to zoning or different contact phenomena related to mass transfer and affecting both the core and the rims of the studied samples. The fact that the changes that have occurred are not always reversible upon restoration of conditions close to the initial ones [25,26] should also be considered.

6. Conclusions

The present work offers an overview of the perceptions of previous researchers regarding Al-Si ordering in the structures of the studied compounds, the choice of space groups for solving their structures, the ranges and limits of distribution of the latter on the scapolite members in the marialite–meionite series, and the manifestations of violation of the Lowenstein rule or the so-called aluminum avoidance rule.

New crystal–chemical data are reported for scapolite samples from different localities whose crystal structures have been solved in the space groups I4/m or P4₂/n.

An analysis was performed to examine the types of possible Al-O-Al bonds that can occur in the structures at different Al:Si ratios and their influence on Al-Si ordering in the light of Lowenstein’s rule.

Genetic considerations about Al-Si ordering in the framework construction during the mineral formation processes are proposed.