Merohedral Mechanism Twining Growth of Natural Cation-Ordered Tetragonal Grossular

Abstract

Garnet supergroup minerals are in the interest of different applications in geology, mineralogy, and petrology and as optical material for material science. The growth twins of natural tetragonal grossular from the Wiluy River, Yakutia, Russia, were investigated using single-crystal X-ray diffraction, optical studies, Raman spectroscopy, microprobe, and scanning electron microscopy. The studied grossular is pseudo-cubic (a = 11.9390 (4), c = 11.9469 (6) Å) and birefringent (0.01). Its structure was refined in the Ia$\overline{3}$d, I4₁/acd, I4₁/a, and I$\overline{4}2$d space groups. The I4₁/a space group was chosen as the most possible one due to the absence of violating reflections and ordering of Mg²⁺ and Fe³⁺ in two independent octahedral sites, which cause the symmetry breaking according to the group–subgroup relation Ia$\overline{3}$d → I4₁/a. Octahedral crystals of (H₄O₄)⁴⁻-substituted grossular are merohedrally twinned by twofold axis along [110]. The mechanism of twining growth led to the generation of stacking faults on the (110) plane and results in the formation of crystals with a long prismatic habit.

1. Introduction

Minerals of the garnet supergroup are one of the most widely occurring minerals in the earth crust and upper mantle. They are stable in a wide range of temperatures (T) up to 2000 °C and pressures (P) of ~25 GPa and occur in different PT conditions, including rocks from lower greenschist facies to ultra-high-temperature granulites and ultra-high-pressure eclogites [1]. Owing to the flexibility of their structure, garnets demonstrate great chemical capacity and cationic diversity, which intensively are used for the determination of the PT evolution and oxygen fugacity of rocks [2,3,4], determining the absolute timing and rates of geological processes [5,6]. Their synthetic counterparts, YAl-garnet, Y₃Al₅O₁₂, doped with Nd, are the most famous kinds of oxide crystals widely used as the active medium in solid-state lasers [7,8].

The general formula for garnet is X₃Y₂Z₃ϕ₁₂, where X, Y, and Z refer to dodecahedral, octahedral, and tetrahedral sites, respectively, and ϕ is O, OH, or F [9]. In natural garnets, the tetrahedral sites are usually populated by Si⁴⁺ [1]. Low-temperature garnets are sometimes characterized by the hydrogarnet-type (H₄O₄)⁴⁻ ↔ (SiO₄)⁴⁻ substitution, which leads to the formation of hydrogarnet katoite, Ca₃Al₂(OH)₁₂ [10]. Katoite is cubic, Ia$\overline{3}$d; however, noncubic garnets with a significant amount of the hydrogarnet-type substitution have been reported: I4₁/acd spessartine, ideally Mn²⁺₃Al₂[(SiO₄)₂(H₄O₄,F₄)₁]_Σ3 [11,12]; I4₁/acd henritermierite, ideally Ca₃Mn³⁺₂[(SiO₄)₂(H₄O₄)₁]_Σ3 [13]; I4₁/acd holtstamite, ideally Ca₃(Al,Mn³⁺)₂[(SiO₄)₂(H₄O₄)₁]_Σ3 [14]; and R$\overline{3}$c Fe-bearing grossular [15] and R$\overline{3}$ nikmelnikovite, ideally ^X{Ca₁₂}Y[Fe²⁺Al₄Fe³⁺₂□]^Z(Si₆O₆)O₂₄(OH)₂₀ [16]. It should be noted that the crystal structure of vesuvianite, which contains a one-dimensional columnar fragment of the grossular structure, may contain a significant amount of the (H₄O₄)⁴⁻ ↔ (SiO₄)⁴⁻ substitution [17,18,19].

The presence of (H₄O₄)⁴⁻ hydrogarnet defects or unusual chemical composition typically exhibits optical birefringence that is accompanied by oscillatory or sector zoning [20]. In trigonal and tetragonal garnet, a birefringence is connected with lowering symmetry. Birefringence in cubic garnets was reported since the 19th century [21,22]; however, its origin is still discussed. An anomalous birefringence of cubic garnets is not characteristic for end-member compositions and usually observed for complex solid solutions of garnets. Birefringence was reported for almandine, grossular, spessartine, andradite, uvarovite, and hydrogarnet series [23,24,25,26]. The main reason for the birefringence is cation order at the X and Y sites that causes symmetry reduction [27,28].

The mechanism of twinning growth is one of the most common crystal-growth defects in organic and inorganic crystallography [29,30,31,32]. Twinning can occur whenever a compound crystallizes in a unit cell with a higher point group than that corresponding to the space group [33]. Twins are expected for the tetragonal symmetry, because it is lower than the ideal Ia$\overline{3}$d garnet structure. For the first natural trigonal garnet (space group R$\overline{3}$), nikmelnikovite was observed as merohedrally twinned crystals (twining by twofold axis along [110]) [16].

The presence of the garnet supergroup minerals with unusual morphology (octahedral, short prismatic, etc.) from the Wiluy River, Yakutia, Russia, was reported previously [34]. This contribution reports the occurrence of a tetragonal grossular with a prismatic habit characterized by a possible ordered arrangement of the hydrogarnet defects, Mg²⁺ and Fe³⁺. A complex way of merohedral twinning growth is discussed in detail in the context of lowering garnet symmetry.

2. Materials and Methods

2.1. Morphology and Composition

The morphology of minerals was studied using a Phenom XL scanning electron microscope (Faculty of Natural Sciences, University of Silesia).

The chemical composition of tetragonal (H₄O₄)⁴⁻-substituted grossular was determined by wavelength-dispersive spectrometry on a Hitachi S-3400N scanning electron microscope equipped with an INCA Wave 500 WDS (wavelength-dispersive spectroscopy) spectrometer. The system was operated at 20 kV and 10 nA, and the electron beam was focused to a 5 µm spot. The standards used were: pyrope (Al, Mg), lorenzenite (Si, Ti), anhydrite (Ca), synthetic MnCO₃ (Mn), hematite (Fe), chalcopyrite (S), metallic (Cr) fluorapatite (F), and atacamite (Cl). Cation contents were calculated with the Minal software [35].

2.2. Raman Spectroscopy

The Raman spectra (RS) of (H₄O₄)⁴⁻-substituted grossular collected from an uncoated individual grain were recorded with a Horiba Jobin-Yvon LabRAM HR800 spectrometer equipped with an Olympus BX-41 microscope in backscattering geometry (Saint Petersburg State University). Raman spectra were excited by a solid-state laser (532 nm) with an actual power of 2 mW on a sample using the 50× objective (NA 0.75). The spectra were obtained in the range of 70–4000 cm⁻¹ at a resolution of 2 cm⁻¹ at room temperature. To improve the signal-to-noise ratio, the number of acquisitions was set to 15. The spectra were processed using the algorithms implemented in the LabSpec and OriginPro 8.1 software packages.

2.3. Single-Crystal X-ray Diffraction

The crystal-structure study of (H₄O₄)⁴⁻-substituted grossular was carried out at the X-ray Diffraction Resource Centre of St. Petersburg State University by means of an Oxford diffraction Xcalibur EOS diffractometer equipped with a CCD detector using monochromatic MoKα radiation (λ = 0.71069 Å) at room temperature. More than a half of the diffraction sphere was collected with scanning step 1° and an exposure time of 30 s. The data were integrated and corrected by means of the CrysAlisPro program package, which was also used to apply empirical absorption correction using spherical harmonics, implemented in the SCALE3 ABSPACK scaling algorithm [36]. The structure was refined using the SHELXL software package [37]. The crystal structure was drawn using the VESTA 3 program [38]. Polyhedral volumes were calculated according the formula proposed by Baur [39]. Occupancies of the cation sites were calculated from the experimental site-scattering factors in accordance with the empirical chemical composition. Hydrogen sites could not be located.

3. Occurrence

Samples of “achtarandite”-bearing rodingite-like rocks with prismatic crystals of the grossular–katoite series were collected in 1992–1994 at the right shore of the Wiluy River within an area of the Siberian Traps development 7 km from Chernyshevsky, Republic of Sakha (Yakutia), Russia [40]. After flooding in 1966, the Wiluy water power station building has only a few outcrops of rodingite-like rocks and skarns in the shores of the Wiluy River from the unique deposit of wiluite, grossular, and “achtarandite”, discovered in 1790 by Eric Laksman [40,41]. Magnesian limestones and marls of the Lower Ordovician, which were altered at the contact of the large Erbeyek gabbro-dolerite intrusion of the Lower Triassic age, are the protolith of skarns and rodingite-like rocks [40]. This place is the type of locality for the two garnets—grossular [42] and eringaite [43]—as well as a mineral of the vesuvianite group, wiluite [44]. Additionally, that is the only place on earth where large tetrahedral sponge hydrogarnet pseudomorphs after a mayenite-like mineral named achtarandite are met (Figure 1a) [34,45,46,47].

Fine-grained rodingite-like rocks are composed of minerals of the grossular–katoite series, chlorite, and diopside with an admixture of minerals of the kaolinite–serpentine and vesuvianite group, large, up to 2–3 cm, crystals of “Werner’s” grossular with epitaxial overgrowths of “achtarandite” (Figure 1b) [45]. The “achtarandite” pseudomorphs has a sponge structure built by the three-dimensional framework of flattened grossular–katoite aggregates [46]. The aggregates are represented by an overgrowth of octahedral and rhombic dodecahedral hydrogarnet crystals and splitting Si-deficient, (H₄O₄)^4–-substituted, B-bearing vesuvianite crystals [17,19] (Figure 1c). The octahedral morphology is characteristic only for microcrystals of relatively strongly hydrated garnet [34]. The (pseudo)prismatic garnet crystals often grow on the hydrogrossular plates (Figure 1d,e). The morphology of prismatic hydrogarnet crystals indicates that these crystals can be elongated along the twofold axis in the [110] direction or along the fourfold axis in the [001] direction of the crystal [34]. A cross section of these pseudo-prismatic crystals changes from rhombic to quadratic. A prismatic hydrogarnet crystal 0.14 × 0.02 × 0.02 mm in size elongated along [111] with a quadratic cross section was used for the structural investigation (Figure 1f).

The genesis of rodingite-like rocks with large grossular crystals (Figure 1b) and also other types of rocks of this deposit, for example, serpentinite with large wiluite crystal and “achtarandite” pseudomorphs, specimens of which are in many mineralogical museums of the world, is connected with low-temperature alterations of early formed high-temperature skarns. At the early stage, as a result of the incorporation of a big block of argillaceous carbonate sedimentary rocks of the Ordovician age by a huge body of the Siberian Traps at the closed-surface conditions, high-temperature skarns were formed [40].

These skarns were represented by pyrometamorphic rocks of the sanidine facies (low P, high T > 800 °C), probably of melilite composition, in which large metacrysts of wiluite, grossular, and minerals of the chlormayenite–wadalite series and high-Al diopside crystallized [40]. At the hydration stage, skarns were practically completely altered to rodingite-like rocks with relic large grossular and wiluite crystals, and minerals of the chlormayenite–wadalite series were transformed to “achtarandite” pseudomorphs.

4. Results

4.1. Composition

The chemical data for (H₄O₄)⁴⁻-substituted grossular is shown in

Table 1. Chemical composition of (H₄O₄)⁴⁻-substituted grossular from the Wiluy River, Yakutia, Russia.

Spot	1	2	3	4
SiO2	34.23	34.86	35.25	34.52
TiO2	0.02	0.03	bdl	0.04
Al2O3	20.52	20.72	20.12	20.51
Fe2O3	2.84	2.93	3.15	2.72
Mn2O3	0.04	0.08	0.15	0.07
MgO	0.77	0.65	0.72	0.81
CaO	36.92	37.05	36.74	37.25
H2O 1	3.52	3.32	2.79	3.38
Total	98.89	99.66	98.93	99.32
Atoms per formula unit normalized on the basis of 12 anions
Si4+	2.56	2.59	2.65	2.57
Al3+	1.81	1.81	1.78	1.80
Fe3+	0.16	0.16	0.18	0.15
Mn3+	0.00	0.00	0.01	0.00
Mg2+	0.09	0.07	0.08	0.09
Sum Y	2.06	2.04	2.05	2.04
Ca2+	2.96	2.95	2.96	2.98
H+	1.75	1.64	1.40	1.68

¹ Content of H₂O calculated according to charge-balance requirements at Z site: H^x = 4(Z-Si).

. Admixtures with a total content <0.01 apfu and not holding in the empirical formula include Cr, Ti, S, F, and Cl. It should be noted that the negative correlation between Fe and Al content is in agreement with grossular–andradite substitution. All Fe and Mn were assumed as trivalent and hydrogarnet-type defects located at the Z sites according to the detailed crystal chemical data on the Wiluy garnets [40]. The crystal chemical formula of the studied garnet was normalized on the basis of 12 anions [9].

The empirical calculated formula can be written as Ca_2.97(Al_1.80Fe³⁺_0.16Mg_0.09)_Σ2.05([SiO₄]_2.59[H₄O₄]_0.41)_Σ3.00, which agrees well with the results of the crystal-structure refinement (see below).

4.2. Raman Spectroscopy

The Raman spectra of (H₄O₄)⁴⁻-substituted grossular are shown in Figure 2. The spectrum of tetrahedral grossular is close to that of grossular from rodingites in Dobšiná, Western Carpathians, described in [48]. The assignments of the absorption bands were made by an analogy with published data for Ca-silicate garnets [49,50,51,52,53].

The weak bands at 176, 243, and 275 cm⁻¹ are assigned to the lattice vibrations. The strength at 367 cm⁻¹ is attributed to the symmetric bending Si–O vibrations of the (SiO₄)⁴⁻ group. A relatively intense band at 535 cm⁻¹ and a weak band at 622 cm⁻¹ are related to the antisymmetric bending Si-O vibrations of (SiO₄)⁴⁻ or overlapping stretching Al-O vibrations of AlO₆ octahedra [43]. A weak and broad band at 622 cm⁻¹ also can be assigned to the hydroxyl deformation (librational) mode [50,54,55,56]. The doublet of intense bands at 819 and 873 cm⁻¹ is assigned to symmetric Si–O stretching modes of (SiO₄)⁴⁻. A weak split peak with two maxima at 982 and 999 cm⁻¹ is related to antisymmetric stretching Si–O vibrations [48].

The bands in the region of 3400–3800 cm⁻¹ (Figure 2) correspond to the stretching vibrations of the OH groups. The deficit of Si in garnet composition (Table 1) together with observed bands in this region confirms the presence of hydrogarnet-type defects (H₄O₄)⁴⁻ in grossular with a prismatic habit from the Wiluy River, Yakutia, Russia. The band at 3673 cm⁻¹ may be also related to the OH groups in the thin crusts of clinochlore on grossular crystals.

4.3. Single-Crystal X-ray Diffraction

The crystal structure of (H₄O₄)⁴⁻-substituted grossular initially was refined in the cubic Ia$\overline{3}$d space group to R₁ = 0.027 (R_int = 0.030) for 245 independent reflections with F_o > 4σ(F_o). There are observed free types of reflections violating Ia$\overline{3}$d symmetry. No violation of an I-centered lattice could be detected. The hhl condition (2h + l = 4n) relating to the d-glide plane in (110) was violated by the 222 (mean I/σ(I) = 4.0) group of reflections and 114 (I/σ(I) = 4.0) reflection. The h00 condition (h = 4n) reflected with 41 axes was violated for 00l and 0k0 reflections (41 axis parallel to [001] and [010], respectively) by the group of 002 and 020 (mean I/σ(I) = 5.2) reflections. Additionally, the observed 015 reflection violated the hk0 (h,k = 2n) condition (Figure 3).

Prismatic habit and moderated (0.010) birefringence together with systematic absence violations compelled us to refine the crystal structure in the tetragonal I-centered space groups. Refinement in the most common tetragonal space group I4₁/acd resulted in R₁ = 0.038 (R_int = 0.020) for 676 independent reflections with three systematic absence violations (for c and d glide planes). However, this model does not show significant difference between parameters of Si sites for lowering symmetry from cubic to tetragonal.

The I$\overline{4}2$d space group is one of the most possible for (H₄O₄)⁴⁻-substituted grossular. Only two reflections of 222 were observed, which violate the hhl condition (2h + l = 4n) relating to the d-glide plane. The crystal structure was refined to R₁ = 0.032 (R_int = 0.017) for 916 independent reflections with F_o > 4σ(F_o).

There are no systematic absence violations observed for the I4₁/a space group model. The crystal structure was refined using a merohedral twin model (twofold axis along [110]) with the 1:1 twin ratio to R₁ = 0.032 (R_int = 0.017) for 951 independent reflections.

The SCXRD data for the Ia$\overline{3}$d, I4₁/acd, I$\overline{4}2$d, and I4₁/a structure models are deposited in CCDC under entry nos. 2213563, 2213559, 2213564, and 2133541, correspondingly. Crystal data, data collection information, and refinement details are given in

Table 2. Crystal data, data collection information, and refinement details for (H₄O₄)⁴⁻-substituted grossular from Wiluy River, Yakutia, Russia.

Parameter	Data
Temperature/K	293 (2)
Crystal system		Tetragonal		cubic
Space group	I41/acd	I41/a	$I\overline{4}2$d	$\mathrm{Ia}$d
a = b/Å	11.9390 (4)	11.9390 (4)	11.9390 (4)	11.9416 (4)
c/Å	11.9469 (6)	11.9469 (6)	11.9469 (6)	11.9416 (4)
α = β = γ /°	90
Volume/Å3	1702.91 (14)	1702.91 (14)	1702.91 (14)	1702.88 (15)
Z	8
ρcalcg/cm3	3.461	3.459	3.460	3.468
μ/mm−1	2.851	2.843	2.840	2.883
F(000)	1763.0	1762.0	1763.0	1766.0
Crystal size/mm3	0.14 × 0.02 × 0.02
Radiation	Mo Kα (λ = 0.71073)
2Θ range for data collection/°	6.826 to 63.662
Index ranges	−8 ≤ h ≤ 16, −15 ≤ k ≤ 17, −6 ≤ l ≤ 17	−6 ≤ h ≤ 15, −14 ≤ k ≤ 15, −6 ≤ l ≤ 15	−6 ≤ h ≤ 15, −14 ≤ k ≤ 15, −6 ≤ l ≤ 15	−15 ≤ h ≤ 17, −6 ≤ k ≤ 17, −7 ≤ l ≤ 16
Reflections collected	2158	1916	1860	2003
Independent reflections	676 (Rint = 0.0198, Rsigma = 0.0210)	951 (Rint = 0.0167, Rsigma = 0.0242)	916 (Rint = 0.0171, Rsigma = 0.0239)	245 (Rint = 0.0301, Rsigma = 0.0164)
Data/restraints/parameters	676/0/52	951/0/96	916/6/97	245/0/19
Goodness-of-fit on F2	1.161	1.098	1.072	1.212
Final R indexes (I >= 2σ (I))	R1 = 0.0377, wR2 = 0.0974	R1 = 0.0324, wR2 = 0.0897	R1 = 0.0324, wR2 = 0.0883	R1 = 0.0270, wR2 = 0.0741
Final R indexes (all data)	R1 = 0.0544, wR2 = 0.1055	R1 = 0.0503, wR2 = 0.0997	R1 = 0.0488, wR2 = 0.0978	R1 = 0.0358, wR2 = 0.0790
Largest diff. peak/hole/e Å−3	0.78/−0.34	0.61/−0.38	0.65/−0.38	0.34/−0.28
Flack parameter			0.57 (14)

. Atom coordinates and isotropic parameters of atomic displacements are given in Table S1, and interatomic distances in Table S2, and the anisotropic parameters of atomic displacements are given in Table S3.

$I\overline{4}2$$\mathrm{Ia}$ The crystal structure of (H₄O₄)⁴⁻-substituted grossular refined in the Ia$\overline{3}$d model (Figure 4a) is characterized by one independent X1 dodecahedra (X1: 24c) with a mean <Ca–O> distance of 2.418 Å and consistent with full occupancy by Ca (Figure 4b). The Y1 octahedra (Y1: 16a) have a mean <Al–O> distance of 1.936 Å and refined occupancy of (Al_0.91Fe_0.09)_1.00. The Z1 tetrahedra (Z1: 24d) have a slightly increased mean <Si–O> distance of 1.671 Å compared with a <Si–O> distance in anhydrous cubic grossular of 1.649 Å [57]. The refined occupancy of the Si1 site is (Si_0.86□_0.14)_1.00.

The structural formula of (H₄O₄)⁴⁻-substituted grossular determined from the structure refinement in the Ia$\overline{3}$d space group can be written as: Ca₃(Al_1.81Fe_0.19)₂([SiO₄]_2.59[H₄O₄]_0.41)_Σ3.00.

The I4₁/acd structural model contains two independent X sites (X1: 16e; X2: 8b) fully populated by Ca atoms with mean <Ca1–O> and <Ca2–O> distances of 2.420 and 2.420 Å, respectively. The unique Y1 octahedron (16c) has a mean <Al–O> distance of 1.937 Å. The refined occupancy of the Y1 site is (Al_0.90Fe_0.10). There are two independent Z tetrahedra (Z1: 16e; Z2: i8a) with mean <Si1–O> and <Si2–O> distances of 1.673 and 1.666 Å, respectively. The refined occupancy for the Si1 site is (Si_0.85□_0.15)_1.00, and for the Si2 site, it is (Si_0.88□_0.12)_1.00.

The structural formula of (H₄O₄)⁴⁻-substituted grossular determined from the structure refinement in the I4₁/acd space group can be written as: Ca₃(Al_1.81Fe_0.19)₂([SiO₄]_2.61[H₄O₄]_0.39)_Σ3.00 and agrees with the cubic structure model.

The I4₁/a structure model contains two independent X sites (X1: 8e; X2: 16f) fully occupied by Ca atoms. The mean <Ca1–O> and <Ca2–O> distances are 2.420 and 2.419 Å, respectively. There are two independent Y sites (Y1: 8c; Y2: 8d), which differ in mean Y-O distances of 1.941 and 1.931 Å. The octahedral sites significantly differ in their refined occupancies of (Al_0.97Fe_0.03) for the Y1 site and (Al_0.87Fe_0.13) for the Y2 site. There are three independent Z tetrahedra (Z1: 4a; Z2: 4b; Z3: 16f) with mean <Si1–O>, <Si2–O>, and <Si3–O> distances of 1.662, 1.672, and 1.672 Å, respectively. The refined occupancies for the Si1, Si2, and Si3 sites are (Si_0.87□_0.13)_1.00, (Si_0.86□_0.14)_1.00, and (Si_0.86□_0.14)_1.00.

The structural formula of (H₄O₄)⁴⁻-substituted grossular determined from the structure refinement in the I4₁/a space group can be written as: Ca₃(Al_1.84Fe_0.16)₂([SiO₄]_2.58[H₄O₄]_0.42)_Σ3.00

The I$\overline{4}2$d structural model contains three independent X sites (X1: 8d; X2: 8d; X3: 8c) fully occupied by Ca atoms. The mean <Ca1–O>, <Ca2–O>, and <Ca3–O> distances are 2.413, 2.421, and 2.423 Å, respectively. The exclusive Y site (Y1: 16e) has a mean <Y–O> distance of 1.936 Å. The refined occupancy of the Y1 site is (Al_0.91Fe_0.09). There are four independent Z tetrahedra (Z1: 4a; Z2: 8d; Z3: 4b; Z4: 8d) with mean <Si1–O>, <Si2–O>, <Si3–O>, and <Si4–O> distances of 1.648, 1.686, 1.684, and 1.662 Å, respectively. The refined occupancies for the Si1, Si2, Si3, and Si4 sites are (Si_0.93□_0.10)_1.00, (Si_0.92□_0.08)_1.00, (Si_0.84□_0.16)_1.00, and (Si_0.80□_0.20)_1.00, respectively.

The structural formula of (H₄O₄)⁴⁻substituted grossular determined from the structure refinement in the I$\overline{4}2$d space group can be written as: Ca₃(Al_1.82Fe_0.18)₂([SiO₄]_2.61[H₄O₄]_0.39)_Σ3.00.

5. Discussion

A decrease in the symmetry of hydrated and anhydrous natural garnets from cubic Ia$\overline{3}$d to tetragonal I4₁/acd or I4₁/a is described more and more often recently [20]. The I4₁/a space group was reported for the synthetic majorite, Mg₃[SiFe²⁺]Si₃O₁₂ [58], and natural composition in the majorite–pyrope series as a result of a high degree of ordering Mg and Si at the two symmetrically unique octahedral sites [59]. The tetragonal majorite (I4₁/a) was also found in a shocked chondritic meteorite [60].

The I4₁/acd space group was proposed for garnets with a different origin, including those produced by subduction-zone-metamorphism pyralspite–grandite composition [61]. More often, this space group is used for the description of low-temperature OH-bearing garnets. Two tetragonal members of the garnet supergroup, henritermierite, Ca₃Mn³⁺₂[Si₂(□)O₈(OH)₄], and holtstamite, Ca₃Al₂[Si₂(□)O₈(OH)₄], crystallize in the I4₁/acd space group [13,14]. In both cases, a lowering of symmetry is connected to Jahn–Teller distortion of Mn³⁺O₆ octahedra (holtstamite contains up to 15 wt.% Mn₂O₃). The spessartine from different localities contained (O₂H₂)F₂ groups also is refined in the I4₁/acd structure model, the lowering symmetry by scheme Ia$\overline{3}$d → I4₁/acd is connected with different occupancy of (Si1_0.82□_0.18)_1.00 and (Si2_0.97□_0.03)_1.00 sites [11,12].

The refined formula from structural data for the cubic Ia$\overline{3}$d model of (H₄O₄)⁴⁻-substituted grossular Ca₃(Al_1.81Fe_0.19)₂([SiO₄]_2.59[H₄O₄]_0.41)_Σ3.00 well agrees with chemical data Ca_2.97(Al_1.80Fe³⁺_0.16Mg_0.09)_Σ2.05([SiO₄]_2.59[H₄O₄]_0.41)_Σ3.00. At the same time, all tetragonal models also well agree with the garnet chemistry. The prismatic habit and moderated (0.010) birefringence and the presence of seven strong violating reflections for the Ia$\overline{3}$d space group are substantial arguments to the tetragonal symmetry choice.

The location of different Z sites for both tetragonal models is shown in Figure 4a,b. It should be noted that the maximal occupancy difference of the Z sites 0.93 and 0.80 observed for the I$\overline{4}2$d model indicates ordering of H₄O₄ defects at Z sites. For the I4₁/a model, its occupancies are 0.86 and 0.87. According to our experimental data, the polyhedral volume of Z sites depends from the occupancy or, in other words, the amount of (H₄O₄)⁴⁻↔ (SiO₄)⁴⁻ substitution (Figure 5).

In the garnet structure, each octahedral site is connected through a shared vertex with six tetrahedra (Figure 6). Increasing of the polyhedral volume of Z tetrahedra affects the charge balance. Theoretically, the local charge balance mechanism includes increasing of Z–O distances for low occupied Z sites, accommodating decreasing of the corresponding Y–O distances. For example, in the crystal structure of henritermierite, the shortest Mn³⁺–O distance of 1.904 Å is observed for oxygen atom with shared Si-vacant tetrahedra. In the I$\overline{4}2$d model, the maximal degree of the (H₄O₄)⁴⁻ ↔ (SiO₄)⁴⁻ substitution is related to Z3 and Z4 sites with occupancies of 0.83 and 0.82 (Figure 6a). The observed mean Y–O distance with the shared O atoms related to Z3 and Z4 sites is 1.928 Å, whereas the same Y–O distance with shared Z1 and Z2 sites is 1.942 Å and agrees with the proposed local charge balance mechanism.

According to our data refinement in the I4₁/acd space group, the occupancy of both tetrahedral sites (Si1_0.86□_0.14)_1.00 and (Si2_0.87□_0.13)_1.00 is very close and does not explain symmetry lowering from cubic to tetragonal. The Y–O distances vary in the range of 1.907–1.960 Å and are not correlated with the occupancy of Z sites (Figure 6b,c).

The tetragonal distortion for the I4₁/a model was connected to the cation ordering at Y1 and Y2 octahedral sites. The Fe³⁺ cations unequally distributed between octahedral Y1 and Y2 sites with refined occupancies are (Al_0.97Fe_0.03) and (Al_0.87Fe_0.13). According to the systematic studies of interatomic distances [62], the estimated Y–O distances (for refined occupancies) would be 1.933 Å for the Y1 site and 1.944 Å for the Y2 site, which is in contrast with the observed distances of 1.941 and 1.931 Å, correspondingly. The data of refinement do not consider 0.09 apfu of Mg, whose scattering is close to Al. If the ordering of Mg at the Y1 site (Al_0.88Mg_0.09Fe_0.03) is taken into account, the estimated Y–O distances would be 1.950 Å for the Y1 site and 1.944 Å for the Y2 site, which is in good agreement with the observed distances. Owing to exceeding the effective ionic radius Mg²⁺(0.72) under Fe³⁺(0.645 Å), the polyhedral volume of the Mg-bearing Y1 site is 9.74 ų more than 9.59 ų for the Y2 site preferentially occupied by Fe³⁺. The preference occupancy of Mg²⁺ and Fe³⁺ at octahedral sites was previously indicated for vesuvianite [63].

The tetragonal models I$\overline{4}2$d and I4₁/a reasonably (adequately) describe the crystal structure of (H₄O₄)⁴⁻-substituted grossular with the close values of the R₁ factor. Which structural model would be more appropriate? On the one hand, ordering of H₄O₄ defects at the Z sites with the I$\overline{4}2$d model, and on other hand, ordering of Mg at the Y1 site and Fe³⁺ at the Y2 sites with the I4₁/a model. Summarizing diffraction data (systematic absence violations) and literature data on the cation ordering among octahedral sites, the I4₁/a model is preferred.

Individual untwinned (H₄O₄)⁴⁻-substituted grossular crystals are octahedrally shaped {111} with small {110} dodecahedral faces previously described in the [34] paper (Figure 7a). According to our SC XRD data, the most possible model described by the I4₁/a space group contains merohedral twining by twofold axis along [>110]. The evolution of the natural system with an increase in the Fe amount during the time in garnet composition causes the change in crystal habit from {111} octahedral in Fe-free garnets to {110} dodecahedral in Fe-bearing garnets [34]. The growth of perfect individual crystals is expected for the equilibrium system. The change of system conditions during the crystal growth may produce stacking faults [30]. The applied model of fault with a 0.05 shift along the c parameter for the proposed model of the merohedral twin is shown in (Figure 7c). This model is in good agreement with the observed shape of twinned (H₄O₄)⁴⁻-substituted grossular crystals (Figure 7b). Consequently, we propose that the merohedral twinning observed in tetragonal grossular results in the generation of stacking faults on the (110) plane during growth. This leads to the formation of long prismatic grossular grains consisting of merohedral twins.