Berthierine-2H₁ from Lovozero Alkaline Massif, Kola Peninsula, Russia: First Structure Model for Berthierine and Complexity-Stability Relations

Abstract

Berthierine was found in a natrolite vein intersecting volcanogenic-sedimentary rocks on the slope of Mt. Quamdespakh in the upper reaches of the Suolwai River, Lovozero alkaline massif, Kola peninsula, Russian Arctic. The mineral occurs as well-formed translucent pyramidal crystals up to 250 μm in size. The chemical composition determined by electron microprobe analysis corresponds to the empirical formula ^VI(Fe²⁺_1.99Al_0.94Mg_0.03Mn_0.04)_Σ3.00[^IV(Si_1.15Al_0.85)_Σ2.00O₅] [(OH)_3.92O_0.08]_Σ4.00; the idealized formula is ^VI(Fe²⁺₂Al)[^IV(SiAl)O₅](OH)₄. The crystal-structure determination (the first detailed crystal-structure characterization of berthierine) shows that the Lovozero mineral is hexagonal, P6₃cm (a = 5.3903(4), c = 14.0146(10) Å, V = 352.64(6) ų, R₁ = 0.053 for 338 unique observed reflections), and corresponds to the 2H₁ polytype of serpentine-group minerals with 1:1 tetrahedral-octahedral layers. The unit cell contains two M₃[T₂O₅](OH)₄ layers (M = Fe²⁺,Al; T = Si,Al) stacked along the c axis. The calculations of information-based structural and topological complexity parameters indicate that berthierine is structurally and topologically simpler than its chlorite-group polymorph chamosite. Since berthierine usually crystallizes metastably in the stability field of chamosite, the complexity analysis is agreement with the Goldsmith rule that states that, in Ostwald sequences of crystallization, metastable phases are simpler and more disordered than their stable counterparts. This observation can be applied to a general case of the metastable formation of serpentine-group minerals prior to the crystallization of chlorites.

1. Introduction

Berthierine, or (Fe²⁺,Fe³⁺,Al)₃(Si,Al)₂O₅(OH)₄, is a 1:1 layered silicate that belongs to the serpentine subgroup of the kaoline-serpentine group. It has been found in a number of different geological environments, mostly in low-temperature sedimentary formations, including laterites [1,2], polar soils [3], coal measures [4], bauxites (where it may occur as a rock-forming mineral) [5,6,7,8], siderite sediments [9], etc. Berthierine is also known as a secondary mineral formed as a result of alteration of primary Fe-Mg silicate minerals [10,11,12,13]. The hydrothermal origin of berthierine was reported for pegmatites [14,15].

In low-temperature environments, berthierine forms metastably as a precursor to chamosite, its polymorph that belongs to the chlorite group. The studies of the thermodynamic properties of berthierine and chamosite [16,17,18,19,20] indeed demonstrate that the latter is stable in relation to the former. It has also been observed experimentally that a serpentine-group mineral usually forms metastably prior to the formation of a chlorite-group mineral [16,18,21,22], obeying the famous Ostwald rule of stages [23,24,25,26,27]. J. Goldsmith [28] proposed that metastable polymorphs forming in the Ostwald cascade of phases are usually structurally simpler than their stable counterparts, which was confirmed through the recent application of information-based structural complexity measures [29,30,31,32,33,34,35,36,37,38]. It is of interest to verify whether the Goldsmith principle holds for the pair of berthierine (metastable) and chamosite (stable). However, despite the mineralogical and petrological importance of berthierine, information about its crystallography and crystal chemistry is very scarce [16,39] with no full crystal-structure determination of the mineral reported so far. The obvious reason for this lacune in data is the mode of occurrence of berthierine, which is usually found as fine-grained aggregates intermixed or intergrown with other minerals. Herein, we report on the find of berthierine in pegmatites of the Lovozero alkaline massif, Kola peninsula, Russia, where the mineral occurs in crystals of good enough quality to be studied using modern X-ray diffraction crystallography equipment. We provide a full mineralogical, chemical, and structural description of the sample and discuss the validity of the Goldsmith principle for the metastable formation of berthierine.

2. Materials and Methods

2.1. Materials

The crystals of berthierine studied in this work originated from the Lovozero alkaline massif, Kola peninsula, Russian Arctic [15]. The mineral was found in a natrolite vein intersecting volcanogenic-sedimentary rocks on the slope of Mt. Quamdespahk in the upper reaches of the Suolwai River. Bertierine is represented by well-formed translucent pyramidal crystals up to 250 μm in size (Figure 1a,b), fine-grained mass of xenomorphic excretions up to 0.4 mm, as well as paramorphoses in magnetite crystals among natrolite crystals. The replacement of berthierine by clay minerals is observed. The association includes loparite-(Ce), minerals of the ilmenite-pyrophanite series, zircon, fluorapatite, pyrrhotite, and rhabdophane-(Ce). Along with this, small (up to 100 μm) nests are observed, composed of the smallest (less than 1 μm) crystals of berthierine and baddeleyite. Berthierine forms pyramidal crystals with the {20$\overline{2}$1}, {000$\overline{1}$}, and {0001} forms (Figure 1c–f). Intergrowth or twins on {0001} are common (Figure 1c,f).

2.2. Chemical Composition

Several crystals of berthierine were mounted in epoxy blocks and polished. The elemental analysis was carried out using scanning electron microscope LEO-1450 (Carl Zeiss Microscopy, Jena, Germany) equipped with an energy-dispersive spectrometer ULTIM MAX 100 (OXFORD Instruments, Great Britain, Abingdon, UK) at an accelerating voltage of 20 kV, with a probe current of 2 nA. The results are given in

Table 1. Chemical composition (in wt.%) of berthierine from Lovozero.

	1	2	3
SiO2	19.59	19.95	20.01
Al2O3	26.16	26.08	26.97
FeO *	40.79	41.84	40.54
MgO	0.41	0.34	0.34
MnO	0.87	0.89	1.00
H2O **	10.29	10.42	10.43
Total	98.89	99.52	99.29
Si	1.14	1.15	1.15
IVAl	0.86	0.85	0.85
Total	2.00	2.00	2.00
VIAl	0.93	0.92	0.98
Fe	1.99	2.01	1.95
Mg	0.04	0.03	0.03
Mn	0.04	0.04	0.05
Total	3.00	3.00	3.00
OH	3.92	3.97	3.94
O	5.08	5.03	5.06
Total	9.00	9.00	9.00

* Total Fe as FeO; ** calculated from stoichiometry.

. The energy-dispersive spectra were processed automatically using the AzTec Energy software package. The following standards were used: pyrope (Mg, Al), wollastonite (Si), hematite (Fe), and synthetic MnCO₃ (Mn).

The average empirical chemical formula calculated on the basis of Fe + Mn + Mg + Al + Si = 5 can be written as ^VI(Fe²⁺_1.99Al_0.94Mg_0.03Mn_0.04)_Σ3.00[^IV(Si_1.15Al_0.85)_Σ2.00O₅][(OH)_3.92O_0.08]_Σ4.00; the idealized formula is ^VI(Fe²⁺₂Al)[^IV(SiAl)O₅](OH)₄, where VI and IV indicate octahedral and tetrahedral sites, respectively. Both empirical and chemical formulas are in agreement with the results of crystal-structure determination (see below). Brindley [40] recommended calculation of the chemical formulae of berthierine on the basis of the total valence of cations in octahedral and tetrahedral positions equal to 14+, assuming possibility of vacancies in the cation sites. No vacancies have been observed in the Lovozero berthierine on the basis of crystal-structure analysis, so the formula was calculated based on the 5 cation sites.

2.3. Single-Crystal X-Ray Diffraction Analysis

The crystal-structure study of berthierine was carried out by means of the Synergy S single-crystal diffractometer equipped with the Hypix detector using monochromatic MoKα radiation (λ = 0.71069 Å) at room temperature. More than half of the diffraction sphere was collected with scanning step of 1° and exposure time of 90 s. The data were integrated and corrected by means of the CrysAlis program package, which was also used to apply empirical absorption correction using spherical harmonics, implemented in the SCALE3 ABSPACK scaling algorithm [41]. The structure was refined using the SHELXL software package [42]. The positions of H atoms could not be located. The occupancies of the octahedral and tetrahedral sites were refined using mixed site-scattering curves of Fe and Al and Si and Al, respectively. The refined occupancy of the octahedrally coordinated M site is Fe_0.72(4)Al_0.28(4), which agrees well with the results of the chemical analyses. In order to achieve stable refinement, the occupancy of the tetrahedral T site was fixed at Si_0.564Al_0.436, in agreement with the chemical data. The final structure model was refined with anisotropic approximation for all atoms, except for O4, which could not be refined with physically realistic anisotropic displacement parameters. The possible crystal chemical reason for this is the bridging role of the O4 atoms in linking two adjacent TO₄ tetrahedra (T = Si, Al); we suppose that some disorder is observed with regard to the orientation of the silicate sheets in adjacent 1:1 layers, which results in different rotations of tetrahedra around the c axis (see discussion below). Crystal data, data collection information, and structure refinement details are given in

Table 2. Crystal data and structure refinement for berthierine.

Crystal data
Chemical formula	Fe2+1.99Al1.79Mg0.03Mn0.04Si1.15O9H4
Mr
Crystal system, space group	Hexagonal, P63cm
Temperature (K)	296(2)
a, c (Å)	5.3903(4), 14.0146(10)
V (Å3)	352.64(6)
Z	2
µ (mm−1)	4.612
ρ (g/cm3)	3.227
Crystal size (mm3)	0.03 × 0.03 × 0.08
Data collection parameters
Diffractometer	Rigaku XtaLAB Synergy-S
Radiation type	MoKα
Absorption correction	Gaussian
2Θmin, 2Θmax	2.907, 27.986
No. of measured, independent and observed [I > 2σ(I)] reflections	3355, 339, 338
Rint	0.037
Refinement parameters
R1 [F2 > 2σ(F2)], wR(F2), S	0.053, 0.110, 1.157
No. of reflections	338
No. of parameters	27
Δρmax, Δρmin (e Å−3)	0.884, −1.470

; atom coordinates and displacement parameters are in

Table 3. Atomic coordinates and displacement parameters (Ų) for berthierine.

Atom	x	y	z	Ueq	U11	U22	U33	U23	U13	U12
M *	0.3361(6)	0	0.2570(1)	0.0107(7)	0.009(1)	0.009(1)	0.0141(9)	0	−0.001(1)	0.0046(7)
T **	2/3	1/3	0.4541(3)	0.007(1)	0.006(2)	0.006(2)	0.009(2)	0	0.000	0.0030(8)
O1	2/3	1/3	0.3331(9)	0.018(3)	0.020(5)	0.020(5)	0.012(6)	0	0.000	0.010(3)
Oh2	0	0	0.331(1)	0.019(5)	0.026(8)	0.026(8)	0.007(8)	0	0.000	0.013(4)
Oh3	0.669(3)	0	0.1883(7)	0.020(3)	0.027(5)	0.025(7)	0.007(5)	0	−0.003(5)	0.013(4)
O4 ***	0	0.444(2)	0.4936(7)	0.010(2)

* site occupancy—Fe_0.72(4)Al_0.28(4); ** site occupancy—Si_0.564Al_0.436; *** refined isotropically.

, and selected interatomic distances are in

Table 4. Selected interatomic distances (Å) for the crystal structure of berthierine.

M—Oh3	2.036(14)	T—O4	1.679(4) 3×
M—Oh3	2.040(8) 2×	T—O1	1.696(15)
M—O1	2.083(7) 2×	<T—O>	1.683
M—Oh2	2.087(9)
<M—O>	2.055

.

3. Results

The only crystallographic information on berthierine available so far was the unit-cell parameters for two berthierine polytypes studied by Brindley in 1951 [39], who reported orthorhombic (a = 5.391, b = 9.333, c = 7.040 Å) and monoclinic (a = 5.411, b = 9.333, c = 7.040 Å, β = 104.5°) varieties. Bertoldi et al. [18] synthesized berthierine as a metastable precursor to chamosite (see below) and determined the following unit-cell parameters for the synthetic sample with the composition (Fe²⁺_1.83Al_0.67Fe³⁺_0.33)_Σ2.83[Si_1.33Al_0.67O₅](OH)₄: a = 5.388, b = 9.377, c = 7.040 Å, α = 89.96, β = 104.5, γ = 90.16°, indicating the triclinic symmetry of their material. No atom coordinates have ever been published for berthierine, and our study is the first report on detailed structure determination for this interesting and important mineral.

The crystal structure of berthierine from Lovozero is shown in Figure 2a. The mineral belongs to the kaoline-serpentine group of 1:1 phyllosilicates, which means that it is based upon double layers formed by trioctahedral sheets of MO₆ octahedra and [T₂O₅] aluminosilicate sheets of corner-sharing TO₄ tetrahedra (Figure 2b).

There is one crystallographically independent octahedrally coordinated M site with an average <M-O> distance of 2.055 Å. Taking into account the average ^VIAl³⁺-O and ^VIFe²⁺-O distances of 1.904 and 2.147, respectively [43,44], and, assuming the approximate ratio Fe²⁺:Al³⁺ = 2:1, the expected <M-O> distance is 2.066 Å, well in agreement with the experimental value. Similarly, for one crystallographically independent T site with the Si⁴⁺:Al³⁺ ratio of ca. 1:1, the expected <T-O> distance (taking into account average ^IVSi⁴⁺-O and ^IVAl³⁺-O distances of 1.625 and 1.746 Å, respectively [45]) is 1.686 Å, in good agreement with the experimental value of 1.683 Å.

In phyllosilicates, the six-membered silicate rings are usually distorted according to the mechanism known as a ditrigonal rotation [46], resulting from the adaptation of silicate anion to interlayer cation or hydrogen bonding. The rotation angle, α, may assume positive or negative values depending upon the position of the bridging O atom that may move forward or backward from the octahedral cation of the same layer [47]. In berthierine, α = +20.8°, and ditrigonal distortions of silicate sheets in the adjacent layers are opposite to one another (Figure 2c).

4. Discussion

4.1. End-Member Chemical Formula

As was pointed out above, the idealized chemical formula of bethierine from Lovozero can be written as ^VI(Fe²⁺₂Al)[^IV(SiAl)O₅](OH)₄, assuming one octahedral and one tetrahedral site with total cation disorder in each site. The ideal chemical formula of berthierine approved by the International Mineralogical Association is (Fe²⁺,Fe³⁺,Al)₃(Si,Al)₂O₅(OH)₄, suggesting an end-member chemical formula ^VIFe²⁺₃[^IVSi₂O₅](OH)₄. This corresponds to the berthierine sample reported here with Fe²⁺ predominant at the octahedral site and Si⁴⁺ predominant at the tetrahedral site. Any cation ordering with the decrease of symmetry from the ideal P6₃cm space group would correspond to a separate mineral species, which opens up the possibility of future discoveries of new mineral species in the kaolinite-serpentine group that should be regulated by some nomenclature rules absent in the current literature.

4.2. Polytype Identification and Symmetry

Taking into account the large amount of work done on berthierine, it is rather remarkable how little crystallographic information is available on this mineral, which can be explained by its occurrence as fine-grained aggregates and its poor crystallinity. As has already been mentioned, Brindley [39] identified two polytypes of berthierine, orthorhombic and monoclinic, whereas Bertoldi et al. [18] reported triclinic cells for a synthetic analog of berthierine. The different symmetries reported for berthierine as well as the hexagonal symmetry reported here most probably correspond to different polytypes or species with different degrees of cation ordering; the unambiguous explanation is currently impossible, taking into account the absence of direct structure determinations, except for the one presented in this paper.

In our study, the overall hexagonal symmetry of berthierine from Lovozero was found with the space group P6₃cm, which is characteristic of the 2H₁ polytypes of the 1:1 serpentine-group minerals. In fact, berthierine from Lovozero is isotypic to lizardite-2H₁, Mg₃[Si₂O₅](OH)₄, described by Mellini and Zanazzi from Coli, Italy [47]. Its unit-cell dimensions (a = 5.318, c = 14.541 Å) can be compared with those of berthierine-2H₁ reported herein (a = 5.3903, c = 14.0146 Å). The a parameter of berthierine is significantly larger than that of lizardite, whereas the c parameter is shorter. The explanation for such a behavior lies in the mechanism of mutual geometric adaptation between the octahedral and tetrahedral sheets, which is achieved through the ditrigonal rotation on one hand and octahedral flattening on the other. The latter is characterized by the octahedral flattening angle (ψ), which is calculated according to the following formula [46]:

ψ = arccos[(octahedral thickness)/(2<M-O>)],

(1)

where octahedral thickness is measured as the distance between the planes of opposite triangular faces of octahedra parallel to the plane of the octahedral sheet.

It is worth noting that the <M-O> distances for berthierine-2H₁ and lizardite-2H₁ are not very different, 2.087 and 2.067 Å, respectively. However, their ψ values are 61.5 and 59.8°, respectively, which means that the MO₆ octahedra in berthierine are essentially flattened compared to those in lizardite. The octahedral flattening is explained by the larger dimensions of the aluminosilicate sheets in berthierine compared to the almost pure silicate sheets in lizardite. The ditrigonal rotation parameter in lizardite-2H₁ is +6.4°, much smaller than that in berthierine-2H₁ (+20.8°).

Zheng and Bailey [48] reported on the crystal structure of the 2H₁ polytype of amesite, (Mg₂Al)[(SiAl)O₅](OH)₄, which is an Mg analog of berthierine. They found distortions of the crystal structure from an ideal configuration with the P6₃cm symmetry and refined it in the non-standard triclinic C$\overline{1}$ space group with the unit-cell parameters a = 5.299, b = 9.181, c = 14.050 Å, α = 90.06, β = 90.30, γ = 90.00°, and V = 683.6 ų. The partial ordering was reported for both octahedral and tetrahedral sites with the <M-O> bond lengths in the range of 2.003–2.080 Å and the <T-O> bond lengths in the range of 1.671–1.710 Å. The ditrigonal rotation angle α is equal to +15.6 and 14.8° for two independent silicate sheets, approaching the value observed for berthierine-2H₁. The octahedral flattening parameters ψ vary from 59.9 to 61.0° (<ψ> = 60.4°), indicating a rather flattened average configuration of MO₆ octahedra, which explains the value of the c parameter close to that of berthierine-2H₁. In contrast to the crystal of amesite-2H₁ studied in [48], no indications of cation ordering (e.g., additional reflections or satellites violating X-ray diffraction absence conditions) had been observed for berthierine-2H₁.

4.3. Structural Complexity and Relative Stability of Berthierine and Chamosite

As has been mentioned in the introduction, the formation of berthierine, at least in some geochemical environments, proceeds in accord with the metastable crystallization scenario defined by the Ostwald rule of stages [23], where berthierine forms prior to the formation of its chemical analog (polymorph) chamosite (see also: [49]). As pointed out by Bertoldi et al. [16,18], this is the general observation for the formation of a serpentine-group mineral preceding the formation of a chlorite-group mineral, observed in both nature and experiment. The Goldsmith rule [28,38] states that metastable phases formed in Ostwald sequences are usually structurally simpler and more disordered than the stable final phases. The crystal-structure model for berthierine reported in this work allows us to verify the validity of the Goldsmith rule for the pair berthierine-chamosite using the information-based parameters of structural complexity developed in [29,50,51].

According to this approach, structural complexity can be estimated as the amounts of Shannon information per atom (^strI_G) and per unit cell (^strI_G,total) by means of the following equations:

$${}^{\mathrm{str}}I_G=-{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{p}}_i{\log }_2{p}_i(\mathrm{bit}/\mathrm{atom}),$$

(2)

$${}^{\mathrm{str}}I_{G,\mathrm{total}}=-v{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{p}}_i{\log }_2{p}_i(\mathrm{bit}/\mathrm{cell}),$$

(3)

where information is measured in binary digits (bits), k is the number of different crystallographic orbits (Wyckoff sites) in the structure, and p_i is the random choice probability for an atom from the ith crystallographic orbit, that is:

p_i = m_i/v,

(4)

where m_i is a multiplicity of a crystallographic orbit (i.e., the number of atoms of a specific Wyckoff site in the reduced unit cell) and v is the total number of atoms in the reduced unit cell.

The only full report on the crystal structure of chamosite is that of its Mg-rich IIb polytype determined by Walker and Bish [52] (Figure 3a). Similar to those of other chlorite-group minerals, the crystal structure of chamosite is based upon two types of layers: a 2:1 layer of trioctahedral sheet sandwiched between two tetrahedral [T₂O₅] sheets (Figure 3b) and a trioctahedral sheet of edge-sharing (MO₆) octahedra (Figure 3c). The layers are stacked along the c axis in an alternating fashion and are linked by hydrogen bonding only. It should be noted that the crystal structure of chamosite-IIb reported in [52] possesses a certain degree of cation ordering absent in berthierine-2H₁ reported herein.

The information-based structural complexity parameters for berthierine-2H₁ and chamosite-IIb calculated according to Equations (2)–(4) are given in

Table 5. Structural complexity and thermodynamic parameters for berthierine and chamosite.

Chemical Formula	IG [Bit/Atom]	IG,total [Bit/Cell]	ΔfH°298, kJ.mol−1	S°298, J.mol−1K−1	ΔfG°298, kJ.mol−1	Ref.
Berthierine *
(Fe2+1.99Al0.94Mg0.03Mn0.04) [(Si1.15Al0.85)Σ2.00O5](OH)3.92O0.08	2.891	104.078				This work
2{(Fe2+1.422Al0.975Fe3+0.182Mg0.157Li0.035Mn0.002) [(Si1.332Al0.668)O5](OH)4}			−6944.56	514.54	−7548.92	[20]
2{(Fe2+1.44Al0.976Fe3+0.182Mg0.157) [(Si1.332Al0.668)O5](OH)4}			−6936.62	514.00	−7548.92	[20]
2{(Fe2.5Al0.5)[Si1.5Al0.5O5](OH)4}				568.2	−7140.60	[18]
Chamosite
(Fe2+2.72Al1.33Mn0.08□0.10) [(Si2.85Al1.145Ti0.005)O10](OH)8	4.225	152.117				[52]
(Fe2+5Al)[(Si3Al)O10](OH)8			−7120.85	559.4		[17]
(Fe2+4Al2)[(Si2Al2)O10](OH)8			−7607.46	514.8		[19]

* Thermodynamic parameters for berthierine are given for two formula units in order to ease the comparison with the parameters for chamosite.

, which also contains thermodynamic data on both minerals available from literature (the chemical composition is given for each particular sample). In order to calculate the correct values of structural information including contributions from H atoms not determined from X-ray diffraction analysis, the procedure of H-correction was applied as described in [51,53].

The relative stability of berthierine and chamosite was a subject of extensive discussion in the literature [20,54,55,56,57]. The problem is complicated by the variability of chemical compositions of both berthierine and chamosite. Blanc et al. [20] considered the following reaction of transition from berthierine to chamosite of the same composition:

2[(Fe²⁺_1.422Al_0.975Fe³⁺_0.182Mg_0.157Li_0.035Mn_0.002)(Si_1.332Al_0.668)O₅(OH)₄ (berthierine)] →
(Fe²⁺_2.844Al_1.95Fe³⁺_0.364Mg_0.314Li_0.07Mn_0.004)(Si_2.664Al_1.336)O₁₀(OH)₈ (chamosite)

The corresponding Gibbs energy of this reaction was estimated to be in the range from 86 to 88 kJ mol⁻¹ at 25 and 150 °C, respectively, indicating that, for the same composition, berthierine is significantly less stable than chamosite [20]. However, berthierine may crystallize and persist metastably in natural environments, especially low-temperature ones, as outlined in the introduction. In general, the comparison of thermodynamic parameters for both minerals shows that chamosite is more stable than berthierine, whereas the structural complexity calculations indicate that it is also more complex, which conforms to the Goldsmith rule: in an Ostwald sequence of polymorph crystallization, metastable phases are simpler and more disordered than their stable counterparts. As was put out by Goldsmith [28], structurally simpler phases crystallize more easily, which may be related to the smaller size of their critical nuclei [58], their lower densities, and their lower interfacial energies [38] compared to the stable and more complex phases.

4.4. Note on Relative Topological Complexity of Berthierine and Chamosite

The structural complexity parameters given in Table 5 are based on the experimental structure models determined from single-crystal X-ray diffraction analysis. It makes sense to consider the complexity of the serpentine- and chlorite-group minerals in topological terms, i.e., in terms of the complexity of their structural units with ideal (maximal) symmetries. Since both serpentine- and chlorite-group minerals have layered crystal structures, one should consider the topological complexities of layers that serve as bases for the respective structure types. Figure 4 shows the ideal versions of basic layers in the crystal structures of serpentine- and chlorite-group minerals: the [M(OH)₂] layer of edge-sharing M(OH)₆ octahedra from chlorite-group minerals (Figure 3c and Figure 4a), the 1:1 heteropolyhedral [M₃[T₂O₅](OH)₄] layer in serpentine-group minerals (Figure 2b and Figure 4b), and the 2:1 heteropolyhedral layer M₃[T₂O₅]₂(OH)₂ in chlorite-group minerals (Figure 3b and Figure 4c). The ideal layer groups of the layers are given in Figure 4d,e,f, respectively, whereas

Table 6. Ideal symmetries, independent site distributions, and topological complexity parameters of layers in the crystal structures of serpentine- and chlorite-group minerals.

Mineral Group	Serpentine	Chlorite
General formula	M3[T2O5](OH)4	M6[T2O5]2(OH)8 = M3[T2O5]2(OH)2 + 3M(OH)2
Layer formula	M3[T2O5](OH)4	M(OH)2	M3[T2O5]2(OH)2
Layer symmetry group	p31m	$p\overline{3}$m1	c2/m11
Site distribution	M:[3], T:[2], O:[2+3], Oh:[3+1], H:[3+1]	M:[1], Oh:[2], H:[2]	M:[1+2], T:[4], O:[2+4+4], Oh:[2], H:[2]
IG [bit/atom]	2.891	1.522	2.869
IG,total [bit/cell]	52.039	7.610	60.239

provides ideal symmetries, independent site distributions, and topological complexity parameters of the layers. The minimal total topological complexity of the double-layer structure of chlorite-group minerals can be calculated, taking into account the equation M₆[T₂O₅]₂(OH)₈ = M₃[T₂O₅]₂(OH)₂ + 3M(OH)₂, as 60.239 + 3 × 7.610 = 83.069 bit/cell. On the other hand, the serpentine-type 1:1 layers possess 52.039 bit/cell only. Therefore, from the viewpoint of topological information, serpentine-group minerals are simpler than chlorite-group minerals, which provides additional support for the validity of the Goldsmith principle for metastable crystallization of serpentines in the stability field of chlorites.

5. Conclusions

The results of the present study of berthierine from hydrothermal veins of the Lovozero alkaline massif, Kola peninsula, Russian Arctic, provide the first crystal-structure determination for this mineral and demonstrate that the Lovozero sample belongs to the 2H₁ polytype with overall hexagonal symmetry and the highest possible for this polytype space group P6₃cm. In natural environments and experiments, berthierine (a serpentine-group mineral) usually forms metastable prior to the formation of its polymorph chamosite, a chlorite-group mineral. Thus, the berthierine crystallization is in agreement with the Ostwald rule of stages that postulates the step-like phase formation with increasing thermodynamic stability [23]. According to Goldsmith [28], in Ostwald cascades, metastable phases are usually structurally simpler and more disordered than stable phases, which agrees with the calculations of structural and topological complexity parameters for berthierine and chamosite. Moreover, this observation is also valid and can be applied to the general case of metastable serpentine-group minerals’ crystallization and their subsequent transformation into chlorite-group minerals.