‘Rhythmite’, Ca₂₉(SiO₄)₈Cl₂₆, an Anthropogenic Phase from the Chelyabinsk Coal Basin (Ural, Russia) with a Complex Modular Structure Related to α-Ca₃SiO₄Cl₂ (‘Albovite’): Crystal Structure, Raman Spectra, and Thermal Expansion

Abstract

‘Rhythmite’, Ca₂₉(SiO₄)₈Cl₂₆, an anthropogenic calcium chloride silicate from the Chelyabinsk coal basin (South Ural, Russia), was investigated using chemical microprobe analysis, in situ single-crystal X-ray diffraction analysis (27–727 °C), and Raman spectroscopy. ‘Rhythmite’ is orthorhombic, Pnma: a = 17.0749(6), b = 15.1029(5), c = 13.2907(4) Å, and V = 3427.42(18) ų (R₁ = 0.045). The crystal structure of ‘rhythmite’ consists of a porous framework formed by Ca-O bonds and SiO₄ tetrahedra with additional Ca²⁺ cations and Cl⁻ anions in the structure interstices. The framework is built up from multinuclear [Ca₁₅(SiO₄)₄]¹⁴⁺ fundamental building blocks (FBBs) cut from the crystal structure of α-Ca₃SiO₄Cl₂ (‘albovite’). The FBBs are linked by sharing common Ca atoms to form a network with an overall pcu topology. The empirical chemical formula was calculated as Ca_29.02(Si_7.89Al_0.05P_0.05)_Ʃ7.99O₃₂Cl₂₆ (on the basis of Cl + O = 58). ‘Rhythmite’ is stable up to 627 °C and expands slightly anisotropically (α_max/α_min = 1.40) in the ab and bc planes and almost isotropically in the ac plane (α₃₃/α₁₁ = 1.02) with the following thermal expansion coefficients (×10⁶ °C⁻¹): α₁₁ = 14.6(1), α₂₂ = 20.5(4), α₃₃ = 15.0(3), and α_V = 50.1(6) (room temperature). During expansion, the silicate tetrahedra remain relatively rigid with average bond length changes of less than 0.5%. A structural complexity analysis indicates that ‘rhythmite’ is complex, with I_G,total = 920.313 (bits/u.c.), which significantly exceeds the average value of structural complexity for silicates and is caused by the modular framework construction and the presence of a large number of independent positions in the crystal structure.

1. Introduction

The technological activity of humankind in the 20th and 21st centuries has led to the creation of various technogenic geochemical environments producing remarkable amounts of anthropogenic mineral phases, including new crystalline compounds unknown in either nature or technology. A drastic example of such environments is burnt coal dumps, and in particular the burnt coal dumps of the Chelyabinsk coal basin (ChCB, South Ural, Russia). A spontaneous fire that was ignited at the ChCB dumps resulted in the high-temperature crystallization of a large suite of unique and diverse mineral-like phases, including mainly silicates, sulphates, oxides, and halides [1]. More than fifty of these phases were described there for the first time, and eight of them have been approved as new mineral species by the International Mineralogical Association (IMA) [2,3,4,5,6,7,8]. In the 1990s, the IMA policy with respect to the ChCB phases was changed, and they were no longer considered mineral species. However, recent IMA documents allow the recognition of the mineral status of the mineral phases formed at the burnt coal dumps if it can be confirmed that the coal ignition was not of anthropogenic origin [9].

The current work is a continuation of a series of studies on the crystal chemistry and spectroscopy of the mineral-like phases of ChCB and is devoted to ‘rhythmite’, an anthropogenic calcium silicate chloride [10,11,12,13,14,15,16,17,18,19,20]. This phase was first described by B.V. Chesnokov and co-authors in the dump of mine no. 45, and its composition was primarily determined as Ca₄(SiO₄)₂·3CaCl₂ [1]. ‘Rhythmite’ forms coarse-grained, marble-like aggregates (with grains up to 1 cm) and is closely associated with ‘aquasidite’, CaCl₂, ‘igumnovite’, Ca₃Al₂(SiO₄)₂Cl₄, graphite, cohenite, and iron monosulphides. According to B.V. Chesnokov, ‘rhythmite’ is a typical phase of so-called ‘black blocks’, which include products of the oxidative burning of clay and carbonate components of coal dumps. Thus, its formation occurs at extremely high temperatures (up to 1000 °C) under strongly reducing conditions with the participation of gaseous chlorine. ‘Rhythmite’ was not approved as a mineral species by the IMA and received its name from B.V. Chesnokov due to a system of thin subparallel strips on its crystals, which are composed of finely dispersed carbon with the admixture of small grains of ‘igumnovite’. The striation is irregular, and its nature is not clear. Throughout the text of this paper, the name ‘rhythmite’ is enclosed in quotation marks to emphasize its anthropogenic origin.

Herein, we present for the first time the results of the crystal structure solution of ‘rhythmite’ and its refinement in a wide temperature range (27–727 °C with 100 °C steps), obtained using in situ single-crystal X-ray diffraction studies. This allowed us to analyse the thermal expansion of the compound and to determine its major thermal expansion coefficients. In addition, we report on the chemical composition, Raman spectra, and structural complexity of ‘rhythmite’.

2. Materials and Methods

2.1. Sample

The sample of ‘rhythmite’ studied in this work was provided by the Natural Science Museum of the Ilmen State Reserve (Miass, Russia) from the personal collection of B.V. Chesnokov (Chelyabinsk coal basin, dump of mine no. 45) [21]. The mineral phase forms colourless transparent crystals up to 0.05 mm in diameter. It is hygroscopic and becomes damp after prolonged exposure to open air (Figure 1). This fact strongly affects the quality of single crystals and complicated our investigations.

2.2. Raman Spectroscopy

The Raman spectrum of ‘rhythmite’ was recorded using a Horiba Jobin-Yvon LabRam HR800 spectrometer (solid state laser, 532 nm, 50× objective). The equipment was calibrated according to a silicon standard (520.7 cm⁻¹). The studied sample was placed on a slide without a given orientation. The Raman spectrum was recorded at room temperature in the range of 70–4000 cm⁻¹, and the power on the sample reached 8 mW. The data accumulation time took from 2 to 10 s, and number of cycles was 10 (the spectral resolution was 2–3 cm⁻¹ and the lateral resolution was 1 mkm). The visualization of the spectra was performed using OriginPro 2018 SR1 b9.5.1.195 software.

2.3. X-Ray Diffraction Data

A suitable crystal of ‘rhythmite’ was fixed in a quartz capillary with 10-micron wall thickness and placed in a Rigaku Xtalab Synergy-S diffractometer (MoKα radiation, 50 kV/1.0 mA) equipped with a high-speed direct-action detector (HyPix-6000HE). The measurements were carried out at a temperature range of 27–727 °C with 100 °C steps. The hemisphere of the diffraction data was collected for each temperature. The frame width and counting time were 1° and 13 s, respectively. The orientation of the crystal was unchanged during the measurement process. The heating of the crystal was controlled by a ‘Hot Air gas blower system’. CrysAlisPro [22] software was used for further processing. An absorption correction was introduced using the SCALE ABSPACK algorithm. The crystal structures were solved and refined using the SHELX program package included in the Olex2 shell [23,24]. The previously reported instability of ‘rhythmite’ in the open air impacted the quality of the data obtained in the process of measurement and further refinement. Herein, in

Table 1. Crystal data and structure refinement parameters of ‘rhythmite’ at 27 °C (1) and at 327 °C (2).

Sample	1	2
Crystal system	orthorhombic	orthorhombic
Temperature (°C)	27	327
Space group	Pnma
a, Å	17.0749(6)	17.1494(7)
b, Å	15.1029(5)	15.1980(7)
c, Å	13.2907(4)	13.3550(5)
Volume, Å3	3427.42(18)	3480.8(3)
Z	2
Dcalc (g/cm3)	2.736	2.691
μ/mm−1	3.423	3.365
F(000)	2783.0	2780.0
Radiation	MoKα (λ = 0.71073)
2Θ range for data collection/°	6.58 to 59.418	6.548 to 59.408
Index ranges	−16 ≤ h ≤ 21, −19 ≤ k ≤ 20, −16 ≤ l ≤ 12
Reflections collected	18,310	18,679
Independent reflections	4179 [Rint = 0.0623, Rsigma = 0.0610]	4245 [Rint = 0.0843, Rsigma = 0.0894]
Data/restraints/parameters	4179/0/232	4245/0/232
Goodness-of-fit on F2	1.066	1.072
Final R indexes [I >= 2σ (I)]	R1 = 0.0449, wR2 = 0.0875	R1 = 0.0569, wR2 = 0.1007
Final R indexes [all data]	R1 = 0.0869, wR2 = 0.1112	R1 = 0.1348, wR2 = 0.1359
Largest diff. peak/hole/e Å−3	2.30/−1.19	1.55/−1.10

, Table 2 and Table 3 the best data obtained for room temperature and for 327 °C are given. The crystal data and structure refinement parameters are given in Table 1, the atomic coordinates and displacement parameters are given in Table 2 and Table S1, respectively, and selected bonds lengths at room temperature and at 327 °C for ‘rhythmite’ are provided in Table 3 and Table S2.

The values of the main thermal expansion coefficients were calculated and visualized using the TTT program package [25].

The rigid-body motion was controlled using the following formula [26] for all bond lengths in the crystal structure of ‘rhythmite’:

L² = l²₀ + 3/8π²(B_eq(A2) − B_eq(A1))

where L and l₀ are the corrected and observed A1–A2 bond lengths, respectively. B_eq(A1) and B_eq(A2) are the equivalent temperature factors of cation (A1) and anion (A2).

2.4. Chemical Analysis

The chemical composition of ‘rhythmite’ was studied using a Hitachi S-3400N scanning electron microscope equipped with an Oxford Instruments Energy Dispersive Spectrometer X-Max 20 (20 kV/1.7 nA, the working distance is 10 mm). Suitable grains were placed in epoxy blocks and polished without using water. The automatic recording of spectra was conducted using the AzTec Energy software package using the TrueQ technique. The following standards were used in the study of chemical composition: CaSO₄ for Ca, albite for Si and Al, InP for P, and NaCl for Cl.

2.5. Structural Complexity

The structural complexity of ‘rhythmite’ was calculated on the basis of Shannon information per atom (I_G) and per unit cell (^strI_G,total) using the following equations [27,28]:

$$I_G=\sum _{i=1}^K{p}_i{\mathit{log}}_2{p}_i\left({\displaystyle \frac{bit}{atom}}\right)$$

$$I_{G,total}=-\nu \sum _{i=1}^K{p}_i{\mathit{log}}_2{p}_i(bit/u.c.)$$

Herein, k is a multiplicity of a crystallographic orbit, and p_i is a random choice probability for an atom from the ith crystallographic orbit, that is

$$p_i=m_i/\nu$$

where m_i is a multiplicity of a crystallographic orbit of the reduced unit cell and ν is the number of atoms in the reduced unit cell. TOPOS Pro software was used for the calculation of structural complexity parameters [29].

Table 2. Atomic coordinates, equivalent isotropic displacement parameters (Ų), and bond valence sums (BVS, in v.u. = valence sums) of ‘rhythmite’ at 27 °C.

Atom	x	y	z	BVS 1	BVS 2 EcoN21	U(eq)
Ca1	0.4396(1)	1/4	0.1858(2)	1.95	1.96	0.0341(5)
Ca2	0.55835(6)	0.40634(7)	0.45282(8)	2.10	2.04	0.0127(2)
Ca3	0.3723(1)	1/4	0.4963(1)	2.54	2.45	0.0177(4)
Ca4	0.21231(7)	0.40009(8)	0.27646(8)	1.95	1.94	0.0168(2)
Ca5	0.0945(2)	1/4	0.5009(2)	0.96	1.03	0.0169(7)
Ca6	0.23618(7)	0.44771(8)	0.59401(8)	1.88	1.89	0.0168(2)
Ca7	0.3535(1)	1/4	0.7576(1)	1.72	1.85	0.0157(3)
Ca8	0.40536(7)	0.42937(8)	0.92237(8)	1.94	2.02	0.0164(2)
Ca9	0.22429(10)	1/4	0.96939(13)	1.89	1.93	0.0184(4)
Ca10	0.07294(7)	0.0911(1)	0.78615(9)	1.84	1.85	0.0243(3)
Si1	0.40373(8)	0.4265(1)	0.6563(1)	3.90	3.94	0.0107(3)
Si2	0.23326(9)	0.4294(1)	0.8711(1)	3.98	3.97	0.0107(3)
Cl1	0.63220(1)	1/4	0.3546(2)	0.92	0.93	0.0216(4)
Cl2	0.41432(9)	0.1321(1)	0.3501(1)	0.92	1.00	0.0223(3)
Cl3	0.5218(1)	1/4	0.5767(2)	1.14	1.12	0.0209(4)
Cl4	0.23090(1)	1/4	0.4031(2)	1.12	1.21	0.0274(5)
Cl5	0.0535(1)	0.1223(1)	0.3420(1)	0.81	0.84	0.0378(4)
Cl6	−0.0520(1)	1/4	0.5339(2)	1.12	1.19	0.0232(4)
Cl7	0.07256(9)	0.4414(1)	0.5794(1)	1.18	1.22	0.0294(4)
Cl8	0.1572(2)	1/4	0.6994(2)	0.91	0.66	0.0374(6)
Cl9	0.18480(8)	0.6365(1)	0.6142(1)	1.01	1.03	0.0197(3)
O1	0.3439(2)	0.3509(3)	0.6119(3)	2.10	2.00	0.0153(8)
O2	0.4804(2)	0.4490(2)	0.5884(3)	2.06	2.02	0.0143(8)
O3	0.3518(2)	0.5176(2)	0.6587(3)	2.00	1.97	0.0133(8)
O4	0.4382(2)	0.3890(2)	0.7623(3)	1.89	1.89	0.0118(8)
O5	0.2040(2)	0.4646(2)	0.7615(3)	1.94	1.89	0.0144(8)
O6	0.2948(2)	0.3475(2)	0.8683(3)	2.11	2.06	0.0132(8)
O7	0.2822(2)	0.5115(2)	0.9230(3)	1.94	1.86	0.0143(8)
O8	0.1573(2)	0.3928(2)	0.9316(3)	1.89	1.93	0.0146(8)

¹ Bond valence parameters according to Brese and O’Keeffe (1991) [30]. ² Bond valence values calculated on the basis of a crystallographic information file (CIF) using the ECoN21 program [31].

Table 2. Atomic coordinates, equivalent isotropic displacement parameters (Ų), and bond valence sums (BVS, in v.u. = valence sums) of ‘rhythmite’ at 27 °C.

Atom	x	y	z	BVS 1	BVS 2 EcoN21	U(eq)
Ca1	0.4396(1)	1/4	0.1858(2)	1.95	1.96	0.0341(5)
Ca2	0.55835(6)	0.40634(7)	0.45282(8)	2.10	2.04	0.0127(2)
Ca3	0.3723(1)	1/4	0.4963(1)	2.54	2.45	0.0177(4)
Ca4	0.21231(7)	0.40009(8)	0.27646(8)	1.95	1.94	0.0168(2)
Ca5	0.0945(2)	1/4	0.5009(2)	0.96	1.03	0.0169(7)
Ca6	0.23618(7)	0.44771(8)	0.59401(8)	1.88	1.89	0.0168(2)
Ca7	0.3535(1)	1/4	0.7576(1)	1.72	1.85	0.0157(3)
Ca8	0.40536(7)	0.42937(8)	0.92237(8)	1.94	2.02	0.0164(2)
Ca9	0.22429(10)	1/4	0.96939(13)	1.89	1.93	0.0184(4)
Ca10	0.07294(7)	0.0911(1)	0.78615(9)	1.84	1.85	0.0243(3)
Si1	0.40373(8)	0.4265(1)	0.6563(1)	3.90	3.94	0.0107(3)
Si2	0.23326(9)	0.4294(1)	0.8711(1)	3.98	3.97	0.0107(3)
Cl1	0.63220(1)	1/4	0.3546(2)	0.92	0.93	0.0216(4)
Cl2	0.41432(9)	0.1321(1)	0.3501(1)	0.92	1.00	0.0223(3)
Cl3	0.5218(1)	1/4	0.5767(2)	1.14	1.12	0.0209(4)
Cl4	0.23090(1)	1/4	0.4031(2)	1.12	1.21	0.0274(5)
Cl5	0.0535(1)	0.1223(1)	0.3420(1)	0.81	0.84	0.0378(4)
Cl6	−0.0520(1)	1/4	0.5339(2)	1.12	1.19	0.0232(4)
Cl7	0.07256(9)	0.4414(1)	0.5794(1)	1.18	1.22	0.0294(4)
Cl8	0.1572(2)	1/4	0.6994(2)	0.91	0.66	0.0374(6)
Cl9	0.18480(8)	0.6365(1)	0.6142(1)	1.01	1.03	0.0197(3)
O1	0.3439(2)	0.3509(3)	0.6119(3)	2.10	2.00	0.0153(8)
O2	0.4804(2)	0.4490(2)	0.5884(3)	2.06	2.02	0.0143(8)
O3	0.3518(2)	0.5176(2)	0.6587(3)	2.00	1.97	0.0133(8)
O4	0.4382(2)	0.3890(2)	0.7623(3)	1.89	1.89	0.0118(8)
O5	0.2040(2)	0.4646(2)	0.7615(3)	1.94	1.89	0.0144(8)
O6	0.2948(2)	0.3475(2)	0.8683(3)	2.11	2.06	0.0132(8)
O7	0.2822(2)	0.5115(2)	0.9230(3)	1.94	1.86	0.0143(8)
O8	0.1573(2)	0.3928(2)	0.9316(3)	1.89	1.93	0.0146(8)

¹ Bond valence parameters according to Brese and O’Keeffe (1991) [30]. ² Bond valence values calculated on the basis of a crystallographic information file (CIF) using the ECoN21 program [31].

Table 3. Selected bond lengths (Å) of ‘rhythmite’ at 27 °C.

Si1―O1	1.625(4)	Si2―O5	1.623(4)
―O2	1.628(4)	―O6	1.624(4)
―O3	1.638(4)	―O7	1.629(4)
―O4	1.642(4)	―O8	1.647(4)
<Si1―O>	1.633	<Si2―O>	1.631
Ca1―Cl2	2.850(2)2X	Ca2―O2	2.332(4)
―Cl5	2.763(3)2X	―O2	2.347(4)
―Cl6	2.924(3)	―O3	2.422(4)
―Cl9	2.891(2)2X	―O8	2.292(4)
<Ca1―Cl>	2.847	―Cl1	2.978(2)
Ca3―O1	2.218(4)2X	―Cl2	2.872(2)
―Cl2	2.731(2)2X	―Cl3	2.946(2)
―Cl3	2.767(3)	<Ca2―O,Cl>	2.598
―Cl4	2.713(3)	Ca4―O3	2.279(4)
<Ca3―O,Cl>	2.563	―O5	2.501(4)
Ca5―Cl4	2.667(4)	―O7	2.364(4)
―Cl5	2.944(3)2X	―Cl1	3.169(2)
―Cl6	2.539(4)	―Cl4	2.841(2)
―Cl7	3.096(2)2X	―Cl5	2.868(2)
―Cl8	2.848(4)	―Cl9	2.836(2)
<Ca5―Cl>	2.876	<Ca4―O,Cl>	2.694
Ca7―O1	2.470(4)2X	Ca6―O1	2.361(4)
―O4	2.550(4)2X	―O3	2.398(4)
―O6	2.309(4)2X	―O5	2.308(4)
―Cl6	3.206(1)	―O7	2.375(4)
<Ca7―O,Cl>	2.552	―Cl7	2.802(2)
Ca9―O6	2.329(4)2X	―Cl9	2.996(2)
―O8	2.492(4)2X	<Ca6―O,Cl>	2.540
―Cl1	2.818(3)	Ca8―O4	2.283(4)
―Cl9	3.009(2)2X	―O6	2.369(4)
<Ca9―O,Cl>	2.639	―O7	2.441(4)
Ca10―O2	2.376(4)	―Cl5	3.181(1)
―O4	2.408(4)	―Cl6	2.865(1)
―O5	2.413(4)	―Cl7	2.861(2)
―O8	2.423(4)	―Cl7	2.882(2)
―Cl3	3.138(2)	―Cl9	3.140(2)
―Cl7	2.792(2)	<Ca8―O,Cl>	2.753
―Cl8	3.026(2)
<Ca10―O,Cl>	2.653

Table 3. Selected bond lengths (Å) of ‘rhythmite’ at 27 °C.

Si1―O1	1.625(4)	Si2―O5	1.623(4)
―O2	1.628(4)	―O6	1.624(4)
―O3	1.638(4)	―O7	1.629(4)
―O4	1.642(4)	―O8	1.647(4)
<Si1―O>	1.633	<Si2―O>	1.631
Ca1―Cl2	2.850(2)2X	Ca2―O2	2.332(4)
―Cl5	2.763(3)2X	―O2	2.347(4)
―Cl6	2.924(3)	―O3	2.422(4)
―Cl9	2.891(2)2X	―O8	2.292(4)
<Ca1―Cl>	2.847	―Cl1	2.978(2)
Ca3―O1	2.218(4)2X	―Cl2	2.872(2)
―Cl2	2.731(2)2X	―Cl3	2.946(2)
―Cl3	2.767(3)	<Ca2―O,Cl>	2.598
―Cl4	2.713(3)	Ca4―O3	2.279(4)
<Ca3―O,Cl>	2.563	―O5	2.501(4)
Ca5―Cl4	2.667(4)	―O7	2.364(4)
―Cl5	2.944(3)2X	―Cl1	3.169(2)
―Cl6	2.539(4)	―Cl4	2.841(2)
―Cl7	3.096(2)2X	―Cl5	2.868(2)
―Cl8	2.848(4)	―Cl9	2.836(2)
<Ca5―Cl>	2.876	<Ca4―O,Cl>	2.694
Ca7―O1	2.470(4)2X	Ca6―O1	2.361(4)
―O4	2.550(4)2X	―O3	2.398(4)
―O6	2.309(4)2X	―O5	2.308(4)
―Cl6	3.206(1)	―O7	2.375(4)
<Ca7―O,Cl>	2.552	―Cl7	2.802(2)
Ca9―O6	2.329(4)2X	―Cl9	2.996(2)
―O8	2.492(4)2X	<Ca6―O,Cl>	2.540
―Cl1	2.818(3)	Ca8―O4	2.283(4)
―Cl9	3.009(2)2X	―O6	2.369(4)
<Ca9―O,Cl>	2.639	―O7	2.441(4)
Ca10―O2	2.376(4)	―Cl5	3.181(1)
―O4	2.408(4)	―Cl6	2.865(1)
―O5	2.413(4)	―Cl7	2.861(2)
―O8	2.423(4)	―Cl7	2.882(2)
―Cl3	3.138(2)	―Cl9	3.140(2)
―Cl7	2.792(2)	<Ca8―O,Cl>	2.753
―Cl8	3.026(2)
<Ca10―O,Cl>	2.653

3. Results and Discussion

3.1. Raman Spectroscopy

The Raman spectrum of ‘rhythmite’ is shown in Figure 2 in comparison with that of another anthropogenic calcium chloride-silicate ‘albovite’, α-Ca₃SiO₄Cl₂ [20]. The main bands of both spectra correspond to symmetric and asymmetric vibrations of silicate tetrahedra [32]. The most intensive bands at 848 cm⁻¹ are identical for ‘rhythmite’ and ’albovite’ and are due to symmetric stretching vibrations of SiO₄ (ν₁), whereas the asymmetric stretching vibrations (ν₃) of the ‘rhythmite’ spectrum are presented by middle-intensity bands at 886 and 936 cm⁻¹. In-plane bending vibration modes (ν₄) are located near 600 cm⁻¹ (600 cm⁻¹ for ‘albovite’). Several low- and middle-intensity bands at 379, 436, and 474 cm⁻¹ (372 and 466 cm⁻¹ for ‘albovite’) are attributed to out-of-plane vibration modes (ν₂). Lattice modes are up to 200 cm⁻¹, and the low-intensity bands in the range of 200–300 cm⁻¹ are probably connected with vibrations of Ca-O(Cl) bonds. The similarity of the spectra of ‘rhythmite’ and ‘albovite’ can be explained by their close structural relations, as outlined below.

3.2. Crystal Structure

3.2.1. Cation Coordination

The crystal structure of ‘rhythmite’ contains ten symmetrically independent Ca sites (Figure 3), where all positions are fully occupied except for the Ca5 site, which has the occupancy of 0.5. The Ca1 and Ca5 sites are coordinated by seven Cl atoms, each with the CaCl₇ polyhedra that can be described as capped trigonal prisms. The same type of coordination with various distortion degrees is also observed for the Ca2, Ca4, Ca7, Ca9, and Ca10 sites. However, the composition of the Caφ₇ polyhedra (φ = O, Cl) is different and can be described as Ca2O₄Cl₃, Ca4O₃Cl₄, Ca7O₆Cl, Ca9O₄Cl₃, and Ca10O₄Cl₃. Such a variable coordination of Ca²⁺ cations in the same crystal structure is quite remarkable and is in obvious violation with the parsimony principle by Pauling, stating that “the number of essentially different kinds of constituents in a crystal tends to be small” [33].

The SiO₄ tetrahedra in ‘rhythmite’ are isolated from each other and have typical geometrical characteristics with the average bond lengths of <Si1-O> = 1.633 Å and <Si2-O> = 1.631 Å.

3.2.2. Structure Description

The crystal structure of ‘rhythmite’ can be described as a dense framework consisting of Ca polyhedra connected to each other primarily through common vertices or edges and to a lesser extent through faces (Figure 4a). In order to make the structure description more straightforward, we consider the crystal structure as being based upon Ca silicate framework formed by Ca²⁺ cations and SiO₄ tetrahedra (Figure 4b).

According to this model, the Cl⁻ ions and Ca1 and Ca5 sites bonded solely to Cl are removed from the consideration. The Ca silicate framework is porous and can be subdivided into fundamental building blocks (FBBs) with contours outlined by red dashed lines in Figure 4b. The atomic structure of this FBB is shown in Figure 5a.

The formula of a single FBB is [Ca₁₅(SiO₄)₄]¹⁴⁺, and this unit can be considered as extracted from the crystal structure of α-Ca₃SiO₄Cl₂ (‘albovite’) [20]. The latter structure can be considered as based upon Ca silicate [Ca₃(SiO₄)]²⁺ layers with the Cl⁻ ions in the interlayer (Figure 6a). The projection of the layer is shown in Figure 6b, where the red dashed line shows the contours of the FBB topologically identical to that observed in ‘rhythmite’ (Figure 6c). Thus, the crystal structures of ‘rhythmite’ and ‘albovite’ are closely related, based upon the same type of multinuclear Ca silicate FBBs. However, whereas in ‘albovite’ the FBBs are polymerized to form 2-dimensional layers, in ‘rhythmite’ they are linked by sharing common Ca atoms to form a 3-dimensional framework.

The linkage modes of the FBBs in ‘rhythmite’ are illustrated in Figure 5b,c. First, the FBBs share common Ca10 atoms to form chains running parallel to the a axis (Figure 5b), with a separation between the FBBs of ca. 8.54 Å (measured as the distance between the Ca7 atoms at the centres of the FBBs). Along the b and c axes, the FBBs are linked in a chessboard fashion by forming Ca-O bonds involving Ca2 and Ca6 atoms (Figure 5c). The distance between the FBB centres is ~10.66 Å. Each FBB is thus coordinated by two FBBs at 8.54 Å and four FBBs at 10.66 Å. The topology of the linkage of the FBBs corresponds to the distorted pcu net, which is the simplest net with 6-coordination of vertices [34]. The net drawn as the linkage of the Ca7 atoms (FBB centres) is shown in Figure 7.

3.3. Chemical Composition

The chemical composition of ‘rhythmite’ in wt (%) is provided in

Table 4. Chemical composition (wt (%)) of ‘rhythmite’ (1—Chesnokov et al. [1]; 2—our data) and formula coefficients calculated on the basis of our data (apfu).

Component	1	2	Component	2	Apfu (Cl + O = 58)
Ca	41.22	40.11	CaO	57.13	29.02
Fe	0.38	-
Si	8.05	7.79	SiO2	16.65	7.89
P	-	0.09	P2O5	0.125	0.05
Al	0.22	0.05	Al2O3	0.09	0.05
Cl	31.06	30.16	Cl	32.32	26.00
F	0.22	-	–O=Cl2	7.283
			Total	99.032

. It can be seen that our data are in general agreement with the data reported previously. The small admixtures of iron and fluorine noted earlier are absent in our analyses, while phosphorus was not detected in measurements by Chesnokov et al. [1,21]. As it was mentioned above, the chemical formula of ‘rhythmite’ was determined as Ca₄(SiO₄)₂·3CaCl₂ [21]. Taking into account the results of the crystal structure study, the empirical formula of ‘rhythmite’ can be given as Ca_29.02[(Si_7.89Al_0.05P_0.05)_Ʃ7.99O₃₂]Cl₂₆ (on the basis of Cl + O = 58). The ideal formula calculated on the basis of the results of the single-crystal X-Ray diffraction analysis is Ca₂₉(SiO₄)₈Cl₂₆, in perfect agreement with the chemical data. The formula reported by Chesnokov et al. agrees well with these results, taking into account that Ca₄(SiO₄)₂·3CaCl₂ × 4 = Ca₂₈(SiO₄)₈Cl₂₄. Thus, the formula given by Chesnokov et al. [21] and the formula reported herein differ in the minor relative amounts of Ca and Cl only.

3.4. Thermal Behaviour

‘Rhythmite’ is stable up to 627 °C and starts to lose its crystallinity in the temperature range of 627–727 °C. Further heating results in the formation of ‘albovite’, α-Ca₃SiO₄Cl₂, which is confirmed by the fact that about 30% of reflections in the diffraction pattern recorded at 727 °C can be assigned to this phase with the unit cell parameters corresponding to ‘albovite’: a = 9.969(5), b = 6.795(4), c = 10.966(6) Å, β = 105.96(5)°, and V = 714.2(7) ų. However, the quality of the diffraction data did not allow for perfect refinement (R_int = 0.167 and R_sigma = 0.3814).

The temperature dependencies of the unit cell parameters of ‘rhythmite’ and the section of the figure of thermal expansion coefficients are presented in Figure 8. The unit cell parameters increase uniformly in all temperature ranges, where the compound is stable. The following equations were used for the linear approximation of the temperature dependencies of the unit cell parameters (×10⁶ °C⁻¹):

a = 17.0030 + 0.2 × 10⁻³ T, R² = 0.9998;

b = 15.00958 + 0.3 × 10⁻³ T, R² = 0.9983;

c = 13.23346 + 0.1 × 10⁻³ T, R² = 0.9979;

V = 3375.84 + 0.17 × T, R² = 0.9933.

The calculation of the thermal expansion coefficients shows that the crystal structure of ‘rhythmite’ expands slightly anisotropically (α_max/α_min = 1.40) in the ab and bc planes and almost isotropically in the ac plane (α₃₃/α₁₁ = 1.02) with the following values (×10⁶ °C⁻¹): α₁₁ = 14.6(1), α₂₂ = 20.5(4), α₃₃ = 15.0(3), and α_V = 50.1(6) (room temperature) (Figure 8). Such character of thermal expansion can be explained by the framework construction of the crystal structure of ‘rhythmite’. The bond length analysis in the temperature range of 27–627 °C shows that SiO₄ tetrahedra remain relatively rigid with the relative changes in the average bond lengths equal to 0.12% and 0.24% for the Si1O₄ and Si2O₄ groups, respectively. The lowest thermal expansion is observed along the a axis, which can be explained by the presence of the chains of FBBs running parallel to this direction (Figure 5b). The thermal expansion of the structure along the b axis is the strongest, probably due to zigzag linkage of the Ca silicate FBBs (Figure 5c), which allows for the hinge mechanism of the temperature-induced structure distortions. It was also observed that the bond length changes are more significant for the Ca-Cl bonds compared to the Ca-O and Si-O bonds, in agreement with their lower bond valences.

3.5. Structural Complexity

The calculation of the structural complexity parameters for ‘rhythmite’ as the amounts of information per atom and per unit cell indicates that the crystal structure is complex and close to very complex compounds (>1000 bits), with I_G = 4.793 (bit/atom) and I_G,total = 920.313 (bit/u.c.). The high structural complexity can be explained by the modular construction of the Ca silicate framework built from multinuclear FBBs with the dimensions of ~12 × 10 × 9 ų. The modular construction was indicated as one of the factors leading to the increasing structural complexity in minerals and inorganic compounds [28], which also explains the high diversity of Ca coordination environments in ‘rhythmite’. It is of interest that the average total structural complexity for silicate minerals is about 400 bit per unit cell, which means that ‘rhythmite’ belongs to the group of rather complex inorganic silicate structures.

4. Conclusions

The results of the chemical, spectroscopic, and structural studies reported herein allowed us to refine the crystal chemical formula of ‘rhythmite’ as Ca₂₉(SiO₄)₈Cl₂₆, which differs from that proposed earlier by Chesnokov et al. [1]. ‘Rhythmite’ is chemically, structurally, and genetically related to α-Ca₃SiO₄Cl₂ (‘albovite’), with which it also has similar Raman spectra and thermal stability. The structure analysis reveals that ‘rhythmite’ is based upon a three-dimensional framework composed of the FBBs extracted from the crystal structure of ‘albovite’, which means that the latter can be considered as a parent structure for the former. This explains why the two structures are so different in their complexities: the derivative structures are usually more complex than their archetypes. It is also of interest that ‘rhythmite’ and ‘albovite’ form in technogenic environments under similar thermodynamic conditions, and the decomposition of the former results in the formation of the latter. Finally, it is noteworthy that, as far as we know, ‘rhythmite’ has no analogues among the known natural and synthetic compounds, which further proves that technogenic processes may lead to the formation of novel structural architectures of high information complexity [17,35].