Spectroscopic and Crystal-Chemical Features of Sodalite-Group Minerals from Gem Lazurite Deposits

: Five samples of di ﬀ erently colored sodalite-group minerals from gem lazurite deposits were studied by means of electron microprobe and wet chemical analyses, infrared, Raman, electron spin resonance (ESR) and UV-Visible spectroscopy, and X-ray di ﬀ raction. Various extra-framework components (SO 42 − , S 2 − and Cl − anions, S 3 •− , S 2 •− and SO 3 •− radical anions, H 2 O, CO 2 , COS, cis- as well as trans - or gauche -S 4 neutral molecules have been identiﬁed. It is shown that S 3 •− and S 4 are the main blue and purple chromophores, respectively, whereas the S 2 •− yellow chromophore and SO 3 •− blue chromophore play a subordinate role. X-ray di ﬀ raction patterns of all samples of sodalite-group minerals from lazurite deposits studied in this work contain superstructure reﬂections which indicate di ﬀ erent kinds of incommensurate modulation of the structures. The Baikal samples were taken from lazurite calciphyres which are coarse-grained, massive rocks consisting mainly of calcite, with subordinate diopside and lazurite, and minor pyrite, phlogopite, sodalite, nepheline, and bystrite. Calcite (white, gray, yellowish, with abundant gas–liquid inclusions) gives o ﬀ a pungent smell of hydrogen sulﬁde. Diopside forms white, grayish or colorless transparent prismatic, partly ﬂattened crystals. Pyrite occurs as separate crystals up to 1 mm across and their aggregates. Sodalite-group minerals form separate anhedral grains up to 5 mm across and granular aggregates. Their color is lilac (for the LSh sample, Figure 2), light blue (for the MD sample, Figure 3), blue (for the PH and KL samples), and dark blue (for the ZK sample, Figure 4). Electron microprobe analyses of the samples from lazurite deposits were carried out with a electron microprobe Tokyo, Japan) equipped with a high-resolution scanning electron microscope, an energy dispersion system (EDS) with SiLi detector with resolution of 133 eV, and ﬁve wave dispersion spectrometers (WDS); analyst: Lyudmila F. Suvorova. The chemical composition was measured with an electron microprobe that operated at an acceleration voltage of 20 kV, a current intensity of 10 nA, and a counting time of 10 s. The beam was scanned to 20 µ m in order to decrease thermal damage of the samples. Under these conditions, the studied minerals are stable with respect to the beam e ﬀ ect. The following standards and analytical lines were used: pyrope (Si, K α ), albite (Al, Na, K α ), diopside (Ca, K α ), orthoclase (K, K α ), barite (S, K α ), and Cl-apatite (Cl, K α ). The contents of the elements were calculated using the ZAF procedure. The relative standard deviation did not exceed 1.3% for Al and Si; 2% for Na, S, and Ca; 3% for Cl and K, which indicates a rather low degree of chemical heterogeneity for all studied samples. The back-scattered images obtained by scanning sample areas did not reveal sulﬁde inclusions (FeS 2 , FeS) which could be a source of errors in the determination of sulfur. The electron microprobe analyses were used for the determination of the total sulfur content in the mineral. Sulfate sulfur was determined by conventional “wet” chemical analysis using acidic decomposition Galina A. The content of sulﬁde sulfur was calculated as the di ﬀ erence between the total and sulfate sulfur.


Introduction
The crystal structures of sodalite-group minerals and related compounds are based on the aluminosilicate framework (Al x Si 1-x O 2 ) xbuilt by alternating layers of six-membered rings of (Si,Al)O 4 tetrahedra around the 3-fold axes, [0 0 z], [1/3 2/3 z], and [2/3 1/3 z] and hosting large cavities (so-called β-cages). The crystal-chemical diversity of these compounds is determined by the contents of extra-framework components including alkali and alkaline-earth cations (mainly, Na + , K + , Ca 2+ [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Metasomatic rocks enriched in blue sodalite-group minerals are used as a decorative stone with the general name "lapis lazuli" or "lazurite". The latter name is also applied to minerals of the sodalite group containing sulfide sulfur. Sodalite-group minerals from gem lazurite deposits have metasomatic origin and formed at temperatures below 600 • C [17]. The oldest Sar-e Sang deposit was discovered in ancient times in the Koksha valley, Badakhshan, Afghanistan, and now Afghan lapis lazuli is considered the best in the world. Its color varies from light blue and turquoise to deep blue and blue-violet. The most expensive stone is bright blue with a violet tint. The Baikal samples were taken from lazurite calciphyres which are coarse-grained, massive rocks consisting mainly of calcite, with subordinate diopside and lazurite, and minor pyrite, phlogopite, sodalite, nepheline, and bystrite. Calcite (white, gray, yellowish, with abundant gasliquid inclusions) gives off a pungent smell of hydrogen sulfide. Diopside forms white, grayish or colorless transparent prismatic, partly flattened crystals. Pyrite occurs as separate crystals up to 1 mm across and their aggregates. Sodalite-group minerals form separate anhedral grains up to 5 mm across and granular aggregates. Their color is lilac (for the LSh sample, Figure 2), light blue (for the MD sample, Figure 3), blue (for the PH and KL samples), and dark blue (for the ZK sample, Figure 4).
The Hn7981 sample (used for comparison) is typical bright blue gem-quality haüyne ( Figure 5) forming crystals up to 5 mm across in cavities of sanidinite from the Laach Lake volcano, Eifel paleovolcanic region, Germany. The associated minerals are sanidine, amphibole, and titanite. The Baikal samples were taken from lazurite calciphyres which are coarse-grained, massive rocks consisting mainly of calcite, with subordinate diopside and lazurite, and minor pyrite, phlogopite, sodalite, nepheline, and bystrite. Calcite (white, gray, yellowish, with abundant gas-liquid inclusions) gives off a pungent smell of hydrogen sulfide. Diopside forms white, grayish or colorless transparent prismatic, partly flattened crystals. Pyrite occurs as separate crystals up to 1 mm across and their aggregates. Sodalite-group minerals form separate anhedral grains up to 5 mm across and granular aggregates. Their color is lilac (for the LSh sample, Figure 2), light blue (for the MD sample, Figure 3), blue (for the PH and KL samples), and dark blue (for the ZK sample, Figure 4). Minerals 2020, 3       Electron microprobe analyses of the samples from lazurite deposits were carried out with a JXA_8200 electron microprobe (Jeol, Tokyo, Japan) equipped with a high-resolution scanning electron microscope, an energy dispersion system (EDS) with SiLi detector with resolution of 133 eV, and five wave dispersion spectrometers (WDS); analyst: Lyudmila F. Suvorova. The chemical composition was measured with an electron microprobe that operated at an acceleration voltage of The Hn7981 sample (used for comparison) is typical bright blue gem-quality haüyne ( Figure 5) forming crystals up to 5 mm across in cavities of sanidinite from the Laach Lake volcano, Eifel paleovolcanic region, Germany. The associated minerals are sanidine, amphibole, and titanite.  Electron microprobe analyses of the samples from lazurite deposits were carried out with a JXA_8200 electron microprobe (Jeol, Tokyo, Japan) equipped with a high-resolution scanning electron microscope, an energy dispersion system (EDS) with SiLi detector with resolution of 133 eV, and five wave dispersion spectrometers (WDS); analyst: Lyudmila F. Suvorova. The chemical composition was measured with an electron microprobe that operated at an acceleration voltage of Electron microprobe analyses of the samples from lazurite deposits were carried out with a JXA_8200 electron microprobe (Jeol, Tokyo, Japan) equipped with a high-resolution scanning electron microscope, an energy dispersion system (EDS) with SiLi detector with resolution of 133 eV, and five wave dispersion spectrometers (WDS); analyst: Lyudmila F. Suvorova. The chemical composition was measured with an electron microprobe that operated at an acceleration voltage of 20 kV, a current intensity of 10 nA, and a counting time of 10 s. The beam was scanned to 20 µm in order to decrease thermal damage of the samples. Under these conditions, the studied minerals are stable with respect to the beam effect. The following standards and analytical lines were used: pyrope (Si, Kα), albite (Al, Na, Kα), diopside (Ca, Kα), orthoclase (K, Kα), barite (S, Kα), and Cl-apatite (Cl, Kα). The contents of the elements were calculated using the ZAF procedure. The relative standard deviation did not exceed 1.3% for Al and Si; 2% for Na, S, and Ca; 3% for Cl and K, which indicates a rather low degree of chemical heterogeneity for all studied samples. The back-scattered images obtained by scanning sample areas did not reveal sulfide inclusions (FeS 2 , FeS) which could be a source of errors in the determination of sulfur. The electron microprobe analyses were used for the determination of the total sulfur content in the mineral. Sulfate sulfur was determined by conventional "wet" chemical analysis using acidic decomposition (analyst Galina A. Pogudina). The content of sulfide sulfur was calculated as the difference between the total and sulfate sulfur.
Electron microprobe analyses of the Hn7981 sample were carried out using a Tescan VEGA-II XMU electronic microscope (EDS mode, 20 kV, 400 pA; TESCAN, Brno, Czech Republic). Data reduction was carried out by means of the INCA Energy 450 software package (Oxford Instruments, Oxfordshire, UK). The size of the electron beam was 157-180 nm. The beam was scanned on an area 20 µm × 20 µm in order to minimise sample damage. The time of data acquisition was 50 s. The sample-to-detector distance was 25 mm. The standards used are: albite for Na and Si, sanidine for K, wollastonite for Ca, Al 2 O 3 for Al, BaSO 4 for S, CaF 2 for F, and NaCl for Cl.
The contents of CO 2 belonging to CO 2 molecules in sodalite cages were determined from IR spectra using the technique described in [21]. H 2 O in the Hn7981 sample was determined by gas chromatography of the products of ignition in oxygen at 1200 • C with a Vario Micro Cubeanalyser (Elementar GmbH, Frankfurt, Germany).
In order to obtain infrared (IR) absorption spectra, powdered samples were mixed with dried KBr, pelletized and analyzed using an ALPHA FTIR spectrometer (Bruker Optics, Karlsruhe, Germany) in the range of 360-4000 cm −1 with a resolution of 4 cm −1 . A total of 16 scans were collected for each spectrum. An IR spectrum of an analogous pellet prepared from pure KBr was used as a reference. The absorbance of the bands at 2341-2346 cm −1 was measured relative to the absorbance at 2500 cm −1 . The absorbance of the band used as an internal standard was measured at the absorption maximum in the range of 656-668 cm −1 ; the common tangents to two deepest minima in the range of 500-830 cm −1 were used as baselines.
Raman spectra of randomly oriented samples were obtained using an EnSpectr R532 spectrometer based on an OLYMPUS CX 41 microscope (Enhanced Spectrometry, San Jose, USA) coupled with a diode laser (λ = 532 nm) at room temperature. The spectra were recorded in the range from 100 to 4000 cm −1 with a diffraction grating (1800 gr mm -1 ) and spectral resolution about 6 cm −1 . The output power of the laser beam was in the range from 5 to 13 mW. The diameter of the focal spot on the sample was 5-10 µm. The backscattered Raman signal was collected with a 40× objective; signal acquisition time for a single scan of the spectral range was 1 s, and the signal was averaged over 50 scans. Crystalline silicon was used as a standard.
The X-ray diffraction study was carried out by the photo method on a single crystal (KFOR-4 camera, Burevestnik, Leningrad (St. Petersburg), USSR, CuKα radiation) and the powder diffraction method with an automatic powder diffractometer (D8 ADVANCE, Bruker, Berlin, Germany) equipped with a Göbel mirror. The powder X-ray diffraction patterns were obtained in step scan mode (in the 2θ range from 5 to 70 • ), using CuKα radiation, at an accelerating voltage of 40 kV, current of 40 mA, time per step of 1 s, and 2θ step of 0.02 • . The calculations of interplanar distances and intensities of diffraction lines were performed using the computational software that was delivered with the diffractometer (DIFFRAC Plus Evaluation package EVA, Bruker AXS, Karlsruhe, Germany). The description of the modulated structure was carried out following a previously published scheme [33].
Diffuse-light optical absorption spectra were measured at room temperature with a Perkin-Elmer Lambda 950 spectrophotometer (Perkin-Elmer, Shelton, CT, USA) in an integrating sphere. For measurements, the samples were placed in a quartz test tube made of KU-1 glass, which is transparent in the range of 200-1300 nm. The light beam was completely concentrated on the sample. Other details of the measurement procedure are described in previous reports [34][35][36].
The photoluminescence spectra were measured with excitation by laser radiation with a wavelength of 405 nm. The luminescence signal was recorded using a Hamamatsu H6780-04 photo module (185-850 nm) operating in the photon counting regime equipped by a MDR-2 monochromator (LOMO, St. Petersburg, Russia) with a diffraction grating of 600 lines per mm, at a spectral slit width of 0.2 nm. The measurements at 77 K were carried out in a flooded nitrogen cryostat; the sample was attached to a cryofinger and the temperature was recorded using a thermocouple.
ESR spectra were recorded using a RE-1306 X-band spectrometer (KBST, Smolensk, Russia) with a frequency of 9.358 GHz. Powdered samples were placed in a quartz test tube. The measurements were carried out at room temperature and in a quartz cryostat at 77 K.

Chemical Composition
Chemical data for the studied sodalite-group minerals are given in Table 1. Kinds and amounts of S-bearing extra-framework components were determined based on spectroscopic data (see below) and the charge-balance condition. Taking into account that the S 3 •− radical anion is an extremely strong blue chromophore, its contents were calculated only for the samples having bright blue to dark blue color.

Infrared Spectroscopy
The IR spectra of the studied samples are given in Figures

Infrared Spectroscopy
The IR spectra of the studied samples are given in Figures 6 and 7. All of them contain bands of O-H stretching and H-O-H bending vibrations (in the ranges of 3300-3700 and 1620-1690 cm -1 , respectively) which are due to the presence of H2O molecules (zeolitic water).  Characteristic IR bands of S-bearing groups which can occur in sodalite-group minerals are in the ranges of 1124-1142 cm -1 (asymmetric stretching vibrations of the SO4 2-group, the F2(ν3) mode), 610-650 cm -1 (bending vibrations of the SO4 2-group, the F2(ν4) mode), 583-587 cm -1 (antisymmetric stretching vibrations of the cis-conformer (C2v) of the chain-like S4 •radical anion, the B1 mode), 655-659 (antisymmetric stretching vibrations of the cis-conformer (C2v) of the linear S4 molecule, the B1   [21].
In IR spectra of most samples of sodalite-group minerals from lazurite deposits, a band of O-(Si,Al)-O bending vibrations in the range of 655-658 cm −1 is observed. In the IR spectrum of the LSh sample, this band is shifted towards 650 cm −1 which may be due to the presence of S 4 molecules (based on high-level quantum chemical calculations, the expected wavenumber of the antisymmetric stretching mode of free cis-S 4 (C 2v ) molecule is 655 cm −1 , but this band can shift towards lower wavenumbers because of the transformation of this molecule to gauche-S 4 in the sodalite cage: [32]). This assumption is in agreement with the Raman and electronic spectra (see below) as well as lilac color of this sample.
A shoulder at 530 cm −1 is observed in the IR spectrum of the LSh sample, but is absent in the spectra of other samples studied in this work. According to Raman and UV-Visible spectroscopic data (see below), this sample contains neutral S 4 molecules. Based on this fact and taking into account results of quantum chemical calculations [32,41], this band was tentatively assigned to stretching vibrations of trans-S 4 (C 2h ).
It is to be noted that the S 2− anion does not have inner degrees of freedom and, consequently, its absorption bands could not be observed in the wavenumber range of 360-3800 cm −1 .
The band at 1422 cm −1 in the IR spectrum of the ZK sample corresponds to calcite inclusions. A narrow and weak band at 2340-2342 cm −1 observed in the IR spectra of all studied samples is due to antisymmetric stretching vibrations of CO 2 molecules [11,21,32]. This band is accompanied by a very weak isotope satellite at 2275-2279 cm −1 corresponding to 13 C 16 O 2 . The samples LSh and KL are most CO 2 -rich.
The band at 2040 cm −1 observed in the IR spectrum of the KL sample is most probably due to the C-O stretching frequency of the COS molecule [42], which is to be expected in samples containing both sulfide sulfur and CO 2 . Noteworthy, a similar band (at 2044 cm −1 ) is present in the IR spectrum of lazurite with the highest content of carbon dioxide (0.44 CO 2 molecules per formula unit) [21].

Raman Spectroscopy
Raman spectra of the samples studied in this work are given in

Absorption Spectra in the Range of 250-1000 nm
Diffuse-light optical absorption spectra of sodalite-group minerals from lazurite deposits in the visible and near UV ranges are given in Figure 12. In the absorption spectra of blue PH and KL samples, a broad table-like absorption band is observed in the 450-800-nm region. It obviously consists of several absorption bands, but it is impossible to resolve its structure even when measuring the absorption at a temperature of 77 K. In the wavelength range below 450 nm, a smooth rise is Another specific feature of the Raman spectrum of the LSh sample is the presence of the strong bands at 331 and 681 cm −1 which are absent in the Raman spectra of other samples and correspond to symmetric and antisymmetric stretching vibrations of the chain-like cis-S 4 molecule [32]. It is to be noted that the LSh sample differs from other samples studied in this work by the position of the IR active band of the cis-S 4 molecule in the range of 650-658 cm −1 (Figure 6).
The assignment of Raman bands in the samples studied in this work ( Table 2) was made based on literature data [21,28,[30][31][32]43,44]. In particular, it was taken into account that the S 3 •− radical anion (a blue chromophore) is characterized by a series of characteristic bands in the ranges of 245-265, 543-550, and 578-585 cm −1 (bending, symmetric stretching and antisymmetric stretching fundamentals, respectively) [21,30,44] as well as a series of rather strong bands of overtones and combination modes. The high intensities of overtones may be due to partial absorption of the laser light resulting in the Resonance Raman effect. It was also shown by means of quantum chemistry methods that fundamental modes of the most stable cis-conformer of free S 4 •− radical anion correspond to the Raman shifts of 277-286, 284-296, 583-587, and 609-610 cm −1 (the band at 583-587 cm −1 is IR active) [32]. Corresponding predicted ranges of wavenumbers for the free cis-S 4 molecule are 319-334, 326-339, 655-659, and 684-688 cm −1 whereas for the nonplanar gauche-conformer of S 4 in sodalite cage wavenumbers in the range 533-577 cm −1 are predicted [32]. The bands at 588-589 cm −1 in Raman spectra of green and blue lazurite have been assigned to stretching vibrations of the S 2 •− radical anion (a yellow chromophore) [30]. Analogous weak bands (at 580 and 605 cm −1 ) are observed in the Raman spectrum of yellow F-dominant sodalite-group mineral ( Figure 11) with the empirical formula (Na 5

Absorption Spectra in the Range of 250-1000 nm
Diffuse-light optical absorption spectra of sodalite-group minerals from lazurite deposits in the visible and near UV ranges are given in Figure 12. In the absorption spectra of blue PH and KL samples, a broad table-like absorption band is observed in the 450-800-nm region. It obviously consists of several absorption bands, but it is impossible to resolve its structure even when measuring the absorption at a temperature of 77 K. In the wavelength range below 450 nm, a smooth rise is

Absorption Spectra in the Range of 250-1000 nm
Diffuse-light optical absorption spectra of sodalite-group minerals from lazurite deposits in the visible and near UV ranges are given in Figure 12. In the absorption spectra of blue PH and KL samples, a broad table-like absorption band is observed in the 450-800-nm region. It obviously consists of several absorption bands, but it is impossible to resolve its structure even when measuring the absorption at a temperature of 77 K. In the wavelength range below 450 nm, a smooth rise is observed associated with the Urbach edge of the fundamental absorption of lazurite-related minerals. The spectrum of the ZK sample contains a broad absorption band with a maximum at about 600 nm. The width of this band at its half height (FWHM = 200 nm) is smaller than that in the spectra of the PH and KL samples (FWHM = 300 nm). The absorption spectra of the LSh and MD samples have a more pronounced structure. In the spectrum of the LSh sample, two local absorption maxima can be distinguished at 525 and 600 nm. The absorption band at 525 nm can be associated with the S4 neutral molecule (the C2v conformer [32,41]). The absorption spectrum of the MD sample contains bands with distinct absorption maxima at 420 and 600 nm and a weakly pronounced maximum at 680 nm. Upon excitation with 420 nm radiation, the LSh and MD samples exhibit characteristic luminescence in the yellow-red region of the spectrum, 530-700 nm. The luminescence spectrum has a vibrational structure with a distance between the satellites of about 590 cm -1 . When the sample is cooled to 77 K, the vibrational structure becomes more pronounced (Figure 13). The observed luminescence and absorption at 420 nm are associated with the S2 •centers [45].  The absorption spectra of the LSh and MD samples have a more pronounced structure. In the spectrum of the LSh sample, two local absorption maxima can be distinguished at 525 and 600 nm. The absorption band at 525 nm can be associated with the S 4 neutral molecule (the C 2v conformer [32,41]). The absorption spectrum of the MD sample contains bands with distinct absorption maxima at 420 and 600 nm and a weakly pronounced maximum at 680 nm. Upon excitation with 420 nm radiation, the LSh and MD samples exhibit characteristic luminescence in the yellow-red region of the spectrum, 530-700 nm. The luminescence spectrum has a vibrational structure with a distance between the satellites of about 590 cm −1 . When the sample is cooled to 77 K, the vibrational structure becomes more pronounced (Figure 13). The observed luminescence and absorption at 420 nm are associated with the S 2 •− centers [45].

ESR Spectroscopy
The ESR spectra of the KL and PH samples have similar broad bands with the g-factors of 2.046, 2.030, and 2.012 ( Figure 14). In the spectra of the samples cooled to 77 K, these bands are only slightly resolved. The observed ESR signal is typical of many samples of lazurite-related minerals and ultramarine and is associated with the S3 •radical anion [46]. The ESR spectrum of the ZK sample contains one broad band with a g-factor of 2.030. This signal is also associated with the S3 •centers [8,47]. It is noted [46] that the presence of a single isotropic band in the ESR spectrum of ultramarine samples with a high sulfur content is associated with the presence of the S3 •radical anions having the same local environment in sodalite cages. The observed structure of the ESR spectra of the PH and KL samples can be explained by different degree of distortion of S3 •radical anions due to their different local environments. This can also be responsible for the plateau-like absorption of the spectra of these samples in the visible region. The absorption with a maximum at 600 nm in the spectrum of the ZK sample corresponds to the transition from the ground state 2B1 of S3 •to the excited state, 2A2. The transition to the 2A1 state, which corresponds to a wavelength of 690 nm, is also possible. This transition may be related to the red edge in the absorption spectrum.
In the LSh and MD samples, the ESR signal is an order of magnitude weaker than in PH, KL, and ZK. A weak signal from S3 •centers is observed in the ESR spectrum of the LSh sample. In the ESR spectrum of the MD sample, this signal has a higher intensity, which also correlates with the absorption spectrum: the intensity of the band with a maximum at 600 nm in the spectrum of MD is higher than in the spectrum of LSh. Additionally, in both samples, absorption with a g-factor of 2.008 is observed, which may be due to the S2 •radical anion [48]. This assumption is confirmed by the luminescence spectra. In the ESR spectrum of the MD sample, one more band was recorded with a g-factor of 2.002. This signal is close to the signal of a free electron and can be associated both with

ESR Spectroscopy
The ESR spectra of the KL and PH samples have similar broad bands with the g-factors of 2.046, 2.030, and 2.012 ( Figure 14). In the spectra of the samples cooled to 77 K, these bands are only slightly resolved. The observed ESR signal is typical of many samples of lazurite-related minerals and ultramarine and is associated with the S 3 •− radical anion [46]. The ESR spectrum of the ZK sample contains one broad band with a g-factor of 2.030. This signal is also associated with the S 3 •− centers [8,47]. It is noted [46] that the presence of a single isotropic band in the ESR spectrum of ultramarine samples with a high sulfur content is associated with the presence of the S 3

X-ray Diffraction
The X-ray diffraction patterns of all samples of sodalite-group minerals from lazurite deposits studied in this work contain basic and superstructure reflections. Basic reflections correspond to cubic pseudo-cells and space group P-43n. Superstructure reflections observed as satellites of the basic reflections (Figures 15 and 16) define the kind of incommensurate modulation which cannot be described by integer hkl indices, unlike commensurate modulation when X-ray diffraction pattern can be described by integer hkl indices of an unit cell with a cell parameter being multiple of the basic a parameter. The modulation parameter n is determined by the displacement of the satellite from the main reflection along the reciprocal lattice axis.  In the LSh and MD samples, the ESR signal is an order of magnitude weaker than in PH, KL, and ZK. A weak signal from S 3 •− centers is observed in the ESR spectrum of the LSh sample. In the ESR spectrum of the MD sample, this signal has a higher intensity, which also correlates with the absorption spectrum: the intensity of the band with a maximum at 600 nm in the spectrum of MD is higher than in the spectrum of LSh. Additionally, in both samples, absorption with a g-factor of 2.008 is observed, which may be due to the S 2 •− radical anion [48]. This assumption is confirmed by the luminescence spectra. In the ESR spectrum of the MD sample, one more band was recorded with a g-factor of 2.002. This signal is close to the signal of a free electron and can be associated both with an anion vacancy that has captured an electron [49] and with the SO 3 •− paramagnetic center [50].
This signal practically does not change during cooling.

X-Ray Diffraction
The X-ray diffraction patterns of all samples of sodalite-group minerals from lazurite deposits studied in this work contain basic and superstructure reflections. Basic reflections correspond to cubic pseudo-cells and space group P-43n. Superstructure reflections observed as satellites of the basic reflections (Figures 15 and 16) define the kind of incommensurate modulation which cannot be described by integer hkl indices, unlike commensurate modulation when X-ray diffraction pattern can be described by integer hkl indices of an unit cell with a cell parameter being multiple of the basic a parameter. The modulation parameter n is determined by the displacement of the satellite from the main reflection along the reciprocal lattice axis.
pseudo-cells and space group P-43n. Superstructure reflections observed as satellites of the basic reflections (Figures 15 and 16) define the kind of incommensurate modulation which cannot be described by integer hkl indices, unlike commensurate modulation when X-ray diffraction pattern can be described by integer hkl indices of an unit cell with a cell parameter being multiple of the basic a parameter. The modulation parameter n is determined by the displacement of the satellite from the main reflection along the reciprocal lattice axis.  Analysis of powder diffraction patterns showed that the distribution pattern of satellites in the samples studied in this work is the same as in the previously studied lazurite from the Baikal Lake region and Afghanistan [51]. The only difference is in the value of the modulation parameter. The n parameters of the samples LSh, PH, and MD are close to each other and are equal to 0.218, 0.218, and 0.214, respectively. The samples KL and ZK are characterized by different n values, 0.164 and 0.147, respectively. The powder X-ray diffraction pattern of the ZK sample has been discussed in detail elsewhere [8]. Powder data for the samples MD and KL are given in Tables 3 and 4. The calculated interplanar distances of the satellites (ds) were obtained from the modified quadratic form for cubic crystals: ds -2 = [(h ± n) 2 + (k ± n) 2 + l 2 ]: a 2 where a is the parameter of the cubic pseudo-cell calculated from the basic reflections; h, k, and l are the indices of the main reflection, near which a given satellite is located; n is the incommensurate modulation parameter.   Analysis of powder diffraction patterns showed that the distribution pattern of satellites in the samples studied in this work is the same as in the previously studied lazurite from the Baikal Lake region and Afghanistan [51]. The only difference is in the value of the modulation parameter. The n parameters of the samples LSh, PH, and MD are close to each other and are equal to 0.218, 0.218, and 0.214, respectively. The samples KL and ZK are characterized by different n values, 0.164 and 0.147, respectively. The powder X-ray diffraction pattern of the ZK sample has been discussed in detail elsewhere [8]. Powder data for the samples MD and KL are given in Tables 3 and 4. The calculated interplanar distances of the satellites (d s ) were obtained from the modified quadratic form for cubic crystals: d s -2 = [(h ± n) 2 + (k ± n) 2 + l 2 ]: a 2 where a is the parameter of the cubic pseudo-cell calculated from the basic reflections; h, k, and l are the indices of the main reflection, near which a given satellite is located; n is the incommensurate modulation parameter.
The powder X-ray diffraction pattern of the MD sample (Table 3) contains superstructure reflections of two types, which correspond to commensurate and incommensurate superstructures. A small number of reflections of a commensurate superstructure are observed, lying between the rows of the main reflections, at equal distances from them (these reflections correspond to the d values of 4.859, 4.139, 3.862, 3.111, and 2.943 Å (Table 3). More than half of the total number of lines in the diffraction pattern of the MD sample are satellites corresponding to an incommensurate superstructure. A low value of the reliability index R = [Σ(|d meas − d calc |)]P -1 = 0.002 Å (where P is the total number of satellites) indicates constancy of incommensurate displacement of all satellites from the main reflections.  In Table 4, three quarters of the total number of lines in the diffraction pattern of the KL sample are satellites. The value of the reliability index calculated using the value of the parameter of incommensurate modulation n = 0.164, refined from the powder X-ray diffraction pattern, is R = 0.001 Å. If the superstructure were considered as commensurate (n = 1/6), then the calculated value of R would be equal to 0.002 Å, which is twice as high as the above result. Thus, the superstructure in the KL sample is incommensurate.

Discussion
The empirical formulae of most sodalite-group minerals from gem lazurite deposits, being calculated under the assumption that all sulfur belongs to the SO 4 2 Application of a combination of spectroscopic methods makes it possible to identify the S-bearing species, which are most abundant in a given sample.
Following an established tradition, the name "lazurite" is usually applied to blue sulfur-bearing minerals of the sodalite group, or even to all sulfur-rich sodalite-group minerals from lapis lazuli deposits, independent of their color. However, according to the nomenclature of minerals accepted by the International Mineralogical Association [18], cubic members of the sodalite group with the idealized formulae Na 6  ratio may be an indication of oxygen and sulfur dioxide fugacities during mineral formation [23]. Based on this hypothesis, we can suppose that there are indications of a high activity of sulfur and low oxygen fugacity at latest stages of the formation of lazurite-bearing assemblages at these localities.
Minerals 2020, 3, x 20 of 24 [17][18][19]. The fact of epitaxy was established by us based on the cleavage direction. In mineral assemblages containing S3 •--rich lazurite ZK (earlier described in detail in [8]), grains of forsterite and pyroxene are corroded by lazurite, and some lazurite crystals formed as a result of recrystallization of an initial sodalite-group mineral.    [17][18][19]. The fact of epitaxy was established by us based on the cleavage direction. In mineral assemblages containing S3 •--rich lazurite ZK (earlier described in detail in [8]), grains of forsterite and pyroxene are corroded by lazurite, and some lazurite crystals formed as a result of recrystallization of an initial sodalite-group mineral.    Hypothetically, anionic and neutral extra-framework components (Cl -, OH -, F -, AlF6 3-, SO4 2-, S 2-, S3 -, CO3 2-, C2O4 2-, CO2, H2O, CH4 etc.) occurring in β-cages of minerals belonging to the sodalite and cancrinite groups could be used as important geochemical markers [21][22][23], and the SO4 2-/S3 •ratio may be an indication of oxygen and sulfur dioxide fugacities during mineral formation [23]. Based on this hypothesis, we can suppose that there are indications of a high activity of sulfur and low oxygen fugacity at latest stages of the formation of lazurite-bearing assemblages at these localities.
Author Contributions: N.V.C., A.N.S., and R.S. wrote the paper. N.V.C. obtained and interpreted the IR spectra and obtained a part of the chemical data. M.F.V. obtained and interpreted the Raman spectra. R.Y.S. obtained and interpreted the ESR and UV-Visible spectra. A.N.S. obtained X-ray diffraction data, and interpreted compositional and X-ray diffraction data.
Funding: This work was supported by the Russian Foundation for Basic Research, grant no. 18-29-12007-mk. A part of this work (IR spectroscopy and a part of chemical analyses) has been carried out in accordance with the state task, state registration number ААAА-А19-119092390076-7.