EMP analyses of biotite were performed with a Cameca SX100 SEM (scanning electron microscope) system with a wavelength-dispersive detector by using the following operating conditions: 15 kV electron accelerating voltage, 20 nA beam current, and a ∼ 10 µm beam-spot size on the sample surface. The employed standards were LiF for F; albite for Na; MgO for Mg; corundum for Al; andradite for Si, Ca, and Fe; vanadinite for Cl; orthoclase for K; MnTiO3 for Ti and Mn; NiO for Ni; olivenite for Cu; Pb-containing glass for Zn; SrTiO3 for Sr; and Ba-containing glass for Ba and Cr2O3 for Cr. The acquisition times were 20 s for Mg, Al, Si, K, Ca, and Fe; 30 s for Na, Cl, and Ti; 60 s for Mn, Ni, Cu, Zn, Sr, Ba, and Cr; and 120 s for F. EMP data were acquired on 50–100 separate spots on each sample and then averaged to yield the chemical compositions and statistical standard deviations (σ) presented in Table S1 in the Supplement. The content of hydroxyl groups, as well of tetrahedrally and octahedrally coordinated Fe3+ (TFe3+ and MFe3+, respectively), was calculated using the charge-balance approach of Li et al. (2020), who developed a machine learning method based on principal component regression (PCR). This method was built up on a dataset of more than 150 well-characterized biotite reference samples whose crystallochemical data have previously been refined. Biotite samples have randomly been categorized into two groups, namely the training and the test set, where the latter one has been used to testify the performance of the model and to establish a linear regression coefficient matrix. Based on the derived matrix, the atomic proportions of elements, including TFe3+, MFe2+, MFe3+, XOH, and XO2-, can be precisely calculated with R2>0.95 for the major elements. We have assumed that the analyzed biotite samples are lithium-free, which did not affect the quality of the calculated chemical formulae, as pointed out by Li et al. (2020). Elements whose standard deviation was greater than the average content were not included in the calculated chemical formulae. Moreover, biotite formulae were calculated by assuming that the valence state of Ti is 4+, after Scordari et al. (2013).

Selected biotite samples were further subjected to 57Fe Mössbauer spectroscopy to verify the fraction of Fe3+ cations and their distribution over the T and M sites, using the setup available at the Universität Salzburg, Austria. Data were acquired at room temperature using an apparatus in a horizontal arrangement (57Fe Co / Rh single-line thin source, constant acceleration mode with symmetric triangular velocity shape, multi-channel analyzer with 1024 channels, and regular velocity calibration against metallic Fe). Absorbers were prepared with a nominal density of about 5 mg Fe cm-2 with the mica sample being filled into Cu rings, with an inner diameter of 10 mm and depth of 2 mm and fixed with epoxy resin. The spectra were recorded with the absorber being oriented at the so-called magic angle (54∘) to the source to avoid texture effects. Data evaluation was done with the RECOIL program suite, using the Voigt-based hyperfine distribution approach; for details on data evaluation, see Redhammer et al. (2005).

Raman spectra were collected with a Horiba Jobin Yvon T64000 triple-monochromator system coupled with a Symphony LN2-cooled CCD (charge-coupled device) detector and an Olympus BH41 confocal microscope with a 50× long working distance objective. The green line (λ=514.532 nm) of a Coherent Innova 90C FreD Ar+ laser was used to excite the Raman scattering. The spectral resolution achieved with the green laser was ∼ 2 cm-1, while the instrumental peak position accuracy was ∼ 0.35 cm-1. The Raman spectrometer was calibrated using the 520.5 cm-1 line of a silicon standard wafer. The laser-spot diameter on the sample surface was ∼ 2 µm, while the laser power on the sample surface was 7.9 mW. The spectra were collected in the spectral ranges 15–1215 and 3000–3900 cm-1, with exposure times varying between 20 and 60 s and averaging 10 to 30 repeated acquisitions to improve the signal-to-noise ratio. The measured Raman spectra were baseline-corrected with a polynomial function, temperature-reduced to account for the Bose–Einstein distribution of phonons, and fitted with pseudo-Voigt peak-shape functions PV = μL+(1-μ)G (L and G stand for Lorentz and Gauss peak-shape functions, respectively, while μ is a variable weight coefficient) to define the peak positions ω, FWHMs, and integrated intensities I. The usage of the OriginPro 2019 software package facilitated the Raman data evaluation.

In general, Raman peak intensities depend on the crystal orientation as well as on the mutual orientation of the polarization of the incident (Ei) and scattered light (Es). Considering that in trioctahedral micas such as biotites the OH groups are perpendicular to the cleavage plane (Libowitzky and Beran, 2004), i.e., the crystallographic (001) plane, parallel-polarized (Ei||Es) and cross-polarized (Ei⊥Es) Raman spectra were collected in backscattered geometry from two different orientations of the biotite crystals, with Ei parallel (Fig. 1a) and perpendicular to the cleavage plane (Fig. 1b). This results in four scattering geometries (given in Porto's notation): horizontal parallel-polarized z‾(yy)z, horizontal cross-polarized z‾(xy)z, vertical parallel-polarized y‾(zz)y, and vertical cross-polarized y‾(xz)y geometries, with z perpendicular to the (001) plane and x⊥y⊥z.

Various phyllosilicate mineral groups in a rock sample or a cultural-heritage object can straightforwardly be distinguished, based on their Raman spectra (Fig. 2). Indeed, compositional variations, the stacking sequence of the tetrahedral and octahedral sheets, and the presence or absence of interlayer species affect significantly the Raman spectra. The major differences in the Raman spectra of the main layered silicates (Fig. 2) are in the ranges 100–500 cm-1, dominated by MO6 vibrations; around 600–800 cm-1, generated by TO4-ring modes (i.e., T-Ob-T modes); and 3500–3800 cm-1, generated by OH-stretching vibrational modes (Tlili et al., 1989; McKeown et al., 1999; Lacalamita et al., 2020) and can be used to fingerprint the phyllosilicate mineral group. Particularly, the OH-stretching region is characterized by multiple Raman peaks in the case of 1 : 1 layer silicates (antigorite, (Mg,Fe)3Si2O5(OH)4; dickite, Al2Si2O5(OH)4), whereas in 2 : 1 layer silicates with empty interlayer space (talc and pyrophyllite; Mg3Si4O10(OH)2 and Al2Si4O10(OH)2, respectively), there is only one sharp peak. If the interlayer space is filled by monovalent cations, as in the case of muscovite, biotite, or illite (K0.65(Al,Mg,Fe)2(Si,Al)4O10(OH)2), or by H2O molecules along with mono-/divalent cations, as in the case vermiculite ((Mg,Fe3+,Al3+)3(Al,Si)4O10(OH)2 ⚫ 4H2O), the OH stretching produces broad Raman peaks.

According to group-theory analysis, the most common C2/m polytype of biotite shows a total of 63 optical phonon modes at the Γ point (Kroumova et al., 2003). Among them, 33 are IR active and 30 Raman active (see Table 2). The Raman-active modes of biotite are of Ag and Bg symmetries, and they have the following Raman tensor components: Ag:axxaxzayyaxzazzandBg:axyaxyayzayz. Consequently, the parallel-polarized Raman spectra of oriented crystals will be generated only from the Ag modes, whereas depending on the orientation, both Ag and Bg modes can contribute to the cross-polarized spectra. In our case, the vertical parallel-polarized Raman spectra y‾(zz)y are determined from the zz component of the polarizability tensor α of the Ag mode, Ag(azz), while the vertical cross-polarized spectra y‾(xz)y are dominated by the Ag(axz). Accordingly, the horizontal parallel-polarized spectra z‾(yy)z are characterized by the Ag(ayy) component, whilst the horizontal cross-polarized spectra z‾(xy)z are characterized by the Bg(axy) component. Given that the orientation of the binary b axis with respect to the laboratory coordinate axes (x,y) is usually unknown, Ag(axx) and Bg(azy) may also contribute to the horizontal parallel-polarized and vertical cross-polarized spectra, respectively.

Table 2 reveals that H atoms occupy the 4i Wyckoff position and generate 2Ag+Bg Raman-active modes. Considerations of the directions of the atomic vector displacements via the Bilbao Crystallographic Server (Kroumova et al., 2003) reveal that one Ag mode corresponds to the OH-stretching vibration perpendicular to the (001) plane, while one Ag and the Bg mode are related to the OH-librational modes, with H+ motions within the (a,b) plane and causing a change in the M–O–H bond angle. Therefore, the presence of more than one Raman peaks in the OH-stretching region implies a chemical deviation from the endmember composition, due to different types of octahedrally coordinated cations bonded to OH groups. Such behavior has already been observed in other hydrous minerals like amphiboles and tourmalines (Leissner et al., 2015; Watenphul et al., 2016a; Hawthorne, 2016).

As the structure of biotite-group minerals is strongly anisotropic, it is obvious that the Raman scattering can chiefly depend on the crystal orientation with regard to the polarization of the incident and scattered light. However, since C2/m is a nonpolar crystal class, the orientation of the biotite crystals will influence the relative intensities but not the Raman peak positions. Biotite grains, which are exposed on the sample surface and can be non-destructively probed by Raman spectroscopy, can be randomly oriented. Since the relative intensities of the Raman peaks depend on the crystal orientation with respect to the polarization of the incident and scattered light, Raman spectra collected from biotite grains within the same rock/cultural-heritage specimen may appear inconsistent at a first glance. Moreover, some of the Raman peaks may be suppressed in specific experimental geometry. Therefore, to clarify the effect of the grain orientation on the Raman spectra and identify Raman signals that can be resolved independently of the grain orientation, we have systematically measured representative biotite single crystals in different scattering geometries. Figure 3 presents the Raman spectra of a phlogopite measured in the four different scattering geometries specified above. It is apparent that parallel-polarized spectra are much stronger than the cross-polarized ones, and hence the latter do not provide any additional information that is not included in the former. Therefore, Ag modes should dominate the spectra regardless of the crystal orientation. For the framework vibrations the y‾(zz)y spectrum differs considerably from the z‾(yy)z, in accordance with the group-theory prediction (azz≠ayy). At the same time, although axx and ayy are allowed to be different by symmetry constraints, in a horizontal orientation z‾(yy)z Raman spectra remained practically the same upon rotation of the biotite samples around the laser beam direction, indicating that the axx and ayy Raman tensor components are almost equal. The OH-stretching modes contribute only to the parallel-polarized spectra, generating a multi-component Raman band. The overall OH-stretching Raman scattering is stronger in y‾(zz)y than in z‾(yy)z, but the relative intensities of band components are the same in both scattering geometries. Thus, regardless of selected orientation and induced photoluminescence, the strongest Raman peaks of biotite samples can be identified at wavenumbers close to 190, 650, 680, 730, 780, and 1020 cm-1 and between 3500–3800 cm-1 and used for crystallochemical analysis.

Figure 4 shows the characteristic Raman spectra of selected biotite samples with different Mg contents at the M site. One can divide the Raman scattering into four spectral ranges according to the dominant atomic displacements: range I (15–600 cm-1), dominated by octahedral vibrations; range II (600–800 cm-1), dominated by TO4-ring modes comprising vibrations of T–Ob–T linkages; range III (800–1215 cm-1), generated by TO4-stretching modes; and range IV (3500–3800 cm-1), arising from OH-stretching modes.

The strongest Raman feature of spectral range I in both parallel-polarized spectra (Fig. 4) occurs near 190 cm-1 for phlogopite, and it shifts considerably towards lower wavenumbers for annite with MMg < 0.70 apfu (Figs. 5a and 6a). As in general ω∼Kμ (K is the force constant and μ is the reduced mass of atoms participating in the mode) and mFe>mMg while K(Fe2+-O) > K(Mg-O), this trend indicates one-mode behavior of the mode near 190 cm-1, due to the change in mass of the M cations (Chang and Mitra, 1971). In this case, only one peak can be observed corresponding to the mixed (Mg3-xFex) concentration at the M site and whose ω lineally depends on the concentration x. Our experimental observations are in accordance with previous studies indicating that MO6 vibrations contribute considerably to the Raman scattering below 600 cm-1 (Loh, 1973; Tlili et al., 1989; McKeown et al., 1999; Tutti and Lazor, 2008). Moreover, the strong Raman scattering near 150 cm-1 observed in monoclinic amphiboles shows the same trend of ω vs. MMg content (Waeselmann et al., 2020), implying that this is a general feature of complex silicates containing strips of linked tetrahedral and octahedral sheets. Biotites are also similar to amphiboles (Waeselmann et al., 2020) by the appearance of additional Raman scattering between 500–550 cm-1 when MFe3+ is present (see z‾(yy)z spectra in Fig. 4 and Table 1).

The spectral profile of range II changes in a rather complex way from one sample to another (Figs. 4 and S2) and can be fitted with up to four components, near 650, 680, 730, and 780 cm-1. The Raman-active phonon modes near 650 and 680 cm-1 produce strong peaks in both z‾(yy)z and y‾(zz)y geometries, but only the wavenumber of the former mode turned to be exclusively sensitive to T-site occupancy (see Fig. 7a). In fact, this is in accordance with the peak assignment by Tlili et al. (1989) and Lacalamita et al. (2020), attributing the peaks near 650 and 680 cm-1 to Si–Ob–Al and Si–Ob–Si bond vibrations, respectively. Our analysis revealed that both ω680 and FWHM680 are sensitive to MTi content (see Fig. 7c and e). Given that Ti occupies predominantly the M2 site, this result is in agreement with previous studies suggesting that the chemistry of the M2 site can affect the T–Ob–T vibrations (e.g., McKeown et al., 1999; Wang et al., 2015; Lacalamita et al., 2020). In addition, the Raman signal near 730 cm-1, well-resolved in z‾(yy)z and y‾(zz)y spectra (see Figs. 3 and 4), tends to shift to higher wavenumbers in the presence of A-site vacancies (see Fig. 8a).

We have expected the TO4-stretching modes in range III to be sensitive to the octahedral site occupancy, as in the case of Mg-Fe-Mn amphiboles (Waeselmann et al., 2020); however, we were not able to establish a rational dependence of the spectral parameters of these modes on the chemistry neither at the M site nor at the T site.

The reported observations for the framework phonon modes should be combined with the Raman-scattering results arising from OH-stretching modes to gain a detailed description of the entire biotite Raman spectrum and to comprehend its dependence on the site occupancy. As expected, range IV exhibits more than one peak generated by OH-stretching vibrations due to two-mode behavior, typical of complex hydrous silicates (Leissner et al., 2015; Watenphul et al., 2016a; Hawthorne, 2016). In such a case, more Raman peaks than those predicted by group-theory analysis can appear in the spectra, whose fractional intensities correlate with the composition x. This two-mode behavior of the OH-stretching phonon modes is caused by the perturbation of the K(O-H) force constant by the averaged M–O interactions in the surrounding triplet of MO6 octahedra sharing oxygen atom with the X-site hydroxyl group, 〈δK(M-O)〉. Thus the OH-stretching wavenumber will be ωOH∼K(O-H)-〈δK(M-O)〉μ, resulting in different Raman/IR peaks for different M1M2M2 chemical configurations (paper on Raman; e.g., Lacalamita et al., 2020, paper on IR; Redhammer et al., 2000). It should be emphasized that according to group theory two H+ in the primitive unit cell participate into the OH-stretching Ag mode. At the same time, two instances of X(OH)- in the chemical formula correspond to three octahedrally coordinated M cations (M1M2M2). Hence, 〈δK(M-O)〉 is related precisely to those three octahedra, and consequently the intensities of the OH-stretching peaks arising from different M1M2M2 triplets can be used for the correct quantification of the chemical composition of the octahedral sheets in biotite.

Table 3 presents the assignment of the multi-component Raman scattering in the OH-stretching region of the analyzed biotites to specific M-site local arrangements, following the categorization by Vedder (1964) based on the valence state of the M1M2M2 triplet surrounding the OH groups and the possibility of a vacancy at the M site: (i) the N-type bands (normal; M2+M2+M2+), where the hydroxyl groups are surrounded by three divalent cations; (ii) the I-type bands (impurity; M2+M2+M3+), where the stretching modes are caused by hydroxyl groups surrounded by one trivalent and two divalent M-site cations; and (iii) the V-type bands (vacancy; M2+M2+□/M2+M3+□/M3+M3+□), where the local atomic arrangement of the OH bonds includes a vacancy and two occupied octahedral sites.

In accordance with the two-mode behavior approach, the strongest OH-stretching peak corresponds to the most abundant M1M2M2 chemical configuration. Since biotite represents a solid solution between phlogopite and annite, where Mg and Fe2+ are the dominant octahedrally coordinated cations, for each biotite sample the most intense OH-stretching peak should correspond to the most probable M2+M2+M2+ chemical species. Hence, weaker OH-stretching peaks will correspond to less probable M1M2M2 local configurations. Consequently, peaks related to MgMgMg-OH--K-X local configurations are observed for all of the studied phlogopite samples (B1, B2, B3, B5, B6, B7, B8, B10, B17, and B20) with the exception of sample B12, which shows an intermediate composition in the octahedral layer (see Table 1). However, the peak position slightly varies depending on the X-site anion adjacent to AK. Furthermore, the majority of the phlogopite samples exhibits OH-stretching modes in the range 3660–3670 cm-1 corresponding to MgMgFe3+ and MgMgAl, whose OH groups are involved in an OH--K-OH- local environment (Tlili et al., 1989; Scordari et al., 2006; Lacalamita et al., 2011; Scordari et al., 2012; Schingaro et al., 2013). It is worth noting that the gradual substitution of Mg by Al at the M site, emerging from the Al-Tschermak substitution mechanism, will downshift the peak position of the initial MgMgMg-OH--K-OH- local configuration by ∼ 30–35 cm-1, i.e., from ∼ 3705–3715 to 3670–3675 cm-1. This assumption corroborates the conclusions by Hawthorne et al. (2000), Scordari et al. (2012), and Watenphul et al. (2016a), who showed that a similar Raman peak shift towards lower frequencies has been monitored for the OH-stretching peaks in tremolites and phlogopite as well as for the W-site OH stretching in tourmalines.

At the same time, most of the examined annite samples (B4, B13, B14, B16, B18, B19, and B21) display the strongest OH-stretching N-type Raman peak between 3650 and 3660 cm-1 (Figs. S2 and S3, Table 3), corresponding to Fe2+Fe2+Fe2+-OH--K-X (Redhammer et al., 2000). For sample B16, an aluminian F-rich annite, the Raman peak at ∼ 3596 cm-1 is assigned to a Fe2+Al□-OH- local configuration (Redhammer et al., 2000) rather than to MgMg□-OH-, by taking into account the following aspects: (i) the peak centered at ∼ 3596 cm-1 being the strongest feature of the z‾(yy)z Raman spectrum of sample B16 (Fig. S2), indicating that it should be assigned to the most abundant cations at the M site, and (ii) the cationic distribution of the M site with MFe2+=1.54 apfu, MAl = 0.88 apfu, and MMg = 0.10 apfu.