Effect of Fe–Fe interactions and X -site vacancy ordering on the OH-stretching spectrum of foitite

. The OH-stretching infrared absorption spectrum of a tourmaline sample close to the foitite end-member is interpreted in the light of the density functional theory (DFT) modeling of iron-bearing Y 3 Z 6 clusters in tourmaline. The iron-bearing clusters reﬂect the Al-rich and Na-deﬁcient character of foitite and contain either two Fe 2 + and one Al 3 + or one Fe 2 + and two Al 3 + ions at the Y sites. The clusters are embedded in a tourmaline host structure with dravite composition. For the iron dimer models, the structural and vibrational properties corresponding to the ferromagnetic (FM) or anti-ferromagnetic (AFM) arrangement of the iron spins and the effect of vacancy ordering along the [001] axis are considered. A signiﬁcant difference in the relaxed structure of the FM and AFM clusters is observed, stemming from the electron delocalization and Fe–Fe bonding interactions in the FM cluster. These bonding interactions are not allowed in the AFM cluster. In this case, the valence electrons with opposite spins remain separately localized on the two Fe atoms. The AFM conﬁguration is more stable than the FM one in the theoretical models, provided that the description of the on-site Coulomb repulsion in Fe(3d) orbitals is improved within the DFT + U framework. Based on the theoretical results, the two bands at 3630 and 3644 cm − 1 in the vibrational spectra of iron-rich and Na-deﬁcient tourmalines are assigned to W OH groups associated with Y Fe 2 + 2 Y Al 3 + environments with an AFM coupling of Fe ions and surrounded by one and two vacant X sites, respectively. The two major V OH bands of the experimental spectrum are interpreted on the same basis, and these interpretations are extrapolated to Mn-bearing tourmalines


Introduction
The OH-stretching modes of hydrous minerals lead to characteristic signals in their infrared or Raman spectra (Libowitzky and Beran, 2006). The high vibrational frequency and short correlation length of the related excitations support the use of OH-stretching vibrations as local probes of structural order and site occupancies in complex minerals (Hawthorne, 2016). This property is particularly useful for the study of direction of the hexagonal supercell. Three equivalent Y sites and six equivalent Z sites occur in the cluster. The X a and X b sites are equivalent by translational symmetry but occur at different distances from the W OH belonging to a given cluster. Fe 2 Al 7 (Si 6 O 18 )(BO 3 ) 3 OH 4 , respectively, correspond to a higher complexity level from both experimental and theoretical perspectives. The frequent occurrence of Fe 3+ ions in experimental or natural samples increases the number of potential cationic configurations associated with OH groups (e.g., Bosi and Lucchesi, 2004). The importance of electronic correlation (e.g., Hsu et al., 2011) as well as potential metal-metal interactions (e.g., Sherman, 1987) also deserves special attention in the theoretical modeling of iron-bearing systems. Accordingly, the extrapolation of the band assignment proposed for the Mg-Al tourmalines (Fuchs et al., 2022) to Fe-bearing tourmalines might not be straightforward. However, iron-bearing tourmalines are important petrogenetic indicators due to their ubiquity and to their sensitivity to f O 2 conditions (e.g., Foit et al., 1989;Fuchs et al., 2002;Pieczka and Kraczka, 2004), which motivates a detailed study of their vibrational properties. Here, we analyze the infrared spectrum of a natural foitite sample close to the foitite end-member. Its low content in Mg 2+ , Fe 3+ and alkali cations facilitates comparison with the theoretical properties of selected iron-bearing clusters in a model tourmaline structure. A revised interpretation of the OH-stretching bands in alkali-deficient ferrous tourmalines is then proposed.

Provenance, composition and FTIR analysis of the foitite sample
The LH12 sample belongs to a series of Fe-bearing tourmaline samples previously studied by Paulet et al. (1991) and Fuchs et al. (1995Fuchs et al. ( , 2002. It is has been collected from the core of the alteration system of Lincoln Hill in the Humboldt Range (Pershing County, Nevada). Hydrothermal alteration affected volcanic and volcano clastic piles that had accumulated in pull-apart-type basins. Foitite appears in heavily transformed zones in association with quartz and pyrophyllite (Al 2 Si 4 O 10 (OH) 2 ). Based on Mössbauer spectroscopy, the LH12 sample only contains Fe 2+ ions at the Y (86.5 %) and Z (13.5 %) site, which leads to the formula assuming full B and OH occupancies (Fuchs et al., 1995): This sample is thus close to the foitite-schorl join, which is characterized by the alkali-defect type substitution (Foit and Rosenberg, 1977): where in the present case M + , M 2+ and M 3+ stand for Na + , Fe 2+ and Al 3+ , respectively. The Li content is below 200 ppm (Fuchs et al., 1995). The low amount of Mg and the lack of Fe 3+ should facilitate the interpretation of its OHstretching spectrum by limiting the number of relevant local configurations. The transmission powder infrared spectrum of the LH12 sample was recorded at room temperature on a pellet containing 1.5 and 300 mg of sample and KBr, respectively, using a Nicolet Magna 560 FTIR spectrometer with a resolution of 2 cm −1 . The OH-stretching spectrum was fitted using Fityk software (Wojdyr, 2010). Depending on the bands, Lorentzian or Gaussian profile shapes have been used (Table 1).

Theoretical modeling
The theoretical properties of iron-bearing clusters in dravitic tourmaline have been investigated using density functional theory (DFT) with the generalized gradient approximation (GGA) to the exchange-correlation functional as proposed by Perdew, Burke and Ernzerhof (PBE) (Perdew et al., 1996). The modeling was done as in Fuchs et al. (2022) using a plane-wave and pseudo-potential scheme, as implemented in the PWscf and PHonon codes from the Quantum ESPRESSO package (Giannozzi et al., 2009; http://www. quantum-espresso.org, last access: 12 February 2023). The ionic cores were described by optimized norm-conserving pseudo-potentials from the SG15 ONCV library (Hamann, 2013;Schlipf and Gigy, 2015). The wave functions and the charge density were expanded in plane waves with 80 and 480 Ry cutoffs, respectively. Relaxation of atomic positions was performed until the residual forces on atoms were less than 10 −4 Ry a.u. −1 . The models of iron-bearing clusters ( Table 2) have been obtained by selectively substituting Fe for one or two Y Mg atoms in specific 1 × 1 × 2 supercell configurations of Fuchs et al. (2022). Although being a significant simplification, the study of isolated iron-bearing clusters in Al-Mg tourmaline ensures a proper control of the magnetic properties of the system using spin-polarized calculations. The high-spin state has been assumed for the Fe 2+ ions, and ferromagnetic (FM) order and anti-ferromagnetic (AFM) order have been considered for the iron dimers. The theoretical (super)cell parameters are identical to those previously used, which facilitates the comparison with the results of Fuchs et al. (2022). For the electrostatically charged models, the macroscopic neutrality of the periodic system was ensured by a compensating homogeneous background charge spread over the cell. Harmonic vibrational properties (atomic displacements and frequencies of the transverse optical modes at the Brillouin zone center) were calculated using the density functional perturbation theory (DFPT) (Baroni et al., 2001) as implemented in the PHonon code (Giannozzi et al., 2009). The OH-stretching frequencies have been determined by only considering the displacements of the oxygen and hydrogen atoms belonging to the OH groups of the Fe-bearing cluster as in Fuchs et al. (2022). Additional information on the theoretical approach is provided in the Supplement. Due to the approximations involved in the calculation, the theoretical frequencies can differ from their experimental counterparts by several dozens of wavenumbers (cm −1 ). However, previous studies suggest that this difference is mostly systematic for a given mineral, making it possible to establish well-defined correlations between experimental and theoretical frequencies (e.g., Balan, 2020;Fuchs et al., 2022).
In addition, more realistic DFT + U calculations have been performed to improve the treatment of inter-electron repulsion in the partially occupied Fe(3d) orbitals. This approach was previously used for the modeling of iron pairs in beryl (Lin et al., 2013). In DFT + U calculations, an effective correction based on the Hubbard model of electron correlations in solids is introduced to account for imperfect cancellation of self-interaction between strongly localized 3d electrons. The correction, described by the U eff parameter, removes spurious Coulomb repulsion of an electron with itself. It favors the localization of electrons and therefore integer occupancy of the atomic orbitals. In the present study, the U eff value was set to 4 eV. It is in the range of the U eff parameters self-consistently determined in various Fe-bearing minerals (2.9 to 4.9 eV) (Cococcioni and De Gironcoli, 2005;Hsu et al., 2011;Blanchard et al., 2008).
Although implemented in the PWscf code, the DFPT calculation of vibrational frequencies at the DFT + U level is Table 1. Profile function, frequency (ω exp ), full width at half maximum (FWHM) and relative area of OH-stretching bands in the LH12 sample (Fig. 2).
Profile ω exp (cm −1 ) FWHM (cm −1 ) Area (%) Assignment L 3674.5 ± 0.1 6.5 ± 0.9 0.3 traces of pyrophyllite L 3643.6 ± 0.05 prohibitively slow for large system sizes. Selected W OHstretching frequencies were thus obtained using a finitedifference method (Balan et al., 2007). The total energy of the system was calculated for O and H displacements along the OH bond direction, while keeping the mass center of the OH group stationary. A total of eight displacements, symmetric with respect to the equilibrium position, were considered, corresponding to OH distance variations from −0.04 to 0.04 a.u. The total energy values were fitted using a fourth-order polynomial, and the harmonic OH-stretching frequency was obtained from the quadratic coefficient. Testing of the method on a standard GGA configuration led to a stretching frequency within 0.1 cm −1 of that obtained using DFPT.

The infrared spectrum of the LH12 sample
Two regions can be identified in the OH-stretching spectrum of tourmalines. Above 3600 cm −1 , the bands are usually ascribed to W OH groups, whereas the more intense signals observed below 3600 cm −1 are related to V OH groups. However, both types of signal can overlap in the 3600-3620 cm −1 region. The FTIR spectrum of the LH12 sample ( Fig. 2) displays two narrow bands at 3644 and 3630 cm −1 related to W OH groups. Comparison with other samples from the same locality indicates that the weak narrow band at 3674 cm −1 originates from trace amounts of pyrophyllite in the powder sample. The V OH groups produce two strong peaks at 3468 and 3546 cm −1 . The 3468 cm −1 peak is asymmetric, with a significant broadening on its low-frequency side. The position of the broad contributions on its low-frequency tail was assessed from the local minima observed in the first derivative of the spectrum and was kept fixed during the fit of the spectrum. A satisfactory fit of the spectrum (Fig. 2) could then be achieved using six bands at 3137, 3270, 3343, 3407, 3474 and 3549 cm −1 and three narrow bands at 3644, 3630 and 3674 cm −1 (Table 1). A shoulder on the high-frequency side of the strong 3546 cm −1 peak corresponds to an ad- Figure 2. Powder infrared absorption spectrum of the LH12 sample in the OH-stretching range. The spectrum was decomposed into individual components (Table 1). The inset shows the first derivative spectrum that was used to assess the position of the four broader components accounting for the low-frequency tail of the broad peak at 3468 cm −1 . The residue reported at the bottom was arbitrarily shifted for clarity's sake. ditional band at 3606 cm −1 in the fit. Due to its overlap with the other bands, its parameters are however affected by a significant uncertainty. Note also that the positions (Table 1) of the two components corresponding to the two major peaks slightly differ from the peak maximum at 3468 and 3546 cm −1 . This difference can be ascribed to the constrained symmetric Gaussian shape adopted for these components.
As pointed out by Gonzalez-Carreño et al. (1988), the interpretation of the broad bands in the 3100-3400 cm −1 range (Table 1) is not straightforward. In this low-frequency range, the tourmaline powder spectra can involve contributions re- Table 2. Local configuration, relative energy, theoretical interatomic distances and OH-stretching frequencies (ω OH ) of iron-bearing clusters in tourmaline. The d(O corresponds to the length of the edge shared by the Y octahedral sites occupied by iron atoms. Model structures are given as .cif files in the Supplement. lated to anomalous dispersion effects (e.g., Prost, 1972), to traces of molecular water (Castañeda et al., 2000), and to low amounts of tetrahedral boron (Bosi et al., 2012;Kutzscbach et al., 2016;Bronzova et al., 2019) or aluminum (Nishio-Hamane et al., 2014;Bosi et al., 2022b). Accordingly, the four broad bands accounting for the low-frequency tail of the 3468 cm −1 peak (Fig. 2) will not be further discussed in the present study.

Structural and electronic properties of iron-bearing clusters in tourmaline
A series of iron-bearing clusters in tourmaline have been investigated ( Table 2). They correspond to various schemes of Y -site occupancy and vacancy ordering and reflect the Alrich and X-site-deficient character of foitite. The model with a local configuration closer to the foitite end-member, which has a fully vacant X site, consists in a cluster of two Fe atoms (Fe dimer) and one Al atom at the Y site surrounded by two vacant X sites along the c axis. As X sites are often partially occupied, an equivalent model with a single vacancy in the X site facing the W OH group (referred to as X a , Fig. 1) has also been considered. In this case, the X site on the opposite side of the Y 3 Z 6 cluster (referred to as X b , Fig. 1) is occupied by Na. A third model consists in one Fe and two Al atoms at the Y site surrounded by two vacant X sites. All these models display a mirror symmetry, leading to two equivalent V OH groups in Y Fe Z Al 2 environments for the Y Fe dimers and to two equivalent V OH groups in Y Al Z Al 2 environments for the Y Al dimer (Table 2). Both the FM and the AFM configurations of the Y Fe dimers have been considered. The results obtained with one or two vacant X sites are roughly similar ( Table 2). The magnetic configuration has a significant effect on the structure of the iron dimers. Considering the Fe dimers with two vacant X sites, the Fe-Fe distance is 2.6 Å in the FM configuration and increases to 2.94 Å in the AFM configuration. The bond length of the W OH groups is shorter by more than 10 −3 Å in the AFM configuration than in the FM one. In contrast, the magnetic coupling at the Y site has a negligible effect on the V OH bond length with variations <10 −4 Å. At the GGA level, the FM configuration of the Y Fe dimer is found to be more stable than the AFM configuration by 0.19 eV. In the models with a single vacancy at the X site, similar variations in the Fe-Fe and OH distances are observed between the AFM and FM configurations ( Table 2).
The Hubbard correction applied in DFT + U calculations has a moderate effect on the structure of the clusters (Table 2). Bond length variations in the W OH and V OH coordinated to iron atoms are smaller than 10 −3 Å. For the V OH group solely coordinated to Al atoms, the variation is negligible (<10 −4 Å). In the AFM-coupled iron dimers, the Fe-Fe distance increases by ∼ 0.04 Å. However, the Hubbard cor- rection significantly affects the relative energy of the magnetic configurations, reversing the relative stability of the AFM and FM configurations. In the DFT + U calculation, the AFM configuration is systematically found to be more stable than the FM one, with an energy difference reaching 1.44 eV for U eff = 4 eV. Calculations using intermediate U eff values of 1, 2 and 3 eV indicate that the energy difference between the two magnetic configurations is linearly related to the U eff value (Fig. 3).

Theoretical OH-stretching frequencies related to
Fe-bearing clusters The investigated clusters display significant variations in OH bond length which correlate with the related OH-stretching frequencies (Fig. 4). For the V OH group the distancefrequency relation matches that previously determined on theoretical models of dravite and Mg-foitite (Fuchs et al., 2022). For the W OH groups, the frequencies tend to be downshifted by 10 to 20 cm −1 from the previously established relation. A minor splitting (∼ 1 cm −1 ) occurs for the two symmetric V OH groups due to their weak vibrational coupling, as discussed by Fuchs et al. (2022). The average frequencies are reported in Table 2 and Fig. 4. As in the Mg-Al system, the occupancy of the X site affects the vibrational frequencies of the W OH and Y OH groups. The W OH frequency associated with the iron dimers surrounded by two vacancies is higher by 16 to 19 cm −1 than that calculated when a Na atom occupies the X b site (Fig. 1). The presence of a vacancy (instead of a Na atom) at the X b site decreases the V OH frequency by 25 to 35 cm −1 Figure 4. Relation between theoretical OH-stretching frequency (ω OH ) and OH bond length (d(OH)) (  (Fuchs et al., 2022). for the Y Fe Z Al 2 and Y Al Z Al 2 environments (from ∼ 3640 to ∼ 3615 cm −1 and from ∼ 3580 to ∼ 3545 cm −1 , respectively; Table 2). It is also noteworthy that the V OH in the Y Al Z Al 2 environment is affected by the presence of one or two Fe 2+ ions in the Y 3 cluster. In contrast, the frequency of the V OH in the Y Fe Z Al 2 environment is less affected (Table 2).
The effect of cationic vacancies on the V OH and W OH stretching can be qualitatively understood by considering that local electric fields acting on OH groups in solids can strongly affect their stretching frequency (e.g., Hermansson, 1991). From this perspective, the removal of the Na + cation is equivalent to locating a negative charge at the X site. The electric field induced by the X a vacancy is directed from O to H, resulting in a lengthening of the W OH group and significant vibrational frequency decrease, as observed between dravite and Mg-foitite (∼ 100 cm −1 ; Fuchs et al., 2022). The presence of an X b vacancy, more distant from the W OH group (Fig. 1), partly counterbalances the effect of the X a vacancy, explaining why the W OH-stretching frequency depends on the vacancy ordering along the [001] axis. As only the longitudinal component of the electric field is effective in inducing a frequency shift (Hermansson, 1993), the X vacancies predominantly affect the W OH groups, which are located on the 3-fold structural axis (Fig. 1). Due to a more lateral configuration, the X b vacancy has a weaker effect on the neighboring V OH groups but still decreases their stretching frequency.
When considering the magnetic configurations, the shorter W OH bond length in the AFM configuration (with respect to the FM one) increases the OH-stretching frequency by more than 27 cm −1 . In the DFT + U -corrected models, the W OH frequencies further increase by ∼ 10 cm −1 for both the AFM and the FM configurations with respect to those obtained using the standard DFT (Table 2). Accordingly, the U correction does not significantly affect the difference in W OH-stretching frequencies, which mostly reflects the structural differences between the FM and AFM configurations. Thanks to the significant structural relaxation and frequency variation due to the Fe-Fe interactions, it is thus possible to distinguish the different magnetic configurations of Fe 2+ pairs through their vibrational OH-stretching signature. Note that the effect of the U correction on the W OH-stretching frequency of the cluster with a single Fe atom is negligible (<1 cm −1 ), reflecting the weakness of the OH bond length variation (∼ 10 −4 Å, Table 2).

Interplay of magnetic ordering and electronic structure in Fe-Fe clusters
The magnetic ordering of the iron dimers in tourmaline significantly affects their local structure. The shortening of the Fe-Fe distance, as well as concomitant lengthening of the O 1 -O 2 distance along the edge shared by Fe-occupied octahedral sites (Table 2), is noteworthy. This suggests that the magnetic ordering exerts a strong influence on the electronic structure of the cluster, driving the structural relaxation. The electronic structure of (Fe 2 O 10 ) 15− dimers has previously been studied by Sherman (1987) to model the intervalent charge transfer between high-spin Fe 2+ and Fe 3+ ions in minerals. Fe 2+ -Fe 3+ charge transfer is a common feature of iron-bearing minerals. In tourmaline, thermally activated transfers are attested by the detection of intervalent iron atoms in Mössbauer studies (e.g., Fuchs et al., 1995;Andreozzi et al., 2008). In high-spin iron ions, the minority-spin (β) 3d states are split off from the fully occupied majorityspin (α) states by the intra-atomic exchange interaction. The Fe(3d) β states of the dimer also occur at an energy significantly higher than the O(2p) states, favoring their localization and explaining why a molecular-type approach is more relevant to modeling the charge transfer than approaches related to band theory (Sherman, 1987). In the ground state of the FM configuration of the symmetric (Fe 2 O 10 ) 15− dimer, the highest occupied molecular orbital (HOMO) results from an axial (σ ) bonding interaction between two Fe(3d) β orbitals. Due to the FM order, the minority-spin electron can be delocalized over the two Fe atoms. In the AFM configuration, the minority spin of one Fe atom corresponds to the majority spin  Table 2). The energy is reported with respect to that of the top of the valence band (O(2p) states) in the theoretical model of pristine dravite. The majority (α) and minority (β) spin states correspond to the green and orange bars, respectively. Isosurfaces corresponding to the spin-selected density of states of the two highest occupied spin orbitals are reported. Fe-Fe interaction in the FM configuration is attested by the electron delocalization over the two Fe atoms. In the AFM configuration, the electrons with opposite spin states are localized on each Fe atom. of the other. As the majority-spin states are fully occupied and occur at a lower energy than the minority-spin states, the delocalization of the minority-spin electron present on one Fe atom on the other one is not possible. Thus, the ground state of the AFM configuration corresponds to the localization of the minority-spin electron on a single Fe atom of the dimer, giving distinguishable Fe 2+ and Fe 3+ ions (Sherman, 1987). In the present system (Fig. 5), the iron valence states occur at an energy ∼ 2 eV above the top of the valence band related to O(2p) states, as determined on the pristine dravite model of Fuchs et al. (2022). The Y Fe 2+ dimers in tourmaline differ from the (Fe 2 O 10 ) 15− dimer by significantly stronger site distortions, involving O atoms bonded to H, Al, Si or B atoms, and by the occurrence of the two minority-spin electrons related to the two Fe 2+ ions (instead of one in the Fe 2+ -Fe 3+ pairs). However, their calculated properties can be analyzed from a molecular perspective and a comparison can be drawn with those of the (Fe 2 O 10 ) 15− dimer.
The ground state of the FM configuration in tourmaline is noticeably consistent with that determined for the symmetric (Fe 2 O 10 ) 15− dimer by Sherman (1987). In the present case, the lowest-energy state occupied by minority-spin electrons is a molecular orbital resulting from the axial interaction between two Fe(3d) orbitals (Fig. 5), similar to the 16a 1 state of the dimer. The other state, located just above and corresponding to the HOMO of the system, reveals a lateral interaction (mostly π ) between two Fe(3d) orbitals (Fig. 5) similar to that observed in the 10b 1 state of the dimer (Sherman, 1987). In contrast, the electronic delocalization over the two Fe atoms is not possible in the AFM configuration, as discussed by Sherman (1987). Accordingly, the highest occupied states correspond to two degenerate Fe(3d) atomic orbitals with opposite spins localized on the adjacent Fe atoms (Fig. 5). In the FM configuration, the electronic delocalization over the two Fe atoms leads to a bonding interaction and explains the significant shrinking of the Fe-Fe distance in the relaxed structure compared with the AFM configuration in which no specific Fe-Fe interaction occurs.
In the light of these results, it is therefore possible to understand why the improved treatment of the on-site Coulomb repulsion in Fe(3d) orbitals reverses the relative stability of the AFM and FM configurations with respect to the standard DFT result, even for relatively low values of the U eff parameter. As mentioned in the Methods section, the explicit inclusion of an on-site Hubbard U term for the Fe(3d) electrons represents a strong energy penalty for the delocalized FM solution compared to the already localized AFM one, overcoming the stabilization resulting from Fe-Fe covalent interactions even for low values of the U eff parameter. Accordingly, the U correction favors the localized states with respect to the delocalized ones, explaining the relative stabilization of the localized AFM configuration with respect to more delocalized FM configuration for U eff values as small as ∼ 0.5 eV (Fig. 3).

Assignment of OH-stretching bands in foitite
The infrared and Raman spectra of tourmaline usually display a series of bands in the 3300-3800 cm −1 range typical of OH-stretching modes. The bands observed above 3620 cm −1 are related to W OH groups, whereas those below 3600 cm −1 are assigned to V OH groups. The V OH bands are generally stronger and broader than the W OH ones. In the LH12 foitite spectrum, a doublet related to the W OH groups is observed at 3630 and 3644 cm −1 , with a stronger intensity of the 3644 cm −1 band. Consistently, a doublet at the same frequencies is observed in the Raman spectra of natural black tourmaline samples (Lensing-Burgdorf et al., 2017). In this series of samples, the relative intensity of the two bands is variable, with a stronger intensity of the 3644 cm −1 component in the foitite samples (Lensing-Burgdorf et al., 2017). A similar doublet is observed in the Raman spectrum of the foitite sample (S44) studied by Watenphul et al. (2016). The polarized infrared spectrum of the schorl sample (T3) with partial X-site occupancy investigated by Bosi et al. (2015) displays a doublet at 3628 and 3645 cm −1 , with a stronger intensity of the 3628 cm −1 band in this case. Two bands at 3632-3633 and 3644-3646 cm −1 are also observed in the spectra of the Mn-bearing counterpart of the ferrous tourmalines. In the spectrum of the celleriite co-type, with about half occupancy of the X site, the two components have similar intensities (Bosi et al., 2022a). In the princivalleite sample, which has approximately one-third of the X sites vacant, the low-frequency component at 3632 cm −1 is dominant (Bosi et al., 2022b).
The two bands at 3630 and 3644 cm −1 are usually ascribed to W OH groups in Y M Y Al 2 and Y M Y 2 Al (M denotes Fe 2+ or Mn 2+ ) environments, respectively. This assignment is however hardly reconciled with the more aluminous character of foitite (dominant contribution at ∼ 3644 cm −1 ) with respect to schorl (dominant contribution at ∼ 3630 cm −1 ). In addition, the 14 cm −1 downshift related to the substitution of a trivalent for a divalent cation would be significantly weaker than that observed in Mg-foitite. In the Mgfoitite spectrum, the Y Mg Y Al 2 and Y Mg Y 2 Al bands are observed at 3619 and 3657 cm −1 , corresponding to a downshift of 38 cm −1 (Berryman et al., 2016;Fuchs et al., 2022). In contrast, a smaller splitting is consistent with the frequency shift related to the occurrence of one or two vacancies sandwiching the Y 3 Z 6 cluster along the [001] direction. When it is surrounded by two vacancies at the X site in synthetic Mg-foitite, the W OH group in a Y Mg Y 2 Al environment leads to a band at 3657 cm −1 , whereas it is observed at 3641 cm −1 when it is associated with a single X a vacancy in dravite, corresponding to a 16 cm −1 shift. The effect of vacancy ordering on the W OH-stretching frequency in Fe-foitite is supported by the theoretical results obtained on iron-bearing clusters, which indicate a 16-to-19 cm −1 shift between configurations with one or two X vacancies along the [001] direction (Table 2). Based on these theoretical results, the bands at 3630 and 3644 cm −1 in the foitite spectrum can be ascribed to W OH groups in Y Fe Y 2 Al environments associated with one and two vacancies, respectively, at the X site. This interpretation is consistent with the relative variations in the two band intensities in Fe-or Mn-bearing tourmaline samples with different concentrations of X vacancies (Watenphul et al., 2016;Lensing-Burgdorf et al., 2017;Bosi et al., 2015Bosi et al., , 2022a. It suggests that the relative intensity of these two bands could be used to determine the concentration of vacant X sites in tourmaline samples. Even though the W OH groups can suffer partial deprotonation in tourmaline, the relative intensity of the bands should reflect the probability that a vacancy occurs at the X b site, which should be weakly affected by the protonation state of the more distant W O site. In the LH12 sample, the relative intensity of the 3430 and 3444 cm −1 bands (Table 1) indicates that ∼ 70 % of the X sites are vacant. This value can be compared with the concentration of vacant X sites inferred from the chemical composition (81 %).
It can be noticed that the band related to W OH groups in a Y Fe Y 2 Al-X Na environment and reported at 3726 cm −1 in the Raman spectra of Watenphul et al. (2016) is not observed in the FTIR spectrum of the LH12 sample. Its absence could be related to a preferential deprotonation of the W OH sites facing an occupied X site (Watenphul et al., 2016) combined with the weaker infrared (IR) activity of OH groups vibrating at higher frequencies (e.g., Libowitzky and Rossman, 1997). This last assumption was ascertained on ideal Mg-foitite and dravite models, revealing that   (Fuchs et al., 2022). the corresponding W OH IR activity decreases from 1.2 to 0.4 (D Å −1 ) 2 amu −1 between Mg-foitite and dravite, respectively. In comparison, the Raman activity assessed at the local density approximation (LDA) level displays a relative variation in the opposite direction, increasing from 255 to 346 Å 4 amu −1 from Mg-foitite to dravite, which could favor the observation of Y Fe Y 2 Al-X Na environments in the Raman spectra. The relative variations in the theoretical IR (6.5 and 5.7 (D Å −1 ) 2 amu −1 ) and Raman (491 and 464 Å 4 amu −1 ) activities of the V OH groups in Mg-foitite and dravite, respectively, suggest a weaker influence of the X-site occupancy on the properties of the V OH groups.
Comparing the theoretical frequencies determined for the iron-bearing clusters with their experimental counterparts in foitite (Fig. 6), the two experimental bands better match the frequencies determined for the Y Fe Y 2 Al environments in the AFM configuration. The corresponding theoretical overestimation of experimental frequencies by ∼ 75-80 cm −1 is similar to that previously determined for dravite and Mg-foitite (Fuchs et al., 2022), while the W OH-stretching frequencies related to the FM configurations plot significantly out of the correlation (Fig. 6).
The comparison of theoretical and experimental frequencies also supports the assignment of the band at 3606 cm −1 (Fig. 6) to a W OH group in a Y Fe Y Al 2 environment associ-ated with two vacancies. However, an overlapping contribution from V OH groups in this frequency range cannot be fully excluded (Fuchs et al., 2022). The strong band at 3546 cm −1 can be assigned to the V OH group in a Y Fe Z Al 2 environment associated with a vacant X b site, whereas the V OH group in Y Al Z Al 2 environments leads to the broad peak with a maximum at 3468 cm −1 . These interpretations are similar to those given to the bands at 3551 and 3459 cm −1 in Mgfoitite (Fuchs et al., 2022). As in Mg-foitite, the large width of the V OH bands indicates that they are most likely associated with more than a single local configuration of the V OH group. Assuming a 75 cm −1 shift between theoretical and experimental frequencies, contributions related to V OH group in Y Fe Z Al 2 and Y Al Z Al 2 environments with a Na-occupied X b site are expected at ∼ 3566 and 3502 cm −1 , respectively, but they are not resolved in the infrared spectrum of the LH12 sample. Two bands are observed at 3570 and 3517 cm −1 in the Raman spectrum of the S44 foitite sample reported by Watenphul et al. (2016), but the presence of Li in this sample precludes their straightforward assignment. The V OH groups are also sensitive to the occupancy of the other sites of the cluster through the induced structural relaxations. For example, the stretching of V OH groups in Y Al Z Al 2 environments is downshifted by more than 20 cm −1 when the cluster contains a single Fe atom instead of two. Such a configuration could therefore contribute to the broadening of the V OH band on its low-frequency side (Fig. 2). Other configurations not explicitly considered in the theoretical models could also contribute to the V OH signals, such as those related to the partial inversion of Y -and Z-site occupancies as previously discussed for dravite and Mg-foitite (Fuchs et al., 2022).
Based on the observation that the stretching frequencies of OH groups coordinated to Mn 2+ and to Fe 2+ ions in the trioctahedral structure of talc are similar (Wilkins and Ito, 1967), the present results could also bring constraints for the interpretation of the celleriite spectrum (Bosi et al., 2022a). As discussed above, the two bands at 3633 and 3646 cm −1 should correspond to W OH groups in Y Mn Y 2 Al environments associated with one and two vacant X sites, respectively. The band at 3604 cm −1 is close to that observed at 3606 cm −1 in foitite and likely related to W OH groups in a Y Mn Y Al 2 environment. The broader bands at 3487 and 3562 cm −1 can be assigned to V OH groups in Y Al Z Al 2 and Y Mn Z Al 2 environments, respectively. With the presence of a vacancy at the X b site having a stronger effect on the V OH groups related to Y Al Z Al 2 environments than on those related to Y M Z Al 2 environments, the band at 3518 cm −1 could be related to an Y Al Z Al 2 environment, pointing to an occupied X b site. However, as for the foitite sample studied by Watenphul et al. (2016), vibrational contributions related to the presence of Li in this celleriite sample are also expected, which makes a straightforward assignment of the minor V OH bands more difficult.
We have theoretically analyzed the OH-stretching spectrum of foitite. A revised interpretation of the W OH bands at 3630 and 3644 cm −1 is proposed, suggesting that the relative intensity of these two bands could be a sensitive probe of the vacancy concentration at the X site. In addition, significant structural differences related to the Fe-Fe magnetic coupling were observed in models with Y Fe 2+ pairs. These differences can be traced back to the Fe-Fe bonding which occurs between edge-sharing octahedrally coordinated Fe 2+ with a FM spin arrangement and is forbidden for an AFM order. The comparison of observed and predicted OH-stretching frequencies supports an AFM coupling of Y Fe 2+ pairs in tourmaline, which is also found as the most stable solution in DFT + U .
Data availability. Relaxed theoretical structures of the models are provided in the Supplement. Specific requests should be addressed to Etienne Balan (etienne.balan@sorbonne-universite.fr).
Author contributions. EB, GR and LP performed the calculations. CF, YF and HAH performed the fieldwork and the spectroscopic measurements. All co-authors contributed to the discussion of the results and preparation of the manuscript.
Competing interests. At least one of the (co-)authors is a member of the editorial board of European Journal of Mineralogy. The peerreview process was guided by an independent editor, and the authors also have no other competing interests to declare.
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Special issue statement. This article is part of the special issue "Probing the Earth: spectroscopic methods applied to mineralogy". It is not associated with a conference.