Two topaz crystals from different locations were studied. The samples were chosen among several dozen of potential crystals from various locations based on clarity, crystal size, and low fluorescence in preliminary Raman tests. The latter was important since it allows better-quality Raman data and indicates low concentration of transition metals as trace elements, which might otherwise interfere with NMR analysis due to their magnetic properties.

The first sample was obtained commercially, and no precise provenance was available other than the country of origin, Pakistan. We will hereinafter call this sample TopP. The specimen was clear and colorless, with a length of about 1.5 cm along [001] and a diameter of about 1.0 cm. The {001} faces terminated in cleavage plains, whereas crystal faces and sedimentary rounding are found perpendicular to those. Judging by the size and shape of the TopP specimen, we speculate that it most likely originated from a pegmatite but was either transported in water some way or was rounded by some process during the mining of the pegmatite. The specimen was poor in fluid inclusions. Before powdering the samples for XRD and solid state NMR analysis, the sample was coarsely crushed and only chunks without visible inclusions were picked for powdering. The samples were powdered using a Fritsch Pulverisette 7 agate ball mill.

The second sample, TopT, comes from Topaz Mountain, Thomas Range, Juab County, Utah, USA, and is also clear and colorless. This locality is known for gem-quality topaz crystals very close to F end-member composition hosted in light-gray rhyolite (Patton, 1908; Ribbe and Rosenberg, 1971). Topaz is associated in this locality with other minerals typical of pneumatolytic alteration in highly evolved rhyolite, such as bixbyite, beryl, garnet, pseudobrookite, durangite, and cassiterite (Holfert et al., 1996). Topaz crystals from this locality are typically brown or reddish but will bleach in direct sunlight (Holfert et al., 1996). The crystal used for this study was colorless, approximately 0.5 cm long and wide, and had well-developed crystal faces and few inclusions. The specimen was coarsely crushed and only chunks without visible inclusions were picked under the microscope for powdering. These were then powdered as finely as possible by hand using an alumina ceramic mortar to avoid the slight agate contamination caused by the mill observed in sample TopP (see Results). The grain sizes of neither powder were analyzed, but the TopT powder was visibly coarser than the TopP powder.

The micro X-ray fluorescence (µ-XRF) measurements were performed at the Museum für Naturkunde Berlin using a Bruker Nano M4 Tornado Plus. The machine was operated under vacuum conditions of 0.2 mBar, using a rhodium target material anode as X-ray source and a polycapillary lens system to minimize beam size and maximize localized sample excitation. Emitted characteristic X-ray fluorescence was measured with two energy dispersive silicon drift detectors with an active area of 60 mm2 and a super light element window for element detection down to carbon.

Single point analysis was conducted at 50 kV acceleration voltage and 300 µA current, with a focused X-ray beam size of 20 µm. In order to eliminate diffraction peak interference, every analysis spot was measured sequentially with both detectors. Quantification was performed by peak area integration using a fundamental parameter algorithm included in the M4 Tornado software. A well-characterized in-house standard of gem-quality andalusite (with 0.15 wt % Fe2O3 as the only significant trace element) was used as reference material for the type calibration of Al and Si values. The quantification of F and O was standardless. Trace element detection limits for topaz as matrix are <200 µg g-1 for Na–Ca, <100 µg g-1 for Sc–Zn, and <50 µg g-1 for elements ≤ Ga. Elemental mapping was performed in a continuous measurement mode (which sets the dwell time per pixel by adjusting the stage movement velocity) using both detectors simultaneously at 50 kV, 600 µA, and with a dwell time of 50 ms per pixel. Pixel size was 20 µm for the mapping of sample TopP and 13 µm for TopT.

The X-ray diffractometry (XRD) data were obtained at the Institute of Geological Sciences, Free University Berlin, using a PANalytical Empyrean diffractometer, equipped with a PIXcel1D-Medipix3 detector. Copper Kα radiation at λ=1.54060 Å was used with 40 kV acceleration voltage and 40 mA tube current. A 10 mm beam mask, 0.04 rad soller slits, and a fixed 1/8∘ divergence slit were used on the incident beam, and 7.5 mm anti-scatter slit, 0.04 rad soller slit, and a 20 µm thick Ni Kβ filter were used on the diffracted beam. The powders were placed on a rotating stage and scanned from 15 to 80∘ 2θ in 4950 steps of 0.013∘ 2θ with a total counting time of 118 s.

Rietveld refinement of the XRD data was performed with the GSAS-II software package (Toby and Von Dreele, 2013). Plots of the observed and fitted XRD patterns are shown in Fig. S1 (Supplement). The instrument parameter file was produced from quartz powder as reference material, using the same measurement conditions as for the samples. Refined structural data of natural topaz obtained with neutron diffraction (Gatta et al., 2006) were used as a starting point for the refinement. The lattice parameters were refined, but the symmetry of the structure was kept fixed at Pbnm. The atomic positions of all atoms except H were refined. All parameters of the F anion and the O of the OH group were constrained to be identical. The occupancy of the F site was originally taken from Gatta et al. (2006) for the refinement as a first guess. The real occupancy was then calculated from the lattice b parameter provided by this first guess fit, using the calibration of Ribbe and Rosenberg (1971), and then manually fed back into the Rietveld software for another round of refinement. This was repeated until the b-parameter value converged to the fourth decimal. Three iterations were necessary for both samples.

The uncertainty of F/OH fraction stems predominantly from the error of the fluorine determination in the input data of the calibration by Ribbe and Rosenberg (1971). This absolute error of approximately ± 0.2 wt % F translates to 0.02 on the F-site occupancy or 0.01 on the F/OH fraction, based on then individual errors of the 13 samples reported by these authors. However, based on the excellent correlation of r=-0.967 between F content and b parameter in the data from n=13 samples of Ribbe and Rosenberg (1971), we know that the relative error between any two topaz specimens is lower.

Most of the 19F, 1H , 27Al, and 29Si MAS NMR spectra were measured at Humboldt University Berlin on a Bruker Avance 400 spectrometer (static field: 9.4 T; Larmor frequencies ν1H=400.1, ν19F=376.4, ν27Al=104.3, ν29Si=79.5 MHz) using a 2.5 mm MAS probe (Bruker BioSpin) and applying a rotation frequency of 20 kHz unless otherwise indicated.

19F MAS NMR spectra were measured with a π/2 pulse duration of 4.4 µs, a spectrum width of 400 kHz, and a recycle delay of 240 s. The isotropic chemical shifts δiso of 19F resonances are given below with respect to the CFCl3 standard. 1H MAS NMR spectra were recorded with different recycle delays ranging from 5 to 60 s to check the characteristics of the signals, a π/2 pulse duration of 3.5 µs, and a spectrum width of 100 kHz. The number of accumulations (ns) is given in the captions to the figures for comparison (where appropriate). Existent background signals of 19F and 1H were suppressed with the application of a phase-cycled depth pulse sequence according to Cory and Ritchey (1988).

The 27Al MAS NMR spectra were recorded with a recycle delay of 2 s, and the chemical shifts are given with respect to an aqueous AlCl3 solution. For the 29Si MAS NMR spectrum a 4 mm probe (Bruker BioSpin) was used applying a rotation frequency of 10 kHz. With a recycle delay of 300 s and 522 accumulations a total measurement time of about 5.5 d was necessary. Both the 29Si chemical shifts and the 1H chemical shifts are given with respect to tetramethylsilane (TMS).

Additional 19F MAS NMR experiments were performed at BAM (German Federal Institute for Materials Research and Testing) with a Bruker Avance 600 spectrometer under a static field of 14 T (ν19F= 564.7 MHz). The samples were packed into 2.5 mm zirconia rotors with Vespel top and bottom plugs and spun at 35 kHz under the magic angle (MAS) in an HFX triple resonant wide bore probe at room temperature. Typical acquisition parameters were a repetition period (d1) of 240 s and 4.4 µs for the 90∘ pulses. The EASY pulse program (Jaeger and Hemmann, 2014) was applied, in which two 90∘ pulses were irradiated with a short delay (0.1–10 ms) in between. By subtracting the free induction decay (FID) after each of those pulses, the background signal was canceled. Subsequent processing involved Fourier transformation, phase adjustment, and baseline correction (Bernstein polynomials, fourth order or higher).

The Raman spectra were recorded in reflection geometry on a WITec alpha300 R with a 532 nm laser, using a Zeiss EC Epiplan 10x/0.25 objective and ca. 20 mW laser power on the sample. Measurements were taken on the cleavage plane (001) and on well-developed (010) crystal faces. The incident laser was circular polarized with a λ/4 plate. No analyzer or other filter was applied to the signal. A UHTS300 VIS spectrometer with a 1800 mm-1 grating and a 1650 line charge coupled device (CCD) area detector was used. Recording time for single spectra was 10 s in all cases, with 360 accumulations for the high-resolution measurements of the OH-band region around 3650 cm-1 and 30 accumulations for the lattice band region spectra (ca. 100–1200 cm-1). Calibration of the spectrometer was preformed immediately before each measurement and verified after each measurement, using the integrated Hg(Ar)-lamp calibration routine of the instrument. Correctness of this procedure was verified via the 520.7 cm-1 band of a silicon wafer. This band was fitted using a pseudo-Voigt profile, and the deviation from 520.7 cm-1 was less than 1 cm-1 in all measurements. Cosmic ray events were filtered out by removing all single spectrum pixels that deviated by more than 5σ from the average for the same pixel over the course of all accumulations. All spectra were subsequently corrected for the read-out and dark-current background of the detector, which were recorded as 1200 accumulations of 1 and 10 s, respectively, with no signal on the detector. Fitting of the Si and OH bands was performed with a custom Python 3 script utilizing the NumPy and SciPy libraries.

All computations in this work were performed by applying the Vienna Ab Initio Simulation Package (VASP) (Kresse and Hafner, 1993, 1994; Kresse and Futhmüller, 1996a, b). Within the VASP code, plane wave DFT with the Perdew–Burke–Ernzerhof (PBE) functional (Perdew et al., 1996), together with the projector augmented wave (PAW) potentials (Kresse and Joubert, 1999) and the Γ-centered Monkhorst–Pack grid of size 24×12×12 (Monkhorst and Pack, 1976), is employed. Dispersion corrections were included via the D3 method (Grimme et al., 2010) including Becke–Johnson damping (Grimme et al., 2011). The convergence criteria for the electronic self-consistent field loop were set to 1×10-6 eV. The plane wave cut-off criterion was set to 500 eV for the optimizations, which are done by applying the residual minimization method with direct inversion in the iterative subspace (RMMDIIS) (Wood and Zunger, 1985; Pulay, 1980), together with the tetrahedron method with Blöchl corrections (Blöchl et al., 1994).

The composition of the samples as measured by µ-XRF is given in Table 1. Each sample was analyzed on multiple spots, and averages are reported along with 2σ variation among the spots. Several factors complicate the analysis of the major element composition of topaz. It is known that X-ray emission intensity of fluorine in topaz is strongly dependent on the orientation of the crystal lattice to the detector (Ottolini et al., 2000) due to orientation-dependent absorption in the crystal. This means that adequate correction of the absorption effects, which is necessary for any accurate analysis based on X-ray emission (like XRF and electron microprobe analysis), requires either standardization to an orientation-matched reference topaz of similar composition or a theoretical absorption correction that takes orientation into account. Neither of these are currently available. Similar but less well documented problems affect the silicon absorption correction. The Kα emission line of Si is strongly affected by the absorption edge of Al, which makes the correction highly sensitive to density and anisotropy of the sample, especially if it contains much more Al than Si, as is the case for topaz. These challenges impose additional (not generally quantifiable) uncertainties on the analysis for F and Si. The µ-XRF data are therefore used primarily to check for the presence of significant minor or trace elements and of potential zonation in the major element composition. The only detectable trace elements were Ge in sample TopP and Ti, as well as Fe, in TopT. No zonation or heterogeneity was observed for Al, Si, or F in either sample (see Supplement Figs. S2 and S3). The trace elements do show growth zoning in sample TopP (Ge shown in Fig. S2) and growth, as well as sector zoning, in sample TopT (Ti shown in Fig. S3). However, due to the low concentrations of the trace elements (Table 1), neither of these are expected to have any observable effect on the 19F NMR signal or the OH band in Raman spectra. Therefore, these results will not be further discussed. Based on the observation that no tetrahedrally coordinated Al was identified with NMR, the Al/Si ratio can be assumed to be near ideal, which is in agreement with the µ-XRF data, considering the respective analytical uncertainties. Due to the large uncertainty on F quantification, we rely on the correlation of lattice parameters with the F/OH ratio (Ribbe and Rosenberg, 1971) to determine the latter.

The XRD patterns are shown in Fig. S1. Sample TopP shows a small reflection at 2θ=26.6∘, which corresponds to the main peak of quartz and contamination by agate from the ball mill used for this sample. Therefore, sample TopT was pulverized using a corundum hand mortar, which did not cause visible contamination but instead textured particles due to the single cleavage plain of topaz in (001), as can be seen as a texture effect in Fig. S1b. The F/OH content of the samples was calculated from the b lattice parameter results of the Rietveld analysis of the XRD data using the calibration (F[wt %] = 892.5–99.2b) in Table 2 of Ribbe and Rosenberg (1971). The results of the Rietveld analysis and the corresponding F/OH contents are listed in Table 2. If we assume a perfect statistical distribution of fluoride and hydroxide on the F/OH site, we can calculate the probability of any two neighboring F/OH sites being occupied by either two fluorides, one fluoride and one OH group, or two OH groups from the proportions XF and XOH on the lattice site. The probability for two fluoride neighbors is simply XF2, and for two OH neighbors it is XOH2. For two different neighbors, the probability is 2⋅ XF ⋅ XOH. For sample TopP with XF= 0.94 ± 0.01, 88.36 % of the F/OH site pairs should have two fluoride ions sitting in the two neighboring positions, whereas 11.28 % should have one fluoride and one hydroxide neighbor, and 0.36 % should have two hydroxide neighbors, assuming perfect disorder on this site. The result of XF= 0.99 ± 0.01 for sample TopT is consistent with an end-member fluorine topaz composition, within experimental error. However, if we assume XF= 0.99, 98.01 % of all F/OH site pairs would have two fluorides, 1.98 % would have one fluoride and one hydroxide, and 0.01 % would have two hydroxides.

Two signals can be unambiguously distinguished in the 19F MAS NMR spectrum of the sample TopP (Fig. 3a). With measurements applying different recycle delays up to 240 s, an identical spin–lattice relaxation behavior was found, and the relative intensity of both signals did not change. The spectrum recorded at 14 T (Fig. 3a, dashed) allows a higher resolution and the identification of an additional small shoulder at ca. -132 ppm. The deconvolution of the spectrum resulted in a contribution of about 90 % of the resonance with the maximum at -135 ppm and about 10 % for the second resonance at -130 ppm. Here we assume that the EASY pulse program will only slightly compromise the quantitative fidelity of the acquired signals.

In accordance with the data from X-ray diffraction the signal at -135 ppm (∼ 90 %) represents F/OH sites in the chains with two F- ions in neighboring positions, while the signal at -130 ppm (∼ 10 %) originates from F/OH sites with one fluoride and one hydroxide as neighbors. Rotor-synchronized spin-echo experiments confirm these findings and suggest a completely different spin–spin relaxation behavior of both F sites. Signals with good spin–spin interaction, i.e., two neighboring F- ions with short spin–spin relaxation time, disappear first, which is clearly visible for the behavior of the resonance at -135 ppm (Fig. 3b). For comparison, similar 19F MAS NMR spectra of two commercially available zharchikhite and topaz samples are also shown in Fig. S4.

Only one signal at -0.2 ppm can be detected in the 27Al MAS NMR spectrum (Fig. 3c). Its chemical shift indicates exclusively six-fold coordinated Al sites with the possibility of local (AlO4F2) or (AlO5F) coordination environments (König et al., 2008a, b). The existence of the latter two mentioned local units is also confirmed by the position of the 19F signals in Fig. 3a (König et al., 2008a).

The 29Si MAS NMR spectrum of TopP is depicted in Fig. 3d. The NMR signal at -85.6 ppm is typical for the presence of SiO4 units in the structure. The small shoulder at -84.5 ppm hints at deviations due to the hydrogen bridging network, which is also verified by 1H–29Si cross-polarization experiments (not shown here). The signal at -107.8 ppm is in the typical range for so-called SiO4–Q4 groups with Si–O–Si bonds and is very likely due to the contamination by agate from the ball mill used for sample TopP, which is also observed in the XRD data.

The 1H MAS NMR spectrum of TopP is shown along with the rotor-synchronized spin-echo 1H spectra in Fig. 4. Four 1H containing entities can be identified with signals at 4.9, 2.8, 1.1, and -0.3 ppm. The deconvolution of the spectrum in Fig. 4a is shown in Fig. S5 (Supplement). All 1H nuclei differ not only in chemical shift but also in the spin–lattice and spin–spin relaxation behavior. The spin–lattice relaxation time of the narrow 1H signal at 2.8 ppm is very long, and even with a recycle delay of 60 s the relaxation is not finished. This is an unusual behavior for most of the 1H species but typical for isolated 1H sites in well-ordered systems. The spin-echo spectra clearly show the disappearance of the signal at 4.9 ppm (dashed line in Fig. 4), which is generated by hydrogen-bonded H positions (Figs. 4b, c, S5), whereas the 1H signals at 2.8 and 1.1 ppm can be attributed to isolated OH groups.

The 19F, 27Al, and 1H MAS NMR spectra of the OH-poor topaz TopT are given in Fig. 5. Only one 19F signal at -135 ppm can be detected representing fluoride with another fluoride in neighboring positions, as found by X-ray diffraction with a portion of about 99 %. An extremely small signal at -130 ppm can be visualized only with rotor-synchronized spin-echo measurements (Fig. 5b). As for the OH-rich sample TopP, the symmetric 27Al signal at -0.2 ppm has the typical chemical shift for six-fold coordinated Al sites with one to two fluorine atoms in their first coordination sphere (König et al., 2008a, b). The low OH content of TopT manifests also in the very large number of accumulations (ns = 1024) necessary for the registration of the 1H MAS NMR spectrum with a good signal-to-noise ratio (Fig. 5d). All observed signals, and especially the narrow signal at 1.3 ppm, are in the typical range for isolated OH groups (Scholz et al., 2010).

Raman spectra of both samples are shown in Fig. 6. Sample TopT is homogeneous with respect to the Raman spectrum; therefore only one exemplary analysis is shown. Sample TopP shows slight differences in the overall fluorescence background, as well as the shape of the OH band between the innermost core and the rim of the sample. Therefore, one point from the core and one from the rim were chosen for detailed analysis with the incident laser direction parallel [001]. An additional analysis with the laser parallel [010] is also shown.

The lattice band positions and height ratios show fairly little difference between the two samples when measured in the same orientation (Fig. 6a). However, TopP has a clear OH band at 3650 cm-1, which TopT does not have. TopT also has a higher fluorescence background that increases to higher wave numbers. The region around 3650 cm-1 is shown in detail in Fig. 6b, not stacked but in raw counts per second from high-resolution spectra with 360 accumulations of 10 s. No OH band was found in any of the analyzed TopT spots; therefore only one representative spectrum is shown. It is obvious that the elevated background of TopT is less smooth than the background of the two TopP spectra. However, this is not statistical noise but the texture of the fluorescence that causes the background elevation. It is not clear what the lowest OH group concentration in the sample would be that would still result in a visible OH band. We can only state with certainty that there is no Raman evidence for OH groups in TopT. This is in agreement with the XRD findings.

The OH bands of TopP in Fig. 6a show a shoulder to lower wavenumbers of the main peak. This band splitting has been described previously, and we will call the two bands OHA and OHB in keeping with the convention used by Pinheiro et al. (2002). Fitting of the peak parameters was performed assuming a linear background between 3610 and 3690 cm-1 and two pseudo-Voigt profiles. The resultant fit parameters are summarized in Table 3.

We have performed DFT calculations for various different OH substitutions in the fully fluorinated topaz structure. The crystallographic unit cell contains eight fluoride ions, which can be replaced by hydroxide ions. Because the investigated natural topaz samples are on the fluorine-rich side, we performed structure optimizations at XF= F / (F + OH)molar=0.5, 0.75, and 0.875. For the former two, various symmetrically non-equivalent substitution patterns are possible. The lattice parameters of the optimized structures are summarized in Table 4.

The substitution pattern for the XF=0.5 case yields an interesting insight in the local structure. It is theoretically possible to sort OH and F into two separate planes (Fig. 7b), but this distribution is the least energetically favorable (Table 4). In this structure, both six-fold coordinated aluminum centers with two fluoride and ones with two hydroxide ions occur. If the same local pattern occurs, but not all OH are arranged in one plane, the structure (Fig. 7c) is stabilized by 0.26 eV per unit cell. A further reduction in energy by 0.08 eV can be achieved, when each aluminum center carries one F and one OH anion, yielding the most stable structure (Fig. 7d) for XF=0.5 distribution. All OH groups have the same O–H bond length of 0.974 Å in this structure.

The local environments of Al and Si depicted by 27Al and 29Si MAS NMR spectra are in agreement with the published structure of topaz (e.g., Gatta et al., 2006) and the X-ray diffraction results (Figs. 3, 5). Aluminum is exclusively octahedrally coordinated, and silicon is exclusively tetrahedrally coordinated, which, in this simple structure, suggests that the Al/Si ratio is very close to the theoretical stoichiometric ratio of 2. We therefore assume that the samples are ideally stoichiometric topaz (Al2SiO4(F, OH)2), which is in agreement with the µ-XRF results. The small shoulder of the 29Si signal around -84.5 ppm (Fig. 3d) is likely indicative of some H⋯O bonding involving the O2 site, which is part of the SiO4 tetrahedron and the closest oxygen position to the hydrogen of the OH group (Gatta et al., 2006). O2 is the only oxygen position in the anion layers marked “B” and “C” in Fig. 1 (although additional oxygen may reside in the F/OH site as part of an OH group).

The 19F and 1H MAS NMR measurements provide structural information about the F/OH site. Two fluorine positions can be clearly distinguished: -130 and -135 ppm. Their relative intensities in sample TopP (Fig. 3a) correlate well with the calculated abundance of F- ions with another F- in its neighboring position (∼ 90 %, -135 ppm) and with an OH group as neighbor (∼ 10 %, -130 ppm), respectively. This interpretation is corroborated by the fact that the latter signal cannot be observed for TopT (Fig. 5a).

In the 1H MAS NMR spectra, two narrow signals can be identified at 2.8 and 1.1 ppm. Both are typical signals for OH groups that are part of an octahedral coordination around Al3+ (Scholz et al., 2010), as is expected for the TopP sample and can be correlated with the OHA and OHB Raman bands. The broad 1H resonance with its maximum at 4.9 ppm (Figs. 4, S5) most likely stems from water molecules adsorbed on the very fine powder of sample TopP. The sample was not dried prior to the experiment, and structurally bound molecular water does not appear to be likely to occur in the topaz structure. The disappearance of this signal applying spin-echo measurements, which is an indication for strongly bonded protons, typical for water molecules (Scholz et al., 2010), supports this assumption (Fig. 4b, c). The extremely low OH content in sample TopT required a large number of accumulations, and the 1H MAS NMR spectrum gives only a very narrow signal at 1.3 ppm for the few isolated OH groups still present in the sample (Fig. 5d). No OH band is visible in the Raman spectrum of TopT (Fig. 6). Although our method does not allow quantification of the 1H concentration in the sample, we can state that structurally bound OH groups are present in sample TopT but at extremely low concentrations.

The cause of the splitting of the OH band in vibrational spectroscopy in topaz with XOH≤0.5 has been a matter of debate in the past (e.g., Wunder et al., 1999; Pinheiro et al., 2002; Prasad and Gowd, 2003; Watenpuhl et al., 2010). The conclusion of Watenpuhl et al. (2010) that the band position of any individual OH group depends on whether the neighboring F/OH site is occupied by F or by OH works well for their IR spectroscopic data on 17 synthetic topaz samples synthesized by Wunder et al. (1999) and also their two natural samples. In their model, the proportion of the OHA band (lower wavenumber, OH neighbor) to the OHB band (higher wavenumber, F neighbor) can be calculated from the F / (F + OH) ratio XF and the OH / (F + OH) ratio XOH as 2XF / XOH. The crossover point, where both bands have the same area under the peak, is thus at XOH=0.66. The fact that the ratio of the observed integrated intensities of both bands correlates almost perfectly with the ratio of OH groups having F or OH as neighbors raises the question of the origin of the frequency shift between the two bands. It is also interesting to note that the model that Watenphul et al. (2010) applied successfully is not compatible with the “proton avoidance model” of Barton (1982), in which no two OH groups should be direct neighbors. This is somewhat surprising because repulsion between neighboring protons provides a convincing explanation for the fact that OH-rich topaz has two distinct hydrogen atom positions (Northrup et al., 1994; Wunder et al., 1999), and this repulsion would be expected to lead to proton avoidance.

Based on these observations, hydrogen bonds between the OH group and fluoride or oxide anions seem the most plausible cause for the band splitting, with the role of the repulsion between protons of neighboring OH groups being unclear. Hydrogen bonds are known to influence the strength, polarization, and polarizability of OH molecular bonds and thereby the frequency, as well as the intensity of absorption and scattering bands in vibrational spectroscopic methods, particularly IR and Raman spectroscopy (e.g., Lutz et al., 1996; Rozenberg et al., 2000; Steiner, 2002). The effect on frequency decreases strongly with increasing H⋯O distance (Rozenberg et al., 2000). However, the effect on intensity is typically more pronounced (e.g., Lutz et al., 1996; Steiner, 2002).

The atomic distances for potential hydrogen bonds in topaz are approx. 2.377 Å for H⋯F and 2.215 Å for H⋯O2 at standard conditions, with a θ angle (Steiner, 2002) of the prospective hydrogen bond of 139 and 138∘, respectively (using the H position determined by Gatta et al., 2006, obtained with neutron diffraction at 298 K). Because O2 is part of the tetrahedral coordination of Si, H⋯O2 bridging should influence the NMR signal of 29Si. Outside the a-c plane, oxygen position O1 is the closest to H. Using the values of Gatta et al. (2006) for a and c and the range for b given by Ribbe and Rosenberg (1971), the distance H⋯O1 works out to 2.300 ± 0.005 Å, thereby being shorter than the H⋯F distance of 2.377 Å. However, the θ angle for a possible hydrogen bond involving O1 would be about 94∘, making this bond unlikely due to the preference of hydrogen bonds for linear configuration (Steiner, 2002).

Considering the distances of <2.4 Å from the H site to the (potential) F position, as well as the O2 site of the SiO4 tetrahedron (Fig. 2), together with the angle of <140∘ between the OH group and either the F or the O2, it seems very likely that hydrogen bonds can form with both these anions. Depending on the occupation of two neighboring F/OH sites, two different constellations of hydrogen bonds may form: (1) OH⋯O⋯HO or (2) F⋯H⋯O (Fig. 2). Although formation of hydrogen bonds generally tends to shift the frequency of the OH stretching band to lower values (red shift) compared to free OH groups, this effect decreases with the length of the hydrogen bond and is relatively small compared to other influences at hydrogen bond lengths of >2 Å (Rozenberg et al., 2000; Steiner, 2002). It is therefore difficult to predict which of the constellations depicted in Fig. 2 should show the lower or higher frequency IR or Raman band. Based on the results of Watenphul et al. (2010), we are confident that the lower IR absorption frequency indeed belongs to the OH⋯O⋯HO configuration and the higher frequency to the F⋯H⋯O hydrogen bond. Results of Pinheiro et al. (2002) in their Raman study on 27 natural topaz samples with different OH concentrations corroborate this interpretation for Raman spectroscopy as well. However, while the IR band intensities of Watenphul et al. (2010) correlate very well with the statistically expected ratios of the two different hydrogen bond constellations, Pinheiro et al. (2002) found much higher relative intensities of the OHA band, with the point of equal intensity at around XOH=0.14. Our own Raman data show OHB / OHA ratios between 1.5 and 2.0 for sample TopP with XOH = 0.06.

There are two possible and mutually non-exclusive explanations for the discrepancy in OH-band intensity ratios between IR and Raman spectroscopy: (1) the sensitivity of the different bands is very similar in IR spectroscopy but drastically different in Raman spectroscopy, or (2) the distribution of F and OH on the F/OH sites is different for the samples in the different studies. If there is a difference in the sensitivity ratios between IR and Raman, it must stem from the selection rules for these two spectroscopic methods. While IR absorption intensities scale with the polarization of a molecular bond, Raman band intensities scale with the square of the polarizability (Nafie, 2017). OH groups with hydrogen bonds to nearby anions typically show a large increase in intensity compared to OH groups without hydrogen bonds due to an increase in the polarization of the OH group (e.g., Rozenberg et al., 2000). This effect occurs so reliably that it is used as an indicator for the presence or absence of hydrogen bonds (Steiner, 2002). In case of topaz, there seems to be no significant difference in polarization between the two different OH neighbor constellations or else the correlation of Watenphul et al. (2010) would not work as it does. This is surprising considering the fact that in the OH⋯O⋯HO constellation (Fig. 2 left) one oxygen pulls at the electron fields of two OH groups, whereas in the F⋯H⋯O constellation (Fig. 2 right), oxygen and one fluorine pull at only one OH group together. It has been shown that the formation of hydrogen bonds also influences polarizability and its change upon phonon excitation (e.g., Lutz et al., 1996). According to our data and those of Pinheiro et al. (2002), the change in polarizability of the OH⋯O⋯HO constellation as a result of phonon excitation by incident laser photons during Raman spectroscopy would be larger than in the case of the F⋯H⋯O constellation. How the change in polarizability can be so different while the polarization remains almost unchanged is unclear pending further investigation. This effect may further be influenced by a potential change in proton positions for the OH⋯O⋯HO constellation compared to that for the F⋯H⋯O constellation (Barton 1982; Northrup et al., 1994; Wunder et al., 1999).

If, however, we assume that the difference in OH-band ratios between IR and Raman spectroscopy cannot be caused by differences in polarizability behavior because the polarization is apparently unchanged, we need to consider possible structural explanations. The IR spectroscopic data of Watenphul et al. (2010) were collected using mostly synthetic samples, whereas the Raman spectroscopic study of Pinheiro et al. (2002), as well as the present work, used natural samples. This may suggest that in natural samples more OH groups have OH neighbors than would be expected based on probability calculations for perfectly disordered F/OH site occupation. This can be achieved either by ordering into a super-structure or by unmixing into different domains of OH-rich and OH-poor topaz. Using the method of Watenphul et al. (2010) for sample TopP with XOH= 0.06, the expected OHB / OHA ratio can be calculated. The resulting ratio is 31. This is in stark contrast to the OHB / OHA ratio of 1.5–2.0 determined as the area under the two Raman OH sub-bands with peak fitting (in three different positions and orientations, see Fig. 6b). Calculating backwards from these ratios of 1.5–2.0 would result in XOH=0.5 to 0.6, which is clearly inconsistent with the XRD results. The unexpectedly high proportion of the OHA band may be explained by the formation of OH-rich domains through unmixing. If present, then more OH would have OH neighbors in the OH-rich domains, thus making the OHA band more prominent, while any OH-free domains would of course be simply invisible to the Raman OH band observation. No such domain structure is evident in the F mappings of sample TopP (Fig. S2), although the domains would need to differ by almost 10 wt % F if they were to be the sole cause for the over 10-fold difference in the Raman OH-band ratio between observation and expectation. This means that the domains are either smaller than the resolution of the mapping of sample TopP (20 µm) or are not the cause of the discrepancy. To test this hypothesis, future detailed analysis using transmission electron microscopy will be needed.

In all structures where only one hydroxo group is coordinated to an aluminum center the lattice constants are only slightly changed compared to the fully fluorinated topaz (Table 4), so nearly no strain will be built up in the crystal by local exchange of F for OH groups. Replacing four F atoms by four OH groups in one unit cell (most stable XF=0.5 structure) is energetically more favorable by 0.08 eV per F/OH moiety than replacing only one fluorine atom by one OH group in each of the four unit cells (XF= 0.875). This suggests that, at least in terms of enthalpy, it is favorable for the topaz to form an internal zoning with more fluoride and more hydroxide-rich regions. However, at higher temperatures, this difference will be diminished by the effect of entropy, which always seeks to distribute all components statistically. A separation into layers of F-rich and layers of OH-rich topaz (Fig. 7b), on the other hand, is energetically less favorable by 0.03 and 0.04 eV per F/OH moiety than the two other possible configurations of identical bulk composition of XF= 0.5 (see b, c, and d in Table 4). This is interesting because the “OH-layer” structure (Fig. 7b) is the only one of these three configurations with direct OH neighbors and thus the only one violating the proton avoidance principle (Barton, 1982). It seems that unmixing into OH-rich and OH-poor domains is energetically feasible but only as long as no direct OH neighbors occur. Unmixing according to these simple model structures is therefore unlikely to be the explanation for the over-representation of the OHA band in the Raman spectrum. However, the role of proton avoidance and the energy budget of site occupation closer to the F end-member of topaz need to be investigated further before dismissing unmixing entirely.

One additional factor that may influence the observed Raman band ratios is that the H⋯F bonds may alter the orientation of OHA and OHB groups, which would affect the Raman experiments of Pinheiro et al. (2002) and our samples but not the IR spectroscopic data on powder pellets used by Watenpuhl et al. (2010). Due to the geometry of the neighboring F/OH sites (Fig. 2), the influence of the hydrogen bonds can only rotate the OH group in the (010) plane and should therefore be averaged out in observations with circular polarized light in [010] viewing direction. The orientation effect, if it exists, should be most prominent in observations along [001]. However, only about 15 % relative difference in the band area ratios is observed between those two ratios (Table 3), and the observation along [010] still has a much more prominent OHA band than should be expected. A change in orientation of the OH group therefore does not seem to play a significant role in the observed apparent over-representation of the OHA band in the Raman data.