Micro- and nano-size hydrogrossular-like clusters in pyrope crystals from ultra-high-pressure rocks of the Dora-Maira Massif, western Alps

The supracrustal metamorphic rocks of the Dora-Maira Massif, western Alps, have been intensively studied. Certain ultra-high-pressure lithologies contain coesite and nearly end-member composition pyrope, Mg3Al2Si3O12, making this locality petrologically and mineralogically unique. Structural OH-, loosely termed “water”, in pyrope crystals of different composition has been investigated numerous times, using different experimental techniques, by various researchers. However, it is not clear where the minor OH- is located in them. IR single-crystal spectra of two pyropes of composition {Mg2.79,Fe2+0.15,Ca0.04}Σ2.98[Al]2.02(Si)2.99O12 and {Mg2.90,Fe2+0.04,Ca0.02}Σ2.96[Al]2.03(Si)3O12 were recorded at room temperature (RT) and 80 K. The spectra show five distinct OH- bands located above 3600 cm-1 at RT and seven narrow bands at 80 K and additional fine structure. The spectra were curve fit and the OH- stretching modes analyzed and assigned. It is argued that OH- is located in microscopic- and nano-size Ca3Al2H12O12-like clusters. The basic substitution mechanism is the hydrogarnet one, where (H4O4)4- ⇔ (SiO4)4-, and various local configurations containing different numbers of (H4O4)4- groups define the cluster type. The amounts of H2O range between 5 and 100 ppm by weight, depending on the IR calibration adopted, and are variable among crystals. Hydrogrossular-like clusters are also present in a synthetic pyrope with a minor Ca content grown hydrothermally at 900 °C and 20 kbar, as based on its IR spectra at RT and 80 K. Experiment and nature are in agreement, and OH- groups are partitioned into various barely nano-size hydrogrossular-like clusters. This proposal is new and significant mineralogical, petrological, and geochemical implications result. Ca and proton ordering occur. Hypothetical “defect” and/or coupled-substitution mechanisms to account for structural OH- are not needed to interpret experimental results. OH- incorporation in pyrope of different generations at Dora-Maira is discussed and OH- could potentially be used as an indicator of changing PH2O(aH2O) -T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ P_{{{\text{H}}_{{\text{2}}} {\text{O}}}} {\text{(}}a_{{{\text{H}}_{{\text{2}}} {\text{O}}}} {\text{) - }}T $$\end{document} conditions in a metamorphic cycle. Published experimental hydration, dehydroxylation, and hydrogen diffusion results on Dora-Maira pyropes can now be interpreted atomistically.


Introduction
Estimates of the amount of H 2 O held in Earth's mantle range between 0.5 and 5.5 oceans worth (Hirschmann et al. 2005). Regardless of the exact quantity, such magnitudes are of global geochemical and geophysical significance. The key reservoir for H 2 O in the upper mantle lies in the small amounts of OHthat are structurally bound in the nominally anhydrous minerals (NAMs) olivine, orthopyroxene, clinopyroxene and garnet, as shown by Bell and Rossman (1992a). These four silicates can hold small concentrations of OHthat, when integrated over their volumes contained in the upper mantle, give rise to such large-scale, global amounts of water. Much research has concentrated on investigating the concentration of OHin these phases (e.g., Bell et al. 1995;Ingrin and Skogby 2000;Rossman 2006;Peslier 2010). The presence of OHin silicates, and here garnet, is of key mineralogical, petrological, geochemical, and even rheological significance (e.g., Bell and Rossman 1992a, b;Xu et al. 2013;Zhang et al. 2019;Geiger and Rossman 2020a, b). Great strides have been made in several scientific areas and a good deal has been learned with respect to water in NAMs. Surprisingly, on the other hand, understanding is still lacking in some most fundamental questions.
Take the high-pressure garnet pyrope, ideal end-member formula {Mg 3 }[Al 2 ](Si 3 )O 12 . There have been numerous investigations on the nature of its OH -. IR singlecrystal spectroscopy, which is generally the experimental method of choice for documenting the presence of OHin minerals, has been used in most of the investigations on both natural and synthetic pyrope crystals (Rossman et al. 1989;Geiger et al. 1991;Khomenko et al. 1994;Hösch and Langer 1996;Wang et al. 1996;Bell and Rossman 1992b;Lu and Keppler 1997;Withers et al. 1998;Matsyuk et al. 1998;Geiger et al. 2000;Blanchard and Ingrin 2004a, b;Mookerjee and Karato 2010;Xu et al. 2013;Schmädike et al. 2015;Gose and Schmädicke 2018;Schmädicke and Gose 2019). The hydrogarnet substitution, namely (H 4 O 4 ) 4-⇔ (SiO 4 ) 4or (4H) + ⇔ (Si) 4+ , as proposed several times Withers et al. 1998;Mookerjee and Karato 2010), and later argued for, based on an IR spectral analysis of different garnet species measured at different temperatures , is probably operating for synthetic end-member composition pyropes grown hydrothermally in the laboratory. The hypothetical garnet component would be Mg 3 Al 2 (H 4 O 4 ) 3 .
Supracrustal rocks of this Massif, containing coesite and nearly end-member pyrope, have been of great interest. Some garnet crystals, found in whiteschists and quartzites from the Brossasco-Isasca Unit, have about a 98 mole % Mg 3 Al 2 Si 3 O 12 component. The rocks of Dora-Maira and their paleo-geologic, -petrologic and -geochemical conditions have been investigated numerous times (e.g., Chopin 1984;Schertl et al. 1991;Avigad 1991;Sharp et al. 1993;Chopin and Schertl 1999;Simon and Chopin 2001;Compagnoni and Hirajima 2001;Zechmeister et al. 2007;Ferrando et al. 2009;Gauthiez-Putallaz et al. 2016;Groppo et al. 2019). The IR spectra of various composition pyropes have been measured and studied as well (Rossman et al. 1989;Lu and Keppler 1997;Guastoni et al. 2001;Blanchard and Ingrin 2004a, b;. The common-sense reasoning was that OHin them could be structurally similar to OHfound in synthetic end-member pyrope. However, the observed IR-active OHstretching modes in the spectra are completely different, in terms of number and energy, between both types of crystals. The conclusion was that OHis incorporated differently in the natural crystals compared to the synthetics and, thus, apparently not through the hydropyrope component, Mg 3 Al 2 (H 4 O 4 ) 3 , substitution. The OHin the Dora-Maira pyropes has been termed as defect in nature (Lu and Keppler 1997;Blanchard and Ingrin 2004a,b). The reason(s) for the difference in the spectra of natural versus synthetic crystals is(are) all very puzzling and the problem has stumped the mineral-science community for about 30 years.
We are investigating further the nature of small amounts of structural OHin various end-member garnet species as well as in intermediate solid-solution compositions Geiger and Rossman 2020a, b;Geiger and Rossman unpub.). As a part of this greater research effort, and based on our findings and analysis up to now, we studied again the IR spectra and the nature of OHof the previously much-investigated, but poorly understood, pyrope from Dora-Maira. The emphasis of our analysis is on atomic vibrational behavior and crystal chemistry and not on "defect" considerations. We think previous research studies have been "barking up the wrong tree" so to speak. Our conclusions are fundamentally new, but, when interpreted together in light of our recent work on OHin garnet, are quite logical and common sense. For the first time, they allow different published experimental results to be interpreted in a new atomistic light. In addition, petrologic information relating to the complex metamorphic history of the rocks at Dora-Maira can potentially be obtained.

Samples used for study and experimental methods
Two Dora-Maira pyropes, Mas-2b from Masueria, Italy, and Ch-2, unknown locality, were investigated and are from the personal collection of C.A.G. via C. Chopin. A geologic map of the Massif, showing localities, is presented in Simon and Chopin (2001). The same crystals have been studied before using both an IR microscope and in the spectrometer itself using metal apertures with various size pinholes (Geiger and Rossman 1994;. Ch-2 is colorless and transparent to the eye, whereas Mas-2b shows a pinkish tint (Fig. 1). IR single-crystal spectra were collected on both garnets in the energy range between 3000 and 4000 cm -1 at room temperature (RT) and at different low temperatures ultimately down to 80 K. The sample preparation method and experimental IR setup have been described . In addition, the RT and 80 K spectra of a synthetic pyrope (P-27) synthesized from a gelstarting material are also analyzed. This garnet and its RT spectrum are discussed in Geiger et al. (1991). We use these results as well as unpublished IR data recorded at 80 K from their study. Spectral results were curve fit using the WiRE program of Renishaw that is part of their Raman systems (see Geiger and Rossman 2020a, b).
Chemical analyses were obtained on the two natural pyropes at Caltech with a JEOL JXA-8200 electron microprobe interfaced with Probe Software, Inc.'s program "Probe for EPMA" and operated in focused beam mode at 15 kV and 15 nA. Quantitative elemental microanalyses were processed with the CITZAF correction procedure (Armstrong 1995). X-ray fluorescence micro-analyses were conducted on the synthetic pyrope (P-27) sample with an INAM Expert 3L tabletop XRF under helium purge with a Ti target using INAM's built-in fundamental parameter software. The composition of synthetic crystal, P-27, was only measured using these XRF methods, as the crystal was later lost during preparation of the microprobe mount.

IR spectra and microprobe results
Infrared data for the three studied garnets (Ch-2, Mas-2b, P-27) can be found in supplementary files 1-4. The microprobe and micro-XRF results are summarized in Tables 1 and 2. The anhydrous crystal-chemical formulae of the Dora-Maira garnets were calculated, using the formulation of Locock (2008) The IR single-crystal spectra of pyrope Mas-2b, in the energy range of the OHstretching vibrations, at RT and 80 K are shown in Fig. 2a. The spectra of sample Ch-2 are similar in appearance and, therefore, not shown here. The RT spectrum shows five main OHbands with peak maxima at 3602, 3618, 3641, 3651, and 3660 cm -1 . The latter mode shows a clear shoulder on its high-energy flank. Previous measurements on these garnets (Geiger and Rossman 1994; show that the same OHband pattern is obtained at different locations on the crystal platelets and that the mode intensities remain nearly the same. No significant zoning in H 2 O content is present. The spectrum recorded at 80 K shows a narrowing of the bands and better spectral resolution. New modes occur, which were not observed before. The five bands observed at RT shift slightly to higher wavenumbers at the lower temperature and have peak maxima at 3604, 3622, 3644, 3654, and 3666 cm -1 . Two weak modes at 3676 and 3708 cm -1 can also be observed. There are, in addition, weak shoulders on the low-energy flanks of the bands at 3604 and 3644 cm -1 and a noticeable shoulder on the high-energy flank of the band at 3654 cm -1 . The RT spectrum can be fit with six bands and the spectrum recorded at 80 K with nine bands (more modes are also possible, for example, the very weak shoulder on the high energy flank of the band at 3604 cm -1 ) (Supplementary Fig. 2b and c).
The IR spectra of the synthetic pyrope synthesized from a gel-starting material (P-27) at RT and 80 K are shown in Fig. 3a. At room temperature, peak maxima of the OHmodes are observed at 3606 (shoulder), 3618, 3641, 3651, and 3664 cm -1 . At 80 K, OHmodes are observed at 3605(?), 3612, 3622, 3639, 3649 (asymmetric band shape), 3666, and 3674 cm -1 . The RT spectrum can be fit with eight bands and the spectrum recorded at 80 K with nine bands (Supplementary Fig. 3b and c). We do not consider the broad fitted bands occurring below 3600 cm -1 , because their exact nature is uncertain. The wavenumbers of the different OHmodes in the various spectra are listed in Table 3. Table 4 lists the amounts of H 2 O in the garnets, which are discussed below.

Discussion
There has been for the past 30 years the unanswerable question of why the IR spectra of various synthetic end-member silicate garnets are different from their nearly end-member natural analogues (see, though, Geiger and Rossman 2018, for the case of andradite and Geiger and Rossman 2020a, b, for grossular). Moreover, it was not understood why the IR spectra of Dora-Maira pyropes are so different in terms of their OHmodes compared to numerous pyropes from Earth's upper mantle. Standard thinking has been that minor OHin garnets occurs as defects, for example, {2H + ⇔ Ca 2+ } and [3H + ⇔ Al 3+ ] in grossular (e.g., Basso et al. 1984;Birkett and Trzcienski 1984;Basso and Cabella 1990), or through coupled solid-solution mechanisms such as {Li + -H + ⇔ Mg 2+ }, [Mg/Fe 2+ -H + ⇔ Al/ Fe 3+ ], (B 3+ -H + ) ⇔ (Si 4+ ) and (Al 3+ -H + ) ⇔ (Si 4+ ) in various garnets (e.g., Kühberger et al 1989;Khomenko et al. 1994; Fig. 2 a IR single-crystal spectra at room temperature (RT) and 80 K of pyrope, Mas-2b, from the Dora-Maira Massif, western Alps, Italy. Both spectra were collected in the cooling stage at the same measuring spot. The crystal thickness is 2.308 mm Fig. 3 a IR single-crystal spectrum at room temperature (RT) and 80 K of synthetic pyrope (P-27) grown hydrothermally from a gel. The crystal thickness is 0.251 mm  Lu and Keppler 1997;Reynes et al. 2018). It was thought that these and other similar mechanisms "explain" the spectral differences between synthetic and natural garnets and among different natural crystals of the same species. Our spectroscopic and crystal-chemical analyses given below permit these questions and other outstanding issues and published results to be addressed in a new light. It also permits possible new insight into petrological processes using OHin garnet. We discuss them.

State of understanding of IR spectra and OHin "end-member" garnet species: published results
Synthetic "end-member" pyrope crystals synthesized hydrothermally from high-purity oxides under different P-T-X conditions show a single broad (i.e., FWHH = 60 cm -1 ) asymmetric OHband with a peak maximum at 3629 cm -1 in IR spectra at RT and two much narrower bands (both  (Khomenko et al. 1994;Geiger et al. 2000). The amount of OHin "end-member" pyrope expressed as H 2 O is less than about 0.1 wt. % and has been argued, based on an analysis of IR spectra collected at RT and 80 K of multiple garnet species, to be held as a hydropyrope, Mg 3 Al 2 H 12 O 12 , component with isolated and local (H 4 O 4 ) 4groups in an "anhydrous matrix" . The IR spectra of pyropes with an 83 to 98 mol % Mg 3 Al 2 Si 3 O 12 component from Dora-Maira (Rossman et al. 1989;Lu and Keppler 1997;Guastoni et al. 2001;Blanchard and Ingrin 2004a, b; are completely different in appearance from all the above synthetic pyropes. It was initially thought that the OHincorporation mechanism in most pyrope-rich crystals could be similar to that of the "end-member" synthetics, but this was shown not to be the case. The pyropes from Dora-Maira also have less H 2 O, calculated as 0.002-0.003 wt. % (Rossman et al. 1989), 13 to 36 ppm (Blanchard and Ingrin 1994a, b) and 58 ppm by weight (Lu and Keppler 1997), than the synthetics.
The IR spectra of OH --bearing and natural nearly "endmember" grossular and andradite, ideal anhydrous endmember formulae Ca 3 Al 2 Si 3 O 12 and Ca 3 Fe 3+ 2 Si 3 O 12 , respectively, are, in general, more variable and complex (Rossman and Aines 1991;Maldener et al. 2003;Phichaikamjornwut et al. 2011;Dachs et al. 2012;Reynes et al. 2018) than those of Dora-Maira pyrope. OHstretching modes of a number of different energies are observable in the former. Geiger and Rossman (2020a, b) analyzed the available spectra and introduced an atomic vibrational and a crystal-chemical model to assign most of the observed OHmodes, which were previously not assignable and whose physical origin was not understood. They argued that various local, microscopic and barely nano-scale hydrogarnet (hydrogrossular and hydroandradite)-like clusters could be distributed throughout an anhydrous calcium-silicate-garnet "host matrix". The basic substitution mechanism is the hydrogarnet one, where (H 4 O 4 ) 4-⇔ (SiO 4 ) 4-, and various local configurations containing different numbers of (H 4 O 4 ) 4groups define the cluster type. The OHmodes associated with different hydrogrossular-like (Ca 3 Al 2 H 12 O 12 ) groups (one (H 4 O 4 ) 4unit) or clusters (more than one (H 4 O 4 ) 4group) have energies of about 3599, 3612, 3622, 3633, 3641 and 3657 cm -1 at RT, being fairly regularly spaced in wavenumber (Table 3). A further OHmode at about 3660 cm -1 reflects the presence of OHin more extended, yet finitesized katoite (Ca 3 Al 2 H 12 O 12 )-like clusters or larger domains. The presence or absence of the various modes can vary from grossular to grossular sample, as can the mode intensities.

Dora-Maira pyrope: IR spectra, OHband assignments, and hydrogrossular-like clusters
The IR spectra of Dora-Maira pyrope crystals show five OHbands at 3602, 3618, 3641, 3651, and 3660 cm -1 at RT (Fig. 2a). We think that the general similarity in wavenumber of these OHmodes with those observed in grossular (Table 3) is no coincidence (Note, though, that an equivalent OHmode at about 3633 cm -1 is absent in Dora-Maira pyrope. A mode at 3651 cm -1 is also present, whereas its possible equivalent is located at about 3657 cm -1 in grossular). It should also be stated that the IR spectra of many spessartine garnets show "OHmode patterns" broadly similar to those of pyrope from Dora-Maira Geiger and Rossman unpub.).
Thus, we think that OHin Dora-Maira garnets is also contained in different micro-and barely nano-size hydrogrossular-like clusters. In fact, OHpartitioning into these clusters in the pyrope appears quantitative. We find no evidence for any "hydropyrope-like" (H 4 O 4 ) 4groups, as proposed for synthetic pyrope. The assignments of the different energy OHmodes for both grossular and Dora-Maira pyrope are listed in Table 3 and the associated clusters are shown in Fig. 4 (see also Geiger and Rossman 2020a). A key point in this analysis is that the OHstretching vibration can couple or is affected by other cation-related vibrations that share the same common oxygen atom (the atomic vibrational "fragment" shown in Fig. 2 of Geiger and Rossman 2020a). Furthermore, it is also possible, that more extended mode Table 4 Concentration of H 2 O in ppm by weight calculated for different pyrope samples from Dora Maira using three different garnet absorption coefficients in Rossman (2006) In three samples, the second listed value includes a correction to the spectra to remove a band related to molecular H 2 O occurring in fluid inclusions * Spectra from Geiger and Rossman (2018) coupling can occur in as much as crystals have lattice vibrations and not isolated modes. These effects give rise to the different energies, either large or small, in OHstretching wavenumbers among the various garnet species. The spectrum of pyrope Mas-2b recorded at 80 K reveals more information. At least nine bands can be fit to the spectrum ( Supplementary Fig. 2c). We think those at 3604, 3622, 3644, and 3653/3656 cm -1 are related to various hydrogrossular-like clusters ( Table 3). The mode at 3666 cm -1 is related to larger katoite-like clusters or domains and the weak mode at 3599 cm -1 may arise at low temperatures, as described by Kolesov and Geiger (2005) in the spectra of a synthetic end-member katoite. The precise nature of the two closely spaced bands at 3653 and 3656 cm -1 at 80 K is not fully clear to us (see discussion below).
The weak high-wavenumber OHmodes above about 3666 cm -1 can have other origins. The band at 3676 cm -1 can be assigned to the possible presence of tiny talc inclusions (see the case for talc in andradite in . The mode at 3708 cm -1 is also possibly related to a layer silicate and, here, phlogopite may come into play (Farmer and Russell 1967;Beran 2002). Spectral fine structure can be complicated, because pyrope crystals at Dora-Maira are chock-full of various solid-inclusion phases (e.g., Simon and Chopin 2001;Ferrando et al. 2009;Schertl et al. 2018) including Mg-rich phlogopite and talc. They may be present as minute crystals not observable using standard microscope techniques. Geiger et al. (1991) investigated the nature of OHincorporation in a large number of synthetic pyropes grown with different starting materials under different P, T and fluidcomposition conditions. They noted that the IR spectra of pyropes synthesized from a gel were fundamentally different in appearance (Fig. 3a) from those grown from high purity oxides. A spectrum of the former type (i.e., sample P-27) could not be interpreted at that time.

Synthetic pyrope grown from a gel: IR spectra, OHband assignments, and hydrogrossular-like clusters
From the RT IR spectrum of sample-P-27, OHmodes can be fit at 3565, 3597, 3606, 3617, 3630, 3642, 3651 and 3665 cm -1 (Supplementary Fig. 3b). For the 80 K spectrum, OHmodes can be fit at 3603, 3612, 3621, 3638, 3648, 3654, 3666, 3674 and 3686 cm -1 (Supplementary Fig. 3c). This synthetic pyrope crystal contains small amounts of Ca (Table 2). Apparently, the gel-starting material used for the synthesis experiments contained small concentrations of Ca and Fe "impurities". From this, we think that the OHis also probably partitioned into hydrogrossular-like clusters (Table 3). This is notable, because this is the first case where OHincorporation mechanisms are similar-but not exactly the same-between a natural and synthetic garnet solid solution.
A comparison of the spectra at 80 K of synthetic pyrope P-27 and Dora-Maira garnet MAS-2b is shown in Fig. 5. There is a match in energy for most of the OHmodes, but the intensities can be different. The lowest wavenumber mode in the spectrum of the natural pyrope is intense, while it is weak in the spectrum of the synthetic. We have presently no explanation for this. We can only state that mode intensity depends on the nature of the dipole interaction and this can be expected to be complex, especially if mode coupling and mixing come into play.

Local crystal-chemical properties and (H 4 O 4 ) 4groups and clusters
If hydrogrossular-like clusters are present in pyrope crystals, then this has key crystal-chemical implications. Both local structural and compositional heterogeneities can exist in garnet because of short-range Ca and proton ordering. Slight short-range Ca and Mg cation ordering has been proposed to occur in synthetic anhydrous pyrope-grossular garnets based on 29 Si MAS NMR experiments and empirical pairpotential calculations (Bosenick et al. 1995(Bosenick et al. , 1999(Bosenick et al. , 2000, but it has not yet been determined for any rock-forming, natural silicate garnet (see Palke et al. 2015), as best as we know. The latter workers did investigate pyropes from Dora-Maira, using paramagnetically shifted 27 Al and 29 Si MAS NMR resonances, but they did not document any cation ordering. The dimensions of the clusters, based on the placement of the (H 4 O 4 ) 4groups, cannot be determined from the IR spectra, but they can be estimated. The atomic crystal structures of end-member pyrope, grossular, and katoite are known (Armbruster et al. 1992;Geiger and Armbruster 1997;Lager et al. 1987). The distance across a single (H 4 O 4 ) 4group is roughly 3 Å (Fig. 4b). A hydrogrossular-like cluster of the type shown in Fig. 4g should be a little less than 10 Å in dimension, as measured from outer opposing (H 4 O 4 ) 4to (H 4 O 4 ) 4group. A more extended, yet finite size, katoitelike-cluster or domain should have a minimum dimension of roughly 15 Å (Fig. 4a). Its exact upper size limit is not known.
A given cluster type is characterized by the number of (H 4 O 4 ) 4groups, but they can have different local arrangements (see Geiger and Rossman 2020a, b). It can be expected that the nature of local structural relaxation will be different depending on the cluster type and precise (H 4 O 4 ) 4group arrangements for each cluster type. This could give rise to slight variations in OHmode energies and intensities, as observed between the spectra of Dora-Maira and synthetic pyrope (i.e., P-27).

Determination of H 2 O content in Dora-Maira pyrope: consequences of the cluster model
The fact that the various hydrogrossular-like clusters have different OH --mode energies indicates that the molar IR absorption coefficients associated with each type could have different values (Libowitzky and Rossman 1997). How different they could be remains to be determined. The analysis, herein, and in Geiger and Rossman (2020a, b), sets out how absorption coefficient determinations for H 2 O in garnet should be undertaken and what spectral aspects need to be considered.
We calculated the H 2 O concentrations for the pyropes Mas-2b and Ch-2 (Table 2), as well as SB-1 (locality San Bernardo) and Mas-2a (locality Masueria), discussed in  and Palke et al. (2015), and the Dora-Maira garnets GRR 1266.1, GRR 1266.2 and GRR 945 described in Rossman et al. (1989). Three different absorption coefficients were used, namely those for pyrope, H 2 O-poor grossular and H 2 O-rich grossular ("hydrogrossular"), as given in Rossman (2006). Results are listed in Table 4. All three coefficients were used to illustrate the differences in the amounts of H 2 O obtained. Based on the analysis and arguments made herein, the absorption coefficient for H 2 O-poor grossular should give the best measure of H 2 O concentrations and not that for pyrope.
Consider, further, the issue regarding the use of the proper absorption coefficients for H 2 O and even for the same garnet species. There is a significant difference in the absorbance coefficients between H 2 O-rich and H 2 O-poor grossular. They are different by about a factor of two and at first thought this may seem illogical considering that both are for grossular garnet (see Fig. 1 of Geiger and Rossman 2020a). However, an analysis of their respective IR spectra and their crystalchemical properties can possibly explain the difference. The IR spectra of katoite (end-member formula Ca 3 Al 2 (H 4 O 4 ) 3 ) and H 2 O-rich grossular are characterized by broad OHstretching bands (for GRR 1059, the 3662 cm -1 band is ~30 cm -1 FWHH; for GRR 1329, the 3668 cm -1 band is ~ 32 cm -1 FWHH and the 3596 cm -1 band is ~65 cm -1 FWHH), whereas these bands in the spectra of H 2 O-poor grossular are much narrower (see Geiger and Rossman 2020a). The nature of IR mode broadening in garnet was discussed in that study. We think that the large vibrational amplitudes associated with the light hydrogen atoms in "expanded garnet structures" such as katoite or in extended katoite-like domains in katoite-grossular solid solutions, compared to the case for H 2 O-poor grossular, are the cause for the broader OHmodes in the spectra of the former. In other words, the vibrational behavior of hydrogen atoms in hydrogrossular-like clusters in nearly end-member grossular will be controlled by the smaller volume anhydrous grossular host structure. Narrower OHstretching modes result. We think that the nature of local structural relaxation is important in controlling the vibrational behavior of hydrogen atoms. It follows that the areas associated with the respective OHbands will be different, as will the absorption coefficients.
Returning back to the spectra of Dora-Maira pyrope, the narrow OHstretching modes of these garnets are most similar in terms of vibrational behavior (i.e., both energy and band widths) to those in H 2 O-poor grossular.

There are pyropes and there are pyropes: differences in composition, origin, and OHincorporation mechanisms
Mantle pyropes display completely different IR spectra than pyropes at Dora-Maira. The former are often characterized, for example, by a prominent OHmode at 3570 cm -1 (Bell and Rossman 1992b). It goes without out saying that pyropes from Earth's mantle, as found in various xenoliths from kimberlites (e.g., Bell and Rossman 1992b;Matsyuk et al. 1998), and in other types of eclogites (e.g., Schmädike et al. 2015;Liu et al. 2016;Gose and Schmädicke 2018;Zhang et al. 2019) and pyroxenites (Li et al. 2018), have a completely different petrologic origin than those found in the UHP whiteschists and quartzites at Dora Maira. The chemistries of mantle garnets are more complex and varied, as they contain a number of chemical components (Dawson and Stephens 1975). Bell and Rossman (1992b) wrote "OH abundances in garnet are closely linked to host rock paragenesis and cannot be explained purely by any crystal chemical factors which we have investigated". The results of this study indicate that crystal-chemical factors can play a role in the incorporation of OHin pyrope. Dora-Maira pyropes show a distinctive IR "signature" reflecting OHincorporation mechanisms similar to that found in crustal grossulars, andradite (Geiger and Rossman 2020a, b) and many spessartines (Geiger and Rossman unpub.). In light of this observation, we discuss briefly the petrologic history at Dora-Maira.

Petrology of the UHP rocks at Dora-Maira and the role of pyrope
Investigations of the metamorphic conditions of the different garnet-bearing lithologies of the UHP Dora-Maira Massif have been undertaken (e.g., Simon et al. 1997;Chopin and Schertl 1999;Ferrando et al. 2009;Groppo et al. 2019). The crystallization of pyrope within the Brossasco-Isasca Unit is complex, involving different stages during the P-T-t cycle. Pyropes of different types (i.e., megablasts, porphyroblasts and neoblasts) and generations have different compositions, and zoning within some crystal types can be observed. Ferrando et al. (2009) discuss, in detail, the complex metamorphic evolution consisting of five stages from A to E, and we summarize their findings. Three generations of pyrope growth (stages C, D and E) can be recognized by their forms, compositions and mineral inclusions. The first generation (i.e., their Pyp I: Pyr 69-81 Almd 16-26 ) was considered prograde and it contains inclusions of kyanite, talc, phlogopite (regressed to vermiculite), Mg-chlorite and other phases. We note that the IR spectrum of pyrope Mas-2b may possibly record very minor minute inclusions of talc and phlogophite (Fig. 2). The P-T conditions for stage C were estimated to be 2.1 < P < 2.8 GPa and 590 < T < 650 °C. A second generation of pyrope (Pyp II: Pyr 82-98 Almd 1-16 ) crystallized at peak metamorphic conditions (stage D) and it contains only rarely talc but never Mg-chlorite and phlogopite. P-T conditions were T ~ 730 °C and P ~ 4.0 to 4.3 GPa. A third generation of pyrope (Pyp III: Pyr 86-67 Almd 4-11 ) is considered to be retrograde (stage E) and it is usually replaced by phengite, biotite, talc, kyanite, and chlorite. Here, Ferrando et al. (2009) give T ~ 720 °C and P ~ 3.6-3.9 GPa. Sharp et al. (1999) argued that the water activity, a H2O , during metamorphism must have been lower than 1.0, lying between 0.4 and 0.75 at 700-750 °C. Ferrando et al. (2009) describe two generations of fluid inclusions (i.e., type-I and type-II) with type-I forming during prograde metamorphism. The fluid was complex in composition being termed a NaCl-MgCl 2 -bearing brine with 6 to 28 NaCl eq (in wt. %). At peak metamorphic conditions (stage D), the fluid was different in nature, here, being described as "an aluminosilicate aqueous solution with a composition intermediate between an aqueous fluid and a silicate melt".
We note that the IR spectra of all pyrope samples from Dora-Maira that have been studied to date, regardless of their composition and locality, are similar in terms of the number and energies of the OHbands (Rossman et al. 1989;Lu and Keppler 1997;Guastoni et al. 2001;Blanchard and Ingrin 2004a, b;this work). The mechanism of OHincorporation in all crystals appears to be similar. The spectra do not indicate the presence of any hydropyrope-like substitution only a hydrogrossular-like one. The phase relations of the grossular-katoite ("hydrogrossularite") system have been studied to P H2O = 15.5 kbar and to 850 °C (Pistorius and Kennedy 1960). They allow a possible, simple interpretation of the behavior of hydrogrossular-like clusters in pyrope. Their results show that the amount of H 2 O in garnet (i.e., "hydrogrossular") is mostly a function of temperature. Above about 800 °C, garnet is "anhydrous". Though not investigated by Pistorius and Kennedy (1960), a lowering of a H2O below 1.0 should also act to decrease the amount of H 2 O in garnet. We think both factors could possibly explain the low-water contents (Table 4) in the pyropes at Dora-Maira. In other words, low temperatures and high a H2O act to stabilize the hydrogrossular component. It follows that the precise type of the hydrogrossular-like cluster, and its concentrations in pyrope, could reveal information about the P-T-X crystallization conditions assuming chemical equilibrium prevailed.
Based on the compositions of our different pyropes (Table 2b), we can consider that samples SB-1 and possibly Mas-2a and GRR 1266 (interior) represent "Pyp-I" garnets that crystallized at metamorphic stage C. The more pyroperich samples Ch-2, Mas-2b and GRR 945 possibly represent peak metamorphic "Pyp-II" crystals. We analyzed the concentrations of H 2 O (Table 4) for the different pyrope samples as a function of their atomic Ca and Fe 2+ contents using the data in Table 2. We could not discern any clear relationship. It appears that the amounts of CaO and Al 2 O 3 in the pyrope crystals should be more than enough to account for all the structural OHin hydrogrossular-like clusters (a calculation of various anhydrous garnet components, using the formulation of Locock 2008, gives 1.4 mol % grossular for sample Mas-2b and 0.8 mol % for sample Ch-2). Finally, Fig. 6 shows the concentration of H 2 O for possible Pyp-I and Pyp-II samples. There might be a tendency for the latter peak-metamorphic garnets to have on average more H 2 O.
Additionally, pyrope GRR 1229 (Table 4) has roughly twice as much H 2 O at its rim as it does at its core. At the simplest level, one could suggest, because the temperature of metamorphic stage D was greater than that of stage C, that a H2O may have been the deciding factor and it could have been higher at peak metamorphic conditions. This analysis is preliminary and elementary, and research needs to be done in this direction to explain the H 2 O amounts and their distribution in garnet crystals at Dora-Maira.
Finally, we note, to end this section, that Geiger et al. (1991) synthesized pyrope from high purity oxides, at high P and T in H 2 O solutions containing NaOH and HCl (basic and acidic conditions, respectively). The IR spectra of these garnets were, though, the same as those crystals grown in pure H 2 O. That is, they show a broad asymmetric OHband at RT with a peak maximum at 3629 cm -1 . This would seem to indicate that fluid brines, alone, operating during metamorphism of the Dora-Maira rocks, are probably not the cause for the unusual OHincorporation mechanism in the pyrope crystals.

Reinterpretation of published results relating to OHin Dora-Maira pyrope
Hydration behavior of Dora-Maira pyrope at high P H2O and T Our cluster model allows the experimental results of Lu and Keppler (1997)  To study the nature of H 2 O incorporation, they treated their crystal to varying high P H2O and T conditions in the laboratory. In short, they observed in the IR spectra of the pyrope single crystals, following treatment, that the OHmodes at 3641, 3651 and 3661 cm -1 increased in intensity, while that at 3602 cm -1 decreased. We think that these results indicate that more H 2 O-rich clusters, like the types shown in Fig. 4a, f and g, increase in number. In a simple and general sense, a local-cluster hydration reaction could be given, for example, by This reaction is based on the assumption of a 12 oxygen formula unit and it requires that SiO 2 be precipitated locally. This proposal could be tested experimentally. It is of note that (1) would require the breaking and reforming of strong Si-O bonds, but the hydrothermal experiments were made at 800 to 1200 °C (Lu and Keppler 1997).
The cluster model explains, furthermore, why H 2 O incorporation is not noticeably dependent on f O2 (the hydrothermal experiments were done under f O2 conditions defined by the Fe-FeO and Ni-NiO buffers). The crystal-chemical nature of the different cluster types also explains why the OHstretching mode at 3602 cm -1 is "stiffer in behavior", as based on IR measurements made on the pyrope crystal in a diamond-anvil cell (Lu and Keppler 1997), compared to the higher energy OHmodes at 3641, 3651 and 3661 cm -1 . The latter represent larger clusters having greater numbers of (H 4 O 4 ) 4groups. Indeed, the structure of Ca 3 Al 2 (H 4 O 4 ) 3 , is considerably more compressible than Ca 3 Al 2 (SiO 4 ) 3 , as shown by X-ray diffraction experiments undertaken in a diamond-anvil cell (Olijnyk et al. 1991).

High-temperature behavior and hydrogen loss at 1 atm of Dora-Maira pyrope
Dehydroxylation and hydrogen-diffusion behavior were studied at ambient pressure by heating a Dora-Maira pyrope crystal at 1073 and 1323 K followed by IR measurements (Blanchard and Ingrin 2004a, b). Their crystal was zoned with a rim composition of Py 88 Al 9 Gr 3 and a core composition of Py 81 Al 15 Gr 3 . Their results showed that hydrogen associated with the so-called OHband "triplet" centered at 3651 cm -1 (i.e., the modes at 3641, 3651 and 3661 cm -1 ) diffused three times faster than hydrogen associated with the band at 3602 cm -1 . This was interpreted as indicating "the presence of two distinct H defects" (Blanchard and Ingrin 2004a, b).
The cluster model permits these experimental results to be interpreted in terms of atomistic-level structure and crystal-chemical considerations. That is, it could be expected that larger hydrogrossular-like clusters containing two or more (H 4 O 4 ) 4groups behave differently than a single, isolated group at elevated temperatures. The latter could be (1) Ca 3 Al 2 H 2.0 Si 2.5 O 12 + 3H 2 O → Ca 3 Al 2 H 8.0 Si 1.0 O 12 + 1.5SiO 2 .  (Table 4), in different pyrope crystals from Dora Maira as a function of the number of Mg cations in the formula unit. The more pyrope-rich samples (Pyp II-see text and Ferrando et al. 2009) could have crystallized during peak metamorphism, whereas the more pyrope-poor samples (Pyp I) during prograde metamorphic conditions (see text) more stable at elevated temperatures (see discussion in Geiger and Rossman 2020b). The experimental high P-T phase relations of grossular-hydrogrossular garnets (Yoder 1950;Pistorius and Kennedy 1960) lend general support to this proposal. Under the assumption that garnet is stoichiometric (12 oxygens), and where the substitution (H 4 O 4 ) 4-⇔ (SiO 4 ) 4occurs, a local dehydration reaction of the general type may occur at 1 atm and high T: or alternatively an amorphous-like phase could be produced.
To close and on a further note, we propose that the term "hydrogrossular-like cluster" (Geiger and Rossman 2020a, b) describes the crystal-chemical situation better than the term "OHdefect". The latter can be interpreted as indicating that the H + atoms are not an integral part of the garnet structure and that they cannot be described by any crystallographic relationships. We do not think that this is the case. There is solid-solution of the type (H 4 O 4 ) 4-⇔ (SiO 4 ) 4in garnet, which is most pronounced in grossular and andradite, and its extent is a f(P,T,X) of the system and garnet crystal chemistry.

Conclusions
There are notable consequences that derive from this research. First, views on crystal chemistry and various experimental results relating to H 2 O incorporation and loss in Dora-Maira pyrope crystals need to be rethought. Second, we think that analytical determinations of H 2 O concentrations in all types of garnet using IR spectroscopy need to consider the precise OHsubstitution mechanism for the garnet in question (Bell et al. 1995;Maldener et al. 2003;Reynes et al. 2019). Third, in terms of IR measurements and the study of hydrogen-bearing species (e.g., H 2 O, OH -, H + ) in crystals, a full vibrational mode determination is often only possible at the lowest temperatures accessible experimentally. This has been shown in several works on different minerals containing H 2 O and OH - (Kolesov and Geiger 2005;Kolesov 2006;Geiger 2012; and shown again here. This is because the H atom can have large amplitudes of vibration at room temperature depending on the local bonding situation. This can lead to substantial mode broadening. Finally, if a given hydrogarnet cluster formed under chemical equilibrium, it must reflect the pressure, temperature, and composition (P-T-X) conditions during crystallization. And here H 2 O activity is important. IR spectroscopy could be of potential use in investigating the petrological conditions under which a garnet, and the rock in which it is contained in, grew. It goes without saying (2) Ca 3 Al 2 H 12 O 12 (cluster) → Ca 3 Al 2 O 6 (tricalcium aluminate) + 6H 2 O, that possible kinetic aspects relating to hydrogarnet cluster formation also need consideration.