Ferrous/ferric (Fe²⁺/Fe³⁺) partitioning among silicates in metapelites

Abstract

Fe³⁺ and X_Fe3+, defined as Fe³⁺/(Fe²⁺ + Fe³⁺) on a molar basis, are now recognised as key parameters in phase equilibrium modelling. A hindrance is that it is only possible to routinely measure total Fe, and not Fe³⁺ and Fe²⁺, in minerals using the electron microprobe. Charge balance techniques can be used to estimate Fe³⁺ and Fe²⁺ for some minerals, but not for those that contain vacancies. Whilst other analytical techniques can determine X_Fe3+ in minerals, these are not commonly applied by metamorphic petrologists. Therefore, researchers must rely on estimates. This study collates wet chemical, Mössbauer spectroscopy, and X-ray absorption near edge structure (XANES) spectroscopy analyses of X_Fe3+ in metapelitic minerals and rocks from the literature. The resulting database of 77 studies contains 591 samples, of which 261 have X_Fe3+ determined for the whole rock. There are X_Fe3+ measurements for 483 biotites, 192 white micas, 78 chlorites, and 32 staurolites. Average (± 1σ) X_Fe3+ values in whole rock, biotite, white mica, chlorite, and staurolite are 0.23 ± 0.16, 0.11 ± 0.08, 0.55 ± 0.18, 0.08 ± 0.07, and 0.07 ± 0.06, respectively. The average (± 1σ) number of Fe³⁺ cations in biotite, white mica, chlorite, and staurolite is 0.28 ± 0.19 (22 O + Ti cations per formula unit, pfu), 0.17 ± 0.13 (22 O pfu), 0.31 ± 0.27 (28 O pfu), and 0.20 ± 0.17 (46 O pfu), respectively. The mean whole rock X_Fe3+ is similar for metapelites containing ilmenite and magnetite, as well as those that report no Fe-oxide, but is considerably higher for hematite-bearing rocks. Whilst there is little variation with pressure and temperature, there is an increase in the number of Fe³⁺ cations and X_Fe3+ of both white mica and biotite with the type of Fe-oxide present. Our observations are compared with the predictions of phase equilibrium modelling using thermodynamic dataset 6.2 (Holland and Powell, J Metamorph Geol 29:333–383, 2011) and the solution models of White et al. (J Metamorph Geol 32:261–286, 2014a) for Fe³⁺ and X_Fe3+ in these minerals. The predicted X_Fe3+ and number of Fe³⁺ cations in biotite, chlorite, and staurolite broadly match natural observations, but for white mica the predicted mean X_Fe3+ is underestimated by 0.2–0.4 and the number of Fe³⁺ cations by 0.05–0.2. Whilst modelling correctly predicted increases in the X_Fe3+ of white mica and biotite with whole rock X_Fe3+, it also predicted variations in mineral X_Fe3+ as a function of pressure and temperature which are not observed in the natural samples.

Introduction

Since the advent of the electron probe micro-analyser (EPMA) as an analytical tool for geologists, major element geochemical characterisation of minerals has become routine. However, routine EPMA analysis can only determine total Fe, not Fe oxidation states (Fe²⁺ and Fe³⁺). This has long been recognised as a problem for metamorphic petrologists. For example, Fe–Mg thermometry is based on the exchange of Fe²⁺ and Mg, not total Fe, yet several minerals contain enough Fe³⁺ to affect the Fe/Mg ratio and thus the temperature estimate (Guidotti and Dyar 1991; Holdaway et al. 1997; Schumacher 1991). As a result, authors have attempted to determine Fe³⁺ from EPMA data using recalculation schemes based on charge balancing (Droop 1987), or a procedure known as the Flank Method (Höfer et al. 1994). These techniques are mainly applicable to anhydrous silicates and oxides (e.g., garnet, pyroxene, spinel, and Fe-oxides). Whilst empirical estimates of ferric iron contents have been developed for some hydrous minerals, (e.g., amphibole; Hawthorne et al. 2012; Holland and Blundy 1994; Robinson et al. 1982; Schumacher 1991, 2007; Stout 1972), the same cannot be done for minerals that contain more than one partially filled site such as biotite, white mica, chlorite, and staurolite (Schumacher 1991). Li et al. (2019) attempted to expand the Flank Method for use in biotite, but this approach is not widely used and requires further testing. Whilst other analytical techniques, such as Mössbauer spectroscopy, electron energy-loss spectroscopy (EELS), X-ray photoelectron spectroscopy (XPS), and X-ray absorption near edge structure (XANES) spectroscopy at the K edge have been used to determine Fe³⁺ in minerals, they have only been applied in a relatively small number of studies. Therefore, when considering Fe³⁺, researchers must rely on estimates of Fe³⁺ in several rock-forming minerals.

Before the widespread use of EPMA, authors painstakingly separated minerals from rocks and used wet chemical techniques to determine their compositions, including Fe²⁺ and Fe³⁺. Several compilations of wet chemical data exist in the literature from studies concerned with crystal–chemical classifications of individual silicates (e.g., Foster 1960, 1962, 1964); however, these works generally collated analyses from a wide variety of rock types (felsic to mafic igneous and/or metamorphic) and most only considered Fe³⁺ contents in a single mineral from each sample. This study focuses on the ferrous/ferric ratios of silicates in metamorphosed siliciclastic rocks (e.g., pelites and semi-pelites), which are widespread in the rock record and widely used as indicators of metamorphic grade. Only one extensive study to date has measured Fe²⁺ and Fe³⁺ in multiple metapelitic minerals from individual rocks (Dyar 1990; Dyar et al. 1991, 2002; Guidotti et al. 1994; Guidotti and Dyar 1991). These authors examined the Fe³⁺ contents of different minerals from across a regional, medium-pressure metamorphic sequence (garnet–staurolite–sillimanite–K–feldspar) in West-central Maine using both XANES and Mössbauer spectroscopy. Whilst the samples from Maine encompass a range of metamorphic grade, they equilibrated at approximately the same pressure and represent a narrow range of bulk compositions. Therefore, it may not be appropriate to use the Maine dataset as the basis for estimates of Fe³⁺ contents in other metapelites that equilibrated at different pressure–temperature (P–T) conditions and oxidation states.

Here, we have collated a database of Fe³⁺ contents in minerals from studies that analysed Fe²⁺ and Fe³⁺ using wet chemistry, Mössbauer spectroscopy, and XANES spectroscopy. The emphasis is on the metapelitic minerals biotite, white mica, chlorite, and staurolite because Fe³⁺ in these minerals cannot be estimated from EPMA data. We examine variation in the number of Fe³⁺ cations and X_Fe3+ in these minerals as a function of metamorphic grade, pressure, and oxidation state using the type of Fe-oxide present in the rock as a proxy. We compare these observations with the predictions of phase equilibrium modelling using the Holland and Powell (2011) thermodynamic dataset 6.2 and White et al. (2014a) solution models.

Methods

Data selection and extraction

Papers and theses containing measurements of Fe²⁺ and Fe³⁺ in minerals were discovered through a series of Google Scholar and ProQuest searches using combinations of the following key words: ferrous, ferric, Fe³⁺, wet chemical, metapelitic, metasedimentary, and metamorphism. Some searches were restricted to the date range 1955–1975 to filter out the many EPMA-based studies of later years which lack measurements of Fe³⁺. To ensure we captured as many data as possible, manual searches through online archives between the years of 1955 and 1975 were conducted for the following journals: American Mineralogist, Bulletin de la Société Géologique de France, Contributions to Mineralogy and Petrology, Journal of the Faculty of Science University of Tokyo, Journal of the Geological Society of Japan, Journal of Petrology, Neues Jahrbuch für Mineralogie—Abhandlungen, Neues Jahrbuch für Mineralogie—Monatshefte, and Schweizerische Mineralogische und Petrographische Mitteilungen. Whilst it is inevitable that some data have eluded our searches, the resultant database is still substantial.

Three main criteria had to be met for a sample to be included in the database: (a) a measurement of Fe²⁺ and Fe³⁺ in one or more of white mica (e.g., muscovite, phengite, sericite), biotite, chlorite, and staurolite; (b) a list of the major minerals in the assemblage; and (c) a description indicating that the sample was a metamorphosed siliciclastic rock (e.g., mudstone/siltstone/immature sandstone protolith; pelite/semi-pelite). Since the majority of samples included in the database are metapelites, we use this term throughout the rest of the paper to describe the samples; however, the reader should note that a small subset of the samples would be strictly classified as semi-pelites or metagreywackes.

Some studies also presented analyses of garnet, cordierite, and chloritoid in the same selected samples; however, these have not been included in the database for the following reasons: measurements of Fe³⁺ in garnet and cordierite from pelites and semi-pelites indicate that there is negligible Fe³⁺ in them (e.g., Dyar et al. 2002, 2012; unpublished; Geiger et al. 2000a, b; Williams and Grambling 1990); Fe³⁺ in garnet and chloritoid can be estimated from EPMA data using a charge-balancing approach (Droop 1987); and there are relatively few Fe³⁺ analyses of cordierite and chloritoid in the literature.

For analyses of minerals and rocks, the weight per cent oxides for all elements (not just FeO and Fe₂O₃) were taken from the original sources. In some cases, only the cations per formula unit (e.g., Dyar et al. 1991), or the reported ratio of Fe³⁺ to total iron for each mineral (e.g., Dyar et al. 2002) were available.

Mineral formulae recalculation

Mineral formulae were recalculated from the original weight per cent oxides wherever possible. Cations could not be determined for partial analyses (e.g., Albee 1965; Card 1964; Chinner 1960; Goossens 1970). Using a fixed number of OH⁻ anions to calculate mineral formulae for phyllosilicates can be problematic since hydrogen contents may be non-stoichiometric (Dyar et al. 1993a). If the H₂O content of the mineral was measured then this problem could be negated, since normalisation could be based on the measured number of O/OH atoms per formula unit (pfu). However, only a few authors included H₂O contents in their analyses and most of these studies did not indicate whether H₂O contents were measured or estimated. To be consistent in our recalculations, we did not incorporate stated H₂O contents. Careful consideration was therefore needed when deciding on the number of negative charges, using O²⁻ as the effective anion, in formula recalculation for biotite, white mica, and chlorite analyses.

Eugster and Wones (1962) first noted a correlation between the number of Fe³⁺ cations and the OH⁻ content of biotite. Since then, numerous workers have investigated how tetra- and tri-valent cations (e.g., Fe³⁺, Ti⁴⁺, Al³⁺, Cr³⁺, etc.) may be incorporated in the octahedral site of phyllosilicates through the loss of H⁺ from the OH groups. This process is known by several names including: “oxy-substitution”, “dehydrogenation”, and “deprotonation”. Foster (1964) found a low degree of correlation between Fe³⁺ and excess O in micas and chlorite, suggesting that whilst deprotonation may account for the excess charge in some samples, it did not in others. She concluded that Fe³⁺ contents are mainly determined by the redox state of the rock, as has been found in several subsequent studies (e.g., Dodge et al. 1969; Guidotti et al. 1994; Guidotti and Dyar 1991; Redhammer et al. 1993; Wones and Eugster 1965). Dyar et al. (1993a) demonstrated that in biotite, muscovite, and chlorite, deprotonation involving only the exchange of H⁺ and Fe³⁺ is rare and is better considered as an exchange involving all tetra- and tri-valent cations in a mineral. Cesare et al. (2003) concluded that Ti⁴⁺ accounts for the majority of the H deficiency in biotite from metapelitic samples, in agreement with the observations of Righter et al. (2002) and Waters and Charnley (2002). Since our study focusses on metapelitic rocks, we accept the findings of these studies and have therefore determined our biotite formulae based on a 22 O + Ti cations recalculation.

Concerning muscovite, deprotonation is thought to be minor (Dyar et al. 1993a; Guidotti and Sassi 1998a, b), whereas for chlorite, some have postulated that deprotonation may aid incorporation of Fe³⁺ in the octahedral site (Lempart et al. 2018, 2020; Masci et al. 2019; Walshe 1986). We have found no well-documented studies of the H⁺ and Fe³⁺ contents of chlorite or muscovite in metapelitic rocks. Therefore, we have recalculated muscovite and chlorite analyses using a fixed number of anions: 22 and 28 O pfu, respectively. Staurolite analyses were recalculated using 46 O pfu (Deer et al. 2013). The number of oxygens per formula unit chosen for each mineral here is the same as in the White et al. (2014a) solution models, which maintains consistency between our natural data and thermodynamic predictions to be discussed below.

Two important parameters related to variations in Fe²⁺ and Fe³⁺ are X_Fe3+ and X_Mg. These are defined on a molar basis as follows:

$${\text{X}}_{{\text{Fe3+ }}} = \frac{{2{\text{Fe}}_{{2}} {\text{O}}_{{3}} }}{{2{\text{Fe}}_{{2}} {\text{O}}_{{3}} + {\text{FeO}}}} = \frac{{{\text{Fe}}^{{3 + }} }}{{{\text{Fe}}^{{3 + }} + {\text{Fe}}^{{2 + }} }}\quad \left( {{\text{molar}}} \right),$$

$${\text{X}}_{{{\text{Mg}}}} = \frac{{{\text{MgO}}}}{{{\text{MgO}} + {\text{FeO}}}} = \frac{{{\text{Mg}}^{{2 + }} }}{{{\text{Mg}}^{{2 + }} + {\text{Fe}}^{{2 + }} }}\quad \left( {{\text{molar}}} \right).$$

X_Mg is the ratio of Mg²⁺ to (Mg²⁺  + Fe²⁺), not Mg²⁺ to (Mg²⁺  + Fe^total) as is commonly assumed in microprobe analyses that do not distinguish between Fe²⁺ and Fe³⁺. Note that the above definition of X_Fe3+ is equivalent to the oxidation ratio of Chinner (1960) divided by 100.

Analytical techniques

Measurements of Fe³⁺ in metapelitic rocks and minerals in our database were determined by wet chemistry, Mössbauer spectroscopy, or XANES spectroscopy. We briefly summarise these methods and refer the reader to the original studies for detailed descriptions. In the majority of wet chemical studies, Fe³⁺ was determined using a two-step dissolution process (see Fritz and Popp 1985 for a review). One portion of the sample is either completely oxidised, so that total iron can be measured as Fe₂O₃ by atomic absorption spectrophotometry, or alternatively completely reduced, so that total iron can be measured as FeO by colorimetry. A separate portion of the sample is dissolved without oxidation or reduction, in order to measure the sample’s original FeO content using titration or colorimetry. The difference between the two values provides the amount of Fe³⁺ in the sample. Comparatively, XANES and Mössbauer spectroscopy measurements can only determine X_Fe3+ (Bajt et al. 1994) and therefore must be combined with an EPMA analysis of Fe in order to quantify Fe³⁺. Note that XANES spectroscopy is a microbeam technique that analyses X_Fe3+ in-situ, whereas Mössbauer spectroscopy is similar to wet chemistry, in that it requires the sample to be crushed and the mineral of interest separated so that it may be analysed in bulk. As a result, XANES measurements have sometimes found a wide range of Fe³⁺ contents at the scale of a thin section (e.g., Delaney et al. 1998; Dyar et al. 2002; Masci et al. 2019), which would not be detected in either Mössbauer spectroscopy or wet chemical analyses.

Database analysis

When compiling a database of this nature, there is inherent uncertainty and bias from several sources. First, we filtered the data by applying some quality controls (described below) to remove poor analyses. Second, we explored whether it is appropriate to pool analyses completed in different laboratories using a range of analytical techniques. Finally, we examined whether there is any bias in the database towards certain minerals, P–T conditions, or oxidation states.

Data filtering

It is not possible to independently verify that the values for individual elemental oxides (e.g., Fe₂O₃ and FeO) in analyses from literature studies are “good”. However, we can assess the overall stoichiometry of an analysis in samples for which a complete chemical analysis was provided.

In micas we scrutinised the total number of octahedral and interlayer site cations per formula unit (Fig. 1). Micas with a full interlayer site have 2.0 cations (Ca, Na, and K); values greater than 2.0 or less than 1.6 are considered suspect, the lower value sometimes arising from inter-layer chlorite. To be conservative, we therefore only included analyses with total interlayer cations between 1.4 and 2.2 (Fig. 1). White micas are dominantly dioctahedral with 4.0 cations in the octahedral site, whilst biotites are dominantly trioctahedral with 6.0 cations in the octahedral site. Some solid solution is possible, meaning that values between 4.0 and 6.0 cations are plausible (c.f. Tischendorf et al. 2007). Values outside 4.0–6.0 are unlikely, and where measured suggest some contamination. Being conservative, we only included analyses with total octahedral cations between 3.8 and 6.2 (Fig. 1). In chlorite the total number of cations per formula unit ranges from 8.0 (di-dioctahedral) to 10.0 (tri-trioctahedral), therefore to be conservative, we only included analyses with total cation sums between 7.8 to 10.2 (c.f. Zane and Weiss 1998). In staurolite, the total number of cations per formula unit is typically between 29.0 and 30.0, therefore, we only included analyses with total cation sums of 28.8–30.2 (c.f. Hawthorne et al. 1993).

Fig. 1

Total interlayer site cations vs. total octahedral site cations for a white mica (22 O pfu) and b biotite (22 O + Ti cations pfu). Colour bars show the 2D probability density estimate for the data. Grey dots represent analyses which were removed. Dashed lines show the stoichiometric constraints used to filter analyses

The resulting database of 77 studies contains 591 samples from 47 localities, the latter listed in Table 1. Online Resource 1 (Table S1) details the full database of samples including name, metamorphic zone, assemblage, minerals analysed, and whether whole rock data are available. 261 samples (44.2%) were analysed for whole rock X_Fe3+ (Online Resource 1—Table S2). There are 785 individual minerals with measured X_Fe3+ including 483 biotites, 192 white micas, 78 chlorites, and 32 staurolites (Online Resource 1—Tables S3–6). After omitting partial analyses, the number of Fe³⁺ cations could be calculated for 456 biotites, 190 white micas, 60 chlorites, and 26 staurolites.

Table 1 Geographic and/or geologic locations of regions with ferrous/ferric data for silicate minerals, listed alphabetically

Comparison of analytical techniques

For the 785 mineral X_Fe3+ values in our database, 83.4% were measured using wet chemical methods, 12.5% via Mössbauer spectroscopy, and 4.2% by XANES. All whole rock X_Fe3+ values in the database were determined by wet chemical methods. For the mineral analyses, an important question is whether different analytical techniques produce comparable measurements of Fe³⁺. Only a small number of the minerals in the database were analysed using multiple techniques (4.1%). Williams and Grambling (1990) examined their biotite separates using both Mössbauer spectroscopy and wet chemical methods (six analyses; 0.8% of the database); they found that the techniques gave similar results, except in cases where there were local patches of alteration or fine mineral inclusions in biotite. Ten of the biotites studied using Mössbauer spectroscopy in Dyar (1990) were later analysed using XANES and wet chemical techniques by Delaney et al. (1998), who found that results of all three compared well with each other. Following this work, Dyar et al. (2002) published XANES analyses of biotite, muscovite, and chlorite, for which X_Fe3+ had previously been determined using Mössbauer spectroscopy (3.3% of the database; Dyar 1990, unpublished; Guidotti et al. 1994; Guidotti and Dyar 1991; Moeller 1991). They found good agreement between the two techniques in all minerals except muscovite, for which the Mössbauer spectra typically showed lower values than XANES, especially at lower metamorphic grade; these authors interpreted this discrepancy as being due to contamination of the muscovite separates analysed by Mössbauer spectroscopy by fine-grained chlorite. We therefore replaced the values of X_Fe3+ determined from the earlier Mössbauer studies with the X_Fe3+ values determined by XANES.

Due to the relatively small number of samples in our metapelite database for which analyses were performed using more than one technique, we also examined studies in the literature from other rock types that employed multiple techniques. These studies were from igneous rocks or metamorphic rocks of a non-sedimentary nature, so the analyses were not included in our database. Several studies found good agreement between wet chemical and Mössbauer analyses in a range of minerals including micas, amphiboles, garnets, and pyroxenes (Bancroft and Brown 1975; Dodge et al. 1969; Dyar et al. 1993a, b; Dyar and Burns 1986; Ernst and Wai 1970; Fritz and Popp 1985; Lalonde et al. 1998; Whipple 1974; Williams and Grambling 1990). Lalonde et al. (1998) conducted a study of biotite that compared Mössbauer spectroscopy to the most common wet chemical methods in use. They found that results from the Pratt (1894) wet chemical method matched the results of Mössbauer spectroscopy better than the wet chemical results from the Wilson (1955,1960) method. Unfortunately, for the analyses in our database determined by wet chemistry, many authors did not provide detailed methods for how Fe²⁺ and Fe³⁺ were measured using wet chemistry, meaning we were unable to assess possible discrepancies arising from different techniques. For those authors that did fully detail their methods, they typically followed those outlined by Shapiro and Brannock (1956), which is similar to that of Pratt (1894).

Previous studies have also demonstrated a good agreement between Mössbauer and XANES data for several minerals including biotite, chlorite, staurolite, amphibole, olivine, pyroxene, and garnet (Delaney et al. 1996, 1998; Dyar et al. 2001, 2002; Evans et al. 2014; Righter et al. 2002). As noted above, one difference in the results of the two techniques is that in-situ XANES measurements have sometimes found a wide range of Fe³⁺ contents at the scale of a thin section (e.g., Delaney et al. 1998; Dyar et al. 2002; Masci et al. 2019). As a result, we have opted to only include XANES data from Dyar et al. (2002), where it showed good agreement with previous Mössbauer measurements.

In addition to measurements of Fe³⁺ and X_Fe3+, mineral analyses in the database include other elements (SiO₂, Al₂O₃, MgO, etc.) that were determined using either EPMA or wet chemistry. Although these analyses are not the focus of this paper, we note that many of the studies included in the database found good agreement between EPMA and wet chemical measurements of major elements in the same mineral (e.g., Fleming 1971; Hietanen 1969; Kretz 1990; Kwak 1968; Mielke et al. 1979; Okrusch 1969, 1971; Stephenson 1979; Zen 1981).

Number of analyses per mineral

Here we examine the number of analyses of each mineral included in the database. First, we calculate an analysis percentage, which is the number of times a mineral’s X_Fe3+ was analysed as a percentage of the number of times it was reported in an assemblage. Biotite has the most analyses of any mineral (483), and the greatest analysis percentage (90.3%). This is a result of its stability over a wide range of P–T space, its typically high mode in metapelites allowing for easy separation during crushing, and its role in geothermometry. White mica is the second most analysed mineral (192, 42.3%), followed by chlorite (78, 57.4%) and staurolite (32, 21.6%). Chlorite and staurolite have more restricted stability ranges than white mica and biotite, and staurolite may be difficult to analyse due to its commonly inclusion-rich nature.

Data classification with respect to pressure, temperature, and oxidation state

Here we consider any bias in the database towards rocks of certain pressures, temperatures, or oxidation states. Due to the different methods used to estimate P–T conditions in the original studies, we have opted for a mineral assemblage-based approach, in which samples have been categorised based on the metamorphic zone (temperature), prograde mineral assemblage sequence or “facies series” (pressure), and the type of Fe-oxide present (oxidation state). The rationale for each of these is given below and the categories are summarised in Fig. 2. The metamorphic zone, facies series, and type of Fe-oxide present for each sample is included in the overview summary of the database in Online Resource 1 (Table S1). Abbreviations for minerals follow Whitney and Evans (2010).

Fig. 2

Pressure (P, kbar), temperature (T, °C), and oxidation state (X_Fe3+) diagram illustrating the metamorphic zones, facies series, and Fe-oxide classifications used in this study. The aluminosilicate triple point calculated using the Holland and Powell (2011) dataset is shown for reference. Mineral abbreviations after Whitney and Evans (2010)

Temperature conditions were delineated based on five metamorphic zones found in metapelites: Chl/Bt, Grt, Crd/And/St/Ky (minerals whose initial development occurs at different pressures but similar temperature), Sil, and Kfs (Fig. 2). The Chl/Bt zone spans the greenschist facies of metabasic rocks, whilst the Grt, Crd/And/St/Ky, and Sil zones encompass the amphibolite facies. The Kfs zone covers the upper amphibolite–granulite facies transition. These zones are depicted on diagrams by the colour red, with progressively darker shades indicating higher grades (Fig. 2).

The pressure of metamorphism was distinguished based on five pressure-dependent prograde mineral assemblage sequences or “facies series” (Hietanen 1967; Miyashiro 1961): Crd-And-Sil (low-P Buchan), St-And-Sil (high-P Buchan), St–Ky–Sil (Barrovian), polymetamorphic, and unspecified (Fig. 2). The first three of these classifications represent broader, more inclusive versions of the facies series of Pattison and Tracy (1991); the Crd-And-Sil group incorporates facies series types 1a–2a, the St-And-Sil category includes types 2b-3, and the St–Ky–Sil group comprises type 4. Polymetamorphic rocks include those with three aluminosilicates reported by the authors (e.g., Williams and Grambling 1990) and those where contact metamorphism overprints regionally metamorphosed rocks (e.g., Chinner 1962; Okrusch 1969, 1971). Unspecified rocks comprise those of the greenschist or granulite facies that could not be linked to a facies series up- or down-grade, such as granulite facies xenoliths from El Hoyazo (Cesare et al. 2003, 2005). These pressure-dependent facies series are depicted on diagrams by the colour blue, with progressively darker shades indicating higher pressures (Fig. 2).

Concerning oxidation state, there are a number of ways that this parameter can be defined. One is to use the measurement of X_Fe3+ in the whole rock, however, this would neglect 55.8% of the samples. Therefore, we have opted to use the type of Fe-oxide in the assemblage as a proxy for the oxidation state, since only 33.2% of the samples lack this information. The rationale for this categorisation is that hematite-bearing samples are probably more oxidised than magnetite–hematite-bearing ones, which, in turn are probably more oxidised than samples containing magnetite–ilmenite, ilmenite, or no Fe-oxide (Diener and Powell 2010). Complications arise when comparing rocks of different grade, or rocks that contain greater or lesser amounts of a silicate capable of incorporating significant Fe³⁺ (e.g., muscovite, biotite, etc.). Despite these caveats, this method provides a convenient first-order, observation-based proxy for oxidation state. The reliability of this approach is assessed in more detail later in the paper.

Multiple Fe-oxides can coexist within the same rock. Our original attempt at classifying the samples based on the type of Fe-oxide led to eight categories (unknown, no Fe-oxide, Ilm, Ilm + Mag, Mag, Ilm + Mag + Hem, Mag + Hem, and Hem). Several of these had few (1–5) analyses and therefore some categories were combined in order to form five broader classifications: unknown; no Fe-oxide; Ilm-bearing; Mag-bearing (± Ilm); Hem-bearing (± Mag ± Ilm) (Fig. 2). Where authors simply stated the presence of opaque minerals (e.g., Atherton 1968; Kutsukake 1977; Miyashiro 1956, 1958; Stephenson 1979) or did not list any minor minerals as part of the assemblage (e.g., Snelling 1957), samples were included in the unknown category. Any sample where opaque minerals or Fe-oxides were not specifically identified, yet the authors noted other accessory minerals in the assemblage (e.g., Rt, Sph, Zr, Ap, Py, Po; Kwak 1968; Lundgren 1966), or the presence of Fe-oxides in different rocks in the same study (e.g., Mather 1970; Ono 1969), were included in the no Fe-oxide category. The type of Fe-oxide present in the sample is depicted on diagrams by the colour grey, with progressively darker shades indicating higher oxidation states (Fig. 2).

Figure 3a shows the percentage of minerals and rocks analysed for X_Fe3+ in each of the five metamorphic zones. There are relatively few analyses in rocks from the Chl/Bt zone. Whole rock, white mica, and biotite analyses are well represented across a range of grade, whilst chlorite analyses are restricted to low metamorphic grade and staurolite analyses are restricted to intermediate metamorphic grade (Fig. 3a). Figure 3b shows the distribution of analyses as a function of the pressure-dependent facies series. The majority of analyses are from the Barrovian St–Ky–Sil series. Concerning the higher-P Buchan St-And-Sil facies series, a significant number of white mica, biotite, and chlorite analyses come from the West-central Maine sequence (Dyar et al. 1991, 2002; Guidotti et al. 1994; Guidotti and Dyar 1991; Moeller 1991). Figure 3c shows the distribution of analyses in relation to the type of Fe-oxide present in the rocks. In many samples, unfortunately, the Fe-oxide is unknown. The rarest samples are those that contain hematite.

Fig. 3

Distribution of analyses as a percentage for each a metamorphic zone, b facies series, and c Fe-oxide type. The data are separated into five categories: X_Fe3+ analyses of whole rock, white mica, biotite, chlorite, and staurolite. The total number of samples included in the database for each category is listed at the top

X_Fe3+ and Fe³⁺ variation in metapelitic rocks and minerals

This study

In this section we analyse the database to elucidate broad patterns. Average (± 1σ) X_Fe3+ values are listed in Table 2 and are as follows: whole rock, 0.23 ± 0.16 (261 analyses); biotite, 0.11 ± 0.08 (483); white mica, 0.55 ± 0.18 (192); chlorite, 0.08 ± 0.07 (78); and staurolite, 0.07 ± 0.06 (32). The average (± 1σ) number of Fe³⁺ cations per formula unit are also listed in Table 2 and are as follows: biotite, 0.28 ± 0.19 (460); white mica, 0.17 ± 0.13 (190); chlorite, 0.31 ± 0.27 (60); and staurolite, 0.20 ± 0.17 (25). The large standard deviations of some minerals highlight the wide range of X_Fe3+ reported in the literature. To what degree this represents real variation in X_Fe3+ of these minerals, rather than disparate results from a range of laboratories, is uncertain.

Table 2 Mean (± 1σ) number of Fe³⁺ cations and X_Fe3+ for whole rock and minerals

Variation in the Fe³⁺ contents and X_Fe3+ of minerals and whole rock were considered in terms of the three main variables defined above. Figure 4 plots the mean, standard deviation, and range of X_Fe3+ in rocks, biotite, and white mica classified by metamorphic grade, facies series, and type of Fe-oxide. Additionally, for biotite and white mica, Fig. 4b, c plots the mean, standard deviation, and range for the number of Fe³⁺ cations using the same classifications. The average X_Fe3+ and Fe³⁺ contents for whole rock, biotite, and white mica as a function of the type of Fe-oxide are presented in Table 2. Chlorite and staurolite were not considered due to the small number of analyses and their relatively restricted stability ranges.

Fig. 4

X_Fe3+ of a whole rock, b white mica, and c biotite, as well as the number of Fe³⁺ cations in b white mica, and c biotite, for different metamorphic zones, facies series, and types of Fe-oxide (colours as in Fig. 2). For each category the symbol represents the mean, the error bar one standard deviation, and the coloured rectangle the range

Mean whole rock X_Fe3+ appears to decrease with increasing metamorphic grade (Fig. 4a; 0.31–0.18) as has been noted by several previous authors (Ague 1991; Barth 1936; Joyce 1970; Mason 1962; Schwarcz 1966; Shaw 1956). However, analysis of other compilations of whole rock data, specifically those from the Dalradian, has shown no correlation of X_Fe3+ with grade (Atherton and Brotherton 1982; Leake 1958; Senior and Leake 1978; Yardley, 1977). Given that the averages presented here are well within uncertainty of each other and that there is a large spread in X_Fe3+ for a given zone, it is not possible to say whether the apparent trend to lower values is significant. Whole rock X_Fe3+ increases as a function of pressure (Fig. 4a). The slightly higher mean of the St–Ky–Sil series may be a result of a higher proportion of hematite-bearing rocks being included in this category, as suggested by the wide range in Fig. 4a. The mean whole rock X_Fe3+ value is similar for ilmenite- and magnetite-bearing rocks, as well as those with no Fe-oxide reported, but is considerably higher for hematite-bearing rocks (Fig. 4a; Table 2).

White mica X_Fe3+ values are always higher than that of the whole rock and range from 0.0 to 1.0. Within overlapping ranges and standard deviations, mean white mica X_Fe3+ is highest in the intermediate grade Crd/St/And/Ky zone, whereas the mean number of Fe³⁺ cations decreases with increasing metamorphic grade (Fig. 4b). Mean white mica X_Fe3+ broadly increases as a function of pressure (Fig. 4b); the average number of Fe³⁺ cations for the lower pressure facies series is similar, but is about half the value of the St–Ky–Sil facies series white micas (Fig. 4b). White mica in magnetite- and hematite-bearing rocks has a higher mean X_Fe3+ than in ilmenite and Fe-oxide-free rocks (Fig. 4b; Table 2). The mean number of Fe³⁺ cations in white mica similarly increases from ilmenite- to magnetite- to hematite-bearing rocks (Fig. 4b; Table 2). Average X_Fe3+ and Fe³⁺ cations in biotite show no consistent trends with respect to metamorphic grade and facies series. However, both show a slight correlation as a function of Fe-oxide, with maximum values in hematite-bearing rocks (Fig. 4c; Table 2).

Comparison to other studies

Previous studies have demonstrated that metapelites of the same metamorphic grade containing hematite have higher whole rock X_Fe3+ contents than ilmenite–magnetite-bearing rocks (Chinner 1960; Hounslow and Moore 1967), as found here. No previous studies that we are aware of have compared whole rock X_Fe3+ contents amongst magnetite-bearing, ilmenite-bearing, and Fe-oxide-free rocks.

The only previous systematic study of Fe³⁺ in metapelitic minerals is that of Guidotti, Dyar, and others from across a Grt–St–Sil–Kfs sequence in West-central Maine (Dyar 1990; Dyar et al. 1991, 2002; Guidotti et al. 1994; Guidotti and Dyar 1991). In this region, the average (± 1σ) X_Fe3+ of biotite was 0.11 ± 0.05 for 45 ilmenite-bearing rocks, 0.24 ± 0.05 for five magnetite-bearing rocks, and 0.46 in a single hematite-bearing rock. Comparatively, the average (± 1σ) X_Fe3+ of white mica was 0.45 ± 0.11 for twelve graphite–ilmenite-bearing schists, 0.72 ± 0.07 for five ilmenite–magnetite-bearing samples, and 0.82 in a single hematite-bearing rock. In our database, the average X_Fe3+ values of biotite for magnetite- and hematite-bearing samples are significantly lower than those reported by Dyar (1990). For white mica, our values are similar to those of Guidotti et al. (1994), apart from our average X_Fe3+ for hematite-bearing samples which is 0.20 lower than their single sample.

Biotite is the only mineral considered here for which researchers have previously estimated Fe³⁺ contents from recalculated EPMA data based on stoichiometric constraints. Dymek (1983) developed an iterative cation-based normalisation procedure that eliminates excess charge associated with Ti⁴⁺ and Al³⁺ using octahedral vacancies, and then estimates Fe³⁺ based on the difference between the total positive charge and 22 oxygens. However, this calculation assumes that titanium is incorporated at the octahedral site through vacancies and not via deprotonation, in contrast to the studies noted earlier, making these Fe³⁺ estimates equivocal (Cesare et al. 2003; Dyar et al. 1993a; Waters and Charnley 2002). Li et al. (2020) used an Fe³⁺ estimation method based on principal components regression; we tested its ability to reproduce the X_Fe3+ contents of the biotite analyses in our database. To do so, our separate determinations of Fe₂O₃ and FeO were combined into FeO^total and the amount of Fe³⁺ in biotite calculated using the spreadsheet provided by Li et al. (2020). Figure 5 plots the observed X_Fe3+ in biotite against that calculated using the Li et al. (2020) method; samples for which X_Fe3+ was exactly predicted by the spreadsheet lie on the 1:1 line. We find a poor fit between the observed and predicted X_Fe3+.

Fig. 5

Observed X_Fe3+ in biotite vs. the predicted X_Fe3+ in biotite calculated using the method of Li et al. (2020)

Phase equilibrium modelling considerations

The next part of this study compares our observations from the natural database with the predictions of thermodynamic modelling. The following section outlines the average bulk composition used for phase diagram calculations, overviews the various substitution mechanisms by which Fe³⁺ is incorporated in minerals, and summarises the different thermodynamic solution models and datasets available for Fe³⁺-bearing phases. Finally, we discuss the various types of phase equilibrium modelling calculation conducted, before contrasting thermodynamic predictions to the natural data in a subsequent section.

Average bulk composition

Phase diagram calculations were performed for the average composition of the 261 whole rock compositions in the database. This bulk composition is provided in Table 3 alongside the mean whole rock compositions determined by Shaw (1956), Ague (1991), and Atherton and Brotherton (1982). H₂O and CO₂ have been removed and values renormalised to 100% to provide a uniform basis for comparison. The weight per cent oxide concentrations for major elements in our bulk composition are close to those of previous authors for average pelitic rocks. This average composition was converted to mole per cent and an apatite correction was applied to remove P₂O₅ and a corresponding stoichiometric amount of CaO. The value of X_Fe3+  = 0.23 in our average metapelite is lower than in Shaw’s (1956) low-grade pelite (X_Fe3+  = 0.46) and Ague’s (1991) slate/shale (X_Fe3+  = 0.40), but similar to Shaw’s (1956) high-grade pelite (X_Fe3+  = 0.28) and Ague’s (1991) amphibolite–facies pelite (X_Fe3+  = 0.25). It also lies between the values for average Dalradian Buchan pelite (X_Fe3+  = 0.17) and average Dalradian Barrovian pelite (X_Fe3+  = 0.32) presented by Atherton and Brotherton (1982).

Table 3 The average database bulk rock composition determined in this study compared to the averages of Shaw (1956, table 9), Ague (1991, table 2), and Atherton and Brotherton (1982, table 4)

Fe³⁺ substitution mechanisms

Here we briefly review the crystallographic sites and exchange mechanisms by which Fe³⁺ is incorporated in white mica, biotite, chlorite, and staurolite. For white mica, biotite, and chlorite, most studies (including the present one) assume that Fe³⁺ replaces Al³⁺ in an octahedral site. However, some authors debate which site or sites Fe³⁺ can occur in, as well as the various ways in which the excess charge associated with this substitution is accommodated (see “Mineral formulae recalculation” section). In biotite, Guidotti and Dyar (1991) suggested that 8 ± 3% of total Fe is tetrahedral Fe³⁺, whilst 4–13% of total Fe is octahedral Fe³⁺. However, these site-assignments were subsequently questioned (Dyar 1993; Rancourt 1993; Rancourt et al. 1992), and when these data were refit, Fe³⁺ was assigned exclusively to the octahedral site (Dyar et al. 2002). As previously discussed, some authors have suggested that the extra charge associated with Fe³⁺ in an octahedral site is accommodated by deprotonation, but it is now thought that deprotonation related to Fe³⁺ is minor compared to Ti⁴⁺ (Cesare et al. 2003; Waters and Charnley 2002). In muscovite, Fe³⁺  = Al^VI is the dominant substitution by which Fe³⁺ is incorporated, with only a minor contribution from deprotonation (Dyar et al. 1993a; Guidotti and Sassi 1998a, b). For chlorite, whilst Fe³⁺ typically replaces Al^VI, it may also substitute for octahedral Fe²⁺ or Mg²⁺ as part of a deprotonation substitution (Lempart et al. 2018, 2020; Masci et al. 2019; Walshe 1986). In staurolite, Fe³⁺ replaces Al³⁺ in the tetrahedral site (Dyar et al. 1991).

Fe³⁺ in thermodynamic databases

Of the four minerals considered here, attention has been focussed on thermodynamic properties of Fe³⁺ end members in biotite and chlorite. In biotite, Vieillard (1994) predicted the enthalpy of formation for ferri–annite and ferri–phlogopite in which Fe³⁺ replaces Al³⁺ on the tetrahedral site. In contrast, White et al. (2000, 2005, 2007) and Tajčmanová et al. (2009) considered that Fe³⁺ resides exclusively on the octahedral M1 site and consequently use a single Fe³⁺ end member [fbi = KMg₂Fe³⁺Al₂Si₂O₁₀(OH)₂]. These studies derived the equation of state for fbi using stoichiometrically weighted linear combinations of the properties of phases with known thermodynamic properties, specifically eastonite, corundum, and hematite from the Holland and Powell (1998) dataset (fbi = Eas – ½ Crn + ½ Hem). White et al. (2014a) used the same Fe³⁺ end member but derived the equation of state with thermodynamic properties for eastonite, grossular, and andradite from the Holland and Powell (2011) dataset (fbi = Eas – ½ Grs + ½ Adr).

For chlorite, Walshe (1986) included two Fe³⁺ end members in his solid solution model. In the first of these Fe³⁺ replaces Al³⁺ on the tetrahedral and octahedral sites (Fe²⁺₅Fe³⁺₂Si₃O₁₀(OH)₈), whilst in the second, Fe³⁺ is incorporated on the octahedral site via deprotonation (Fe²⁺₄Fe³⁺Al₂Si₃O₁₁(OH)₇). White et al. (2014a) used a single Fe³⁺ end member in chlorite (f3clin = Mg₅Fe³⁺AlSi₃O₁₀(OH)₈), deriving the equation of state for f3clin using the thermodynamic properties from Holland and Powell (2011) for clinochlore, grossular, and andradite (f3clin = Clc – ½ Grs + ½ Adr). Based on examination of Fe³⁺ and OH contents in chlorite from a large natural dataset, Masci et al. (2019) suggested that for thermodynamic modelling at least two ferric end-members are necessary: one with low Fe content where Fe³⁺ replaces Al and one where Fe³⁺ is incorporated by deprotonation. In contrast, some authors have chosen not to derive equations of state for Fe³⁺ end members in chlorite, since variation in X_Fe3+ is argued to be systematic and continuous with temperature, meaning that the incorporation of Fe³⁺ is intrinsically included in the derivation of other standard state and solution properties (Lanari et al. 2014; Vidal et al. 2005, 2006).

To our knowledge, White et al. (2014a) are the only authors to propose thermodynamic properties for Fe³⁺ end members in muscovite and staurolite. They considered Fe³⁺ to be partitioned onto the octahedral site in muscovite, and the tetrahedral site in staurolite, using a single Fe³⁺ end member for each mineral (fmu, KFe³⁺Al₂Si₃O₁₀(OH)₂; msto, Fe³⁺₂Mg₄Al₁₆Si_7.5O₄₄(OH)₄). White et al. (2014a) derived the equations of state for fmu and msto using the thermodynamic properties from Holland and Powell (2011) for muscovite, staurolite, grossular, and andradite (fmu = Ms – ½ Grs + ½ Adr; msto = St – ½ Grs + ½ Adr).

Choice of thermodynamic database

The thermodynamic datasets of Berman (1988) and Holland and Powell (1998, 1990) have relatively few Fe³⁺-bearing end members for silicate phases, as well as few associated solution models describing mixing between end members. Whilst some other solution models exist for chlorite and biotite (e.g., Vieillard 1994; Walshe 1986), the properties of end members are derived from thermodynamic data that are inconsistent with one another and thus cannot be combined. Of the thermodynamic databases currently available, only the dataset of Holland and Powell (2011) and associated solution models of White et al. (2014a) incorporate enough Fe³⁺ end members to simulate natural Fe³⁺-bearing phase equilibria. We therefore conducted phase equilibrium modelling in the internally consistent dataset of Holland and Powell (2011; update dataset 6.2, 6th February 2012) with the following solution models: chlorite, biotite, garnet, chloritoid, staurolite, cordierite, orthopyroxene, muscovite, paragonite, margarite, and silicate melt (White et al. 2014a, b); plagioclase and K-feldspar (Holland and Powell 2003; ternary feldspar, Cbar1 field); epidote (Holland and Powell 2011); ilmenite–hematite (White et al. 2000, 2014a, b); magnetite–spinel (White et al. 2002). Pure phases included quartz, albite, rutile, sphene, and the aluminosilicates. H₂O was assumed to be in excess.

Calculation details

Phase diagrams were computed in the 11-component MnNCKFMASHTO system (MnO–Na₂O–CaO–K₂O– FeO–MgO–Al₂O3–SiO₂–H₂O–TiO₂–O₂), using Theriak–Domino (De Capitani and Brown 1987; De Capitani and Petrakakis 2010; version 11th February 2015, modified by D. Tinkham). First, our average bulk composition (X_Fe3+  = 0.23) was used to calculate a P–T equilibrium assemblage diagram (Fig. 6a). Second, an isobaric T-X_Fe3+ (whole rock) equilibrium assemblage diagram at a pressure of 5 kbar was constructed (Fig. 6b). In this diagram, the proportions of Fe²⁺ and Fe³⁺ were varied between X_Fe3+  = 0.0 and X_Fe3+  = 1.0, with all other elements kept at the same values. The pixelmaps routine of Domino was utilised to calculate the modal abundances and compositions of minerals across these two diagrams. The predicted number of Fe²⁺ and Fe³⁺ cations pfu and in turn the X_Fe3+ of each mineral, were then determined. The scientific colour map ‘batlow’ (Crameri 2021) is used for pixelmaps in this study (Crameri et al. 2020).

To gain further insight into the interplay of pressure, temperature, and oxidation state, P–T diagrams like that shown in Fig. 6a were constructed for ten separate whole rock X_Fe3+ values between 0.0 and 0.9 with an interval of 0.1. Calculations for a whole rock X_Fe3+ of 1.0 were not included, because the highest whole rock X_Fe3+ value in our database is 0.84. Each P–T diagram was gridded with 11 × 11 pixels spaced 40 °C and 1 kbar apart, resulting in 121 datapoints per map and 1210 datapoints total. At every point, the model predicts the stable mineral assemblage, including Fe-oxides, and the mineral compositions for which each Fe³⁺-bearing mineral will have an associated X_Fe3+. Using the predicted Fe-oxide, we categorised each point according to the scheme presented in the “Data classification with respect to pressure, temperature, and oxidation state” section. We then grouped all the points into one of the Fe-oxide categories described above for the natural data (e.g., magnetite), and calculated the predicted mean, standard deviation, and range in X_Fe3+ and the number of Fe³⁺ cations for the whole rock and mineral compositions (Ms, Bt, Chl, and St).

Fig. 6

a P–T and b T-X_Fe3+ phase diagrams calculated using the average bulk composition listed in Table 3. The cross patterned field denotes the domain of predicted melt-bearing assemblages. The dashed lines show the pressure and X_Fe3+ content at which the corresponding diagram was calculated. Smaller diagrams depict the change in volume per cent of ilmenite, magnetite, and hematite

Phase equilibrium modelling results and comparison to natural data

Predicted Fe-oxide

Figure 6 shows the P–T and T-X_Fe3+ equilibrium assemblage diagrams produced for our average metapelite composition, with the shades of grey highlighting which Fe-oxide is present, according to the scheme presented in the “Data classification with respect to pressure, temperature, and oxidation state” section. The dashed line on Fig. 6a shows the 5 kbar pressure used to calculate the isobaric phase diagram in Fig. 6b, whilst the dashed line on Fig. 6b shows the average rock X_Fe3+ value. Magnetite-bearing assemblages are stable at pressures below ~ 8 kbar and 450–650 °C, whilst hematite-bearing assemblages are stable above ~ 8 kbar (Fig. 6a). At temperatures below ~ 450 °C either no Fe-oxide is predicted to be present, or a small amount of hematite is predicted (< 0.3%; Fig. 6a). A small field where only ilmenite is predicted to be stable lies between 5 and 9 kbar and 450–500 °C. The predicted volume proportion of Fe-oxides is < 2% for the entire range of P–T conditions (Fig. 6a).

Fig. 7

Change in biotite a, c X_Fe3+ and b, d Fe³⁺ cations with a, b P–T and c, d T-X_Fe3+ conditions. Isomodes are plotted as black lines with associated white numbers showing the volume per cent of the mineral present

Referring to Fig. 6b, no Fe-oxide phase is predicted at low temperatures and oxidation states because epidote, a mineral with considerable Fe³⁺, is present (Fig. 6b). Ilmenite is the only oxide at 450–650 °C and X_Fe3+  < 0.1, forming 0.6–1.2 volume per cent of the predicted assemblage. Magnetite enters the assemblage above X_Fe3+  = 0.1 and reaches a maximum volume of ~ 2% at X_Fe3+  = 0.5 and 550 °C. Hematite is predicted to be stable at X_Fe3+  > 0.3 and occurs with both ilmenite and magnetite at X_Fe3+  = 0.4 (Fig. 6b). Hematite is the only Fe-oxide predicted to be stable at X_Fe3+  > 0.6 and its volume percent increases from ~ 2% at X_Fe3+  = 0.4 to ~ 5% at X_Fe3+  = 1.0 (Fig. 6b). The stability of some silicate phases also changes as a result of the whole rock X_Fe3+, however, this is probably a result of increasing X_Mg associated with a reduction in Fe²⁺ as X_Fe3+ increases (c.f., Diener and Powell 2010). The temperature interval over which staurolite and garnet are stable decreases with increasing whole rock X_Fe3+ until neither is present above X_Fe3+  = 0.6 (Fig. 6b).

Figure 6b can be compared with the T-X_Fe3+ diagram in figure 4  of Diener and Powell (2010). Their diagram was constructed for a typical pelitic composition, using the older dataset of Holland and Powell (1998; update ds55, 4th August 2004), and the following solution models: garnet, biotite, and silicate melt (White et al. 2007); plagioclase and K-feldspar (Holland and Powell 2003; ternary feldspar, Cbar1 field); orthopyroxene and magnetite–spinel (White et al. 2002); muscovite–paragonite (Coggon and Holland 2002); ilmenite–hematite (White et al. 2000); chloritoid, staurolite, cordierite, and epidote (Holland and Powell 1998). Fewer of these silicate solution models incorporate Fe³⁺ end members (only garnet, biotite, orthopyroxene, and epidote) and the average predicted X_Fe3+ in biotite is significantly lower than that predicted using the solution models of White et al. (2014a) in combination with the dataset of Holland and Powell (2011). The result is that the predicted stability fields and modal abundances of the Fe-oxides differ from Fig. 6b of this study because more Fe³⁺ must be included in the Fe-oxide phases. For example, at 550 °C, magnetite and hematite are predicted to be stable at significantly lower whole rock X_Fe3+ contents in their diagram compared to ours (0.05 vs. 0.10 for magnetite and 0.25 vs. 0.35 for hematite).

Predicted mineral X_Fe3+ and Fe³⁺

Figures 7, 8, and 9 display the predicted number of Fe³⁺ cations and X_Fe3+ values, across the P–T and T-X_Fe3+ equilibrium assemblage diagrams in Fig. 6, for biotite, muscovite, and chlorite/staurolite, respectively. These are contoured with modal abundance isopleths for each mineral in order to elucidate if any changes are associated with the volume percent of the phase predicted.

Fig. 8

As for Fig. 7, but for muscovite

Fig. 9

As for Fig. 7, but for chlorite and staurolite

In biotite, gradual increases with temperature of X_Fe3+ from ~ 0.03 to ~ 0.17 and in Fe³⁺ cations from ~ 0.10 to ~ 0.40, are punctuated by more abrupt changes at the Ep-out and Chl-out lines (Fig. 7a, b). At lower pressures (< 6 kbar), increases in the X_Fe3+ and the number of Fe³⁺ cations in biotite correlate with increases in its modal abundance; however, at higher pressures (> 6 kbar) X_Fe3+ and the number of Fe³⁺ cations in biotite are more uniform despite changes in modal abundance (Fig. 7a, b). There is no significant variation in the X_Fe3+ and number of Fe³⁺ cations in biotite as a function of pressure. Predicted biotite Fe³⁺ cations and X_Fe3+ increase with increasing whole rock X_Fe3+, whereas the modal abundance of biotite decreases (Fig. 7c, d). The predicted rates of increase in biotite Fe³⁺ cations and X_Fe3+ with respect to whole rock X_Fe3+ are different. The number of Fe³⁺ cations in biotite rapidly increases at lower whole rock X_Fe3+ (Fig. 7d), whilst X_Fe3+ in biotite increases most rapidly at higher whole rock X_Fe3+ (Fig. 7c).

In muscovite, X_Fe3+ is predicted to increase from ~ 0.20 to ~ 0.50 with increasing temperature and decreasing pressure (Fig. 8a), whilst the number of Fe³⁺ cations contemporaneously decreases from ~ 0.06 to ~ 0.01 (Fig. 8b). Muscovite has the greatest X_Fe3+ and lowest number of Fe³⁺ cations at the Chl-out reaction, and the lowest X_Fe3+ and greatest number of Fe³⁺ cations at > 10 kbar and < 450 °C (Fig. 8a, b). No correlation is found across P–T space between muscovite’s modal abundance and its number of Fe³⁺ cations or X_Fe3+. However, both the predicted X_Fe3+ of muscovite and its modal abundance increase with increasing whole rock X_Fe3+ (Fig. 8c). Above whole rock X_Fe3+  = 0.2, the number of Fe³⁺ cations predicted in muscovite shows greater variation with temperature than with whole rock X_Fe3+ (Fig. 8d).

In chlorite, X_Fe3+ decreases from ~ 0.19 to ~ 0.07 with increasing temperature, whilst the number of Fe³⁺ cations decreases from ~ 1.5 to ~ 0.5 (Fig. 9a, b). At lower pressures (< 6 kbar), increases in the number of Fe³⁺ cations and X_Fe3+ in chlorite correlate with increasing modal abundance; however, at higher pressures (> 6 kbar) values are more uniform despite change in chlorite’s modal abundance (Fig. 9a, b). There is negligible change in the number of Fe³⁺ cations and X_Fe3+ in chlorite with pressure. Predicted chlorite Fe³⁺ cations and X_Fe3+ increase with increasing whole rock X_Fe3+, whilst its modal abundance decreases (Fig. 9c, d). The predicted rates of increase in the number of Fe³⁺ cations and X_Fe3+ are comparable to those previously described for biotite.

The number of Fe³⁺ cations in staurolite and its X_Fe3+ remain constant (~ 0.2 and ~ 0.05; Fig. 9a, b). No correlation is found between the modal abundance of staurolite and either its number of Fe³⁺ cations or X_Fe3+ across P–T space. The number of Fe³⁺ cations and X_Fe3+ in staurolite remain relatively unchanged with whole rock X_Fe3+, however, its modal abundance decreases with increasing whole rock X_Fe3+ (Fig. 9c, d).

Comparison of models to nature

Figure 10a compares means of the modelled whole rock X_Fe3+ values that correspond to the Fe-oxide predicted (e.g., ilmenite or magnetite), with those observed in our database (Fig. 4). Mean whole rock X_Fe3+ values where no Fe-oxide or only ilmenite were predicted (~ 0.08), are lower than the mean whole rock X_Fe3+ determined from our database (~ 0.2). In contrast, the mean whole rock X_Fe3+ values where magnetite or hematite were predicted are close to the mean whole rock X_Fe3+ found in our database. It should be noted that a limitation of this assessment is that a single average bulk composition was used in the predictions, with only whole rock X_Fe3+ varied, whereas the natural data integrate results from a wider range of rock compositions.

Fig. 10

Comparison of the observed and predicted X_Fe3+ and number of Fe³⁺ cations in a whole rock, b white mica/muscovite, c biotite, d chlorite, and e staurolite for different types of Fe-oxide. Observed chlorite and staurolite X_Fe3+ values are not separated by the type of Fe-oxide due to the small number of analyses. For each category the symbol represents the mean, the error bar one standard deviation, and the coloured rectangle the range, as in Fig. 4

Figure 10b, c, d, e compares the predicted number of Fe³⁺ cations and X_Fe3+ values in white mica, biotite, chlorite, and staurolite with those observed in our database (Fig. 4; Table 2). Mean muscovite X_Fe3+ values where no Fe-oxide, or only ilmenite, were predicted, are lower than those where magnetite or hematite were predicted, as observed in our natural database (Figs. 8c, d, 10b). However, the mean predicted values of X_Fe3+ and the number of Fe³⁺ cations in muscovite are always lower than those observed (Fig. 10b). For biotite, the models predict the observed increase in the number of Fe³⁺ cations and X_Fe3+ with increasing whole rock X_Fe3+ and with Fe-oxide present (Figs. 7c, d,  10c). Whilst the mean predicted values of X_Fe3+ in biotite for different types of Fe-oxide broadly match those observed, the mean number of predicted Fe³⁺ cations is only similar when magnetite and hematite are the predicted Fe-oxide (Fig. 10c). The predicted variations in biotite Fe³⁺ cations and X_Fe3+ contents as a function of pressure and temperature are not observed in the natural database (Figs. 4,  7). Predicted mean X_Fe3+ values of staurolite and chlorite are generally low (< 0.2), in good agreement with the few analyses included in the database (Fig. 10d, e); however, both the mean number of predicted Fe³⁺ cations and the range of X_Fe3+ in chlorite extend to higher values than those observed (Fig. 10d). The predicted decrease in chlorite X_Fe3+ with increasing temperature shown in Fig. 9 cannot be corroborated by the small number of data in our database, but has been observed elsewhere in databases that incorporate a wider range of bulk rock compositions (e.g., Lanari et al. 2014; Vidal et al. 2006).

Discussion

Fe³⁺ estimates in natural minerals

In the absence of direct measurements of X_Fe3+ in minerals, petrologists need to use estimates in order to account for Fe³⁺ when conducting phase equilibrium modelling and thermobarometry. Ignoring Fe³⁺ in minerals is the same as making an estimate of X_Fe3+  = 0 (see discussion in appendix III of Hawthorne et al. 2012). Various approaches have been taken to estimate Fe³⁺ in minerals where it has not been measured. Powell (1973) in his programme RECALC built in “guesses” for the X_Fe3+ content of several minerals including muscovite (= 0.85), biotite (= 0.15), and chlorite (= 0.20). For biotite, Dymek (1983) developed an iterative cation-based normalisation procedure that estimates Fe³⁺, whilst Li et al. (2020) used an estimation method based on principal components regression.

On the basis of the measurements from West-central Maine presented above, Guidotti et al. (1994) argued that corrections for the effect of Fe³⁺ on EPMA-measured X_Mg of biotite and muscovite should be routinely applied to metapelites. Whilst it may be appropriate to use the values provided by Guidotti and Dyar as estimates for Fe³⁺ in certain minerals and settings, the applicability of these estimates to metapelites that equilibrated at different P–T conditions and contrasting oxidation states is unknown. Our database, which incorporates the Guidotti and Dyar data, covers a wider range of P–T conditions and oxidation states. Analysis of the database shows that the type of Fe-oxide present is linked to the X_Fe3+ in the whole rock and in specific minerals (Table 2). Therefore, it is important to identify the Fe-oxide in an assemblage in order to estimate how much Fe³⁺ may be present before conducting phase equilibrium modelling or thermobarometry.

Fe³⁺ in phase equilibrium modelling

Here we suggest some ‘best practices’ for incorporating Fe³⁺ as a component in phase equilibrium modelling calculations. First, the proportion of total iron in the bulk composition that is Fe³⁺ must be determined (i.e., whole rock X_Fe3+). Whilst, measurement of whole rock X_Fe3+ by titration is more common than measurement of X_Fe3+ in minerals, these values should be considered a maximum, due to surface weathering processes or post-crushing, pre-analysis oxidation (Diener and Powell 2010). An alternate or complementary method is for authors to note the identity and modal abundance of the Fe-oxide in their sample. A value of X_Fe3+ can be estimated by comparison with whole rock X_Fe3+ analyses from similar rock types with the same oxide assemblage (e.g., using the whole rock database presented here for metapelites). However, as noted above the reliability of this method may be affected by varying modal abundances of silicate minerals that can contain Fe³⁺ (Diener and Powell 2010). Another method is to construct a bulk composition by combining phase proportions with their representative compositions in which Fe³⁺ contents have been estimated (e.g., Forshaw et al. 2019; George et al. 2021; Palin et al. 2016).

We recommend using as many of the above methods as possible to help constrain the whole rock X_Fe3+. These measured or estimated whole rock X_Fe3+ values may then be used as input for phase equilibrium modelling. For a thorough assessment of the effects of varying whole rock X_Fe3+ on predicted equilibrium assemblage diagrams, we suggest, similarly to Diener and Powell (2010), that P-X_Fe3+ and T-X_Fe3+ phase diagrams be calculated. These diagrams can be used to determine the range of whole rock X_Fe3+ values for which the observed Fe-oxide mineral assemblage is most closely predicted. In addition, matching the predicted X_Mg values of silicate minerals to those observed in the sample provides a further constraint on the whole rock X_Fe3+ (e.g., Doukkari et al. 2018; Schorn and Diener 2019). Adopting these measures helps ensure that the whole rock X_Fe3+ used for the modelling is consistent with the thermodynamic dataset and solution models chosen.

Of the thermodynamic datasets and solution models currently available, only Holland and Powell (2011; dataset 6.2) and the solution models of White et al. (2014a) incorporate enough Fe³⁺ end members to simulate natural Fe³⁺-bearing phase equilibria. This dataset broadly predicted the correct Fe-oxide combinations for a variety of whole rock X_Fe3+, and the correlation amongst the observed Fe³⁺ contents and X_Fe3+ values of white mica and biotite with whole rock X_Fe3+ and the type of Fe-oxide present (Figs. 6, 7, 8, 10). It also correctly predicted the decrease in the number of Fe³⁺ cations in white mica with increasing temperatures (Figs. 4, 8). However, the predicted variations in the X_Fe3+ of white mica and biotite with pressure and temperature are not observed in the natural database, recognising that the magnitude of these predicted changes may be within the uncertainty of the measured values (Figs. 4, 7, 8). In terms of quantitative estimates, predicted values of Fe³⁺ cations and X_Fe3+ in biotite, chlorite, and staurolite broadly match those observed in nature, but the predicted number of Fe³⁺ cations and X_Fe3+ in white mica are below those observed in the database (Fig. 10).

Database of X_Fe3+ in natural rocks and minerals

An important question for future studies is what new data are needed to improve the natural database presented in this paper? Probably the most significant piece of data missing from many samples in the database is the Fe-oxide present in the assemblage (unknown category in Fig. 3c). Only a half to two-thirds of the whole rock, white mica, and biotite X_Fe3+ data have a specified Fe-oxide as part of the assemblage (Fig. 3c). In addition, it would be helpful to know the modal abundance of the Fe-oxides and the possible presence of lamellae within these resulting from the solid solutions of ilmenite–hematite and magnetite–ulvöspinel–hercynite (e.g., Ague et al. 2001; Chinner 1960; Dougan 1974; Hounslow and Moore 1967; Okrusch 1969; Rumble 1973). Analysis of our database was only able to delineate four broad categories (no Fe-oxide, Ilm-, Mag-, and Hem-bearing), whereas future analysis might be able to separate rocks further, perhaps allowing for better estimation of Fe³⁺ in rocks and minerals.

In our database, there is a lack of X_Fe3+ data for chlorite and staurolite. This is probably in part due to the restricted stability range of these minerals in P–T space, and the relatively low measured values of staurolite and chlorite that have been analysed, such that many authors assume Fe³⁺ is negligible. Nevertheless, these minerals may be modally abundant in some metapelites and they have large FeO contents, meaning that even at low X_Fe3+, they may contain a non-negligible portion of the Fe³⁺ in the rock.

Another aspect of our database is that it is dominated by analyses of rocks and minerals from samples with relatively low oxidation states. Whilst more oxidised, hematite-bearing schists may not be as common in the geological record, there are many examples of regions world-wide where they occur alongside the more prevalent rocks of lower oxidation state: Barrow’s zones, Scotland (Ague et al. 2001; Chinner 1960; Dempster 1983; McNamara 1965); Northern Apennines, Italy (Lo Pò and Braga 2014); New Hampshire, U.S.A. (Rumble 1978, 1973); South Dakota, U.S.A. (Helms and Labotka 1991); New Mexico, U.S.A. (Grambling and Williams 1985; Williams and Grambling 1990); California, U.S.A. (Labotka 1980, 1981); Ontario, Canada (Carmichael et al. 1978; Hounslow and Moore 1967); Anosyen, Madagascar (Boger et al. 2012); and Ryoke, Japan (Hiroi 1983). Finally, the majority of mineral X_Fe3+ measurements included in the database are bulk analyses, which do not record variation in Fe³⁺ contents at the micrometre scale, such as has been documented in recent XANES studies (e.g., Dyar et al. 2002; Masci et al. 2019; Schmid et al. 2003). Documenting changes in X_Fe3+ with respect to the textural setting of the minerals, and possible zoning of X_Fe3+ in minerals, may provide greater insight into the phase relations of these silicates and how Fe³⁺ is distributed amongst minerals in metapelites.

Conclusions

We have collated a database of 591 natural metapelites from 47 localities in which measurements of Fe²⁺ and Fe³⁺ were made for one or more of the rock composition and constituent minerals. There are 785 individual minerals with measured X_Fe3+, in decreasing order of abundance: biotite, white mica, chlorite, and staurolite. We compare our observations of the number of Fe³⁺ cations and X_Fe3+ in these minerals to the predictions of phase equilibrium modelling using dataset 6.2 (Holland and Powell 2011) and the solution models of White et al. (2014a). The main conclusions of this work are:

• Determinations of X_Fe3+ in minerals using wet chemical, Mössbauer spectroscopy, and XANES spectroscopy techniques are generally consistent.

• Average (± 1σ) X_Fe3+ values for whole rock, biotite, white mica, chlorite, and staurolite are 0.23 ± 0.16, 0.11 ± 0.08, 0.55 ± 0.18, 0.08 ± 0.07, and 0.06 ± 0.05, respectively.

• The average (± 1σ) number of Fe³⁺ cations in biotite, white mica, chlorite, and staurolite is 0.28 ± 0.19 (22 O + Ti cations pfu), 0.17 ± 0.13 (22O pfu), 0.31 ± 0.27 (28O pfu), and 0.20 ± 0.17 (46O pfu), respectively.

• Mean whole rock X_Fe3+ is similar for ilmenite- and magnetite-bearing metapelites, as well as those with no Fe-oxide, but is significantly higher for hematite-bearing ones.

• The mean number of Fe³⁺ cations and X_Fe3+ values in white mica and biotite correlate with the type of Fe-oxide present in the rock, with the highest values in magnetite- and hematite-bearing rocks.

• The mean predicted number of Fe³⁺ cations and X_Fe3+ in biotite, chlorite, and staurolite broadly match those observed in nature, but for white mica the mean predicted X_Fe3+ is underestimated by 0.2–0.4 and the number of Fe³⁺ cations by 0.05–0.2.

• Thermodynamically-predicted increases in the number of Fe³⁺ cations and X_Fe3+ of white mica and biotite with whole rock X_Fe3+ mirror those observed in nature.

• Thermodynamically-predicted grade- and pressure-related variations of X_Fe3+ in white mica and biotite are not observed in nature.