Biotite was synthesised in sodic alkaline melts of tephriphonolite to phonolite composition to obtain a range of mineral compositions consistent with those in natural alkaline-silicate magmas. Three synthetic, trace-element doped starting glass compositions were investigated (compositions M3, M5 and H5 from Beard et al., 2019, Table 1), and fluorine was added to some of the charges as trace metal grade 40% hydrofluoric acid (Beard et al., 2020; see Appendix). Powders of starting glass (0.125–0.190 g) were loaded into platinum capsules of 3.0–3.5 mm internal diameter and 16–25 mm length, with distilled water in excess of saturation HF added immediately prior to closure and welding. Capsule mass was monitored throughout the loading procedure and verified after the experiments to check for leaks.

Crystallisation experiments were conducted in Pt capsules in a Harwood-type internally heated pressure vessel in the HP-GeoMatS laboratory at the GeoForschungsZentrum, Potsdam, Germany. Run temperatures were chosen between liquidus and solidus for each of the compositions of interest, corresponding to 650 to C at 200 MPa total pressure. Oxygen fugacity was buffered using an Ar- gas pressure medium, with exchange of through the experiment capsule walls resulting in log O    FMQ +1 in our -saturated charges (see Berndt et al., 2002, Jugo et al., 2010). Our vessel did not feature a Shaw membrane for measurement and control of fugacity (Berndt et al., 2002). Charges were placed into the apparatus, pressurised, then homogenised at 1100–1200C for at least 16 h. Following homogenisation, the charges were cooled to run temperature at 1C/min to facilitate slow growth of crystals and to impede development of melt heterogeneities adjacent to phase boundaries. Temperature was then cycled twice between run temperature and run temperature + C to encourage dissolution of small crystals at the expense of larger grains, and to promote crystal growth close to the run temperature (one cycle equals 30 min at , 30 min at + C, then cooling to at 1C/min). The final run temperature was held for >45 h to allow for homogenisation of the melt and Ostwald ripening of the biotite crystals. Capsules were then quenched to room temperature. Wherever possible, rapid quench apparatus was used to limit the growth of groundmass crystals. Here, the vessel was mounted vertically on a trunion, with capsules hung from a fusible Pt wire allowing them to fall out of the hot zone on experiment termination. Even without rapid quench apparatus, cooling to below the glass transition (C; Giordano et al., 2005) was achieved in less than 150 seconds. Following quench the capsules were weighed, pierced, dried and re-weighed, which confirmed in all cases the presence of a free fluid phase. Capsules were then torn open with pliers and charges split along their vertical axis with a low-speed wafering saw. Half of each charge was mounted in epoxy and polished for microanalysis (Fig. 1). A more detailed experimental methodology is presented in Beard et al. (2019, 2020).

Biotite crystals were separated from fifteen pyroclastic deposits from the Canary Islands with basanitic to phonolitic compositions (see Appendix and Beard et al., 2019). The pumices and scoria were rinsed under tap water, dried at 110C overnight, then gently hand crushed with a hammer. Crystals and glass fragments were hand-picked from sieved size fractions of 125–1180 m, and 5–20 crystals of biotite from each sample were mounted in epoxy for microanalysis. The pyroclastic rocks also contain augite clinopyroxene, anorthoclase to sanidine feldspars, spinel, amphibole, olivine, titanite, sodalite [see analyses in Beard et al., 2019). The glass analysed for partition coefficients was adhered to the walls of the mounted clinopyroxene crystals.

The Canaries biotite are elongate faceted crystals with vesicular glass adhered to the surface of some grains (Fig. 2). The mounted biotite crystals were examined using backscattered electron imagery and all from the selected samples appeared to be free of chemical zoning.

Biotite crystals from all of the samples were analysed by electron probe microanalyser (EPMA) to determine their major-element composition (Fig. 3). A subset of four samples were selected for determination of apparent biotite/melt trace-element partition coefficients by laser ablation ICP-MS (see Appendix). These samples were chosen because, in addition to biotite, they contain unzoned crystals of clinopyroxene, a mineral that readily records chemical and physical perturbations to the magmatic system during growth (e.g., Masotta et al., 2020, Ubide et al., 2019). The clinopyroxene-melt pairs within these fall deposits preserve near-equilibrium crystallisation (Beard et al., 2019), and their biotite most probably formed under similar conditions. The samples comprise phonolitic, plinian fall deposits from the 2 ka eruptions of Montaña Blanca (units LMB and UMB-II) and Pico Viejo, Tenerife (Ablay et al., 1995), as well as a basanite pyroclastic deposit from Montaña Samara, a monogenetic cinder cone, also on Tenerife (Albert et al., 2015). Pre-eruptive magma storage conditions for Montaña Blanca unit UMB-II have been constrained with phase equilibrium experiments to be 85015C, 5020 MPa, with 2.50.5 wt% at log O  NNO –0.5 (Andújar & Scaillet, 2012).

Major-element compositions of the experiment run products and natural biotite and glass were measured using a JEOL 8900 instrument at McGill University and a JEOL 8230 instrument at the University of Ottawa, with analyses calibrated using natural mineral standards. Biotite crystals were measured with a 15 nA beam of 2–5 m diameter, accelerated by a potential of 15 kV. Quenched melts were measured with a 4 nA beam of 50 m diameter. At Ottawa, all major-elements, including fluorine, were measured for 60 s. At McGill, counting times for the elements Al, K, Fe, Na, Si, Mg and Ca were 20 s, Cl 30 s, Ti 40 s and F 150 s. For fluorine, a notoriously challenging element to measure, we used TAP diffraction crystals with intensities calibrated against natural fluorite reference materials. Fluorine detection limits at Ottawa were 275 ppm and at McGill were 1100–3600 ppm. With these routines, we observed no sodium loss, nor amplification of signals for the rest of the major-elements over the measurement time period (e.g., Al, F; Morgan vi & London, 2005). Melt compositions for the Canary Islands rocks were determined by analyses of glass rims adhered to clinopyroxene grains separated from the same samples (see Beard et al., 2019).

Data for two mica and twelve glass secondary standards are in the Appendix. Reproducibility of major and minor element oxide abundance in mica standards is 1–7% RSD (1) and for F and Cl is 8.7–13.6%. Accuracy relative to GeoRem compiled values is better than 10%, except for Na and Cl, which are within 20%. Glass secondary standard reproducibility ranges from 0.17–1.06% for and is better than 5% for most major elements (>1 wt.%).

The trace-element concentrations of biotite crystals and glass were measured with a NewWave 213 nm Nd-YAG laser system coupled to a Thermo Finnigan iCAP-Qc quadrupole ICP-MS instrument at McGill University. A pulse frequency of 10 Hz was used, and beam fluence was typically 6–10 J/cm. Ablated material was carried to the ICP-MS instrument in a He flow of 800 mL/min and mixed with Ar prior to injection into the plasma. The primary standard glass BCR-2G was used to monitor and correct for drift, and accuracy was determined by the analyses of secondary standards NIST-610, USGS-RGM-1 rhyolite, UTR-2 peralkaline rhyolite glass, and Mg-mica and Fe-mica reference materials. Sample surfaces were pre-ablated to remove residues from polishing and to improve coupling between the laser beam and sample. A list of analytes with typical precision, as determined from multiple analyses of reference materials, is given in the Appendix.

Experiment biotite crystals were measured with a beam of 12–40 m diameter, along line scans of 4–12 m/s, with 5–15 grains measured per experimental charge. To minimise downhole fractionation among analytes we used faster scans where target phases required a smaller beam size. Experiment glass was measured with a beam size of 20–60 m along line scans at 4–8 m/s, and 8–16 areas of glass were measured per charge. These settings resulted in ca. 4–60 sec of signal per analysis. Canary Islands biotite crystals were analysed along line transects at 4 m/s with a beam of 40 m diameter and fluence of 9.5 J/cm. A total of 4–10 crystals of biotite were measured per sample. Corresponding quenched melts were measured with a static beam of 20–30 m.

Drift corrections and data reduction were performed with the Iolite v2.5 software (Paton et al., 2011), running in the Igor Pro environment. For the glass and Canary Islands biotite, the Al concentration from electron probe analyses was used as an internal standard. For the majority of biotite crystals in the experimental charges, mixed analyses of biotite and glass resulted. In this case, a robust linear unmixing model was applied to determine the trace-element composition of these crystals using their Mg/Al ratio as determined by electron probe to constrain mixing ratios (see Appendix, cf. Beard et al., 2019, 2020, Rubatto & Hermann, 2007, Yang et al., 2018). For some samples, glass analyses by LA-ICP-MS also required unmixing, and here the mixing ratio was constrained using the Na/Al ratio as determined by electron probe analysis. A series of three MATLAB scripts for reduction of laser ablation data from both unmixed and mixed analyses are available in the Appendix.

Results were obtained for eight experimental charges (Tables 2–3). The experiments equilibrated at near-liquidus conditions (< 35% crystals, Figs 1, 2), and glass in most charges is free of quench crystals. Charges run without fluorine are homogeneous with respect to melt composition and phase proportions, containing an assemblage of quenched melt, aqueous fluid, biotite, sodic clinopyroxene magnetite titanite alkali feldspar. Charges run with fluorine contain quenched melt, aqueous fluid, biotite sodic clinopyroxene Fe-oxide F-rich titanite fluorite a F-Ti-Ca-Na phase with a composition consistent with the sorosilicate minerals hiortdahlite and kochite. The fluorine-bearing charges are internally zoned, with higher quenched melt fluorine contents and greater modes of fluorine-rich biotite and titanite toward their top, grading to clinopyroxene-rich assemblages toward their bottom (maximum melt F variation in a single capsule was 0.16–1.57 wt.%; see Fig. 1). Vertical variation in fluorine concentration results from addition of concentrated HF to the top of capsules and subsequent downward migration of fluorine through the charges. The concentration of other major-elements in quenched melt show limited variation with position in the capsule, with small offsets associated with changes to phase relations that follow melt fluorine. While capsule-wide equilibrium was not attained, our earlier Cpx/melt study that uses these same charges demonstrated close approach to local equilibrium between minerals and melt (Beard et al., 2020). Phase relations and Cpx/melt partition coefficients are similar among charges with differing fluorine concentration gradients, as well as with unzoned charges where fluorine was pre-homogenised throughout the starting glass. A detailed description of the textures, phase relations and variations in melt chemistry and a discussion of the implications of capsule stratification are presented in Beard et al. (2020).

Capsules with a melt fluorine gradient are split into up to five zones for a total of 39 zones including the fluorine-free compositions. A total of twelve zones contain biotite and are discussed below.

Major-element compositions of the experiment and natural biotite are given in Table 2 and Fig. 3 and A12. Major- and minor-element ions were assigned to lattice sites following the method of Li et al. (2020), including the ratio, Li, and the proportions of fluorine, hydroxyl, and chlorine at the biotite W-site (calculations are for a charge of 22 per formula unit). This method is based on a principle component regression machine learning model, calibrated on a training set of 155 biotite references with measured chemistry and crystal structural refinement. Absolute errors reported for this model are 0.2 apfu for octahedral , octahedral and at the W site, and 0.3 apfu for total and .

Biotite crystals from the experiments are phlogopite to fluorophlogopite following Rieder et al. (1998), with molar Mg# of 57–78, tetrahedral Al of 0.43–1.14 c.f.u., octahedral Al of 0.04–0.34 c.f.u, Ti of 0.13–0.26 c.f.u. and F contents of 0–1.45 a.f.u (Fig. 3). With increasing fluorine content in the synthesised biotite, exchanges for (Fig. A12a), and exchanges for (Fig. A12b), the latter consistent with the Ti-oxy-hydroxide coupled substitution mechanism reported by Schmidt et al. (1999):

Further, potassium at the A-site increases at the expense of sodium with increasing fluorine at the biotite W site. These trends are observed across all experiment bulk compositions.

The Canary Islands crystals selected for this partitioning study (large triangles in Fig. 3) are phlogopite to biotite in composition and sit toward the upper end of the and range defined by a larger Canaries biotite dataset (including our measurements and those from Sliwinski et al., 2017). They show no notable zonation in BSE intensity across grains, suggesting minimal compositional variation during growth (Fig. 2). When compared to our experiment biotite, the Canaries minerals extend the compositional range to slightly lower Mg# (54–72), higher (1.05–1.30 c.f.u.) and Ti (0.23–0.44 c.f.u.), and have a narrower range of F contents (0.05–0.30 a.f.u). The Canary Islands biotite follow compositional trends defined by the experiment biotite and additionally display a positive correlation between Mn and F content (the experiments are Mn-free).

The most abundant trace-elements in both the experiment and natural biotite are Ba and Rb (ca. 100–3700 and 200–350 g/g, respectively). Our Canary Islands biotite have Ba, Zr, Sr and Nb concentrations that fall within the typical range for biotite from Tenerife zoned phonolitic ignimbrites (Sliwinski et al., 2017). They have Li contents of 3.5–28 g/g and REE contents close to or below the detection limit of our setup (ca. 0.1 g/g).

Quenched silicate melts from the experiments are trachyte and phonolite on the TAS classification of Le Maitre et al. (2005), with molar (Na + K)/Al of 0.86–1.34, Mg# of 6–14, and F contents of up to 2.85 wt.% (Fig. 4). The final experiment glasses have higher and lower , MgO and CaO relative to their respective starting material, consistent with crystallisation of the produced mineral phases. A superliquidus experiment using the H5 composition lost 0.82% relative to its starting glass via alloying with the Pt capsule (see Beard et al., 2019). This alloying phenomenon will contribute to changes in experiment Mg#, but is not enough to explain the all of the Fe-Mg systematics of the experiment glass data set. The Canary Islands tephra glasses are tephriphonolite and phonolite and overlap with the composition of experiment glass with molar (Na + K)/Al 0.78–1.16 and F contents <0.07–0.28 wt.%. Canary Islands glass extends to higher Mg# (13–39) than the experiments.

All experiments produced an aqueous fluid phase in addition to silicate melt. The water content of the silicate melt was estimated as 6.19–7.62 wt.% using a solubility model calibrated on andesite and rhyolite compositions that takes into account the effects of fluorine (Zhang et al., 2022). The model assigns water dissolved in the silicate melt to molecular water () and hydroxyl species () using equilibrium constants for water dissociation from Botcharnikov et al. (2006), which are optimised for andesitic melts. This approach is valid as there is little variation in water dissociation constants between rhyolitic and basaltic melts (Behrens, 2020). Following this scheme, / for the quenched melt in our fluorine-bearing experiments is 0.02–0.29. The melt ratio of non-bridging oxygen anions per tetrahedrally coordinated cation (NBO/T) was calculated following Mills (1993). This calculation method does not consider the potential role of ferric iron, nor that of water or the halogens. It was chosen to maximise applicability of our empirical models, especially considering scenarios where only routine whole-rock geochemical measurements have been made.

Close approach to local equilibrium in the experiments is indicated by consistency of results among duplicate charges, and in the case of experiments with vertical zonation in fluorine content, in vertical zones within charges (see below, for both Cpx/melt and Bt/melt values; cf. Beard et al., 2020) and the presence of mineral phases with limited to no chemical zoning. Biotite crystals from our experiments are homogeneous with respect to major-element compositions, as determined from EPMA mapping (Fig. 1), although they are too small to assess whether zonation of trace-elements is present. Quenched melts are homogeneous with respect to both major- and trace-elements, showing no discernible gradients in composition adjacent to crystal boundaries. Zonation of lanthanides within clinopyroxene from the same experiments is minimal (Beard et al., 2019, 2020), suggesting that trace-element zonation within the experimental biotite would also be minor.

Numerous fluorine-bearing charges in this study are vertically-zoned (Fig. 1), an effect attributed to the incomplete homogenisation of fluorine, which was added as concentrated HF to the top of the capsules (see discussion in Beard et al., 2020). For these charges, local equilibrium between the minerals and melt is demonstrated by the following observations: (1) minerals and glass have the same composition within horizontal bands of equal melt F content among separate experimental charges; (2) charges with pre-homogenised fluorine contents (added as NaF and KF powders) developed similar mineral and melt compositions for a given melt fluorine content, and return similar mineral/melt values (Beard et al., 2020); and (3) mineral compositions, melt compositions and partitioning behaviour are consistent among experiments and natural samples, including literature data (Figs 3, 4 and below).

Homogenisation of major and trace-element concentrations within the mica structure is generally assumed to occur quickly relative to that of inosilicates and the feldspar minerals, because biotite in natural igneous systems rarely displays zonation [e.g., optical zonation related to composition, Deer et al., 1992). Biotite grains that preserve major-element or trace-element zoning have been reported for volcanic systems and pegmatites (Azadbakht & Lentz, 2020, Sliwinski et al., 2017). The experimental diffusion database for micas is limited, with published studies focused on the diffusion of LILE cations, Ar, O, H and the OH-F exchange [see review by Cherniak & Dimanov, 2010). For Sr, the activation energy for diffusion in mica is significantly lower than that for hornblende, which in turn is lower than for diopside. Diffusion in melt is faster. It can thus be assumed that our experiment biotite and glass compositions represent the equilibrium partitioning of elements at the run conditions.

In the Canary Islands samples, biotite is unzoned in backscattered electron images (e.g., Fig. 2), and the compositional consistency between crystals in each pyroclastic fall sample supports the hypothesis of equilibrium. This interpretation is further corroborated by the presence of unzoned clinopyroxene in the same samples that record a relatively constant physical and chemical environment in the magma chamber during crystal growth (see Beard et al., 2019). Icenhower & London (1997) suggested that fluorine partition coefficients determined from pyroclastic rocks are biased toward higher values due to oxidation reactions and reequilibration associated with degassing and decline of the ratio of biotite. We do not see F-rich rims on biotite from our Canary Islands rocks, suggesting this phenomenon does not affect our results.

Biotite incorporates fluoride as a structural anion, replacing as much as 100% of the and anions (e.g., Fig 3c), and can therefore exert a major control of the fluorine budget of alkaline-silicate magmatic systems (Munoz, 1984, Speer, 1984). Fluoride can be incorporated into biotite via the following exchange reaction:

Fluorine in the investigated system acts as a major to minor element, with its partitioning expected to be in the Raoult’s law domain. We therefore discuss the exchange of fluorine between biotite and silicate melt in terms of exchange coefficients () rather than a Nernst partition coefficient ();

where and are mole fractions of F and OH on the biotite W site, and and are mole fractions of and in the silicate melt. A spreadsheet to calculate these terms is provided in the Appendix.

The are 9.3–47.0 for our experiments, and 4.9–11.4 for the Canary Islands natural mineral-melt pairs (Fig. 9), ranges that are broadly consistent with literature experiments on granitic compositions (Icenhower & London, 1997; 1.9–20.6), and on alkali-rich basalt to tephriphonolite compositions (Zhang et al., 2022; 6.1–51.1). This shows that F is compatible to highly compatible in biotite (for alkaline compositions in particular) and that if sufficient biotite is crystallising, it will deplete the residual melt of fluorine.

In experiments containing greater concentrations of fluorine, the biotite are offset to higher Mg contents and lower Ti contents, indicating that the exchange mechanism (Eqn. 1) is driven to the left in biotite dominated by F rather than OH. This finding confirms that the Ti-in-biotite thermometer of Henry et al. (2005) should not be applied to fluorine-bearing systems since variations in fluorine content reduce the amount of Ti in biotite at a given Mg# and temperature, resulting in an over-prediction of temperature (also see Li & Zhang, 2022, Patiño Douce, 1993, Patiño Douce et al., 1993).

Apparent Nernst partition coefficients ( values) are reported for twelve experimental and four Canary Islands biotite-glass pairs (Fig. 5, Table 4). values are highly consistent among our experiments and are broadly similar to those reported from existing experiments on mafic or granitic compositions (Adam & Green, 2006, Adam et al., 1993, Green et al., 2000, Icenhower & London, 1995, LaTourrette et al., 1995, Schmidt et al., 1999).

Biotite/melt partition coefficients for the large cations (Na, K, Rb, and Cs) cover a narrow range of values (Figs 5, A15), with K and Rb being compatible in biotite ( 1.43–2.67, 1.74–3.08), and Na and Cs being incompatible to weakly compatible ( 0.05–0.51, 0.41–1.02). values for these four monovalent ions define Onuma parabolae (Onuma et al., 1968), consistent with their partitioning onto the 12-fold coordinated A-site (interlayer) of biotite (Fig. 7). Increases to the fluorine content of the biotite subtly elevate partition coefficients for Rb while having little influence on the behaviour of Na, K and Cs (Fig. A15).

Lithium is weakly incompatible to strongly compatible in biotite, with values in our experiments and natural samples from 0.24–32.8 that are decoupled from those for larger R cations (Fig. 5). This decoupling results from the cation being too small for the XII A-site, and instead sitting in the octahedral M-sites of the biotite lattice ( Å; with M-site radii from X-ray diffraction on natural biotite = 0.50–0.86 Å; Brigatti & Guggenheim, 2002, Fig. 7). Our apparent values overlap partly with compiled experimental studies on mafic and granitic compositions. There is excellent correspondence of between the Canaries samples and the M3 composition experimental charges ( 0.24–0.90, Fig. 6). Fluorine-rich experiments on the M5 and H5 compositions have strongly elevated relative to the Canaries rocks and M3 composition experiments (Fig. 6c; e.g., for M5 and H5 experiments with 1.25–2.5% bulk fluorine, is 12.0–32.8). Lithium values further show positive correlations with biotite and inverse temperature (Fig. 6a, b).

The large cations Ca, Sr, Ba and Pb (residing on the biotite A-site) show a larger range of partitioning behaviour compared with cations on this site. Their values generally fall within the range of published experimental values for mafic and granitic compositions (Fig. 5). Ca is strongly incompatible in biotite ( 0.004–0.06), Sr and Pb are incompatible to weakly compatible ( 0.10–0.29, 0.02–1.54) and Ba is compatible ( 1.3–11.8). This trend reflects the decreasing mismatch in radius between the ions and the biotite site. from our experiments and Canary Islands rocks define a negative log-linear correlation with inverse temperature (temperature based on phase equilibrium experiments of Andújar & Scaillet, 2012; Fig. A14), which contrasts with the positive log-linear correlation reported by Wood & Blundy (2014). We attribute this mismatch to a smaller decrease in biotite solubility with increasing temperature (and hence A-site ) in our alkali-rich compositions relative to those mafic and granitic data compiled by Wood & Blundy (2014). Calcium partition coefficients could not be calculated for all of our samples owing to low concentrations of Ca in the biotite and high LA-ICP-MS background counts for due to interferences from and .

The ions and are compatible in biotite ( 1.3–3.5, 3.3–19.0, Fig. 5), while the 4+ and 5+ HFSE are incompatible to weakly compatible ( 0.02–0.17, 0.05–1.2), and actinides U and Th are incompatible. This behaviour is similar to that in the compiled literature data (Fig. 5b).

The REE and Y are strongly incompatible, with the biotite usually containing concentrations of REE below the detection limit of our laser ablation setup (Fig. A13). Their partition coefficients are less than . The cations have ionic radii intermediate between the size of the M and A-sites of biotite (cf. Schmidt et al., 1999), and their very low biotite/melt partition coefficients reflect this. Partition coefficients for La are highest as it has the smallest mismatch in radius with the A-site of biotite (our Canaries data and Adam & Green, 2006, see Fig. A13).

The equilibrium partitioning of trace-elements between minerals and silicate melts is controlled largely by the size and elasticity of the crystal lattice sites (Blundy & Wood, 1994, Brice, 1975, Onuma et al., 1968, Wood & Blundy, 2014) and the ability of the mineral to accommodate a local excess or deficit in charge (Blundy et al., 1998, Mollo et al., 2020). This behaviour is quantitatively described by the lattice-strain equation:

where is the ideal radius for the lattice site (Å), is its Young’s modulus (i.e., stiffness in GPa), is the strain-free partition coefficient, is Avagadro’s number, is the gas constant, is temperature (Kelvin) and is the ionic radius of each element (Å). The is controlled by mineral composition as the lattice site dimensions change systematically with, for example, exchange or substitution. The same is true for the elastic properties of the lattice, and hence , and mineral solubility, which is tracked by . Lattice strain parameters also vary with the physical conditions, for example via thermal expansion of the lattice with increasing temperature and its compression with increasing pressure. These trends can (in part) be estimated from independently obtained data, e.g., thermal expansion from high-temperature X-ray diffraction.

To investigate the systematics in values and the mechanisms by which alkali elements are incorporated into biotite, element partitioning behaviour was explored using the lattice strain model. Parabolae for 1+ ions were fitted for the A-site (XII coordination) using the elements Na, K, Rb and Cs, with fits weighted based on analytical uncertainties on the partition coefficients (Fig. 7). For 1+ ions in 12-fold coordination, the data define values of 1.7–1.73 Å, 35–75 GPa and 1.2–7.5. The parameter is similar for our experimental biotite, our natural Canaries biotite, and for biotite grown from mafic melts (Fig. 8). Biotite in granitic experiments has a smaller of 1.64–1.68 Å. A–O bond lengths determined for biotite via single-crystal X-ray diffraction are reported as inner and outer sphere values (Fleet, 2003). After subtraction of the ionic radius of tetrahedral , their A-site cation radii are 1.586–1.579 Å (median 1.587 Å) for the inner sphere, and 1.976–1.988 Å (median 1.980 Å) for the outer sphere; bracketing the range of values fitted to element partitioning data (Fig. 8).

The low Young’s modulus values (35–75 GPa) for the A-site of biotite indicate its relative flexibility compared with the M2-site of clinopyroxene, or the cation site of plagioclase (cf. Wood & Blundy, 2014). These elastic moduli are similar to values measured for biotite using a spherical nanoindentation apparatus at room temperature (30.8–51.4 GPa, layer-normal; Lanin et al., 2021).

values for 1+ ions at the A-site have a narrow range of positive values 1.2–7.5. A positive correlation exists between and for our experiments and for mafic compositions (Fig. 8a, Adam & Green, 2006, Schmidt et al., 1999). No such correlation is observed for granitic experiments (Icenhower & London, 1995). As tracks the solubility of an ideal monovalent cation in the biotite A-site (cf. Wood & Blundy, 2014), a similar chemical substitution may be related to expansion of the A-site () facilitating incorporation of 1+ ions.

Lattice strain fits were attempted for the large 2+ cations onto the A-site (Ca, Sr, Ba), but generation of a satisfactory parabola was not possible in most cases owing to the low concentrations of Ca in biotite, and corresponding high analytical uncertainty. Fits with Pb were attempted, but Pb plotted consistently below lattice strain parabolae defined by the other three elements, an effect reported elsewhere and attributed to the non-ideal electronic structure of the ion (Wood & Blundy, 2014).

The 4+ and 5+ HFSE ions Ti, Zr, Hf, Nb and Ti provide an insufficient spread of radii for the fitting of lattice strain parabolae for the two M-sites in biotite.

To determine the principal physicochemical controls on the exchange of F and OH anions between silicate melt and the W-site of biotite a least-squares multiple linear regression analysis was performed using our new values, alongside a compilation of previously published experimental data. Candidate fitting parameters were initially examined in binary scatter diagrams (e.g., Fig. 9) to check for covariance and to ascertain whether correlations were linear. Intensive variables for multiple linear regression models for were introduced following a hierarchical forward selection criterion with switching. Only parameters with student t-tests showing statistical significance at the 95% confidence level were retained, with the preferred model incorporating five biotite compositional terms (Table 5). Uncertainties on the model coefficients were determined via bootstrapping. The PRESS value obtained by repeated random sub-sampling of the data set is similar to the value calculated for the full data set, indicating that the model is robust and has high predictive power. Full regression reports are in the Appendix.

The final set of significant parameters defines the model equation:

Compositional coefficients are included for the T, M and W sites of the biotite structure, and for the oxidation state of iron in the biotite (Table 5). The positive coefficient is consistent with Pearson acid-base theory: The W and T sites are adjacent in the biotite lattice, meaning there is a direct bond between Al or Si in the T site and OH or F in the W site (Brigatti & Guggenheim, 2002, Munoz, 1984). has a higher relative to , therefore is expected to bond preferentially with , which has a higher electronegativity than . The positive correlation between and and negative correlation with and are consistent with avoidance in silicate minerals (Finch et al., 1995, Fleet, 2003, Munoz, 1984, Rosenberg & Foit, 1977), a phenomenon attributed to crystal field theory. The negative correlation between and biotite might result from non-ideal mixing of and on the biotite W-site, or in the silicate melt.

As model equation 5 includes biotite compositional terms only it can be applied to biotite grains from natural igneous systems where one cannot directly determine melt composition, and the pressure and temperature of equilibration. The multiple linear regression procedure did not identify temperature, pressure or melt compositional terms as strong predictors for F/OH exchange, relative to the biotite compositional parameters shown above.

An empirical model to predict F/OH exchange between biotite and melt was recently presented by Zhang et al. (2022), and was calibrated using experiments on alkaline-silicate bulk compositions, though most were not peralkaline (grey circles on Fig. 9e). On a measured vs predicted diagram (Fig. 10d), we note that the Zhang et al. (2022) model accurately reproduces some of our calibration data set; for example values for our experiments with peralkaline bulk compositions are predicted to within a factor of 2–3 of measured values. However, the Zhang model systematically under-estimates values for some peraluminous granite experiments (e.g., Icenhower & London, 1995) and for our Canary Islands natural biotite-melt pairs, in extreme cases by over an order of magnitude (Figs 10d, A18a). The peraluminous granite experiments of Icenhower & London (1995) have much higher ASI values (mean 1.76 of the melt) than the calibration data set for the model of Zhang et al. (2022)(1.17), which may be why their model predicts such low values for these compositions.

The partitioning of 1+ cations between silicate melt and the A-site of biotite is described below using empirical models to predict the lattice strain parameters , and as a function of pressure, temperature and composition. Firstly, we fitted Onuma curves for the monovalent ions Na–Cs, with weighting based on analytical precision on the experimental and literature reported values. Uncertainty on the fits was determined via bootstrapping. Where precision on biotite or glass analyses was not reported (e.g., Evensen & London, 2002) we attempted fits using uncertainty determined on other charges from the same study (see Appendix). For several experiments from the literature compilation, values for one or more ions fell outside the 95% confidence interval on the LST parabola. We do not consider these charges further as we suspect issues with either the analytical or experimental procedure. Onuma curves for each experiment, and histograms showing LST parameters determined via bootstrapping are given in the Appendix.

Lattice strain parameters for 43 experiments were used to fit empirical models that describe partitioning of the monovalent ions Na–Cs. A least-squares multiple linear regression analysis was performed following the method described above for F-OH exchange. The largest number of significant terms was five for the parameter (Table 5). Equations from the multiple linear regression are given below:

where are the regression coefficients for each variable (Table 5) is temperature in Kelvin and is pressure in MPa. The resultant empirical models account well for changes to the lattice-strain parameters over a range of compositions from basanite to peralkaline phonolite to peraluminous granite, reproducing the larger for the interlayer site typical for biotite grown from sodic alkaline silicate melt (Fig. 8b). PRESS values are similar to overall values, indicating that the models are robust and have high predictive power. Fitted vs predicted diagrams for the lattice strain parameters are in Fig. 10a–c, and full multiple regression reports are in the Appendix.

The model for Ln includes a compositional term from the A-site of biotite, two melt compositional terms and a term for inverse temperature. The positive correlation between A-site and is the largest contribution to the model, indicating that elevated concentrations of large ions other than K on the interlayer site (e.g., Na, Ca, Ba) are associated with higher values of . The relationship between and the melt compositional terms NBO/T (non-bonding oxygens per tetrahedral cation; i.e., the degree of melt depolymerisation; Mills, 1993) and the molar (Na + K)/Al ratio, and with inverse temperature are tied to the solubility of the mineral in the melt (Wood & Blundy, 2003). These terms are physically grounded as they are consistent with increased stabilisation of biotite in systems with a depolymerised melt structure (with high volatile and alkali content), and at low temperature.

The model for incorporates compositional controls on the M and W sites of biotite. Model fitting was performed with weights for each experiment assigned by . For this reason the model reproduces more accurately the for experiments where fits have been determined to higher precision (Fig. 10b). While our model has a lower predictive power than our and models it still has physical grounding: The positive and terms, and a negative term, are consistent with a larger interlayer separation, as determined via X-ray diffraction, in Mg-rich micas relative to Ti-rich ones (Brigatti & Guggenheim (2002), Fig. A16). The model also contains a small negative contribution from , which has a small effective ionic radius relative to hydroxyl anions it substitutes for.

The model for has compositional terms from the A, M and W sites of biotite, as well as the iron oxidation state in biotite. The negative term suggests that the interlayer of K-rich micas is less stiff than those with higher proportions of smaller, and perhaps less readily deformed, ions. The compositional term is positively correlated with , whereas has a strong negative correlation. The polarity of these terms are physically grounded, as is a small ion that form bonds that are not as readily deformed, compared to bonds including larger Mg and Fe cations. Similarly, the large anion will form relatively less stiff bonds than the smaller W-site and anions that it substitutes for.

Diagrams of measured vs predicted values for individual cations are given in Fig. 11. For the A site all of the measured partition coefficients, except for , are reproduced to better than a factor two. values for the elements K and Rb are reproduced most faithfully because their XII-coordinated ionic radius is closer to the biotite and therefore prediction of their partitioning behaviour is influenced less strongly by inaccuracies in predicted values. Partitioning behaviour for Na is not predicted accurately by our lattice strain model, with the lowest measured values being underpredicted (Fig. 8a). As the effect is of similar magnitude for EPMA and higher-precision LA and SIMS measurements this bias is unlikely to be an analytical artefact. It may reflect incorporation of a small amount of Na cations on the biotite M sites.

Using the methodology described above, we fitted three empirical models that describe the partitioning behaviour of Li between silicate melt and the M-sites of biotite. The same training data set described above was used, with 43 entries for lithium. Partitioning was explored directly, rather than in the frame of lattice strain theory, owing to the lack of other 1+ cations with radii similar to the biotite M-sites. The ‘Best fit’ equation for the partitioning of lithium, as obtained from multiple linear regression, is given below:

where are the regression coefficients for each variable (Table 5). Measured vs predicted values are shown in Figs 10e and A19.

The first model for includes one melt composition term, a term for inverse temperature, and a term for biotite composition and reproduces accurately the two order of magnitude range of values in the training data set (Fig. 10e; A19). The positive term is consistent with the low whole-rock lithium content of peralkaline magmatic rocks (e.g., Teng et al. (2009)), and the association between lithium-caesium-tantalum pegmatites and peraluminous granites (Gardiner et al., 2024). The positive correlation between and inverse temperature likely results from broad variations in melt and mineral composition that are correlated with temperature. It is consistent with the observation that F-Li rich micas form at low temperatures in evolved granitic systems (Černý et al., 2005, Förster et al., 1999) and that silicate minerals from slowly-cooled alkaline and calc-alkaline lavas and ignimbrites are enriched in Li relative to rapidly cooled portions of the same volcanic deposits (Neukampf et al., 2023). Correlations between the fluorine and lithium content of micas are widely reported from rare metal granites, pegmatites and metamorphic rocks (Breiter et al., 2023, Kunz et al., 2022, Martins et al., 2012).

A second temperature-free model for lithium partitioning was calibrated, as when interrogating minerals from natural systems, the temperature of equilibration and melt composition can be challenging to constrain. The above procedure was used, but only biotite compositional terms were included in the list of permitted intensive variables. The temperature- and melt-free equation for the partitioning of lithium is as follows:

The predictive power of the temperature-free model for lithium partitioning is slightly weaker than that our ‘best fit’ model ( = 0.799 vs 0.859), but reproduces all measured and compiled values to within a factor of two (Fig. 10e, A19). The fit coefficients are physically grounded: and have relatively low charge compared to and and their positive fit coefficients indicate their relative readiness to substitute for . Additionally, increasing the content of the T-site of biotite over may promote incorporation of in place of more highly-charged M-site cations such as , and (cf. Breiter et al., 2023).

A third empirical biotite partitioning model is designed for integration directly with the current generation of phase equilibrium model systems that do not include fluorine (e.g., MELTS family, HPx-eos; as implemented in Gibbs energy minimisation software such as thermocalc, and MAGEMin; Asimow et al., 2004, Ghiorso et al., 2002, Green et al., 2025, Gualda et al., 2012, Weller et al., 2024). For this reason, our best-fit model cannot currently be applied to forward model lithium behaviour in silicate magmatic systems. Instead, we recommend using the following empirical relationship:

The predictive power of this fluorine-free model for lithium partitioning is intermediate between that of our ‘best fit’ model and temperature-free model ( = 0.840 vs 0.799 and 0.859; Table 5). The fit coefficients in model 11 are physically grounded, with a negative term tracking an increasingly positive charge of the biotite M-site, and corresponding increased difficulty of incorporating monovalent cations. The positive and coefficients follow mechanisms discussed for our best fit model (Equation 9) above.

We fitted an empirical model to describe Nb partitioning between biotite and silicate melt. The model has physical grounding with a compositional term for the M-sites of biotite, and an inverse temperature term:

The coefficients and describe a negative correlation between incorporation in biotite and the and Mg content of biotite. The substitution of for or incurs a charge penalty of 3+ that must be balanced elsewhere within the biotite structure, a larger penalty than if Nb replaced or . The positive correlation between and melt NBO/T suggests that Nb activity in the silicate melt might rise with increasing depolymerisation of the silicate melt. However, this finding is reverse to that of Aseri et al. (2015) who report increases to solubility of HFSE oxide and silicate minerals with increasing melt alkalinity. We suggest the correlation incorporated into our model reflects broad variation activity of Nb in the silicate melt as well as that of biotite composition, which across our calibration data set may be stronger than the melt activity effect alone. The subtle negative correlation with pressure also likely results from broad correlations with melt and mineral composition. A second model fit was attempted where no melt, pressure or temperature terms were permitted to facilitate application to biotite grains from natural systems. However, a satisfactory fit was not possible.

A waypoint file for field localities for the Canary Islands pyroclastic rock samples

A spreadsheet containing (1) Compositions of starting materials for the IHPV experiments; (2) Experiment run conditions; (3) Electron microprobe (EPMA) major-element data for experiment and Canary Islands biotite; (4) EPMA major-element data for experiment and Canary Islands glass; (5) EPMA reference material measurements, including comparison to values retrieved from the GeoReM database (Jochum et al. (2005); compiled values from Govindaraju (1994)); (6) Laser ablation ICP-MS measurements of Canary Islands biotite and glass; (7) Laser ablation measurements of experimental run products; (8) Laser ablation analyses of reference materials compiled across several measurement sessions, including comparison to compiled values retrieved from the GeoReM database (Jochum et al. (2005, 2016, 2011), Smith (1995); John Stix 2015 compilation) (9) Deconvolved analyses of biotite and glass via LA-ICP-MS; (10) Nernst partition coefficients ( values) for major- and trace-elements as determined from EPMA and LA-ICP-MS analyses; (11) and finally a spreadsheet for assigning biotite major-element ions to lattice sites following Li et al. (2020) modified after Zhang et al. (2022), for calculating silicate melt water speciation following Behrens (2020), and subsequently melt F and OH values, melt NBO/T following Mills (1993), and for determining modelled F-OH and Cl-OH exchange coefficients following Zhang et al. (2022), and F-OH exchange, -site lattice strain parameters, values for Na, K, Rb, Cs, Li and Nb using our new empirical partitioning models.

A folder containing MATLAB scripts for reduction of laser-ablation trace-element measurements from both unmixed and mixed analyses of silicate glass and biotite. These codes require installation of the MATLAB machine learning and curve fitting toolbox. All input files required by these codes containing EPMA and LA-ICP-MS data are included in this folder. The codes generate a series of robust regression diagrams of biotite or glass proportion, constrained by the Mg/Al and Na/Al ratio respectively, a diagram showing the determined biotite and glass trace-element concentrations with their associated uncertainty and finally a diagram of trace-element values.

A folder containing (1) a subfolder of Onuma diagrams (Onuma et al., 1968) for the biotite -site per experiment showing 1 uncertainty on 1+ partition coefficients and a 1 error envelope on the lattice strain curve. The folder also contains histograms for fitted lattice strain parameters as determined via bootrapping; (2) multiple regression reports for empirical element partitioning models as generated using the NCSS software.