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Volume 31 Issue 3
Jul.  2020
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Xiaoyan Li, Chao Zhang, Lianxun Wang, Harald Behrens, Francois Holtz. Experiments on the Saturation of Fluorite in Magmatic Systems: Implications for Maximum F Concentration and Fluorine-Cation Bonding in Silicate Melt. Journal of Earth Science, 2020, 31(3): 456-467. doi: 10.1007/s12583-020-1305-y
Citation: Xiaoyan Li, Chao Zhang, Lianxun Wang, Harald Behrens, Francois Holtz. Experiments on the Saturation of Fluorite in Magmatic Systems: Implications for Maximum F Concentration and Fluorine-Cation Bonding in Silicate Melt. Journal of Earth Science, 2020, 31(3): 456-467. doi: 10.1007/s12583-020-1305-y

Experiments on the Saturation of Fluorite in Magmatic Systems: Implications for Maximum F Concentration and Fluorine-Cation Bonding in Silicate Melt

doi: 10.1007/s12583-020-1305-y
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  • The effects of melt composition, temperature and pressure on the solubility of fluorite (CaF2), i.e., fluorine concentration in silicate melts in equilibrium with fluorite, are summarized in this paper. The authors present a statistic study based on experimental data in literature and propose a predictive model to estimate F concentration in melt at the saturation of fluorite (CF in meltFl-sat). The modeling indicates that the compositional effect of melt cations on the variation in CF in meltFl-sat can be expressed quantitatively as one parameter FSI (fluorite saturation index):FSI=(3AlNM+Fe2++6Mg+Ca+1.5Na-K)/(Si+Ti+AlNF+Fe3+), in which all cations are in mole, and AlNF and AlNM are Al as network-forming and network-modifying cations, respectively. The dependence of CF in meltFl-sat on FSI is regressed as:CF in meltFl-sat=1.130-2.014·exp (1 000/T)+2.747·exp (P/T)+0.111·CmeltH2O+17.641·FSI, in which T is temperature in Kelvin, P is pressure in MPa, CmeltH2O is melt H2O content in wt.%, and CF in meltFl-sat is in wt.% (normalized to anhydrous basis). The reference dataset used to establish the expression for conditions within 540-1 010 ℃, 50-500 MPa, 0-7 wt.% melt H2O content, 0.4 to 1.7 for A/CNK, 0.3 wt.%-7.0 wt.% for CF in meltFl-sat. The discrepancy of CF in meltFl-sat between calculated and measured values is less than ±0.62 wt.% with a confidence interval of 95%. The expression of FSI and its effect on CF in meltFl-sat indicate that fluorine incorporation in silicate melts is largely controlled by bonding with network-modifying cations, favorably with Mg, AlNM, Na, Ca and Fe2+ in a decreasing order. The proposed model for predicting CF in meltFl-sat is also supported by our new experiments saturated with magmatic fluorite performed at 100-200 MPa and 800-900 ℃. The modeling of magma fractional crystallization emphasizes that the saturation of fluorite is dependent on both the compositions of primary magmas and their initial F contents.KEY WORDS:fluorine, fluorite solubility, silicate melt, experimental petrology.
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Experiments on the Saturation of Fluorite in Magmatic Systems: Implications for Maximum F Concentration and Fluorine-Cation Bonding in Silicate Melt

doi: 10.1007/s12583-020-1305-y

Abstract: The effects of melt composition, temperature and pressure on the solubility of fluorite (CaF2), i.e., fluorine concentration in silicate melts in equilibrium with fluorite, are summarized in this paper. The authors present a statistic study based on experimental data in literature and propose a predictive model to estimate F concentration in melt at the saturation of fluorite (CF in meltFl-sat). The modeling indicates that the compositional effect of melt cations on the variation in CF in meltFl-sat can be expressed quantitatively as one parameter FSI (fluorite saturation index):FSI=(3AlNM+Fe2++6Mg+Ca+1.5Na-K)/(Si+Ti+AlNF+Fe3+), in which all cations are in mole, and AlNF and AlNM are Al as network-forming and network-modifying cations, respectively. The dependence of CF in meltFl-sat on FSI is regressed as:CF in meltFl-sat=1.130-2.014·exp (1 000/T)+2.747·exp (P/T)+0.111·CmeltH2O+17.641·FSI, in which T is temperature in Kelvin, P is pressure in MPa, CmeltH2O is melt H2O content in wt.%, and CF in meltFl-sat is in wt.% (normalized to anhydrous basis). The reference dataset used to establish the expression for conditions within 540-1 010 ℃, 50-500 MPa, 0-7 wt.% melt H2O content, 0.4 to 1.7 for A/CNK, 0.3 wt.%-7.0 wt.% for CF in meltFl-sat. The discrepancy of CF in meltFl-sat between calculated and measured values is less than ±0.62 wt.% with a confidence interval of 95%. The expression of FSI and its effect on CF in meltFl-sat indicate that fluorine incorporation in silicate melts is largely controlled by bonding with network-modifying cations, favorably with Mg, AlNM, Na, Ca and Fe2+ in a decreasing order. The proposed model for predicting CF in meltFl-sat is also supported by our new experiments saturated with magmatic fluorite performed at 100-200 MPa and 800-900 ℃. The modeling of magma fractional crystallization emphasizes that the saturation of fluorite is dependent on both the compositions of primary magmas and their initial F contents.KEY WORDS:fluorine, fluorite solubility, silicate melt, experimental petrology.

Xiaoyan Li, Chao Zhang, Lianxun Wang, Harald Behrens, Francois Holtz. Experiments on the Saturation of Fluorite in Magmatic Systems: Implications for Maximum F Concentration and Fluorine-Cation Bonding in Silicate Melt. Journal of Earth Science, 2020, 31(3): 456-467. doi: 10.1007/s12583-020-1305-y
Citation: Xiaoyan Li, Chao Zhang, Lianxun Wang, Harald Behrens, Francois Holtz. Experiments on the Saturation of Fluorite in Magmatic Systems: Implications for Maximum F Concentration and Fluorine-Cation Bonding in Silicate Melt. Journal of Earth Science, 2020, 31(3): 456-467. doi: 10.1007/s12583-020-1305-y
  • There are several experiments involving saturation of fluorite in fluorine-rich magmatic systems (Li et al., 2018; Hou et al., 2017; Lukkari and Holtz, 2007; Dolejš and Baker, 2006; Gabitov et al., 2005; Scaillet and Macdonald, 2003; Xiong et al., 2002; Price et al., 1999; Icenhower and London, 1997; see summary Table 1 and details in Table S1), which cover relatively wide ranges in pressure (50–500 MPa), temperature (540–1 010 ℃), and melt composition (e.g., SiO2 59 wt.%–79 wt.%, CaO 0.1 wt.%–5.8 wt.%). Particularly, the silicate melts in equilibrium with fluorite involve peralkaline, metaluminous and peraluminous compositions, spanning a large range in aluminum saturation index [ASI=molar Al2O3/(CaO+Na2O+K2O), also termed as A/CNK] of 0.4–1.7 (Fig. 1a).

    References n P (MPa) T (℃) fO2 (ΔNNO) aH2O Melt composition (wt.%) A/NK A/CNK
    SiO2 Al2O3 TiO2 FeOT MnO MgO CaO Na2O K2O F
    Icenhower and London (1997) 14 200 640–680 0 1.0 67–70 13–14 0–0.04 0.3–0.6 ~0.04 ~0.05 ~0.4 3.0–4.0 4.1–4.8 0.8–2.0 1.2–1.4 1.1–1.3
    Price et al. (1999) 7 200 850 0 1.0 70–73 12–13 ~0.2 1.0–1.7 ~0.06 0.1–0.2 0.6–1.1 3.5–4.0 4.0–5.0 1.2–1.6 1.1–1.2 0.9–1.0
    Xiong et al. (2002) 1 150 540 0 1.0 65.73 17.05 0.00 0.55 0.00 0.00 0.56 4.82 2.78 3.03 1.6 1.4
    Scaillet and Macdonald (2003) 25 52–156 661–794 -3–+4 n.d. 64–78 8–12 0.0–0.7 1.3–8.8 0.0–0.2 ~0.02 0.1–0.3 3.9–8.9 3.6–5.1 0.4–4.3 0.4–1.0 0.4–0.9
    Gabtiov et al. (2005) 18 100 850–1 000 -3–0 n.d. 68–76 8–12 0.00 0.00 0.00 0.00 0.2–3.0 3.5–8.0 3.4–6.3 0.3–1.7 0.5–1.3 0.4–1.1
    Dolejs and Baker (2006) 43 100 800–950 n.d. 1.0 66–74 10–13 0.00 0.00 0.00 0.00 0.1–2.5 2.9–5.1 3.3–4.5 0.3–6.0 0.8–1.5 0.6–1.2
    Lukkari and Holtz (2007) 36 100–500 575–750 0 0.6–1.0 62–69 14–18 0.00 0.2–0.9 0.00 ~0.01 0.1–0.8 3.2–5.2 3.4–4.7 1.8–5.9 1.2–1.7 1.1–1.7
    Hou et al. (2017) 14 100–200 1 010 -2.5–+2.5 0.1–1.0 59–73 8.1–10.2 0.1–1.2 6.6–13.1 0.2–0.4 0.1–0.7 1.9–5.5 1.3–2.2 3.5–4.8 2.4–4.2 1.0–1.6 0.5–0.7
    Li et al. (2018) 1 50 900 0 1.0 60.89 17.90 0.70 2.00 0.10 0.48 2.21 6.78 3.43 3.59 1.2 0.9
    Notes: n denotes the number of experiments. The value of fO2 is expressed as deviation in log unit from nickel-nickel oxide (NNO) oxygen buffer. n.d. not determined. * Details of experimental data are listed in Table S1.

    Table 1.  Summary of experiments with saturation of fluorite*

    Figure 1.  Plots of compositional key parameters of experimental silicate melts at the saturation of fluorite. (a) A/NK vs. A/CNK. (b) F concentration in melt (wt.%, normalized on anhydrous basis) vs. A/CNK. (c) F concentration vs. CaO content. The field of natural glasses and melt inclusions are after the compilation of Dolejš and Baker (2006). (d) Mole fractions of CaO vs. F2O-1. The solid line denotes stoichiometry ratio of fluorite. Data from different references are grouped with different legends.

    The fluorine concentration in silicate melt at the saturation of fluorite ($ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $) varies widely from 0.3 wt.% to 6.7 wt.%, which does not show any apparent correlation with A/CNK (Fig. 1b). Scaillet and Macdonald (2004) and Lukkari and Holtz (2007) proposed that $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ is largely dependent on ASI: for melts with ASI < 1, $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ increases with decreasing ASI, while the opposite behavior is observed for melts with ASI > 1. However, this simple correlation may be correct for compositions in which only the Al proportions are changing but it is not systematically observed for a much larger dataset summarized in this study (Fig. 1b), suggesting that the potential effects of other cations (e.g., Fe and Mg) must be considered.

    There seems to be a dichotomy between $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ and CaO content (Fig. 1c): melts with high F contents usually contain less than 1 wt.% CaO; on the other hand, most high Ca melts plot around the stoichiometry line of CaF2 (the fluorite saturation is attained in melts with a molar ratio of Ca : F of 1 : 2). Compared to natural glasses and melt inclusions, which show a much stronger dichotomy between Ca and F (Dolejš and Baker, 2006), the experimental melts at the saturation of fluorite (except for having a lower limit at ~0.3 wt.%) show a roughly overlapping range in fluorine concentration, but a large range in CaO content. These data imply that, saturation of fluorite is preferentially achieved in either high F or high Ca magmatic systems; in both cases, the concentration of the less abundant component is more crucial than the other for the saturation of fluorite (Dolejš and Baker, 2006). However, for magmatic systems rich in both F and Ca, their concentrations in silicate melt seem to be buffered by the stoichiometry of fluorite, which do not follow the general dichotomy distribution.

    According to Dolejš and Baker (2006), the formation of fluorite in magmatic systems is controlled by the simplified reaction as follows

    and the apparent equilibrium constant K can be written as

    in which XCaO and XF2O-1 are mole anion fractions on an anhydrous basis, and c indicates the stoichiometric coefficient. Particuarly, the virtual component of F2O-1 is defined by the substitution of 2F-1 for 1O2- in silicate melts. At the saturation of fluorite, aCaF2 equals to unity, and thus log XCaO and log XF2O-1 should be correlated in a linear relation. Dolejš and Baker (2006) suggested that, based on their experimental data, the value of c increases systematically from peraluminous, through subaluminous, to peralkaline systems; however, this simple trend is not valid for all the data compiled in Fig. 1d, implying there should be important contributions from other cations, such as Fe and Mg, to the value of c.

  • Quantitative relations have been proposed in literature to correlate $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ as a function of melt composition. Scaillet and Macdonald (2004) introduced a cation ratio (MFe), which is expressed as

    MFe exhibits a negative linear correlation with $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ for the peralkaline silicate melts of Scaillet and Macdonald (2004), which indicates that the solubility of fluorite is controlled by the abundance of network-forming cations (Si, Al, Fe3+) relative to network-modifying cations (Na, K, Ca2+, Fe2+). For peraluminous silicic melts, Dolejš and Baker (2006) introduced the excess Al2O3 over alkali oxides for correlating melt composition with $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $, which is calculated as

    in which the cation oxides denote mole fractions.

    In order to correlate melt composition with $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ for more complex natural multicomponent silicate melts, we propose a new melt composition parameter, termed as Fluorite Saturation Index (FSI), to treat peralkaline, metaluminous and peraluminous silicate melts consistently. As inspired by the MFe proposed by Scaillet and Macdonald (2004), a preliminary expression of FSI is

    AlNF indicates network-forming Al, whereas AlNM indicates network-modifying Al. Fe2+ and Fe3+ fractions have been calculated with the model of Kress and Carmichael (1991). With network-forming cations in the denominator and network-modifying cations in the numerator, FSI is supposed to be positively correlated to $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $.

    According to Dolejš and Baker (2006), for peralkaline and metaluminous melts (A/CNK≤1),

    and

    in which Altot is total Al mole fraction. For peraluminous melts (A/CNK > 1),

    and AlNM is calculated as

    As shown in Fig. 2a, a positive linear correlation can be approximately observed between measured $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ and FSI for the majority of data collected in this study. A few significant deviations occur for melt compositions with high F contents (> 4.5 wt.%) from Dolejš and Baker (2006) that are difficult to interpret; one possibility would be due to analytical issue involving assimilation of fine-grained fluorite in glass measurements.

    Figure 2.  Plots of F concentration in melt at the saturation of fluorite ($ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $) vs. fluorite saturation index (FSI). (a) $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ vs. preliminary FSI. (b) $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ vs. updated FSI. The data in the marked circles are excluded from multiple linear regression. Data from different references are grouped with different legends.

    For evaluating the potential effect of FSI on $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $, as well as the potential effects of pressure, temperature, and melt H2O content, we regress the following multiple linear equation based on experimental data

    in which T is temperature in Kelvin, P is pressure in MPa, $ {C}_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{H}2\mathrm{O}} $ is melt H2O content in wt.%, and a, b, c, d and e are constants. The F concentration, $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $, is given in wt.% on an anhydrous basis. The regression result of Eq. 10 involving the preliminary FSI (expressed as Eq. 5) is listed as No. 1 in Table 2, which yields a coefficient of determination (R2) of 0.749 and supports a dominant effect of FSI as indicated by the low relative standard deviation of the coefficient of FSI, in comparison to that of other coefficients.

    Model No. R2 Intercept Exp (1 000/T) Exp (P/T) Melt compositional parameters
    H2O FSI (preliminary) FSI (updated) AlNM/NFC Fe2+/NFC Mg/NFC Ca/NFC Na/NFC K/NFC
    1 0.749 -2.870 -0.836 2.291 0.069 17.686 - - - - - -
    sd 0.890 0.367 0.805 0.048 0.994 - - - - -
    2 0.781 1.491 -2.010 2.739 0.079 - - 54.985 16.590 102.931 16.793 24.970 -19.087
    sd 1.504 0.508 0.764 0.064 - - 4.449 5.197 54.320 10.594 2.718 12.594
    3 0.789 1.130 -2.014 2.747 0.111 - 17.641 - - - - -
    sd 0.874 0.355 0.733 0.044 - 0.881 - - - - - -
    Notes: For multiple linear regression, temperature in Kelvin, pressure in MPa, H2O content in wt.%. NFC (network-forming cations)=Si+Ti+AlNF+Fe3+. sd is standard deviation. Expressions of preliminary FSI and updated FSI are shown as Eq. 5 and Eq. 14 in the text, respectively.

    Table 2.  Coefficients of multiple linear regression for CF in meltFl-sat

    In order to better constrain quantitatively the individual contributions of different network-modifying cations, we performed another multiple linear regression for the following equation

    in which NFC is the sum of network-forming cations

    The constant hn denotes the effect of each network-modifying cation. The regression result of Eq. 11 is listed as No. 2 in Table 2, which yields a better R2 of 0.781 and indicates that

    The above quantitative relation demonstrates that the largest contribution is predicted from Mg compared to other network modifiers. Correspondingly, an updated expression of FSI can be written as

    Introducing the updated FSI into Eq. 10, the new regression result is further slightly better with a R2 of 0.788 and a lower standard deviation of the coefficient of FSI (see regression result No. 3 in Table 2). Therefore, we propose that the updated FSI is an appropriate parameter to describe collectively the effect of melt composition on $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ (see Fig. 2b), with additional minor influences from pressure, temperature and melt H2O content. The calculated FSI values according to Eq. 14 of reference data range from 0.04 to 0.42.

    A comparison between experimentally determined $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ and that predicted from the empirical model shows that they are in general agreement and the discrepancy is mostly within ±1 wt.% (Fig. 3a). The variation is less than 0.62 wt.% with a confidence interval of 95%. However, the maximum discrepancy of $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ between calculated and measured values can be large (ca. ±2.0 wt.% F) in some cases. We propose that these large discrepancies between modeled and measured $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ may be partly due to large analytical errors [e.g., see Zhang et al. (2016) for the potential analytical issues in EPMA of F concentration] in some studies.

    Figure 3.  (a) Plots of measured and estimated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $. The solid line is 1 : 1 line. The two dotted lines denote uncertainty of ±0.62 wt.% with a confidence interval of 95%. (b) Histogram of discrepancy in F concentration between measured and estimated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $. Data from different references and from this study are grouped with different legends.

    The uncertainty of calculated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ by the solubility model expressed as Eq. 11 is dependent on the uncertainties of the input parameters, namely temperature, pressure, $ {C}_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{H}2\mathrm{O}} $ and FSI. We modeled this uncertainty propagation by Monte Carlo simulation, and the results indicate that the primary uncertainty of calculated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ is derived from temperature and FSI, of common uncertainty ranges of these parameters are considered. As shown in Fig. 4a, for a given condition with temperature of 700 ℃, pressure of 100±10 MPa, $ {C}_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{H}2\mathrm{O}} $ of (4.0±1.0) wt.% and FSI of 0.2±0.02, with an increasing standard deviation (sd) of temperature from zero to 100, the sd value of $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ increases from 0.35 to 0.75. Alternatively, as shown in Fig. 4b, for a given condition with temperature of 700±50 ℃, pressure of 100±10 MPa, $ {C}_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{H}2\mathrm{O}} $ of (4.0±1.0) wt.% and FSI of 0.2, with an increasing sd of FSI from zero to 0.03, the sd value of $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ increases from 0.3 to 0.6. The sd values of calculated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ in these two simulated cases are roughly overlapping with the model intrinsic uncertainty of ±0.62 wt.% at the confidence interval of 95% (Fig. 3a).

    Figure 4.  Monte Carlo simulation of propagated uncertainty (standard deviation, 1sd) for the calculated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $. (a) The dependence of 1sd of $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ on variable 1sd of temperature. (b) The dependence of 1sd of $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ on variable 1sd of FSI.

  • In order to test our empirical model for predicting melt F concentration at fluorite saturation in magmatic systems, we performed dissolution experiments for a variety of magmatic systems with fluorite as a stable phase. The starting materials, experimental approaches, analytical methods and experimental results are described below.

  • Four different starting glasses were used in our experiments, and their compositions corresponded to tephriphonolite (SG-01, ref. Wengorsch, 2013), andesite (SG-02, ref. Botcharnikov et al., 2008), dacite (SG-03, ref. Holtz et al., 2005) and rhyolite (SG-04, ref. Bartels et al., 2013) (Table S2). Starting glasses SG-01 and SG-03 were synthesized from natural rocks by melting into glass. Starting glasses SG-02 and SG-04 were synthesized by melting mixed powders of oxides (SiO2, Al2O3, TiO2, Fe2O3, Mn3O4, MgO) and carbonates (CaCO3, Na2CO3, K2CO3) in the desired proportion. For both cases, the melting was performed in a platinum crucible at 1 600 ℃ in a muffle furnace for about 3 hours, and the obtained glasses were subsequently crushed in a steel mortar and grinded in an agate mortar. The melting and crushing were repeated two or three times for yielding homogeneous starting glasses. A colorless gem-quality natural fluorite was used as source of fluorite, which was added to the experimental systems for ensuring saturation of fluorite. The fluorite was crushed and powdered, and grains with a size of 100−200 μm were sieved for experimental use.

  • Powders of dry silicate glass and fluorite were weighed with an assigned ratio of 9 : 1 and mixed in a mortar by hand. For each experimental run, about 50 mg mixed powders were added to a gold capsule together with ~8 wt.% water. The capsules were then closed by arc welding, and during the procedure the capsules were cooled with a surrounding wet paper that had been frozen by liquid N2. The experiments were performed in an Ar-pressurized internally heated pressure vessels (IHPV) at the Institute of Mineralogy, Leibniz University Hannover. Details about the apparatus were described in Berndt et al. (2002). The experimental duration was 7 days for all runs, at pressures of 1 or 2 kbar and temperatures of 800, 850 or 900 ℃. All experiments were performed at the same oxygen fugacity (fO2) close to the nickel-nickel oxide (NNO) oxygen buffer, by adjusting H2 partial pressure in the vessel and applying the equation of Schwab and Küstner (1981) assuming a water-saturated condition. Sample quenching in IHPV was achieved by dropping the capsule directly down to a cold zone at ~50 ℃, yielding a rapid quench rate of ~150 ℃/s (Berndt et al., 2002). After confirming that there was no potential leakage by weighing the capsule again after the experiment, we opened the capsules and mounted experimental products in epoxy for compositional analysis.

  • Compositions of the experimental products were measured with electron probe microanalysis (EPMA) using a CAMECA SX100 electron microprobe at the Institute of Mineralogy, Leibniz University Hannover. The calibration materials included synthetic oxides (Al2O3 and TiO2, Fe2O3, MgO, MnO), wollastonite (for Si and Ca), albite (for Na), orthoclase (for K), apatite (for P) and strontium fluoride (for F). For analyzing glass compositions, a beam size of 20 μm and a beam current of 10 nA were used. F concentration was analyzed using PC1 crystal as diffraction crystal applying the method of Zhang et al. (2016). In order to minimize potential losses of Na and K during analysis, these two elements were analyzed first. Peak-intensity counting time was 20 s for F and 10 s for other elements.

  • Fluorite and silicate melt (i.e., quenched as glass) were observed as stable phases in all experimental products. For experiments using the granitic starting glass (SG-4), no other phases were observed. For other experiments using the tephriphonolitic, andesitic and dacitic starting glasses (SG-1, SG-2 and SG-3), there were variably other phases including amphibole, biotite, titanite, ilmenite and apatite (Table 3). As we used fluorite powders as a starting material in our experiments, it is important to examine if a global saturation of fluorite has been achieved inside the capsules. For this purpose, we performed element mapping for selected samples (No. 1a and No. 4b), and the results show that there is no gradient in any cation or F in experimental glasses as a function of distance from fluorite grains (Fig. 5), indicating homogeneous distributions of these elements in silicate melts. In addition, EPMA of experimental glasses performed at 10 to 15 random locations shows identical compositions within analytical error (Table 3). Therefore, we conclude that near equilibrium conditions were achieved and the analytical data on glasses were representative for the fluorine concentrations in melts saturated with fluorite.

    No. Starting glass P (MPa) T (℃) fO2 (ΔNNO) Duration (hour) H2O (wt.%) a Phases b Glass composition (wt.%) c
    SiO2 Al2O3 TiO2 FeOT MnO MgO CaO Na2O K2O P2O5 F -O=F Total
    1a SG-1 200 900 0 168 8.01 Gl, Fl, Amp, Bt, Ttn, Ap 46.47 17.14 0.83 4.53 0.15 1.31 8.43 6.50 3.14 0.10 6.76 2.85 94.12
    0.38 0.11 0.03 0.10 0.04 0.05 0.17 0.17 0.03 0.09 0.16
    1c SG-1 200 850 0 168 8.13 Gl, Fl, Amp, Ttn 51.17 19.32 0.33 2.84 0.14 0.39 4.84 7.32 4.24 0.04 4.09 1.72 94.03
    0.54 0.24 0.02 0.02 0.01 0.04 0.15 0.05 0.08 0.07 0.08
    2a SG-2 200 900 0 168 8.10 Gl, Fl, Amp 49.15 15.28 0.85 5.81 0.01 1.93 11.44 2.89 1.38 0.07 6.74 2.84 94.19
    0.33 0.21 0.03 0.20 0.02 0.08 0.20 0.11 0.04 0.04 0.19
    2c SG-2 200 850 0 168 7.92 Gl, Fl, Amp, Plg 58.00 15.48 0.36 3.78 0.02 0.76 7.67 3.20 2.00 0.04 3.56 1.50 94.12
    0.57 0.22 0.02 0.20 0.04 0.23 0.21 0.17 0.05 0.05 0.04
    3a SG-3 200 900 0 168 8.00 Gl, Fl, Ap 52.75 15.22 0.57 4.42 0.11 1.65 9.61 3.10 2.10 0.13 5.81 2.45 94.24
    0.30 0.12 0.03 0.09 0.06 0.06 0.13 0.17 0.04 0.06 0.09
    3b SG-3 200 800 0 168 8.20 Gl, Fl, Ap, Amp, Plg 64.18 15.33 0.17 2.17 0.08 0.23 4.56 3.30 3.32 0.02 1.90 0.80 94.71
    0.22 0.11 0.02 0.09 0.05 0.04 0.16 0.06 0.09 0.04 0.11
    3c SG-3 200 850 0 168 8.09 Gl, Fl, Amp, Plg, Ttn 58.58 16.29 0.32 3.42 0.13 0.59 7.29 3.39 2.65 0.05 2.24 0.94 94.16
    0.35 0.16 0.01 0.04 0.04 0.02 0.17 0.10 0.04 0.06 0.09
    3d SG-3 100 850 0 168 8.96 Gl, Fl, Amp, Plg, Ilm 66.36 15.13 0.29 2.47 0.08 0.34 4.57 3.49 3.59 0.06 1.17 0.49 96.93
    0.45 0.16 0.02 0.09 0.05 0.03 0.18 0.15 0.05 0.05 0.16
    4a SG-4 200 900 0 168 8.36 Gl, Fl 61.90 18.73 0.01 0.02 0.02 0.00 1.88 7.63 3.80 0.03 3.42 1.44 96.45
    0.21 0.19 0.01 0.03 0.02 0.01 0.09 0.23 0.06 0.04 0.17
    4b SG-4 200 800 0 168 8.15 Gl, Fl 62.94 18.88 0.00 0.03 0.02 0.01 1.32 7.63 3.85 0.02 2.91 1.23 96.78
    0.21 0.18 0.01 0.03 0.02 0.01 0.05 0.19 0.07 0.05 0.09
    4c SG-4 200 850 0 168 8.22 Gl, Fl 62.52 18.65 0.01 0.02 0.03 0.01 1.55 7.08 4.08 0.03 3.12 1.31 96.23
    0.30 0.16 0.01 0.02 0.02 0.01 0.04 0.18 0.05 0.05 0.09
    4d SG-4 100 850 0 168 8.06 Gl, Fl 62.96 18.68 0.01 0.03 0.02 0.01 1.43 7.66 4.19 0.02 2.95 1.24 97.12
    0.35 0.13 0.01 0.03 0.03 0.01 0.12 0.18 0.07 0.03 0.07
    a. Initial water added to starting glass; b. phase abbreviations: Ap. apatite; Amp. amphibole; Bt. biotite; Fl. fluorite; Gl. glass; Ilm. ilmenite; Plg. plagioclase; Ttn. titanite; c. each glass composition is average of 10–15 analytical points; numbers in italics are one standard deviation.

    Table 3.  Conditions and results of equilibrium experiments with saturation of fluorite performed in this study

    Figure 5.  Back scattered electron (BSE) images and element mapping (AlKα, CaKα and FKα) for selected experimental products. (a) Run No. 1a. (b) Run No. 4b. Phase abbreviations: Ap. apatite; Bt. biotite; Fl. fluorite; Gl. glass; Ttn. titanite. See experimental conditions and results in Table 3.

    The new experimental glasses with fluorite saturation obtained at variable experimental temperatures (800−900 ℃) and pressures (100 and 200 MPa) span relatively wide ranges for major cation contents and F concentration (1.2 wt.%−6.8 wt.%), which are used as independent tests of our proposed empirical model for estimating $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ (Eq. 10 and Eq. 14). The experimental glasses show a metaluminous affinity with A/CNK ranging within 0.6−1.0. The calculated updated FSI values for the new experimental glasses according to Eq. 14 range from 0.1 to 0.4, which are within the range of the reference data. As plotted in Fig. 3a, the estimated $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ values for the glass compositions based on our model are well consistent with the measured F concentrations, and the discrepancies between estimated and measured values are less than 0.7 wt.% (Fig. 3b). Therefore, our new experiments confirm that, at least for metaluminous melts, the predictive model proposed above based on reference data is reliable within uncertainty for estimating melt F concentration at the saturation of fluorite.

  • The formulation of the updated FSI in Eq. 14 is confirmed by studies focusing on the incorporation mechanisms of fluorine in silicate melts, which have been investigated for less complex synthetic aluminosilicate glasses using NMR spectroscopy and Raman spectroscopy. The Al-F bonding is predominant in aluminosilicate glasses, while the Si-F bonding is subordinate (Mysen et al., 2004; Zeng and Stebbins, 2000). Fluoride ion is preferentially bonded to network modifying cations with higher field-strength, such as F-Ca bonding (Baasner et al., 2014; Stebbins and Zeng, 2000). In K-bearing aluminosilicate glasses, fluorine is bonded as Si-F, Al-F, and Na-F complexes whereas no K-F bonding is detected (Dalou et al., 2015), which is confirmed by the negative term for K in Eq. 11. To our knowledge, spectroscopic studies about potential bonding of F with Ti, Fe and Mg in aluminosilicate glasses are lacking. In this study, the results of multiple linear regression relating $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ and the updated FSI (Eq. 12 and Eq. 14) demonstrate that the incorporation of F in silicate melt is predominantly controlled by the abundance of network-modifying cations (AlNM, Fe2+, Mg, Ca, Na) relative to network-forming cations (Si, Ti, AlNF, Fe3+). Equation 11 indicates that fluorine tends to form F-cation bonding in an order of Mg > AlNM > Na > Ca > Fe2+, while F-K bonding is negligible. The findings are in general agreement with the F bonding mechanism associated with Al, Si, Ca, Na and K inferred from NMR spectroscopy and Raman spectroscopy.

  • Because F in silicate melts may play a unique and important role in petrological, geochemical and ore-forming processes, quantitative constraints on the maximum F concentrations that can be reached in evolved magmatic systems are of great importance. F usually behaves as an incompatible element in magmatic differentiation processes, except if apatite, mica, amphibole or fluorite occur a major solid phase. Our empirical model can be used to evaluate the initial F concentration in the parental magma and enrichment of F in melt as a consequence of magma crystallization prior to the saturation of fluorite, which can hardly be reflected by bulk rock F concentration because of fluid-exsolution induced loss at late magmatic stages (e.g., Zhang et al., 2012).

    Here we show an example of application of our predictive model to granitic rocks from the Jiuhuashan region, South China, for evaluating the potential saturation of fluorite at a late stage of magma evolution (Wang et al., 2018). Two distinctive rocks were chosen from the study of Wang et al. (2018), including a fluorite-bearing syenogranite (sample 14JHS18-1, bulk F ~150 ppm) and a fluorite-free granodiorite (sample 14JHS23-2, bulk F ~660 ppm). We modeled variation of melt composition due to magma differentiation using rhyolite-MELTS (Gualda et al., 2012) and the bulk rock major element compositions as starting melts. As a result of fractional crystallization, the composition of residual melt evolves and results in variations in $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $, which is highly dependent on melt composition as revealed above. As shown in Fig. 5, if the crystallization proceeds from the initial stage to a near-solidus condition with a residual melt proportion of 5 wt.% or 15 wt.%, the modeled $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ for the syenogranitic magma increases remarkably from ~4 wt.% to ~13 wt.% or 7 wt.% respectively. Meanwhile, the $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ for the granodioritic magma decreases strongly from ~8 wt.% to ~2 wt.%. Therefore, if the interstitial fluorite that is observed in the syenogranite sample crystallized at a late magmatic stage corresponding to a residual melt proportion of 5 wt.%–15 wt.%, the parental magma should have an initial F concentration of 0.7 wt.%–1.0 wt.% (Fig. 6a). This estimated value is dramatically higher than the measured bulk rock F concentration (~150 ppm), indicating that abundant F must have been lost due to fluid extraction, which is actually consistent with the wide occurrence of miarolitic cavities along zones which are rich in quartz and fluorite (Wang et al., 2018). In contrast, because no fluorite has been observed in the granodiorite, its parental magma should have an initial F concentration lower than 0.12 wt.%–0.35 wt.%, otherwise the F concentration in residual melt would approach the modeled $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ at the assumed late magmatic stage (Fig. 6b).

    Figure 6.  Modeling of the evolution of F concentration in melt along the crystallization path as a function of the residual melt proportion for two F-bearing rocks from the Jiuhuashan region, South China. (a) Syenogranite (sample 14JHS18-1, fluorite-present) as bulk magma composition. (b) Granodiorite (sample 14JHS23-2, fluorite-free) as bulk magma composition. The modeling of crystallization is performed using rhyolite-MELTS (Gualda et al., 2012) at constant pressure of 100 MPa, a buffered oxygen fugacity of FQM+1, and an initial H2O content of 1 wt.%. $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ is calculated using Eq. 10 and updated FSI (i.e., prediction model No. 3 in Table 2). For both cases, the initial F content in the primary melt is adjusted to achieve final fluorite saturation (i.e., so that F in residual melt equals to $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $) with a residual melt proportion of 5 wt.% or 15 wt.%.

    In addition, F usually behaves as a compatible element for apatite, titanite, biotite and amphibole against silicate melt (e.g., Li et al., 2018; Iveson et al., 2017; Webster et al., 2009; Chevychelov et al., 2008), and thus crystallization of these minerals in the magmatic system may suppress the saturation of fluorite due to an earlier partitioning of F from melt into these minerals. Nevertheless, the existence of other F-bearing minerals does not affect the solubility of CaF2 in silicate melt as expressed in Eq. 11. In such cases, the example discussed above illustrates an approach that can be used to constrain the minimum F content in primary melt leading to crystallization of magmatic fluorite.

  • A parameter of fluorite saturation index (FSI) is proposed to describe the melt compositional effect on fluorine concentration at the saturation of fluorite, which implies that the tendency of bonding mechanism between fluorine and network-modifying cations is in the order of Mg > AlNM > Na > Ca > Fe2+ > K. Our model predicting $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ has the advantage to be applicable to a very wide compositional range, covering peraluminous, to calc-alkaline and peralkaline. However, the fit between predicted $ {C}_{\mathrm{F}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{F}\mathrm{l}-\mathrm{s}\mathrm{a}\mathrm{t}} $ and experimental results is not always satisfying (discrepancy up to 2 wt.% F in some rare cases), which may be due in part to analytical problems, especially at high F contents of the glasses. The reliability of the empirical model is supported by our new equilibrium experiments in fluorite-saturated magmatic systems.

  • This study was supported by the National Natural Science Foundation of China (No. 41902052) and the German Research Foundation (DFG) (No. BE 1720/40). We thank two anonymous reviewers for their helpful comments that have substantially improved this paper. The final publication is available at Springer via https://doi.org/10.1007/s12583-020-1305-y.

    Electronic Supplementary Materials: Supplementary materials (Tables S1–S2) are available in the online version of this article at https://doi.org/10.1007/s12583-020-1305-y.

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