The effect of titanium and phosphorus on ferric/ferrous ratio in silicate melts: an experimental study

Abstract

The effect of TiO₂ and P₂O₅ on the ferric/ferrous ratio in silicate melts was investigated in model silicate melts at air conditions in the temperature range 1,400–1,550 °C at 1-atm total pressure. The base composition of the anorthite–diopside eutectic composition was modified with 10 wt % Fe₂O₃ and variable amounts of TiO₂ (up to 30 wt %) or P₂O₅ (up to 20 wt %). Some compositions also contained higher SiO₂ concentrations to compare the role of SiO₂, TiO₂, and P₂O₅ on the Fe³⁺/Fe²⁺ ratio. The ferric/ferrous ratio in experimental glasses was analyzed using a wet chemical technique with colorimetric detection of ferrous iron. It is shown that at constant temperature, an increase in SiO₂, TiO₂, and P₂O₅ content results in a decrease in the ferric/ferrous ratio. The effects of TiO₂ and SiO₂ on the Fe³⁺/Fe²⁺ ratio was found to be almost identical. In contrast, adding P₂O₅ was found to decrease ferric/ferrous ratio much more effectively than adding silica. The results were compared with the predictions from the published empirical equations forecasting Fe³⁺/Fe²⁺ ratio. It was demonstrated that the effects of TiO₂ are minor but that the effects of P₂O₅ should be included in models to better describe ferric/ferrous ratio in phosphorus-bearing silicate melts. Based on our observations, the determination of the prevailing fO₂ in magmas from the Fe³⁺/Fe²⁺ ratio in natural glasses using empirical equations published so far is discussed critically.

Introduction

Iron in silicate melts is stable in two oxidation states, Fe³⁺ and Fe²⁺, with the first species prevailing at high fO₂ and the second one at low fO₂ values. The ferric/ferrous equilibrium in melts can be described by the reaction:

$$ {\text{FeO}} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 4$} {\text{ O}}_{2} = {\text{FeO}}_{ 1. 5} $$

(1)

with the reaction constant:

$$ K = a_{{{\text{FeO1}} . 5}} /\left( {a_{\text{FeO}} \cdot f{\text{O}}_{ 2}^{ 1 / 4} } \right) = \left( {X_{{{\text{FeO1}} . 5}} /X_{\text{FeO}} } \right)\cdot\left( {\gamma_{{{\text{FeO1}} . 5}} /\gamma_{\text{FeO}} } \right)/f{\text{O}}_{ 2}^{ 1 / 4} $$

(2)

where a _i and γ _i are the activities and activity coefficients, respectively, of iron oxides in silicate melts, X _i refers to the mole fraction on oxide basis, and fO₂ is the oxygen fugacity. The Eq. (2) may be further converted into

$$ {\text{log}}(X_{{{\text{FeO}}_{{1.5}} }} /X_{{{\text{FeO}}}} ) = \frac{1}{4}{\text{log}}\,f{\text{O}}_{2} + {\text{log}}\,K-{\text{log}}(\gamma _{{{\text{FeO}}_{{1.5}} }} /\gamma _{{{\text{FeO}}}} ) $$

(3)

In this equation, the coefficient (k) at logfO₂ is equal to 1/4 in an ideal case, when γ _FeO1.5/γ _FeO is approximately constant in the fO₂ range under consideration. However, small deviations of k from the ideal value have been reported and are the subject of discussion (e.g., Kress and Carmichael 1988, 1991; Jayasuriya et al. 2004; Borisov 2010).

At constant T-fO₂ conditions, log(X _FeO1.5/X _FeO) must be proportional to log(γ _FeO1.5/γ _FeO) in the silicate liquid, which reflects the compositional dependence of the ferric/ferrous ratio. In a simple case such a dependence may be approximated as a linear function of the mole fractions of the main oxide component in silicate melts (SiO₂, Al₂O₃, MgO, CaO, Na₂O, and K₂O), Σd _i X _i, where d _i and X _i are empirical coefficients and mole fractions of individual oxides in the melt, respectively. This results in empirical equations in which Fe³⁺/Fe²⁺ ratio is a function of T, fO₂, and melt composition in the form (e.g., Sack et al. 1980; Kilinc et al. 1983):

$$ \ln \left( {X_{\text{Fe2O3}} /X_{\text{FeO}} } \right) = \, k \cdot \ln f{\text{O}}_{2} + h/T \, + \Upsigma d_{\text{i}} X_{\text{i}} + c $$

(4)

where T is in K, and k, h, and c are constants. The type (4) empirical equations are important from two points of view:

• 1. For given experimental or suggested natural T-fO₂ conditions, such equations allow to recalculate Fe³⁺ and Fe²⁺ species in glasses in which only the total Fe (Fe_t) is known, typically determined with EPMA. For example, the determination of the Fe–Mg partition coefficient between olivine and melt (Roeder and Emslie 1970; Toplis 2005) requires prior calculation of the proportions Fe³⁺/Fe_t. The different size and charge of Fe³⁺ and Fe²⁺ imply that physical and chemical properties of silicate melts are affected by the Fe³⁺/Fe²⁺ ratio and also explain why the distribution of Fe³⁺ and Fe²⁺ is different in melts and coexisting crystalline phases.

• 2. The Fe³⁺/Fe²⁺ ratio, similar to some other redox pairs, may be used for the estimation of the redox conditions of magmas and of the regions of magma generation. The best example is an estimation of fO₂ of the mantle from which mid-ocean ridge basalt (MORB) was derived (Christie et al. 1986; Nikolaev et al. 1996; Bézos and Humler 2005; Cottrell and Kelley 2011, 2013). The approach is based on the determination of Fe³⁺/Fe_t ratios in MORB glasses by applying empirical equations such as Eq. (4). Christie et al. (1986) conducted wet chemical analyses of 78 hand-picked MORB glasses, applied Kilinc’s et al. (1983) equation and estimated fO₂ to be l–2 log units below the quartz–fayalite–magnetite buffer (QFM). Cottrell and Kelley (2011) analyzed 103 MORB glasses with micro-X-ray absorption near-edge structure (μ-XANES), applied Kress and Carmichael’s (1991) equation, and estimated fO₂ to be around QFM. Note that the reason for such a large discrepancy between these two fO₂ estimations is primarily due to very different average Fe³⁺/Fe_t ratios found for MORB glasses (0.07 ± 0.03 in the first case and 0.16 ± 0.01 in the second one), because of the possible presence of microcrystals in the samples analyzed by wet chemistry. However, using different equations may also affect fO₂ determination. For example, Nikolaev et al. (1996) re-estimated fO₂ in fourteen MORB glasses already analyzed by Christie et al. (1986) using their own calibration, and fO₂ was found to be higher by 0.55 log unit in average than reported in the previous paper.

In most empirical equations proposed so far to model the link between Fe³⁺/Fe²⁺ ratio and fO₂, oxides such as TiO₂, MnO, Cr₂O₃, and P₂O₅ are ignored because they “have very low concentrations in silicate liquids and are often not reported in the published data” (Sack et al. 1980, p. 373). However, the effects of such minor components on ferric/ferrous ratio may be not negligible.

Two of these minor components such as Mn and Cr occur in silicate melts in different valence states, Mn³⁺ and Mn²⁺ and Cr⁶⁺, Cr³⁺ and Cr²⁺, depending on fO₂ (e.g., Johnston 1965; Schreiber and Haskin 1976; Pretorius et al. 1992; Schreiber et al. 1996). The investigation of the effect of these oxides on ferric/ferrous ratio is not a trivial task, because of the possible exchange of electrons between redox pairs during quenching of melts into glasses (e.g., Lahiri et al. 1974; Rüssell 1989; Borisov 2013). The study of such equilibria in situ at high temperature may be an option, but is technically difficult (Berry et al. 2003). The two other minor components such as Ti and P exist only in one valence state and Ti⁴⁺ and P⁵⁺ in silicate melts at fO₂ conditions typically used in experiments on ferric/ferrous determination (from air to about QFM-2). Trivalent titanium in silicate melts is present in reasonable amount only at fO₂ below iron–wüstite (IW) buffer conditions (Johnston 1965; Schreiber et al. 1978; Borisov 2012). Phosphorus as phosphide ion (P³⁻) was found in slags under strongly reducing conditions, more than 9 orders of magnitude below IW (Momokawa and Sano 1982). Due to the lacking redox variation of Ti and P under oxidizing to intermediate conditions (up to iron–wüstite buffer), the effect of these elements on ferric/ferrous ratio in silicate melts can be studied by “classical techniques,” i.e., by analyzing quenched samples (glasses).

TiO₂ is one of the main components of lunar high-Ti basalts, which were collected in the Apollo 11 and 17 missions, with concentrations up to 15 wt % (BVSP, 1981). Terrestrial magmatic rocks are usually poor in titania, but in some cases they may contain up to 5 wt % (e.g., Pik et al. 1998). Phosphorus content in primitive mantle is estimated to be very low (86 ppm, Palme and O’Neil 2003). However, being highly incompatible, P content may increase in a melt during partial melting and fractional crystallization processes. The main P-bearing phase, apatite, has high solubility in high-temperature basaltic silicate melts (Watson 1980), and P₂O₅ content in such melts may reach a few weight percents before the saturation with apatite (up to 2 wt % P₂O₅ in Fe-rich basaltic systems, e.g., Auwera and Longhi 1994).

Even such small P₂O₅ contents may be essential in affecting iron redox ratio but, in the absence of experimental calibrations, such effects are not well constraint. Jayasuriya et al. (2004) stressed “the extraordinarily high” ability of P₂O₅ to decrease Fe³⁺/Fe²⁺. Mysen (1992) found two opposite trends in changing ferric/ferrous ratio by diluting an initial Ca silicate melt either with P₂O₅ or with Ca₃(PO₄)₂. At last, Gwinn and Hess (1993) revealed a significant increase in Fe³⁺/Fe²⁺ with the addition of P in very silicic melts with SiO₂ concentrations up to 78 wt %.

Although the effect of melt composition on the Fe³⁺/Fe²⁺ ratio is small in comparison with the effects of temperature and, especially, oxygen fugacity, it cannot be ignored. To clarify the compositional dependence of the ferric/ferrous ratio in silicate melts, investigations in rather simple systems have been conducted, e.g., Na₂O–FeO–Fe₂O₃–SiO₂ (Lange and Carmichael 1989), K₂O–FeO–Fe₂O₃–SiO₂ (Tangeman et al. 2001), and CaO–FeO–Fe₂O₃–SiO₂ (Kress and Carmichael 1989). Alternatively, natural melts may be modified by adding the components of interest. For example, Thornber et al. (1980) modified an initial diabase composition by increasing Al₂O₃ up to 28.7 wt %, CaO up to 24.3 wt %, K₂O up to 7.6 wt %, which are the concentrations well above that of typical basaltic melts. One may argue that the effect on Fe³⁺/Fe²⁺ may be different for low and high amounts of components. However, often variation over a large compositional range is required to properly resolve such effects. Following this approach, we have added up to 30 wt % TiO₂ and up to 20 wt % P₂O₅ to a haplobasaltic melt to quantify the effect of these components on the redox state of iron.

Experimental procedure

A synthetic iron-free melt of diopside–anorthite eutectic composition (DA) was chosen as the base composition for the experiments. This composition was modified by adding about 10 wt % Fe₂O₃ (total iron expressed as Fe₂O₃) and different amounts of TiO₂ or P₂O₅ to obtain two sets of melt compositions: DAFT series (DAF, DAFT10, DAFT20, and DAFT30) with a total formula of 10Fe₂O₃·xTiO₂·(90-x)DA and DAFP series (DAF, DAFP05, DAFP10, DAFP15, and DAFP20) with a total formula of 10Fe₂O₃·xP₂O₅·(90-x)DA. Some Ti-containing mixtures were additionally modified by adding silica (DAFST series: DAFS, DAFST15, and DAFST25) with a total formula of 10Fe₂O₃·xTiO₂·(90-x)·(0.5DA·0.5SiO₂). One P-containing mixture (DAFP10) was also modified by adding silica (marked as DAFSP08). In all cases, the two-digit numbers in the mixture label denote the rough amount of TiO₂ or P₂O₅ (wt %) and x in formulas refer to wt % of the respective components.

The experiments were conducted in a one-atmosphere vertical tube furnace with the loop technique (e.g., Donaldson et al. 1975). Platinum wire (0.125 mm thick and 99.9 % pure, Chempur^®) was used to prepare loops about 2 or 3 mm in diameter. Silicate powder mixed with weak polyvinyl alcohol–water solution was inserted into the loops that were then suspended on the sample holder and transferred into the furnace. The investigated temperature range was 1,400–1,550 °C. Temperatures were determined with a Pt/PtRh₁₀ thermocouple that was calibrated against the melting point of Au (1,064 °C) and expected to be accurate within ±2 °C. All experiments were conducted in air.

Two sample sizes were used in this study: 2-mm loops with average sample weight of about 14 mg for preliminary investigations of phosphorus loss from DAFP10 composition (Table 1) and 3-mm loops with average sample weight of about 30 mg for the main series of experiments (Table 2). In the last case, up to 7 samples of different composition were simultaneously placed into the furnace at a given temperature.

Table 1 Phosphorus loss from samples at oxidizing (air) and reducing (IW) conditions

Table 2 Experimental conditions, microprobe composition (wt %) of experimental glasses and ferric/ferrous ratios determined by wet chemical colorimetric analyses

In order to determine equilibration times, experimental series with different run duration were conducted with basic (DAF) and more silicic (DAFS) compositions at 1,500 °C. Although redox equilibrium was found to be reached quickly (see below), most of the experiments with Ti-containing compositions were carried out with relatively long duration (e.g., 70 h at 1,450 °C).

The loss of phosphorus from the melts even at air conditions (see below) forced us to reduce experimental duration with P-containing compositions to a minimum needed to reach equilibrium Fe³⁺/Fe²⁺ ratio. However, DAFSP08 composition was found to be very viscous in comparison with all other mixtures and thus potentially to be most problematic in reaching equilibrium. Thus, a few longer runs with DAFSP08 were performed to have a time series at 1,500 °C.

After the experiments, the samples were quenched by quickly withdrawing the sample holder from the furnace. The small weight of the loop samples (30–35 mg) guarantees fast quenching. The samples were then crushed, and at least two small glass fragments of each sample were mounted in epoxy, polished, and carbon-coated for electron microprobe analysis (EMPA).

Bulk compositions of experimental glasses were determined by EMPA using a Cameca SX100. Conditions of measurements were 15 keV accelerating voltage, 15 nA beam current, 10 s counting time, and focused beam. At least twenty points were analyzed in each glass sample, and the average composition of the run products is given in Table 2.

The ferric/ferrous ratio in experimental glasses was analyzed using a wet chemical technique, based on the colorimetric method of Wilson (1960) and modified following the procedure given by Schuessler et al. (2008). In brief, the analytical procedure is as follows: 5–7 mg of powdered sample was weighed into a 15-mL Teflon beaker containing 1 mL of an ammonium vanadate solution dissolved in sulfuric acid (5 M H₂SO₄). After the addition of 0.5–1 mL concentrated HF, the beaker was tightly sealed and left overnight at room temperature. It is assumed that V⁵⁺ in vanadate solution oxidizes Fe²⁺ as soon as it is released from the sample according to the reaction:

$$ {\text{V}}^{5 + } + {\text{ Fe}}^{2 + } = {\text{V}}^{4 + } + {\text{Fe}}^{3 + } $$

(5)

with V⁴⁺ in solution being much more resistant to oxidation when compared to Fe²⁺. After sample dissolution, 5 mL saturated boric acid solution was added to neutralize the excess HF. The content of the beaker was then quantitatively transferred into a 100-mL volumetric flask, containing 10 mL ammonium acetate solution and 5 mL 2:2′ bipyridyl solution, and the remaining volume was filled with distilled water. The ammonium acetate buffer adjusted the pH value to about 5, which brings the reaction (5) to the left and regenerates Fe²⁺ from Fe³⁺. The complex of Fe²⁺ with 2:2′ bipyridyl shows an intensive absorption band at about 523 nm. Measurements of Fe²⁺ and Fe_tot were taken with Shimadzu UV-1800 spectrometer on the same solution before and after adding 5–10 mg solid hydroxylamine hydrochloride to an aliquant of about 10 mL. This reducing agent converts all Fe³⁺ into Fe²⁺. The advantage of such modification is that uncertainties in ferric/ferrous ratios arise mainly from the spectrometric measurements, whereas weighing and dilution errors cancel out.

All experimental glasses were analyzed in three sessions (Table 2). An in-house standard PU-3 (see Schuessler et al. 2008 for details) with known Fe²⁺ and Fe_t was included in every session. The Fe³⁺/Fe²⁺ ratios were found to be 1.47 ± 0.08, 1.53 ± 0.08, and 1.52 ± 0.08, which are identical within error limits to the values 1.60 ± 0.11 (1σ for the average of 33 measurements collected over a time period of about 1 year) determined by Schuessler et al. (2008).

Results

Phosphorus evaporation from experimental samples at high temperatures

The results of the phosphorus loss from the melts of DAFP10 composition at air conditions are given in Table 1. Previous studies (Borisov, unpublished data) of phosphorus evaporation from the melts of DAP composition (DAP = Diopside–Anorthite eutectic composition + Ca₂P₂O₇) demonstrated a severe P loss at IW buffer conditions adjusted by CO/CO₂ gas mixture, and the results are also shown in Table 1. Note that the errors of P₂O₅ contents given in Table 1 are standard deviations for an average of ten measurements, typically made along a profile across the whole sample. The low values of these errors reflect relatively homogeneous phosphorus content even in samples that suffered substantial loss of phosphorus. One of the reasons of such homogeneity can be convection, which can occur in the melt droplets (Borisov 2001). In addition to T-fO₂ conditions, the sample size (surface exposed to air or gas flux) and melt composition may also affect the extent of P loss by evaporation. Considering that the compositions are rather similar (DA as a base) and that the samples have a similar weight (13.4 ± 1.5 mg for DAFP10 vs. 15.3 ± 2.3 mg for DAP samples), we will discuss them together (Fig. 1).

Fig. 1

Effect of temperature and redox conditions on P loss from experimental melts

Run duration and redox conditions are found to be most critical for P loss (Fig. 1). At 1,450 °C and IW buffer conditions, about 45 % of initial P content was lost from the sample after 15 h. At the same temperature in air conditions during similar duration, only 10 % of phosphorus was lost. The temperature of experiments is also important. For example, at air condition and similar duration of 15–17 h, a temperature increase from 1,450 to 1,500 °C results in an increase in P loss from 10 to 17 %.

The phosphorus loss at constant T-fO₂ conditions seems to be a quadratic function of the run duration τ (h). For example, at air conditions and 1,450 °C, the phosphorus content can be predicted for the applied experimental setup with following equation (R ² = 0.999):

$$ {\text{P}} /{\text{P}}_{\text{ini}} = 1-0.00728 \cdot \tau + 4.993 \cdot 10^{ - 5} \cdot\tau^{2}$$

(6)

It is emphasized that the phosphorus loss is less problematic in the experiments conducted to determine the Fe³⁺/Fe²⁺ ratio. As it was mentioned above, the samples of the main P series (compositions used for the experiments listed in Table 2) were melted on 3-mm loops and had an average weight of about 30 mg, which is roughly two times higher than that used for the experiments investigating the phosphorus loss. Thus, the phosphorus loss from these samples is smaller. For example, a ~30 mg sample DAFP10–30 (1,450 °C, 9 h, see Table 2) contains 10.5 ± 0.1 wt % P₂O₅, whereas a small sample (~15 mg) of the same initial composition melted at the same conditions would contain only 9.9 wt % P₂O₅ according to Eq. (6).

Equilibrium series for the investigation of the Fe³⁺/Fe²⁺ ratio

The results of the time series experiments with the basic DAF and more silicic DAFS compositions are shown on Fig. 2a. The Fe³⁺/Fe²⁺ ratio in samples of the same composition equilibrated for 2, 8, 14.5, and 24 h are the same within 1σ error limits, demonstrating fast achievement of equilibrium between melt and air at 1,500 °C. Additionally, the coincidence of the results in four independent experimental charges of the same composition validates the very good reproducibility of ferric/ferrous determination at least within the same analytical session. Fast equilibration of Fe³⁺/Fe²⁺ was previously found in natural melts equilibrated with air by the loop technique (e.g., <5 h at 1,350 °C, Kilinc et al. 1983).

Fig. 2

Effect of equilibration time on ferric/ferrous ratio at 1,500 °C: a in basic (DAF) and more silicic (DAFS) melts; b in melts of DAFSP08 composition

The results of the time series experiments with the most viscous DAFSP08 composition at 1,500 °C are shown on Fig. 2b. Although the Fe³⁺/Fe²⁺ ratios in samples equilibrated for 2, 4, and 8 h are identical within 1σ error limits, a small trend in increasing the ratio with run duration is evident. Note that one cannot guarantee exactly the same composition in time series because P loss even from large samples at temperature as high as 1,500 °C is not negligible. Indeed, P₂O₅ content decreases from 8.0 wt % for the shortest experiment to 7.1 wt % for longest one. We will further demonstrate that the addition of phosphorus results in an essential decrease in Fe³⁺/Fe²⁺ ratio in silicate melts. It means that P loss should raise this ratio, and slightly different phosphorus content could explain the trend observed on Fig. 2b.

The effect of TiO₂ and P₂O₅ contents on the Fe³⁺/Fe²⁺ ratio

The decrease in Fe³⁺/Fe²⁺ with TiO₂ content is evident for the three investigated temperatures both for basic DAFT and silicic DAFST series (Fig. 3). Note that the Fe³⁺/Fe²⁺ ratio is systematically lower in the more silicic than in the basic samples (data at 1,500 and 1,450 °C) independent from TiO₂ concentration. The comparison of the Ti-free samples, DAF-9 (1,500 °C) and DAFS-10 (1,450 °C) having exactly the same Fe³⁺/Fe²⁺ = 1.87 (see Table 2), indicates that increasing silica content in the melt by 20 wt % is equivalent to a temperature increase of 50 °C in affecting the ferric/ferrous ratio.

Fig. 3

Effect of TiO₂ on ferric/ferrous ratio in the experimental samples

On Fig. 4, the effect of P₂O₅ on ferric/ferrous ratio in the DAFP series is shown. The decrease in Fe³⁺/Fe²⁺ value upon P addition is intense for all investigated temperatures, about 1.6 times when comparing P-free DAF and DAFP10 (av. 10.5 wt % P₂O₅) compositions and up to 2.3 times when comparing DAF and DAFP20 (av. 19.9 % P₂O₅) compositions.

Fig. 4

Effect of P₂O₅ on ferric/ferrous ratio in the experimental samples of DAFP series

Discussion

Phosphorus evaporation from silicate melts

The phosphorus behavior is similar to that of the sodium loss from the melt at high temperatures and low fO₂ values, which is a main problem of the loop technique and which is well documented (e.g., Corrigan and Gibb 1979; Tsuchiyama et al. 1981; Sugawara 1999). Following Tsuchiyama et al. (1981), who suggested sodium evaporation as metallic species, we suggest a similar reaction for the phosphorus loss from the melt:

$${\text{PO}}_{{2.5}} \left( {{\text{melt}}} \right) = {\text{P}}\left( {{\text{gas}}} \right) + 1.25\;{\text{O}}_{2} \left( {{\text{gas}}} \right)$$

(7)

with the following equilibrium constant:

$$ K_{ 7} { = }f_{\text{P}} \cdot {f{\text O}}_{2}^{1.25} /a_{{{\text{PO2}} . 5}} $$

(8)

where f _P, fO₂, and a _PO2.5 are the fugacities of P and O₂ in a vapor phase and the activity of PO_2.5 in silicate melt, respectively. The Eq. (8) may be further converted into

$$ { \log }f_{\text{P}} = - 1.25{ \log }\;{f{\text O}}_{ 2} + { \log }a_{{{\text{PO2}} . 5}} + K_{ 7} $$

(9)

Thus, at constant temperature, P fugacity (and, therefore, P loss) will increase with decreasing fO₂ and increasing P content in a sample.

Note that the phosphorus loss at air conditions found in the present study is substantial but not as crucial as was revealed by Kilinc et al. (1983) (see their Table 3 and Fig. 1). These authors found that natural andesite melt with an initial P₂O₅ of 0.25 wt % lost all phosphorus after 70 h at 1,359 °C. More data are required to construct a complete model of P evaporation from silicate melts, similar to what Sugawara (1999) has suggested for Na loss from experimental charges.

SiO₂, TiO₂, and P₂O₅ components: efficiency of network-forming cations in decreasing the Fe³⁺/Fe²⁺ ratio.

On Fig. 5, we plotted Fe³⁺/Fe²⁺ ratio as a function of (SiO₂ + TiO₂). At constant temperature, both DAFT and DAFST compositions lie on the same regression line, implying that adding SiO₂ and TiO₂ roughly equally decreases ferric/ferrous ratio.

Fig. 5

Effect of SiO₂ + TiO₂ contents on ferric/ferrous ratio in the experimental samples

Following Sack’s et al. (1980) model, we approximated log ferric/ferrous of all experimental glasses as a linear function of the reciprocal absolute temperature and mole fractions of SiO₂, TiO₂, and P₂O₅, taking into account that only these four parameters are variable

$$ { \log }\left( {X_{{{\text{FeO1}} . 5}} /X_{\text{FeO}} } \right) = 5 9 1 9/T-0.674 \cdot X_{\text{SiO2}} - \, 0.673 \cdot X_{\text{TiO2}} -4.377 \cdot X_{\text{P2O5}} -2.734 $$

(10)

The high value of R ² = 0.988 shows that Eq. (10) is successful to model to the experimental dataset with a good accuracy. The temperature slope 5,919 ± 223 (1σ) is in reasonable agreement with values for natural melts following the empirical equations of Sack et al. (1980) and Kilinc et al. (1983): 5,730 ± 420 and 5,500 ± 390, respectively. However, it is emphasized that the temperature effect is investigated over a range of 150 °C only.

The values of the coefficients d _SiO2 = −0.674 ± 0.037 (1σ) and d_TiO2 = −0.673 ± 0.044 are identical within error. This implies that adding SiO₂ and TiO₂ to a melt is equally effective (on a molar basis) in decreasing Fe³⁺/Fe²⁺ ratio. On the other hand, the value of the coefficient d _P2O5 of −4.377 ± 0.113 (1σ) is much lower than that of d _SiO2 or d _TiO2. This implies that adding P₂O₅ to a melt is much more efficient in decreasing Fe³⁺/Fe²⁺ ratio than adding silica or titania.

The form of Eq. (10) implies that the relative effect of any two components on the Fe³⁺/Fe²⁺ ratio is given by the difference in those empirical coefficients, d_i. Indeed, from Eq. (10), it can be deduced that Δlog(X _FeO1.5/X _FeO) at exchanging 10 mol  % SiO₂ in a melt by 10 mol  % P₂O₅ is equal to (d _P2O5–d _SiO2)/10 = −0.37. Such an effect is equivalent to a decrease in oxygen fugacity by approximately 1.5 log unit, assuming a slope of log (X _FeO1.5/X _FeO) versus logfO₂ to have an ideal value of 0.25.

Thus, the present finding ranks the efficiency of network-forming oxides to decrease the ferric/ferrous ratio in CaO–MgO–FeO–Fe₂O₃–SiO₂–TiO₂–P₂O₅ melts in the following order: P₂O₅ ≫ TiO₂ ≈ SiO₂.

A comparison with the published data

Experiments with TiO₂-bearing compositions

Matsuzaki and Ito (1997) conducted experiments in ternary FeO–TiO₂–SiO₂ melts, resembling slag compositions, with TiO₂/SiO₂ (wt) varying from 0.5 to 2. These experiments were carried out in equilibrium with metallic iron and fO₂ was buffered with H₂/CO₂ gas mixtures. The authors used own data obtained at 1,400 °C along with the similar data of Ban-ya et al. (1980) in FeO–TiO₂ and FeO–SiO₂ binaries to plot Fe³⁺/Fe²⁺ versus X_TiO2 + X_SiO2 (Fig. 2 in Matsuzaki and Ito 1997). We additionally recalculated Fe³⁺/Fe²⁺ ratio in these slags to a constant oxygen fugacity of 10⁻¹⁰ atm (an ideal slope k = 0.25 of log Fe³⁺/Fe²⁺ vs. logfO₂ was assumed) in attempt to minimize the data scattering. The results are shown on Fig. 6. The scattering is still large and reflects perhaps problems in the accuracy of the Fe³⁺/Fe²⁺ determination at these extremely low fO₂ conditions where ferric content in the slags is very small. Nevertheless, the trend is evident: there is a decrease in the ferric/ferrous ratio with increasing SiO₂ + TiO₂ with approximately equal effects of SiO₂ and TiO₂.

Fig. 6

Effect of SiO₂ + TiO₂ contents on ferric/ferrous ratio in simple slags in equilibrium with metallic iron at 1,400 °C. Experimental data from Ban-ya et al. (1980) and Matsuzaki and Ito (1997) recalculated to a constant fO₂ = 10⁻¹⁰ atm

Alberto et al. (1992) studied redox equilibria in more complex CaO–TiO₂–SiO₂ melts modified either with 5 or 15 wt % Fe₂O₃ total at 1,500 °C in air. Experimental data were not tabulated but plotted as Fe³⁺/ΣFe versus Ti/(Ti + Si) (Fig. 2 in Alberto et al. 1992). For the same Fe₂O₃ total, the most polymerized melts (more silicic, NBO/T = 1.2, X _SiO2 + X _TiO2 ≈ 0.63 in iron-free matrix) display much lower Fe³⁺/ΣFe ratio than less polymerized melts (more basic, NBO/T = 2, X _SiO2 + X _TiO2 ≈ 0.51 in iron-free matrix), similar to our results obtained with the DAFST and DAFT series. The exchange of Si by Ti is either negligible in terms of Fe³⁺/Fe²⁺ (series MIN(I-VI)F5) or results in a slight oxidation of iron (e.g., series CS(VII-XV)F5, see Fig. 2 in Alberto et al. 1992).

Summarizing, increasing both SiO₂ and TiO₂ results in a decrease in the Fe³⁺/Fe²⁺ ratio in simple slags and complex silicate melts, with TiO₂ tending to be either equally (like in present experiments) or slightly less effective in comparison with SiO₂. This observation is in agreement with structural studies indicating that at least part of the Ti incorporated in silicate melts is in fourfold coordination as Si (e.g., Dingwell et al. 1994; Farges et al. 1996; Henderson et al. 2002). However, part of the Ti may also be five- and sixfold coordinated.

Experiments with P₂O₅-bearing compositions

Toplis et al. (1994) investigated the effects of phosphorus on Fe³⁺/Fe²⁺ ratio in synthetic ferro-basaltic compositions. They revealed, for example, that at air conditions and fixed temperature of 1,446 and 1,545 °C, the ferric/ferrous ratio decreases by a factor of 1.3 as a result of the addition of 9.5 wt % P₂O₅ (4.4 mol  %) to the initial P-free composition (see Table 2 and Fig. 1 in Toplis et al. 1994). This decrease is very similar to that observed in the present study. Note that Toplis et al. (1994) were the first who concluded that the incorporation of a P₂O₅ term is necessary in empirical equations to calculate Fe³⁺/Fe²⁺.

Large effects of P₂O₅ on ferric/ferrous ratio, much more pronounced when compared with SiO₂, may also be extracted from the experimental data of Turkdogan and Bills (1957 ) in FeO_t–SiO₂–P₂O₅ melts at 1,550 °C. The authors report the CO/CO₂ ratio in the buffering gas mixture [Table 1 in Turkdogan and Bills (1957)], which we converted into fO₂ values using the thermodynamic data of Deines et al. (1974). The Fe³⁺/Fe²⁺ ratios in these slags (49 experiments in total) were then described as a function of logfO₂, X _SiO2, and X _P2O5 to obtain the following equation:

$$ { \log }\left( {X_{{{\text{FeO1}} . 5}} /X_{\text{FeO}} } \right) = { 0} . 2 0\cdot \text{l} {\text{og}}f{\text{O}}_{2} - \, 0.963 \cdot X_{\text{SiO2}} -3.105 \cdot X_{\text{P2O5}} + 0.641 $$

(11)

The parameter k = 0.20 ± 0.01 at logfO₂ is reasonably close to the ideal value of 0.25, which, together with the high correlation coefficient (R ² = 0.95), demonstrates the high quality of the experiments and the appropriate form of Eq. (11). Thus, one can compare the efficiency of SiO₂ and P₂O₅ in these slags in changing ferric/ferrous ratio. The substitution of 10 mol  % SiO₂ by the same amount of P₂O₅ lowers the log(X _FeO1.5/X _FeO) by a value of 0.21, which is equivalent to a decrease in the oxygen fugacity of ca. 0.9 log unit.

Jayasuriya et al. (2004) were the first who included phosphorus in the empirical equation proposed by Sack et al. (1980). They fitted ln(X _Fe2O3/X _FeO) versus ln fO₂, 1/T and mole fraction of oxides, including X _P2O5 (Eq. 12 in Jayasuriya et al. 2004). Converting ln (X _Fe2O3/X _FeO) into log(X_FeO1.5/X_FeO) for a correct comparison of their results with our Eqs. (10) and (11) would lead to a value of d _P2O5 = −27.3 (error was not given) and d _SiO2 = 0 (silica was not included in the fitting). Here, Δlog (X _FeO1.5/X _FeO) after exchanging 10 mol  % SiO₂ by 10 mol  % P₂O₅ is equal to −2.73 corresponding to an extremely high fO₂ decrease by about 11 log unit, which seems unrealistic. The conclusion that the effect of phosphorus on Fe³⁺/Fe²⁺ ratio may be much less than suggested by Jayasuriya et al. (2004) is also confirmed by the comparison of two experimental series (PW and P series) made at 1,500 °C in air by Mysen (1992). In both cases, the author used a composition close to 44CaO·56SiO₂ (wt %) as a base modified with 5 wt % Fe₂O₃. In the P series, P₂O₅ was added to the base composition and a moderate decrease in ferric/ferrous ratio was observed. In the PW series, however, phosphorus was added as Ca₃(PO₄)₂ and this resulted in increase in ferric/ferrous ratio (see Fig. 8 in Mysen 1992). The addition of CaO to a melt in the SiO₂–CaO–FeO_t system is known to increase Fe³⁺/Fe²⁺ ratio (Kress and Carmichael 1989). Thus, the addition of three moles CaO for one mole P₂O₅ (Ca₃(PO₄)₂ = 3CaO·P₂O₅) largely compensates the possible decrease in ferric/ferrous induced by the addition of phosphorus.

In summary, the results in this study and the most published data suggest a significant decrease in ferric/ferrous ratio with increasing of P₂O₅ content. It is worth noting however that our most SiO₂-rich composition DAFSP09, being recalculated on P-free base, contains only about 55 wt % SiO₂. The synthetic ferro-basalt used by Toplis et al. (1994) contains about 51 % SiO₂. Mysen’s (1992) initial composition has about 53 % SiO₂. Finally, the SiO₂ contents of the P-containing slags of Turkdogan and Bills (1957), even after recalculation on P-free base, do not exceed 47 wt %. Thus, on the basis of the available data, a stabilizing effect of P₂O₅ on ferrous iron can be inferred only for the basic to intermediate melts. However, it is emphasized that the data from Gwinn and Hess (1993) indicate that the effect of P₂O₅ on Fe³⁺/Fe²⁺ may be the opposite in very silicic melts (>70 wt % SiO₂, Fig. 7). Although there is a large data scatter for the K-rich compositions, the P-bearing liquids have systematically higher Fe³⁺/Fe²⁺ ratios than P-free melts, independently on the K/Al ratio (peraluminous or peralkaline). Note that the addition of only 0.5 mol  % P₂O₅ at fixed K/Al ratio and SiO₂ content may increase the ferric/ferrous in a melt by a factor of 2–3. The contrasting behavior of phosphorus in very silicic and more basic melts was also noted by Ryerson (1985) who calculated SiO₂ activity coefficients (γSiO₂) in binary and ternary melts. Ryerson (1985) showed that adding P₂O₅ to SiO₂ results in a decrease in γSiO₂, even more pronounced than adding K₂O or Na₂O. In forsterite/clinoenstatite or crystoballite/clinoenstatite saturated melts, the addition of P₂O₅ results in an increase in γSiO₂.

Fig. 7

Effects of K/Al ratio on Fe³⁺/Fe²⁺ in P-free, P-poor, and P-rich silicic melts at 1,400 °C in air. Experimental data from Gwinn and Hess (1993). We present three series of experiments with zero, 0.5 mol % (1.6 wt %), and 2.6 mol % (5.4 wt %) P₂O₅ (data from Tables 1, 3a, b in Gwinn and Hess 1993). All melts have approximately the same SiO₂ content (about 76 wt % ≈85 mol %) and total Fe₂O₃ (1 mol %) but with variable K/Al ratio

A detailed discussion of the structure of P-bearing aluminosilicate melts is out of the scope of this study, especially because structural information on the Fe-bearing compositions studied here is not available. However, the contrasting effects of P₂O₅ on the Fe³⁺/Fe²⁺ ratio in basic and felsic melts are most probably related to structural changes. Based on the experimental studies of phase relationships and applying the concepts of Korzhinskii (1959) relating mineral stability fields and melt properties, Kushiro (1975) proposed that P⁵⁺ could be a network former in basaltic and intermediate melts. However, more recent studies in basic to intermediate compositions emphasized the crucial role of alkalis in alkali-rich aluminosilicate melts in forming phosphate complexes (Toplis and Dingwell 1996; Mysen and Cody 2001). It is possible that phosphate complexes may also form with alkaline-earth elements, which would apply for the compositions investigated in this study. In contrast, in more silicic compositions, part of the phosphorus can enter the network as P⁵⁺ charge compensated by Al³⁺ and Fe³⁺ (Gwinn and Hess 1993; Toplis and Dingwell 1996).

Empirical equations including Ti and P components

As mentioned in the introduction, most of the equations developed to predict Fe³⁺/Fe²⁺ as a function of oxygen fugacity, temperature, and melt composition ignore TiO₂ and P₂O₅. However, a few exceptions are known. Borisov and Shapkin (1990) and Moretti (2005) included titanium oxide as a component in their equations and we compare the predictions of their models with our DAFT series at 1,450 °C in air on Fig. 8a. Jayasuriya et al. (2004; Eq. 12) and Moretti (2005) included phosphorus oxide as a component in their equations, and we compare the predictions of their models with our DAFP series at the same conditions on Fig. 8b. In both cases, calculations with Kress and Carmichael’s (1991) model, where TiO₂ and P₂O₅ are not considered, are also shown. Note that the equations under discussion were calibrated on the experiments carried out mostly with natural compositions. And the differences with our experimental results obtained with model melts can be expected, but the predicted trends of Fe³⁺/Fe²⁺ versus TiO₂ or versus P₂O₅ contents may be informative.

Fig. 8

Effects of “minor” components on Fe³⁺/Fe²⁺ in melts of 10Fe₂O₃·90DA composition modified either with TiO₂ (a) or P₂O₅ (b) at 1,450 °C in air. A comparison of experimental results and calculation according to the published models: Moretti (2005), Kress and Carmichael (1991), Borisov and Shapkin (1990), Jayasuriya et al. (2004)

The contrasting results of Borisov and Shapkin (1990) and Moretti (2005) shown in Fig. 8a are related to the different approaches that have been used in the models. The empirical equation of Borisov and Shapkin (1990) has a form suggested by Sack et al. (1980) but with some additional complexity, the coefficients d _i and X _i are assumed to be T-fO₂-dependent. The TiO₂ was included in the regression along with other main components and no special assumption was made. The approach of Moretti (2005) follows that suggested earlier by Ottonello et al. (2001) and is based on the concept of “thermochemical models.” These models, in addition to other important assumptions, are based on the Temkin (1945) approach, subdividing the melt structure in anion and cation sublattices. Thus, either a network-forming or network-modifying behavior should be assumed a priory for every melt component. Moretti (2005), following Ottonello et al. (2001), treated Ti⁴⁺ as a network modifier.

The trend predicted by Borisov and Shapkin (1990) shows decreasing Fe³⁺/Fe²⁺ similar to the experimental data, but clearly overestimates the effect of TiO₂ (see Fig. 8a). The reason is that at these conditions (1,450 °C, air), d_TiO2 in the equation of Borisov and Shapkin (1990) is about 2.6 times higher than d_SiO2 (−6.3 and −2.4, respectively). Note that at lower temperature, the difference between d _TiO2 and d _SiO2 becomes lower, at 1,330 °C, they are approximately equal, and at even lower temperatures, SiO₂ is assumed to be more effective than TiO₂ in decreasing the ferric/ferrous ratio. The trend predicted by Moretti (2005) is opposite to that of the experimental results. Surprisingly, the best fit between experiments and calculations is found in Kress and Carmichael’s (1991) model, which simply ignores TiO₂ as a component affecting Fe³⁺/Fe²⁺ ratio. The explanation is that the small decrease in ferric/ferrous ratio with increasing TiO₂ content expected by this model is simply due to a dilution effect. The equation of Kress and Carmichael (1991) includes Al₂O₃, FeO_t, CaO, Na₂O, and K₂O as components affecting Fe³⁺/Fe²⁺. The alkali oxides are absent in the present melts and X _FeO is approximately constant since total Fe₂O₃ was fixed on the level of 10 wt %. Thus, the higher the TiO₂ content, the smaller X _Al2O3 and X _CaO in model melts are expected to be. Because d _Al2O3 = −2.243 and d _CaO = 3.201, the Fe³⁺/Fe²⁺ ratio in any melt with X _CaO > X _Al2O3 (like in present case) is expected to decrease with increasing concentration of additional components not included in the regression. Note that for a hypothetical melt with X _Al2O3/X _CaO > |d _CaO/d _Al2O3| ≈ 1.427, the effect would be the opposite. In any case, for typical basaltic melts, ignoring TiO₂ seems to be the best approach.

However, this simplification is not recommended in case of P-containing melts (see Fig. 8b). The simple “dilution” effect resulting from the application of the model of Kress and Carmichael (1991) would not predict accurately the decrease in ferric/ferrous ratio with increasing P₂O₅ content. As observed for TiO₂, the trend predicted by Moretti (2005) is opposite to that observed in the experimental results. The model of Jayasuriya et al. (2004) predicts a decrease in the ferric/ferrous, but dramatically overestimates the effect of phosphorus.

On Fig. 9, we plotted TiO₂ and P₂O₅ contents in experimental glasses of three largest datasets of natural P-containing melts, which were used by Jayasuriya et al. (2004) to constrain their equation. One can note that the P-rich melts also contain large amounts of Ti. However, Jayasuriya et al. (2004) ignored titanium, following the usual practice of previous researchers, Since adding TiO₂ was demonstrated to decrease Fe³⁺/Fe²⁺ ratio (see above), the apparent effect of P₂O₅ on ferric/ferrous ratio found by Jayasuriya et al. (2004) is most probably overestimated because it also include the effects of TiO₂.

Fig. 9

TiO₂ versus P₂O₅ content in three largest datasets from experiments with natural melts: Sack et al. (1980), Kilinc et al. (1983) and Kress and Carmichael (1988)

Implications for fO₂ determinations of MORBs

As already mentioned in the introduction, the Fe³⁺/Fe²⁺ ratio measured in natural glasses may be used for the estimation of the redox conditions of magmas. This implies (1) an accurate determination of ferric/ferrous determination in glasses and (2) the choice of correct parameters for Eq. (4). The discussion below demonstrates that there is still a large uncertainty on the values of fO₂ deduced from the interpretation of Fe³⁺/Fe²⁺ ratio in natural glasses to constrain the fO₂ prevailing in natural systems.

Accuracy of the determination of Fe³⁺/Fe²⁺ ratio in natural glasses

A comprehensive review of possible wet chemical techniques and sources of error in ferric/ferrous determination is given by Bézos and Humler (2005). In most cases, if experimental glasses are free of crystalline phase and Fe²⁺ is determined with wet chemistry (and total iron with EPMA), the Fe³⁺/Fe²⁺ ratio is considered to have an uncertainty of about 6 % (Sack et al. 1980), which propagates to a logfO₂ uncertainty of about ±0.15. In the case of natural MORBs, however, variable amounts of plagioclase microphenocrysts or microlites in glasses may be a problem (Bézos and Humler 2005; Cottrell and Kelley 2011). Thus, choosing local techniques of ferric/ferrous determination are getting mandatory for natural samples. For example, XANES measurements may give a precision on Fe³⁺/Fe_t determination of ±0.005 (about 3 %, Cottrell and Kelley 2011), which propagates to logfO₂ precision of about ±0.07.

Role of compositional parameters and temperature in empirical equation

Most equations proposed in the literature reproduce the fO₂ of experimental dataset obtained at 1 bar with a standard error of about 0.26 log units or higher (e.g., Kress and Carmichael 1988). However, natural glasses are quench products of high-pressure melts with a pre-eruptive temperature, which is usually poorly constrained, and the absolute errors in fO₂ determination are expected to be higher.

To test the accuracy of the models for predicting fO₂ from natural glasses, Eq. (4) can be formulated as follows:

$$ \text{log} f{\text O}_{2} = \, H/T + { \log }\;(X_{\text{Fe2O3}} /X_{\text{FeO}} )/k \, -\Upsigma d_{\text{i}} X_{\text{i}} /\left( {k\cdot\ln 10} \right)-c/\left( {k\cdot\ln 10} \right) $$

(12)

where H = −h/(k·ln10). For most empirical equations, H values are rather similar (e.g., −26,251 in Sack et al. 1980, −25,183 in Kilinc et al. 1983, and −27,422 in Jayasuriya et al. 2004) and also very close to the slope of the QFM buffer in the logfO₂ versus 1/T diagram (e.g., −24,442 for the calibration of Myers and Eugster 1983). Thus, by fixing arbitrary one temperature in Eq. (12) (e.g., of 1,200 °C for basaltic systems), the fO₂ of various samples relative to the QFM buffer can be estimated and compared, even when the real pre-eruptive temperatures are not known accurately (e.g., Christie et al. 1986; Bézos and Humler 2005; Cottrell and Kelley 2011). Clearly, in this case, the compositional parameter Σd _i X _i is getting especially important.

On Fig. 10 for the same set of rocks, we compare Σd _i X _i/(k·ln10) (these values are in logfO₂ units, see Eq. 12) calculated with two different models, Kilinc et al. (1983) and Kress and Carmichael (1991). A set of 103 MORB glasses analyzed by Cottrell and Kelley (2011) was chosen as an example. Although the glasses have a moderate variation in composition (they are all basalts), there is nearly no correlation between the two models. It implies that conclusions drawn from a fO₂ variation observed for a given dataset with one model will not necessarily be confirmed with another one. For example, two arbitrary samples (a and b) are marked on Fig. 10. Let us assume them to have the same ferric/ferrous ratio. If the fO₂ of these samples is calculated with Kress and Carmichael’s (1991) model, the sample b would be ~0.2 log unit more reduced than sample a. On the other hand, Kilinc’s et al. (1983) model would indicate that ample b is ~0.4 log unit more oxidized than sample a.

Fig. 10

A comparison of Σd _i X _i/(k·ln10) values calculated with two different models, Kilinc et al. (1983) and Kress and Carmichael (1991), for 103 MORB glasses analyzed by Cottrell and Kelley (2011). Note that Σd _i X _i/(k·ln10) values are in logfO₂ units. Two samples a and b are chosen arbitrary to discuss the models’ difference (see text for details)

Additional problems may arise by ignoring minor components in the empirical equation. On Fig. 11a, we plotted the difference between fO₂ calculated without taking TiO₂ or P₂O₅ and fO₂ calculated considering the role of TiO₂ or P₂O₅. As mentioned above, the effect of TiO₂ is not significant, but the effect of P₂O₅ is more pronounced. The phosphorus variation in the range typical for MORB (0.05–0.25 wt % P₂O₅, Konzett and Frost 2009 ) is equivalent to 0.7 % variation in Fe³⁺/Fe_t, which is below the precision of the Fe³⁺/Fe_t determination in glasses. However, P₂O₅ variation of 2 wt % as observed for other basalts will be equivalent to about 7 % variation in Fe³⁺/Fe_t, which would propagate to an error of 0.16 logfO₂.

Fig. 11

Possible errors of fO₂ determination, a if TiO₂ or P₂O₅ is ignored, b if temperature slope differs from QFM buffer

Other minor problems in fO₂ recalculation may arise if the pre-eruptive temperature of basaltic glasses differs from conventional 1,200 °C and if the temperature slope H of these glasses differs from QFM slope (Fig. 11b). As mentioned above, H value estimated by Kilinc et al. (1983) has only a minimal deviation from the QFM buffer slope and the resulting fO₂ errors will not exceed 0.02 log unit when the difference between conventional 1,200 °C and real temperature does not exceed 50 °C (see Fig. 11b). Other equations show slightly higher but comparable errors. However, all these equations are statistically derived and a similar temperature slope for all compositions is assumed a priory. This is not the necessary case, and identical values for H for all melt compositions would be surprising. For example, Sato and Wright (1966) directly measured fO₂ in a few boreholes drilled in tholeiitic basalts through the crust of Makaopuhi lava lake, Kilauea Volcano, Hawaii. They found that logfO₂ changes linearly with the reciprocal absolute temperature, with slopes varying from −18,600 to −21,900. Assuming that measured fO₂ values reflect fO₂ of cooling basalt, the corresponding H slope is 11–31 % lower than that of QFM buffer. On the other hand, a slope of −41,327 can be calculated for a phonotephritic composition from the data given by Moore et al. (1995, composition MAS-49), which is about 70 % higher than that of the QFM buffer. More examples and the detailed discussion on the effect of temperature on the Fe³⁺/Fe²⁺ ratio in model and natural melts can be found in Borisov and McCammon (2010).

Figure 11b shows to which extent the calculated fO₂ may change as a function of temperature if the H value differs from that of QFM by +30 % and −30 % (−31,775 and −17,109). A difference of 50 °C between conventional 1,200 °C and real pre-eruptive temperature results in fO₂ error of about 0.17 log units.

Conclusions

• 1. At constant temperature, the increase in TiO₂ or P₂O₅ content in synthetic DA-Fe₂O₃-TiO₂/P₂O₅ ± SiO₂ compositions (DA represents the eutectic of the system Diopside-Anorthite) results in a decrease in the ferric/ferrous ratio both in basic and silicic melts. The effects of TiO₂ and SiO₂ on Fe³⁺/Fe²⁺ are mostly identical. In contrast, adding P₂O₅ was found to decrease ferric/ferrous much more effectively than adding silica. Thus, the efficiency of network-forming oxides to decrease the ferric/ferrous ratio may be ranked in the following order: P₂O₅ ≫ TiO₂ ≈ SiO₂.

• 2. A comparison of our results with the predictions from the published empirical equations demonstrates that the effects of TiO₂ are minor and that the formulation of Kress and Carmichael (1991) is sufficient to account (indirectly) for the role of TiO₂ on Fe³⁺/Fe²⁺ ratio in terrestrial basaltic melts. In contrast, the effects of P₂O₅ should be taken into account in new formulations to better describe its role on the ferric/ferrous ratio in natural basaltic melts.

• 3. An average ΔQFM value for MORB compositions may be estimated with reasonably good accuracy (ca. 0.3 log unit) if the ferric/ferrous ratio in glasses is determined with an uncertainty of ±3 % relative. The concentration of P₂O₅ is low and will not affect significantly the fO₂ estimations. However, our present knowledge and published empirical equations do not allow us to account correctly for the effect of compositional changes on fO₂ determination.