Journal of Petrology | Volume 43 | Number 6 | Pages 1049-1087 | 2002
© Oxford University Press 2002
The Sulfide Capacity and the Sulfur Content at Sulfide Saturation of Silicate Melts at 1400°C and 1 bar
HUGH ST. C. O’NEILL1,* and
JOHN A. MAVROGENES1,2
1RESEARCH SCHOOL OF EARTH SCIENCES, AUSTRALIAN NATIONAL UNIVERSITY, CANBERRA, ACT 0200, AUSTRALIA
2DEPARTMENT OF GEOLOGY, AUSTRALIAN NATIONAL UNIVERSITY, CANBERRA, ACT 0200, AUSTRALIA
Received
August 15, 2001;
Revised typescript accepted
January 9, 2002
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ABSTRACT
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The solubility of sulfur as S
2– has been experimentally
determined for 19 silicate melt compositions in the system CaO–MgO–Al
2O
3–SiO
2(CMAS)
± TiO
2 ± FeO, at 1400°C and 1 bar, using CO–CO
2–SO
2 gas mixtures to vary oxygen fugacity (fO
2) and sulfur fugacity
(fS
2). For all compositions, the S solubility is confirmed to
be proportional to (fS
2/fO
2)
1/2, allowing the definition of
the sulfide capacity (C
S) of a silicate melt as C
S = [S](fO
2/fS
2)
1/2.
Additional experiments covering over 150 melt compositions,
including some with Na and K, were then used to determine C
S as a function of melt composition at 1400°C. The results
were fitted to the equation
, where A
Fe >>
A
Ca > A
Mg,A
Na/K,A
Ti. The FeO content of natural basalts is
the dominant control on C
S. The equation for C
S was then combined
with the equation for the thermodynamic equilibrium between
silicate melt and immiscible FeS-rich sulfide melt, to develop
an expression for the sulfur content at sulfide saturation (SCSS)
of the silicate melt. The value of SCSS is independent of fO
2 and fS
2, but shows an asymmetric U-shaped dependence on the
FeO content of the silicate melt. Many of the experiments on
Fe-containing melt compositions were saturated with immiscible
FeS melt, and these experiments were used to calibrate quantitatively
SCSS at 1400°C as a function of melt composition.
KEY WORDS: sulfur; sulfide capacity; silicate melts; thermodynamics
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INTRODUCTION
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Quantitative knowledge of the solubility of sulfur in silicate
melts is fundamental to an understanding of many geological
processes, such as: the origin of magmatic sulfide ores; sulfur
degassing from volcanic eruptions and hence global climate change;
the geochemical behaviour of the chalcophile trace elements,
including the platinum group elements and the Re–Os isotopic
system, and their use as tracers of core–mantle and crust–mantle
differentiation in the Earth. The solubility of sulfur in silicate
slags is also an important topic in extractive metallurgy, and
has been much studied in this context, both theoretically and
experimentally. In a classic paper, Fincham & Richardson
(1954)
proposed that at low
fO
2 [more reducing than that defined
by the quartz–fayalite–magnetite equilibrium (QFM)],
sulfur dissolves in silicate melts as S
2-, and does so by replacing
O
2- on the anion sublattice:
Because the number of O atoms in silicate melts greatly exceeds the number of other potential anions including S2-, the concentration of O2- is assumed to be constant. Reaction (1) therefore suggests the relationship
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where [S] is the sulfide content of the melt (conveniently, in parts per million), and CS is the ‘sulfide capacity’ of the melt, which may be thought of as analogous to an equilibrium constant for reaction (1). CS is therefore a function of temperature (T) and pressure (P), and also of melt composition. Fincham & Richardson (1954) experimentally verified this relationship for silicate melts in the system CaO–Al2O3–SiO2 by holding slag compositions constant while varying fO2 and fS2 independently at atmospheric pressure. So influential was this study that subsequent experimental studies reported in the metallurgical literature, aimed at expanding the range of silicate slag compositions studied, have usually assumed the universality of the Fincham–Richardson relationship, rather than actually testing it. The experimental studies in the metallurgical literature have been reviewed comprehensively by Young et al. (1992) to c. 1990, but the field is still active, and more recent work has been reported by Seo & Kim (1999). These references show that all the silicate slag compositions studied by the metallurgists are far removed from natural silicate melt compositions, and it is not clear to what extent the metallurgical results can be applied to geologically relevant compositions.
Obviously CS only has meaning if the concentration of sulfur (as S2-) in a silicate melt is proportional to (fS2/fO2)0·5 as postulated by Fincham & Richardson (1954). Although this relationship has been confirmed for a Hawaiian tholeiite composition by Katsura & Nagashima (1974) as a function of fO2, and for a komatiitic composition by Shima & Naldrett (1975) as a function of fS2, other studies (Haughton et al., 1974; Buchanan & Nolan, 1979; Buchanan et al., 1983) have shown deviations from the relationship. If real, these deviations require reanalysis of sulfide solubility theory as developed by the metallurgists. In fact, an attempt to account for S solubilities over a wide range of melt compositions including geologically relevant compositions has led to the development of a complicated theoretical model that is not based on the Fincham–Richardson relation (Poulson & Ohmoto, 1990). By contrast, Li & Naldrett (1993) considered only geologically relevant compositions and concluded that the solubility of S2- in these melts depended only on the activity of their FeO component.
We have experimentally studied sulfur solubilities in silicate melts under controlled fO2 and fS2, first to test the (fS2/fO2)0·5 relationship over a wide range of silicate melt compositions, and hence, if the relationship is confirmed, to determine the compositional dependence of CS. We then use these data to develop a model to describe the sulfur content at sulfide saturation (SCSS) of silicate melts as a function of composition.
We have used the ‘wire loop’ technique, in which a small amount (
50 mg) of silicate melt is held on a loop of metal wire or ribbon by surface tension, and suspended in a gas mixing furnace, with fO2 and fS2 controlled using CO2, CO and SO2 as input gases. The experiments reported here have been undertaken at the relatively high T of 1400°C, to access a wide range of silicate melt compositions. Although even higher temperatures would have permitted the investigation of more MgO-rich compositions, such compositions typically cannot be quenched to glasses, causing potential analytical difficulties. Future work will address the important question of the temperature dependence of the sulfide capacity, and will also extend the study to oxidizing conditions where S dissolves in silicate melts as sulfate (SO42-) rather than sulfide (S2-). Previously published work (Mavrogenes & O’Neill, 1999) reported the effect of pressure on SCSS.
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EXPERIMENTAL METHODS
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Experimental procedures
Starting compositions were prepared from dried oxides and carbonates,
mixed under acetone and then sintered at 1100°C. Small amounts
of these mixes were made into a slurry using polyethylene oxide.
The slurries were mounted on wire loops, and converted into
glass beads by lowering into a furnace at
1400°C. The resulting
beads were typically about 3 mm in diameter. Several of these
wire loops plus beads could be hung in the furnace in a single
experiment, by suspending the loops from a ring made of 0·5
mm Pt–Rh wire; typically, six or seven loops were used
in most experiments.
Pt wire was used for mounting the Fe-free compositions. A few early experiments on Fe-bearing compositions mounted on Pt resulted in massive Fe loss to the Pt, as expected given the low fO2 used in this study (e.g. Sugawara, 1999). The Fe-loss problem was solved by using Re ribbon (99·9% pure), which is commercially available as filament material for thermal ionization mass spectrometry. Fe loss to Re is almost negligible (Borisov & Jones, 1999), even when an immiscible FeS-rich sulfide melt develops during the experiment. The FeS melts seem to wet the Re ribbon, and are invariably found in the quenched run products as layers between Re ribbon and the silicate glass; but despite this intimate contact between Re and FeS, the observed solubility of Re in FeS is small (generally <0·2 wt %).
We also report a few experiments on Fe20–Ir80 alloy loops. These work fairly well, but are inconvenient in that the FeO content of the silicate melt in equilibrium with an alloy of given composition is fixed by fO2. A different alloy composition is thus needed for each combination of FeO content and fO2. Making Fe–Ir alloys and loops is an arduous business, so this approach was abandoned in favour of Re loops.
Experiments were performed in a vertical muffle tube furnace equipped for gas mixing. Both fO2 and fS2 were controlled independently using CO2–CO–SO2 gas mixtures, supplied to the furnace in accurately measured flow rates using Tylan F2800 mass flow controllers. Two controllers were available for each gas, with ranges 10 and 200 SCCM (standard cubic centimetres per minute) for CO and CO2, and 10 and 100 SCCM for SO2. The availability of two mass-flow controllers allows accurate control of gas mixtures to fairly extreme mixing ratios. The direction of flow was in at the bottom of the furnace and out at the top, as is conventional for this type of experiment (see Darken & Gurry, 1946). Values of fO2 and fS2 from the gas mixes were calculated using thermodynamic data for gas species in the NIST-JANAF tables (Chase, 1998), by free energy minimization. For this calculation, we considered the species CO, CO2, COS, SO2, SO3, S, S2, S3, S4, S6, S8, CS, CS2, and O2, although only CO, CO2, COS, and S2 are calculated to be present in significant amounts at equilibrium for the mixtures used here. We checked our calculation routine against similar calculations reported in the studies of Haughton et al. (1974) and Buchanan & Nolan (1979). There is complete agreement between our calculations and those of the earlier studies.
Samples were introduced into the furnace at 600°C, which is a low enough T that they do not stick to each other or to the muffle tube if they happen to touch. The CO and CO2 gases appropriate to the final gas mixture were then switched on, and the furnace was heated at 6°C/min to 1400°C. The SO2 gas was added to the mixture when this T was reached.
We found that the performance of yttria-doped zirconia oxygen sensors (SIRO2) degraded rapidly in an S2-rich atmosphere at 1400°C. Consequently, oxygen sensors were employed only at intervals during this experimental campaign, as additional checks on the performance of the CO and CO2 mass flow controllers. These tests were carried out at 1200°C. Sensors were not used during the actual experiments employing S-bearing gases.
At the end of the run, samples were quenched by dropping into water. They were mounted in epoxy and polished for analysis by electron microprobe.
Electron microprobe analysis
Each individual glass was analysed by combined wavelength- and energy-dispersive spectrometry (WDS and EDS, respectively) on the Cameca Camebax electron microprobe (EMP) at the Research School of Earth Sciences, ANU. Four separate EDS analyses provided a mean (and standard deviation) for each glass, which was used to calculate a ZAF correction coefficient. At 15 kV, each spectrum contained >600 000 counts.
WDS analyses for S were performed at 25 kV and 50–60 nA with a PET crystal. An analytical procedure was developed for analysis of samples with variable S2-/SO42-, whereby the combined sulfide plus sulfate peak was accurately measured for total dissolved sulfur. The sulfide and sulfate peak positions (located on FeS and CaSO4 standards, respectively) were measured for 100 s, and backgrounds on each side of the combined peak were measured for 50 s each. A defocused 5 µm beam was used. At least 10 replicate analyses were performed on each sample to check for variability, to constrain the analytical error, and to lower the S detection limit. Each analysis took 5 min. Thus each sample took 1 h to analyse. Detection limits were 15 ppm S. During each analytical session, NBS 610 was used as a secondary standard. Ten to 15 spot analyses were made on the NBS 610 glass, and the C s-1 A-1 were adjusted to obtain a total of 580 ppm S. The standard deviations of the NBS 610 analyses were generally around 3–5%.
Our calibration was checked on VG2 (Jarosewich et al., 1979), a natural glass used by several other workers for this purpose. We obtained 1403 ± 31 ppm, which is in excellent agreement with the previous determinations by EMP analysis (all in ppm, uncertainties 1 SD): 1340 ± 80 (Dixon et al., 1991); 1420 ± 40 (Wallace & Carmichael, 1992); 1400 (Nilsson & Peach, 1993); 1365 ± 29 (Thordarson et al., 1996); 1450 ± 30 (Métrich et al., 1999); 1416 ± 36 (De Hoog et al., 2001). In addition, Wallace & Carmichael (1992) reported 1320 ± 50 ppm from wet-chemical analysis. Available evidence for Fe2+/Fe3+ of silicate melts (e.g. Kilinc et al., 1983) indicates that Fe2+ should make up >95% of the total Fe in the silicate melts under the conditions of this study. We have therefore treated all Fe as Fe2+.
Equilibration times
The time needed to achieve steady-state S contents (hence by inference, equilibrium) in Fe-free CMAS compositions was investigated by running the ‘CMAS-7’ compositions for different times, from 1 h to 50 h. Results are summarized in Fig. 1. Times are taken from when the gas mixture was switched on (furnace reached 1400°C). There should be zero S in all compositions at zero time. All subsequent Fe-free compositions were run for longer than 8 h (mostly 16 h).
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Fig. 1. Time series showing the time needed for sulfur solubilities of Fe-free silicate melts (CMAS7—see Table 1 for compositions) to reach steady-state values (hence, by inference, equilibrium). The time needed is 8 h. It should be noted that the approach to steady state does not follow a smooth curve with time, probably because sample geometry was not controlled.
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These Fe-free CMAS compositions are envisaged to approach equilibrium
by the simple one-stage process of exchange of S for O [e.g.
reaction (1)]. By contrast, equilibration of the Fe-containing
samples also requires the reduction of Fe
3+ in the starting
material to Fe
2+, to establish the equilibrium Fe
2+/Fe
3+ appropriate
for the
fO
2 of the run. Furthermore, for those runs that produced
an immiscible sulfide liquid, segregation of this liquid [according
to reaction (3), see below] also needs to take place. These
reactions presumably take place sequentially rather than concurrently,
as it is first necessary to establish the equilibrium Fe
2+/Fe
3+ and build up S in the silicate before segregation of an immiscible
sulfide liquid can occur. From this perspective, it could be
anticipated that equilibrium in the Fe-bearing compositions
would take longer to reach than in the CMAS compositions. Against
this, Fe-bearing compositions are usually less viscous than
the CMAS compositions, and appear to have different wetting
characteristics. Rather than form nearly spherical beads, many
of the Fe-bearing samples appear to have crept along their Re
ribbon, which gives these samples a different aspect ratio with
greater surface area to volume, more favourable for equilibration
with the gas. In fact, for the Fe-bearing compositions, the
results (Fig.
2) show that a constant value of dissolved S was
achieved even in the shortest time attempted (4 h), for both
FeS-saturated and FeS-undersaturated conditions. An additional
feature of the time series shown in Fig.
2 is the effectiveness
of Re in minimizing Fe loss to almost negligible levels.
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Fig. 2. Time series for ‘Fe6’ compositions on Re loops, all at log fO2 = -9·60, log fS2 = -1·91. At these conditions, three compositions are FeS undersaturated, and three compositions have exsolved some immiscible FeS melt. Regardless, all compositions appear to have reached the steady-state S solubility in the shortest run time, 4 h. The FeS-undersaturated compositions show a slight decrease in FeO from Fe loss to the Re at the longest run time (47 h), the most loss being 8% of the initial FeO. In the FeS-saturated compositions, the amount of FeO in the silicate melt is buffered, and Fe loss to the Re does not result in decreasing FeO content of the silicate melt. Error bars (2 SD) are shown for one composition only.
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Experimental uncertainties
A priori knowledge of experimental uncertainties is required to judge whether the model used to fit the data is adequate. The accuracy of most of the results reported here depends almost entirely on three experimental variables: fO2, fS2 and the EMP analyses for S. The accuracy with which FeO is determined also becomes significant for high-FeO samples because of the very strong dependence of S solubilities on FeO content. Temperature is not a significant experimental uncertainty. All uncertainties reported in this paper are 1 SD.
The accuracy of reported fO2 and fS2 values depends on the input gas mixture (see Table 3, below). The accuracy of fS2 decreases greatly as fS2 decreases, because the proportion of SO2 in the input gas mixture becomes very small. Also, fO2 and fS2 are not independent variables, but the degree to which the one depends on the other also varies with the particular input gas mixture. For each group of six or seven samples run together, the errors in fO2 and fS2 are obviously the same, i.e. should not be treated as independent, uncorrelated uncertainties. To simplify matters, we assume that the uncertainties in log fO2 and log fS2 for every sample are independent of each other, and were both ±0·05 in the earlier experiments, but improved to ±0·03 in later experiments. These uncertainties in fO2 and fS2 propagate through equation (2) to produce uncertainties in CS of 8·1% and 4·9%, respectively.
Observed standard deviations from EMP analyses are given for each experiment in the tables of results. In relative terms, these uncertainties range from 100% as S contents approach the limit of detection (15 ppm), down to 1% in many of the experiments with the highest S contents (that is, those with S > 2000 ppm). However, these uncertainties do not include errors in the setting up of the calibration for S on the EMP. This procedure involves normalization of the C s-1 A-1 to the value of the S content that we have assumed for the NBS 610 glass standard (namely, 580 ppm); this value is determined to 3–5% in each session, which must be included in the analytical uncertainty. There is also the possibility of instrument drift during an analytical session. We have therefore taken the total non-systematic uncertainty in S analyses (1 SD) to be either 5%, or as observed, whichever is the larger.
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RESULTS
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Testing the Fincham–Richardson relationship: [S ] 
(fS2/fO2)1/2
Twelve Fe-free compositions in the system CaO–MgO–Al
2O
3–SiO
2 (CMAS) plus one composition in the system CMAS–TiO
2 were
selected to test thoroughly the Fincham–Richardson hypothesis
over as wide a range of
fO
2 and
fS
2 as is possible using CO–CO
2–SO
2 gas mixtures. The compositions were selected to cover a wide
compositional range while still being above the liquidus at
1400°C, and quenching to homogeneous glasses. They include
both relatively low melting point compositions [eutectic or
peritectic compositions, mostly estimated from Longhi (1987)
],
plus compositions based on the anorthite–diopside eutectic,
to which were added the following components: SiO
2, MgSiO
3,
CaSiO
3, Mg
2SiO
4, and TiO
2 in amounts close to the maximum possible
at 1400°C. These compositions were run in two groups, one
of six compositions (called AD6, where AD stands for anorthite–diopside)
and the other of seven (CMAS7). The compositions are given in
Table
1.
The low fO2 limit of these experiments was determined by the O2 content of the input gas mixture; we cannot produce conditions more reducing than are obtained with CO2-free input mixtures (i.e. CO–SO2 only). The high fO2 or low fS2 limits occur as the solubility of S approaches the analytical limit of detection, which is 15 ppm. Also, the control of fS2 at values of fS2 <10-3·5 bars becomes too imprecise to be useful, because the input flow rate of SO2 is so low. The high fS2 limit is defined by the experimental requirement for the input gas, pCO2 + pCO + pSO2 = 1 bar. Caution also dictates that fS2 should not be too high lest condensing elemental S clogs up the gas outlet of the furnace. Nevertheless, within these limits, we can vary fO2 by four orders of magnitude and fS2 by nearly two orders of magnitude, while keeping the major-element composition of the silicate melt constant.
Experimental sulfur solubilities are given in Table 2, and are plotted as a function of fO2 at constant fS2 in Fig. 3a and b, and as a function of fS2 at constant fO2 in Fig. 4a and b. It may be seen that the solubility of S follows the Fincham–Richardson relationship completely. Statistical analysis of the data by least-squares regression is summarized in Table 1. It should be noted that the very low S contents in the experiments at the highest fO2 values are consistent with negligible sulfate (SO42-) or sulfite (SO32-).
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Fig. 3. S solubilities in Fe-free compositions as a function of fO2 at constant fS2 (log fS2 = -1·91). (a) AD6 compositions; (b) CMAS7 compositions (only four shown for clarity). The lines are not best fits to the data, but the theoretical slope of -0·5, positioned arbitrarily for comparison with the data.
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Fig. 4. S solubilities in Fe-free compositions as a function of fS2 at constant fO2 (log fO2 = -10·28). (a) AD6 compositions; (b) CMAS7 compositions (only four shown for clarity). The lines are not best fits to the data, but show the theoretical slope of 0·5.
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Six Fe-containing compositions were selected for a similar test. These compositions (called ‘Fe6’) were chosen in part to replicate previous experimental work (Table 3). Although approaching natural basaltic silicate melts, these compositions do not contain alkalis (Na or K) because these are lost by evaporation under the conditions of the experiment.
For Fe-bearing systems, the composition of the silicate melt cannot be kept constant over such wide ranges of fO2 and fS2, as FeO is lost from the silicate melt when the sulfide (FeS) saturation surface is reached. This happens as fO2 is lowered or fS2 raised, according to the reaction
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Because of loss of FeO from the original starting compositions by this means (and by alloying of Fe with the Re wire, although this is minimal), full major-element analyses of all experiments are reported (Table 4). Results with no loss of Fe by FeS exsolution are plotted as a function of fO2 in Fig. 5. Again, the data are in complete agreement with the Fincham–Richardson relationship [reaction (1)]. Although this result is not unexpected, other possibilities are conceptually possible. For example, the present results rule out significant solubility of molecular S. This contrasts with the solubility in silicate melts of other volatile components such as H2O and CO2, both of which dissolve not only as the anionic species OH- and CO32- but also as the molecular species H2O and CO2 (Kohn, 2000; Brooker et al., 2001a, 2001b). The results from the iron-bearing compositions imply that only a component with FeS stoichiometry occurs, and not, for example, a component with pyrite stoichiometry (FeS2). We find no evidence in our data for an Fe3SO2 component as postulated by Poulson & Ohmoto (1990) from modelling of previous experimental work. As will be discussed below, this may be because of errors in previous experimental work.
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Fig. 5. S solubilities in FeS-undersaturated ‘Fe6’ compositions as a function of fO2, at constant fS2 (log fS2 = -1·91). The theoretical slope of -0·5 is shown.
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Once the actuality of the Fincham–Richardson relationship is taken as established, measuring S solubilities over a range of fO2 and fS2 becomes redundant. Instead, it suffices to choose just one experimentally convenient condition of fO2 and fS2 to explore further the influence of the major-element composition of the silicate melt on S solubility.
Effect of silicate melt composition—the FeO component
As noted above, the six FeO-containing compositions reach sulfide saturation at both the higher fS2 and lower fO2 conditions of this study. Precipitation of FeS then lowers the FeO content of the silicate melt, but all other components (i.e. CaO, MgO, Al2O3, SiO2, TiO2) are conserved, so that the resulting compositions lie on binaries between FeO and an Fe-free end-member composition in the system CMAS ± TiO2. Similar binary joins arise in experiments that measure the activity of FeO (
) in silicate melts by equilibrating the melt with Fe metal under controlled fO2. In such experiments, the FeO component in the melt increases as fO2 is increased, according to the reaction
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Doyle & Naldrett (1986) and Doyle (1988, 1989), who undertook several series of experiments of this type, used the term ‘Matrix’ to describe the FeO-free end-members of their binary joins. The FeO-free end-member or ‘Matrix’ compositions of this study are given in Table 5.
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Table 5: Compositions of simplified, synthetic FeO-bearing melts (‘Fe6’ compositions) recalculated to a FeO-free basis from data in Table 4
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The values of CS, calculated from the sulfur solubilities in Table 4, are plotted against the FeO content of the melt for two of the binaries in Fig. 6. The data form a smooth curve, which is well described by a linear relationship between the logarithm of CS and cFeO. For a preliminary fitting of the data, we use the empirical relationship
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Fig. 6. Sulfide capacity, CS, vs FeO in wt % for two ‘Fe6’ compositions. The curves are exponential fits to the data. These plots emphasize the great influence of the FeO content of the melt on its CS. For basaltic compositions (with rare exceptions that have FeO >8 wt %) other aspects of their composition have only a slight effect on CS.
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The rationale for this relationship is that is the sulfide capacity
of the FeO-free end-member or ‘Matrix’ component
(i.e. for the FeO-free compositions as given in Table
5). A
more complete equation that takes into account the dependence
of
CS on all major-element oxide components will be introduced
later (in the section ‘Thermodynamic theory’), with
more theoretical justification. The quality of the fits is demonstrated
in Fig.
7a–f.
Examination of these plots, supported by the preliminary fitting, indicates that the value of the B parameter is the same in five of the six FeO–‘Matrix’ binaries, the exception being the high-Ti mare basalt. The value of the B parameter for the high-Ti mare basalt is 25% lower. The results of this fitting are given in Table 6.
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Table 6: Results of fitting the sulfide capacities (CS) of Fe-bearing compositions to the relation CS=CSo (1 -cFeO]/100) exp{B.cFeO/100}, where cFeO is the amount of FeO in wt % and CS° is the sulfide capacity of the Fe-free composition renormalized to 100% (given in Table 3)
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As previous geologically oriented investigators have all noted, CS greatly depends on the FeO content of the melt. This is not quite so apparent from the data in metallurgical literature, as these experimental studies are mainly concerned either with very low-FeO compositions, or with compositions near the FeO–SiO2 binary [see, for example, studies listed by Young et al. (1992)]. As Fig. 6 shows, the exponential nature of the relationship between CS and FeO means that the effect of FeO on CS increases as FeO increases. Thus, at a few wt % FeO, the FeO content of the melt does not completely dominate CS. On the other hand, for melts with more than 10 wt % FeO, the other components are more-or-less irrelevant; the total variation in the value of 
among the five‘terrestrial’ compositions is only 0·01, which is equivalent to a change of 0·2 wt % FeO at 10 wt % FeO. This is close to the analytical error. It should be noted that a recent inter-laboratory comparison of some homogeneous glasses produced from natural compositions demonstrates differences in reported FeO contents of about this level (see Jochum et al., 2000).
The dominant effect of FeO on CS also means that FeO-rich compositions are not suitable for studying the dependence of CS on other oxide components. Although this may seem of little practical importance for geological applications, it is important for understanding the fundamental thermodynamic basis for the effects of composition on CS.
CS in other FeO-free systems at 1400°C
Accordingly, we have made an extensive study of the compositional dependence of CS in FeO-free systems to supplement the data in Table 2. Results are given in
Tables 7–9
, and are plotted in
Figs 8–11
. The general approach has been to start with the anorthite–diopside eutectic composition (ADeu) and add various components (SiO2, Al2O3, TiO2, CaSiO3, Mg2SiO4, and MgSiO3) to this composition. The binary between diopside and anorthite was also studied (Fig. 8). Relative to ADeu, TiO2 and CaSiO3 cause an increase of CS, whereas Al2O3 and SiO2 cause a decrease. In most cases, CS changes approximately linearly with the added component, but where large amounts of the component can be added (e.g. CaSiO3 and SiO2), the relationship is clearly non-linear. As for FeO, these systems follow a logarithmic relationship between CS and composition.
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Fig. 8. S solubility at log fO2 = -9·60, log fS2 = -1·91 across the CaMgSi2O6–CaAl2Si2O8 binary join (anorthite–diopside).
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Fig. 9. Effect of adding SiO2 to anorthite–diopside eutectic composition (ADeu). The trend is fitted well by an exponential curve.
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Fig. 11. Effect of adding CaSiO3 to a CMAS composition near the ADeu composition. The trend is well fitted by an exponential curve.
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We also attempted to study the effects of alkali components (Na2O and K2O). Results are given in Table 10. The alkalis are volatile under the conditions of the experiment, hence composition changes continuously during the experiment and the extent to which equilibrium is achieved with respect to S solubility is uncertain. However, taking this into account, it nevertheless seems a robust conclusion that neither Na2O nor K2O causes a significant increase in CS.
A spin-off from using the AD-eutectic composition as the basis of studying compositional effects is that we have generated a number of replicate experiments on this composition at identical conditions, providing a test of the reliability of our experimental procedure. This is shown in Fig. 12.
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Fig. 12. Replicate measurements on the ADeu composition at log fO2 = -9·60 and log fS2= -1·91. These experiments were run over a period of more than 2 years and analysed in different sessions over a similar period. The mean and standard error of the mean are given.
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The join AD eutectic–FeO
The FeO–‘Matrix’ binaries discussed so far were generated by removing FeO from the starting compositions by exsolution of FeS liquid. Thus all samples are FeS saturated with the exception of those with the original FeO content of the starting composition (allowing for minor FeO loss to the Re loops). An alternative way to study the effect of FeO on CS is to add FeO to an original FeO-free starting composition. We have done this by adding FeO to the AD-eutectic composition. Two experiments were performed (Table 11). The earlier experiment used Pt loops and resulted in massive loss of Fe to the Pt (which illustrates well how important the use of the Re wires has been to our experimental campaign). Nevertheless, the results of this experiment are consistent with those on the Re loops (Fig. 13). More importantly, the results plot on the same slope of ln CS vs FeO as the five ‘terrestrial’ Fe6 compositions, demonstrating that values of CS are not affected by FeS saturation. Fitting the data to the same empirical relation [equation (5)] shows this. The results of the fitting are given in Table 6.
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Fig. 13. CS vs wt % FeO for ADeu plus FeO. All samples are undersaturated in FeS. The experiments on Pt wire have lost most of their original FeO, but still plot on the same curve as those on Re.
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Because the value of for AD eutectic is very similar to that for the anomalous sixth composition (the high-Ti mare basalt), these data also imply that the different slope of CS vs FeO for the high-Ti mare basalt composition is not due to its high value for .
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THERMODYNAMIC THEORY
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Thermodynamic theory of the compositional dependence of the sulfide capacity, CS
The choice of the thermodynamic components used to describe
the thermodynamic properties of silicate melts is to some extent
discretionary. If the simplest-looking components, namely the
single oxide components (SiO
2, MgO, FeO, etc.), are used, deviations
from ideal thermodynamic mixing can be fairly complex, requiring
the use of impractically complex mixing models. Conversely,
it has long been appreciated that more complex components that
mimic the stoichiometry of common silicate minerals mix almost
ideally, and this approach currently underlies most practical
thermodynamic modelling of silicate liquids in the geological
literature. However, it is not immediately obvious how the modelling
of sulfide capacities can best be grafted onto this approach.
As the purpose of this section is to derive an appropriate algebraic
form for the dependence of
CS on composition, we shall begin
using the simple oxide components. We briefly discuss the implications
of using a mineral-stoichiometry approach in a later section.
As the Fincham–Richardson theory envisages S2- replacing O2- on the anion sublattice, it is convenient to define the oxide components of the silicate melt in terms of a single oxygen ion (e.g. Si0·5O, Ti0·5O, Al0·67O, CaO, Na2O, etc.) and the sulfide components as Si0·5S, Ti0·5S, Al0·67S, CaO, Na2S, etc.
The concept of mixing on different sublattices logically requires that the activities of the MzO and MzS components be formulated in the context of the reciprocal solution model, which was first developed for molten salts (Flood et al., 1954), and introduced into the geological literature (for crystalline solid solutions) by Wood & Nicholls (1978). In this formulation, the total free energy of the solution comes from three kinds of contributions:
- the sum of the free energies of the pure end-member components, weighted according to the mole fractions of these components:
- ideal mixing of cations and anions on each sublattice:
- excess free energies of mixing, which account for deviations from the ideal mixing on sublattices given by the term. This contribution is expressed empirically using activity coefficients for cations and anions separately on each sublattice:
where and are functions of the other cations and anions (respectively) on each sublattice, but it is assumed that there are no interactions between the sublattices, i.e. does not depend on the composition of the anion sublattice nor on the cation sublattice. Unfortunately, as far as we know, this important assumption has never been tested against experimental measurement for any silicate system, liquid or solid.
The mole fractions of both the cations on the cation sublattice and the anions on the anion sublattice are taken to sum to unity, i.e. we assume no vacant sites.
For any oxide component MzO, there is a reaction
(It should be noted that the Fincham–Richardson theory implies that z must be the same in MzO and MzS for each M.) Hence at equilibrium
where
and
It should be noted that XS + XO = 1 and XM = 1 – 
XN. From the assumption that deviations from ideal mixing on the cation and anion sublattices are independent of each other, for small amounts of S2- dissolved in the melt, XO 
1, hence 
O = 1 by definition, and S is a constant (i.e. Henry’s law). This is effectively the same approximation as used by Fincham & Richardson (1954) in defining CS. Substituting (11)–(14) into (10) and rearranging gives
The definition of the sulfide capacity, CS is
Combining equations (2) with (16) eliminates the term in (fO2/fS2)1/2, and shows that the equation relating CS to silicate melt composition requires the form
where
The term kS is to convert from mole fractions of sulfide (XS) to parts per million (ppm); although it is not strictly a constant, it varies little over the entire range of silicate melts considered in this study, and will therefore be ignored for the convenience of working with S concentrations in ppm. The ‘constant’ term in (18) and (19) appears because the A0 and AM terms cannot be uniquely determined from (17), because ?XM is constrained to be unity.
The form of this equation is that adopted previously by Haughton et al. (1974). The importance of the thermodynamic derivation presented here is that it shows that the coefficients AM should be directly related to the difference in the free energies of formation of the components, i.e. 
. This is something that can be readily tested using our experimental results.
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DATA FITTING AND TESTING THE MODEL
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Data fitting by non-linear least-squares regression
To fit the data, we adopted the expression
The last term is an empirical addition to the equation as derived theoretically, and was included to account for the anomalous slope of CS vs FeO found for the high-Ti lunar mare basalt composition (see Table 6). The data were fitted both with and without this term.
The silicate melt compositions in wt % given in the tables were converted to mole fractions on the cation sublattice according to
and so on for the other oxides. We set ASi = 0, as the constraint that 
means that the equation would be over-determined if all the oxide components were used. Haughton et al. (1974) also set AAl = 0, and we decided to test this option too.
We included the following experimental data, weighted for non-linear least-squares regression using the uncertainties in analysed compositions propagated through equation (20), and uncertainties in CS calculated from the uncertainties in [S], fO2 and fS2 as indicated:
- 12 CMAS compositions plus one CMAS–TiO2 composition, from Table 1, using values of CS and the standard deviations of these values, also given in Table 1; these data were obtained from 133 experiments (Table 2);
- 31 more CMAS data (Tables 7 and 8), nine CMAS–Na2O and five CMAS–K2O data (Table 10) and four CMAS–TiO2 data (Table 9), weighted assuming ±0·05 in log fO2 and log fS2, and either the observed standard deviation of the EMP analyses as given in the tables, or 5% of [S], whichever is the larger;
- 81 CMAS–TiO2–FeO compositions from Table 4, and 11 compositions from ADeu–FeO (Table 11), weighted as above, but assuming ±0·03 in log fO2 and log fS2.
Thus 274 experiments were used. The result of the regressions, both with and without the terms in AAl and BFe–Ti, are summarized in Table 12.
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Table 12: Results of data fitting by non-linear least-squares to the expression ln CS=A0+ACaXCa+AMgXMg+AFeXFe+ANa/K(XNa+XK)+ATiXTi±AAlXAl±BFe–TiXFeXTi, where CS= [S (in ppm)](fO2/fS2)1/2
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The value of the reduced chi-squared (
) for the regression including both the AAl and BFe–Ti terms is 2·33, which is higher than that required for a satisfactory fit, given the assumed uncertainties in the input data (the value of should be unity for a large number of data if the uncertainties in the input data are estimated correctly). The AAl parameter is only of marginal significance and setting this parameter to zero increases the value of only to 2·57. However, the BFe–Ti term is significant and leaving out this term increases to 4·00.
The uncertainties in each parameter from the regressions are also presented to indicate the effectiveness with which the parameter is constrained by the range of compositions studied. Because there is a fairly high correlation between some of these parameters, full error propagation would require the complete error matrix including cross-terms. Obviously, for a seven- or eight-parameter model this involves a tedious number of terms (28 or 36, respectively), and it suffices to note that the input values of CS are reproduced with a root-mean square deviation (RMSD) of 9% (eliminating seven runs with very low S and consequently very high uncertainty). A detailed examination of the residuals of the regression shows that probably only the value of CS for one composition, namely CMAS-E, is significantly misfit. The calculated value of CS for this composition is 0·104, which is 20% lower than the experimentally measured value of 0·125 (Table 1). But because the experimentally measured value is derived from 10 separate experiments (Table 2), we have confidence in it, and this anomaly must be taken as a real indication that the model does not provide a perfect description of CS at all possible silicate melt compositions. The quality of the fit for the eight-parameter model is demonstrated in Fig. 14.
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Fig. 14. Sulfide capacities observed vs calculated from equation (19), using coefficients for the seven-term model (with AAl = 0) in Table 12. Dashed lines delineate ±25% deviations from the 1:1 line. The two rather anomalous samples at very low CS are the NaAlSi3O8–Al2O3–SiO2 composition (i.e. albite with Na loss) and a similar high Na–Al–Si composition, from Table 10.
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Further experimental tests
The data in Table 13 on the ADeu–Fe2SiO4–SiO2 system and in Table 14 on the ADeu composition with variable FeO substituting for MgO were not included in the regression as most experiments were on Pt loops and accordingly suffered heavy Fe loss. On these grounds their reliability might be considered dubious. On the other hand, there is demonstrably good agreement between Pt-loop and Re-loop experiments on the related join ADeu–FeO (Fig. 13). Accordingly, we decided that the best use of these data was as a test of the other results. The comparison between observed and calculated values of CS is made in Fig. 15. Although most data are fitted well by the model, we draw attention to three data points at high FeO contents (>20 wt %), which lie on a trend away from the one-to-one correlation line (Fig. 15). This is an indication that the model breaks down at very high FeO contents, in the range relevant to lunar basalts and other extraterrestrial compositions. Future work will address this issue.
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Fig. 15. Test of the model against data for the ternary ADeu–Fe2SiO4–SiO2, which were not used in the calibration. Data from Table 13. It should be noted that the three data points with >20 wt % FeO are not fitted by the model.
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We also further tested the need for the BFe–Ti term to describe high FeO and TiO2 compositions, by adding TiO2 to two of the low-Ti ‘Fe6’ compositions, namely the ‘average MORB’ and the ‘Cape Vogel high-Mg andesite’. Results are given in Table 9. For the seven-term model (i.e. without the BFe–Ti term), the RMSD between calculated and observed values of CS is 8%, whereas for the eight-term model (with the BFe–Ti term), the RMSD is only 3·6%, thus confirming the desirability of including this extra term. The match between calculated and observed values, using the eight-term model, is given in Fig. 16.
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Fig. 16. Test of the model against compositions made by adding TiO2 to the average MORB and Cape Vogel high-Mg andesite compositions. Data from Table 9.
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We also performed a few experiments based on a high-K2O basaltic composition (Table 15), which we had previously used for investigating sulfide saturation in high-P experiments (Mavrogenes & O’Neill, 1999). The comparison between calculated and observed values of CS for these data is shown in Fig. 17.
TOP
ABSTRACT
INTRODUCTION
