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
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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 TOP ABSTRACT INTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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The solubility of sulfur as S2– has been experimentally determined for 19 silicate melt compositions in the system CaO–MgO–Al2O3–SiO2(CMAS) ± TiO2 ± FeO, at 1400°C and 1 bar, using CO–CO2–SO2 gas mixtures to vary oxygen fugacity (fO2) and sulfur fugacity (fS2). For all compositions, the S solubility is confirmed to be proportional to (fS2/fO2)1/2, allowing the definition of the sulfide capacity (CS) of a silicate melt as CS = [S](fO2/fS2)1/2. Additional experiments covering over 150 melt compositions, including some with Na and K, were then used to determine CS as a function of melt composition at 1400°C. The results were fitted to the equation
, where AFe >> ACa > AMg,ANa/K,ATi. The FeO content of natural basalts is the dominant control on CS. The equation for CS 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 fO2 and fS2, 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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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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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 fO2 [more reducing than that defined by the quartz–fayalite–magnetite equilibrium (QFM)], sulfur dissolves in silicate melts as S2-, and does so by replacing O2- on the anion sublattice:
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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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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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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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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 Fe3+ in the starting material to Fe2+, to establish the equilibrium Fe2+/Fe3+ appropriate for the fO2 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 Fe2+/Fe3+ 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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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.
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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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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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Testing the Fincham–Richardson relationship: [S ]
(fS2/fO2)1/2Twelve Fe-free compositions in the system CaO–MgO–Al2O3–SiO2 (CMAS) plus one composition in the system CMAS–TiO2 were selected to test thoroughly the Fincham–Richardson hypothesis over as wide a range of fO2 and fS2 as is possible using CO–CO2–SO2 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: SiO2, MgSiO3, CaSiO3, Mg2SiO4, and TiO2 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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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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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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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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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.
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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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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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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.
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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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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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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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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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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 (SiO2, 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
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(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
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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
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The definition of the sulfide capacity, CS is
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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
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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
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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
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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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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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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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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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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.
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COMPARISON WITH PREVIOUS WORK |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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Danckwerth et al. (1979)
The high-Ti mare basalt composition was selected for this study partly because it had been used previously in an experimental study of S solubility, by Dankwerth et al. (1979)
, at lower T (mainly 1250°C with a few results at 1200 and 1300°C). Their experimental approach was similar to that used here, but with samples suspended on Fe-plated Pt wire. Their experiments were conducted over a range of both fO2 and fS2; at most of these conditions, variable amounts of immiscible FeS liquid exsolved causing a decrease of the FeO content of the silicate melt, just as in this study. Hence their original composition changes along a binary between an FeO-free end-member or ‘Matrix’ composition, and FeO, and their results may conveniently be assessed and compared with ours by plotting log CS vs FeO (Fig. 18). Their data plot on a line with identical slope to our data, but displaced to lower values of log CS by 0·4 units. This is in agreement with the trend for CS to decrease with T that is well established in the metallurgical literature (e.g. Young et al., 1992). Future experiments will allow more exact comparison. In the mean time, it is interesting to note that the exact parallelism of the slopes of log CS vs FeO at 1400 and 1250°C suggests that only the A0 term in equation (17) depends significantly on T.
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Haughton et al. (1974)
In a study of somewhat similar scope to that reported in this paper, Haughton et al. (1974) investigated the solubility of S in Fe-containing silicate melts of approximately basaltic composition, as a function of melt composition and fO2 and fS2. They employed an experimental approach similar to that in our work, using CO–CO2–SO2 gas mixtures at atmospheric P, with quenched run products analysed by EMP. They reported 101 results, 100 of which were at 1200°C and one at 1300°C. The major difference in experimental technique was that the samples were held in alumina crucibles rather than on Re wire loops, and were stirred with alumina rods to decrease the equilibration time. The alumina crucibles and rods reacted with the silicate melt during the experiment to form spinel. This means that the major-element composition of the melt changes with time during the experiment. Most of their experiments were saturated in immiscible sulfide, and often also contained crystalline phases, mainly olivine and plagioclase. In principle, this should not affect matters, and a direct comparison of their results with ours is possible, provided, of course, that allowance is made for the difference in T. Given the dominance of FeO in controlling CS, this is again most easily done by plotting CS as a function of wt % FeO. This has been done in Fig. 19.
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Of the 100 experiments of Haughton et al. (1974) at 1200°C, 37 were conducted on a single starting composition but with variable FeO content, at various values of fO2 and fS2 (their Series I). These data form an array on the log CS vs FeO diagram parallel to our data at 1400°C, but displaced to lower values of CS, as expected for the temperature difference. The other 63 experiments (their Series II) were performed at constant fO2 and fS2 (namely, fO2 = 10-9·31 bars, fS2 = 10-0·98 bars), to study the effect of silicate melt composition. These data plot on a significantly shallower slope in the log CS vs FeO diagram. This is inconsistent not only with our results, but also with their Series I experiments.
There are also major internal inconsistencies in their Series I data. For example, Haughton et al. reported three experiments, with the same starting composition, at the same fO2 and fS2, and in equilibrium with immiscible FeS-rich sulfide melt (namely runs 4 DF2, 7 DF2 and 7F2 in their appendix). The activity of FeO is constrained to be identical, but FeO contents were 0·88, 1·30 and 4·47 wt %, respectively. This large range cannot be explained by the modest differences in alumina and other major-element contents in these melts but must be taken as evidence of disequilibrium or other experimental malfunction.
The sheer number of data reported by Haughton et al. (1974) has dominated attempts to quantify the role of S in magmatic systems (e.g. Poulson & Ohmoto, 1990; Wallace & Carmichael, 1992; Li & Naldrett, 1993), so our suggestion that their results may be in error is significant. It is our intention to test their results more directly by replicating experiments on their reported compositions at their experimental T of 1200°C.
Attempted replication of some results from Buchanan et al. (1983)
In a series of papers, Buchanan, Nolan and coworkers reported the results of sulfur solubility experiments in several CMAS–FeO compositions at T between 1200 and 1400°C (Buchanan & Nolan, 1979; Buchanan et al., 1983; Nolan & Buchanan, 1984). Both the aims and the experimental approach of these papers are similar to those of this study, and indeed we have adopted two of the compositions used by Buchanan & Nolan (DB/3 and PAL 685 in Table 5), to facilitate comparison. This was felt to be important, as the results of Buchanan & Nolan do not follow the Fincham–Richardson relationship ([S] 
(fS2/fO2)1/2). Thus the values of CS calculated from their experiments appear to change as a function of fS2 (e.g. see Buchanan et al., 1983, fig. 4). Generally, Buchanan & Nolan reported anomalously high [S] at low fS2, leading to slopes in log [S] vs log fS2 plots that are far less than the slope of 1/2 required by the Fincham–Richardson relationship. This occurs for all their sulfide-undersaturated compositions throughout the T range of their work (1200–1400°C).
In contrast, our results on the Buchanan & Nolan compositions (DB/3D and PAL/D) do obey the Fincham–Richardson relationship when we vary fO2 at constant fS2 (Fig. 5). However, at fO2 of 10-10·28 bars, which we chose to keep constant while varying fS2, these compositions are saturated with immiscible FeS-rich sulfide melt, and hence the FeO content in the silicate melt also varies. This change of composition foils the simple, direct test of the Fincham–Richardson relationship vs fS2. Therefore, to test the relationship, two additional experiments were performed at sulfide-undersaturated conditions, replicating two Buchanan et al. (1983) experiments at 1400°C. We used exactly the same CO–CO2–SO2 gas flow rates as Buchanan et al. (1983). The results are given in Table 16, along with the original results from Buchanan et al. (1983), and compared in Fig. 20. There are clearly large differences in the results. Most importantly, our results show [S] (fS2)1/2, in accordance with the Fincham–Richardson relationship.
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DISCUSSION |
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Sulfur content at sulfide saturation (SCSS)
For most geological applications, the main question of interest concerning S solubility in magmas is at what point the magma becomes saturated in immiscible sulfide. Many of the experiments on Fe-containing compositions in this study produced an immiscible FeS-rich sulfide melt, and therefore bear directly on this question.
The equilibrium between a silicate melt and an FeS-rich immiscible sulfide phase can be described by the reaction
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Substituting equation (2) into (23) to eliminate fO2 and fS2 gives
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where [S]SCSS is the ‘sulfur content at sulfide saturation’, a term introduced by Shima & Naldrett (1975). Thermodynamic data for liquid FeO and FeS from O’Neill & Eggins (2002) and Barin et al. (1989) respectively, give
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Sulfur saturation therefore depends on the amount of S in the magma, the major-element composition of the magma, the composition of the immiscible sulfide, and T and P. As pointed out by Mavrogenes & O’Neill (1999), the SCSS of a magma is independent of fO2 and fS2, provided that the silicate melt composition is kept constant (no gain or loss of FeO, for example), except for the effects that fO2 and fS2 have on the composition of the immiscible sulfide, i.e. on 
. For example, at very low fO2 the composition of the immiscible sulfide has Fe/S >1 (i.e. solution of Fe in FeS), lowering and causing SCSS to fall, as experimentally demonstrated by Mavrogenes & O’Neill (1999). But for all fO2 conditions used in this study, we assume that the immiscible sulfide melt produced in our experiments is effectively pure FeS, hence 
. In detail, there may be small variations in as a result of dissolved oxygen in the sulfide melt, and deviations from atomic Fe/(S + O) ratios of unity (e.g. Kress, 1997). However, preserving the compositions of sulfide melts during quenching requires extremely fast quench rates (Kress, 1997), which were not attempted in this study. Probably in consequence, electron microprobe analysis of the quenched immiscible sulfide gave >99% FeS in all experiments. In particular, we were not able to find any quenched iron oxide phases associated with the sulfide. Some natural magmas, including those of economic interest, contain chalcophile elements such as Ni, Co and Cu, in sufficient abundances to reduce significantly.
The interesting feature of equation (24) is that it shows that the SCSS of a silicate melt depends on its FeO content from two different terms, namely ln CS, which is dominated by its dependence on XFe, and . This latter term may be split up into two parts:
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where Fe is the activity coefficient of FeO in the silicate melt. Experimental evidence shows that Fe is reasonably close to unity for a wide variety of silicate melt compositions (e.g. Roeder, 1974; Doyle & Naldrett, 1986; Doyle, 1988; O’Neill & Eggins, 2002). In detail, Fe at low XFe is usually slightly greater than unity for most compositions in the system CMAS–FeO at 1400°C, when referred to a standard state of liquid FeO. For most of the compositions measured by O’Neill & Eggins (2002), 1·1 < Fe < 1·5. However, Fe becomes less than unity for compositions high in TiO2 (Roeder, 1974; Doyle, 1989; O’Neill & Eggins, 2002).
For the compositions along the binary joins between ‘Matrix’ (the FeO-free end-member) and FeO that are produced in our experiments on the ‘Fe6’ starting compositions (Table 4), equation (24) then becomes
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Here the parameters 
are the mole fractions of the ‘Matrix’ compositions, which are given in Table 5. The 
term is omitted for this exercise, as discussed above. Because Fe 
1 as XFe 1 by definition, the term in ln Fe is also generally a function of XFe. However, as accurate values of Fe are not available for the ‘Fe6’ compositions of interest here, we will adopt the simplifying approximation that Fe is unity. Equations (24) and (27) of course apply only to equilibrium with FeS-rich sulfide, and are not defined for Fe-free systems. Because 0 < XFe < 1, the AFeXFe term has a positive sign with a positive slope vs FeO, and dominates at high XFe, whereas the –ln XFe term has a positive sign, a negative slope vs FeO, and dominates at low XFe. The net result is that [S]SCSS should show an asymmetric U-shaped dependence on XFe. To illustrate this, we have fitted the S solubilities from the FeS-saturated ‘Fe6’ samples to equation (27), treating only the term in 
Go(22)/RT as an unknown. The results of the fitting are given in Table 17, and illustrated in Fig. 21. All five compositions with minor TiO2 give essentially identical values of Go(22)/RT, of 6·35 ± 0·02, which when compared with the theoretical value expected from equation (25) of 6·69 at 1400°C, imply Fe of 1·4, in good agreement with measurements on similar compositions in the CMAS system (O’Neill & Eggins, 2002). The higher calculated value of Go(22)/RT for the high-Ti mare basalt series (6·72) is consistent with the expected lower value of Fe for this composition.
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) are constrained to lie below this curve. In (a) the observed S contents of natural oceanic basaltic glasses are also plotted (Mathez, 1976
However, the fits to some compositions, particularly the synthetic tholeiite PAL 685, are not good. In truth, our present experimental data do not really extend to low enough values of XFe to demonstrate unambiguously the upturn expected in [S]SCSS. The required combination of low fO2 and high fS2 to produce low-FeO silicate melts in equilibrium with FeS melt cannot be attained in atmospheric-pressure experiments using CO–CO2–SO2 gas mixtures (as may be seen from the gas mixtures used for the experiments, which are given in Table 3). In any case, at lower fO2, the increasing solubility of Fe in the FeS melt would produce significant errors in the assumption that 
. Nevertheless, logic dictates that there must be an upturn, as saturation with FeS-rich sulfide must become more difficult as the Fe content of the system decreases towards zero.
Significance of the AM terms in the equation for CS
The derivation of the equation relating CS to composition derived in the section on ‘Thermodynamic theory’ [equation (17)] identifies the coefficients AM with the difference in the free energies of formation of MzS and MzO, i.e.
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This shows that the reason why Fe has such a great influence on CS is simply that FeS is rather stable, thermodynamically, compared with FeO. This simple observation is of great importance, as it goes to the heart of why approaches that do not take into account the specific identity of cation–anion interactions are bound to fail. These approaches include those based on optical basicity, or the ratio of non-bridging oxygens to tetrahedrally co-ordinated cations (often designated NBO/T). A feature of such approaches is that they seek to explain a wide range of silicate melt properties through one or a few chosen parameters; hence a convenient collective term for them might be ‘universal melt descriptors’. We discuss the inadequacies of this type of approach later, but first we will discuss the deficiencies in our own model.
Thermochemical data (e.g. Barin et al., 1989) show that the relationship of equation (19) is not correct in detail, and does not supply quantitative estimates of the values of the AM terms. Nor does it predict the relative values of these terms among cations completely correctly. For example, for the divalent cations Ca, Mg and Fe, the thermochemical data for 
predict that ACa > AFe >> AMg, whereas empirically we find AFe >> ACa > AMg.
In any case, many studies of silicate melts (or strictly speaking, their quenched glasses) have shown that the number of O2- anions in compositions richer in silica than the orthosilicate ratio is negligibly small (e.g. Mysen, 1988). All the melt compositions investigated in this study lie in this category. Rather, such melts are better modelled as consisting of a range of polymer units, whose general formula may be written (SiO4–y/2)(4–y)–, with 0 
y 4. When y = 0, the unit is the orthosilicate unit 
, in which Si is co-ordinated by four non-bridging oxygens. At the opposite extreme, y = 4 gives the fully polymerized silicate unit 
, with no non-bridging oxygens. Thus the hypothetical degree of polymerization of a silicate melt can be described by the ratio of non-bridging oxygens to tetrahedral cations, NBO/T, which ranges from four for an orthosilicate composition melt such as Mg2SiO4 to zero for a completely polymerized melt such as pure SiO2 or NaAlSi3O8. Melts more basic than the orthosilicate composition must indeed have free O2- anions, but these melts have NBO/T > 4 and are of limited importance geologically. A melt of a pure simple oxide such as MgO has NBO/T of infinity. This structural view of silicate melts is reflected in the choice of components with mineral-like stoichiometries to model their thermodynamic properties (e.g. Ghiorso & Sack, 1995).
This all suggests that, as the next increment of sophistication, the Fincham–Richardson reaction could be modified for natural silicate melts to
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As a simplifying approximation, we have ignored intermediate polymer units. Hence
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This reaction still requires the dependence of CS on (fO2/fS2)1/2 that is seen in the experiments, but suggests that CS should also depend on the ratio of polymerized silica units to orthosilicate units, i.e. effectively NBO/T. By analogy with the thermodynamic derivation of the compositional dependence of CS given above for simple oxide components, the coefficients AM for this approach would be expected to be proportional to 
rather than to 
. This is qualitatively in accord with the observation that AFe >> ACa > AMg. The reason that the AFe term is so large is not only the relatively large thermodynamic stability of FeS, but also the relatively low stability of Fe2SiO4 compared with its oxide components FeO and SiO2.
As a first step to test this approach, we examined the residuals from the regression of our data to equation (19) against NBO/T. No correlation is observed. Second, we included the term 
in the regression, using various strategies to calculate 
and ignoring the possibility of intermediate polymer units. The ambiguity comes from how Al and to a lesser extent Ti are assigned in the polymer model. For example, Al could be treated as a simple cation Al3+ (mixing on the cation sublattice with Ca2+, Mg2+, Fe2+, Na+, etc.), or as an isolated octahedral or tetrahedral unit equivalent to the orthosilicate unit, 
, or as a fully polymerized tetrahedral unit, 
. The way in which mole fractions of other cations are defined depends on such assignments, and is therefore also equivocal. Clearly, there is a wide range of possible formulations even though the conceptual basis of this approach is very simplified. The important point is that nothing we tried could achieve as good an empirical fit as the simple-oxide approach of equations (17) and (20). Rather surprisingly, the better results came from models in which Al was treated as a simple Al3+ cation.
It is probable that further theoretical work will result in more sophisticated models that fit the sulfur solubility data better than the naive model used here. In anticipation of such progress, we have made a point in this paper of giving all our experimental data on equilibrium S solubilities in full.
Comparison with optical basicity models
Optical basicity is ‘a measure of the donor power of the oxides ... [that] has been used to relate slag composition to sulfur capacities’ (Young et al., 1992). The concept is closely related to Pauling’s scale of electronegativity (Duffy, 1993). Optical basicities were originally quantified through ‘spectroscopic measurements of the shift of frequency in the UV region of a selected absorption band of a doping agent (Bi3+, Pb2+ or Tl+) caused by the electron donor environment of a glass made from the oxide system being investigated’ (Young et al., 1992). Such measurements are not possible for glasses containing transition element oxides, and instead various empirical methods have been developed to improvise fictive ‘optical basicity’ values directly from the chemical analysis of a glass (Duffy & Ingram, 1975; Sosinsky & Somerville, 1986; Young et al., 1992). Thus Sosinsky & Somerville (1986) and Young et al. (1992) defined their fictive optical basicity 
as
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where M are the values of optical basicity assigned to each oxide component. In the formulation of Young et al. (1992), Si = 0·46, Al = 0·60, Mg = 0·78, Ca = Fe =1·00, Na = 1·15, and K = 1·4. The 
are ‘equivalent cation fractions’, and are given the distinguishing superscript as they are defined somewhat differently from any customary way of defining mole fractions, including that adopted here (see Sosinksky & Somerville, 1986). For example, in the system CaO–Al2O3–SiO2:
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Young et al. (1992) gave an empirical expression for the sulfide capacity as a function of optical basicity, calibrated against an extensive compilation of experimental results from the metallurgical literature, for melts with < 0·8 (which covers all the compositions used in this study):
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We have applied this expression to the 154 data used in fitting our own model. The results are shown in Fig. 22. Obviously the model does not reproduce the experimental data well. In fact, for the terrestrial Fe-bearing compositions that are of most practical interest, the discrepancy is over an order of magnitude.
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Part of the reason for this is that the ‘optical basicity’ model is calibrated against slag compositions that tend to be more basic than the geologically relevant melt compositions used in this study. However, the main reason is the failure of the optical basicity approach to handle the strong affinity that the FeO component in the silicate melt has for sulfide.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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The CS of a natural basaltic silicate melt depends mainly on its FeO content. In fact, the FeO content so dominates CS that the other major-element oxide components are largely irrelevant when computing CS for typical terrestrial basaltic compositions, and a good approximation may be achieved by using a simple empirical expression:
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where cFeO is the concentration of FeO in the melt in weight percent [see equation (5) and Table 6]. This equation is of course only valid at reasonably low oxygen fugacities where S dissolves in the melt as S2- and most of the Fe occurs as Fe2+.
The overarching importance of FeO in controlling S solubilities may explain the different approaches to the modelling of CS as a function of composition that the metallurgical and geological scientific communities have used. The slag compositions of most interest to metallurgists are either very poor in FeO or, more rarely, very rich in FeO (i.e. the FeO–SiO2 binary), but do not include compositions with intermediate values of FeO comparable with those found in natural silicate magmas. Nor does the metallurgical literature include any work in which the effect of FeO is studied systematically by adding it to originally FeO-poor compositions, as in this study. The result is that metallurgists have sought to model CS in terms of ‘universal melt descriptors’ such as optical basicity (e.g. Young et al., 1992), whereas geologists have emphasized simply the FeO content. The data of this study show unambiguously that the optical basicity and related approaches are misguided, as substituting Fe for Mg or Ca on a one-to-one molar basis makes negligible difference to optical basicity (or no difference at all to other universal melt descriptors such as NBO/T), whereas it has a huge effect on CS. It is the identity of the cations that is important in controlling CS. ‘Carbonate capacities’ or ‘phosphate capacities’, describing the solubilities of CO32- and PO43–, can be defined in a similar way to the sulfide capacities, but, because FeCO3 and Fe-phosphates are not particularly stable thermodynamically (e.g. relative to CaCO3 and Ca-phosphates), we would not expect the FeO content of the silicate melt to have such a strong influence on them. Rather, from the same thermodynamic reasoning as used to derive our equation for CS as a function of melt composition, we would expect that CaO and alkali oxides (Na2O and K2O) should greatly outweigh FeO in increasing carbonate and phosphate capacities.
An equation describing the sulfur content at sulfide saturation (SCSS) of a silicate melt is obtained by combining three equations: (1) the definition of CS [equation (2)]; (2) the equilibrium between FeO in the silicate melt and FeS in immiscible sulfide melt [equation (23)]; (3) the compositional dependence of CS. This equation [equation (27)] predicts that SCSS should show an asymmetric U-shaped dependence on the FeO content of the silicate melt. Experiments that produced immiscible FeS melt conform reasonably well with this expectation (Fig. 21). SCSS also depends on T [illustrated here in Fig. 21f, where our results on the high-Ti mare basalt at 1400°C may be compared with the earlier work of Danckwerth et al. (1979) on the same compositions at 1250°C], and on P (Mavrogenes & O’Neill, 1999), but does not, we emphasize, depend on fS2 or fO2 (provided that the immiscible sulfide is nearly stoichiometric FeS). It is true that fS2 and fO2 must vary in inverse proportion to each other along the sulfide saturation surface in T–P–fS2–fO2–composition space [equations (22) and (23)]. The point is that, whereas the location of the sulfide saturation surface depends on (fO2/fS2)1/2, the actual value of SCSS on this surface depends only on T, P and the composition of the silicate and sulfide melts [equation (24)]. If this fairly simple truth has evaded previous discussion of sulfide equilibria in basaltic systems, this may be because much of the previous theoretical (‘thermodynamic’) treatment has been fallacious. It is important to point this out, as those unfamiliar with the thermodynamic treatment of phase equilibria may become confused if they consult previous work without a great deal of scepticism. The implications of the present observations for the deposition of sulfide ores will be discussed elsewhere (Mavrogenes & O’Neill, in preparation).
It has long been inferred from the sulfur contents of MORB glasses that SCSS increases with increasing FeO in natural magmas (Mathez, 1976; Wallace & Carmichael, 1992). The data from Mathez (1976) are plotted for comparison with our experimental results in Fig. 21a. The linear trend of the Mathez data is reproduced well by the experimental curve, but Fig. 21a also shows that this linear trend is in fact expected only over a limited range of FeO contents. It should be noted, also, that the oceanic basaltic glasses are likely to record equilibrium between melt and immiscible sulfide from a rather lower temperature than the 1400°C of the experiments.
The extraordinary nature of this increase of S with increasing FeO has perhaps not been appreciated fully. It is extraordinary because the ‘law of mass action’ (a simplified and admittedly primitive precursor to the concept of the equilibrium constant in chemical thermodynamics) would predict that dissolved S in equilibrium with immiscible FeS-rich sulfide should decrease with increasing FeO. This may be seen by considering the reaction
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for which, if the sulfide melt is pure FeS:
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[It should be noted that 
(34) is not a thermodynamic equilibrium constant, as charged species such as O2- and S2- are not proper thermodynamic components, because they cannot be varied independently.] Assuming [O2-] is constant [compare the assumption in the Fincham–Richardson model, as in equation (2)], then a constant (34) would imply that [S2-] 1/[FeO], i.e. that S in a silicate melt should decrease as FeO increases. That this does not happen in natural compositions follows from the enormous effect that FeO has on CS.
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ACKNOWLEDGEMENTS |
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We thank Nick Ware for the EMP routine for analysing S by WDS, and many helpers for carrying out the analyses, both EDS and WDS, on our EMP, which dates from the pre-automatic era. Prominent among these helpers was Dean Scott, who also assisted by making many of the starting compositions and loading these onto wire loops. Mike Shelley kept the gas plumbing and the mass flow controllers in good shape, and also undertook the checking of the flow-rate calibrations as required. J.A.M. acknowledges support from Western Mining Corporation during the early stages of this work. Ed Mathez and Roger Powell are thanked for helpful reviews, and Richard Arculus for editorial handling.
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FOOTNOTES |
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*Corresponding author. Telephone: +61 2 6125 5159. Fax: +61 2 6125 5989. E-mail: hugh.oneill{at}anu.edu.au
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REFERENCES |
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TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSTHERMODYNAMIC THEORYDATA FITTING AND TESTING...COMPARISON WITH PREVIOUS WORKDISCUSSIONCONCLUSIONSREFERENCES |
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