The Effect of Alkalis on the Silica Content of Mantle-Derived Melts

Geochimica et Cosmochimica Acta, Vol. 62, No. 5, pp. 883–902, 1998 Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/98 $19.00 1 .00

Pergamon

PII S0016(98)00028-3

The effect of alkalis on the silica content of mantle-derived melts M. M. HIRSCHMANN,1 M. B. BAKER,2 and E. M. STOLPER2 1

Dept. of Geology and Geophysics, University of Minnesota, Minneapolis, Minnesota 55455-0219, USA 2 Division of Geological and Planetary Sciences, Caltech, 170-25, Pasadena, California 91125, USA (Received May 7, 1997; accepted in revised form November 13, 1997)

Abstract—A large body of experimental evidence shows that at low and moderate pressure (,1.5 GPa), alkali-rich silicate liquids coexisting with Mg-rich olivine and orthopyroxene are richer in silica than typical basalts. This phenomenon is caused by the tendency of alkali ions to reduce the number of Si-O-Si linkages in the melt, which translates to negative deviations from ideality for mixing between alkalis and silica and which requires increases in alkalis to be accompanied by increases in silica for liquids in equilibrium with mantle peridotite. P2O5 and TiO2 have an effect opposite to alkalis, and when these elements are also enriched in the liquid, the high silica contents caused by alkali-enrichment may be reduced or eliminated. The effect of alkalis on the silica content of melts equilibrated with magnesian olivine and orthopyroxene is reduced at higher pressure, such that silica enrichments in alkali-rich melts will be small if the equilibration pressure is greater than ;1.5 GPa. This pressure effect is largely the result of decreases with pressure in the extent of polymerization for all olivine 1 orthopyroxene-saturated liquids. As pressure increases and liquids in equilibrium with olivine and orthopyroxene become less polymerized, proportionally fewer alkalis break up highly polymerized (Q4) silica tetrahedra, and, therefore, alkalis have less effect on the activity coefficient of silica. Secondarily, the observed changes with pressure may also be related to changes in the energetics of alkali-silica interactions. Because equilibration of alkali-rich melts with mantle peridotite only produces high silica at low and moderate pressures, small degree partial melts of anhydrous peridotite formed during adiabatic upwelling will not typically be silica-rich. However, if liquids rich in alkalis, perhaps formed by selective leaching of Na2O and K2O from peridotite during upward percolation, equilibrate with the mantle at depths ,1.5 GPa, they will become silica-rich. Such silica-rich liquids, now preserved as glass inclusions in spinel peridotite xenoliths, are probably restricted to the shallowest part of the mantle (,45 km). Copyright © 1998 Elsevier Science Ltd mantle. We introduce these three topics in more detail in the following paragraphs. Experiments designed to simulate small degrees of partial fusion of fertile peridotite at 1 GPa produced alkali- and silica-rich liquids at ,5% partial melting (Baker et al., 1995). This result has been controversial (Walter et al., 1995; Baker et al., 1996; Falloon et al., 1996), in part because it seemed to conflict with earlier experimental work that suggested that near 1 GPa the SiO2 contents of small degree partial melts of peridotite would be similar to, less than, or only slightly greater than higher degree melts (Mysen and Kushiro, 1977; Jaques and Green, 1980; Falloon and Green, 1987; Falloon and Green, 1988; Kinzler and Grove, 1992a; Hirose and Kushiro, 1993). However, it has long been known that alkalis cause increases in the silica contents of liquids in equilibrium with olivine (ol) and orthopyroxene (opx) in simple systems (Kushiro, 1975); Baker et al. (1995) argued that they had merely observed this same effect in a natural system. In recent years, many experimental studies have been published that document compositions of silicate liquids in equilibrium with natural and synthetic peridotite mineral assemblages (Kinzler and Grove, 1992a; Hirose and Kushiro, 1993; Soulard and Wood, 1994; Walter and Presnall, 1994; Kushiro, 1996; Kinzler, 1997). One of the major goals of this paper is to examine whether the high silica liquids first reported by Baker et al. (1995) are consistent with this body of data. Alkalis are enriched in near-solidus melts because they

1. INTRODUCTION

Although alkalis represent a minor fraction of typical mantle rocks, silicate liquids equilibrated with mantle minerals can be quite enriched in alkalis under certain circumstances. For example, because K2O and Na2O are incompatible with respect to the minerals in spinel and garnet peridotites, liquids formed by small extents of partial melting of fertile peridotite can contain 6 – 8 wt% alkalis (Baker et al., 1995; Kushiro, 1996). Silica-rich glass inclusions in spinel peridotite xenoliths contain up to 13 wt% alkalis (Draper, 1992; Schiano and Clocchiatti, 1994) and provide an even more extreme natural example. It has long been known that alkalis have profound effects on the thermodynamic properties of silicate liquids, and in particular on the activity of silica (Kushiro, 1975; Ryerson, 1985). However, the quantitative effects of high concentrations of alkalis on the silica contents of liquids equilibrated with mantle minerals are controversial (Baker et al., 1995; Walter et al., 1995; Baker et al., 1996; Falloon et al., 1996). In this paper we review existing experimental evidence to clarify the effect of alkalis on the silica content of mantle melts and to explore the effects on the compositions of alkali-enriched mantle magmas of pressure and of other elements (P and Ti) that are enriched in near-solidus melts. We also review the significance of these observations for the thermodynamic properties of such liquids and for magmatic processes in the 883

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are usually incompatible in peridotite minerals. There are, however, other incompatible minor elements such as P and Ti that also may be enriched in small-degree melts sufficiently to affect phase equilibria. These elements have effects on mineral cotectics that differ from those of alkalis (Kushiro, 1975; Ryerson, 1985; Toplis et al., 1994), and, therefore, the character of near-solidus melts may be influenced by the possibly competing effects of several different incompatible elements. Also, because the solidus is crossed at depths substantially greater than 1 GPa in most or all regions where peridotite partial melting occurs, it is important to examine whether the effect observed by Baker et al. (1995) is to be expected at higher pressures. The second goal of this paper is to explore the influence of minor elements such as Ti and P and of pressure on the silica contents of partial melts of peridotite. A quantitative understanding of the mixing properties of mantle-derived magmas is a prerequisite for constructing accurate thermodynamic models of mantle melting (Hirschmann et al., 1998). In the geochemically important nearsolidus region, this requires a description of the energetics of mixing of alkalis, P2O5, and TiO2 with other melt components. Early attempts to use thermodynamic models to predict the character of near-solidus partial melts of peridotite appear to capture the major characteristics of the melting behavior of fertile peridotite and have even had success at predicting some subtle effects observed in the experiments (Baker et al., 1995), but further improvements are necessary. Of particular importance is an accurate model of the activliq ity of silica, aSiO , which in partial melts of peridotite is 2 fixed by the coexistence of olivine and Ca-poor pyroxene. Variations in the silica contents of liquids coexisting with lherzolitic (ol 1 opx 1 clinopyroxene (cpx) 6 spinel (sp) 6 garnet (gt) 6 plagioclase (plag)) or harzburgitic (ol 1 opx 6 sp) residues thus provide a direct measure of the activity coefficient of silica in mantle-derived magmas, and consequently can be used to explore those compositional factors and mixing properties that most influence the silica contents of mantle-derived melts. The third and final emphasis of this paper is to show how data on the relationship between alkalis and silica in such systems can provide important constraints on mixing properties of mantle melts and on thermodynamic models that are emerging as useful tools for modeling petrogenesis (Hirschmann et al., 1994; Asimow et al., 1995; Asimow et al., 1997; Hirschmann et al., in press). 2. ALKALI-SILICA RELATIONS FOR MELTS COEXISTING WITH OLIVINE 1 LOW-CA PYROXENE

2.1. Moderate and Low Pressures We first examine experimental evidence at moderate and low pressures, which for the purposes of this paper we define as being less than 1.5 GPa. Using the diamond aggregate technique at 1 GPa, Baker and Stolper (1994) and Baker et al. (1995) reported compositions of partial melts of a fertile peridotite composition, MM3, for melt fractions ranging from 2 to 22%. Revised analyses of the glasses from these experiments are given in Appendix A of this paper. There is a strong correlation between silica and alkalis, with glasses

Fig. 1. SiO2 vs. wt% total alkalis for (a) partial melts of MM3 peridotite for liquids coexisting with ol 1 opx 1 cpx 1 sp with revised analyses of Baker et al. (1995) glasses given in Appendix A. Line is best fit to data. (b) Partial melts coexisting with ol 1 opx 1 cpx 6 sp 6 plag for systems NCMAS (Walter and Presnall, 1994), NCMFAS (Soulard and Wood, 1994), and PHN-1611 peridotite (Kushiro, 1996), compared to best fit MM3 trend from (a). Pressures are indicated in GPa. (c) Compositions of liquids in equilibrium with forsterite 1 enstatite at 1 bar in systems K2O-SiO2-MgO and Na2O-SiO2-MgO (Roedder, 1951; Schairer et al., 1954).

from experiments performed at lower temperatures (and consequently smaller melt fractions) having both elevated alkalis and SiO2 (Fig. 1a). All of the liquids shown in Fig. 1a

Effect of alkalis on the silica content of mantle-derived melts

coexist with a spinel lherzolite (ol 1 opx 1 cpx 1 sp) mineral assemblage. Most importantly from the point of view of alkali-silica relations is that the silica activity of the liquids is fixed by the coexistence of magnesian ol and opx with nearly constant composition, i.e., as melt fraction increases from 2 to 22%, the forsterite content of ol only increases from 90.2 to 91.2. Glass compositions from partial melts of MM3 can be compared to other experimental glasses quenched from melts coexisting with magnesian ol and opx and having high or variable alkali contents (Fig. 1b). At pressures between 0.7 and 1.1 GPa, NCMAS peridotite-analogue experiments (Walter and Presnall, 1994) show alkali-silica trends similar to the MM3 results. In addition, alkali-rich, small-degree partial melts of a different fertile peridotite composition, PHN-1611, are also enriched in silica (Kushiro, 1996), and the slope of the PHN-1611 data at each pressure is similar to the MM3 trend. PHN-1611 differs in composition from MM3 in several respects, but most importantly it has much more K2O (0.14 wt%) than MM3 (which has approximately 0.01 wt% K2O, judging from the K2O content of nearsolidus liquids of known melt fraction, see Appendix A). Thus, partial melts of PHN-1611 are richer in alkalis for any fixed melt fraction, and their K2O/Na2O ratios approach unity near the solidus (Kushiro, 1996). However, owing to the greater molecular weight of K2O, the molar concentrations of alkalis in partial melts of PHN-1611 are less than those of other liquids depicted in Fig. 1b at similar Na2O 1 K2O weight percent. With this distinction in mind, alkalisilica trends of partial melts of PHN-1611 and MM3 are quite similar. Sandwich-technique experiments in which alkali-rich melts were reacted with peridotite assemblage minerals in the synthetic system CMFAS also yield silica-rich liquids (Soulard and Wood, 1994). The two glass compositions reported produce a trend parallel to that observed in experiments on MM3 (Fig. 1b). Additionally, two recent studies near 1 GPa also report silica- and alkali-rich liquids buffered by magnesian ol and opx (Robinson et al., 1996; Draper and Green, 1997). The trend between alkali and silica contents found near 1 GPa for complex liquids in equilibrium with lherzolitic minerals is paralleled by results at 1 atmosphere for forsterite 1 enstatite-saturated liquids in simple Na2OMgO-SiO2 and K2O-MgO-SiO2 systems (Roedder, 1951; Schairer et al., 1954; Fig. 1c). The near-parallelism of these trends with the 1 GPa data is the key observation; the higher silica contents of the 1 bar liquids primarily reflect differences in the location of cotectics on a wt% basis between synthetic and natural systems. Also, the results of nearsolidus, 1 bar partial melting experiments on the fertile KLB-1 peridotite are qualitatively similar in that the nearsolidus melts are markedly enriched in silica relative to higher temperature melts, although Na2O and K2O analyses were not reported (Takahashi, 1993). It is important to note that for the studies reviewed in this section, variations in alkali content are accompanied by variations in the concentrations of other oxides (e.g., CaO, MgO, FeO, Al2O3) and in temperature and that these parameters also affect the silica contents of liquids in equilibrium with ol and opx. As alkalis increase along each of the trends

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in Fig. 1b., MgO, FeO, CaO, and temperature decrease and Al2O3 increases. However, based on data in simple systems, it is unlikely that these variations can account for the observed increases in SiO2 content, and in fact, most of them probably partially counteract the observed trends. For example, experiments in simple ternary systems suggest that decreases in FeO and CaO result in decreases in the SiO2 contents of liquids coexisting with ol 1 opx (Kushiro, 1975). Decreases in MgO cause decreases in the SiO2 conliq centrations of liquids where aSiO is buffered by other co2 tectics, such as pseudowollastonite plus tridymite and diopside plus tridymite and changes in Al2O3 have little effect on any of these cotectics (Kushiro, 1975). Decreases in temliq perature cause small decreases in aSiO buffered by ol 1 opx 2 (Sack and Ghiorso, 1989) and thus, all other things being equal, in the silica contents of ol 1 opx-buffered liquids. So the trends depicted in Fig. 1 would likely be more pronounced were it not for covariations of temperature and these other melt components with alkalis. Differing concentrations of other oxides (CaO, MgO, FeO, Al2O3) in the bulk compositions do, however, partially explain why the trends in Fig. 1b are offset from one another, as different bulk compositions lead to different liquid compositions and temperatures at any given liquid alkali content. In order to avoid too great an influence of variations in these additional compositional parameters, in examining peridotite and synthetic peridotite partial melting experiments we consider only liquids coexisting with lherzolitic residue. (In the case of Na2O-MgO-SiO2 and K2O-MgO-SiO2 experiments, where there is no effect of other oxides, we consider liquids saturated with just ol 1 opx.) High temperature partial melts of peridotite that coexist with only ol and opx have low alkalis and wide ranges of concentrations of other oxides (Hirose and Kushiro, 1993; Takahashi, 1993; Baker and Stolper, 1994). For these high temperature liquids, it is very likely that variations in these other oxides affect SiO2 more than their small variations in alkali contents. For example, this is probably why SiO2 varies inversely with Na2O at large extents of melting (Baker and Stolper, 1994). Although the nine experimental studies reviewed above vary in detail, they all show that at low and moderate pressures, liquids in equilibrium with lherzolitic or harzburgitic mineral assemblages have silica contents that are strongly correlated with total alkali contents, and remarkably, considering the wide range of compositions involved in the comparison, the slopes of the silica-total alkali trends are similar in nearly all of these cases. In addition, liquids with .4 –5 wt% total alkalis all have .52 wt% SiO2; i.e., more than that typical of basalt. These results contrast strongly with what has been conventional wisdom; i.e., it is generally accepted (McKenzie and Bickle, 1988; Albarede, 1992; Kinzler and Grove, 1992b; Langmuir et al., 1992) based primarily on earlier experimental studies (Mysen and Kushiro, 1977; Jaques and Green, 1980; Falloon and Green, 1987; Falloon and Green, 1988; Kinzler and Grove, 1992a) that the SiO2 content of small degree partial melts of peridotite is lower, similar to, or only slightly higher than larger degree melts. However, none of the early (pre-1992) experimental studies included glasses with .4 wt% alkalis and most only included a few experiments in which liquid co-

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exists with cpx. Extrapolation of the above-mentioned trend of SiO2 increasing with melt fraction for harzburgitic residues (e.g., Baker and Stolper, 1994) to low melt fractions is at least in part responsible for the inaccurate conventional view of SiO2 vs. melt fraction trends. The incorrect conclusions that are drawn from this extrapolation illustrates well one of our major points, i.e., that such direct extrapolations of experimental data at high melt fractions to near-solidus conditions are very poorly constrained and should be viewed with caution. 2.2. Role of P2O5 and TiO2 Although the experiments summarized in Fig. 1 show a strong correlation between alkali and silica contents in liquids coexisting with lherzolitic residue at low to intermediate pressure, two important studies in which alkali-rich silicate liquids were equilibrated with peridotite minerals at moderate pressure (Kinzler and Grove, 1992a; Hirose and Kushiro, 1993) reported only small increases in liquid SiO2 relative to less alkali-rich liquids. For example, at 1 GPa, the composition of a near-solidus partial melt of fertile peridotite KLB-1 with 4.87 wt% Na2O 1 K2O has only 0.8 wt% more SiO2 than a higher-degree partial melt of KLB-1 with only 2.56 wt% alkalis (Hirose and Kushiro, 1993). Isobaric trends for liquids equilibrated with lherzolitic minerals from the study of Kinzler and Grove (1992a) show either small increases or small decreases in silica with increasing alkali concentrations. These results therefore appear to be inconsistent with the those of the studies summarized above and in Fig. 1. However, most of the alkali-rich liquids in these two studies contain appreciable P2O5 (and elevated TiO2 in the case of the experiments of Kinzler and Grove, 1992a), and as we describe in this section, this may explain the apparent conflict. Most of the high alkali (Na2O 1 K2O . 4 wt%) glasses from the experiments of Kinzler and Grove (1992a) contain 0.3– 0.4 wt% P2O5, and except for a subset of P2O5-free experiments at 1.2 GPa, the P2O5 contents of these glasses are positively correlated with total alkali contents (Fig. 2a). Moreover, many of the high-alkali glasses also contain between 1.5 and 2.5 wt% TiO2 (Kinzler and Grove, 1992a), more than the 1.0 –1.5% reported in most other near-solidus partial melts of fertile peridotite (Hirose and Kushiro, 1993; Baker and Stolper, 1994), and much more than the 0.6 wt% TiO2 reported in near-solidus experiments by Baker et al. (1995) (though 3 GPa partial melts of PHN-1611 reported by Kushiro (1996) contain up to 2.2 wt% TiO2). P2O5 concentrations in glasses are not reported in the study of Hirose and Kushiro (1993), but the peridotite starting compositions, KLB-1 and HK-66, have 0.03 and 0.07 wt% P2O5, and so small degree partial melts of these peridotites are expected to be P2O5-rich; e.g., if the bulk distribution coefficient for P is 0.02 (Anderson and Greenland, 1969), ,5% partial melts of KLB-1 and HK-66 will have .0.4 wt% and .1 wt% P2O5, respectively. In contrast, experimental studies in which strong increases in silica accompany alkali enrichment were all performed with low-P2O5 starting materials. The MM3 composition used by Baker et al. (1995) contains very little P2O5, as it was constructed from acid-washed

Fig. 2. (a) P2O5 vs. total alkalis in wt% for liquids coexisting with ol 1 opx 1 cpx 6 sp 6 plag from experiments of Kinzler and Grove (1992a). (b) SiO2 vs. total alkalis for the same set of liquids. There is little correlation between SiO2 vs. total alkalis at most pressures, but for the P2O5-free experiments at 1.2 GPa, this correlation is significant. Line is best fit through P2O5-free 1.2 GPa data and has an r2 of 0.79. Note that the high alkali-high P2O5 liquids (circled) have low SiO2.

mineral separates; the lowest temperature liquids contain ;0.1 wt% P2O5 (Appendix A). The studies of Soulard and Wood (1994) and Walter and Presnall (1994) used synthetic P2O5-free materials. To our knowledge, the P2O5 content of the PHN-1611 peridotite investigated by Kushiro (1996) is not known; it is listed as trace in the analysis of Nixon and Boyd (1973). Not all liquids in the study of Kinzler and Grove (1992a) contain elevated P2O5 (Fig. 2a). In one series of experiments at 1.2 GPa, P2O5-free starting materials were used and liquids saturated with ol 1 opx 1 cpx from this series show a strong positive correlation between SiO2 and alkalis (Fig. 2b). This suggests that the correlation between alkalis and P2O5 in most of the Kinzler and Grove (1992a) experiments

Effect of alkalis on the silica content of mantle-derived melts

(and that we also infer for the Hirose and Kushiro, 1993 experiments) is partially responsible for the differences in the silica-alkali trends observed in these studies and those depicted in Fig. 1. The influence of highly-charged cations such as P and Ti on the silica content of ol-opx-saturated liquids has not previously been noted in experiments on actual or complex model peridotites. However, it was anticipated from experiments on simple systems showing that such cations increase the stability of opx at the expense of ol and cause decreases in SiO2 of liquids in equilibrium with both minerals (Kushiro, 1975; Ryerson, 1985). These highly charged cations are believed to complex with network modifying cations, thereby causing increases in the degree of silica polymerization of silicate tetrahedra (Ryerson, 1985). As this is the opposite of the effect of alkalis, the effects of P2O5 and alkalis on liquid SiO2 would be expected to cancel one another for a suite of liquids in which P2O5 and alkalis are positively-correlated (e.g., Fig. 2a). Experiments on simple systems and basalts at 1 atmosphere demonstrate the effect of P and Ti on the SiO2 content of ol 1 opx-saturated liquids. In the system MgOSiO2-P2O5 at 1 atmosphere, addition of P2O5 decreases the silica content of liquids in equilibrium with forsterite 1 enstatite by 1.1 wt% for each weight percent P2O5 added (Ryerson, 1985). One atmosphere experiments on a natural basalt show an even greater effect for P2O5: the SiO2 contents of liquids on the ol 1 pigeonite cotectic decrease by at least 2.5 wt% per weight % P2O5 added (Toplis et al., 1994). Water-saturated experiments in the system forsterite-diopside-SiO2-P2O5-H2O at 2.0 GPa show that addition of 2 wt% P2O5 decreases the silica content of the ol 1 opx cotectic by approximately 6 wt% (Kushiro, 1975). In the system MgOSiO2-TiO2, SiO2 is reduced by 0.9 wt% for each 1 wt% TiO2 added (Ryerson, 1985), though phase diagrams deduced by MacGregor (1969) suggest that TiO2 has a smaller effect on SiO2 as pressure increases. Thus, concentrations of P2O5 on the order of 0.3– 0.4 wt% P2O5, combined with high TiO2 concentrations, could decrease the silica concentrations of ol 1 opx-saturated liquids significantly, and we consider it very likely that the correlation between alkalis and P2O5 in the Kinzler and Grove (1992a) (and inferred for Hirose and Kushiro 1993) experiments mask the effect of alkalis on silica content. 2.3. Effects of Pressure An important aspect of the relationship between alkali and silica contents of silicate liquids in equilibrium with ol and opx is that the increase in silica accompanying increases in alkalis is pressure-dependent. The increases in silica content associated with high alkalis diminish as pressure increases. This is illustrated in Fig. 3a, where variations in wt% SiO2 vs. wt% alkalis over a range of pressures are shown for peridotite partial melting (Kushiro, 1996) and NCMAS synthetic peridotite experiments (Walter and Presnall, 1996). Note that the trends based on three or more experiments at a given pressure are generally linear. Thus, at each pressure, the rate of change in wt% SiO2 vs. wt% total alkalis can be encapsulated as a slope, and Fig. 3b shows the slopes for a

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wide range of experiments from a number of studies of synthetic and natural systems. In Fig. 4a, alkali vs. SiO2 trends (plotted using mole fractions) are shown for a larger set of NCMAS experiments; slopes from simple and natural systems are plotted in Fig. 4b; the use of mole fractions is thermodynamically more meaningful and in Fig. 4b corrects somewhat for the difference in molecular weight between Na2O and K2O. Figures 3 and 4 demonstrate that experimental studies on liquids coexisting with ol 1 opx 1 cpx show large increases in silica content associated with high alkali contents at low and moderate pressures; however, the effect of alkalis decreases with increasing pressure and is near zero (or may be negative) at 3 GPa. This generalization applies whether the experiments are conducted on naturally-occurring, complex bulk compositions or compositionally simpler model systems. Moreover, this is not a small effect; for example, at 1 GPa the increase in wt% SiO2 per wt% increase in alkalis is about 1.0 6 0.3 (Fig. 3b), indicating that an alkali-rich liquid having 6 wt% total alkalis in equilibrium with lherzolitic minerals would have 3–5 wt% more SiO2 than a higher degree melt with only 2 wt% total alkalis. At 3 GPa, the expected difference in silica content for similar differences in alkali contents would be only 0 –1.5%. The scatter in Figs. 3b and 4b may reflect differences in the bulk compositions of the various systems (i.e., ranging from simple alumina-free synthetic systems to natural peridotite), differences between the effect of Na2O and K2O, or from experimental or analytical artifacts. However, the scatter does not obscure the trend of decreasing influence of alkalis on silica content for ol 1 opx-saturated liquids (and thus on their activity coefficients for silica; see below) with increasing pressure. To our knowledge, a pressure dependence to the effect of alkalis on the silica-content of peridotite partial melts has not been noted previously, though related effects have been inferred from analyses of simple system phase diagrams (Kushiro, 1975; Morse, 1980). The increase in the silica contents of liquids of constant silica activity with increasing alkali contents at low and moderate pressures is thought to be related to breaking up of adjoining silica tetrahedra by alkalis, thereby reducing the activity coefficient of silica (Kushiro, 1975; Ryerson, 1985). As pressure increases, dry melts in equilibrium with ol and opx, even those without alkalis, have a higher proportion of network-modifying cations (notably Mg and Fe) and, relative to lower pressure ol 1 opx-saturated melts, have fewer silica tetrahedra linked to one another. So the structural effect of alkalis and its influence on silica activity may, therefore, become less important at higher pressure. Note that pressure affects this aspect of melt structure indirectly, via changes in the composition of higher pressure ol 1 opx 6 cpx-saturated liquids, and not primarily owing to a pressure-induced change that would occur at constant melt composition. However, a secondary cause of the observed effect may be a more direct influence of pressure on melt structure. These phenomena can be explored via a thermodynamic analysis, which we detail in the following sections.

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Fig. 3. (a) Wt% SiO2 vs. wt% Na2O 1 K2O over a range of pressure (labeled in GPa) for partial melts of lherzolite (PHN-1611 Kushiro, 1996) and of NCMAS model peridotite (Walter and Presnall, 1994) coexisting with ol 1 opx 1 cpx 6 sp 6 plag 6 gt. Also shown are compositions of high alkali, high silica glasses from spinel peridotite xenoliths (Draper, 1992; Schiano et al., 1992; Schiano and Clocchiatti, 1994; Schiano et al., 1994; Schiano et al., 1995), and three estimates of average continental crust (Taylor and McLennan, 1985; Shaw et al., 1986; Rudnick and Fountain, 1995). (b) The slope ol2opx W ­XSiO 2 of wt% SiO2 vs. wt% Na2O 1 K2O, vs. P in GPa for liquids in equilibrium with Mg-rich ol 1 opx 1 cpx ­XW Alk P 6 plag 6 sp 6 garnet. Included are partial melting experiments on peridotite compositions MM3 (Baker and Stolper, 1994; Baker et al., 1995) and PHN-1611 (Kushiro, 1996), NCMAS (Walter and Presnall, 1994 with Na-free data at 2.3, 3.2, and 3.4 GPa from Gudfinnsson and Presnall, 1996) and NCMFAS model peridotites (Soulard and Wood, 1994), the 1.2 GPa P2O5-free experiments of Kinzler and Grove (1992a), and data from the Na2O-MgO-SiO2 (NMS) and K2O-MgO-SiO2 (KMS) liquids coexisting only with ol 1 opx (Roedder, 1951; Schairer et al., 1954). Also plotted are slopes extracted from liquids saturated in ol 1 opx 1 cpx 1 sp at 1.5, 1.7 and 1.9 GPa from Kinzler (1997). Large uncertainties for the Kinzler (1997) data are probably because trends at each pressure combine experiments with differing starting compositions. Slopes of experiments at 2.1 and 2.3 GPa from Kinzler (1997) are not plotted because the data are too scattered to allow regression ol2opx W dXSiO 2 of a meaningful trend. For NMS and KMS experiments, is from the interval between 0 and 5 wt% Na2O or W dXAlk P K2O (see Fig. 1c). Error bars are 1s errors from linear regression of SiO2 vs. alkali trends. Where absent, errors are smaller than plotting symbol or slopes are determined from two points.

S D

S D

Effect of alkalis on the silica content of mantle-derived melts

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Fig. 4. (a) Na2O vs. SiO2 mole fractions for liquids in equilibrium with ol 1 opx 1 cpx 6 sp 6 plag 6 gt in the system NCMAS (Walter and Presnall, 1994). Data at XNa2O 5 0 at 3.2 and 3.4 GPa from Gudfinnsson and Presnall (1996). Datum at 2.3 GPa and XNa2O 5 0 interpolated from CMAS data at 2 and 2.4 GPa from Walter and Presnall (1994) and Gudfinnsson and Presnall (1996) (b) As in Fig. 3b, but with SiO2 and total alkalis calculated in mole fractions rather than wt%.

3. SILICA ACTIVITY OF MANTLE-EQUILIBRATED MELTS

The effect of alkalis on silica content of liquids in equilibrium with an olivine 1 orthopyroxene-bearing mineral assemblage can be understood in terms of the activity of silica, which is fixed by equilibrium between liquid, ol, and opx through the reaction Mg 2SiO 41SiO 2 N Mg 2SiO 6 olivine

liquid

(1)

orthopyroxene

During small and moderate degrees of mantle melting, vari-

ations in ol and opx compositions are small. Therefore, as partial melting of peridotite progresses at fixed pressure, liq aSiO will be nearly constant, even though liquid composi2 tions vary considerably. This is illustrated using the MELTS algorithm (Ghiorso and Sack, 1995), with which we have calculated the silica activity prevailing during calculated partial melting of MM3 peridotite at 1 GPa (Fig. 5). From the solidus up to the exhaustion of cpx, calculated to be near liq 18% melting, aSiO increases from 0.29 to 0.33. This modest 2 increase is caused primarily by the increase in temperature; the small changes in ol and opx composition have little

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M. M. Hirschmann, M. B. Baker, and E. M. Stolper

liq liq Fig. 5. Activity (aSiO ), activity coefficient (gSiO ) and mole frac2 2 tion (XSiO2) of silica in partial melt of MM3 fertile peridotite (Baker and Stolper, 1994) at 1 GPa calculated as a function of extent of melting (F) using the MELTS algorithm (Ghiorso and Sack, 1995). Standard state is unit activity of pure silica liquid at any T and P. liq Inset: aSiO buffered by pure forsterite and enstatite at 1 GPa, 2 calculated from the models of DePaolo (1979) (dashed line; D’79), and Ghiorso and Sack (1989) (solid line; GS’89). The difference in liq calculated temperature dependence of aSiO reflects improved mea2 surements of the thermochemical properties of the minerals and silicate liquid.

liq effect on aSiO over this interval. If mixing of melt compo2 nents in silicate liquids were close to ideal, then the change liq in aSiO would cause the mole fraction of SiO2, XSiO2, in a 2 mantle-equilibrated melt to increase slightly with increasing amounts of melting. But mixing is not ideal, and, therefore, changes in the mole fraction of SiO2 at these low melt fractions are dictated largely by the effects of changing melt composition. liq Because aSiO in ol 1 opx-saturated liquids varies little 2 with melt fraction, any changes in liquid composition that liq affect the activity coefficient, gSiO , must be accompanied by 2 compensating changes in XSiO2 (i.e., such that their product is approximately constant). As shown in Fig. 5, MELTS liq calculations predict that at 1 GPa gSiO is significantly lower 2 (0.6) in alkali-rich near-solidus partial melts of peridotite than it is near the exhaustion of cpx (1.2). Because of the liq near-constancy of aSiO over this range in melt fraction, 2 liq lower near-solidus values of gSiO must be accompanied 2 by higher XSiO2. Thus, even though liquids formed from varying degrees of melting of peridotite will all have essenliq tially the same aSiO , those formed near the solidus at 2 low and intermediate pressures (whether by equilibrium or fractional fusion) will be considerably richer in SiO2. From a purely thermodynamic perspective, the large decreases liq in gSiO predicted by MELTS for alkali-rich liquids are 2 the result of a strong negative enthalpy of mixing between Na2SiO3 and SiO2 in the silicate liquid model of Ghiorso and Sack (1995). This feature is consistent with independent thermochemical and phase equilibrium measurements in compositionally simple silicate melts at low pressure that indicate strong negative enthalpies of mixing

along alkali-silica binaries (Navrotsky, 1995) and with valliq ues of gSiO less than unity derived from thermodynamic 2 analysis of the effect of alkalis on mineral cotectics (Ryerson, 1985; Hess, 1995). In contrast to the results of calculations based on MELTS, liq early calculations of variations in aSiO for systems buffered 2 by ol and opx showed more pronounced temperature dependencies (Carmichael et al., 1974; DePaolo, 1979; see inset to liq Fig. 5). Because they predicted much lower aSiO near the 2 solidus, these calculations reinforced the prevailing view that silica contents of near-solidus partial melts of peridotite would be lower than in melts formed by higher degrees of melting (Green, 1971). However, more accurate estimates of the thermodynamic properties of forsterite, enstatite, and liquid silica (Richet et al., 1982; Berman, 1988) show that these earlier calculations significantly overestimated the liq temperature dependence of aSiO , which in turn led to incor2 rect predictions of the dependence of XSiO2 on melt fraction near the solidus. Note that the differences between the earlier and current calculations largely reflect standard state properties and are not sensitive to assumed mixing properties of ol or opx. Thus, those experimental studies that indicate that the silica contents of near-solidus partial melts of fertile peridotite increase with increasing melt fraction (e.g., Mysen and Kushiro, 1977; Jaques and Green, 1980; Falloon and Green, 1987) cannot be explained in terms of a liq temperature dependence to aSiO , as suggested by DePaolo 2 (1979), and either experimental or compositional factors (e.g., elevated Ti or P) must be invoked. The key point is that at fixed, low to intermediate pressures, variations in XSiO2 of partial melts produced near the fertile peridotite solidus are controlled primarily by melt composition (especially the influence of high, near-solidus concentrations of incompatible elements on the activity coefficient of silica in melts), and not by variations in temperature. 4. QUANTITATIVE MODEL OF ALKALI-SILICA INTERACTIONS

To this point, our explanation of the effect of alkalis on the silica content of liquids near the solidus of mantle peridotite has been largely qualitative. Although it is clear that this phenomenon at low and intermediate pressures relates directly to the large influence of alkalis on the activity coefficient of silica in silicate melts and to the large range and rapid variations in alkalis in near-solidus partial melts of fertile peridotite, a more quantitative treatment of liquid thermodynamic properties is necessary to understand fully the origin of the observed pressure dependence. For this analysis we focus on the effect of Na2O and specifically on experiments in the NCMAS system (Walter and Presnall, 1994; Gudfinnsson and Presnall, 1996), both because this simple system is ideal for thermodynamic analysis and because these studies provide full characterization of phase compositions of liquids coexisting with ol 1 opx 1 cpx 6 plag 6 sp 6 gt over a wide range of pressures and alkali contents. Note that although the low variance of this system helps to isolate the effects of Na2O, the resulting analysis can also give insights into the behavior of natural peridotite because the phenomena of interest occur

Effect of alkalis on the silica content of mantle-derived melts

both in NCMAS and more complex natural systems (e.g., Figs. 1 and 3). 4.1. Activity Coefficients of SiO2 For each of the NCMAS experiments (Walter and liq Presnall, 1994; Gudfinnsson and Presnall, 1996), gSiO can 2 liq liq be calculated by dividing aSiO2 by XSiO2. Values of aSiO are 2 calculated from coexisting ol and aluminous opx based on the equilibrium given in Eqn. 1. In NCMAS, ol is essentially pure forsterite, and the Fo activity can be assumed to be unity, but the activity of enstatite in opx, aopx En , is less than unity, owing to substitution of considerable Al2O3 as well as small amounts of CaO and Na2O (Walter and Presnall, 1994). For orthopyroxenes from the NCMAS experiments, we evaluate aopx En using the model of Sack and Ghiorso (1994). Alternative calculations using the ideal site-mixing model of Gasparik and Newton (1984) yield similar values of aopx En ; e.g., for the opx compositions reported by Walter and Presnall (1994) at 1.1 GPa and 1350°C; the Sack and Ghiorso model yields aopx En of 0.75; the ideal site mixing model yields 0.74. Combining calculated aopx En with the standard state properties for forsterite and enstatite (Berman, 1988) and those for pure silica liquid (1 bar properties from Richet et al., 1982; thermoelastic properties as in Ghiorso and Sack, 1995) allows calculation liq liq liq of aSiO . Calculated aopx En , a SiO2 and g SiO2 for each of the 2 NCMAS experiments (except those where only one experiment is reported at a particular pressure) are tabulated in Appendix B. To isolate the effects of composition, we correct calculiq lated values of gSiO to a common temperature, 1400°C, by 2 assuming that the partial molar excess free energy of mixing # XS ­G is temperature-independent. This assumption, ­n SiO2 n ,T,P i which is justified because heat capacities of mixing of magmatic liquids are negligible (Lange and Navrotsky, 1991), liq allows calculation of activity coefficients at 1400°C, gSiO 2 liq T 1400, from values at any temperature, g SiO , based on the 2 relation

S D

liq g SiO 5exp 2

1

S D # XS ­G ­n SiO2

2

ni,T,P

RT

(2)

so that liq 1400 g SiO 5exp 2

S

D

liq T T ln g SiO 2 1673

(3)

liq It is not necessary to correct gSiO to a common pressure 2 because excess volumes of mixing are small (e.g., Bottinga and Weill, 1970; Lange and Carmichael, 1987). Temperature-corrected activity coefficients for the NCMAS experiments are tabulated in Appendix B. liq Except at the highest pressure (3.4 GPa), gSiO of lherzo2 lite-saturated liquids in NCMAS decreases with increasing XNa2O (Fig. 6a). This illustrates quantitatively for this particular system the strong effect of alkalis on silica activity described in the previous section. The rate of decrease

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liq in gSiO with XNa2O along isobaric NCMAS lherzolite cotec2 liq cotectic ­gSiO 2 tics, (i.e., the slope of the trend at each pres­X Na2O P sure in Fig. 6a) is plotted vs. pressure in Fig. 6b; it is strongly negative at low pressures, but tends to zero as pressure increases. This apparent pressure dependence to alkali-silica mixing behavior mirrors the pressure ol2opx W ­XSiO 2 shown in Fig. 3, but puts these dependence of ­X Alk P observations in a quantitative thermodynamic context.

S D

S D

4.2. Thermodynamic Model Having calculated silica activities for lherzolite-saturated liquids in the NCMAS system, we can now use them to construct a simple thermodynamic model of liquids in this system and explore quantitatively the relationships between liq gSiO , melt composition, and pressure. Our goal in construct2 ing this simple model is to allow us to evaluate the source of liq cotectic ­gSiO 2 (Fig. 6b). The model we the observed trend in ­X Na2O P adopt is a symmetric regular solution formulation with oxide components. Details of the model and its calibration are given in Appendix C and in the captions to Figs. 6 and 7. Except for the choice of components, this approach is mathematically similar to the liquid mixing model incorporated into MELTS (Ghiorso and Sack, 1995). Note that accurate prediction of the thermodynamic properties of silicate liquids in simple systems using regular solution theory generally requires third or fourth-order expansions of the excess free energy of mixing (e.g., Berman and Brown, 1984). Thus, the goal of our simplified model, which uses only a quadratic expansion of the excess free energy, liq cotectic ­gSiO 2 varies with is to gain an understanding of why ­X Na2O P pressure rather than to produce a rigorous model for the energetics of NCMAS liquids. liq As detailed in Appendix C and illustrated in Fig. 7a, gSiO 2 for Na-free liquids saturated with ol 1 opx decreases with increasing pressure. This requires that WSZ, the regular solution interaction between SiO2 and components in the melt other than Na2O (i.e., CaO 1 MgO 1 Al2O3), decrease with increasing pressure. The key insight derived from the thermodynamic model is that this decrease in WSZ accounts for much of the observed pressure dependence in liq cotectic ­gSiO 2 liq (Fig. 6b). In other words, when gSiO is al2 ­X Na2O P liq ready low, the relative effect of alkalis in lowering gSiO 2 becomes less important. Quantitatively matching the trend in liq cotectic ­gSiO 2 with pressure also requires pressure-depen­X Na2O P dent alkali-silica interactions (Fig. 6b), but the significance of this pressure dependence is not clear. As discussed below, it may be primarily an artifact of the highly simplified thermodynamic model.

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S D

S D S D

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M. M. Hirschmann, M. B. Baker, and E. M. Stolper 5. DISCUSSION

5.1. Effect of Pressure on Silicate Liquid Mixing Relations liq 5.1.1. Effect of alkalis on gSiO in magmatic liquids 2

Fig. 6. (a) gSiO2 corrected to 1400°C vs. XNa2O for NCMAS synthetic peridotite experiments (Walter and Presnall, 1994), together with best fit lines for each pressure. Symbols as in Fig. 4. (b) Derivative of gSiO2 cotectic liq ­gSiO 2 with respect to XNa2O, for NCMAS experiments as a ­XNa 2O P function of pressure. Solid circles are calculated from NCMAS experiments and are equal to the slopes of the lines in (a). Curves are calculated using the regular solution model described in the text, with the parameters set as follows: XN is set to 0.01. Mole fractions of other components are calculated from the relation X0.01 5 0.529 – 0.0232 P S ­XS cotectic ­XS cotectic (GPa). Values of are given by the relation ­XN P ­XN P 5 1.646 – 0.403 P (GPa), which is regressed for the NCMAS data in Fig. 4b. WSZ is calculated as a function of pressure as detailed in caption to Fig. 7b. Light solid curves are calculated with values of WSN and WZN indicated to right of curves (e.g., 250,0 indicates WSN 5 250 kJ, WZN 5 0 kJ). Note that only the difference between WSN and WZN is significant, as the curve with WSN 5 2200 kJ and WZN 5 0 kJ is almost indistinguishable from the one with WSN 5 2150 kJ and WZN 5 50 kJ. The heavy solid curve is the best fit to the data, calculated with WSN 5 2198.7 1 30.1 P (GPa) and WZN 5 0. Inset: These curves illustrate the relative effects of parameters that vary as a function of pressure in the main figure. Both are calculated with WSN 5 2150 kJ; WZN 5 0 and X0S varying with pressure as described in caption to (a). ­XS cotectic Curve A: is held constant at 1.0, WSZ varies as in (a), ­XN P cotectic liq ­gSiO 2 to increase with showing that decreasing WSZ causes ­XNa 2O P pressure. This is because strongly negative values of WSZ at high pressure diminish the relative effect of negative S-N interactions.

S D

S D

S D

S D

S D

liq can be underThe connection between alkalis and gSiO 2 stood from consideration of the relationship between melt structure and silica activity and from an examination of how alkalis affect melt structure. In pure SiO2 liquid, all tetrahedra are Q4 (McMillan and Wolf, 1995) (i.e., they are all bonded to four other silicate tetrahedra). As this is the structure of liquid SiO2 in its standard liq state, aSiO in multicomponent silicate liquids is a mono2 tonic function of the abundance of Q4 tetrahedra, and for liq a liquid of a given SiO2 concentration, gSiO is related to 2 the ratio of Q4 tetrahedra to the total number of silicate tetrahedra (Ryerson, 1985; Brandriss and Stebbins, 1988; Hess, 1995). Thus, addition of alkalis to silicate liq liquids will affect gSiO if the associated structural 2 rearrangements reduce the ratio of Q4 to total silicate tetrahedra. Addition of alkalis can cause several different structural rearrangements in melts that reduce the abundance of liq Q4 tetrahedra and reduce gSiO . In simple Al-free silicate 2 liquids, alkalis and other network modifying cations (e.g., Mg21 and Ca21) react with Q4 and other silicate tetrahedra, forming nonbridging oxygens, and depolymerizing the melt (Kushiro, 1975). In metaluminous silicate liquids, however, rather than breaking Si-O-Si linkages, added alkalis complex with alumina (Navrotsky et al., 1982; Ryerson, 1985; Maekawa et al., 1991; George and Stebbins, 1996). In such liquids the number of Si-O-Si linkages is reduced by addition of alkalis owing to replacement by Al-O-Si linkages (Ryerson, 1985). As some of the replaced Si-O-Si linkages formerly were part of bonds between Q4 and other silicate tetrahedra, this liq also leads to reduction of gSiO . Also, a small proportion 2 of alkali ions in aluminosilicate liquids might associate with nonbridging oxygens, thereby contributing to reducliq tion in gSiO by the same mechanism as occurs in Al-free 2 liquids, though NMR spectroscopy of alkali-aluminosilicate glasses with molecular Al/Na . 1 suggests that the abundance of such free alkali ions is small (George and Stebbins, 1996).

decreases

S D

S D S D ­XS ­XN

Curve B:

in

cotectic

varies as in 6a and WSZ 5 225 kJ, showing that

P

­XS ­XN

cotectic

with P

pressure

cause

decreases

in

­g . This is because gSiO2 in liquids with intermediate ­XNa 2O P values of XS (i.e., not close to 1 or 0) is sensitive to XS, as increases in XS cause gSiO2 to approach 1 (as the Raoultian region is approached). ­XS cotectic is large, as at low pressure, increases in gSiO2 Thus, when ­XN P owing to the large increase in XS effectively counters some of the reduction in gSiO2 caused by other effects. liq SiO 2

cotectic

S D

Effect of alkalis on the silica content of mantle-derived melts

893

al., 1982; Ryerson, 1985). Thus, as alkali concentrations in magmatic liquids increase relative to cations with higher field strengths, Al-O-Al linkages (and an equal number of Si-O-Si linkages) are replaced by Al-O-Si linkages, leading liq to fewer Q4 polyhedra and correspondingly smaller gSiO . 2 This line of reasoning can thus explain why low degree partial melts of peridotite, which at low and moderate pressure are poor in MgO and CaO and rich in Na2O relative to liq higher degree melts, have lower gSiO . 2 5.1.2. Changes in

S D liq ­gSiO 2 ­XNa 2O

cotectic

with pressure P

liq of lherzolite-saturated NCThe effect of Na2O on gSiO 2 liq cotectic ­gSiO2 , diminishes with increasing MAS liquids, ­X Na2O P pressure (Fig. 6). Our quantitative modeling (Appendix C) suggests that much of this pressure dependence results from changes in the energetics of mixing between SiO2 and conliq stituents other than Na2O. Thus, as gSiO of Na-free liquids 2 decreases with increasing pressure from 0 to 3 GPa (Fig. 7a), liq cotectic ­gSiO 2 decreases from relatively the magnitude of ­X Na2O P large negative numbers to near zero (circles in Fig. 6b). In liq in Na-poor other words, with increasing pressure both gSiO 2 melts saturated with the lherzolite assemblage and the effect liq on gSiO of adding Na2O become smaller, and this occurs 2 simultaneously with a decrease in the difference between silica-alkali interactions and those between silica and other components. A causal relationship between these trends can be rationalized in terms of changes in liquid structure. As pressure increases, melts saturated with ol 1 opx shift to compositions with progressively fewer fully polymerized (Q4) tetrahedra, chiefly because MgO increases (e.g., Stolliq per, 1980). Thus, gSiO decreases significantly when alkalis 2 are added to the relatively polymerized melts found at lower pressure, because many alkali ions and/or alkali aluminate complexes react with Si-O-Si linkages associated with Q4 tetrahedra, resulting in a decrease in the concentration of Q4 liq tetrahedra. However, gSiO is less affected when alkalis are 2 added to less polymerized high pressure melts because less of the SiO2 present is in Q4 tetrahedra: the aluminate complexes (and/or alkalis) are, therefore, more likely to react with Q3 or Q2 tetrahedra (assuming all such tetrahedra are equally susceptible to reaction), which are not directly reliq lated to gSiO . Note that when Q3 or Q2 tetrahedra are 2 converted to lower Q-number species in such reactions, some Q4 tetrahedra will react and convert to less-polymerized units to restore homogeneous equilibrium between the Q species, but the overall effect will still be smaller than is produced at lower pressure where more Q4 are available for direct reaction. liq cotectic ­gSiO 2 Although much of the observed change in ­XNa 2O P with pressure may be related to changes in the character of the melts that are not directly associated with Na2O itself, the fact liq cotectic ­gSiO 2 in NCMAS canthat the experimental trend in ­XNa 2O P not be fit with constant values of WSN (Fig. 6b) could suggest

S D

S D

Fig. 7. (a) gSiO2 extrapolated to XNa2O 5 0 for NCMAS synthetic peridotite experiments (Walter and Presnall, 1994). These are the intercepts to the lines drawn in Fig. 6a (b) WSZ extracted from values of gSiO2 in (a). Regression gives WSZ 5 213871–12325 P (GPa). Inset: Variations with pressure in proportions of MgO, Al2O3, and CaO making up Z component in pseudoternary N-S-Z projection. The increase in MgO and decreases in Al2O3 1 CaO probably account for the pressure variation in WSZ depicted in the main figure.

At first glance it may seem surprising that the addition of alkalis to aluminosilicate liquids would have a large effect liq on the population of Q4 tetrahedra and thus on gSiO . After 2 all, unless the abundance of Al changes, one may expect that the number of Al-O-Si linkages would be approximately the same. However, NMR spectroscopy indicates that whereas Al in alkali aluminosilicate glasses is associated primarily with Al-O-Si linkages (i.e., Al-avoidance is obeyed) (Oestrike et al., 1987), Al in aluminosilicate glasses with high concentrations of network modifying cations with higher field strengths (e.g., Mg21, Ca21) form clusters (i.e., AlO-Al linkages exist and Al-avoidance is not obeyed), and the abundance of Al-O-Si linkages for a given concentration of Al is proportionally smaller (Merzbacher and White, 1991). Thermochemical studies of synthetic glasses also show that liq gSiO is lower in alkali aluminosilicate glasses than in com2 parable Mg- and Ca-aluminosilicate glasses (Navrotsky et

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S D

894

M. M. Hirschmann, M. B. Baker, and E. M. Stolper

that mixing between alkalis and SiO2 may also be pressuredependent. This is qualitatively consistent with spectroscopic observations. NMR spectra of Na2Si2O5 glasses quenched from a range of pressures indicate a small increase in Q4 silica tetrahedra with increasing pressure (Xue et al., 1991), suggesting that with pressure Na becomes less effecliq tive at depolymerizing SiO2 and reducing gSiO . Similar 2 effects in K2Si4O9 glasses quenched at pressures up to 2.4 GPa have been inferred from Raman spectroscopy (Dickinson et al., 1990) and for K- and Li-bearing aluminosilicate glasses (Mysen, 1990). However, although alkalis are indeed less effective in depolymerizing silica and in reducing silica activity at high pressure, the change in speciation of alkali-silicate glasses with pressure is small at pressures below 5 GPa. For example, for Na2Si2O5 glasses quenched from different pressures, the population of Q4 species increases from 7.9% at 0.1 MPa to 8.4% at 5 GPa and 15.4% at 8 GPa (Xue et al., 1991). Furthermore, a decrease with increasing pressure in the relative abundance of Q4 tetrahedra in metaluminous alkali-aluminosilicate glasses has not been identified to our knowledge. Also, a large pressure dependence to alkali-silica mixing energetics would imply large volumes of mixing, contrary to experimental evidence (Bockris et al., 1956; Lange and Carmichael, 1987). Thus, pressure-dependent changes in alkalisilica mixing properties probably have only a small influence liq cotectic ­gSiO 2 on the observed systematics of below 5 GPa, ­X Na2O P and the pressure-dependent mixing properties implied by the mixing model may reflect complexities not directly taken into account in our model.

S D

liq 5.1.3. Changes in gSiO with pressure 2

One of the more striking trends to emerge from the thermodynamic analysis is the negative correlation between pressure liq and gSiO for Na2O-free liquids (Fig. 7a). This relationship is 2 probably a key factor responsible for the limited range of SiO2 concentrations of all but the lowest degree melts of the mantle over a wide pressure range (Takahashi, 1993). For example, as pressure and temperature increase from 1 to 5 GPa along the peridotite solidus, aSiO2 (buffered by ol 1 opx) decreases by about a factor of 2 (Sack and Ghiorso, 1989) but accompanying liq decreases in gSiO compensate and limit the decrease in XSiO2 to 2 a much smaller range. In the context of our model for NCMAS (see Appendix C), the decrease in WSZ with pressure is responsible for liq the decrease in gSiO in Na-free liquids (the other interac2 tion parameters cannot be involved as the concentration of Na is zero). Although some pressure dependence to mixing between SiO2 and the Z components (Al2O3, MgO, and CaO) cannot be ruled out, it is more likely that the pressure dependence of WSZ originates from a steady shift for liquids along the ol 1 opx cotectic to increasing MgO and decreasing CaO and Al2O3 as pressure increases (see inset to Fig. 7b). This interpretation requires that the free energy of mixing between SiO2 and MgO is more strongly negative than that between SiO2 and CaO and/or Al2O3 such that the overall value of WSZ decreases as the MgO content increases and the CaO and Al2O3 contents

decrease. However, phase equilibria and calorimetric data in simple binary and ternary systems generally suggest liq that CaO is more effective than MgO in reducing gSiO (or 2 liq in some cases, less effective in raising gSiO2) (Kushiro, 1975; Ryerson, 1985; Navrotsky, 1995), so the decrease in CaO with increasing pressure probably is not responsible for the pressure dependence of WSZ. We, therefore, suggest that the increase in MgO relative to Al2O3 is responsible for liq the decrease in WSZ (and thus in gSiO ) with increasing 2 pressure. 5.1.4. Implications for H2O-SiO2 mixing There may be some important similarities between the structural and energetic role of alkalis and H2O in silicate liquids. In simple systems, both alkalis and H2O shift the ol 1 opx cotectic to higher SiO2 contents (Kushiro, 1969, 1975; Warner, 1973). Also, it has long been believed that H2O, like alkalis, depolymerizes silica tetrahedra (Kushiro, 1975), though, as is also true for alkalis, spectroscopic data suggest that hydrogen associates with Al in aluminosilicate liquids (Kohn et al., 1992; Sykes and Kubicki, 1994). Although a recent thermodynamic analysis suggests that H2O liq increases, rather than decreases gSiO (Gaetani and Grove, 2 1998), to the extent that alkalis and H2O do play similar structural and energetic roles in silicate liquids, much of the above discussion about the effect of pressure on alkali-silica mixing relations should apply to H2O-SiO2 mixing relations. Thus, with increasing pressure, addition of water may have a diminishing effect on the silica contents of ol 1 opxsaturated mantle melts, and in particular, the increases in SiO2 associated with addition of water to peridotite systems at low to moderate pressures (e.g., Green, 1973; Mysen and Boettcher, 1975) may be reduced or even become reversed at very high pressures. This hypothesis is consistent with the recent work of Kawamoto and Holloway (1997), who observed that at 10 GPa, water-saturated partial melts of peridotite have substantially lower silica contents than dry partial melts of peridotite at the same pressure. 5.2. Silica Enrichment in Small-Degree Partial Melts of Peridotite A large body of experimental data demonstrate that when magnesian ol 1 opx are in equilibrium with alkali-rich liquids at moderate or low pressures, the liquids will be richer in silica than typical basalt (.52 wt% SiO2; Fig. 1). Whether such alkali- and silica-rich liquids ever actually exist in equilibrium with mantle peridotite depends on additional variables, particularly the fertility of the source (i.e., whether there are sufficient alkalis in the source to lead to high concentrations in partial melts), the concentrations of oxides such as P2O5 and TiO2 that tend to counteract the effects of alkalis (Fig. 2), the concentrations of volatile components (e.g., Green, 1973; Nichols and Ringwood, 1973; Mysen and Boettcher, 1975; Gaetani and Grove, in press), and pressure (Fig. 3). Consequently, depending on the source composition and the depth, small degree partial melts of peridotite or alkali-rich liquids in the mantle formed by other processes may or may not be silicarich.

Effect of alkalis on the silica content of mantle-derived melts

If the P2O5 contents of the liquids from the studies of Kinzler and Grove (1992) and Hirose and Kushiro (1993) are characteristic of small-degree mantle melts, the results of these studies may be more relevant to peridotite partial melting than those studies that lacked significant P2O5 and that consequently show large increases in silica associated with near-solidus alkali-enrichment. We estimate that MORB source regions contain on average 0.013– 0.016 wt% P2O5. This estimate, made by assuming that the depleted mantle contains 0.8 –1.1 ppm Nd (Sun and McDonough, 1989; Hirschmann and Stolper, 1996) and noting that the P/Nd ratio of MORB is roughly constant and equal to 66 (Langmuir et al., 1992), suggests that a 2% melt of fertile peridotite should have ;0.4% P2O5 (assuming a bulk D for P of 0.02; Anderson and Greenland, 1969). Thus, the P2O5 concentrations (0.3– 0.4%) in the high-alkali experimental liquids of Kinzler and Grove (1992a) are reasonable for small degree melts of typical MORB source regions. On the other hand, low-degree melts of MM3 peridotite reported by Baker et al. (1995) have 0.12 6 0.07% (Appendix A), near the detection limit of microprobe analysis, and less than typical near-solidus melts of the MORB source. The starting compositions used by Hirose and Kushiro (1993) have two to four times the P2O5 of the estimated average MORB source, and, therefore, low-degree partial melts from that study probably contain more P2O5 than near-solidus melts of MORB sources, though they may be representative of moreenriched regions. Another consideration is the TiO2 content of near-solidus melts. As noted above, alkali-rich liquids coexisting with mantle minerals from the experiments of Kinzler and Grove are richer in TiO2 than low-degree partial melts of peridotite reported by Baker et al. (1995) and Hirose and Kushiro (1993). We believe that the TiO2 concentrations of liquids in these latter two studies are appropriate for low to moderate pressure small-degree melts of MORB source regions because the starting peridotites have TiO2 concentrations (0.11– 0.22 wt% TiO2; Hirose and Kushiro, 1993; Baker and Stolper, 1994) that are consistent with those likely in MORB source regions (0.13– 0.17% TiO2, based on the observation that the Ti/Eu* ratio in MORB is nearly constant and equal to ;6900; Langmuir et al., 1992, and the assumption that the Eu* concentration in MORB source regions is 2–2.5 times chondritic; e.g., Sun and McDonough, 1989). Thus, the alkali-enriched liquids reported by Kinzler and Grove probably are TiO2-enriched relative to low-to moderate pressure small degree melts of typical MORB source regions at moderate pressures, though the TiO2 contents of these liquids may be representative of partial melts MORB source regions at higher pressures, or of some OIB source-regions or of MORB sources locally enriched in TiO2. Although it is possible to estimate average compositions of particular source regions, relative proportions of alkalis, P2O5, and TiO2 may vary regionally, and, therefore, so will the character of near-solidus melts. Also, if melting is fractional, because alkalis, P2O5, and TiO2 have differing bulk distribution coefficients, the SiO2 content of successive increments of melt may vary in a complex fashion. The key point is the likely extreme sensitivity of phase

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equilibria in the near solidus region of peridotite to minor element budgets. This highlights the danger in extrapolating results of experiments and the stoichiometry of melting reactions in simple model systems to formation of small degree partial melts of peridotite (or indeed any lithology). It also underscores that for selection of natural materials for experiments, it is of great importance that the concentrations of minor elements be judiciously evaluated. Above all, it is clear that experimental and theoretical understanding of the individual effects of minor elements such as Na, K, Ti, P, and possibly Fe31 are necessary to understand the near-solidus melting behavior of the mantle. The pressure of equilibration also affects the SiO2 content of alkali-rich mantle-equilibrated liquids. Although large silica enrichments are found in alkali-rich liquids at low to moderate pressures, the effect of alkalis is reduced or eliminated by increasing pressure. It is important to emphasize that this is caused primarily by the changing effect of alkalis on the silica contents of mantle equilibrated melts (see Fig. 3), and only secondarily by reduction in alkali concentrations of near-solidus liquids at high pressures owing to increasing compatibility of Na in cpx. For example, if at 3 GPa, Dcpx/liq 5 0.4 (Blundy et al., 1995), Dopx/liq 5 0.08 Na Na (Walter and Presnall, 1994; Longhi, 1995) and K is perfectly incompatible, a 1% partial melt of a fertile peridotite with 0.33 wt% Na2O, 0.03 wt% K2O, 12% cpx and 30% opx would have more than 7 wt% total alkalis. Although this is lower than the expected concentration at lower pressures, it would be still enough to strongly elevate SiO2 at lower pressure (Fig. 1), but would have only a small effect at 3 GPa (Fig. 3). It should be kept in mind, however, that the effect of pressure on P2O5-SiO2 and TiO2-SiO2 mixing relations is not well-known, and, therefore, SiO2 could be more or less affected by P and Ti at high pressure. Considering that melting in MORB source regions is thought to begin at depths between 60 and 100 km (Salters and Hart, 1989; Johnson et al., 1990; Hirschmann and Stolper, 1996) and that melting in OIB source regions probably begins at similar or even greater depths beneath thick lithosphere, strongly SiO2-enriched near-solidus melts are not expected in these environments. However, as discussed in more detail below in section 5.4, alkali-rich liquids that do equilibrate with the mantle at low or moderate pressures will be silicarich. 5.3. Origin of Silica Rich Glasses in Spinel Peridotite Xenoliths Alkali-rich (4 –13 wt% Na2O 1 K2O) liquids containing high (54 – 65 wt%) SiO2 are found as inclusions and along grain boundaries in spinel peridotite xenoliths from localities all over the world (Draper, 1992; Schiano et al., 1992; Schiano and Clocchiatti, 1994; Schiano et al., 1994; Ionov et al., 1995; Schiano et al., 1995). These glasses, which also contain substantial H2O and CO2, are highly enriched in incompatible trace elements (Schiano et al., 1994; Ionov et al., 1995; Schiano et al., 1995), are generally thought to be related to metasomatic processes (Draper, 1992; Schiano and Clocchiatti, 1994; Schiano et al., 1994; Ionov et al., 1995),

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and are commonly ascribed to partial melting of exotic materials such as metasomatized peridotite (Draper and Green, 1997), subducted oceanic crust (Schiano et al., 1995), or recycled continental crust (Schiano and Clocchiatti, 1994). Consistent with the experimental evidence reviewed above, anhydrous crystallization experiments demonstrate that liquids similar to these glasses are multiply-saturated with mantle minerals near 1 GPa (Draper and Green, 1997) (although the phase relations of at least some of the naturally-occurring glasses are influenced by high volatile contents; Schiano et al., 1994; Ionov et al., 1995; Schiano et al., 1995). However, the diminishing effect of alkalis at higher pressures suggests that high-silica, high-alkali liquids that are not very H2O-rich cannot be in equilibrium with the mantle at high pressure (Fig. 3). This may explain why silica-rich glasses have not been reported from garnet peridotite xenoliths and is consistent with the narrow range of equilibration pressures (0.7–1.4 GPa) estimated for highsilica glasses in spinel peridotites from localities worldwide (Schiano and Clocchiatti, 1994). Because silica-rich liquids are not likely to be in equilibrium with the mantle at high pressures, we do not expect that metasomatic magmas can be silica-rich at great depth. Even given the extreme alkali-enrichment observed in some glass inclusions, it is unlikely that liquids approaching 60 wt% SiO2 can be in equilibrium with the mantle at pressures greater than 1.5 GPa (Fig. 3a), unless they are highly enriched in H2O. Glass inclusions from arc-derived xenoliths contain up to 5 wt% H2O (Schiano et al., 1995), and so SiO2-rich liquids may be stable at somewhat greater depths in mantle wedges. But such H2O-rich glasses have not been observed in inclusions from OIB and continental basalt localities. Also, inclusions from these environments are typically rich in CO2 (Schiano and Clocchiatti, 1994), which counteracts the effect of H2O. Figure 3a shows that the alkali-silica trend of lherzolite-saturated liquids do not project towards compositions of silicic melt inclusions when the pressure is greater than about 1.5 GPa. Thus, the processes responsible for formation of liquids now represented by most SiO2-rich glass inclusions in spinel peridotites must take place in the lithosphere. Alkali-rich liquids originating at depths greater than ;45 km (;1.5 GPa) may become enriched in silica as they reach shallow depths and equilibrate with surrounding peridotite in a mechanism possibly similar to that envisioned by Kelemen (1986, 1995). In fact, the character of the melts now preserved in inclusions could be largely a consequence of percolation through the lithosphere, as the liquids become enriched in alkalis and other incompatible elements by exchange with peridotite and enriched in silica owing to the increase in alkalis and decrease in pressure. So, the incompatible element enrichments of such liquids may not require sources of unusual composition, as is commonly assumed (Schiano and Clocchiatti, 1994; Schiano et al., 1995; Draper and Green, 1997). Liquid-peridotite exchange during percolation may account for both the strong incompatible element enrichments (Navon and Stolper, 1987) and the resultant silicaenrichments.

5.4. Partial Melting of Peridotite and the Origin of Continental Crust Finally, it has been noted (e.g., Kelemen, 1995; Rudnick, 1995) that the high-silica, high-alkali partial melts of peridotite reported by Baker et al. (1995) bear some similarities to inferred average compositions of the continental crust, which has 4 – 6 wt% total alkalis and 57– 63 wt% SiO2 (e.g., Taylor and McLennan, 1985; Shaw et al., 1986; Rudnick and Fountain, 1995). Trace element evidence is consistent with origin of the continental crust by extraction of small degree melts from the mantle, but it has been thought that such a process would produce liquids too poor in silica to match the major element composition of the continents (e.g., O’Nions and McKenzie, 1988). Although at a given alkali content, high alkali, high silica partial melts of peridotite are not quite as siliceous as average continental crust (Fig. 3a), such melts could in theory contribute to continental crust formation, particularly if the source region contains some H2O. However, the pressure-dependence to the effect of alkalis on liquid silica content means that partial melts of nearly anhydrous peridotite will not be even closely similar to the alkali and SiO2 contents of average continental crust at pressures much greater than 1 GPa or depths . 30 km (Fig. 3A). Thus, direct melting of the mantle to produce silicarich, continental crust-like liquids would require a mechanism for melting fertile peridotite to small degrees at relatively shallow depths. It is unlikely that the quantities of near-solidus melts of fertile peridotite produced at shallow depth in the asthenosphere could be sufficient to generate the observed volume of continental crust. Evidence from mid-ocean ridges suggests that the asthenosphere begins to melt at depths substantially greater than 30 km (Klein and Langmuir, 1987; Salters and Hart, 1989; Johnson et al., 1990; Hirschmann and Stolper, 1996). Mantle substantially colder than the present-day asthenosphere would begin to melt at shallower depths, but at least since core formation the convecting mantle has not been cooler than it is at present (Richter, 1985). Small amounts of near-solidus melts of peridotite might be generated at depths near 30 km owing to incursion of hot magmas from below or perhaps by lithospheric stretching during extension, but in these cases the melts would probably be volumetrically subordinate to more basic melts formed at greater depths (White and McKenzie, 1995). Moderate pressure partial melts of amphibole or phlogopite peridotite may be silica-rich, but they tend to be alkalic (e.g., Dunn et al., 1993) and, therefore, not continent-like. So, although direct shallow melting of fertile peridotite could produce liquids that are similar in many respects to average continental crust, it seems unlikely to us that partial melting of relatively dry peridotite yielding silica-rich liquids is an important mechanism for genesis of continental crust. However, the SiO2 contents of H2O-rich magmas originating in subduction zones or elsewhere and equilibrating with the mantle at shallow depth will be enhanced in cases where alkali contents are high (Kelemen and Ghiorso, 1986; Kelemen, 1995).

Effect of alkalis on the silica content of mantle-derived melts

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6. CONCLUSIONS

REFERENCES

The experimental results of Baker et al. (1995), which show that alkali-rich, near-solidus partial melts of fertile peridotite are silica-rich (.55 wt%) at 1 GPa, are consistent with a wide body of experimental data on silicate liquids in equilibrium with lherzolite and harzburgite residua at similar pressures. This behavior can be expected from the reduction by alkalis of the abundance of Si-O-Si linkages, causing reductions in the silica activity coefficient, as first noted for simple systems at low pressure by Kushiro (1975). At low and moderate pressures (,1.5 GPa), anhydrous alkali-rich silicate liquids in equilibrium with mantle assemblages are richer in SiO2 (.52 wt%) than typical basalts. Because P2O5 and TiO2 have an effect on silica activity that is opposite that of alkalis, high concentrations of P or Ti in high-alkali liquids will reduce or eliminate the silica enrichment that characterizes P- and Ti-poor alkali-rich liquids. At moderate pressures, the SiO2 content of small degree partial melts of peridotite may vary considerably, depending on the relative abundances of alkalis, P2O5, and TiO2. With increasing pressure, alkalis have a decreasing effect on the silica content of liquids in equilibrium with ol and opx. Thus, small degree partial melts of peridotite will not be silicarich when melting begins at depths substantially greater that 30 km, as is the case in MORB and OIB source regions. The pressure dependence of alkalis on the liquid silica content of mantle-equilibrated liquids is related in part to a decrease in gSiO2 with increasing pressure for all melts in equilibrium with ol 1 opx. This decrease is attributed to the lower proportion of highly polymerized SiO2 tetrahedra in alkali-poor, ol 1 opx-saturated liquids at elevated pressures. Because proportionally fewer SiO2 tetrahedra are highly polymerized (Q4), many alkalis react with less polymerized species (Q3, Q2, etc.) and alkalis consequently have a smaller effect on gSiO2. An additional factor may be changes in alkali-silica interactions with increased pressure, resulting in less depolymerization of networks of silica tetrahedra upon addition of alkalis. Anhydrous silica-rich liquids are not likely to be stable in the mantle at depths greater than ;1.5 GPa, regardless of their silica-content. At greater depths, metasomatic melts must be relatively poor in silica, though they may possibly be silica-rich if they are also highly enriched in H2O and poor in CO2. Silica-rich liquids, now preserved as glass inclusions in peridotitic minerals, may form by percolation of small volumes of melt through large volumes of mantle, so long as equilibration continues to relatively shallow depth (.45 km), and does not require partial melts of exotic lithologies.

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ular-orbital calculations. Geochim. Cosmochim. Acta 57, 1039 – 1052. Takahashi E., Shimazaki T., Tsuzaki Y., and Yoshida H. (1993) Melting study of a peridotite KLB-1– 6.5 GPa, and the origin of basaltic magmas. Phil. Trans. Royal Soc. Ser. A 342, 105–120. Taylor S. R. and McLennan S. M. (1985) The Continental Crust: Its Composition and Evolution. Blackwell Scientific. Toplis M. J., Libourel G., and Carroll M. R. (1994) The role of phosphorus in crystallization processes of basalt—an experimental study. Geochim. Cosmochim. Acta 58, 797– 810. Walter M. J. and Presnall D. C. (1994) Melting behavior of simplified lherzolite in the system CaO-MgO-Al2O3-SiO2-Na2O from 7 to 35 kbar. J. Petrol. 35, 329 –359. Walter M. J., Sisson T. W., and Presnall D. C. (1995) A mass proportion method for calculating melting reactions and application to melting of model upper-mantle lherzolite. Earth Planet. Sci. Lett. 135, 77–90. Warner R. D. (1973) Liquidus relations in the system CaO-MgO-SiO2H2O at 10 Kbar PH2O and their petrologic significance. Amer. J. Sci. 273, 925–946. White R. S. and McKenzie D. (1995) Mantle plumes and flood basalts. J. Geophys. Res. 100, 17543–17585. Xue X., Stebbins J. F., Kanzaki M., McMillan P. F., and Poe B. (1991) Pressure-induced silicon coordination and tetrahedral structural changes in alkali silicate melts up to 12 GPa: NMR, Raman, and infrared spectroscopy. Amer. Mineral. 76, 8 –26. APPENDIX A New Analyses of Glasses from the Lherzolite-Saturated Experiments of Baker and Stolper (1994) and Baker et al. (1995) Following significant hardware and software upgrades to the Camscan scanning electron microscope at Caltech, and given the controversial nature of the near-solidus melt compositions reported by Baker et al. (1995) (e.g., Falloon et al., 1996; Baker et al., 1996), we decided to reanalyze glasses from the 1 GPa, lherzolite-saturated experiments of Baker and Stolper (1994) and Baker et al. (1995). The analyses are given in Table A1. Table A2 contains SEM and microprobe analyses of secondary standards (both glasses and minerals) that were used to insure consistency between analyses collected with the SEM and those done with the microprobe. Experimental glasses were analyzed with a Camscan scanning electron microscope fitted with a Link energy dispersive system. The beam current was 0.4 nA on fayalite (;0.45 nA in the Faraday cup in the sample holder), and spectra were collected for 50 s. All analyses were done in spot mode. Raw spectra were processed using the NIST Desk Top Spectrum Analyzer (DTSA) program; peak count data were then reduced using CITZAF (Armstrong, 1995). The Link detector and the DTSA program significantly improved the analytical capabilities of the SEM and were not available when the glass analyses reported in Baker and Stolper (1994) and Baker et al. (1995) were collected. Synthetic oxide mixes (1a, 1b, 2, and 5) fused at 1 GPa and 1400 –1450°C for ;3 h were used as secondary standards. Orthopyroxene and clinopyroxene from the Kilbourne Hole nodule used in the starting material in both the Baker and Stolper (1994) and Baker et al. (1995) experimental studies were also analyzed as secondary standards. EDS analyses of the secondary standards were collected during the same two SEM sessions in which the experimental glasses were reanalyzed. In addition to the SEM analyses, the secondary standards were analyzed with the Caltech 5-spectrometer JEOL 733 microprobe. Operating conditions for the microprobe were an accelerating voltage of 15 keV and a beam current of 10 nA (for the glasses) or 20 nA (for the pyroxenes). For the microprobe analyses of the glasses and the pyroxenes, a 1 mm spot was rastered over an area of ;8 –10 mm. Data were reduced using CITZAF. Comparing the WDS (microprobe) and EDS (SEM) analyses showed that there are slight but systematic differences in the two techniques for most oxides, and thus averages of probe/SEM oxide ratios for the secondary standards were used to adjust the experimental glass analyses. For the oxides SiO2, Al2O3, FeO* (all Fe as FeO), MgO, and CaO these adjustments are less than the 1s envelope calculated for the experimental glasses. The ad-

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M. M. Hirschmann, M. B. Baker, and E. M. Stolper Table A1. Experimental glass compositions.

Run# SiO2 TiO2 Al2O3 Cr2O3 FeO* MnO MgO CaO Na2O K2O Cl

24 (20) 49.8 (4) 0.46 (8) 14.6 (2) 0.28 (11) 6.8 (2) 0.15 (8) 13.3 (2) 12.6 (2) 1.58 (11) 0.02 (2) ,0.04

62a (21) 49.7 (2) 0.48 (6) 15.2 (3) 0.24 (11) 6.7 (3) 0.13 (10) 13.0 (2) 12.6 (2) 1.6 (2) 0.07 (3) 0.07 (5)

16 (17) 49.6 (6) 0.54 (10) 16.1 (3) 0.17 (8) 6.5 (2) 0.13 (10) 12.3 (6) 12.2 (4) 2.0 (3) 0.05 (4) 0.07 (4)

15 (20) 50.3 (4) 0.74 (11) 16.8 (2) 0.11 (7) 6.1 (3) 0.10 (8) 11.4 (2) 11.4 (2) 2.6 (2) 0.07 (5) 0.08 (5)

20 (15) 50.3 (4) 0.67 (13) 17.4 (3) 0.13 (6) 6.0 (3) 0.14 (10) 10.7 (2) 11.0 (2) 3.2 (3) 0.08 (7) 0.06 (3)

55a (22) 49.7 (4) 0.70 (8) 18.0 (3) 0.07 (4) 6.0 (2) 0.14 (9) 10.7 (2) 11.3 (2) 2.8 (2) 0.06 (4) 0.09 (4)

73a (22) 52.1 (5) 0.61 (10) 18.0 (3) 0.07 (6) 5.4 (3) 0.10 (9) 8.8 (3) 9.3 (2) 4.4 (2) 0.23 (4) 0.24 (6)

70a (20) 55.5 (6) 0.61 (10) 18.9 (2) 0.02 (2) 4.1 (2) 0.08 (7) 5.7 (3) 6.5 (2) 7.4 (3) 0.43 (7) 0.35 (4)

Table A2. Secondary standards. Synmix 1a Probe (25) SiO2 TiO2 Al2O3 Cr2O3 FeO* MnO MgO CaO Na2O K2O

57.4 (2) 0.71 (4) 16.98 (9)

SEM (16) 57.8 (4) 0.75 (8) 16.9 (2)

7.01 (11)

6.9 (3)

3.47 (9) 4.74 (5) 9.12 (23) 0.40 (1)

3.6 (2) 4.67 (11) 8.6 (3) 0.42 (4)

Synmix 1b

Synmix 2

Synmix 5

KBH-1 opx

KBH-1 cpx

Probe (15)

SEM (17)

Probe (16)

SEM (16)

Probe (29)

SEM (34)

Probe (17)

SEM (7)

Probe (26)

SEM (26)

52.2 (1) 0.98 (6) 15.96 (9) 0.24 (2) 9.97 (11)

52.6 (4) 1.05 (9) 15.8 (2) 0.26 (10) 9.6 (3)

59.0 (3) 0.23 (5) 10.00 (5)

59.3 (5) 0.31 (11) 10.0 (2)

19.8 (3)

19.5 (4)

5.07 (6) 6.83 (5) 8.02 (9) 0.53 (2)

5.2 (2) 6.57 (12) 8.0 (3) 0.58 (7)

58.7 (2) 0.38 (5) 16.1 (2) 0.03 (2) 6.47 (9) 0.06 (2) 4.99 (7) 6.18 (8) 6.25 (7) 0.34 (2)

58.9 (4) 0.43 (8) 16.0 (2) 0.09 (8) 6.3 (2) 0.09 (8) 5.1 (2) 6.02 (13) 6.5 (3) 0.37 (6)

54.3 (2) 0.10 (2) 4.85 (7) 0.55 (4) 6.00 (6) 0.14 (2) 32.9 (14) 0.85 (2) 0.11 (1)

54.4 (4) 0.22 (9) 4.95 (8) 0.56 (14) 6.1 (2) 0.16 (10) 32.2 (3) 0.86 (10) 0.25 (15)

51.72 (9) 0.40 (5) 6.78 (7) 1.04 (5) 2.82 (4) 0.08 (2) 15.3 (1) 19.9 (1) 1.60 (3)

51.6 (3) 0.46 (9) 6.9 (2) 1.09 (8) 2.9 (2) 0.11 (10) 15.2 (2) 19.6 (2) 1.83 (2)

2.03 (5) 5.01 (7) 2.99 (5) 0.22 (1)

2.02 (14) 4.9 (2) 3.3 (3) 0.23 (6)

justments for Na2O varied as a function of Na2O content of the glass and ranged from ,1% to ;12% (relative). Comparing WDS and EDS values for the TiO2, Cr2O3, and MnO contents of the secondary standards showed that the ratio of probe-value/SEM-value decreased with decreasing oxide concentration and could reach a value of 0.5 within 25–150% of the detection limit of the element in question. Smoothed curves fit to the secondary standard analyses were used to adjust the TiO2, Cr2O3, and MnO concentrations of the experiments glasses measured with the SEM. No adjustments were made to the SEM K2O abundances. Details of all of these corrections will be presented in Baker et al. (in prep.). The number of analyses are given in parentheses after each sample number. None of the old analyses reported in Baker and Stolper (1994) and Baker et al. (1995) are included in these averages. The number in parentheses next to each wt% value is 1s in terms of the least units cited; e.g., 49.8 (4) represents 49.8 6 0.4. Further notes on the analyses: The observed Cl abundances in the experimental glasses are probably from trace residues of insoluble chlorides that formed on the surfaces of the mineral separates during washing with dilute HCl. Analyzed P2O5 contents in the experimental glasses were at the detection limit (;0.1 wt% for 50 s counts). This detection limit is based on repeated analyses of P-free primary and secondary standards. The average of fourteen long-duration analyses (200 s) of glass shards from run 70a yield a P2O5 content of 0.12 (7) wt%. This value is twice the detection limit for 200 s analyses, and thus, based on our data for TiO2, Cr2O3, and MnO (see above), probably represents an upper limit for the P2O5 content in the quenched glass from run 70a. Based on ion-microprobe measurements of 1H1/ 30 Si1, the 70a glass contains 0.4 (1) wt% H2O. These measurements were done by Laura Wasylenki and Adam Kent at LLNL with a modified Cameca IMS-3f ion microprobe using energy-filtering techniques similar to those discussed in Ihinger et al. (1994). 1H1/30Si1 values were converted to absolute H2O abundances using a calibration curve constructed from analyses of well-characterized glass standards and the SiO2 content of the 70a glass. Due to some sputtering of the epoxy during the analysis of the small glass shards, the 0.4 wt% value

probably represents an upper limit on the water content in the 70a glass. We expect that water contents in the glasses from the higher temperature experiments are #0.4 wt%. Comparing these new analyses with those reported in Baker and Stolper (1994) and Baker et al. (1995) show that for TiO2, Al2O3 (excluding 70a and 73a), Cr2O3, FeO*, MgO, CaO, and Na2O (excluding 70a), the new and old compositions overlap at the 1s level. The new SiO2 contents are lower than those in the old analyses; for the higher temperature experiments (runs 20, 55a, 15, 16, 24, and 62a) these differences are, on average, ;0.4 wt%, and probably reflect improvements in processing EDS spectra using the DTSA program. For the lowest temperature run (70a), the difference in silica content is 1.8 wt% (57.3, old vs. 55.5 wt%, new). About 60% of this difference in SiO2 content is a result of the difference in the sodium concentrations in the old (5.7 wt%) vs. the new (7.4 wt%) analyses. Raising the Na2O abundance in the old analysis to 7.4 wt% and renormalizing the remaining oxides causes the old and new Al2O3 and SiO2 values to overlap at the 1s and 2s levels, respectively. The low Na2O concentration in the old analysis of the 70a glass probably reflects sodium loss during the 200 s counting time, and is why we lowered the count times to 50 s and analyzed multiple high-sodium glasses as secondary standards. Note that these new analyses do not affect any of the conclusions of Baker et al. (1995). The new analyses still show that at 1 GPa the silica content of the partial melt increases dramatically with decreasing temperature near the peridotite solidus. Finally, while the analysis of the 70a glass reported in Baker et al. (1995) is quartz-normative, the analysis listed above is nepheline-normative. This agrees with the assertion of Falloon et al. (1996); however, the normative character of the near-solidus melt was never an issue in the interpretation of Baker et al. (1995). Most of the glass fragments from run 69a (the other 1250°C, twostage experiment reported in Baker et al., 1995) were lost during repeated polishings needed to remove multiple carbon coats and a gold coat. Thus, this sample was not reanalyzed. However, based on a simple scaling relationship using the new and old analyses of the glass

Effect of alkalis on the silica content of mantle-derived melts from run 70a, we estimate that the glass in run 69a contains 54.6 (7) wt% SiO2 and 8.0 (8) wt% Na2O 1 K2O. APPENDIX B Silica Activity and Activity Coefficients for Liquids in NCMAS Synthetic Peridotite Experiments (Experimental Data of Walter and Presnall, 1994 and Gudfinnsson and Presnall, 1996).

P (GPa) 0.7 0.7 0.7 0.9 0.9 0.9 1.1 1.1 1.2 1.2 1.4 1.4 1.4 1.7 1.7 2.0 2.0 2.0 2.0 2.3 2.3 2.3 2.7 2.7 2.7 3.0 3.0 3.2 3.2 3.4 3.4 3.4

T (°C) 1285 1245 1225 1302 1265 1240 1350 1255 1345 1295 1370 1365 1355 1420 1380 1470 1455 1440 1424 1490g 1490 1480 1535 1518 1507 1575 1531 1595 1580 1615 1585 1580

aopxa En 0.7474 0.7453 0.7436 0.7455 0.7357 0.7329 0.7358 0.7175 0.7274 0.7188 0.7186 0.7156 0.7138 0.7121 0.6997 0.7034 0.7076 0.7089 0.7053 0.6980g 0.7025 0.7050 0.6892 0.6912 0.6970 0.6694 0.6895 0.6819f 0.6817 0.6903f 0.6960 0.6840

liq d gSiO 2

liq e gSiO 2

T 5 1400°C

XSiO2b

XNa2Ob

liq c aSiO 2

T 5 Texp

0.5073 0.5625 0.5805 0.4983 0.5410 0.5578 0.4851 0.5554 0.4851 0.5554 0.4928 0.5046 0.5266 0.4888 0.5284 0.4677 0.4767 0.4888 0.5038 0.4618g 0.4725 0.4750 0.4577 0.4734 0.4826 0.4516 0.4790 0.4500f 0.4537 0.4533f 0.4578 0.4596

0.0000 0.0307 0.0425 0.0000 0.0261 0.0518 0.0000 0.0552 0.0000 0.0552 0.0140 0.0249 0.0435 0.0130 0.0525 0.0000 0.0110 0.0260 0.0484 0.0000g 0.0123 0.0243 0.0116 0.0312 0.0443 0.0000 0.0402 0.0000f 0.0185 0.0000f 0.0202 0.0109

0.3383 0.3332 0.3302 0.3124 0.3043 0.3003 0.2904 0.2731 0.2763 0.2678 0.2571 0.2555 0.2539 0.2359 0.2281 0.2174 0.2175 0.2166 0.2142 0.2003 0.2015 0.2015 0.1813 0.1808 0.1816 0.1657 0.1684 0.1618 0.1611 0.1570 0.1571 0.1542

0.6669 0.5922 0.5688 0.6269 0.5625 0.5384 0.5986 0.4917 0.5695 0.4821 0.5216 0.5063 0.4821 0.4825 0.4317 0.4649 0.4562 0.4432 0.4251 0.4337 0.4263 0.4242 0.3960 0.3818 0.3763 0.3668 0.3516 0.3595 0.3551 0.3447 0.3433 0.3356

0.6858 0.6217 0.6034 0.6443 0.5892 0.5712 0.6078 0.5229 0.5802 0.5047 0.5278 0.5136 0.4917 0.4783 0.4361 0.4502 0.4446 0.4346 0.4199 0.4147 0.4072 0.4071 0.3675 0.3568 0.3535 0.3303 0.3240 0.3303 0.3176 0.3006 0.3050 0.2984

901

working model that allows exploration of the effect of liquid compocotectic liq ­gSiO 2 sition and pressure on . We project NCMAS liquids into ­XNa 2O P a pseudoternary composed of three components, S (5SiO2), N (5Na2O), and Z (5CaO 1 MgO 1 Al2O3). Equation B1 thereby reduces to

S D

liq RT ln g SiO 5~W SNX N1W SZX Z!~12X S!2W ZNX ZX N 2

(C2)

S D S D S D and

­g ­XNa 2O liq SiO 2

liq ­ g SiO 2 ­X Na2O

cotectic

is given by

P

liq g SiO 2 RT

cotectic

5

P

1

S S

~W SN2W ZN! X Z2X N

S D D S D D ­X S ­X N

cotectic

1W SZ X S212~2X Z2X N!

S D

2

1~W SN1W ZN!X N

P

S D

­X S ­X

cotectic

(C3)

cotectic liq ­gSiO ­XS cotectic 2 Note that depends on because the relative ­XNa 2O P ­XN P liq proportions of XS and XZ affect gSiO2. Thus, pressure variations in cotectic liq ­gSiO ­XS cotectic 2 (Fig. 3b) affect the trends in Fig. 6b. In ­XN P ­XNa 2O P cotectic ­XS , which is controlled by the mixing properties of the theory, ­XN P liquid, is predicted by the mixing model and, therefore, need not be used as an input. However, it is preferable to use the empirically ­XS cotectic observed values of from Fig. 4 to understand the mixing ­XN P properties, as the model adopted is too simple to accurately predict both cotectic liq ­gSiO ­XS cotectic 2 and . ­XN P ­XNa 2O P

S D

S D

S D

S D

S D

S D

Model Calibration from NCMAS Experiments (a)

Activity of enstatite in aluminous opx (composition from Walter and Presnall, 1994, except where noted) calculated relative to a standard state of unit activity in orthopyroxene of pure clinoenstatite at any temperature and pressure, using the model of Sack and Ghiorso (1994). (b) Oxide mole fractions of liquids reported by Walter and Presnall (1994), except where noted. (c)Activity of silica in liquid coexisting with ol and aluminous opx at the temperature of the experiment, Texp, calculated relative to a standard state of pure silica liquid at the temperature and pressure of interest. (d)Activity coefficient of SiO2 at Texp. (e)Activity coefficient recalculated to 1400°C, as described in the text. (f)Data from Gudfinnsson and Presnall (1996). (g)Values interpolated at 2.3 GPa from CMAS experiments at 2 and 2.4 GPa from Walter and Presnall (1994) and Gudfinnsson and Presnall (1996). APPENDIX C Quantitative Thermodynamic Model Model formulation In a symmetric regular solution (Hildebrand and Scott, 1964), the liq activity coefficient of silica, gSiO , is given by 2

O n

liq 5 RT ln g SiO 2

i51

W i SiO2X i2

1 2

OO n

n

i51

j51

W ijX iX j

(C1)

where Xi and Xj are mole fractions of liquid components, and Wij are terms describing the energy associated with interaction between components. Because the model is symmetric, Wij 5 Wji. Comprehensive calibration of Eq. B1 for NCMAS or peridotite systems is beyond the scope of this contribution, so for our present purposes, we construct a

The composition of NCMAS liquids along lherzolite cotectics as a function of pressure can be interpolated from the trends determined from the NCMAS experiments (Walter and Presnall, 1994; Gudfinnsson and Presnall, 1996). Because XS is roughly a linear function of XN (Fig. 4a), liquid composition can be described at each pressure by an ­XS cotectic intercept at XN 5 0, X0S, and a slope, , which is the ­XN P 0 parameter shown in Fig. 4b. XS can be taken from the same fits used to ­XS cotectic . Note that X0S is uniquely determined at each determine ­XN P pressure because the assemblage liquid 1 lherzolite minerals is isobarically invariant in CMAS. For interpolation at any pressure, ­XS cotectic and X0S are parameterized as linear functions of pressure, ­XN P with coefficients given in the caption to Fig. 6. The NCMAS experiments also constrain the pressure dependence of liq WSZ because at XN 5 0, gSiO depends only on WSZ. Therefore, WSZ can 2 liq be calibrated from examination of gSiO in CMAS liquids or alterna2 liq tively from NCMAS experiments extrapolated to zero XN (i.e., gSiO 2 liq from the XNa2O 5 0 intercepts in Fig. 6a). These represent gSiO in real 2 or extrapolated CMAS liquids in equilibrium with the lherzolitic asliq semblage. gSiO at X0S decreases systematically with increasing pressure 2 (Fig. 7a), so the calculated value of WSZ decreases linearly as well (Fig. 7b). Note that the ‘‘Z’’ component in this model is the sum of CaO, MgO, and Al2O3, and as elaborated in Section 5.1.3, the calculated variations in WSZ could be related to variations with pressure in the relative proportions of these oxides in the liquid. In principle, WZN and WSN are independent variables affecting the activities of components in NCMAS liquids, but when XN is small only differences in WZN and WSN have a significant impact on mixing

S D

S D

S D

902

M. M. Hirschmann, M. B. Baker, and E. M. Stolper

behavior. This is because WZN and WSN appear in Eqn. B3 only as the difference (WSN 2 WZN), except for the term (WSN 1 WZN)XN, which has negligible effect when XN is small (see lines marked 2200,0 and 2150,250 in Fig. 6b). Thus, the NCMAS experiments of Walter and Presnall (1994), performed over a range of small values of XN, do not strongly constrain the absolute values of WZN and WSN. Given this limitation, we arbitrarily set WZN to zero and explore how variations in liq dgSiO 2 WSN influence . dXNa 2O With all the constraints on the variables we have stipulated, the only remaining independent parameter on the right hand side of Eqn. B3 is WSN. Before trying to estimate values of WSN, we will first explore how cotectic liq ­gSiO 2 . This will pressure variations in other variables affect ­XNa 2O P give an indication of the extent to which these other variables may be cotectic liq ­gSiO 2 responsible for pressure variations in . All calculations ­XNa 2O P are made with XN 5 0.01 and XZ is given by 1 2 XS 2 XN. Although cotectic liq ­gSiO 2 calculated with Eqn. B3 would differ absolute values of ­XNa 2O P slightly if other reasonable (,0.1) values of XN were used, the resulting trends would not be different. In Fig. 6b, curves are drawn for a range of values of WSN, with other variables allowed to vary with pressure as described above. At low cotectic liq ­gSiO 2 with inpressures, all such curves show increases in ­XNa 2O P creasing pressure, a key feature of the trend extracted from the lherzolite-saturated NCMAS liquids; however, they all tend to flatten or have maxima as pressure continues to increase, in contrast to the values extracted from the experiments. Comparison of these curves with

S D S D

S D

S D

values of

S D liq ­gSiO 2 ­XNa 2O

cotectic

based on the NCMAS experiments shows that P

S D

cotectic liq ­gSiO 2 can be accounted for ­XNa 2O P by variations of factors other than the mixing of Na2O and SiO2 (i.e., with a constant value of WSN. For example, the distinctive form of these curves, increasing from low to moderate pressure and then leveling off, ­XS cotectic reflects primarily the variations with pressure of WSZ and ; ­XN P cotectic liq ­gSiO 2 i.e., variations in WSZ result in increases in with pres­XNa 2O P cotectic ­XS sure, whereas the competing effects of variations in lead to ­XN P cotectic liq ­gSiO 2 leveling off or even decreasing at sufficiently high ­XNa 2O P pressures. This can be demonstrated by calculations with each of these variables held constant, rather than allowed to vary with pressure (see the inset to Fig. 6b where curves have been calculated using Eqn. B3 ­XS cotectic holding either (curve A) or WSZ (curve B) constant). ­XN P The curves calculated with constant WSN in Fig. 6b account for some cotectic liq ­gSiO ­XS cotectic 2 variation in , but they cannot match the vs. ­XN P ­XNa 2O P pressure trend extracted from the experiments. The trend can be reproduced if WSN is allowed to increase with pressure, and the best fit to the data is shown as heavy solid line in Fig. 6b and given by

much of the pressure sensitivity of

S D

S D

S D

S D

S D S D

S D

W SN ~kJ!52198.69130.12 P ~GPa!.

(B4)