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The solubility of olivine in basaltic liquids: an ionic model
Grochsmu
*I Cormnchimwo
Pergamon Press
Acm
Vol.
43. pp. 1241 IO 1251
Ltd.1079Printed I” GreatBritain
The solubility of olivine in basaltic liquids: an ionic model CLAUDE T. HERZBERG
Harvard-Smithsonian
Center for Astrophysics. 60 Garden Street. Cambridge. MA 02138. U.S.A.
(Received 16 November 1978; accepted in revised form 22 March 1979)
Abstract-A simple ionic model which describes the solution of the forsterite component in silicate liquids is reported. The melting relation is represented:
of olivine
(MgaSiO,),, = 2(Mg2+), + (SiO:-), and is extended to all silicate liquids by normalizing their compositions to 4 oxygens. At I bar, the temperature at which olivine is in equilibrium with any alkali-depleted basaltic composition can be calculated to within +3O”C. This error is increased considerably when applied to terrestrial basalts which contain several weight percent alkalis. Alkalis interfere with the equilibrium by generating strongly repulsive interionic forces which can be crudely modelled in a manner consistent with constraints imposed by regular solution theory. The model quantifies the reduced activity of SiO:- monomers due to increasing SiOl concentrations in the melt. This is a consequence of polymerization which does not appear to operate gradually over the entire spectrum of mafic and ultramafic compositions. The coordination of alumina in melts which precipitate olivine only appears to be dominantly octahedral. Titanium acts as a polymerizing agent by interconnecting previously isolated SiO:- monomers. Calcium associated with normative diopside tends to exhibit small but perceptible repulsive forces involving Mg”.
INTRODUCTION UNDERSTANDINGhow temperature,
melt composition, and pressure determine the solubility of olivine in basaltic melts is one of the most fundamental problems posed to igneous petrologists who are concerned with modelling the crystallization of basaltic magmas and the partial melting of their source materials. The contribution by ROEDERand EMSLIE(1970) on terrestrial basaltic compositions marked the first serious attempt to quantify olivine solubility as a function of temperature. Subsequent experimental studies on alkali-depleted lunar compositions (LONGHI et al., 1978). the work of ROEDER(1974), and a review of the experimental data in simple and complex chemical systems (LEEMAN,1978) have shown that silica activity and alkalis impose a strong control on olivine solubility. Efforts to quantify the melt composition variable have met with limited success because of the limitations inherent in the component activity models. For a discussion of some of the problems the reader is referred to LONGHI et al. (1978) and LEEMAN(1978). All attempts at modelling component activities in liquid solutions have been based upon the mixing of oxides (MgO, FeO. etc.) with various Temkin-like mixing methods of Al’+ and Si4’ cations to approximate silica activity. It is interesting to note, however, some similarities and differences with respect to solid solutions. Analogues of the simple Temkin model in which different cations’mix on independent sites have been used with some success on pyroxenes (WOOD
and BANNO, 1973; WOOD, 1974, 1975; HERZBERG, 1978 and many others), although recent work on Fe2 + -Mg ordering-disordering between sites. metaloxygen bonding considerations, and reciprocal lattice effects challenge this simplistic model (GRAY, 1978; R. SACK, personal communication; FLEET. 1974; WORD and NICHOLLS, 1978). Other solid solution models involving the mixing of molecular species have been addressed elsewhere (KERRICK and DARKEN, 1975). Despite the complexities and limited progress, implicit in all solid solution mixing models is an integral number of oxygens and sites for stoichiometric solid solutions. Thus, the thermodynamic treatment of liquid solutions for which component activities are expressed as mole fractions of oxide species is fundamentally different. This becomes particularly evident for liquid solutions which change composition because of crystallization of one or more phases. Inspection of such liquids expressed as mole fractions of the components would show a considerable variation in the number of oxygens in the melts. Similarly. a suite of evolved liquids which vary in SiOZ content would be expected to exhibit a range of possible melt structures (HESS. 197 1) which cannot be reflected in oxide component activities. In an analysis.of HZ0 solubility in silicate melts, BURNHAM(1975) extended his mode1 from the system NaAlSisOs-HZ0 to more complex systems by normalizing the liquids to the 8 oxygen albite stoichiometry. The apparent success of this mixing model seems rooted in its ionic character, and is more
1241
C. T. HERZBERG
1242
closely analogous to the thermodynamic treatment of solid solutions than are all other liquid solution models that have been proposed. In this paper the solubility of olivine in anhydrous basaltic liquids at I bar is explored within the constraints imposed by an ionic mixing model: all liquid compositions are expressed in terms of 4 oxygens. An integration of the component activities thus reflects the overall thermodynamic and structural properties of the melt. The analysis begins with forsterite-fayalite solutions in which the activity of the relevant silica anion species remains constant. The effects of SiO, on the activity of the dissociated silica anion is then deduced from experimental results in the system Ca&MgO-A1203-Si02. The results are then extended to natural lunar and eucrite compositions which are depleted in alkalis. Finally, the effects of nonideal Mg2 + -alkali interactions are assessed from available experimental data, and the possibility of extending the model to natural terrestrial basaltic compositions is addressed.
SOLUBILITY OF OLIVINE IN ALKALI-DEPLETED BASALTIC COMPOSITIONS The solubility of the forsterite component can be represented by the reaction: (Mg2Si0& where the equilibrium K =
= 2(Mg”), constant
of olivine
+ (SiOi-),
(1)
can be expressed:
(%ip2+)t(%iO:-)L
sterite is arbitrarily assigned the value of unity. This represents the structural property of SiOi- tetrahedra isolated from each other (total monomerization) by coordination. Olivine Mg2 - cations in octahedral solid solutions in equilibrium with silicate liquid are assumed to be ideal. The condition for equilibrium of the melting reaction is met where: AG: = - RT In K. At 1 bar equation
(4)
(4) becomes:
AH: - TASZ = -RT which can be arranged
In K
(5)
to:
AH:, +$=
Ink.
RT
The term PAI’: should appear in eqns (5) and (6) but. while fundamentally important at high pressures, is insignificantly small at 1 bar and can be neglected. A plot of In K vs 10*/T of eqn (6) was made for the forsterite-fayalite solidus-liquidus loop of BOWEN and SCHAWER (1935; experimental smoothed curves) using the AH; of forsterite = 29,300 cal mole- 1 from BRADLEY (1962). The results are shown in Fig. 1. Assuming that there is no change in the silica activity of the melt along this join, asio;- of eqn (3) remains at a value equal to unity. As would be expected from the Bradley analysis. the experimental data concur with the above enthalpy of fusion for ideal solid and liquid solutions, although it is possible that small departures from ideality may be interpreted from the deviations from the straight line in Fig. 1. The rela-
(aMgSiOJol
An ionic mixing model (BRADLEY, 1962; KERRICK and DARKEN, 1975) is assumed here for the solid (o/) and liquid (L); that is, Mg’+ mixes on two energetically similar sites. and is octahedrally coordinated. The standard state adopted for this model is taken to be the melting of pure forsterite at 1 bar. As can be seen from eqns (1) and (2), in order for this model to be extended to basaltic compositions which are, amongst other things, richer in SiO,, such liquids must be normalized to 4 oxygen units. For stoichiometric solid solutions treated ionically, such normalizations can be overlooked because the number of sites and oxygens remain constant. Normalizing the liquid solutions to 4 oxygens is considered here to be a requirement of the standard state for this ionic model. In order for the activity of pure forsterite melt to take the value of unity, eqn (2) becomes: K=
(Oh,,2 + ’ YMg*+ X (%iO:_ IL [Mg/(Mg + Fe2 + + Ca + Mn)]21
5.8 (3)
where n is the number of Mg cations in the liquid normalized to 4 oxygens, and yh(pZ+ is the activity coefficient of Mgzc m the liquid. The activity of the (SiOt-), monomer in a melt composition of pure for-
6.2
6.6
104/T (“K) Fig. 1. In K vs the inverse of temperature for the solution of forsterite in melts of the join forsterite-fayalite. Filled circles are from the smoothed experimental data of BOWEN and SCHAJRER(1935). Line is from AH: of forsterite estimated by BRADLEY(1962) for ideal solutions.
The solubility of olivine in basaltic liquids tionship
in Fig. 1 can be expressed: - 14720
In K = ___
T
+ 6.806
where 7 is in degrees Kelvin. An attempt to deduce the ‘GO:- activity of SiO,enriched basalt-like melts in equilibrium with forsterite was made by a synthesis of available experimental data in the system Ca@MgO-A1203-Si02. The data used are: 1. Anorthite-forsterite-silica (ANDERSEN, 1915). 2. Anorthite-forsterite-diopside (OSBORN and TAIT, 1952 with minor modifications from PRESNALL et al., 1978). 3. Forsterite-diopside-silica (KUSHIRO, 1972). 4. Anorthite-diopside-enstatite (HYT~~NEN and SCHAIRER. 1961 with minor modifications from KUSHIRO, 1972). 5. Diopside-pyrope [O’HARA and SCHAIRER, 1963 excluding compositions more pyrope-rich than forsterite-anorthite-silica. These four compositions were excluded because of the probability of Mg2* being fixed by A13’ in order to preserve local charge balance. This is due to CaO/Al,O, < 1 for these compositions (cf. BOTTINGA and WEILL, 1972)]. An estimate of the activity of SiOi- can be made from these data by modifying eqn (3) to: ln
(aSiO:-)L
(Yt.te~
+)i
=
In K - ln (0.5n,,2+)~
(8)
where In K at any temperature is evaluated from eqn (7) (i.e. Fig. 1). Equation (8) is essentially an expression of the extent to which the data in the forsterite primary phase volume departs from the relationship in Fig. 1 [eqn (7)]. This departure is shown in Fig. 2A as a function of Si/O. This is only an approximate solution because it does not consider the small amounts of Ca2+ dissolved in the liquidus forsterite (up to 0.77 wt:,: PRESNALLet al., 1978). An expanded explanation and example of the calculations is given in the Appendix. The data in Ca&MgC&A120&i02 fall within the area outlined in Fig. 2A, where the melts with the highest SiO, contents (SiiO) tend to depart from the relationship of Fig. 1 by about 0.25 to 0.35 In units. Although this departure is quantitatively not very large, it appears significant enough to provide information on SiOiactivity and the structure of the melts. For this reason, Fig. 2A has been translated to the activity-composition diagram of Fig. 2B. Several features of Figs 2A and B merit consideration. In general there is a tendency for SiO:- activity [(jlMe2.)t assumed for the moment to be equal to unity] to decrease in value with increasing total SiO, content (SiiO). although this takes effect only at Si/O values which are greater than about 0.29. Melts on the join forsterite-anorthite (Si/O = 0.25) obey the relationship of Fig. 1 to within &7“C irregardless of CaA120, content. Similarly. melts on the join enstatite-anorthite which are multiply saturated
1243
in both forsterite and anorthite (SijO < 0.29) obey the relationship of Fig. 1. Alumina and calcium chargebalanced to alumina (CaAl,O,) apparently have no effect on the solubility of olivine in basaltic liquids. Temperature also has no obvious effect. The term (cI~~~:-)~ (~~,~+)t of melt compositions with Si/O > 0.29 tends to be influenced by the amount of normative diopside. For example, most melt compositions in the primary phase volume of forsterite in the system forsterite-anorthite-silica [ANDERSEN. 1915; (xcal- - O.~Y,,,+)/(X~,~+ - 0.5~,,,+ + nMrl+) = 0] generally tend to have lower activities of SiOi- for any specified value of Si/O than melts in the system forsterite-diopside-silica [KUSHIRO. 1972; (Xca2- - 0.5yA,)+)/(Xca2- - 0.5y,,,* + nMe’.) < 0.51. It appears, therefore, that Ca2’ plays a dual role in such silicate liquids. Calcium which is not charge balanced to alumina appears free to mix and interact with Mg 2+ in the melts. The radial isopleths of Figs. 2A and B are probably an expression of weak Mg” -Ca2+ repulsive interactions which are quantifiable by the (Y”~~+): term. Thus it appears that in the system CaO-MgO-FeO-A1203-Si02 the only perceptible nonideal interactions of concern are those between Mg2+ and Ca2’ associated with a normative diopside component in such melts. The raw experimental data from forsterite-anorthite-silica and forsterite-diopside-silica are given in Fig. 2A in order to show the general nature of the compositional dependence. Although there is some scatter to the data, the isopleths radiating from 0.29 are an attempt to rationalize the control of composition on SiOi- activity from the entire population of data in the system CaO-MgGA120,-Si02. It should be noted that melts which are multiply saturated in forsterite + low calcium pyroxene _t anorthite in the system forsterite-anorthitesilica (open symbols in Fig. 2A) are not consistent with the remainder of the experimental data. For olivine-melt thermometry this problem is minor, but will be addressed below. Once again, it is apparent from Fig. 2B that the activity of SiO:- tends to decrease in value with increasing total Si02 (Si/O) content of the silicate liquids. This apparently reflects the tendency of such liquids to polymerize by forming branch and ring structures from isolated SiOt- monomers (TOOP and SAMIS. 1962: HE% 1971). The activity of SiOiis thus a statistical function of the number of nonbridging Si-0 bonds in the melt (FRASER, 1977). The addition of alumina to such olivine-saturated melts does not affect the activity of SiOi-. It is probable, therefore. that alumina in melts saturated with olivine is dominantly in octahedral coordination, rather than tetrahedral coordination. This is because tetrahedrally coordinated alumina would probably link up previously isolated SiO:- units via Si-GAL0-Si bonds and thus impose a noticeable control on SiOi-- activity. Although octahedrally coordinated alumina contradicts the structure of feldspar glasses (TAYLOR
C. T. HERZBERG
1244
-.5
- .4
-.3
-.2
-.l
0 + .l .25
.27
.31
.29
.33
.35
Si/O Fig. 2A. In (a,,,~.), (yhlpl+)i of silicate liquids saturated in forsterite in the system CaO-MgO-Al,O,Si02 as a function of SijO. Numbered lines are values of (xCsIf - 0.5~A,,+)/(xc.2. - 0.5~,,,- + nMsJ.) where x, y, and n are the number of cations of CaZ’, Al’+, and Mgzc respectively in the melt normalized to 4 oxygens. Circles are from the system forsterite-anorthite-silica (ANDERSEN,1915); open circles are for assemblages. of forsterite + pyroxene + melt. Triangles are from the system forsteritediopside-silica (KUSHIRO, 1972).
1.0
.6
d
.26
.28
,
,
.30
1
.32
1
.34
Si,/b Fig. 2B. Activity of the SiO:- monomer in the system CaO-Mg@A1,03-SiO, as a function of Si/O. Numbered lines are same as Fig. 2A and probably represent the effects of nonideal MgZ f-Ca* + interactions as given by (y,,++)i. This activity coefficient is probably equal to unity for melts containing no normative diopside. See text for details.
The solubility of olivine in basaltic BROWN. 1978), it is consistent with the probable coordination of alumina in melts which precipitate spine1 (MgAI,O,) at 1 bar. If the coordination of alumina m the melt is in general a reflection of its coordination in the solid, melts which crystallize spine1 must have their alumina dominantly in octahedral coordination. Furthermore, it is known that the primary phase volume of spine1 expands at the expense of anorthite with increasing pressure (O’HARA, 1968; FRESNALL er al.. 1978). This reflects the increased stability of Al“ in melts relative to Al“ with increasing pressure. and is compatible with experimental observations on jadeite glasses (VELDE and KUSHIRO, 1978) and the changes in coordination of alumina in the subsolidus of mafic and ultramafic systems (HERZBERG. 1978). The dual role of alumina, discussed previously by BOTTINGAand WEILL (1972) indicates that the coordination of alumina and its structural role is largely determined by the bulk composition of the melt at 1 bar. Since the solubility of olivine in basaltic liquids is not affected by an anorthite component of the liquids, it may be inferred that Al 3+ in octahedral coordination is in close proximity to Ca*+ of similar coordination so that local charge balance is preserved, or vice versa. If this is the case, Ca’+ in the melt may not mix freely with Me*+, but its location in the melt structure would be determined by the locations of alumina. The structure would not be based on random mixing of Mg” with Ca” and A13+, but with units of (Ca*+, 2A13+). For liquids which become sufficiently enriched in an anorthorite component, but also sufficiently silica-undersaturated (e.g. the composition 1 forsterite + 1 anorthite), the octahedrally coordinated alumina in the melt would be retained by spine1 precipitation although Mg2+, being smaller than Ca’+. would enter into the tetrahedral sites of spinel. Finally, for liquids on the join forsteriteanorthite which become sufficiently enriched in the anorthite component A13+ proxies for Si“’ in tetrahedral coordination. An interesting feature of Figs 2A and B is that SiOi- activity appears to decrease significantly only at values greater than about 0.29 Si/O. This may be an indication of a major structural change in the melts whereby polymerization only becomes operative and proceeds in a gradual manner once the threshold Si/O is surpassed. This structural discontinuity of the melts appears to be analogous to orderdisorder transformations in solid alloy systems (BRAGG and WILLIAMS. 1934). However, it appears that there is a critical melt composition (Si/O = 0.29), rather than a critical temperature as in alloys, that determines the transformation from complete disorder (total monomerization) to the onset of order (polymerization). Such a structural discontinuity was similarly observed by IRVINE and KUSHIRO (1976) from nickel partitioning studies between olivine and basaltic liquids. An inadequacy of Figs 2A and B is that it implies and
liquids
1245
the energetics of Mg’+ -0 bonds does not change with variations in Si02 content. In pure olivine liquids each Mg*+ may be irregularly coordinated with the faces of two isolated SiOi- tetrahedra. With increasing SiOZ content of the melt, Mg*+ may become coordinated with the edges and apices of interconnected silica tetrahedra. which may include oxygens of bridging Si-0-Si bonds. It is clear, therefore, that the relation shown in Figs 2A and B includes interactions between Mg*’ and Si4+. From this treatment of the experimental data it is not possible to distinguish the effects of such interactions, which may be quantified by yye2+ of eqn (3). from the effects of SiO:- activity. However if Mg*+-Si4* interactions are significant within the range of melt compositions considered, they are probably repulsive in nature. This would require Y,.,~_~,values greater than unity. Such positive deviations from ideality would have an opposite effect on the solubility of olivine than would reduced SiO:- activity. Assuming repulsive interactions, SiO:activity must be the dominant parameter which determines the extent to which the experimental data in CaO-Mg@A120,Si02 depart from the relationship in Fig. 1. In order to test how well the ionic model is able to predict the experimentally determined forsterite liquidus relations in CaO-MgO-Al,O,-SiO,. the data are now treated as unknowns. The In K for each experimental result was calculated (see Appendix) and plotted in Fig. 3 against the temperature of the experi-
c
.J
-I
lO’/T(‘K)
Fig. 3. In K vs the inverse of temperature for the solution of forsterite in melts of the join forsterite-fayalite (straight line from Fig. 1). the system Ca0-MgO-AI,O,-SiO, (shaded area), and natural lunar and eucrite compositions (filled circles). The experimental data used, method of calculation, and details of the shaded area are discussed in the text and Appendix.
1246
C. T. HERZBERC
ment. The results in the system CaO-MgO-Al,O,Si02 are contained in the shade area in preference to individual melt compositions because the character of the forsterite primary phase volume has been, in part, determined in relation to the primary phase volumes of anorthite, pyroxenes, and spine]. That is. the intersection of the primary phase volume of forsterite with that of another phase(s) defines a divariant (univariant) equilibrium. It is important to note that the melt compositions which crystallized only forsterite and are removed from a divariant or univariant equilibrium by about 50-lO!ZlO”Care confined to the cross-hatched part of the shaded area of Fig. 3. These are in excellent agreement with eqn (7), shown as the straight line. However, the greatest departures from the line are consistently from those data which define the divariant and univariant equilibria of the forsterite primary phase volume (vertical stripped part of the shaded area) and immediately within the olivine-field by 50-100°C (e.g. open circles in Fig. 2A). There are at least three explanations for this. First, the olivines of such liquids may contain the highest CaO contents. Secondly, the liquids may undergo minor structural changes, hence the activity of SiOtmay be in error. Finally, the error may be experimental in nature; that is, it is generally easier to determine the temperature of the first appearance of forsterite than it is to determine the temperature of the first appearance of forsterite + other phases (ROEDER, personal communication). For the entire population of data in CaO-MgO-A1203-Si02, the maximum error in the determination of the temperature at which forsterite is in equilibrium with the melt from eqn (7) is + 32”C/- 12°C. In order to test the applicability of eqn (7) to natural alkali-depleted olivine-melt pairs, K was calculated for lunar and eucrite compositions on which melting experiments were performed. Again, K was calculated from Fig. 2A and eqn (3) as illustrated in the Appendix for one experimental result. The data were obtained from AKELLA et al. (1976), BIGGAR et al. (1971), HUEBNER et al. (1976). LONGHI et al. (1978), MCKAY and WEILL (1977) STOLPER (1977; and unpublished data), and WALKER et al. (1976, 1977). In K and the known temperature for each experiment are plotted in Fig. 3. In calculating K, however, it was noted that both the high- and low-Ti lunar compositions, in particular those of LONGHI er al. (1978). were in excellent agreement with the line of Fig. 3 if the activity of SiOtwas reduced further by using (Si + Ti)/O in Fig. 2. This result indicates that Ti4+ acts to polymerize such liquids by linking SiOttetrahedra via Si-@Ti0-Si bonding. The net result is a decrease in the number of non-bridging Si-0 bonds. This explanation is consistent with the effects of Ti02 on the shifts in the forsterite-enstatite peritectic equilibrium noted by KUSHIRO (1975) and MACGREC~R (1969). Inspection of the data on natural compositions in Fig 3 shows that the agreement with the simple syn-
thetic systems is excellent. For the entire population of natural compositions, the greatest deviation from the line of eqn (7) is + 30°C. Given (1) the assumptions in the ionic mixing model, (2) the diversecompositions of the data, (3) the temperature range involved, and (4) intra and interlaboratory analytical and experimental errors, the ability to predict the measured temperatures of olivine-melt pairs for the lunar and eucrite compositions with such accuracy is, indeed, encouraging. It is concluded that this ionic mixing model may be applied to all low-alkali basaltic melt-olivine pairs, irrespective of magma type. EFFECTS OF NA+ AND K’ ON OLIVINE SOLUBILITY IN BASALTIC MELTS Due to differences in charge and ionic radii of Mg’+ (0.65A) compared with Na* (0.95A) and K+ (1.33 A), strong effects on the solubility of olivine in silicate melts would be expected. Indeed, ROEDER (1974), LEEMAN (1978), and LONGHI er al. (1978) observed that small amounts of alkalis can significantly reduce the amounts of Mgzc and Fez+ in melts coexisting with olivine. One may also expect that K+, being the larger cation of the alkalis, would have the strongest effect. An attempt is now made to quantify these effects by assessing the magnitude of nonideal interactions for aluminous solutions of Mg’ +-Na’, MgZf -K+, and finally MgzC-Na+-Kf. It is assumed that these three cations are coordinated similarly and that they are allowed to mix with each other. Equation (3) can, once again, be modified to:
(0.5n [Mg/(Mg
)2
+ Fe?*;
+ Mn)]:, I (9)
where In K at any temperature is evaluated from Fig. 1. For pseudobinary melts of the type (Mg-Na) and (Mg-K), the activity coefficient can be assessed from the relation: ln (~~~2+)L
= X&C&.MeNp
+ 2X,,PG.Na--Mg RT
-
~G.M+Jl (10)
for asymmetric Mg-Na solutions WOHL, 1953; for Mg-K solutions Na becomes K in eqn (lo)]. The w’s in equation (10) represent Margules excess free energy parameters for Mg’+-Na+ and Na+-Mg2+ interactions, and X,, = Na/(Na + Mg). The nonideal character of Mg-Na solutions was explored from experimental data in the systems forsterite-anorthitealbite (SCHAIRER and YODER, 1967;
The solubility of olivine in basaltic liquids
. //
1
Lc
.2
.6
.4 Na/(No
i
4
3
.8
+Mg)
Fig. 4. In (u .,>.)i ((I~~~:-)~ vs Na/(Na + Mg) for silicate liquids in equilibrium (?) with forsterite in the systems forsterite-anorthite-albite and enstatite-diopside-albite. The isotherms were fitted to the experimental data according to eqn (10) in the text. Closed circles = all data: open circles = data on the join forsterite-albite: open squares = data on the join enstatite-albite. Variations in SiO:activity contributes to the scatter of the data at 10~ Na/(Na + Mg).
WATSON,1977; HART and DAVIS.1979) and enstatitediopside-albite (SCHAIRER and MORIMOTO. 1959). From equation (9) it can be seen that the extent to which such Na-bearing melts in the forsterite primary phase volume depart from the relationship of eqn (7) (Fig. 1) should give an indication of In (yM,l-)f (a~,~:-)~ This is shown in Fig. 4 as a function of Na/(Na + Mg). It is important to note that there is a considerable scatter in the data which bears no obvious relation to any parameter except a very poor correlation with temperature. Although this may in part be due to the sorts of experimental error normally encountered in high alkali systems, it is also a reflection of the inadequacy of eqn (10) and the parameter Na/(Na + Mg) in resolving interactions involving only Mg and Na cations. The ratio Na/(Na + Mg) was chosen only because of its capacity to rationalize the data. The parameter Na/(Na + Mg + total Ca) was tested but found to produce a much greater scatter in the data and the result could not be satisfactorily modelled in conformity to regular solution theory. Other interactions may involve Mg” and Ca*+. although inspection of Figs 2 and 4 indicates that they will probably not be very large. it is also possible that some Interactions may involve Mg’- and AI’from the albite component of the melt. Bearing these uncertainties in mind, it will be assumed that the ac-
1147
tivity coefficient in equations (9) and (10) and Fig. 4 is due only to interactions between Mg and Na cations. The open symbols in Fig. 4 are for calcium-free melts on the joins forsterite-albite (open circles). and enstatite-albite (open squares). In principle, high accuracy experimental data on these two joins should enable the effects of SiO:- activity to be distinguished from those of nonideal Mg”-Nainteractions. However. the avaiiable data in Fig. 4 indicate that for most compositions Na’ dominates the deviations from the relationship of Fig. 1. At very low- Na’ contents. however. the departure from Fig. 1 appears to be dominated by SiO:- activity (note open squares of Fig. 4). The experimental data are too scattered to resolve in detail a temperature dependence to the departure from ideality. However. the two isotherms shown in Fig. 4 were derived by fitting the data to eqn (10). The simplifying assumption is made that SiO:- activity does not vary and remains at a value equal to unity. The activity coefficients so determined become minimum possible values. Similarly the Margules parameters become minimum possible values, and were determined to be: >, 5650 cal mol - ’
(11)
~G.X”--Mr > 8290 cal mol- I.
(1.2)
LVo,,,_,, and
The data do not allow estimates to be made for any possible temperature dependence to the Margules parameters: that is. the excess entropy contribution to the excess free energy was assumed to be zero. With activity coefficients known from eqns (lOt( 12), the activity-composition diagram of Fig. 5 was constructed at 1450°C. Because of the assumption of unity SiO:- activity. the actual activity-composi-
.2
.4 Mg/(Mg
.6
.8
+Na)
Fig. 5. Influence of Na’ on the activtty of Mg’* m sriicate, ltqutds of the system Ca@Na20-MgO-A1lO,-SiOZ whtch crvstalhze forstertte at 1450-C. The actual acirvttycomposnion curve is located m the shaded area due to uncertamtres m the effect of SIO:- activny Isee text).
C. T. HERZBERG
1248
W o, K--M*b 13720 cal mol - ‘.
.2
A
.6
.8
K/(K +hd vs K/(K + Mg) for silicate Fig. 6. ln(r,,l+)t ho:-IL liquids in equilibrium (?) with forsterite in the systems forsterite-leucite-silica and forsterite-anorthite-orthoclasesilica. Experimental error, uncertainties in SiO:- activity, and unknown Mg zc-A131 interactions may contribute to the scattered data Isotherms were fitted to the experimental data according to eqn (10) in the text.
tion curve must be located within the shaded portion of the diagram. The very strong positive deviations from ideality indicate the strength of the repulsive forces separating Mg and Na cations. Indeed, over a range of about 0.4-1.0 Mg/(Mg + Na) the activity of Mg’+ remains at a “very high value of at least 0.9. However, it appears that such repulsive forces are not so strong as to promote unmixing of two liquid phases. From the relation:
G,, = wG.Mg-N.X&
2 x~a + WG.Na-Mg
XNa x6,
(13)
the excess free energy curves at 1250 and 1450°C are positive and without inflexions. indicating no immiscibility. This is consistent with the single liquid phase reported in the experimental results. Encouraged by the results for Mg-Na melts, partially successful attempts to assess interactions for in the Mg’+ -K+ melts were made for compositions systems forsterite-leucite-silica (SCHAIRER, 1954) and forsterite-anorthite-orthoclase-silica (IRVINE, 1976). The paucity data and the uncertainties regarding interactions other than Mg-K cations place severe limitations on the modelling, but the results are shown in Fig. 6. The Margules parameters used to fit the isotherms to the data are very approximate, but have the values: W G.Mg_-K> 8260 cal mol-’
(14)
(15)
A comparison of Figs 4 and 6 illustrates that aluminous pseudobinary solutions of Mg-K display considerably greater departures from ideality than Mg-Na melts. This is consistent with the above ionic radii considerations. In order to proceed with a detailed analysis of olivine solubility in basaltic melts which contain both Na’ and K’, experimental data in the system Na20K20-MgO-A1,03-Si02 is required so that information on Nat-K’ and K’-Naf interactions can be assessed. These data are required before the pseudobinary relations discussed above can be integrated into an asymmetric pseudoternary solution model as discussed by WOHL (1953). To the author’s knowledge these experimental data are not available. The only relevant experimental data is on natural terrestrial basaltic compositions (ROEDER and EMSLJE, 1970; ROEDER, 1974; LEEMANet al., 1976; DUKE, 1976; D. WALKER on DSDP basalts, personal communication). For these it is difficult to be able to resolve the effects of the many interacting chemical variables. Of considerable concern here is the effect of oxygen fugacity which, because it determines Fe2’/Fe3+, may modify the SiOt- activity. Since alkali loss is a common experimental problem, it may be particularly acute in iron-bearing systems where the alkalis, as well as an externally imposed oxygen fugacity, may (G. M. BIGGAR, personal commodify Fe2+/Fe3+ munication). Additionally, alkali loss during the course of an experiment can substantially modify the relations discussed above (Figs 4 and 6). Through simplifying assumptions it is possible to determine the temperature at which olivine is in equilibrium with any alkali-rich basaltic liquid, but the accuracy is limited to about +lOOC. For readers who are partial to equilibria with such large errors, the method of calculation is available from the author on request. It is clear that the alkali-bearing systems must be systematically investigated before olivine crystallization from terrestrial melts can be modelled with the same degree of accuracy as the lunar and eucrite compositions. CONCLUSIONS The ionic model discussed herein enables the temperature at which olivine is in equilibrium with any alkali-depleted basaltic composition to be calculated to within 430°C. This error is increased substantially when applied to terrestrial basalts which contain several weight percent alkalis. This is due in part to a lack of accurate information on the magnitude of non-ideal Mg-alkali repulsive forces which can be modelled crudely but consistently with regular solution theory. The model predicts and quantifies the reduced activity of SiOa- monomers due to increasing Si02 concentrations in the melt. This is consistent with a statistical decrease in the number of nonbridging
1249
The solubility of olivine in basalttc liquids Si-0 bonds with increasing polymerization. Polymerization does not appear to be a gradual process encompassing the entire spectrum of mafic and ultramafic melt compositions. Throughout a limited range of Si!O values the melt appears to be totally disordered (total monomerization). At a threshold SijO value polymerization (ordering) begins and develops in a gradual manner. This process appears temperature independent. Alumina in association with calcium (i.e. CaAl,O, component) does not affect the activity of (SiOt-),, and thus it is inferred that it is dominantly in octahedral coordination in melts which precipitate olivine only. The coordination of alumina in all melt compositions appears largely determined by bulk composition at 1 bar. Titanium tends to decrease the activity of (SiOi-),. and thus it appears to be a polymerizing agent. The model is sufficiently sensitive to show that there are small repulsive forces between Mg*’ and calcium ions which are in association with normative diopside in the melt.
BURNHAMC. W. (1975) Water and magmas; a mixing model. Geochim. Cosmochim. Acta 39. 1077-l 084. DUKE J. M. (1976) Distribution or the period four transitition elements among olivine. calcic clinopyroxene and mafic sthcate hqutd: experimental results. J. Petroi. 17. 499-52 1. FLEETM. E. (1974) Distortions in the coordination polyhedra of M site atoms in olivines. clinopyroxenes. and amphiboles. Am. Mineral. 59, 1083-1093.~ _
FRASERD. G. (1977) Thermodynamic
orooerties of silicate
melts. In fherntodynamicsin Geolog?. pp. 301 -325. Reidel. GRAY N. H. (1978) Statistical thermodynamic models for orthopyroxene solid solution. Geol. Ass. Canada. Mineralogical with Programs
Ass.
Canada,
Geol.
Sot.
Am.
Abstracts
10. 412. HART S. R. and DAVIS K. E. (1978) Nickel
partitiomng between olivine and silicate melt. Earth Planet. Sci. LEII. 40, 203-219. HERZBERC~ C. T. (1978) Pyroxene geothermometry and geo-
barometry: experimental and thermodynamtc of some subsolidus phase relations in the svstem CaO-MeO-AI,O,-SiO,. chim. &to
42, 945-95-T
-
.’
evaluation
involving pyroxenes Geochint. Cosmo-
A~kno~~ledge,~lenrs-This research was supported by NASA grant NGL 09-015-150 to J. A. WOOD.Thanks are extended to E. STOLPERfor providing unpublished experimental data. The author is indebted to the reviewers J. LONGHI and P. L. ROEDERwhose detailed critiques helped to substantially improve the manuscript.
HESS P. C. (1971) Polymer model of silicate melts. Geochim. Cosntochirn. Acra 35. 289-306. HUEBNER J. S.. LIPIN B. R. and WIGGINS L. B. (1976) Partitioning of chromium between silicate crystals and melts. Proc. Serenfh Lunur Sci. Conf.. Geochim. Cosmochint. Acra Suppl. 7, pp. 1195-1220. Pergamon Press. HYT~NENK. and SCHAIRERJ. F. (1961) The plane enstatite-~ anorthite-diopside and its relation to basalts Carnegie Inst. Wash. Yearb. 60, 125-141.
Addendum
IRVINET. N. (1976) Metastable liquid immiscibility and MgO-Fe0_SiO, fracttonation patterns in the system
For melts on the join forsterite-fayalite, the activity of SiO:- will not remain at unity, but will be some function of temperature (P. C. Hess, personal communicat.ion). The assumption of unity activity is only applicable for a stan-
Mg,SiO,-Fe,SiO,-CaAI,SizOe-KAISi30s-SiOz. Wash. Yearb. 75. 597-61 1.
Car-
negie Inst.
IRVINET. N. and KUSHIRO1. (1976) Partitioning
of NI
and Mg between olivine and silicate liquids. Carnegie Inst. B’ush. Yearb. 75. 668-675. dard state at 1 bar and all temperatures. The AC$ throughKERRIC~ D. M. and DARKEN L. S. (1975) Statistical therout this large melting interval was assumed to be zero; modvnamic models for ideal oxide and silicate solid this is not correct (I. S. Carmichael, personal communicasolutions. with application to plagioclase. Geochim. Costion). Errors generated from the above assumptions are ntochim. Acta 39. 1431-1442. probably overwhelmed by experimental and analytical KUSHIRO I. (1972) Determinations of liqutdus relations in errors (Fig. 3). synthetic silicate systems with electron probe analysis: the system forsterite-diopside-silica at 1 atmosphere. Am. MirIeral. 57. 1260-1271. REFERENCES KUSHIRO I. (1975) On the nature of silicate melt and its significance in magma genesis: regularities in the shift A~~ELLAJ.. WILLIAMSR. J. and MULLINS0. (1976) Soluof the liquidus boundaries involving olivine. pyroxene. bility of Cr. Ti and Al in co-existing olivine. spine1 and and silica minerals. Am. J. Sci. 275. 411-431. hquid at 1 atm. In Proc. Secenth Lunar Sci. Co& GeoLEEMAN W. P. (1978) Distribution of Mg2+ between olivine chim. Cosmochim. Acra Suppl. 7, pp. 1179-1194. Pergaand silicate melt. and its implications regarding melt mon Press. structure. Geochim. Cosmochim. Actu 42, 789-800 ANDERSEX0. (1915) The system anorthite-forsterite-silica. LEEMAN W. P., VITALIAN~ C. J. and PRINZ M. (1976) Am. J. Sci. 39, (ser. 4), 407-454. Evolved lavas from the Snake River Plain. craters of BIGC~AR G. M.. O’HARA M. J., PECKETTA. and HUMPHRIES the Moon National Monument. Idaho. Conrrib. Mineral. D. J. (1971) Lunar lavas and the achondrites-petro-
genesis of protohypersthene Sri.
Cont.
617-643.
Geochim. MIT Press.
basalts.
Cosmochim.
Proc. Second Lunar Acta Suppl. 2, pp.
BOTTINC~A Y. and WEILLD. F. (1972) The viscosity mattc silicate liquids: Sri. 272, 438-475.
a model
for calculation.
of magAm.
J.
B~WENN. L. and SCHAIRERJ. F. (1935) The system MgOFe@SiO,.
and
application
to the olivines.
tion of Fe and Mg between olivine and lunar basaltic liquids. Geochim. Cosmochim. Acta 42, 1545-l 558. MACGREGOR I. D. (1969) The system MgO-SiO,-Ti02 and its bearing on the distribution of TiO, in basalts. Am. J. Sri. 26?A.
342-363.
MCKAJ G. A. and WEILL D. F. (19771 KREEP
Am. J. Sci. 29, 151-217.
BRADLEYR. S. (1962) Thermodynamic calculations on phase equilibria involving fused salts. Part II. Solid solutions
Perrol. 56. 35-60. LONGHI J.. WALKER D. and HAYS J. F. (1978) The distribu-
Am. J. Sci. 260,
Cosmochim.
Proc. Eiyhrh Lunar Sci.. Con& Geochim. Acra Suppi. 8, pp. 2339-2355. Pergamon
Press.
O‘HARA M. J. (1968) The
550-554.
BRAC~C~ W. L. and WILLIAMSE. J. (1934) The effect of thermal agitation
on -atomic
R. Sot. Lond.
A l-45, 699-730.
arrangement
in alloys.
Proc.
oetro-
geneses revisted.
bearing of phase equilibria studies rn synthetic and natural systems on the origin and evolution of basic and ultrabasic rocks. Earrlt Sci. Rer. 4, 69-133.
C. T. HERZBERG
1250
O’HARA M. J. and SCHAIRER J. F. (1963) The join diopsidepyrope at atmospheric pressure. Carnegie Inst. Wash. Yen&. 62, 107-115. OSBORN E. F. and TAIT D. B. (1952) The system diopsideforsterite-anorthite. Am. J. Sci. 2SOA, 413-433. PRESNALL D. C., DIXON S. A., DIXON J. R., O’DONNELL T. H.. BRENNER N. L., SCHR~CK R. L. and Dvcus D. W. (1978) Liquidus phase relations on the join diopside-forsterite-anorthite from 1 atm to 20 kbar: their bearing on the generation and crystallization of basaltic magma. Contrib. Mineral. Petrol. 66, 203-220. ROEDER P. L. (1974) Activity of iron and olivine solubility in basaltic liquids. Earth Planet. Sci. Left. 23, 397-410. ROEDER P. L. and EMSLIE R. F. (1970) Olivine-liquid equilibrium. Conrrib. Mineral. Petrol. 29, 275-289. SCHAIRER J. F. (1954) The system KzO-MgO-AllO,SiOl. I. Results of quenching experiments on four joins m the tetrahedron cordierite-forsterite-leucite-silica and on the Join cordierite-mullite-potash feldspar. J. Am. Ceram. Sot. 37. 501-533. SCHAIRER J. F. and MORIMOTO N. (1959) The system forsterite-diopside-silica-albite. Carnegie Inst. Wash. Yearh. 58, 113-118. SCHAIRER J. F. and YODER H. S., JR. (1967) The system albite-anorthite-forsterite at 1 atmosphere. Carnegie Inst. Wash. Yearb. 65, 204-209. STOLPER E. (1977) Experimental petrology of eucritic meteorites. Geochim. Cosmochim. Acta 41, 587-611. TAYLOR M. and BROWN G. E.. JR. (1978) Structure of mineral glasses-I. The feldspar glasses NaAlSi,O,, KAlSi,Os, CaAl,Si,O,. Geochim. Cosmochim. Acra 43, 61-75. Toop G. W. and SAMIS C. S. (1962) Activities of ions in silicate melts. Truns. Met. Sot. A.I.M.E. 224, 878-887. VELDE B. and KUSHIRO I. (1978) Structure of sodium alumina-silicate melts quenched at high pressure: infrared and aluminum K-radiation data. Earth Planet. Sci. Lerr. 40, 137- 140. WALKER D., KIRKPATRICK R. J., LONGHI J. and HAYS J. F. (1976) Crystallization history of lunar picritic basalt sample 12002: phase equilibria and cooling-rate studies. Geol. Sot. Am. Bull. 87, 646-656. WALKER D., LONGHI J., LASAGA A. C., STOLPER E. M.. GROVE T. L. and HAYS J. F. (1977) Slowly cooled microgabbros 15555 and 15065. Proc. Eighth Lunar Sci. Cont. Geochim. Cosmochim. Acta Suppl. 8, pp. 1521-1547. Pergamon Press. WATZQN E. B. (1977) Partitioning of manganese between forsterite and silicate liquid. Geochim. Cosmochim. Acta 41, 1363-1374. WOHL K. (1953) Thermodynamic evaluation of binary and ternary liquid systems. Chem. Engng Progr. 49, 218-219. WOOD B. J. (1974) The solubility of alumina in orthopyroxene coexisting with garnet. Contrib. MineraL Petrol. 46, I-15. WOOD 8. J. (1975) The application of thermodynamic to some subsolidus equilibria involving solid solutions. Forrschr. Mineral. 52, 21-45. WOOD B. J. and BANNO S. (1973) Garnet-orthopyroxene and orthopyroxene-clinopyroxene relationships in simple and complex systems. Contrib. Mineral. Petrol. 42, 109-l 24. WOOD B. J. and NICHOLLS J. (1978) The thermodynamic properties of reciprocal solid solutions. Contrib. Mineral. Petrol. 66, 389-400.
on 4 oxygens is: 02’ Si4 +
4.0000 1.2686
Al’+ Mg’+ Cal +
0.1940 1.0747 0.0970
Therefore .ycd2+ = 0.0970. yA,,. = 0.1940, nMgl+ = 1.0747. SiiO = 0.317, and (.xCaA- - 0.5 )‘&,a+)/(x,-,1* - 0.5 .“A,” + ?I&++.) = 0. From these values we can calculate the liquidus temperature and compare with the experimentally determined temperature. This calculation requires that In K be determined and the temperature derived from eqn (7). Assuming that the liquidus forsterite is pure Mg,SiO,: In K = ln(0.5nM,2+)t
+ ln(as,o:m)r(7Mti+)t
(Al)
where In (0.5~,1-):
= In [(0.5)(1.0747)]’
= - 1.242
(AZ)
and in (u~,~:~)~ (yh(s2+ )t = - 0.205: this is determined
directly
from Fig. 2A.
(A3)
therefore InK
= -1.447
(A4)
Using eqn (7) or Fig. 1, the temperature is calculated to be 1511°C. which compares well with the experimentally determined liquidus temperature. A simple rearrangement of eqn (Al) gives eqn (8). Figures 2A and B were constructed from eqn (8) and the experimental data in the system CaO-MgO-A1,Os-SiO, referenced above. That is. having assumed unity SiO:activity on the join forsterite-fayalite. (a~~~:-)~ (yMIII)i in the system CaO-MgO-Al,09-SiO, is deduced from eqn (8) where In K at the temperature of the experiment is evaluated from eqn (7). An example now follows of the method whereby the temperature of a natural coexisting olivine-melt pair can be estimated. The experimental result considered is the high titanium (13.5 wt% TiO,) lunar basalt 70017 run at 1216°C (LONGHI et al., 1978) and at oxygen fugacities where iron is stable. The electron microprobe analysis of the melt can be converted to the foilowing 4 oxygen structural formula: 02Si4+
4.OQoO I.001 1
Ti4+ ,413+ Cr’ + Fe’+ Mg’+ Mn” Ca’ + Na’
0.2664 0.2697 0.0119 0.4038 0.3582 0.0064 0.2695 0.0099
In this run the composition of olivine coexisting with the melt is Fo,,,, and must be considered. Equation (Al) now becomes: In K = In
(0.5nM 1+)i C[Mgi(Mg + Fe* + Ca + Mn)]:, I +
In i+jiO:)L
(Yh.is’+)t
(A5)
where APPENDIX IN
THE system
anorthite-forsterite-silica studied by ANDERSEN (1915), olivine was found to be a liquidus phase at between 1506 and 1510°C for the composition An,,En,, (wt?:). The structural formula of this composition based
(0.5nM I-):
In [Mg/‘(Mg
+ Fe’+
+ Ca + Mn)]:,
1
= lnCWH0.35W12= _ 2,896 (d.762)’
(A6)
The solubility
of ohvine
and In (asio:-JL (j)Me2.)i = -0.180; this is determined from Fig. 2A using the value (Si + Ti)/O = 0.317 and (xc,1- 0.5J.*,,.)/(SCa“ - 0.5J’*,a+ + nr+>. + or+* + J&*-) = 0.149. For such natural compositions the amount of calcium associated with normative diopside-hedenbergite is considered. That is. some of the Ca2’ interacts interacts with Fe’+ in the with Mg’*, and the remainder melt. Finally In K = -3.076 and the estimated temperature
in basaltic
liquids
1251
of the experiment using eqn (7) = 1217°C. Neglecting the role of Ti as a polymerizing agent by using Si/O of Fig. 2A results in Si/O = 0.25 (i.e. asio:- = 1.0) and In K = -2.896. The estimated temperature then becomes 1244-C, which is 2EWC too high. In all cases overesttmates of 20-30-C are made for very high Ti basahs without using (Si + Ti)/O in Ftg. 2A. The size of the error IS not very great because of the very small difference in SiO:- activity (0.84 vs 1.001.
*I Cormnchimwo
Pergamon Press
Acm
Vol.
43. pp. 1241 IO 1251
Ltd.1079Printed I” GreatBritain
The solubility of olivine in basaltic liquids: an ionic model CLAUDE T. HERZBERG
Harvard-Smithsonian
Center for Astrophysics. 60 Garden Street. Cambridge. MA 02138. U.S.A.
(Received 16 November 1978; accepted in revised form 22 March 1979)
Abstract-A simple ionic model which describes the solution of the forsterite component in silicate liquids is reported. The melting relation is represented:
of olivine
(MgaSiO,),, = 2(Mg2+), + (SiO:-), and is extended to all silicate liquids by normalizing their compositions to 4 oxygens. At I bar, the temperature at which olivine is in equilibrium with any alkali-depleted basaltic composition can be calculated to within +3O”C. This error is increased considerably when applied to terrestrial basalts which contain several weight percent alkalis. Alkalis interfere with the equilibrium by generating strongly repulsive interionic forces which can be crudely modelled in a manner consistent with constraints imposed by regular solution theory. The model quantifies the reduced activity of SiO:- monomers due to increasing SiOl concentrations in the melt. This is a consequence of polymerization which does not appear to operate gradually over the entire spectrum of mafic and ultramafic compositions. The coordination of alumina in melts which precipitate olivine only appears to be dominantly octahedral. Titanium acts as a polymerizing agent by interconnecting previously isolated SiO:- monomers. Calcium associated with normative diopside tends to exhibit small but perceptible repulsive forces involving Mg”.
INTRODUCTION UNDERSTANDINGhow temperature,
melt composition, and pressure determine the solubility of olivine in basaltic melts is one of the most fundamental problems posed to igneous petrologists who are concerned with modelling the crystallization of basaltic magmas and the partial melting of their source materials. The contribution by ROEDERand EMSLIE(1970) on terrestrial basaltic compositions marked the first serious attempt to quantify olivine solubility as a function of temperature. Subsequent experimental studies on alkali-depleted lunar compositions (LONGHI et al., 1978). the work of ROEDER(1974), and a review of the experimental data in simple and complex chemical systems (LEEMAN,1978) have shown that silica activity and alkalis impose a strong control on olivine solubility. Efforts to quantify the melt composition variable have met with limited success because of the limitations inherent in the component activity models. For a discussion of some of the problems the reader is referred to LONGHI et al. (1978) and LEEMAN(1978). All attempts at modelling component activities in liquid solutions have been based upon the mixing of oxides (MgO, FeO. etc.) with various Temkin-like mixing methods of Al’+ and Si4’ cations to approximate silica activity. It is interesting to note, however, some similarities and differences with respect to solid solutions. Analogues of the simple Temkin model in which different cations’mix on independent sites have been used with some success on pyroxenes (WOOD
and BANNO, 1973; WOOD, 1974, 1975; HERZBERG, 1978 and many others), although recent work on Fe2 + -Mg ordering-disordering between sites. metaloxygen bonding considerations, and reciprocal lattice effects challenge this simplistic model (GRAY, 1978; R. SACK, personal communication; FLEET. 1974; WORD and NICHOLLS, 1978). Other solid solution models involving the mixing of molecular species have been addressed elsewhere (KERRICK and DARKEN, 1975). Despite the complexities and limited progress, implicit in all solid solution mixing models is an integral number of oxygens and sites for stoichiometric solid solutions. Thus, the thermodynamic treatment of liquid solutions for which component activities are expressed as mole fractions of oxide species is fundamentally different. This becomes particularly evident for liquid solutions which change composition because of crystallization of one or more phases. Inspection of such liquids expressed as mole fractions of the components would show a considerable variation in the number of oxygens in the melts. Similarly. a suite of evolved liquids which vary in SiOZ content would be expected to exhibit a range of possible melt structures (HESS. 197 1) which cannot be reflected in oxide component activities. In an analysis.of HZ0 solubility in silicate melts, BURNHAM(1975) extended his mode1 from the system NaAlSisOs-HZ0 to more complex systems by normalizing the liquids to the 8 oxygen albite stoichiometry. The apparent success of this mixing model seems rooted in its ionic character, and is more
1241
C. T. HERZBERG
1242
closely analogous to the thermodynamic treatment of solid solutions than are all other liquid solution models that have been proposed. In this paper the solubility of olivine in anhydrous basaltic liquids at I bar is explored within the constraints imposed by an ionic mixing model: all liquid compositions are expressed in terms of 4 oxygens. An integration of the component activities thus reflects the overall thermodynamic and structural properties of the melt. The analysis begins with forsterite-fayalite solutions in which the activity of the relevant silica anion species remains constant. The effects of SiO, on the activity of the dissociated silica anion is then deduced from experimental results in the system Ca&MgO-A1203-Si02. The results are then extended to natural lunar and eucrite compositions which are depleted in alkalis. Finally, the effects of nonideal Mg2 + -alkali interactions are assessed from available experimental data, and the possibility of extending the model to natural terrestrial basaltic compositions is addressed.
SOLUBILITY OF OLIVINE IN ALKALI-DEPLETED BASALTIC COMPOSITIONS The solubility of the forsterite component can be represented by the reaction: (Mg2Si0& where the equilibrium K =
= 2(Mg”), constant
of olivine
+ (SiOi-),
(1)
can be expressed:
(%ip2+)t(%iO:-)L
sterite is arbitrarily assigned the value of unity. This represents the structural property of SiOi- tetrahedra isolated from each other (total monomerization) by coordination. Olivine Mg2 - cations in octahedral solid solutions in equilibrium with silicate liquid are assumed to be ideal. The condition for equilibrium of the melting reaction is met where: AG: = - RT In K. At 1 bar equation
(4)
(4) becomes:
AH: - TASZ = -RT which can be arranged
In K
(5)
to:
AH:, +$=
Ink.
RT
The term PAI’: should appear in eqns (5) and (6) but. while fundamentally important at high pressures, is insignificantly small at 1 bar and can be neglected. A plot of In K vs 10*/T of eqn (6) was made for the forsterite-fayalite solidus-liquidus loop of BOWEN and SCHAWER (1935; experimental smoothed curves) using the AH; of forsterite = 29,300 cal mole- 1 from BRADLEY (1962). The results are shown in Fig. 1. Assuming that there is no change in the silica activity of the melt along this join, asio;- of eqn (3) remains at a value equal to unity. As would be expected from the Bradley analysis. the experimental data concur with the above enthalpy of fusion for ideal solid and liquid solutions, although it is possible that small departures from ideality may be interpreted from the deviations from the straight line in Fig. 1. The rela-
(aMgSiOJol
An ionic mixing model (BRADLEY, 1962; KERRICK and DARKEN, 1975) is assumed here for the solid (o/) and liquid (L); that is, Mg’+ mixes on two energetically similar sites. and is octahedrally coordinated. The standard state adopted for this model is taken to be the melting of pure forsterite at 1 bar. As can be seen from eqns (1) and (2), in order for this model to be extended to basaltic compositions which are, amongst other things, richer in SiO,, such liquids must be normalized to 4 oxygen units. For stoichiometric solid solutions treated ionically, such normalizations can be overlooked because the number of sites and oxygens remain constant. Normalizing the liquid solutions to 4 oxygens is considered here to be a requirement of the standard state for this ionic model. In order for the activity of pure forsterite melt to take the value of unity, eqn (2) becomes: K=
(Oh,,2 + ’ YMg*+ X (%iO:_ IL [Mg/(Mg + Fe2 + + Ca + Mn)]21
5.8 (3)
where n is the number of Mg cations in the liquid normalized to 4 oxygens, and yh(pZ+ is the activity coefficient of Mgzc m the liquid. The activity of the (SiOt-), monomer in a melt composition of pure for-
6.2
6.6
104/T (“K) Fig. 1. In K vs the inverse of temperature for the solution of forsterite in melts of the join forsterite-fayalite. Filled circles are from the smoothed experimental data of BOWEN and SCHAJRER(1935). Line is from AH: of forsterite estimated by BRADLEY(1962) for ideal solutions.
The solubility of olivine in basaltic liquids tionship
in Fig. 1 can be expressed: - 14720
In K = ___
T
+ 6.806
where 7 is in degrees Kelvin. An attempt to deduce the ‘GO:- activity of SiO,enriched basalt-like melts in equilibrium with forsterite was made by a synthesis of available experimental data in the system Ca@MgO-A1203-Si02. The data used are: 1. Anorthite-forsterite-silica (ANDERSEN, 1915). 2. Anorthite-forsterite-diopside (OSBORN and TAIT, 1952 with minor modifications from PRESNALL et al., 1978). 3. Forsterite-diopside-silica (KUSHIRO, 1972). 4. Anorthite-diopside-enstatite (HYT~~NEN and SCHAIRER. 1961 with minor modifications from KUSHIRO, 1972). 5. Diopside-pyrope [O’HARA and SCHAIRER, 1963 excluding compositions more pyrope-rich than forsterite-anorthite-silica. These four compositions were excluded because of the probability of Mg2* being fixed by A13’ in order to preserve local charge balance. This is due to CaO/Al,O, < 1 for these compositions (cf. BOTTINGA and WEILL, 1972)]. An estimate of the activity of SiOi- can be made from these data by modifying eqn (3) to: ln
(aSiO:-)L
(Yt.te~
+)i
=
In K - ln (0.5n,,2+)~
(8)
where In K at any temperature is evaluated from eqn (7) (i.e. Fig. 1). Equation (8) is essentially an expression of the extent to which the data in the forsterite primary phase volume departs from the relationship in Fig. 1 [eqn (7)]. This departure is shown in Fig. 2A as a function of Si/O. This is only an approximate solution because it does not consider the small amounts of Ca2+ dissolved in the liquidus forsterite (up to 0.77 wt:,: PRESNALLet al., 1978). An expanded explanation and example of the calculations is given in the Appendix. The data in Ca&MgC&A120&i02 fall within the area outlined in Fig. 2A, where the melts with the highest SiO, contents (SiiO) tend to depart from the relationship of Fig. 1 by about 0.25 to 0.35 In units. Although this departure is quantitatively not very large, it appears significant enough to provide information on SiOiactivity and the structure of the melts. For this reason, Fig. 2A has been translated to the activity-composition diagram of Fig. 2B. Several features of Figs 2A and B merit consideration. In general there is a tendency for SiO:- activity [(jlMe2.)t assumed for the moment to be equal to unity] to decrease in value with increasing total SiO, content (SiiO). although this takes effect only at Si/O values which are greater than about 0.29. Melts on the join forsterite-anorthite (Si/O = 0.25) obey the relationship of Fig. 1 to within &7“C irregardless of CaA120, content. Similarly. melts on the join enstatite-anorthite which are multiply saturated
1243
in both forsterite and anorthite (SijO < 0.29) obey the relationship of Fig. 1. Alumina and calcium chargebalanced to alumina (CaAl,O,) apparently have no effect on the solubility of olivine in basaltic liquids. Temperature also has no obvious effect. The term (cI~~~:-)~ (~~,~+)t of melt compositions with Si/O > 0.29 tends to be influenced by the amount of normative diopside. For example, most melt compositions in the primary phase volume of forsterite in the system forsterite-anorthite-silica [ANDERSEN. 1915; (xcal- - O.~Y,,,+)/(X~,~+ - 0.5~,,,+ + nMrl+) = 0] generally tend to have lower activities of SiOi- for any specified value of Si/O than melts in the system forsterite-diopside-silica [KUSHIRO. 1972; (Xca2- - 0.5yA,)+)/(Xca2- - 0.5y,,,* + nMe’.) < 0.51. It appears, therefore, that Ca2’ plays a dual role in such silicate liquids. Calcium which is not charge balanced to alumina appears free to mix and interact with Mg 2+ in the melts. The radial isopleths of Figs. 2A and B are probably an expression of weak Mg” -Ca2+ repulsive interactions which are quantifiable by the (Y”~~+): term. Thus it appears that in the system CaO-MgO-FeO-A1203-Si02 the only perceptible nonideal interactions of concern are those between Mg2+ and Ca2’ associated with a normative diopside component in such melts. The raw experimental data from forsterite-anorthite-silica and forsterite-diopside-silica are given in Fig. 2A in order to show the general nature of the compositional dependence. Although there is some scatter to the data, the isopleths radiating from 0.29 are an attempt to rationalize the control of composition on SiOi- activity from the entire population of data in the system CaO-MgGA120,-Si02. It should be noted that melts which are multiply saturated in forsterite + low calcium pyroxene _t anorthite in the system forsterite-anorthitesilica (open symbols in Fig. 2A) are not consistent with the remainder of the experimental data. For olivine-melt thermometry this problem is minor, but will be addressed below. Once again, it is apparent from Fig. 2B that the activity of SiO:- tends to decrease in value with increasing total Si02 (Si/O) content of the silicate liquids. This apparently reflects the tendency of such liquids to polymerize by forming branch and ring structures from isolated SiOt- monomers (TOOP and SAMIS. 1962: HE% 1971). The activity of SiOiis thus a statistical function of the number of nonbridging Si-0 bonds in the melt (FRASER, 1977). The addition of alumina to such olivine-saturated melts does not affect the activity of SiOi-. It is probable, therefore. that alumina in melts saturated with olivine is dominantly in octahedral coordination, rather than tetrahedral coordination. This is because tetrahedrally coordinated alumina would probably link up previously isolated SiO:- units via Si-GAL0-Si bonds and thus impose a noticeable control on SiOi-- activity. Although octahedrally coordinated alumina contradicts the structure of feldspar glasses (TAYLOR
C. T. HERZBERG
1244
-.5
- .4
-.3
-.2
-.l
0 + .l .25
.27
.31
.29
.33
.35
Si/O Fig. 2A. In (a,,,~.), (yhlpl+)i of silicate liquids saturated in forsterite in the system CaO-MgO-Al,O,Si02 as a function of SijO. Numbered lines are values of (xCsIf - 0.5~A,,+)/(xc.2. - 0.5~,,,- + nMsJ.) where x, y, and n are the number of cations of CaZ’, Al’+, and Mgzc respectively in the melt normalized to 4 oxygens. Circles are from the system forsterite-anorthite-silica (ANDERSEN,1915); open circles are for assemblages. of forsterite + pyroxene + melt. Triangles are from the system forsteritediopside-silica (KUSHIRO, 1972).
1.0
.6
d
.26
.28
,
,
.30
1
.32
1
.34
Si,/b Fig. 2B. Activity of the SiO:- monomer in the system CaO-Mg@A1,03-SiO, as a function of Si/O. Numbered lines are same as Fig. 2A and probably represent the effects of nonideal MgZ f-Ca* + interactions as given by (y,,++)i. This activity coefficient is probably equal to unity for melts containing no normative diopside. See text for details.
The solubility of olivine in basaltic BROWN. 1978), it is consistent with the probable coordination of alumina in melts which precipitate spine1 (MgAI,O,) at 1 bar. If the coordination of alumina m the melt is in general a reflection of its coordination in the solid, melts which crystallize spine1 must have their alumina dominantly in octahedral coordination. Furthermore, it is known that the primary phase volume of spine1 expands at the expense of anorthite with increasing pressure (O’HARA, 1968; FRESNALL er al.. 1978). This reflects the increased stability of Al“ in melts relative to Al“ with increasing pressure. and is compatible with experimental observations on jadeite glasses (VELDE and KUSHIRO, 1978) and the changes in coordination of alumina in the subsolidus of mafic and ultramafic systems (HERZBERG. 1978). The dual role of alumina, discussed previously by BOTTINGAand WEILL (1972) indicates that the coordination of alumina and its structural role is largely determined by the bulk composition of the melt at 1 bar. Since the solubility of olivine in basaltic liquids is not affected by an anorthite component of the liquids, it may be inferred that Al 3+ in octahedral coordination is in close proximity to Ca*+ of similar coordination so that local charge balance is preserved, or vice versa. If this is the case, Ca’+ in the melt may not mix freely with Me*+, but its location in the melt structure would be determined by the locations of alumina. The structure would not be based on random mixing of Mg” with Ca” and A13+, but with units of (Ca*+, 2A13+). For liquids which become sufficiently enriched in an anorthorite component, but also sufficiently silica-undersaturated (e.g. the composition 1 forsterite + 1 anorthite), the octahedrally coordinated alumina in the melt would be retained by spine1 precipitation although Mg2+, being smaller than Ca’+. would enter into the tetrahedral sites of spinel. Finally, for liquids on the join forsteriteanorthite which become sufficiently enriched in the anorthite component A13+ proxies for Si“’ in tetrahedral coordination. An interesting feature of Figs 2A and B is that SiOi- activity appears to decrease significantly only at values greater than about 0.29 Si/O. This may be an indication of a major structural change in the melts whereby polymerization only becomes operative and proceeds in a gradual manner once the threshold Si/O is surpassed. This structural discontinuity of the melts appears to be analogous to orderdisorder transformations in solid alloy systems (BRAGG and WILLIAMS. 1934). However, it appears that there is a critical melt composition (Si/O = 0.29), rather than a critical temperature as in alloys, that determines the transformation from complete disorder (total monomerization) to the onset of order (polymerization). Such a structural discontinuity was similarly observed by IRVINE and KUSHIRO (1976) from nickel partitioning studies between olivine and basaltic liquids. An inadequacy of Figs 2A and B is that it implies and
liquids
1245
the energetics of Mg’+ -0 bonds does not change with variations in Si02 content. In pure olivine liquids each Mg*+ may be irregularly coordinated with the faces of two isolated SiOi- tetrahedra. With increasing SiOZ content of the melt, Mg*+ may become coordinated with the edges and apices of interconnected silica tetrahedra. which may include oxygens of bridging Si-0-Si bonds. It is clear, therefore, that the relation shown in Figs 2A and B includes interactions between Mg*’ and Si4+. From this treatment of the experimental data it is not possible to distinguish the effects of such interactions, which may be quantified by yye2+ of eqn (3). from the effects of SiO:- activity. However if Mg*+-Si4* interactions are significant within the range of melt compositions considered, they are probably repulsive in nature. This would require Y,.,~_~,values greater than unity. Such positive deviations from ideality would have an opposite effect on the solubility of olivine than would reduced SiO:- activity. Assuming repulsive interactions, SiO:activity must be the dominant parameter which determines the extent to which the experimental data in CaO-Mg@A120,Si02 depart from the relationship in Fig. 1. In order to test how well the ionic model is able to predict the experimentally determined forsterite liquidus relations in CaO-MgO-Al,O,-SiO,. the data are now treated as unknowns. The In K for each experimental result was calculated (see Appendix) and plotted in Fig. 3 against the temperature of the experi-
c
.J
-I
lO’/T(‘K)
Fig. 3. In K vs the inverse of temperature for the solution of forsterite in melts of the join forsterite-fayalite (straight line from Fig. 1). the system Ca0-MgO-AI,O,-SiO, (shaded area), and natural lunar and eucrite compositions (filled circles). The experimental data used, method of calculation, and details of the shaded area are discussed in the text and Appendix.
1246
C. T. HERZBERC
ment. The results in the system CaO-MgO-Al,O,Si02 are contained in the shade area in preference to individual melt compositions because the character of the forsterite primary phase volume has been, in part, determined in relation to the primary phase volumes of anorthite, pyroxenes, and spine]. That is. the intersection of the primary phase volume of forsterite with that of another phase(s) defines a divariant (univariant) equilibrium. It is important to note that the melt compositions which crystallized only forsterite and are removed from a divariant or univariant equilibrium by about 50-lO!ZlO”Care confined to the cross-hatched part of the shaded area of Fig. 3. These are in excellent agreement with eqn (7), shown as the straight line. However, the greatest departures from the line are consistently from those data which define the divariant and univariant equilibria of the forsterite primary phase volume (vertical stripped part of the shaded area) and immediately within the olivine-field by 50-100°C (e.g. open circles in Fig. 2A). There are at least three explanations for this. First, the olivines of such liquids may contain the highest CaO contents. Secondly, the liquids may undergo minor structural changes, hence the activity of SiOtmay be in error. Finally, the error may be experimental in nature; that is, it is generally easier to determine the temperature of the first appearance of forsterite than it is to determine the temperature of the first appearance of forsterite + other phases (ROEDER, personal communication). For the entire population of data in CaO-MgO-A1203-Si02, the maximum error in the determination of the temperature at which forsterite is in equilibrium with the melt from eqn (7) is + 32”C/- 12°C. In order to test the applicability of eqn (7) to natural alkali-depleted olivine-melt pairs, K was calculated for lunar and eucrite compositions on which melting experiments were performed. Again, K was calculated from Fig. 2A and eqn (3) as illustrated in the Appendix for one experimental result. The data were obtained from AKELLA et al. (1976), BIGGAR et al. (1971), HUEBNER et al. (1976). LONGHI et al. (1978), MCKAY and WEILL (1977) STOLPER (1977; and unpublished data), and WALKER et al. (1976, 1977). In K and the known temperature for each experiment are plotted in Fig. 3. In calculating K, however, it was noted that both the high- and low-Ti lunar compositions, in particular those of LONGHI er al. (1978). were in excellent agreement with the line of Fig. 3 if the activity of SiOtwas reduced further by using (Si + Ti)/O in Fig. 2. This result indicates that Ti4+ acts to polymerize such liquids by linking SiOttetrahedra via Si-@Ti0-Si bonding. The net result is a decrease in the number of non-bridging Si-0 bonds. This explanation is consistent with the effects of Ti02 on the shifts in the forsterite-enstatite peritectic equilibrium noted by KUSHIRO (1975) and MACGREC~R (1969). Inspection of the data on natural compositions in Fig 3 shows that the agreement with the simple syn-
thetic systems is excellent. For the entire population of natural compositions, the greatest deviation from the line of eqn (7) is + 30°C. Given (1) the assumptions in the ionic mixing model, (2) the diversecompositions of the data, (3) the temperature range involved, and (4) intra and interlaboratory analytical and experimental errors, the ability to predict the measured temperatures of olivine-melt pairs for the lunar and eucrite compositions with such accuracy is, indeed, encouraging. It is concluded that this ionic mixing model may be applied to all low-alkali basaltic melt-olivine pairs, irrespective of magma type. EFFECTS OF NA+ AND K’ ON OLIVINE SOLUBILITY IN BASALTIC MELTS Due to differences in charge and ionic radii of Mg’+ (0.65A) compared with Na* (0.95A) and K+ (1.33 A), strong effects on the solubility of olivine in silicate melts would be expected. Indeed, ROEDER (1974), LEEMAN (1978), and LONGHI er al. (1978) observed that small amounts of alkalis can significantly reduce the amounts of Mgzc and Fez+ in melts coexisting with olivine. One may also expect that K+, being the larger cation of the alkalis, would have the strongest effect. An attempt is now made to quantify these effects by assessing the magnitude of nonideal interactions for aluminous solutions of Mg’ +-Na’, MgZf -K+, and finally MgzC-Na+-Kf. It is assumed that these three cations are coordinated similarly and that they are allowed to mix with each other. Equation (3) can, once again, be modified to:
(0.5n [Mg/(Mg
)2
+ Fe?*;
+ Mn)]:, I (9)
where In K at any temperature is evaluated from Fig. 1. For pseudobinary melts of the type (Mg-Na) and (Mg-K), the activity coefficient can be assessed from the relation: ln (~~~2+)L
= X&C&.MeNp
+ 2X,,PG.Na--Mg RT
-
~G.M+Jl (10)
for asymmetric Mg-Na solutions WOHL, 1953; for Mg-K solutions Na becomes K in eqn (lo)]. The w’s in equation (10) represent Margules excess free energy parameters for Mg’+-Na+ and Na+-Mg2+ interactions, and X,, = Na/(Na + Mg). The nonideal character of Mg-Na solutions was explored from experimental data in the systems forsterite-anorthitealbite (SCHAIRER and YODER, 1967;
The solubility of olivine in basaltic liquids
. //
1
Lc
.2
.6
.4 Na/(No
i
4
3
.8
+Mg)
Fig. 4. In (u .,>.)i ((I~~~:-)~ vs Na/(Na + Mg) for silicate liquids in equilibrium (?) with forsterite in the systems forsterite-anorthite-albite and enstatite-diopside-albite. The isotherms were fitted to the experimental data according to eqn (10) in the text. Closed circles = all data: open circles = data on the join forsterite-albite: open squares = data on the join enstatite-albite. Variations in SiO:activity contributes to the scatter of the data at 10~ Na/(Na + Mg).
WATSON,1977; HART and DAVIS.1979) and enstatitediopside-albite (SCHAIRER and MORIMOTO. 1959). From equation (9) it can be seen that the extent to which such Na-bearing melts in the forsterite primary phase volume depart from the relationship of eqn (7) (Fig. 1) should give an indication of In (yM,l-)f (a~,~:-)~ This is shown in Fig. 4 as a function of Na/(Na + Mg). It is important to note that there is a considerable scatter in the data which bears no obvious relation to any parameter except a very poor correlation with temperature. Although this may in part be due to the sorts of experimental error normally encountered in high alkali systems, it is also a reflection of the inadequacy of eqn (10) and the parameter Na/(Na + Mg) in resolving interactions involving only Mg and Na cations. The ratio Na/(Na + Mg) was chosen only because of its capacity to rationalize the data. The parameter Na/(Na + Mg + total Ca) was tested but found to produce a much greater scatter in the data and the result could not be satisfactorily modelled in conformity to regular solution theory. Other interactions may involve Mg” and Ca*+. although inspection of Figs 2 and 4 indicates that they will probably not be very large. it is also possible that some Interactions may involve Mg’- and AI’from the albite component of the melt. Bearing these uncertainties in mind, it will be assumed that the ac-
1147
tivity coefficient in equations (9) and (10) and Fig. 4 is due only to interactions between Mg and Na cations. The open symbols in Fig. 4 are for calcium-free melts on the joins forsterite-albite (open circles). and enstatite-albite (open squares). In principle, high accuracy experimental data on these two joins should enable the effects of SiO:- activity to be distinguished from those of nonideal Mg”-Nainteractions. However. the avaiiable data in Fig. 4 indicate that for most compositions Na’ dominates the deviations from the relationship of Fig. 1. At very low- Na’ contents. however. the departure from Fig. 1 appears to be dominated by SiO:- activity (note open squares of Fig. 4). The experimental data are too scattered to resolve in detail a temperature dependence to the departure from ideality. However. the two isotherms shown in Fig. 4 were derived by fitting the data to eqn (10). The simplifying assumption is made that SiO:- activity does not vary and remains at a value equal to unity. The activity coefficients so determined become minimum possible values. Similarly the Margules parameters become minimum possible values, and were determined to be: >, 5650 cal mol - ’
(11)
~G.X”--Mr > 8290 cal mol- I.
(1.2)
LVo,,,_,, and
The data do not allow estimates to be made for any possible temperature dependence to the Margules parameters: that is. the excess entropy contribution to the excess free energy was assumed to be zero. With activity coefficients known from eqns (lOt( 12), the activity-composition diagram of Fig. 5 was constructed at 1450°C. Because of the assumption of unity SiO:- activity. the actual activity-composi-
.2
.4 Mg/(Mg
.6
.8
+Na)
Fig. 5. Influence of Na’ on the activtty of Mg’* m sriicate, ltqutds of the system Ca@Na20-MgO-A1lO,-SiOZ whtch crvstalhze forstertte at 1450-C. The actual acirvttycomposnion curve is located m the shaded area due to uncertamtres m the effect of SIO:- activny Isee text).
C. T. HERZBERG
1248
W o, K--M*b 13720 cal mol - ‘.
.2
A
.6
.8
K/(K +hd vs K/(K + Mg) for silicate Fig. 6. ln(r,,l+)t ho:-IL liquids in equilibrium (?) with forsterite in the systems forsterite-leucite-silica and forsterite-anorthite-orthoclasesilica. Experimental error, uncertainties in SiO:- activity, and unknown Mg zc-A131 interactions may contribute to the scattered data Isotherms were fitted to the experimental data according to eqn (10) in the text.
tion curve must be located within the shaded portion of the diagram. The very strong positive deviations from ideality indicate the strength of the repulsive forces separating Mg and Na cations. Indeed, over a range of about 0.4-1.0 Mg/(Mg + Na) the activity of Mg’+ remains at a “very high value of at least 0.9. However, it appears that such repulsive forces are not so strong as to promote unmixing of two liquid phases. From the relation:
G,, = wG.Mg-N.X&
2 x~a + WG.Na-Mg
XNa x6,
(13)
the excess free energy curves at 1250 and 1450°C are positive and without inflexions. indicating no immiscibility. This is consistent with the single liquid phase reported in the experimental results. Encouraged by the results for Mg-Na melts, partially successful attempts to assess interactions for in the Mg’+ -K+ melts were made for compositions systems forsterite-leucite-silica (SCHAIRER, 1954) and forsterite-anorthite-orthoclase-silica (IRVINE, 1976). The paucity data and the uncertainties regarding interactions other than Mg-K cations place severe limitations on the modelling, but the results are shown in Fig. 6. The Margules parameters used to fit the isotherms to the data are very approximate, but have the values: W G.Mg_-K> 8260 cal mol-’
(14)
(15)
A comparison of Figs 4 and 6 illustrates that aluminous pseudobinary solutions of Mg-K display considerably greater departures from ideality than Mg-Na melts. This is consistent with the above ionic radii considerations. In order to proceed with a detailed analysis of olivine solubility in basaltic melts which contain both Na’ and K’, experimental data in the system Na20K20-MgO-A1,03-Si02 is required so that information on Nat-K’ and K’-Naf interactions can be assessed. These data are required before the pseudobinary relations discussed above can be integrated into an asymmetric pseudoternary solution model as discussed by WOHL (1953). To the author’s knowledge these experimental data are not available. The only relevant experimental data is on natural terrestrial basaltic compositions (ROEDER and EMSLJE, 1970; ROEDER, 1974; LEEMANet al., 1976; DUKE, 1976; D. WALKER on DSDP basalts, personal communication). For these it is difficult to be able to resolve the effects of the many interacting chemical variables. Of considerable concern here is the effect of oxygen fugacity which, because it determines Fe2’/Fe3+, may modify the SiOt- activity. Since alkali loss is a common experimental problem, it may be particularly acute in iron-bearing systems where the alkalis, as well as an externally imposed oxygen fugacity, may (G. M. BIGGAR, personal commodify Fe2+/Fe3+ munication). Additionally, alkali loss during the course of an experiment can substantially modify the relations discussed above (Figs 4 and 6). Through simplifying assumptions it is possible to determine the temperature at which olivine is in equilibrium with any alkali-rich basaltic liquid, but the accuracy is limited to about +lOOC. For readers who are partial to equilibria with such large errors, the method of calculation is available from the author on request. It is clear that the alkali-bearing systems must be systematically investigated before olivine crystallization from terrestrial melts can be modelled with the same degree of accuracy as the lunar and eucrite compositions. CONCLUSIONS The ionic model discussed herein enables the temperature at which olivine is in equilibrium with any alkali-depleted basaltic composition to be calculated to within 430°C. This error is increased substantially when applied to terrestrial basalts which contain several weight percent alkalis. This is due in part to a lack of accurate information on the magnitude of non-ideal Mg-alkali repulsive forces which can be modelled crudely but consistently with regular solution theory. The model predicts and quantifies the reduced activity of SiOa- monomers due to increasing Si02 concentrations in the melt. This is consistent with a statistical decrease in the number of nonbridging
1249
The solubility of olivine in basalttc liquids Si-0 bonds with increasing polymerization. Polymerization does not appear to be a gradual process encompassing the entire spectrum of mafic and ultramafic melt compositions. Throughout a limited range of Si!O values the melt appears to be totally disordered (total monomerization). At a threshold SijO value polymerization (ordering) begins and develops in a gradual manner. This process appears temperature independent. Alumina in association with calcium (i.e. CaAl,O, component) does not affect the activity of (SiOt-),, and thus it is inferred that it is dominantly in octahedral coordination in melts which precipitate olivine only. The coordination of alumina in all melt compositions appears largely determined by bulk composition at 1 bar. Titanium tends to decrease the activity of (SiOi-),. and thus it appears to be a polymerizing agent. The model is sufficiently sensitive to show that there are small repulsive forces between Mg*’ and calcium ions which are in association with normative diopside in the melt.
BURNHAMC. W. (1975) Water and magmas; a mixing model. Geochim. Cosmochim. Acta 39. 1077-l 084. DUKE J. M. (1976) Distribution or the period four transitition elements among olivine. calcic clinopyroxene and mafic sthcate hqutd: experimental results. J. Petroi. 17. 499-52 1. FLEETM. E. (1974) Distortions in the coordination polyhedra of M site atoms in olivines. clinopyroxenes. and amphiboles. Am. Mineral. 59, 1083-1093.~ _
FRASERD. G. (1977) Thermodynamic
orooerties of silicate
melts. In fherntodynamicsin Geolog?. pp. 301 -325. Reidel. GRAY N. H. (1978) Statistical thermodynamic models for orthopyroxene solid solution. Geol. Ass. Canada. Mineralogical with Programs
Ass.
Canada,
Geol.
Sot.
Am.
Abstracts
10. 412. HART S. R. and DAVIS K. E. (1978) Nickel
partitiomng between olivine and silicate melt. Earth Planet. Sci. LEII. 40, 203-219. HERZBERC~ C. T. (1978) Pyroxene geothermometry and geo-
barometry: experimental and thermodynamtc of some subsolidus phase relations in the svstem CaO-MeO-AI,O,-SiO,. chim. &to
42, 945-95-T
-
.’
evaluation
involving pyroxenes Geochint. Cosmo-
A~kno~~ledge,~lenrs-This research was supported by NASA grant NGL 09-015-150 to J. A. WOOD.Thanks are extended to E. STOLPERfor providing unpublished experimental data. The author is indebted to the reviewers J. LONGHI and P. L. ROEDERwhose detailed critiques helped to substantially improve the manuscript.
HESS P. C. (1971) Polymer model of silicate melts. Geochim. Cosntochirn. Acra 35. 289-306. HUEBNER J. S.. LIPIN B. R. and WIGGINS L. B. (1976) Partitioning of chromium between silicate crystals and melts. Proc. Serenfh Lunur Sci. Conf.. Geochim. Cosmochint. Acra Suppl. 7, pp. 1195-1220. Pergamon Press. HYT~NENK. and SCHAIRERJ. F. (1961) The plane enstatite-~ anorthite-diopside and its relation to basalts Carnegie Inst. Wash. Yearb. 60, 125-141.
Addendum
IRVINET. N. (1976) Metastable liquid immiscibility and MgO-Fe0_SiO, fracttonation patterns in the system
For melts on the join forsterite-fayalite, the activity of SiO:- will not remain at unity, but will be some function of temperature (P. C. Hess, personal communicat.ion). The assumption of unity activity is only applicable for a stan-
Mg,SiO,-Fe,SiO,-CaAI,SizOe-KAISi30s-SiOz. Wash. Yearb. 75. 597-61 1.
Car-
negie Inst.
IRVINET. N. and KUSHIRO1. (1976) Partitioning
of NI
and Mg between olivine and silicate liquids. Carnegie Inst. B’ush. Yearb. 75. 668-675. dard state at 1 bar and all temperatures. The AC$ throughKERRIC~ D. M. and DARKEN L. S. (1975) Statistical therout this large melting interval was assumed to be zero; modvnamic models for ideal oxide and silicate solid this is not correct (I. S. Carmichael, personal communicasolutions. with application to plagioclase. Geochim. Costion). Errors generated from the above assumptions are ntochim. Acta 39. 1431-1442. probably overwhelmed by experimental and analytical KUSHIRO I. (1972) Determinations of liqutdus relations in errors (Fig. 3). synthetic silicate systems with electron probe analysis: the system forsterite-diopside-silica at 1 atmosphere. Am. MirIeral. 57. 1260-1271. REFERENCES KUSHIRO I. (1975) On the nature of silicate melt and its significance in magma genesis: regularities in the shift A~~ELLAJ.. WILLIAMSR. J. and MULLINS0. (1976) Soluof the liquidus boundaries involving olivine. pyroxene. bility of Cr. Ti and Al in co-existing olivine. spine1 and and silica minerals. Am. J. Sci. 275. 411-431. hquid at 1 atm. In Proc. Secenth Lunar Sci. Co& GeoLEEMAN W. P. (1978) Distribution of Mg2+ between olivine chim. Cosmochim. Acra Suppl. 7, pp. 1179-1194. Pergaand silicate melt. and its implications regarding melt mon Press. structure. Geochim. Cosmochim. Actu 42, 789-800 ANDERSEX0. (1915) The system anorthite-forsterite-silica. LEEMAN W. P., VITALIAN~ C. J. and PRINZ M. (1976) Am. J. Sci. 39, (ser. 4), 407-454. Evolved lavas from the Snake River Plain. craters of BIGC~AR G. M.. O’HARA M. J., PECKETTA. and HUMPHRIES the Moon National Monument. Idaho. Conrrib. Mineral. D. J. (1971) Lunar lavas and the achondrites-petro-
genesis of protohypersthene Sri.
Cont.
617-643.
Geochim. MIT Press.
basalts.
Cosmochim.
Proc. Second Lunar Acta Suppl. 2, pp.
BOTTINC~A Y. and WEILLD. F. (1972) The viscosity mattc silicate liquids: Sri. 272, 438-475.
a model
for calculation.
of magAm.
J.
B~WENN. L. and SCHAIRERJ. F. (1935) The system MgOFe@SiO,.
and
application
to the olivines.
tion of Fe and Mg between olivine and lunar basaltic liquids. Geochim. Cosmochim. Acta 42, 1545-l 558. MACGREGOR I. D. (1969) The system MgO-SiO,-Ti02 and its bearing on the distribution of TiO, in basalts. Am. J. Sri. 26?A.
342-363.
MCKAJ G. A. and WEILL D. F. (19771 KREEP
Am. J. Sci. 29, 151-217.
BRADLEYR. S. (1962) Thermodynamic calculations on phase equilibria involving fused salts. Part II. Solid solutions
Perrol. 56. 35-60. LONGHI J.. WALKER D. and HAYS J. F. (1978) The distribu-
Am. J. Sci. 260,
Cosmochim.
Proc. Eiyhrh Lunar Sci.. Con& Geochim. Acra Suppi. 8, pp. 2339-2355. Pergamon
Press.
O‘HARA M. J. (1968) The
550-554.
BRAC~C~ W. L. and WILLIAMSE. J. (1934) The effect of thermal agitation
on -atomic
R. Sot. Lond.
A l-45, 699-730.
arrangement
in alloys.
Proc.
oetro-
geneses revisted.
bearing of phase equilibria studies rn synthetic and natural systems on the origin and evolution of basic and ultrabasic rocks. Earrlt Sci. Rer. 4, 69-133.
C. T. HERZBERG
1250
O’HARA M. J. and SCHAIRER J. F. (1963) The join diopsidepyrope at atmospheric pressure. Carnegie Inst. Wash. Yen&. 62, 107-115. OSBORN E. F. and TAIT D. B. (1952) The system diopsideforsterite-anorthite. Am. J. Sci. 2SOA, 413-433. PRESNALL D. C., DIXON S. A., DIXON J. R., O’DONNELL T. H.. BRENNER N. L., SCHR~CK R. L. and Dvcus D. W. (1978) Liquidus phase relations on the join diopside-forsterite-anorthite from 1 atm to 20 kbar: their bearing on the generation and crystallization of basaltic magma. Contrib. Mineral. Petrol. 66, 203-220. ROEDER P. L. (1974) Activity of iron and olivine solubility in basaltic liquids. Earth Planet. Sci. Left. 23, 397-410. ROEDER P. L. and EMSLIE R. F. (1970) Olivine-liquid equilibrium. Conrrib. Mineral. Petrol. 29, 275-289. SCHAIRER J. F. (1954) The system KzO-MgO-AllO,SiOl. I. Results of quenching experiments on four joins m the tetrahedron cordierite-forsterite-leucite-silica and on the Join cordierite-mullite-potash feldspar. J. Am. Ceram. Sot. 37. 501-533. SCHAIRER J. F. and MORIMOTO N. (1959) The system forsterite-diopside-silica-albite. Carnegie Inst. Wash. Yearh. 58, 113-118. SCHAIRER J. F. and YODER H. S., JR. (1967) The system albite-anorthite-forsterite at 1 atmosphere. Carnegie Inst. Wash. Yearb. 65, 204-209. STOLPER E. (1977) Experimental petrology of eucritic meteorites. Geochim. Cosmochim. Acta 41, 587-611. TAYLOR M. and BROWN G. E.. JR. (1978) Structure of mineral glasses-I. The feldspar glasses NaAlSi,O,, KAlSi,Os, CaAl,Si,O,. Geochim. Cosmochim. Acra 43, 61-75. Toop G. W. and SAMIS C. S. (1962) Activities of ions in silicate melts. Truns. Met. Sot. A.I.M.E. 224, 878-887. VELDE B. and KUSHIRO I. (1978) Structure of sodium alumina-silicate melts quenched at high pressure: infrared and aluminum K-radiation data. Earth Planet. Sci. Lerr. 40, 137- 140. WALKER D., KIRKPATRICK R. J., LONGHI J. and HAYS J. F. (1976) Crystallization history of lunar picritic basalt sample 12002: phase equilibria and cooling-rate studies. Geol. Sot. Am. Bull. 87, 646-656. WALKER D., LONGHI J., LASAGA A. C., STOLPER E. M.. GROVE T. L. and HAYS J. F. (1977) Slowly cooled microgabbros 15555 and 15065. Proc. Eighth Lunar Sci. Cont. Geochim. Cosmochim. Acta Suppl. 8, pp. 1521-1547. Pergamon Press. WATZQN E. B. (1977) Partitioning of manganese between forsterite and silicate liquid. Geochim. Cosmochim. Acta 41, 1363-1374. WOHL K. (1953) Thermodynamic evaluation of binary and ternary liquid systems. Chem. Engng Progr. 49, 218-219. WOOD B. J. (1974) The solubility of alumina in orthopyroxene coexisting with garnet. Contrib. MineraL Petrol. 46, I-15. WOOD 8. J. (1975) The application of thermodynamic to some subsolidus equilibria involving solid solutions. Forrschr. Mineral. 52, 21-45. WOOD B. J. and BANNO S. (1973) Garnet-orthopyroxene and orthopyroxene-clinopyroxene relationships in simple and complex systems. Contrib. Mineral. Petrol. 42, 109-l 24. WOOD B. J. and NICHOLLS J. (1978) The thermodynamic properties of reciprocal solid solutions. Contrib. Mineral. Petrol. 66, 389-400.
on 4 oxygens is: 02’ Si4 +
4.0000 1.2686
Al’+ Mg’+ Cal +
0.1940 1.0747 0.0970
Therefore .ycd2+ = 0.0970. yA,,. = 0.1940, nMgl+ = 1.0747. SiiO = 0.317, and (.xCaA- - 0.5 )‘&,a+)/(x,-,1* - 0.5 .“A,” + ?I&++.) = 0. From these values we can calculate the liquidus temperature and compare with the experimentally determined temperature. This calculation requires that In K be determined and the temperature derived from eqn (7). Assuming that the liquidus forsterite is pure Mg,SiO,: In K = ln(0.5nM,2+)t
+ ln(as,o:m)r(7Mti+)t
(Al)
where In (0.5~,1-):
= In [(0.5)(1.0747)]’
= - 1.242
(AZ)
and in (u~,~:~)~ (yh(s2+ )t = - 0.205: this is determined
directly
from Fig. 2A.
(A3)
therefore InK
= -1.447
(A4)
Using eqn (7) or Fig. 1, the temperature is calculated to be 1511°C. which compares well with the experimentally determined liquidus temperature. A simple rearrangement of eqn (Al) gives eqn (8). Figures 2A and B were constructed from eqn (8) and the experimental data in the system CaO-MgO-A1,Os-SiO, referenced above. That is. having assumed unity SiO:activity on the join forsterite-fayalite. (a~~~:-)~ (yMIII)i in the system CaO-MgO-Al,09-SiO, is deduced from eqn (8) where In K at the temperature of the experiment is evaluated from eqn (7). An example now follows of the method whereby the temperature of a natural coexisting olivine-melt pair can be estimated. The experimental result considered is the high titanium (13.5 wt% TiO,) lunar basalt 70017 run at 1216°C (LONGHI et al., 1978) and at oxygen fugacities where iron is stable. The electron microprobe analysis of the melt can be converted to the foilowing 4 oxygen structural formula: 02Si4+
4.OQoO I.001 1
Ti4+ ,413+ Cr’ + Fe’+ Mg’+ Mn” Ca’ + Na’
0.2664 0.2697 0.0119 0.4038 0.3582 0.0064 0.2695 0.0099
In this run the composition of olivine coexisting with the melt is Fo,,,, and must be considered. Equation (Al) now becomes: In K = In
(0.5nM 1+)i C[Mgi(Mg + Fe* + Ca + Mn)]:, I +
In i+jiO:)L
(Yh.is’+)t
(A5)
where APPENDIX IN
THE system
anorthite-forsterite-silica studied by ANDERSEN (1915), olivine was found to be a liquidus phase at between 1506 and 1510°C for the composition An,,En,, (wt?:). The structural formula of this composition based
(0.5nM I-):
In [Mg/‘(Mg
+ Fe’+
+ Ca + Mn)]:,
1
= lnCWH0.35W12= _ 2,896 (d.762)’
(A6)
The solubility
of ohvine
and In (asio:-JL (j)Me2.)i = -0.180; this is determined from Fig. 2A using the value (Si + Ti)/O = 0.317 and (xc,1- 0.5J.*,,.)/(SCa“ - 0.5J’*,a+ + nr+>. + or+* + J&*-) = 0.149. For such natural compositions the amount of calcium associated with normative diopside-hedenbergite is considered. That is. some of the Ca2’ interacts interacts with Fe’+ in the with Mg’*, and the remainder melt. Finally In K = -3.076 and the estimated temperature
in basaltic
liquids
1251
of the experiment using eqn (7) = 1217°C. Neglecting the role of Ti as a polymerizing agent by using Si/O of Fig. 2A results in Si/O = 0.25 (i.e. asio:- = 1.0) and In K = -2.896. The estimated temperature then becomes 1244-C, which is 2EWC too high. In all cases overesttmates of 20-30-C are made for very high Ti basahs without using (Si + Ti)/O in Ftg. 2A. The size of the error IS not very great because of the very small difference in SiO:- activity (0.84 vs 1.001.