NASA-CR-203792 ......... aMineralogist, Volume 80, pages 115-130, 19_95 Ca-rich carbonate melts: A regular-solution model, with applications to carbonatite magma + vapor equilibria and carbonate lavas on Venus ALLAN H. TREIMAN Lunar and Planetary Institute, 3600 Bay Area Boulevard, Houston, Texas 77058-1113, U.S.A. ABSTRACT A thermochemical model of the activities of species in carbonate-rich melts would be useful in quantifying chemical equilibria between carbonatite magmas and vapors and in extrapolating liquidus equilibria to unexplored PTX. A regular-solution model of Ca-rich carbonate melts is developed here, using the fact that they are ionic liquids, and can be treated (to a first approximation) as interpenetrating regular solutions of cations and of anions. Thermochemical data on systems of alkali metal cations with carbonate and other anions are drawn from the literature; data on systems with alkaline earth (and other) cations and carbonate (and other) anions are derived here from liquidus phase equilibria. The model is validated in that all available data (at 1 kbar) are consistent with single values for the melting temperature and heat of fusion for calcite, and all liquidi are con- sistent with the liquids acting as regular solutions. At 1 kbar, the metastable congruent melting temperature of calcite (CaCO3) is inferred to be 1596 K, with A/Tfus(calcite) = 31.5 _ 1kJ/mol. Regular solution interaction param- eters (W) for Ca2+ and alkali metal cations are in the range -3 to --12 kJ/mol2; W for Ca2+-Ba 2+ is approximately -11 kJ/mol2; W for Ca2+-Mg 2+ is approximately -40 kJ/ mol% and W for Ca2+-La 3+ is approximately +85 kJ/moF. Solutions of carbonate and most anions (including OH-, F-, and SO42-) are nearly ideal, with Wbetween 0 (ideal) and -2.5 kJ/moF. The interaction of carbonate and phosphate ions is strongly nonideal, which is consistent with the suggestion of carbonate-phosphate liquid immiscibility. Interaction of carbonate and sulfide ions is also nonideal and suggestive of carbonate-sulfide liquid immiscibility. Solution of H20, for all but the most H20-rich compositions, can be mod- eled as a disproportionation to hydronium (H30 ÷) and hydroxyl (OH-) ions with W for Ca2+-H30 ÷ _ 33 kJ/mol 2. The regular-solution model of carbonate melts can be applied to problems of carbonatite magma + vapor equilibria and of extrapolating liquidus equilibria to unstudied systems. Calculations on one carbonatite (the Husereau dike, Oka complex, Quebec, Canada) show that the anion solution of its magma contained an OH mole fraction of _0.07, although the vapor in equilibrium with the magma had P(H20) = 8.5 x P(CO2). F in carbonatite systems is calculated to be strongly partitioned into the magma (as F-) relative to coexisting vapor. In the Husereau carbonatite magma, the anion solution contained an F- mole fraction of _6 x 10-5. Calcite and anhydrite may be present on the surface of Venus, but they would not be molten at ambient surface temperature (660-760 K) because the minimum melt temper- ature (eutectic) for the calcite + anhydrite system is calculated to be 1250 K. The Venus atmosphere contains 5 ppb HF, which implies that the anion solution of a carbonate-rich magma in equilibrium with the atmosphere would contain a F- mole fraction of _7 × 10 -3, or about 0.1 wt%. Although this proportion of F is much enriched compared with the atmosphere, it would have little effect on phase relations of the carbonatite. INTRODUCTION (Treiman and Schedl, 1983; Dawson et al., 1990; Keller and Krafft, 1990; Watson, 1991; Norton and Pinkerton, Carbonatites are igneous rocks that formed from car- 1992), their thermochemical properties have been stud- bonate-rich magmas. The petrogeneses of carbonatites are ied little (Bradley, 1962; Treiman, 1989). Thus, investi- imperfectly understood, in part because of uncertainties gations of carbonatites have not benefited from quanti- in the physical and chemical properties of their parent tative thermochemical models such as have been magmas. Although the physical and mass-transport prop- developed for silicate magmas (e.g., Ghiorso et al., 1983; erties of carbonatite magmas are becoming appreciated Berman and Brown, 1987; Ghiorso, 1987). 0003-004X/95/0102-0115502.00 11 • 'i ? • , _ • "J: , " ' i_ "/ 116 TREIMAN: Ca-RICH CARBONATE MELTS For instance, a thermochemical model of carbonate The Temkin model is consistent with ideal behavior in each melts would provide a quantitative link between the ion solution and also with regular behavior, in which there compositions of carbonatite magmas and the composi- is heat of mixing but no excess entropy of mixing (Forland, tions of their associated volatile phases. Carbon dioxide 1955). Here, I use the simplest version of the Temkin mod- is obviously important in carbonatite magmas; H20 has el, in which all cations occupy identical quasi-lattice sites, played a prominent role in experimental studies of car- as do all anions. This model ignores complexation except bonatite genesis (Wyllie, 1989), and the potential impor- as reflected by regular solution behavior and ignores the tance of F has recently been reemphasized (Gittins et al., expectation of differing sites in the liquid quasi-lattice. The 1990; Jago and Gittins, 1991). In addition, most plutonic Temkin model is only an approximation because local charge carbonatites are surrounded by volumetrically significant balance does not permit ions of different charges to inter- zones of metasomatized rock, i.e., fenite (McKie, 1966). change completely freely (e.g., Ca 2+ vs. Na +) and because These zones bespeak large fluxes of volatiles associated common sense (and the Gibbs-Duhem relation) suggest that with carbonatite magmas. It has been possible to con- different ions affect their surrounding ions in different ways. strain the composition of the volatile phases through the For instance, one cannot expect ions of different sizes (e.g., compositions and phases of the solids with which they Ca2+ vs. Mg 2+)and charges (e.g., Ca2+vs. Na +)to maintain equilibrated (e.g., Rubie and Gunter, 1983; Treiman and identical distances and coordinations with surrounding ions. Essene, 1984; Kresten and Morogan, 1986; Andersen, With these caveats, the Temkin model is a good first 1986). However, it has been impossible to constrain com- approximation for the properties of many ionic liquids, positions of carbonatite magma from fluid compositions, including (as I show below) those of Ca- and carbonate- except in the most general terms. With a quantitative rich melts to the level of detail permitted by most avail- thermochemical model of carbonatite magmas, the con- able data. In addition, the regular solution model is fa- nection between fluid and magma compositions would miliar in the geological community and is the simplest be straightforward. formulation of real solutions (e.g., Ghiorso et al., 1983; Similarly, a thermochemical model of carbonate melts Ghiorso, 1987; Berman and Brown, 1987; Helffrich and would permit extrapolation of known liquidus equilibria to Wood, 1989). More physically accurate models for ionic physical and chemical conditions that have not been studied salts (e.g., the reciprocal-salt or conformal-solution mod- experimentally. In this way, a thermochemical model would el: Blander and Topol, 1966; Kleppa, 1977, 1981) may provide a structure for understanding the results of experi- be better representations of reality, but they are not jus- ments already completed, a ready way of applying experi- tified by the quality and quantity of data available. mental results to complex natural systems, and an aid in INTERPRETATIVE METHOD designing new experimental programs. In this paper, I propose a thermochemical model of For some components in carbonate magmas, thermo- carbonate-rich magmas, based on regular-solution theory chemical data can be taken directly from the literature. and the observation that carbonatite magmas are ionic But for many major components, like Ca and Mg car- liquids (Treiman and Schedl, 1983). In the model, all bonates, and for magmas at high pressure, such data must available data (at 1kbar) are consistent with a single tem- be gained indirectly. The most accessible sources of these perature of melting for calcite (metastable congruent data are liquidus phase equilibria (in effect, measure- melting), and a single value for the heat of fusion for ments of freezing point depressions), which can be ma- calcite. Similarly, the locations of all liquidus calcite-sat- nipulated to retrieve heats of fusion and activity-com- urated liquidus surfaces are consistent with the Ca-rich position relationships (Lewis and Randall, 1961). carbonate melts being regular solutions. Portions of this To simplify the interpretation of liquidus surfaces, sol- model were presented by Treiman (1989), which is su- id and liquid phases both must be referred to the same perseded by this work. standard state. For simplicity and consistency with geo- logical applications, the standard state for a component TEMKIN MELT MODEL is taken as the chemically pure phase in its equilibrium Carbonate-rich melts are ionic melts or fused salts, liq- structure at the temperature of interest. Thus, pure solid uids in which the discrete entities (ions) are charged and phases below their melting temperatures have activities bound by electrostatic forces (Zarzycki, 1962; Sundheim, of unity; hypothetical pure liquids below their solidifi- 1964; Lumsden, 1966; Kleppa, 1977, 1981). Polymeriza- cation temperatures have activities exceeding unity. Ac- tion of anions (as in silicate liquids) is unimportant, and tivities of components in solutions (solid and liquid) are ionic complexes can be treated as distinct ionic species. referred to the same standard state. For solid phases be- Ionic liquids are amenable to relatively simple thermo- low their melting temperatures, this is a normal solvent chemical analysis because their cations and anions may be standard state: the ratio of activity to mole fraction for a treated, to a first approximation, as independent solutions. component (a/X) is unity for the pure component (X = This approximation is the quasi-lattice or Temkin (1945) l). For liquid solutions phases, this is also a solvent solid model. It is justifiable because enormous energy would be state, but with the pure solvent having nonunit activity needed to exchange, for instance, a cation surrounded by at subsolidification temperatures. The hypothetical pure anions for an anion surrounded by anions (Blander, 1964). liquid in its standard state must have the same structure TREIMANC: a-RICHCARBONATMEELTS 117 as the solution, which need not be the same liquid struc- (Andersen and Lindsley, 1981). In an ideal solution, all ture as in the pure system at its melting temperature. W= 0, and so 3" = 1. In the Temkin model of ionic Freezing point depression is treated in detail in stan- liquids, the cations and anions are treated independently dard thermodynamics textbooks (e.g., Lewis and Rand- as regular solutions, each with its own X, n, W, and 3" all, 1961). Consider the isobaric melting reaction A (sol- terms. Substituting Equations 3and 5 into Equation 2 for id) _- A (liquid solution) in the system A-B at T < Tr,s, the system A-B and rearranging into the format y = ax the congruent melting temperature of A (solid). One can + b yields approach this state in two steps: melting of pure A at T < Tfos, and isothermal solution of B into the melt and RT ln(SA,melt ) -- RT ln(aA,,olia) solid until they are at equilibrium. For the first step, the T free energy of melting pure A at a temperature below T 1 -- -- Tfus < Tfus is given as X 2 = WAB(1 -- A,melt) ___A/70s(A). (6) AGf, s= - (1) T 1 -- -- T_u, where zkH°,,(A) is the molar enthalpy change on melting If the phase A is purely component A, its activity is unity, (heat of fusion) of pure phase A at Tfus (viz., Flood et al., and Equation 6 simplifies to 1949; Lewis and Randall, 1961, p. 415). Equation 1 as- sumes that the heat of fusion is not a function of tem- _ RT ln(X'Am,elt) _ WA(1 -- X A,melt2) + zMrT0 (A). (7) perature, i.e., the effect of ACe.ru,(A) on melting A is rel- T T atively small, which is justifiable for carbonate melt 1---- 1 Tf.s Tfu_ systems at the present level of precision. Ignoring ACp,fus in carbonate, chloride, or nitrate systems causes < 1% For points on this A-saturated liquidus, a graph of -RT error in the AHrus and < 10% error in regular solution In(XA,me_t)/(1 -- T/Tfus) vs. (1 - XA,melt)2/(1 -- T/T_s) should parameters (Treiman, unpublished calculations). This yield a straight line of slope WAB and intercept AH°u_(A) AG-_,(A) is positive because a melt of pure A composition (e.g., Flood et al., 1949). Typically, phase-equilibrium ex- is not stable relative to the solid at T < Trus. The second periments yield bracketed ranges in T and X within which step is isothermal solution of B into the melt and solid a liquidus must lie, and so this graph would consist of until they are at equilibrium, i.e., AGfuTs(A) + AGsolTution = brackets through which the straight line must pass. These 0. Substituting this and the definition of free energy brackets can typically be satisfied by ranges of WAB and changes with composition into Equation 1 yields a de- zXH°_(A). scription of the liquidus surface, These descriptions of the liquidus surface can be relat- ed to the Temkin model of ionic melts with a few defi- nitions of standard state for ion activities. As with solid 1 - _ 2_°u_(A) = -RT(ln aA,me,t -- In aa,_olia) (2) and liquid phases, the reference state for an ionic species where a is activity of a component in a phase, relative to is a crystalline solid containing that pure ionic species at the standard states given above. the temperature of interest. For example, systems in equi- The activity of A in the melt phase can be calculated librium with the pure solid phase L"+M "- have activities from the assumption of regular solution behavior by of ionic components Ln+ and M" of unity. If a solution means of the activity coefficient 3"A phase contains both L"+ and M"- ions, 3"A= aA/XA. (3) a_.+M°- = aL°+.a_.-. (8) For a multicomponent solution of species A, B, and C, If a solid phase contains only a single cation or anion the heat of mixing is given as species, the activity of that ion species is unity, and the activity of the phase is equal to the activity of the other _/-/mix (hA +nB + nc)(XAXBWAB + XAXcWAc = ion species. Activities of individual ion species in melt + XBXcWBc + XAX.XcWA.¢) (4) solutions can be determined by their mole fractions and regular solution interaction parameters (Eqs. 3 and 5). where n is the number of moles of a species present, and The activity of a component in a melt solution is refer- W is the interaction parameter for that pair (or triplet) of enced, as before, to the pure component in its equilibrium species (Lewis and Randall, 1961). The ternary interac- phase at that T. Thus, in a melt in equilibrium with solid, tion parameter is assumed here to be zero, although this pure L"+M"-, the activity product aL-+'aM- is unity. value is not required by theory (Helffrich and Wood, Other thermochemical quantities are calculated with 1989). The activity coefficient 3' for species A is then standard methods. The molar entropy of melting is cal- RTln 3"A= (X2 + XBXc)WAB -]- (X2 -_-XBXc)WAc culated from the heat of melting as - x.x_w._ (5) mSfus = zX/Tfus/Tfu s (9) 118 TREIMAN: Ca-RICH CARBONATE MELTS TABLE 1. Melting of alkali and alkaline earth carbonates: Molar TABLE2. Melting of alkali and alkaline earth carbonates: Molar properties at 1 bar properties at 1 kbar Compound K kJ/mol J/(moI-K) J/(moI-K) cma/mol Compound K kJ/mol J/(mol. K) J/(mol. K) cm3/mol Na2CO3 1131 29.7 26.3 - 8.5 4.7* Na2CO3 1145" 30.1 26.3 -8.0 4.7 K2CO3 1171 27.6 23.6 - 1.1 7.5** K2CO3 1200" 28.2 23.5 -1.1 4.8 Li2CO3 996 44.8 44.8 -7.6 2.6 Li2CO3 1003"* 45.0 45.0 -7.6 2.6 CaCO3t 1583 30.5 _+1 19 _+2.5 -- -- CaCO3 1596t 31.5 +_1 19.7 _+0.7 -- 2.5 _+0.1 CaCO3:!: 1463 38.5 _+4 26 _+3 -- -- MgCO31: 1750 32 _+25? 18 _+15? -- 0.7 _+0.6? Note: enthalpy and entropy from Janz et al. (1979), heat capacities Note: heats and entropies of alkali carbonates extrapolated from 1-bar from Selman and Maru (1981), and volumes from Klement and Cohen values; Tf_,measured; volumes from high-pressure phase equilibria. Data (1975) and Janz et al.(1979). for alkaline earth carbonates as derived in text. * Volume from Klement and Cohen (1975). Janz et al. (1979) gave 7.5 *Koster van Groos and Wyllie (1966). cma/mol. **Klement and Cohen (1975). ** Volume from Klement and Cohen (1975). Janz et al.(1979) gave 10.3 _-Extrapolated from Irving and Wyllie (1975); see text. cma/mol. :_Tfo,extrapolated from Irving andWyllie (1975).Other values estimated t Appropriate for Ca-rich melts, and those containing significant K vs. from liquidus surface of Ragone et al. (1966) without consideration of Na. Recalculated from Ferland (1955), using Tf,,extrapolated from high possible experimental errors. See text. pressure. These data are consistent with high-pressure determinations; see text. :_Appropriate for lower temperature, Na-rich melts. Recalculated from Forland (1955) and Flood et al. (1949). fraction, rather than from density measurement (used by Janz et al., 1979). because congruent melting of a pure phase is isothermal. CALCIUM CARBONATE Volume changes on melting can be derived from direct Calcite is the most abundant mineral in most carbon- measurement or from polybaric equilibria by the Clau- atites, intrusive and extrusive (Bailey, 1993), and so cal- sius-Clapeyron equation: cium carbonate is likely to be among the most important components in carbonate magmas. The melting proper- -- ASr., (10) ties of CaCO3 at 1 bar and 1 kbar must be inferred in- (dP/dT)f,s" A Vfus directly because calcite does not melt congruently at these Extrapolation of heats of melting over temperatures and pressures; pure calcite decarbonates below 40 bars (Ba- pressures follow from the partial derivatives of enthalpy: ker, 1962) and melts incongruently to liquid + vapor between 90 and _7000 bars (Irving and Wyllie, 1975; 0AHf, s _ AC, f,s and 0AHr,_ ATfus (11) Huang and Wyllie, 1976). However, melting and solution OT " OP properties of CaCO3 can be measured directly for melts where A_p.f,, is the difference in heat capacities between that are not too rich in CaCO3 component, given a tem- molten and solid phases (Tables 1 and 2). Note that perature for its (metastable) congruent melting. ACp.fu_ is negative for the alkali carbonates (Tables 1 and All high-pressure liquidus surfaces and most 1-bar li- 2), as it is for many ionic salts (Robie et al., 1979; DeKock, quidus surfaces are consistent with a single value for the 1986). A negative ACp, fus suggests premelting structural temperature of melting (True) and heat of fusion changes in the solid and does not violate the second law A/70u_(calcite); unless specifically noted, all discussion here of thermodynamics. refers to numerical values consistent with l-kbar liquidus equilibria. However, some 1-bar liquidi are consistent ALKALI CARBONATES with a separate set of Tf_s and AH°_s(calcite) (Table 1); it Alkali carbonates are inferred to be important constit- is possible that Ca-rich carbonate melt might occur in uents of some carbonate magmas (LeBas, 1981; Dawson two distinct structures at 1 bar (viz., Forland, 1955). For et al., 1987, Gittins, 1989), although few carbonatites the most part, melting properties derived for high pres- contain alkali carbonate minerals. There is an extensive sure are appropriate for geological applications. literature on melting and mixing properties of the alkali Melting temperature carbonates, from which much of Table 1 is drawn directly or calculated. The congruent melting temperature for pure CaCO 3in For volume changes on fusion, AVf.s, for the alkali the calcite structure, Trus(calcite), can be estimated by ex- carbonates (Table 1), the data of Klement and Cohen trapolating the high-pressure congruent melting curve to (1975) are preferred over those of Janz et al. (1979), which lower pressures (Irving and Wyllie, 1975; Huang and are larger than those of Klement and Cohen by _20%. Wyllie, 1976). Between l0 and 20 kbar, the congruent The discrepancy in AV r., lies in the volumes of the solid melting curve for CaCO3 has a slope of -12.5 K/kbar, phases, as both groups report comparable melt volumes. implying a congruent Tf.s(calcite) of 1583 K at 1 bar and Klement and Cohen's (1975) data are preferred, because 1596 K at 1 kbar (Tables 1 and 2). This 1-kbar Tf_,(calcite) their solid volumes are from high-temperature X-ray dif- is just above the experimentally determined bracket for , :) 2 • TREIMAN: Ca-RICH CARBONATE MELTS 119 TABLE3. Expressions for ordinate Qvalues inFigs. 1and 2 40 Ol = -RTIn(Xc.+++ )/(1-_) ......... "Xco 2+,........ O h Q_ 20 _ • 05 = - [RTIn(Xc.++..+........)- RT In(ac.c )1 1-- 0 '0.05 0'.1 0._15 ' 0'.2 0.25' 0.3 ........ [RT In(Xc.++.........."Xco+..........)+ WCO+--O(H1--XO......... )2] Q6= (1- T/T,J (1 -- g Ca 2+,carl .... It )2//1 -- _Tfus ) Fig. 1. Regular-solution interpretation of calcite-saturated li- Q7= [R T In(Xc.++........... X co+.......... )It- WCO32 --OH (1 -- XCO2 ....... )2] (1- T/T_,) quidus in CaCO3-BaSO4-CaF2 (500 bars CO2, Kuellmer et al., 1966), following Eq. 12. See Table 3 for definition of QI. Open and filled symbols represent liquid-only and liquid + calcite experiments, respectively. Lines from each data point represent a conservative estimate of errors (+ 5K in T; +0.2 wt% in X), imately zero (derived below, viz., Table 4), so Equation showing only the error bar halves that contribute to uncertainty 8 reduces to in slope and intercept. The liquidus surfaces, linear with slope W and ordinate intercept of AH°+s(calcite), should lie between R T ln(Xca2+,cati .... It"Xco]-,ani .... It) these groups of experiments. Within error, all data are consistent T with AH°us(calcite) = 31.5 + 1kJ/mol and Wca2÷_Ba2=+ --11 + 1 -- -- 9 kJ/moP (thin solid lines). Tfu, (1 -- Xca2+,cati .... 1,) 2 Wca2+_Ba2+ T incongruent melting [1573-1593 K; Wyllie and Tuttle, 1 -- -- 1960 (temperatures corrected by -32 K per Gittins and Try, Tuttle, 1964); Irving and Wyllie, 1975], and is consistent + AH r°,,(calcite). (12) within error with much of the liquidus equilibrium data for 1 bar (Forland, 1955). As discussed below, some li- The data of Kuellmer et al. (1966) are recast by this equa- quidi at 1 bar are consistent with Tfu,(calcite) = 1463 K. tion in Figure 1. If the Temkin regular solution model is valid, and if the anion interaction parameters are effec- Heat of melting tively zero, the liquidus surface separating the liquid-only High pressure. The locations of calcite-saturated liqui- data points (open symbols) and liquid + calcite points di at high pressure (500-1000 bars) imply that (filled symbols) should be representable as a straight line A/7Os(calcite) = 31.5 +_ 1 kJ/mol. This value is con- with slope of WCa2+_Ba 2+ and a Y-axis intercept of AH f°,,(cal- strained most closely by the location of the calcite-satu- cite). The liquidus can in fact be represented as a straight rated liquidus in the system CaCO3-CaF2-BaSO4 (Kuell- line consistent with the error bars of all points, suggesting mer et al., 1966), and is consistent with all available A/7O,(calcite) = 31.05 ___0.25 kJ/mol. However, these determinations of calcite-saturated liquidi at high pres- tight error limits are dictated by a single liquid-only point sure, in which calcite is a pure phase. (the open symbol that extends below the lines). The con- The experimental location of the calcite-saturated li- servative approach taken here is to assume that point is quidus in the system BaSO4-CaCO3-CaF2 (Fig. 1, Table in error and to estimate AH °,,(calcite) = 31.5 __+1kJ/mol 3; Kuellmer et al., 1966) is the most restrictive available and WCa_+-Ba_+= --11 __+9 kJ/mol 2 from the remaining constraint on A/7°u,(calcite). Calcite grown in this system points (Fig. 1). The error limits correspond to a temper- is effectively pure; it does not accept significant SO4z- of ature uncertainty of + 5 K and a compositional uncer- F- in solid solution, and Kuellmer et al. (1966) reported tainty of +0.2 wt% in the most abundant component. no indication of solid solution with Ba. To retrieve This value for A/7°._(calcite) is consistent with all avail- A/70us(calcite) from this system, one substitutes Temkin able high-pressure determinations of liquidi saturated in melt activity models (Eq. 5) for individual anion and cat- pure calcite. Figure 2a-2f show many sets of calcite-sat- ion solutions into Equation 8 and then substitutes the urated liquidi recast following Equation 7. Within uncer- resultant melt activity model into Equation 7, the de- tainty, all these liquidi are consistent with AH°._(calcite) scription of the liquidus surface. The anion interaction = 31.5 _+ 1 kJ/mol. This value is essentially identical to parameters WCO_--F-, Wso_--v-, and Wco_-.so_ are approx- the only independent estimate of AH°,,(calcite) at high !,_il_i¸_ • 120 TREIMAN: Ca-RICH CARBONATE MELTS 35 a. 35 O 3O E 30 v 25 v 25 oJ O4 O 20 (_ 20 150 ' 0.r2 i 0.i4 i 0.i6 i 0.I8 i -1 i 1._2 .4 15 0 0.2 0.4 0.6 0.8 1 (1- Xca2+ca,t it)2/(1 - _/Tf_s) .... (1- Xca2+,cat ..... It)2/(1 - _Tfus) 38 36 c. 34 d. 34 o E 32 30 v co 28 26 24 II f i r i i i i I i i i i 220 0.5 1 1.5 290 '012'014'016'018' 1 1.2 1.4 (1-- SOIl .ani .... lt)2/(1-- _Tfus) 35 (1-- Xv_ an_onm_t)2/(1-_Tf,:,_) i e. 30 45 o 25 p. 40 E o 20 E 35 v LO 15 v, 3O 10 c,o C_ 25 50 ' 0.1 ' 0.2 ' 0.3 ' 0.4 ' 0.5 ' 0.6 (1-- Xca2+,cat i.... lt)2//1 - _fus) 2Oo 0.()2 0.()4 0.06 0.08 011 ' 0.12 160 ,i g. (1-- Xca2+ cad .... 1t)2/(1- _Tfu_) 120 O E pressure, 29 kJ/mol (Bradley, 1962). Bradley assumed that .._ 80 1-kbar melts in CaCO3-Ca(OH)2 were ideal solutions and performed an analysis of the freezing point depression r,-.. similar to that here. Results here on anion solutions are (2I 40 consistent with near-ideal mixing of carbonate and hy- droxide anions (Fig. 2c, Table 4). 0 i One bar. Most of the limited experimental data on the 0 3 melting properties of calcite at 1 bar are consistent with results from high pressure: Tf, s(calcite) = 1583 K and (1- X Ca 2+,cation meh )2/(1 -- _Zfus / AH°,,(calcite) = 31.5 4- 1 kJ/mol [Table 1; Flood et al., TREIMANC: a-RICHCARBONATMEELTS 121 Fig.2. Regular-solutiinotnerpretatioonfcalcite-saturalit-ed _+ 2.5 kJ/mol 2. (c) CaCO3-Ca(OH)2 (1-kbar WCa2+_K + = --14.5 quidifromotherhigh-pressuerxeperimenOtsp. enandfilled CO2; Wyllie and Tuttle, 1960; published temperatures corrected symborlsepreselniqtuid-onlayndliquid+calciteexperimentsb,y -32 K according to Gittins and Tuttle, 1964), following Eq. respectiveSlye.eTable3forexpressioonfsordinat'eQ'values. 7. WCO_--OH= 2.3 --+2.3 kJ/mol 2.(d) CaCO3-CaF2 (Gittins and Heavylinesfromeachdatapointrepreseanctonservatievseti- Tuttle, 1964; Kuellmer et al., 1966), following Eq. 7. The data mateoferrors(_+5KinT; +0.2 wt% in X), showing only the sets are not consistent within error limits; ignoring the two dis- error-bar halves that contribute to uncertainty in slope and in- crepant points (ordinate values of 30.5 and 32) permits tercept. The liquidus surfaces, linear with slope W and ordinate Wco_ -F- = 0 --+2 kJ/mol z. (e) CaCO3-MgCO3 (10-kbar CO2; intercept of AH°us(calcite), should lie between these groups of Byrnes and Wyllie, 1981), following Eq. 6. Activities of CaCO3 experiments. Thin solid lines encompass range of liquidus sur- in calcite calculated from Anovitz and Essene (1987). Wca2+_Mg2=+ faces permitted by these data (with error bars), and AH °us(calcite) --40 + 30 kJ/mol 2.(f) CafO3-fa(OH)2-La(On)3 (l-kbar CO2; = 31.5 +_l kJ/mol (Fig. 1); the given range of W values is for Jones and Wyllie, 1986), following Eq. 13. WCa2+__3÷= 85 ----5-0 these solid lines. (a) CaCO3-Na2C03 (l-kbar CO2; Cooper et al., kJ/moF. (g) CaCO3-H20 (1-kbar CO2; Wyllie and Turtle, 1960, 1975), following Eq. 7. -6 _+2kJ/moP. (b) CaCO3- temperatures corrected by -32 K according to Gittins and Tur- WCa2+_Na+ = K2CO 3 (1-kbar CO2; Cooper et al., 1975), following Eq. 7. tle, 1964), following Eq. 15. Wca2._..o+ = 33 + 2 kJ/mol z. 4---- 1949; Forland, 1955; the location of the calcite-saturated consistent with the earlier liquidus experiments of Flood liquidus in CafO3-Na2CO3 by Poletaev et al., 1975, spans et al. (1949). They determined the CaO-saturated liqui- too small a composition range to constrain AH°us(Calcite)]. dus surfaces in CaCO3-Na2C03, CaCO3-K2CO3, and However, the liquidus position in the CafO3-Na2CO3 CaCOa-Li2CO3 under 1 bar C02, from 1244 to 1378 K. system at temperatures below approximately 1170 K is Activities of calcite in the melt solutions were calculated consistent with Tfus(calcite) = 1463 K and AH°us(calcite) from the pressure of CO2 in equilibrium with calcite and 38 kJ/mol (Table 1; Flood et al., 1949; Forland, 1955). lime; uncertainties were given only as error bars on graphs To account for these discrepancies, Forland (1955) sug- and cannot be readily evaluated. Flood et al. (1949) took gested that lower temperature melts in CaCO3-Na2CO3 the melting temperature for calcite to be 1613 K, used a do not have the same structure as higher temperature molecular mole fraction model for melt activities, and melts and melts in other systems (notably K-bearing). calculated (from Eq. 7) that AH°_(calcite) = 14.2 kJ/mol. There is no evidence that the low-temperature structure Recalculating their data for CaCO3-Na2C03 for melting persists to higher temperature or pressure in the Ca-rich temperatures of 1583 or 1463 K and with a Temkin melt systems examined here. model (e.g., ionic fractions) yields AH°_(calcite) _ 39 kJ/ Extrapolations of Trus(calcite) and AH°u_(calcite) from mol, consistent with Forland's (1955) data on Ca-poor high pressure are consistent with most of the 1-bar liqui- compositions in CaCO3. The determinations for CaCO3- dus experiments of Forland (1955), who calculated both K2CO3 and CaCO3-Li2C03 of Flood et al. (1949) are more values from the compositions of melts saturated with CaO scattered and are consistent with either pair of Tf_(calcite) (lime) in the systems CafO3-Na2CO3, CaCO3-K2CO3, and and AH °u_(calcite). CaCO3-NaKCO3 as functions of CO2 pressure between To explain the discrepancies in AH°_(calcite) and 1203 and 1273 K. Compositions were measured by weight True(calcite), Forland (1955) suggested that the more Na- loss (CO2 loss); a (calcite) was calculated from measured rich and lower-temperature melts in CaCOa-Na2CO 3have CO2 pressure and the known pressure of CO2 in equilib- a different structure from those at higher Ca contents and rium with calcite and CaO; uncertainties were not given temperatures. On the basis of the AHf_(calcite) values, and cannot be evaluated. The linear correlation of AGr._ the Ca-rich melt structure is present in all systems at high (calcite) and T for the systems CaCO3-K2CO 3and CaCO3- pressure. Another speculative explanation is that the sol- NaKCO3 implied Tf_(calcite) _ 1523 K and AH°s(calcite) id in the CaCO3-Na:CO 3 experiments was not actually 35 kJ/mol. The original data are consistent with CaO but a mixed oxide phase in CaO-Na20. I am aware, T_(calcite) = 1583 K (extrapolated above from high-pres- however, of no reports of mixed Na-Ca oxide phases. sure equilibria),which yields AH°_(calcite) _ 30.5 kJ/mol, Melt volume consistent with high-pressure phase equilibria. Liquidus ex- periments at high Ca contents and higher temperatures in The volume change on melting calcite at high pressure the system CaCO3-Na2CO3, are also consistent with the high- may be calculated from Equation 9. The entropy of fu- pressure values, although data are limited. sion, ASrus(calcite), is calculated from AH°_(calcite) and However, at lower temperatures and lower Ca con- True(calcite), as in Table 2. The slope of the polybaric tents, the CaO-saturated liquidus in CaCO3-Na2CO3 is congruent melting for calcite curve is 80 K/bar (Irving not consistent with True(calcite) and AH°u_(calcite) from and Wyllie, 1973, 1975), yielding AV ru_(calcite) = 2.5 _ high-pressure phase equilibria. Rather, Forland (1955) 0.1 cm3/mol at high pressure. This value is comparable found that these liquidus determinations suggested with AV ru_for Li2CO3, but significantly smaller than those Tr_(calcite) = 1463 K and AH°_(calcite) _ 37.5 kJ/mol. for K2CO 3and Na2CO 3(Table 2). This higher A/7°_(calcite) and lower Try(calcite) are also The molar volume of CaCO3 melt could now be esti- 122 TREIMAN: Ca-RICH CARBONATE MELTS TABLE 4. Mixing of ions in molten salts: Regular solution pa- in Na at low pressure and relatively lower temperature, rameters AH%(calcite) _ 38.5 kJ/mol, and Tf_(calcite) = 1463 K. W Counter On the basis of molar entropies, one may speculate that Ions (kJ/tool 2) ion Reference the former melts are structurally comparable to molten K2CO3 and the latter are structurally comparable with CO_--OH- -2.3 _+2.3 Ca2÷ 1 _0 Na+ 2 molten Na2CO3 . CO_ -F- 0 _+2 Ca2÷ 1 -2 K+ 3 MAGNESIUM CARBONATE CO_--CI- -1.7, 0 Na+ 3,4 CO_ -Br - 1.7 Na+ 4 The common presence of magnesian calcite, dolomite, CO_--SO_- 0 Na+ 5 0 _+1.5 Ca2+ 1 and magnesian silicates in carbonatites shows that mag- CO_ -PO,*- >65? Ca2+ 1 nesium carbonate is an important component in carbon- CO_--O 2- _0 Na+ 2 atite petrogenesis. Unfortunately, data on the melting and COX--O_ t0 Na÷ 2 F -OH +4.3 Ca2+ 6 thermophysical properties of magnesium carbonate are F -SO_- _0 Na+ 7 either absent or uncertain. Dolomite, CaMg(CO3)2, is the Ca2+-Na+ -6 _+2 COX- 1 most common Mg-bearing carbonate in carbonatites, but - 10 CO_ 8 Ca2+-K+ 14.5 _+2.5 GO_- 1 it decarbonates at low pressure and melts incongruently - 24 COX 8 at high pressure. In addition, there appear to be no avail- Ca2+-Li+ -2.5 CO_ 4 able liquidus equilibria that can be used as above to de- Ca2+-HaO+ 36 _+2 CO_--OH- 1 Ca2+-Mg 2+ -40 +_20 CO_ 1 rive its melting properties. Data on Mg in carbonate melts Ga2+-Ba2+ -11 _+9 CO_ -SOX- 1 must now come from the limited studies available in- Ca2+-La3+ +85 _+50 CO_--OH- 1 volving MgCO3, magnesite. Mg2+-K+ -20 _+30? CO_ 1 Na+-K+ -5.6 CO_ 9 Magnesite melts incongruently at pressures below 25 Na+-Li + - 11.2 CO_- 9 kbar, and the hypothetical congruent melting tempera- Note: 1 = this work; 2 = Selman and Maru (1981); 3 - from phase ture must be extrapolated from there to the range of in- diagrams inLevin et al.(1964, 1969); 4 = Lumsden (1966); 5 = Flood et terest. Using the high-pressure liquidus determinations of al.(1952); 6=average value from Tacker andStormer (1993); 7=average Irving and Wyllie (1975), the 1 kbar congruent melting value from Kleppa andJulsrud (1980); 8 =Ferland (1955)and recalculation of Flood etal.(1949); 9 =average value from Andersen and Kleppa (1976). temperature for MgCO3 may be extrapolated as 1753 K. The AH °o,(magnesite) is very poorly determined by the single available liquidus location, in MgCO3-KzCO3 (Ra- mated from this if the molar volume of solid CaCO3 were gone et al., 1966), for which magnesite is not a solid so- known. At its 1-kbar melting temperature, CaCO 3would lution. Taken at face value, the brackets of Ragone et al. be in the CaCO 3 (V) polymorph (Carlson, 1983); unfor- (1966) on the magnesite-saturated liquidus surface only tunately, molar volumes have been measured only to 1148 restrict AH°,,(magnesite) to a value of 32 _+ 25 kJ/mol K and 1 bar, where CaCO3 (V) is the stable polymorph and (Table 2), with a corresponding entropy of fusion of (Mirwald, 1979). Recklessly extrapolating molar volume 18 + 15 J/(mol.K) (Table 2) and a W_,_+__+ of -20 + 30 and compressibility data for CaCO 3(IV) (Mirwald, 1979) kJ/moF. However, including reasonable experimental un- to 1583 K and 1 kbar, I estimate a molar volume for certainties in the analysis (5 K and 0.2 mol% MgCO3) only solid CaCO 3of 39 cm3/mol. This value leads to a molar restricts AHf°,,(magnesite)to >7 kJ/mol and WM,=+_K+ to volume for liquid CaCO 3 of 41.5 cm3/mol and a density < 10 kJ/moF. Clearly, much work remains. of 2.4 gm/cm 3. This density is comparable with the 2.2 THERMOCHEMISTRY OF SOLUTION gm/cm 3 inferred for a Ca-rich carbonatite magma (Nes- bitt and Kelly, 1977). In the regular-solution model, there is a heat effect in the formation of a solution, but no entropy effect beyond Structures of CaCO3-rich melts that of random mixing of constituents (Eq. 4; viz., Lewis For modeling Ca-rich carbonate melt systems, it seems and Randall, 1961). The heat effect is described by a sin- reasonable to accept AHfus(calcite) and Tfus(calcite) from gle interaction parameter, W, for each possible pair (or the 1-kbar experiments (Table 2) and as extrapolated to multiplet) of species in a solution. For a Temkin ionic other pressures (Table 1). There are no obvious problems solution, there are independent Ws for the cation and with experiments or interpretation to explain the differ- anion solutions. The regular solution parameters W are ences between the inferences from high-pressure phase obtained simultaneously with estimates of AHru_, and so equilibria and the results of Flood et al. (1949) and some have already appeared above in discussions of Figures 1, results of Forland (1955). It is quite reasonable to infer, 2, and 3. as did Forland (1955), that carbonate melts at low pres- sure can adopt multiple structures. The structure ob- Anion mixing tained at high pressure (1 kbar) seems to be retained at 1 It is likely that the anion solution of carbonatite mag- bar for compositions rich in Ca and those containing sig- mas is dominated by the carbonate anion, but other an- nificant K; for these melts, AH°us(calcite) = 31.5 _+ 1 kJ/ ions may play an important or essential role in carbonate tool and Tfus(calcite) = 1583 K. For melts relatively rich petrogenesis. For instance, the presence of OH anions • ? : • •; i:_¸_ TREIMAN: Ca-RICH CARBONATE MELTS 123 1800 permits carbonate-rich magmas to melt at geologically reasonable temperatures (Wyllie and Tuttle, 1960; Wyl- lie, 1989), and fluoride anions are inferred to have an equally large effect on liquidus phase relations (Gittins et al., 1990; Jago and Gittins, 1991). .--.- 1600 _.L C__C+L The anion solutions (Temkin model) in carbonate-rich I._ 1400 melts are nearly ideal for all nonpolymerizing anions (Ta- ble 4): "... mixed anion-common cation fused salts of- ten are very nearly ideal solutions" (Kleppa and Julsrud, 1200 AH + CC 1980). Data are available from Ca-rich and some other 0 012' 0'.4 0'.6 o'.8 binary systems on the interaction of carbonate anions with fluoride and other halide, hydroxide, oxide, perox- X(CaCO 3) ide, and sulfate ions (Table 4). W values constrained here include those for CO_--OH- (Fig. 2c) and CO_--F- (Fig. Fig. 3. Liquidus phase diagrams for CaCO3-CaSO4: phases 2d). Values of W in Table 4 for all anion solutions except are CC, calcite (CaCO3); AH, anhydrite (CaSO4), not including carbonate-orthophosphate are near zero, confirming their polymorphic transitions; and L, liquid. Solid lines are as pre- nearly ideal behavior. dicted by the regular-solution model (Eq. 7) and ideal mixing of CO_- and SOl (Table 4) for a total pressure of _ 100 bars. Open Mixing of sulfate and carbonate in ionic melts appears squares and dotted lines are experimental determinations of the essentially ideal. Flood et al. (1952) studied melts in the liquidus and solidus by differential thermal analysis (Fuerstenau system Na2CO3-Na2SO4-CO2 for electrochemical appli- et al., 1981). Predicted and experimental positions of the calcite- cations, and found that the melts behaved as ideal solu- saturated liquidus agree within error. The experimentally deter- tions. The ideality of carbonate-sulfate mixing extends to mined position of the anhydrite-saturated liquidus is not con- Ca-rich compositions, as the calcite-saturated liquidus sistent with the predicted liquidus and does not extrapolate to surface in CaCO3-CaSO4 at 1bar (Fuerstenau et al., 1981) the known melting temperature of anhydrite. Since Fuerstenau is consistent with Wco_-_so_- = 0 kJ/mol 2,if AH °us(calcite) et al. (1981) did not characterize their experiment products, it is = 31.5 kJ/mol (Fig. 3). possible that their liquidus surface represents growth of a mixed Mixing properties of carbonate and sulfide anions would anion solid that melts incongruently. be very useful in understanding redox states of natural systems and in some carbonatite-hosted ore deposits, but no definitive data are available. The liquidus location in CaCO3-Ca(OH)2-CaS at 1kbar by Helz and Wyllie (1979) cite) = 31.5 kJ/mol (Table 2), Wco]--OH- = --2.3 kJ/mol 2 cannot be interpreted uniquely here because is (Table 4), and Wpo_--OH- _ --27 kJ/moP (calculated from WS2-.OH not known. Their data on the binary join Ca(OH)2-CaS Table 4 of Tacker and Stormer, 1933). However, Biggar and estimates of the melting temperature and heat of fu- (1969) suggested that these experiments may be faulty sion for CaS suggest that Ws 2-.oH is approximately + 15 and that the liquidus may lie at even higher temperatures, kJ/mol2; this value is obviously suspect. The liquidus lo- in which case Wco{ -PO_ would be even larger. Such a cation in CaCO3-CaSO4-CaS determined at low pressure large positive Wco_ -Po4'-implies that some carbonate-rich by Fuerstenau et al. (1981) cannot be interpreted unam- and phosphate-rich melts might be immiscible. In nature, biguously here because Ws2-.so,_ is not known. However, phosphate-rich segregations (called phoscorite or cama- if Ws2-.so,_ is taken as zero, Ws2-.co_ must be near + 100 forite) are common in some carbonatites (e.g., Eriksson, kJ/tool. 1989), and it has been suggested they form by carbonate- The behavior of phosphate may be far from ideal. The phosphate liquid immiscibility (Lapin, 1976). Continued mixing of carbonate and orthophosphate (PO43-) anions experimentation will be required to understand the ther- was suggested to be nearly ideal by analogy with the mix- mochemistry of phosphate-carbonate mixing. ing of carbonate and sulfate anions (Table 4; Treiman, There are few quantitative data on the mixing behavior 1989). However, Tacker and Stormer (1993) have shown of carbonate and silicate anions in carbonate melts. The that solutions of molten calcium orthophosphate and other mixing of carbonate with orthosilicate (SiO44-) may be calcium salts (hydroxide, chloride, and fluoride) are not close to ideal (Treiman, 1989). However, the limited data ideal, with regular-solution interaction parameters more available (in the system CaO-SiO2-CO2-H20: Wyllie and negative than -20 kJ/moP. They suggested further that Haas, 1965) are difficult to interpret because the propor- carbonate-orthophosphate mixing might also be non- tions and speciations of H20 in the melts are not known. ideal. The data of Biggar (1969) appear to be the only Mixing of carbonate anions with more polymerized alu- minosilicate anions is far from ideal, as shown by the liquidus determinations relevant to the mixing of alkaline earth carbonates and phosphates. His experiments yield- immiscibility of carbonate and silicate melts. This liquid ed only a single bracket on the calcite-saturated liquidus immiscibility covers a wide range of synthetic and natural in a system containing orthophosphate. Taken at face val- compositions (e.g., Koster van Groos and Wyllie, 1966; ue, this liquidus bracket suggests Wco_-.PO,_- _ __+65 kJ/ Treiman and Essene, 1985; Kjarsgaard and Hamilton, tool 2,assuming a symmetrical regular solution, AH °us(cal- 1989). Even in compositions without immiscibility, car- 124 TREIMAN: Ca-RICH CARBONATE MELTS bonate anions tend to form clusters that exclude poly- 1986). As calcite accepts little OH or La 3+ in solid so- merized silicate anions (Mysen and Virgo, 1980). The lution, the calcite-saturated liquidus may be modeled as degree of this nonideality is a function of the composition [ of the silicate melt (Mysen and Virgo, 1980; Fine and Stolper, 1985) and remains to be characterized fully. -- _[RT ln(Xc_2+,_ti .... It"/CO2-,ani .... It) k Cation mixing Within the accuracy limits of available data, cation mixing in Ca-rich carbonate melts is adequately de- = Wc.2+__3+(1 - Xc.2+_.,i.... '02 + zSdT°u_(calcite) (13) scribed by the regular-solution model. The regular-solu- T tion parameters W in Table 4 are taken from the litera- 1 -- -- ture and developed here (Figs. 1, 2a-2b, 2e-2f, and 3). Regular-solution interaction parameters for Ca 2+ and following Equations 7 and 12. This equation is in the monovalent and divalent cations tend to be moderate format y = ax + b; when it is graphed in that manner, and negative, suggesting the association of unlike cations experimental brackets on the calcite-saturated liquidus in the melt. The only value for a trivalent cation, La 3+, ought to permit it to be a straight line with a slope of is large and positive. and an intercept of AH°,_(calcite) = 31.5 + 1 WCa2+_La3+ Alkali cations. The interaction parameters W for Ca- kJ/mol. The limited data are consistent with regular-so- Na and Ca-K carbonate systems at high pressure (Table lution behavior and Wc,_÷_t_+ = +80 _+ 50 kJ/mol 2(Fig. 4) were derived in concert with AH 0us(calcite ) from data 2f, Table 4). of Cooper et al. (1975) in Figure 2a and 2b. The Wc_2+K+value for 1bar are significantly higher (Table 4, Solution of H20 based on Flood et al., 1949, and Forland, 1955); the source H20 is important, both as a flux to permit melting of of the discrepancy is unknown. A Ca2+-Li + interaction carbonates at geologically reasonable conditions (Wyllie parameter is available in the literature (Lumsden, 1966). and Tuttle, 1960) and as a constituent of the vapors as- The WNa+-K+and WN,+.Li+ of Table 4 are averages from sociated with carbonatites (e.g., Rankin, 1975; Nesbitt the data of Andersen and Kleppa (1976); their precise and Kelly, 1977; McKie, 1966; LeBas, 1977; Rubie and calorimetry showed that both values are slight functions Gunter, 1983). H20 is problematic within an ionic melt of composition across the respective joins. model as it is not an ionic liquid. Further, the speciation Alkaline earth cations. Very few data are available for of H20 in ionic solutions may be affected by cation com- the estimation of solution parameters for alkaline earths plexation, formation of mixed anions (like bicarbonate), (besides Ca) in carbonate melts. The value for Wca2+aa2+ and changes in intrinsic variables (like acidity and fo_)- was defined in Figure 1 during determination of In addition, H20 does not behave as OH does in carbon- AH °us(calcite). ate-rich ionic melts; the calcite-saturated liquidus in To estimate the W interaction parameter for the Ca2+- CaCO3-Ca(OH)2 is effectively straight and not inflected, Mg 2+ cation solution in carbonate melts, Equation 6 and whereas the calcite-saturated liquidus in CaCO3-H20 is the activity-composition model of Anovitz and Essene strongly curved and inflected, concave up at high CaCO3 (1987) can be applied to the liquidus phase equilibria of contents, and concave down at lower COCO3 contents Byrnes and Wyllie (1981). Figure 2e shows that liquidus, (Figs. 5 and 6, respectively, of Wyllie and Tuttle, 1960). with the range of permissible liquidus locations forced Even so, the solution of H20 in Ca-carbonate melts through AH°us(calcite) = 31.5 _+ 1kJ/mol on the vertical can be described with a simple regular-solution model, axis. The permissible liquidus locations correspond to on the basis of the liquidus surface in the system CaCO3- W = -40 _+ 30 kJ/mol. This result must be used with H20 (Wyllie and Tuttle, 1960, temperatures corrected by caution because the liquidus of Byrnes and Wyllie (1981) -32 K per Gittins and Tuttle, 1964). I will assume that was determined at 10 kbar; the activity-composition H20 ionizes completely into hydroxide and hydronium model has been extrapolated somewhat beyond its known ions on solution in a carbonate melt: range of applicability, and the validity of the activity 2H20 _- H30 + + OH (14) model is in question (McSwiggen, 1993). As a further caution, a similar analysis performed on the 27-kbar li- and so affects both the cation and anion solutions direct- quidus in CaCO3-MgCO3 (Irving and Wyllie, 1975) is ly. The experiments of Wyllie and Tuttle (1960) were consistent with a regular solution W of approximately done with excess vapor in most cases; because the com- zero. Obviously, data in this system are too sparse for position of the vapor is unconstrained, I must assume firm conclusions, but changes in melt structures are pos- further that the mass of vapor was insignificant compared sible. with that of the solid (i.e., that the mass of H20 input to Other cations. Interpretable liquidus data for other cat- the charge effectively represents the mass of H20 in the ions in carbonate melts are limited to lanthanum in the liquid). With this speciation model, Equations 5 and 7 system CaCO3-Ca(OH)2-La(OH)3 (Jones and Wyllie, can be combined and reduced to yield