The distribution of Fe and Mg between olivine and lunar basaltic liquids

Geochimica et Cosmochimica Acta.Vol.42.pp. 1545to 1558 0 PergamonPressLtd. 1978.Printedin Great Britain

0016-7037/78/1C01-I 545SO2.@3/0

The distribution of Fe and Mg between olivine and lunar basaltic liquids JOHN LONGHI*

Department

of Earth and Planetary Sciences, Massachusetts Cambridge, MA 02139, U.S.A.

Institute of Technology,

and DAVID

Department

and JAMB F. HAYS

WALKER

of Geological Sciences, Harvard University, Cambridge, MA 02138, U.S.A. (Received 5 July 1977; accepted in revised form 16 June 1978)

Abstract-We have examined the Fe and Mg distribution between coexisting olivine and lunar basaltic liquids produced by equilibrium partial melting of natural lunar samples. In agreement with the findings of ROEDERand EMSLIE(Contrib. Mineral. Petrol. 29, 275-289) on terrestrial compositions, the logarithms of the conventional distribution coefficients, Kr&_ and K’jf,, are nearly linear functions of inverse temperature; and the exchange coefficient, K,, = Ko,_,_ Fr-M* , is nearly independent of temperature and composition within a given magma group. There are, however, small but significant differences in conventional and exchange distribution coefficients from one magma group to another, e.g. low-Ti vs high-Ti lunar basalts. It is possible to achieve slightly greater precision for the inverse temperature functions by including terms approximating silica activity in the conventional distribution coefficients. The term (ZSi/Oh is apparently the best simple approximation for silica activity in olivine-saturated liquids based upon data for Fe, Mg, Mn, Ca, Ti and Cr. Pressure has noticeable effects upon Fe and Mg distribution between olivine and liquid only above 5 kbar. The excellent linear correlation of the logarithms of the distribution coefficients with inverse temperature allows calculation of approximate values of AR” for the reactions:

2MgOL + SiOl, it Mg,SiO,O, and 2Fe0,

+ Si02, F? Fe,SiO,,

Values obtained, approx -26 kcal/mole, are comparable with values of the heats of fusion of forsterite and fayalite calculated by BRADLEY (Am. J. Sci. MO, X1-554) and measured by ORR (J. Am. Chem. Sot. 75, 528-529). The exchange distribution coefficient for Fe and Mg, K,, is sensitive to large changes in liquid chemistry. Although K,, is explicitly independent of silica activity, K, apparently changes with silica

concentration. This change is a reflection of changes in the mixing properties of Fe and Mg in liquids with different chemistry and hence structure. Regular solution theory predicts that as the mixing properties of an element in a solution change, the most radical changes in activity coefficients occur in the range of dilute concentrations. Therefore, the distribution coefficients for trace elements will also be dependent upon large changes in liquid chemistry, even if corrections for silica and other liquid component activities are applied.

INTRODUCTION F%TROL~GIST~ are now accumulating

perimental

a wealth of exdata on both trace and major element dis-

tribution between silicate liquids and crystalline phases. The correct application of these data to natural systems requires an understanding of the various theoretical controls on the variation of distribution coefficients and appreciation for the limits to which empirical data can be applied accurately. Experimental studies by ROEDER and EMSIE (1970) and ROEDER(1974) on terrestrial basaltic compositions showed near-linear correlations of the logarithms of the olivine-liquid distribution coefficients of Fe and * Present address: Department of Geology, University of Oregon, Eugene, OR 97403, U.S.A.

Mg with reciprocal temperature. Those studies also showed that the Fe-Mg exchange coefficient, K,, remained nearly constant (0.30 f 0.03) over a range of composition and temperature. The present study was undertaken to search for similar patterns of Fe-Mg distribution between olivine and lunar basaltic liquids. The results have application not only to lunar petrology, but also to the general problems of crystalliquid equilibria. EXPERIMENTAL

METHODS

With one exception, starting materials were powders of natural lunar rocks (15555, 15065, 14310. 70215, 70017, 71569.74275, 71255, 72135, 75035, iOO72)and soils (14259, 74220). One sample of rock 12002 was a fused rock powder which we subsequently reground in an agate mortar. Samples were loaded in iron capsules, sealed in evacuated silica tubes (GE214) and suspended in platinum-wound

1545

1546

J. LQNGWI, D. WALKERand J. F. HAYS

vertical quenching furnaces. The samples were quenched by dropping the tubes into beakers of water or oil at the end of the experiments. Temperatures were measured with Pt/lO Rh therm~ouples calibrated against the melting points of gold f1064”C) and ljthium me&silicate [1203”C). Charges were crushed in an agate mortar: and chips were mounted in epoxy, polished and examined in reflected light. Individual phases were analyzed with the electron microprobe. Data were reduced by the methods of BENCE and ALBEE(1968). Most olivine and glass analyses represent the average readings on five different spots. in those cases where the variation in counts for any major element exceeded a homogeneity index value of three (BOYDet al.. 1969). the analysis was discarded. By comparing the duration and temperature of runs with homogenous olivine with those with inhomogeneous olivine. we set up criteria for discarding the results of runs for which we had only a single analysis of olivine and liquid : acceptable runs were carried out at a single temperature and the minimum run time below 1150°C was 24 hr; above llSO“C it was 10 hr. Most melting experiments took place in high-purity iron capsules (Johnson-Mathey Grade I). Many of the lunar basalts were saturated or nearly saturated with iron during crystallization and hence these high purity capsules are convenient means of conducting equilibrium melting experiments on these lunar basalts at nearly constant composition (WALKERet al., 1975). The remainder of the experiments were carried out in low-purity iron tubing (Armcoingot grade). Dissolved impurities in this iron (probably carbon. phosphorous and sulphur) caused a rapid and severe reduction of ferrous iron in the lunar samples during the experiments, thus extending the range of Fe”+/ (Fe*+ + Mg2+) to values considerably lower than those found in the constant composition experiments. Although no attempt was made to measure ferric iron concentrations in the charges, several lines of evidence suggest that ferric iron concentrations in lunar basaltic liquids saturated with iron are low enough to be ignored. The investigations of SATOet al. (1973) and USSELMANand LOFCREN (1976) on low and high-Ti lunar basalts, respectively. show that at 1200°C log foZ values of approx - I3 are appropriate for iron saturation. When applied to the empirical equation (XF’O)L -= -0.2Ologfo, ‘og (XF‘% S),,

- 1.04

of ROEDERand EMSLIE(1970). this oxygen fugacity predicts approx 3% of the iron in the basaltic liquid to be ferric. Given a typical Fe0 concentration of I5 mol”/, FeO,.s concentrations should be on the order of 0.5 mole/, However, even these low concentrations are probably too high because exhaustive wet chemical and Mijssbauer analyses have failed to detect ferric iron in lunar rocks, glasses or phases in which ferrous iron is a major constituent (e.g. MAXWELLet al., 1970). Therefore, we will ignore effects due to variation in ferric iron concentration. THEORY The distribution of ferrous iron and magnesium between olivine and silicate liquid may be described by the following reactions:

2FeOi. + SiOl, = Fe,SiO_,,

2MgOL + SiO,, = Mg,SiO,,

with equilibrium constants of the form ,.FFrlSiOl

KERRICK and DARKEN (1975) and several others have shown that based upon the Fe and Mg occupancy

of two similar octahedral sites in olivine, the activities of the fayafite and forsterite components in olivine are given by (XT*)’ and (Xfo)‘, respectively, if Fe and Mg mix ideally. If we consider non-ideal solution in olivine as well as in the liquid then equation (2) may be expanded to

where X is mole fraction and 1 is an activity coefficient. We may convert mole fraction of fayalite to mole fraction of Fe0 in olivine via X’”

.

01

0.667

By substituting (4) into (3) and then rearranging we arrive at expressions for the conventional, molar distribution coeflkients for iron and magnesium between olivine and liquid: XF’O Kt;:,_ _= -?!-XF’O L

Even if all the solutions are ideal, these distribution coefficients wil1 vary with (X~o~)“* at constant temperature. We can avoid the direct dependence of the distribution coefficients upon silica activity by considering the exchange equilibrium formed by subtracting equation (la) from (lb) Mg,SiO,,

c 2Fe0,

= Fe,SiO,_, + 2Mg0,.

We may follow a derivation similar to that shown above and obtain an exchange distribution coefficient, Kr{p (or K,), that has no direct composition dependence (except through possible compositional dependence of the As) and can give us information only about the ratios of iron and rna~~iurn in coexisting liquid:

(la)

(lb)

(6)

and K

_

o-

Fe,, (1 - Fe), Fe,.(l

- Fe),,

where Fe z XF@/(XF@ + X”gO),

Fe-Mg

in o&vine-lunar basaltic liquids

1547

difficult to identify statistical units even over a limited range of melt composition. The simplest activity models, based upon mixing of oxides (SiOZ. Al,O,. FeO, etc.) and cations fSi4’, Al3 ‘. Fe’+, etc.), obviously do not reflect the statistical units in the melt and hence activities of oxide components in simple melt systems (e.g. HESS, 1975) deviate markedly from ideality. More complex models based upon mixing of different cations on two independent types of sites (i.e. tetrahedral and large cation sites) also pose difficulties. Simple TEMKIN (1945) models, depending upon the grouping of the aluminum tetrahedral network, give the silica acti-AR0 ASo B vity as Si/(Si + Al) or Si/(Si + iAl). These models In K,., = g = RT+R=T+A (8) erroneously predict unit silica activity for all aluminum-fry silicate melts and imply that the stanif AR* and bso remain approximately constant over dard state for silica may be any aluminum-fry melt. the temperature range of interest. The (negative) The Bottinga-Weill melt model of component activienthalpies of reactions (la) (- A&‘z)) and (lb) (-Afi$tg) are related to the respective enthalpies of ties employed by DRAKE and WEILL (1975) gives fusion of fayalite and forsterite, differing only by essentially the same estimates of silica activity as the enthalpy of mixing terms. Since the enthalpies of Si/(Si + iAl) Temkin model for low-alkali melts, but fusion of fayalite and forsterite are similar (BRADLEY, in the case of large cation components poses severe di~culties because the norm-like calculation of 1962), and since enthalpy of mixing terms for silicate species necessitates that some component activities go liquid components tend to be an order of magnitude less than enthalpy of fusion terms (HON et al., 1977). to zero at predictable liquid compositions (LONGHI we can predict that the temperature dependence of et al., 1976). Recent work on the role of oxygen bonding and Kf,PmM* will be much smaller than that of Kr; or K$ coordination in silicate liquids (HESS, 197 1, 1975; because FRAZER, 1975) leads to additional activity models. There are three basic types of oxygen in a silicate melt: bridging oxygens (0’) which link one Al-Si tetrahedron to another, non-bridging oxygens (O-) which form part of an AI-Si tetrahedron, but also form part of the coordination polyhedron of the It is likely, therefore, that the exchange coefficient, larger cations, and free oxygens (02-) which are KI,YTg, will have a much smaller temperature depenbonded only to the non-tetrahedrally coordinated dence than either Kf&, or KzEL. One drawback to working with exchange coeffi- cations. As the concentration of tetrahedrally coordinated cations increases, more tetrahedralcients is that they relate ratios, not absolute abutetrahedral linkages, hence bridging oxygens, are dances of elements. DRAKE (1976a) has shown that needed to balance charge locally and the melt the compositional dependence of conventional distribecomes more polymerized. A simple index of melt bution coefficients can be diminish~ by formuIating structure then is the ratio (Si + Al)/O. If we assume complex coefficients which include activity approxithat melt structure exerts a strong control upon acmations. In our case we have tivities, a Temkin-like approach to modeling silica activity leads to Over limited ranges of temperature and composition, we may reasonably expect the term (J$.LFa)/ (J$.@@) to remain neatly constant and, therefore, we can expect little variation of K, among olivineliquid pairs from the same magma group (e.g. low-Ti mare basalts). On the other hand, marked differences in melt composition, such as the greater concentrations of Na and K in terrestrial alkali-basalts compared to mare basal&, might well change the value of np”/$‘@ even at constant Fe. The temperature dependence of an equilibrium constant is

l

The best melt activity approximations should be based upon mixing models of the statistical units present in the melt. HESS(1971, 1975), BOTTINGAand WEILL (1972) and others have shown that silicate liquids can be regarded as mixtures of polymerized Si-Al tetrahedra and irregularly coordinated metal cations. The larger cations (Fe, Mg, Ca, etc.) tend to break up the tetrahedral polymers or networks and, hence, as the concentration of large cations increases, the polymerization becomes less extensive, i.e. the structure of the melt changes. Thus, it is very

Since Si/O reaches a maximum value of only 0.5 in pure silica melts, the parameter 2Si/O should be a closer approximation to actual silica activity, so we will employ 2Si/O here. HESS (1975) has proposed a more complicated model of silica activity based upon the original development of oxygen equilibrium by TOOP and SA~IQ~S (1962). Hess observed in simple systems that the condensation parameter, P, seemed to mimic silica activity quite well where P=

(0°)

(0°)

2(0°) + (o-) = wio2

(12)

1548

J.

LONGXI,

D. WALKERand J. F. HAYS

The concentrations of the oxygen species, e.g. (O’), may be calculated from the equation

and other charge balance relations given by TOOP and SAMIS(1962). In natural melts it is necessary to make the denominator of the far right term in equation (12) 2(X10’ + x:‘o~~~] in order to apply the model. This correction will give the approximate number of oxygens bonded to the tetrahedral chains; however, non-bridging oxygens may now include oxygens bonded to Al with a double negative charge. TOOP and SAMIS(1962) also proposed a model for large cation oxide melt activities that has a greater range of appli~tion than that used by Hl~ss (1975): $0

= $“

.&‘-

=

M 2+

(

Z large cations >

. (02 3. (14)

We have tested these various activity models by fitting linear equations to the various forms of log Kf&, and log KifL vs l/T K. With the expressions

of log K* vs l/T thus obtained, we compared the temperatures of equilibration calculated from published analyses of olivine-liquid pairs against measured temperatures. Models which gave the least deviation from straight-line fits and which most accurately predicted equilibration temperatures were judged the most useful as empirical ‘geo-’ or ‘cosmo-’ thermometers. RESULTS Fe, Mg olivine-liquid distribution Table 1 contains analyses of representative olivineliquid pairs in weight percent oxides along with temperature and duration of the experiment. All distribution coefficients presented are in terms of mole or atomic fraction. A complete set of analyses in mol”/, oxides is available from the senior author upon request. Figures la and lb display plots of log Kz,LL and log Kz,_ vs 104/T K for low and high-Ti basalts, respectively. Also plotted in Fig. 1 a& lines fitted to our data and lines fitted to the data on terrestriai olivine-liquid pairs as reported by ROEDER and

Table I(a). Compositions of selected liquid-olivine pairs at low pressure in wt% oxides T(C)

TIP=

siop

TiOz

Al203

15065(H)

1269

24.3

1277

la.8

!I

1175

30.2

1.63 0.09 2.68 0.09 2.82 0.16 4.71 0.21 2.88 0.14 4.38 0.20 2.43 0.16 4.06 i

9.39

15555(H)

47.5 38.3 64.3 3R.7 46.3 36.1 44.1 35.3 43.7 38.3 45.6 36.4 68.1 39.3 49.7 41.2 39.4 36.3 38.3 38.2 38.3 38.8 39.7 38.6 39.5 35.8 37.1 38.6

SAMF'LE

,,

1124

50.0

12002(H)

1328

28.0

II

1156

98.8

14259(H)

1201

48.5

12002(L)

1225

40.7

75035(H)

1158

67.5

70215(H)

1175

18.5

70017(H)

1216

19.5

74220(H)

1300

10.8

72135(H)

1135

67.5

-/4275(H)

1224

24.0

n.a. = not analyzed: i = inhomogeneous; Table l(b).

9.36

0.42 11.8 0.43 13.5 0.37 10.0 0.32 9.74 0.53 13.0 i

a.54 10.1 9.84 a.22 11.1 15.1 11.9 9.33 9.31 a.75 6.63 9.15 8.38

%!O3 0.84 0.70 n.ii. ".a. 0.39 0.38 0.24 0.32 0.82 0.78 0.36 0.55 0.27 0.33 n.a. ".a. 0.17 0.22 0.36 *.a. 0.58 0.41 0.56 0.32 0.14 0.19 n.a. n.a.

F&J 19.3 24.4 20.6 24.2 21.0 32.6 23.4 38.4 21.9 21.6 19.6 31.4 12.7 19.3 a.22 11.8 22.0 34.0 la.5 25.1 la.5 20.9 22.5 20.6 23.0 33.9 20.6 22.7

MgO 9.63 36.1 10.6 36.7 6.60 30.0 4.61 24.9 12.5 38.5 6.26 30.6 8.55 40.7 10.8 46.7 5.35 28.2 7.50 35.9 9.19 38.9 12.2 39.5 5.53 28.7 9.23 38.3

MllO n.a. n.a. R.B. n.d. 0.33 0.38 0.35 0.43 0.35 0.28 0.32 0.39 0.26 0.25 n.a. n.a. 0.25 0.33 0.70 n.a. 0.29 0.26 0.12 0.26 0.25 0.32 11.3. n.n.

$0

Nag0

9.72 0.39 9.73 0.37 11.1 0.42 11.0 0.44 8.39 0.34 11.6 0.45 10.2

0.05

0.05

n-a.

*.a.

".a.

0.10

n.a. n.a. n.a.

0.12

n.a.

0.14

n.a.

0.20

12.i 0.32 11.1 a.45 10.9 0.36 9.61 0.34 7.67 0.27 1l.h 0.48 9.83 0.36

n.a.

n.a.

n.a.

0.06

n.a.

0.29

".a.

0.20

n.a.

0.06

n.a.

0.12

n.a.

n.a.

CaO

0.07

H = high purity iron capsule; L = low purity iron capsule. Time in hours.

Analyses of coexisting olivine and liquid at high pressure in wt% oxides

SAMPLE

T(C)

15555(X) ISkbl 15555(H) f5kbl 12002(H) [12.5kbl 120020l) [lZ.Skbl

1295

TME 2.0

1285

2.1

1375

3.0

1375

3.0

SiOZ

TiO;!

43.9 36.5 43.8 36.4 43.6 38.5 44.5 39.2

2.37 0.09 2.48 0.08 2.94 0.09 2.98 0.13

Al203 8.04 8.09 8.52 8.15

CW3 n.a. n.a. R.z&. n.a. 0.90 0.64 n.8. *.a.

Fe0 22.2 26.2 23.2 26.7 20.6 22.0 18.14 19.2

MS0 10.6 35.2 10.3 34.9 12.7 38.5 14.21 41.2

&O n.a. ".a. n.a. *.a. 0.31 0.26 n.a. n.a.

cao 9.21 0.45 9.15 0.39 8.78 a.42 0.32

W

N.?ZO

*.a.

n.a.

*.a.

n.a.

n.a.

0.19

n.a.

".a.

Fe-Mg in olivine-lunar

W-TI

6.0

6.5

basaltic liquids

1549

BASALTS

7.0

6.0

6.5

7.0

Fig. 1. The logarithms of the distribution coefficients, Kr;l.,. and K?,. as functions of inverse temperature. (a) Low-Ti lunar basalts; dashed lines are from equations of ROEDERand EMSLIE(1970) for terrestrial compositions; dotted lines are from equations of ROEDER (1974) also for terrestrial compositions. (b) High-Ti lunar basalts; dashed and dotted lines as in (a); symbols for samples 72135 and 72155 (*) are concealed in the clusters of points; the “Q” symbols represent analyses at Queen’s University reported by ROEDER(1974, Nos. 25 and 28). while the “H” symbols represent analyses of the same experimental charges performed at Harvard University.

EMSLIE(1970) and ROEDER(1974). Table 2 lists linear study is due to a much wider range of basalt chemisregression and correlation coefficients for these lines. try (tholeiites, alkali basalts, ankaramites) than in the Three features of the data stand out. First, the functwo lunar basalt groups or among tholeiites alone tions of Kr& and Ki!tLfor lunar low-Ti basahs are which comprised most of the study by ROEDERand different from their counterparts for high-Ti basalts EMSLIE(1970). From equation (5) we may predict that and both lunar sets are markedly different from their linear relations between the logarithms of conventerrestrial counterparts. Analyses by both groups tional distribution coefficients, Kr;A. and KZE,,and (Queen’s University and Harvard) of two olivineinverse temperature are unlikely unless the range of liquid pairs reported by ROEDER(1974) agree closely composition is small. The presence of near-linear (Fig. 1b) and indicate that the differences between the trends in these three basalt groups is taken, then, to terrestrial and lunar data are not due to analytical indicate that the compositional variations in a given bias. basalt group are sufficiently small to yield these linear Second, by inspection of Fig. 1 and the correlation patterns which, in turn, may be employed as ‘geo-’ coefficients (r) in Table 2 we see that the distribution or ‘cosmo-’ thermometers where appropriate. of points in Fig. 1 are, in fact, nearly linear (the distriThird, for each basalt type, lines fitted to log KI;lL bution of high-Ti points is skewed towards lower tem- and log Ki'_L vs 104/T K are nearly parallel. As perature, so their fits to straight lines are not as a result, the exchange coefficient, KD = K~~_L/K~'_L, tightly constrained as those of the low-Ti data). will be nearly temperature independent. This ROEDERand EM%~E(1970) noted this linearity in their parallelism reflects the similar enthalpies of fusion of study of terrestrial basalts. Notice, however, that there the forsterite and fayalite components in each magma is a marked difference between the correlation coeffi- type. The enthalpy of the exchange reaction, equation cients for the KL&, (0.80) and KZZ, (0.97) lines from (6), will accordingly be relatively small. the data of ROEDERand EMWE (1970), whereas there Table 2 also contains the error limits for the reis only a small difference between the correlation coef- gression equations expressed as the 99% confidence ficients obtained from the lunar data (0.97-0.98). interval of the standard error of the intercept. For Given that Roeder and Emslie obtained Fe0 concenexample, the estimated temperature error at 1200°C trations in the liquid by mass balance calculations for K!,p-L (low-Ti basalts) is f33”C. Contributing to from analyses of Fe0 and Fe,O, in the whole sample this error are both analytical errors and errors inrather than by direct measurement, the greater scatter duced by ignoring the composition term and activity of the Kr,TTdatais not surprising. Also notice that coefficients on the right hand side of equation (Sb). the correlation coefficients derived from ROEDER’S Accordingly, we attempted to reduce the statistical (1974) data are similar to one another (0.82/0.84) but error somewhat by deriving regression equations inlower than those obtained from the lunar data. The volving complex distribution coefficients which in-’ greater scatter of both Fe and Mg data in the 1974 elude a term approximating silica activity. These

J.

1550 Table 2. Temperature

LONGHI,

D. WALKERand J. F. HAYS

dependence of Fe-Mg distribution coefficients for olivineeliquid based upon the reaction log K = B/T K + A Nn.

1%

[Kl

of points

Roedrr nnd Emslie (1970) Fe c Kl bk kl Roeder (1974) Fe K1 MR Kl Lunar low-Ti hasalts Fe Kl MR Kl Lunar high-Ti basalts Fe KI Ma Kl

B

?(A)"

A

r

27

3911

-2.40

27

5696

-1.847

C.038)

,965

19

3504

-2.226

C.164)

19

3509

-1.709

K(1200"C)

pairs

b kT(1200"C)

.x0

4.60

23

,815

1.42

107

1.148) .843

4.72

88

33

2841

-1.840

C.015)

,979

I .?1

30

33

2798

-1.330

(.Olh)

.9?6

3.71

33

29

1131

-2.121

c.016)

,966

1.01

28

29

2955

-1.477

c.0111

,981

3.62

21

34

.,X ",YJ' LYCI,PFFICiE:!?.“ Lunar

low-Ti basalt5 FC KZ KI;e

Terrestrial - Roder (1974) Fe KZ Fe KI, Fe K5

33

2959

-1.868

(.018)

,973

1.38

33

2906

1.R57

C.017)

,977

1.31

32

33

2858

1.437

c.0131 .985

2.25

25

33

2806

I.647

C.012) .986

l.Rl

25

33

2595

-1.976

C.022) .952

0.390

47

33

2916

-1.359

(.021)

0.390

47

33

2864

-1.347

c.0151 ,969

3.95

37

33

2814

-1.228

C.015) .980

6.80

30

33

2759

-1.135

C.014) ,982

5.48

28

33

2537

-1.649

(.018) .964

1.18

42

.952

19

3528

-2.181

c.169)

,809

1.64

104

19

3492

-2.106

c.129) ,871

2.60

80

19

3463

-2.028

(.121)

.883

2.10

76

19

3535

-1.664

C.154)

.833

5.44

96

K4 "g

19

3500

-1.590

c.123) .882

8.62

77

KS Mg

19

3469

-1.512

(.121) .884

6.97

76

Kyg

K?:= KL

= x;O/x k!OiKY = K:/(Si/Si + A1)‘82;KY = Ky/(fji/Si + j-A])’ 1; KY = K~/(2Si/O~“;

KY = KY/(X:!):

‘: Kz = X~“/[a~” .(c$“~)’ ‘]-oxygen

model.

‘99% confidence interval of the standard error of the intercept, “Error in temperature at 1200°C computed from +(A). ‘As reported by ROEDERand EMSLIE(1970).

are also shown in Table 2 for the low-Ti basalts. We see that not all expressions for silica activity improve the linear correlation and shrink the error limits. Indeed only the simple $l”2 models, (2Si/O), and XF (Si/Z cations), consistently improve the regression. We may further test these models by comparing the calculated temperature of equilibration for published olivine-liquid pairs from low-alkali basalt systems with measured temperatures. Two factors prompt us to consider only comparisons based upon the Ky$ equations: (1) ferric iron concentrations in liquid, although presumed low, are nonetheless uncertam and, given the variety of experimental techniques employed to maintain low oxygen fugacity, undetected ferric iron might be a source of error; (2) if the olivine activity-composition relations reported by WILLIAMS (1972) are approximately correct, then ,I: results

will vary much more than $$ for the range of olivine compositions to be tested (Fe = O.OS-O.50) because regular solution theory (THOMPSON,1967) predicts that the activity coefficient of component i in a nearly symmetrical binary solution will vary much more in the composition range X’ = GO.5 than in the range Xi = 0.5-1.0. Thus, Table 3 contains differences between measured temperature and temperature calculated from the Mg-equations in Table 2. Overall, the results of the comparison reflect the ability of the complex coefficients to improve the regression shown in Table 2. We see that the equations with (2Si/Oh and Xsi as ~$2~2approximations work better than the equations with the Temkin or oxygen model approximations and provide only marginal improvement over the equation with the conventional coefficient, Kp4. Results for the equation with the model silica activity, Si/(Si + jAl), are similar to those of the Tem-

Fe-Mg in olivine-lunar Table 3. Comparison of measured tem~ratures

of o~vin~~iquid pairs and tem~ratur~ equations log

(1)

17

basaltic liquids

11% 1279

K,‘$$ =

1551 calculated from empiricat

GK+A

(6.0)

15.5 (9.9)

-10.5 (16.8)

6.1 (17.7)

-10.6 (20.8)

-12.7 (23.7)

-53.2 (64.3)

12.6

(2)

6

12031252

(3)

7

12201320

(Z)

25.3 (28.8)

(I';::,

<1::;,

-46.7 (53.6)

12251250

-13.6 (17.1)

{I:::,

-16.6 (21.8)

-19.9 (25.2)

-75.0 (86.7)

7

11291179

-11.5 (15.5)

-11.4 (15.9)

-7.9 (11.6)

-6.7 (10.9)

-2.5 (11.6)

41

11291320

&

-0.2 (13.5)

-0.4 (15.2)

-22.2 (40.4)

(4) (51 Total

4

Average values of A~(rne~ur~ - calculated) for each data set are listed with the standard deviation in AT for each data set given in parentheses. +k=*=

0.16 [cf. equation (13); 0.16 is an optimum value for these compositions trial and error].

obtained

by

(1) %OLPER (1977) and unpublished data. (2) HUE~NERet at. (1976~iron capsules. (3) WEILLand MCKAY(1975).

(4) MERRILLand WI~I~S (5) BEGGAR et af. (1971).

(1975).

kin model and are not shown. The presence of some aluminum in non-tetrahedral sites might account for some of the failings of these models. It might be possible to achieve better results with the oxygen-species model by varying values of k [equation (1311,the percentage of Al in tetrahedral sites, and molecular groupings in the liquid (e.g. FLOODand KNAPP, 1968), but it is doubtful that such a model would be more accurate or less empirical than the simple (2Si/C& and X? models. The accurate prediction’of measured temperatures from experiments on lunar mare basalts [ref. (5) -BIGGAR et al., 19713 demonstrates the internal consistency of the empirical models. Small temperature differentials calculated from the data of STOLPER (1977) imply that the Mg-o~vin~liquid equations may also be used as ‘cosmo’-the~ometers in the study of basaltic achondrites. The empirical equations do not predict temperatures as well for the olivineliquid pairs reported by MERRILL and WILLIAMS (1975) and HUEBNERet al. (1976). These liquids have higher Si and Al concentrations and lower FejMg than most of the mare basalt liquids and are similar to KREEP basalt compositions. Note in Fig. la that the KREEP compositions 14310 and 14259 show some of the strongest deviations from the linear regression trends. These deviations are probably due to activity-composition relations not accounted for by the empirical equations~ither changes in silica activity or in the activity coefficients of Fe0 and MgO in the liquid. Such deviations as well as the contrast between the regression equations (Table 2) o.c*.42/10-F

for lunar and terrestrial olivine-liquid pairs indicate that these empirical equations are useful only for specific magma types.

We have derived regression equations for Fe-Mg distribution between olivine and liquid versus l/T K in other systems as well as equations for other elements to see if the patterns observed above have general application. Table 2 contains regression parameters of the Fe-Mg distribution for terrestrial compositions reported by ROEDER (1974). Here again the (2Si/Oh and xSLisilica activity approximations improve the Linear correlation of the data relative to the conventional coefficients and work better than the Temkin approximations (we have not pursued the oxygen models with terrestrial compositions). Tables 4 and 5 contain regression parameters for K:;%, K:__f’, K:!!f, and Kzf$. derived from the lowTi lunar data and also contains parameters for Kz!$ and K$$ obtained from the data of WATSON (1977) in the system Mg,SiOl-CaA1&20s-NaAlSiJOs doped with MnO. From Table 4 it is obvious that the olivine-liquid distribution coefficients for Ti, Cr and Ca do not correlate well with inverse temperature in contrast to the coefficients of Fe, Mg and Mn. ROED~~ (1974) and WATSON (personal communication) have previously noted the poor correlation of log Kz?$_ with l/T K. Furthermore, ROEDER(1974) has reported a significant correlation (r = 0.8) between Xrr& and X$” in his data; a similar correlation (r = 0.7) exists in our data as well. Thus, larger devi-

1552

J. Table 4. Correlation

LONGHI,

D. WALKERand J. F.

HAYS

coefficients and error limits for various regression equations K:_,. = B/T + A

of the form log

r = correlation coefficient; $ T(12oo”C) is the temperature error at 1200°C computed from the 997” confidence interval of the standard error of the intercept. K, = Kz_,. ; K2 = Ky/(Si/Si + Al):‘*: Ks = Ky/(Si/Si + fA1):“; Kd = Ky/(2Si/O):‘: KS = K:/(Xf’)’ M K

r

Kl .30 K:

K3 KI, KS %

TiOa (A) iT(1200”C) 462

.22 .2?

.32 .28

413

r

CrzOs (s1 iT(12OO”C) r .32 .15 .14

455

.20 .23 .26 .23

.39 .29

15.5

.25

740

cao (0 CT(lZOO’C) r

(A) TiOr: low-Ti lunar (25 points). (B) Cr,O, : low-Ti lunar (15 points). (C) CaO: low-Ti lunar (30 points). (D) MnO: low-Ti lunar (12 points). (E) MnO: WATWN (1977) (29 points--‘basaltic’ (F) MgO: WATSON(1977) (29 points-‘basaltic’

ations of Ca-components from ideal mixing in both olivine and liquid, as opposed to Fe, Mg and Mn components, most probably are the cause of the lower correlation coefficients for Kz$. Lower concentrations leading to larger analytical errors and multiple valence effects as we11as more pronounced nonideal&y may contribute to the low correlation coefficients of log K$2 and log K$_f3 vs inverse temperature. The poor correlation of olivine-liquid Cr distribution with temperature is also a feature of the data of HUEBNER et al. (1976). Despite the poorer correlations with temperature, Table 4 does show that the logarithms of complex distribution coefficients of the form Kz_,/(2Si/0),!‘2 correlate slightly better with inverse temperature than do the logarithms of simple distribution coefficients for a variety of elements. Also, in every case the complex coefficients with the simple silica activity approximations, (ZSi/Oh and Xp, correlate as well or better with inverse temperature than the coefficients with Temkin-like silica activity approximations (Kz, K3).These patterns for minor and major elements in lunar and simple synthetic systems are simiTable 5. Regression equations and average distribution coefficients for various olivine-liquid distribution coefficients log K = B/T + A

.88 .74 .78 .YO .87

‘: K, = ~~“/[~~“.(~~“z)“LJ--oxygen

Mno (0) tT(12OO”C) r a7 78

Mn@iE) fT(1200”C)

.A9 .94

85

.94 .94 .8Y

61 63 86

63

I.94 .96 .‘15 .Y7 .Q?

model. *iso (8 tT(lZOO”C) 60 46 52 42 43

compositions). compositions).

lar to those found for Fe and Mg in the lunar and terrestrial basaltic systems. The data suggest, therefore, that (ZSi/Oh is the most useful simple approximation for silica activity in basaltic systems. Table 5 contains regression equations for the compiex coefficients showing a significant temperature dependence in Table 4. Where there is no significant temperature dependence, the average value and standard deviation of the conventional molar coefficient are listed.

Figure 2 is a plot of Fe/(Fe + Mg),,, vs Fe/ (Fe + Mg), for the lunar olivien-liquid pairs along with lines of constant KD, 0.33 (the average of the low-Ti basalt pairs) and 0.30 (the average of the terrestrial basalt pairs from ROEDER, 1974). Again, the low- and high-Ti hmar basalts form distinct groups with limited ranges of K, and these two groups are in turn distinct from the terrestrial average. As with the terrestrial ohvine-liquid pairs, the lunar K, values show only minor dependence upon temperature and Fe/(Fe + Mgf, and thus their average values (0.33 low-Ti and 0.28 high-Ti) may be used as a convenient check of olivine-liquid equilibria, e.g. GROVE et al. (1973). There is an obvious correlation between TiQ, concentration in the liquid and K, (r = -0.95) noted previously by L.QNGHI et al. (1976) and shown in Fig. 3. There is also, however, a strong correlation between KD and XF (r = 0.86, Fig. 4af due to a strong overaIl, negative correlation of TiO, and Si02 among lunar basal% The question then is which relationship is causal and which is coincidental? Although changes in XT’Oz undoubtedly influence Fe-Mg equilibria in silicate liquids, comparisons with terrestriaf I(, data suggest that variation in Pl is the dominant influence: among the terrestrial olivineliquid pairs investigated by ROEDER (1974) there is a large variation in K,,with little variation in TiO,

Fe-Mg

in olivine-lunar

basaltic liquids

1553

Fig. 2. Fe-Mg exchange relations between olivine and lunar basaltic liquid. Kn = 0.33 is average value of low-Ti basalts; K, = 0.30 is average value for terrestrial basalts (ROEDER,1974). Symbols as in Fig. 1. (Fig. 4b); hbwever, a weak correlation (r = 0.45) does exist between Ko and Xsl even in Roder’s data. Also, in a less complex aluminum-free system, IRVINEand

KUSHIRO(1976) have observed a dependence of the Ni-Mg exchange coefficient, Kz_Tg, upon silica concentration. The dependence of K, upon silica concentration in the liquid has a basis in theory even though the exchange coefficient does not explicitly depend upon silica activity. Recall from equation (7) that Ku is equal to a temperature-dependent equilibrium constant times a term involving the ratios of olivine and liquid activity coefficients. Given the similar temperature interval and ranges of olivine composition of the high and low-Ti lunar olivine-liquid pairs, we attribute the systematic differences in Ku between the two

#;;f,,,;,,;iiy/ 0

2.0

4.0

mole Fig. 3. Kpag

GO 8.0 10.0 12.0

% TiO,

as a function of mol% TiO, in coexisting liquid.

groups to systematic differences in the term x&o/@@, which in turn reflect fundamental differences in the mixing properties of iron and magnesium in these two magma types. The mixing properties change in response to liquid structure, i.e., the degree of Al-S tetrahedral polymerization, which is primarily dependent upon silica concentration (e.g. BOITINGA and WEILL, 1972). Thus, we have the basis for the dependence of KD upon XF. There is probably an intrinsic effect of Ti upon Fe-Mg equilibria apart from depolymerizing silicate liquids, but we cannot separate it with our data. We have tested multiple regression models of the linear dependence of K, upon pLi, Xt’, Xra + X2 and Fe/(Fe + Mg), for 62 lunar olivine-liquid pairs and the 19 pairs reported by ROEDER(1974). We employed a modified sequential, stepwise regression procedure (DRAPERand SMITH,1966) by choosing the variable with the best linear correlation with K, as the first variable and then testing the other variables in order of decreasing correlation with K,. At each step an F-test was applied to check if the variable improved the regression at the 0.95 confidence level. The results are shown in Table 6 for each successful test. We observe that the strongest correlation with KD among both the lunar and terrestrial compositions is with Xs,‘, but the overall fit is much better among the lunar compsotions. One of the causes of the poorer correlation among the terrestrial olivineliquid pairs may be the limited number of data points at low XF values. Alternatively, progressive alkali loss during these experiments may have distrupted olivineliquid equilibrium. Also listed in Table 6 is the mul-

1554

J.

.37

-

35

-

I

:

LONGHI.

D. WALKERand J. F. HAYS

0

A

0

08 a

“0,”

.33 -

.35

‘3

m 0

I

(b)

I

Na+K

XL

.33 0

&I

KD -

.31 -

.31

-

.i?s -

.29

-

.2? -

.2? -

. 1.7

.25 -

.

2.0

25 t

.36

36

.40

.42

.44

.46

.40

.52

.50

I

..I6

.36

.46

.42

.44

.46

.46

.60

.52

XSi

XSi L

L

Fig. 4. K, as a function of silica concentration. XT,‘.(a) Lunar basalts, symbols as in Fig. 1. (b) Terrestrial basahs (ROEDER. 1974):open symbols, Xp + Xp < 0.05; closed symbols. Xpa + X: 2 0.05; numbers adjacent to symbols are concentrations of TiO, (mol%) in coexisting liquid. Symbol with “X” represents synthetic lunar basalt. Large arrows show the dependence of Ku on other composition variables (at constant Xy) found to have significant linear correlation with K, (Table 6).

tiple regression equation for the lunar K, data with (2Si/O), as an independent variable. We see that K, increases with Xs,’ and tends to decrease with increasing aluminum and alkalies. These three parameters are believed to exert the greatest effect upon silicate liquid structure (BOTIINGA and WEILL, 1972). Thus, much of the variation in K, observed in lunar and terrestrial ohvine-liquid pairs is consistent with changes in liquid structure. However, if we had only K, data for the low-Ti lunar compositions, the correlation of KD with X”,i or XT02 would have been much less evident. Thus, it apparently takes rather large changes in liquid chemistry and structure to produce significant changes in K,, Table 6. Multiple regression equations K, = K:,tl~~~= A, + A,X:j + A2X:’ + A,Xp”+K

+ A,CFe/(Fe + A3

-0.0773

0.915

Mgk

A*

-0.313

(f.0306)

(2.066)

-0.252 (f.026,

1.446 -0.160 (?.084) (?.078)

Ct.098)

mrrestriat - 29 pts: 0.165 (Z.066,

0.299 (1.143,

-0.0804

0.54: ct.1711

(t.0711)

*R = multiple regression coefficient. **() = standard error of estimate. ***(2Si/D), is the independent variable for A,.

It*

so that it will be more convenient and profitable in most cases for petrologists to employ a single average value of KD for a given magma type taken from Fig. 4 rather than to calculate KD from the regression equations. High pressure

Only four of seven analyzed runs in high purity iron capsules contained olivine and liquid homogenous with respect to Fe and Mg. Analyses of the products of these four runs are listed in Table lb. Average values of the conventional molar distribution coefficients, K,i’,. and Kit?,_, for the two runs at 5 kbar are 1.00 and 2.91, respectively. These values are quite close to the conventional coefficients computed from the regression equations in Table 2 at 1290°C: 0.950 and 2.88; they indicate that pressure has little effect upon Fe-Mg distribution up to 5 kbar. Values of Kf;>L and KzT at 12.5 kbar are 0.908 and 2.54, respectively. These values are distinctly higher than those calculated from the regression equations at 1375°C: 0.765 and 2.33; they indicate that at pressures greater than 12.5 kbar (and probably greater than 5 kbar) pressure is a significant factor affecting Fe and Mg distribution between olivine and liquid. Pressure seems to affect Fe-Mg exchange relations as well. The two runs at 5 kbar are both from rock 15555 and give K, values of 0.354 and 0.341. The seven low pressure runs from rock 15555 in high purity iron have an average KD of 0.342 with 0.019 standard deviation. Thus, there is apparently no significant shift in K, at pressures up to 5 kbar. The two runs at 12.5 kbar are both from rock 12002 and give K, values of 0.365 and 0.352. The eight low pressure

Fe-Mg in olivine-lunar runs from 12002 in high purity iron have an average

Kn of 0.322 with 0.010 standard deviation. Thus, there is a statistically significant increase in Kn at 12.5 kbar. This increase implies that the olivine coexisting with a given liquid at high pressures is more iron-rich than olivine coexisting with the same liquid at low pressures. The effect, however, is not large and may be ignored except where great precision is required: for example, a liquid with Fe, = 0.5 and Kn = 0.32 gives olivine with Fe,, = 0.242, whereas K, = 0.36 gives Fe,, = 0.265. DISCUSSION In deriving the compositional and thermal dependence of the conventional distribution coefficients we have avoided more complicated approximations of @” and 4” (with the exception of the oxygen species model), in order to simplify the use of the empirical equations. A parallel series of empirical equations containing Temkin and other approximations for a?@ and gco in the lunar liquids (e.g. $@ = Mg/E (large cations), @so = Mg/O) were derived, but did not improve the precision, so the simpler equations are preferred. The equations with 8’” approximations, however, did have slopes very similar to those of the simpler equations in Table 2, i.e. B-values ranged from 2500 to 2900. The similarity of the slopes of regression equations with various L$*, $80 and $2’1 approximations holds promise that approximate values for the standard enthalpy of reactions (la) and (lb) may be obtained from these empirical equations where ranges of chemistry are not large. If we substitute equation (8) into (10) and take the logarithm of Kr$, we obtain log K:&,

=

-A%,,

Wh,

2(2.303)RT + 2(2.303)R + log[(O.667)(I;&/LQ)].

(15)

Since we are dealing with relatively small ranges of composition in a given magma group, the activity coefficients, z2” and 22, probably vary in the same direction in response to temperature and composition changes-the excellent linear correlations in Table 2 would be fortuitous otherwise. If the ratios, L[“/Lg and Ay@/Lz, have no net temperature dependence we can obtain average standard enthalpies from the slopes (B-values) of the empirical equations from the relation AR0 o -2.(2.303).R.B.

(16)

Calculated values of AHFia, and Anyi,, for lunar low-Ti basalts range from -23 to -27 k&/mole with a best value of -26 kcal/mole [$Oz o 2(Si/O)L] obtained for both reactions (la) and (lb). Values of As:, a) and AH:, b, for the high-Ti basalts are comparable. These standard enthalpies of crystallization are similar in magnitude to enthalpies of fusion calculated

basaltic liquids

1555

from the Mg,SiOrFe2Si04 phase diagram by BRADLEY (1962): 25.2 (fa) and 29.3 kcal/mole (fo), and to the enthalpy measured by ORR (1953): 22 kcal/mole (fa). Although the magnitude of the enthalpy of fusion of fayalite (Aw), for instance, will not equal the standard enthalpy for reaction (la) (A@‘,,,) unless the heat of mixing along the FeG-SiO, join is zero, the similarity of the various values of AR0 and Aflr is a good indication that the equations derived for the logarithms of KE$ and Kz$ vs inverse temperature reflect equilibrium between olivine and lunar basaltic liquids. Calculating AR0 from the slope of the equations for terrestrial basalts (Table 2-data from ROEDER, 1974) gives AR?,,, z A&,, = - 32 kcal/mole. The Mg data of Watson (K,-Table 5) give AflFib) = -35 k&/mole. Since AR0 for a given equilibrium ought to be the same in all related systems, these higher values of Ai?’ show that the assumptions that led to equation (16) are not entirely correct. Given the excellent linear correlation (r = 0.97) obtained from Watson’s data, the steeper slopes and hence higher calculated values of AR:,,,, are probably due to net differences between the thermal dependence of the term log [(0.667)(L~fi/J.~)] in the terrestrial and synthetic systems as opposed to the lunar systems. Within the lunar and synthetic systems, at least, the variation of log [(0.667)(np@/$$] vs l/T K must be nearly linear; and within the lunar system this variation is probably relatively small. Systematic changes in the activity coefficients of the MgO and Fe0 liquid components due to the higher concentrations of alkalies in the terrestrial and synthetic systems seem the probable cause of the net differences in temperature dependence. BRADLEY (1962) also calculated the enthalpy of fusion of the Mn2Si04 components as 26.2 kcal/mole, which is in good agreement with the value of - 23 kcal/mole calculated from the regression equation (lunar) in Table 4. Again, regression equations for the terrestrial and iron-free systems, which have higher concentrations of alkalies, have larger values of B and hence give higher values of AB’(Mn,SiOJ = -34 and - 35 k&/mole, respectively. The similarity of the slopes of regression equations for analogous Fe and Mg distribution coefficients in a given basalt group (Table 2) is a good indication that the enthalpy of the exchange reaction [equation (6)] has an absolute value less than 1 k&/mole. Accordingly, the Fe-Mg exchange coefficient, K,, will have insignificant thermal dependence in each magma group. We have noted, however, that K, is compositionally dependent and is apparently related to the systematic change of the term, Ly@/L[&, with liquid structure. The change of Lyfl/l[eo with liquid structure can be rationalized in terms of regular solution theory and has important applications to trace element partitioning. From THCMPSON (1967) the activity coefficients of a binary, symmetrical solution are given by

J.

1556

LONGHI,

D. WALKERand J. F.

the equation ,n

1’

=

Wo(l -

X’J2

RT

(18)

where Xi is the mole fraction of component i and W, is a free energy term related to the excess free energy of mixing-the larger the value of IV,, the greater the departure from ideal mixing. Although such an equation is too simple to be applied directly to basaltic liquids, it illustrates that when the mixing properties of a solution change, i.e. when W, varies, the largest absolute changes in the activity coefficient of a component occur at dilute concentrations of that component. We believe that the systematic changes in KpmM” among the lunar and terrestrial basalt systems are reflections of changes in the mixing properties of Fe and Mg with composition, and that it is most probable that the mixing properties of the other elements in these basaltic liquids change as well. Therefore, there should be systematic variations in the activity coefficients of all the elements, but especially trace elements, among the basalt systems. These variations will alter crystal-liquid distribution coefficients. Changes in activity coefficients of elements present in dilute quantities are not contrary to Henry’s Law which predicts only that the activity coefficient of an element will be independent of concentration of that element when the element is present in small quantities. Such changes can be readily demonstrated from partitioning studies in immiscible liquid systems (e.g. RYERS~N and HESS, 1975; WATSON, 1976). Here elements present in dilute quantities are shown to have systematically different concentrations in two coexisting liquids. Since the activity of each element’s component must be the same in both liquids, then different concentrations of an element require different activity coefficients in each of the two liquids even though the activity coefficients are independent of the element’s concentration in each of the two liquids. Although empirical temperature-composition relations for trace element crystal-liquid partitioning are predictably less prone to variation than those of the major elements in a given magma system, the widespread use of a few ‘good numbers’ for trace element distribution coefficients in many different magma systems will inevitably lead to errors. Distribution coefficients ought to be measured in each system of interest (e.g. WEILL and MCKAY. 197.5) even if complex distribution coefficients, such as we have derived in this study, can be employed to diminish the composition dependence of the coefficients within each system. APPLICATIONS When olivine and liquid compositions are both known. calculation of the equilibrium temperature by means of the appropriate equations in Table 2 is straightforward, e.g. FREY et al. (1974). In strongly reduced systems it is possible to check if porphyritic

HAYS

rocks with zoned olivine phenocrysts represent quenched liquids or partial cumulates by computing K, from the composition of the most magnesian olivine and the bulk Fe/Mg ratio of the rock and then comparing the calculated Kn with measured Ku values for the appropriate basalt system. With this technique WALKER et al. (1976a) decided that a lunar picrite (rock 12002) had near-liquid chemistry, whereas WALKER et al. (1976b) were able to show that a magnesian, high-Ti basalt (rock 74275), which had been interpreted as representing a pristine liquid composition by GREEN et al. (1975) contained xenocrystal olivine. Perhaps, the most important application of the data lies in the modeling of evolving magma systems. ROEDER and EMSLIE (1970) have shown that it is possible to calculate the liquidus temperatures of olivine-saturated. basaltic liquids given only the bulk composition. This technique requires a temperatureindependent equation for K, (Table 6) and a temperature-dependent equation for KY&$. (Table 2). From the bulk composition and the computed value of KD, one may calculate Fe/Mg for olivine and, in turn, because of the simple stoichiometry of olivine, Xy@. From the values of Xy@, X2@ and Xs,’ or (2Si/O), one calculates the equilibrium temperature, which in this case is the liquidus temperature. LQNGHI (1977) tested this technique against 41 published and unpublished olivine-liquid pairs from other laboratories and obtained an average difference between reported and calculated temperatures of l.l”C with a standard deviation of 13°C; all estimates lay within +23”C. When one combines the liquidus calculation with empirical temperature-composition relations for olivine and other phases (e.g. DRAKE, 1976a, b) together with a phase diagram appropriate to the basalt system (e.g. WALKER et al., 1973) it is possible to model fractional crystallization of both major and minor elements in olivine-normative systems by a cyclical process of calculating temperature and distribution coefficients, then subtracting a small amount of crystals from the liquid. ROEDER (1975) introduced an alternative approach which involves representing the liquidus surfaces of olivine and plagioclase as multiple linear functions of the oxide concentrations in the liquid. This technique still requires, however, the use of equations such as those in Table 2 to calculate the compositions of the solid phases. The accuracy of such models is dependent upon the various empirical components which can be improved from time to time, but nonetheless these empirical models of fractional crystallization are improvements over models that assume constant distribution coefficients or obtain temperatures of phase appearance from equilibrium experiments on a single bulk composition. CONCLUSIONS The logarithms of olivine-liquid distribution coefficients for Fe0 and MgO vary as near-linear functions

Fe-Mg in olivine-lunar basaltic liquids of inverse temperature for given magma types. We may employ these functions as ‘geo-’ or ‘cosmo-’ thermometers to calculate temperatures of olivine liquid equilibrium in basaltic magmas or melts of similar composition. The linearity of these functions and the accuracy of their predictions can be enhanced by including approximations for silica activity, such as (2%/O),_ or Xs,‘, in the function. Even with expressions for silica activity of the liquid, however, empirical relations obtained for one magma type do not adequately predict temperature-composition relations in a different magma system (e.g., lunar low-Ti basalts vs terrestrial basalts). Systematic changes in the activity coefficients of oxide components in the magmas are to blame. Fe, Mn and Mg distributions between olivine and liquid have similar thermal dependences in lunar, terrestrial and synthetic basalt systems. However, not all elements present in olivine behave in a similar manner: logarithms of the olivine-liquid coefficients of TiO,, Cr,Os and CaO show poor correlations with inverse temperature, and thus only average values for these distribution coefficients are suitable for petrological calculations. We believe large departures from ideal mixing of components in both olivine and liquid to be responsible for the less predictable behavior of Ti, Cr and Ca. Values of KzLL and Kp! show little variation at constant temperature between < 1 atmosphere and 5 kbar pressure. Likewise, the exchange coefficient, Kc, is essentially constant up to 5 kbar. However, at 12.5 kbar values of KE&, Kz8, and K, are noticeably higher than at low pressure. These increases imply that the olivine coexisting with a basaltic liquid of constant composition becomes more magnesian as the liquid ascends from depth. The excellent correlation of the complex Fe and Mg distribution coefficients with inverse temperature provides a means of estimating the average enthalpy difference, AR’, of the olivine formation reactions (e.g. la, b). We may calculate AHo directly from the slope @ term) of the equations in Table 2 if the terms, log [0.667(@“/I+~)] in equation (16) and its Fe analogue, have no net thermal dependence. Values of AR0 obtained from lunar basalts, approx -26 kcal/ mole, are comparable to heats of fusion of olivine components calculated by BRADLEY (1962), 29 kcal/ mole (fo) and 25 kcal/mole (fa), and measured by ORR (1953), 22 kcal/mole (fa). Lower values of Ano obtained from terrestrial (-32 kcal/mole) and synthetic (-34 kcal/mole) systems suggest that the activity coefficient term in equation (16) does have a net, but systematic, thermal dependence related to alkali concentration in the liquid, so that only in the case of the low-alkali lunar basalts do the calculated values of AHo approximate the true values. Exchange relations of Fe and Mg between olivine and liquids with small composition range exhibit nearly ideal behavior with neglible temperature dependence. Hence a single value of the exchange

1557

coefficient, K,, for a given magma type is sufficient for most petrological applications. However, KD apparently varies with liquid structure so that where very large changes in liquid composition occur, the value of K, must be adjusted. Silica concentration in the liquid seems to be the dominant control of K, variation and we may employ empirical corrections to account for much of this variation. The difference between average K, values for the low-Ti (K, = 0.33) and high-Ti (K, = 0.28) lunar basalts is due primarily to the different mixing properties of Fe and Mg in liquids of the two suites. Regular solution theory predicts that variations of activity coefficients will be most pronounced in the range of dilute concentration (trace elements) if the mixing properties of the elements change. Therefore, it is not good practice to apply trace element distribution coefficients, be they conventional or complex, obtained from one magma system to another system with marked chemical differences. Acknowledgements-This research was supported by NASA grants NSG-7081 (M.I.T.) and NGL-22X107-247 (Harvard) and by the Committee on Experimental Geology and Geophysics of Harvard University. We wish to thank J. W. NICHOLLS, P. L. ROEDER and J. M. RICE for helpful reviews, and also P. L. ROEDERand E. M. STOLPERfor sharing data.

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