Olivine-liquid equilibria and the chemical activities of FeO, NiO, Fe2O3, and MgO in natural basic melts

0016.7037/92/$3.00

Geochunico ef Cosmochim~ca Acln Vol. 56, pp. 303-318 Copyright 0 1992 Pergamon Press plc. Printed in U.S.A.

Olivine-liquid

+ .ll

equilibria and the chemical activities of FeO, NiO, Fe,O,, and MgO in natural basic melts

DON A. SNYDERand IAN S. E. CARMICHAEL Department of Geology and Geophysics, University of California at Berkeley, Berkeley, CA 94720, USA (Received July 23, 199 1; accepted in revised form October 30, 199 I )

Abstract-The distribution of the cations Fe+‘, Mg+' , Ni+’ , Mn +*, and Ca’* between olivine and natural basic liquid is experimentally explored at one atmosphere as functions of oxygen fugacity, temperature, and composition. By performing the experiments in equilibrium with NiFe alloys, the chemical activities of FeO, Fe203, and NiO were monitored in the melt and from knowledge of the thermodynamics of olivine mixing, the activity of MgO was also calculated. This is the first time that the activity of Fe203 has been monitored in a natural melt and also the first observations of the variation of aFeo with oxygen fugacity. Empirical models for the variation of the activities of these components as functions of oxygen fugacity, temperature, and composition are presented and the models for Fe0 and MgO are shown to be able to predict the olivine composition. The partition coefficients for FeO, MgO, NiO, and MnO for olivine were found to be invariant over more than 9 orders of magnitude in oxygen fugacity. The calcium partition coefficient decreases with increasing so,, but this is due to the changing olivine composition with oxygen fugacity. Nickel, manganese, and calcium partitioning are functions of composition and temperature, although thermodynamic analysis shows that the temperature variation for NiO and MnO is primarily due to the temperature dependence of the activity coefficients rather than a large enthalpy of the exchange reactions. Empirical predictive models are presented for the partition coefficients of all of the divalent cations. the NizOs/NiO ratio) and (2) by changing the FeZ03 content of the melt and thereby altering the activities of NiO and MnO in the olivine and liquid. Using this logic, MYSENand VIRGO ( 1980) suggested that DNio (sX$io/Xzo where X: is the mole fraction of component i in phase .i) may change as much as 200% from air to the iron-wtistite oxygen buffer (IW). They did not, however, explore this potential relationship experimentally. Two studies have treated oxygen fugacity as a variable which may affect these equilibria in iron-bearing liquids. EHLERSand GROVE ( 1990) varied oxygen fugacity from one log,,, unit above the nickel-bunsenite oxygen buffer (NNO) to the quartz-fayalite-iron oxygen buffer and saw no dependence on oxygen fugacity except in iron saturated runs. TAKAHASHI( 1978) varied fo, from just above the IW buffer to values somewhat less than the quartz-fayalitemagnetite buffer ( QFM ) , a range of approximately three orders of magnitude. Although he resolved no dependence on oxygen fugacity, it is now recognized that the range of oxygen fugacities at which basic lavas equilibrate is much larger, extending from the IW buffer to several orders of magnitude above NNO (a range of more than seven orders of magnitude; CARMICHAEL,199 1). The ferric/ ferrous equilibrium varies considerably over this range changing most rapidly near the NNO buffer ( KRESS and CARMICHAEL,199 1) This effect of changing olivine composition with fo,, coupled with possible valence state changes in Mn and Ni, suggests that the partitioning of these divalent cations may be dependent on oxygen fugacity, a possibility not yet fully explored. Unlike oxygen fugacity, temperature and composition have both been widely recognized as intensive parameters which control element partitioning between olivine and liquid. Regarding Ni, for example, investigators have offered models which place all of the variation in temperature or composi-

INTRODUCIION

SINCE THE STUDY OF HAKLI and WRIGHT ( 1967), the partitioning of divalent cations (viz., Mg+‘, Fe+‘, Ni+*, Mn+*, and Ca+*) between olivine and silicate liquid has been investigated more often than perhaps any other problem in experimental petrology. This frequency is not without reason: olivine-liquid equilibria have contributed greatly to our understanding of magma evolution. Its quantification has led to applications in thermometry (e.g., HAKLI and WRIGHT, 1967; LEEMAN and SCHEIDEGGER,1977); to test for phenocryst-groundmass equilibrium (e.g., ROEDERand EMSLIE, 1970; LEEMANand SCHEIDEGGER,1977 ) and as a criterion for primary mantle melts ( SATO, 1977). Knowledge of the dependence of divalent cation partitioning between olivine and melt on all of the relevant intensive parameters is, however, still incomplete. The effects of pressure and oxygen fugacity (fo,) and resolving the simultaneous effects of temperature and composition remain unsettled. Oxygen fugacity affects chemical equilibria in magmas by changing the valence state of transition metal cations. Significant quantities of both ferric and ferrous iron exist in natural silicate liquids and the redox equilibrium as a function of composition, oxygen fugacity, temperature, and pressure can be calculated ( KRESS and CARMICHAEL, 1991). The equilibria between oxidized and reduced forms of nickel and manganese in natural silicate liquids are, however, poorly known. Both have been assumed to be dominated by the +2 valence state throughout the oxygen fugacity range of natural lavas based on several experiments on simple synthetic systems (JOHNSTON, 1965; PAUL and LAHIRI, 1966). Oxygen fugacity could affect Ni and Mn partitioning in two ways: ( 1) by directly changing the fraction of oxidized cations (e.g.,

303

D. A. Snyder and I. S. E. Carmichael

304

tion.Forexample, LEEMAN and SCHEIDEGCER(~~~~) present a model for which composition plays a minor role and consequently suggest its use as a thermometer. KINZLER et al. ( 1990) on the other hand exclude temperature as a predictive variable, choosing to ascribe all of the variation to composition. If Kinzler et al. are correct, partitioning of these elements serve as poor thermometers. The purpose of this study is to experimentally examine the partitioning of Fe+*, Mg+*, Nit*, Mn+2, and Ca+2 between olivine and liquid focusing on the effect of oxygen fugacity and resolving the roles of temperature and composition at one bar. In doing so, we have chosen a range of natural liquids so that calibrated models need not be extrapolated to temperatures and compositions outside of the experimental database. In addition, we have performed many of the experiments in equilibrium with NiFe alloys which permits the chemical activities of NiO, FeO, Fe203, and MgO to be monitored. We use these activities to formulate models for the partition coefficients and present empirical models for the activities of ferrous iron, ferric iron and magnesia in natural basic liquids. EXPERIMENTAL

AND ANALYTICAL TECHNIQUES

Experimental Procedures Since a major objective of this study was to separate the effects of temperature and composition on element partitioning, a large compositional range of starting materials was chosen. We also sought to bracket the range of temperature and composition of natural lavas in order to obviate extrapolation of partitioning models. Accordingly, the seven samples chosen were: a leucite basalt (08), a basaltic andesite (44), a trachybasalt (46), an absarokite (48), an ugandite (50), a minette ( 77 ) , and a ferrobasalt ( 83 ) Olivine is an equilibrium phase in all of the rocks, although not necessarily on the liquidus. Starting compositions are tabulated in Table 1. Comminuted samples were mixed with a polyvinyl alcohol to form a slurry and placed on wires formed into approximately 2.5 mm

diameter loops. At low oxygen fugacity, Ni alloys readily with platinum leaving (in equilibrium) melts impoverished in nickel. Consequently, nickel or twisted pairs of iron and nickel wires (0.10 mm diameter) were used for runs below NNO whereas platinum (0. I3 mm diameter) was used for more oxidizing conditions. All experiments were conducted at one atmosphere pressure in a vertically oriented MoSil resistance furnace where oxygen fugacity was controlled by mixing CO and COZ and calculated from DEINES et al. ( 1974). Total gas flow velocities were typically 0.25 cm/s. Oxygen fugacity is believed to be accurate to kO.05 log,, units. Temperature was controlled to within 0.5 K and reported temperatures are believed to be accurate to within 3 K. They are relative to IPTS-68 and were monitored by a type-S thermocouple (Pt/Pt 10% Rh) sheathed in A120,. For the samples run with Ni wire, the sample wetted the Ni and reacted with the wire, gaining Ni and losing Fe. The result was a nickel enriched melt and a N&Fe alloy tire. The equilibrium between the wire and the sample is dependent on oxygen fugacity: at oxygen fugacities near IW, the sample loses nearly all of its Ni to the wire, presumably reflecting a low solubility of metallic nickel in the melt. At higher oxygen fugacities, e.g., near the QFM buffer, the sample gains appreciable Ni and the Ni wire gains Fe. Twisted pairs of 0.10 mm Ni and Fe were used in runs 48,5 1, and 58 in order to approach the equilibrium NiFe alloy composition from two directions. In one of these runs (58), the original Fe and Ni wires are both evident and distinguishable. At the end of a run, the original Fe wires have considerably embayed margins whereas the original Ni wire margins are embayed to a lesser extent. The final alloy compositions of the original Ni and Fe wires were indistinguishable and we have used this as evidence for silicate/alloy equilibrium. Nickel was added to the samples which were conducted on Pt wire in air in the form of Ni( OH)* or Ni203. nH*O. The samples were not doped with any other elements. At the start of each experiment, the silicate material and the alloy were out of equilibrium. Olivine began to grow and probably reached its final size before alloy-silicate equilibrium. Since the melt gains Ni from the alloy, after the time required for alloy-silicate equilibrium, the newly grown olivine and melt are out of equilibrium with respect to Ni. In order to reach equilibrium, the run duration must be long enough for the NiO content of the olivine to equilibrate by diffusion. NiO diffusion in olivine is very sluggish (CLARK and LONG, 197 I; MORIOKA, 198 1) and long run times were required to produce ho-

Table 1. Compositions of starting materials in weight percent. Spec.

08’

44=

46’

48

50

77

83’

SiO,

47.84

52.10

49.21

49.23

40.52

50.76

46.2

TiO,

1.24

0.81

1.33

1.81

5.28

1.70

A,O,

17.90

16.44

14.19

12.26

8.17

12.38

Fe@,

1.88

1.56

4.54

5.39

6.33

3.94

Fe0

6.21

6.05

3.75

2.72

6.29

3.02

3.83 13.4 1.59 15.9

MnO

0.17

0.14

0.12

0.13

0.21

0.10

0.22

MgO

3.87

9.29

8.32

11.85

11.57

8.89

4.66

CZIO

8.68

8.46

7.68

8.24

12.55

7.60

7.58

Na,O

2.78

3.47

4.59

2.78

2.50

2.82

3.56

K@

7.43

0.74

2.82

3.58

3.75

5.83

1.03

P,G,

0.92

0.14

1.37

1.02

0.44

1.28

0.35

H,O+

0.45

0.34

0.19

0.73

1.31

0.09

1.16

Total

99.37

99.54

99.11

99.74

98.92

98.41

99.49

‘Specimen 94-8 from BALDRIDGE et al. (1981); see also SACK et al. (1987) ?jpecirnen Jor 44 from LUHR and CARMICHAEL (1985) YSpecimenJor 46 from LUHR and CARMICHAEL (1985) ‘Specimen 4-83C from WIEBE (1988)

305

Activities of metal oxides in silicate melts mogeneous olivines. For each successful experiment, a series of runs were performed for increasing lengths of time. Each successive run produced olivines which were less zoned and showed less grain-tograin variation than the previous shorter run. Experiments on nickel wire at high oxygen fugacity often required longer run times than at lower oxygen fugacity because of gaining more nickel. Only runs in which all of the phases showed no zonation and no grain-to-grain variation were accepted. Run times ranged from 91 to 332 h after which the samples were quenched into water. Due to the long equilibration times, some samples suffered significant losses of NazO and K20. The bulk of the alkali loss occurs early in long runs and remains relatively constant for the remainder of the run ( KILINCet al., 1983). The final olivine and metal compositions are therefore in equilibrium with the alkali impoverished final glass compositions. Despite considerable alkali loss in some runs, using post-run compositions of samples with a wide range of alkali contents has allowed us to address the effects of alkalis on these olivine/liquid equilibria. For most runs, glass, olivine, and metal were the only phases present, although plagioclase, leucite, and Fe-Ti oxides were sometimes observed (see Table 2). Olivines were equant and generally between 30 and 100 pm across. One disadvantage of experiments in these reacting containers is that the sample is open to Fe, Ni, Na20, and K20 exchange. This makes estimates of modes using mass balance unreliable. Based on our visual estimate, all runs contain at least 90% (volume) glass. All reported analyses are post-run compositions.

locations. Each olivine analysis in the average is from a different crystal. Care was taken to position the beam in the olivines at least 20 microns from the boundary with glass in order to avoid secondary fluorescence of CaO. All olivines showing zonation within a crystal or variation among crystals were rejected. Olivines and trace elements in the glasses were analyzed with an accelerating potential of 20 kV and a sample current of 40 nA measured on MgO. Stoichiometric forsterite, fayalite, liebenbergite, tephroite, and a natural diopside were used as standards for MgO, FeO, NiO, MnO, and CaO, respectively. For NiO and MnO in both olivines and glasses, high and low off-peak backgrounds were subtracted from the counts obtained on the peak. Twenty second count times were used for both peaks and backgrounds on trace elements. For all other elements, backgrounds were determined by an empirical fit of the mean atomic number of the matrix. Major elements in the glasses were analyzed for 10 set at 15 kV and 30 nA on MgO in order to lessen volatilization. Mineral glass standards were used when possible (NBS SRM 470: K-41 1 and K-4 12). Both olivine and glass analyses were calculated by modified Bence-Albee techniques (ARMSTRONG, 1988a). Iron-nickel alloys were analyzed at 15 kV accelerating potential with 30 nA sample current on MgO. Pure Fe and Ni were used as standards and the ZAF corrections recommended by ARMSTRONG(1988b) were employed.

Analytical

A wide range of compositions of equilibrium liquid / olivine pairs were measured and analyses of glasses, olivines, and alloys along with run conditions are presented in Tables 2 and 3. All compositional data are in weight percent. For the

Methods

Analyses were all gathered with the ARL-SEMQ eight-channel electron microprobe at UC Berkeley. Each reported analysis of a phase is an average of approximately ten points taken at different

RESULTS

Table 2. Run conditions and alloy compositionsin weightpercent. For each run identifier, the fist number refers to the starting material and the second to the specific set of run conditions. gl=glass, ol=olivine, pl=plagioclase, Ic=leucite, ilm=ilmenite, tmt=titanomagnetite, ox=undetermined Fe-Ti oxide. Run

T CKj

OS-58

1395

44-51

1562

-7.40

116.8

gl+ol

44-57

1461

-10.29

186.9

gl+ol+pl

93.7

6.26

44-60

1468

-9.83

307.5

gl+ol+pl+ox

94.8

4.61

44-64

1503

-7.97

265.7

gl+ol

-10.29

186.9

gl+ol

94.2

6.16

-9.83

307.5

gl+ol

95.6

5.06

46-V 46-60

1468

lOE,J” -11.15

time (hrsj 332.3

ohases

Ni

gl+lc+pl+ol

89.5

Fe 10.7

48-48

1562

-11.39

96.7

gl+ol

73.0

27.7

48-56

1559

-10.36

192.5

gl+ol

89.3

10.7

48-57

1461

-10.29

186.9

gl+ol+ox

94.7

5.71

48-59

1557

-0.68

235.8

gl+ol’

48-60

1468

-9.83

307.5

gl+ol+ox

96.0

4.30

48-61A

1559

-9.11

143.0

gl+ol

94.9

4.61

48-64

-7.97

265.7

gl+ol

50-56

-10.36

192.5

gl+ol

50-59

-0.68

235.8

gl+ol+ox

50-61A

-9.11

143.0

gl+ol

94.2

5.61

93.5

5.94

77-52

-9.80

91.2

gl+ol

77-64

-7.97

265.7

gl+ol

83-58

-11.15

332.3

gl+ol+pl+ilm

-9.28

309.1

gl+ol+pl+tmt

83-66

1395

‘The olivine in this sample contains inclusionsof an Fe-Ti oxide.

85.1

87.8

14.8

11.6

306

D. A. Snyder and I. S. E. Carmichael

Table 3. Analyses of run products. Ah data are in weight percent. Run identifiers read so that the first number corresponds to a starting material and the second number to a set of experimental run conditions (listed in Table 2). This is followed by an abbreviation for the phase analyzed (gl=glass, ol=olivine, lc=leucite and pl=plagioclase). Entries are the mean of n anaiyxed points and with a standard deviation given in parenthesis. For example, for an entry of 9.89(13) the standard deviation is 0.13 and for an entry of 0.53(l) it is 0.01. Fe,O, was calculated according to KRESS and CARMICHAEL (1991).

Run

SiO,

n

55.3(6)

0.08(2)

23.1(2)

48.0(9)

O&(4)

32.9(6)

08-58-01 10

36.5(3)

OS-58-k 10 OS-58-pl 10 44-51-gl 11

51.4(6)

44-51-01 12

37.8(2)

44-57-g] 10

54.6(7)

44-57-01 12

38.9(3)

44-60~gi 10

54.2(5)

44-60-01 13

38.7(3)

44-64-gl 10

53.4(4)

44-64-01 10

38.1(2)

46-57-gl 10

52.9(5)

46-57-01 10

38.9(3)

46-60-g] 10

53.7(4)

46-60-01 10

38.5(2)

48-48-gl 10

52.1(5)

48-48-01 11

40.1(3)

n

Ai,O, 15.5(2)

48.1(4)

Run

TiO, 1.58(5)

OS-58-gl 10

SiO,

48-56-gl 15

54.3(6)

48-56-01 8

40.5(2)

48-57-gl 10

52.6(5)

48-57-01 9

39.4(2)

48-59-gl 10

51.3(5)

48-59-01 10

41.5(2)

48-60-gl 10

53.5(6)

48-60-01 11

39.1(3)

48-61A-gl 11

52.4(4)

48-61A-01 11

39.5(2)

48-64-g] 10

52.3(6)

48-64-01 10

38.9(2)

50-56-gl 19

4X4(3)

50-56-01 10

40.1(3)

50-59-g] 10

42.9(3)

50-59-01 12

40.5(2)

SO-61A-gl 12

44.1(4)

50-61A-01 11

39.1(2)

77-52-gI 10

54.0(S)

77-52-01 6

39.9(2)

77-64-g] 10

53.8(6)

0.78(4)

Fe0

Fe&),

0.202(15)

0.172(13)

28.1(3)

0.435(18)

3.69(20)

7.10(15)

0.43

16.7(l)

7.03(7) 14.2(l)

0.50

16.4(2)

6.73(7) 14.0(l)

0.85(3)

0.99

17.5(3)

6.21(7) 11.3(6)

l-50(5)

0.47

16.0(l)

7.21(S)

0.57

15.5(l)

7.03(17) 14.7(l)

l&(3)

0.16

13.3(l)

9.25(7) 11.5(l)

TiO 2

AW,

Fe@,

0.15(5) 0.122(11)

1.40(2)

0.133(10)

13.48(21)

0.134(13)

0.265(22)

0.214(11)

4.72(40)

0.135(14)

0.375(15)

0.197(15)

6.68(16)

0.130(14) 0.163(12)

14.4(l) 1.47(3)

30.5(5)

Fe0

CaO 9.89(13)

0.897(14) 12.83(13)

0.120(10)

0.352(20)

0.189(18)

5.99(5)

0.113(7)

0.427(13)

0.178(11)

7.35(S)

0.125(6) 0.120(9)

MnO

7.18(12)

0.127(7)

9.17(5) 6.43(13)

8.30(7) 37.1(2) 6.06(16) 40.7(3) 6.27(14) 40.5(4) 6.69(17) 37.8(2) 5.94(11) 39.9(2) 5.96(13)

16.4(4) 8.39(17)

8.86(11)

9.07(19)

8.99(18)

11.8(2)

8.68(15)

0.308(10)

47.9(6)

0.22(2)

CaO

1.93(5)

13.3(l)

0.21

2.17(6)

15.2(2)

0.44

0.183(15)

5.63(11)

41.7(2)

0.36(2)

1.86(7)

12.7(l)

6.91

1.54(9)

0.124(11)

0.510(13)

10.9(2)

8.67(16)

2.15(5)

0.124(16)

5.52(3)

51.2(3)

2.20(9)

14.6(2)

0.50

6.13(18)

0.121(9)

0.333(21)

1.97(6)

13.7(2)

0.45

7.04(6)

2.12(7)

14.6(l)

1.08

12.2(l)

12.5(l)

5.74(7)

8.56(12)

5.42(12)

7.88(9)

5.73(9)

8.58(11)

12.6(2)

8.85(18)

0.121(13)

1.74(2)

48.1(4)

0.21(2)

0.113(12)

0.322(31)

5.63(21)

41.9(3)

0.34(3)

0.637(16)

10.2(2)

9.02(12)

9.94(6)

0.136(11)

6.08(4)

44.5(3)

0.26(2)

6.12(7)

O.llS(ll)

0.602(32)

7.19(17)

11.3(l)

0.164(13)

8.53(21)

41.1(2)

0.210(12)

0.204(10)

12.7(2)

12.4(2)

0.187(10)

1.32(S)

45.9(3)

0.188(18)

0.928(12)

13.0(2)

2.39(16)

0.130(13)

6.79(7)

50.1(4)

0.85 11.0(l)

0.211(13)

0.935(13)

11.7(2)

12.2(l)

0.178(13)

6.14(10)

42.5(2)

Olll(12)

0.326(19)

1.85(S) 13.9(2)

0.50

l&3(5)

1.07

6.50(22) 11.2(l) 5.61(10)

0.154(16)

4.84(18)

0.107(12)

0.715(37)

7.01(29) 43.9(5) 6.08(13)

100.4

1.12(l)

99.3 99.8

2.92(10)

1.23(3)

9.70(16)

2.52(11)

1.28(2)

2.56(13)

1.18(2)

2.56(7)

2.27(3)

2.47(7)

2.24(3)

0.39(4)

1.38(2)

99.0 100.2

&O

Sum

0.24(3)

Na,O

0.91(2)

99.9

1.84(S)

2.87(7)

98.3

1.87(S)

1.92(4)

98.3

1.55(5)

2.57(10)

98.1

0.83(7)

1.99(4)

98.3

1.53(6)

2.67(4)

0.09(3)

0.11(l)

0.35(2)

0.11(l)

0.20(2)

0.29(l)

2.06(15)

4.76(21)

1.58(S)

4.2.5(S)

99.8

99.5

100.7

99.7

100.4 98.1 100.3 99.3 loo.4 98.1 100.6 98.0 100.6

0.33(5) 8.85(23)

98.4 100.2

0.48(3) 8.77(43)

98.3 99.6

0.29(2) 14.3(l)

99.5 100.4

0.49(2) 13.6(l)

98.5 100.3

0.32(2) 14.4(2)

99.2 99.1

0.17(2) 10.0(3)

0.174(16)

0.45 11.4(l)

11.3

9.99(19)

0.126(16)

2.79(16)

14.2(l)

0.208(26)

6.63(27)

0.56(12)

0.31(3)

0.042(S)

6.33(7)

1.90(20) 3.12(15)

0.21(3) 9.03(17)

98.1

100.1

20.5(2)

0.28(2) 9.06(10)

Sum

99.8 0.67(6)

0.30(2)

0.31(2)

MgO

K,O 4.46(5)

0.19(l)

39.2(3)

NiO

Na,O 1.95(6)

0.62(3) 0.03(3)

0.53(l) 1.19

11.1(l)

0.97(4)

MgO 3.72(10)

0.47(S)

16.4(l)

1.01(4)

NiO

MnO

0.83 11.7(l)

99.8 100.3 98.1

Activities of metal oxides in silicate melts

307

Table 3. (Continued)

SiO,

Run n 77-64-0110

38.2(3)

r33-5%gl10

4X7(6)

83-58-olll

34.9(2)

83-66-gl 10

48.9(4)

83-66-0110

34.6(2)

TiO,

AV&

MnO

Fe0

Fe@,

11.2(l) 3.81(9) 13.8(2)

1.05 18.2(2)

3.46(7) 13.1(2)

2.47 14.4(2)

36.5(2)

31.9(2)

0.401(15) 4.23(S)

FUGACITY PARTITIONING

P=latm

T=l285”C f lw

I I QFM NNO

I Air

RG. I. Experimentally measured partition coefficients between olivine and liquid as a function of oxygen fugacity for an ugandite. Composition, pressure,and temperature are held constant. Error bars are 2s (s = standard deviation) from the precision of the probe analyses. All data are in mol %.

7.52(9)

22.7(2)

&O

SUUl

100.0 1.13(Z)

98.2

3.35(12) 1.25(4)

98.8

2.80(9)

99.0

0.39(3) 7.90(12)

3.09(9)

0.452(21) ll.O(ll)

Na,O

0.35(l)

3.69(10)

0.242(12) 0.601(15)

Isolating the contribution of a single intensive parameter is best accomplished by varying only that parameter while holding all others fixed. With oxygen fugacity, this is not stmightfo~ard since varying Fe2 Os/FeO causes changes in the olivine composition and sometimes the stable phase assemblage. Under very oxidizing conditions, the liquidus phase of basalts is often titanomagnetite or hematite. Thus, even while holding temperature constant, variations in foZ create changes in composition. We have selected an ugandite (50) for which olivine is both a stable phase from IW to air and the composition of the liquid remains nearly constant throughout this range (aside of Fe*Os/FeO variation) to explore the variation of the partition coefficients with oxygen fugacity. Partition coefficients for all of the divalent cations for this com~sition are plotted in Figs. 1 and 2. Within ex~~rnent~ resolution, we cannot detect any dependence of nickel partitioning on oxygen fugacity from log,, fo,= - 10.36 to -0.68, nearly the entire stability range of natural olivines ( NITSAN, 1974). Specimen 48 behaved similarly, but composition was

10

39.1(2)

0.234(16) 0.262(8)

THE EFFECT OF OXYGEN

CaO

WO

0.168(12) 10.9(2)

glasses, we calculated the Fe203 con~ntration from the model of KRESS and CARMICHAEL( 199 1) and for the Fe-Ti oxides by assuming stoichiometry. All iron in the olivines was considered to be FeO. Note that all of the reported analyses are in weight percent or weight fraction whereas the mole fraction is used in thermodynamic expressions in the text.

ON CATION

NiO

21.8(3)

0.43(3)

100.2

not as constant due to phase equilib~a changing with ,fo,. These results are consistent with the results of TAKAHASHI ( 1978) and EHLERS and GROVE ( 1990) who investigated this dependence over a much more restricted range of oxygen fugacity but did not hold composition constant. The fact that the variation of DNiowith oxygen fugacity is below analytical resolution puts an upper bound on the concentration of Ni203 in the melt. Assuming that the concentration of Ni20s is negligiblTiqat an oxygen fugacity three log,, units below NNO, XNilo,/XZo m 0.03 in air would cause the observed D&o = Xgio/Xz,o to drop by 6.0% (relative to three log,, units below NNO), which is within the analytical precision of the me~urement (X &-, is the total mole fraction of nickel in the liquid expressed as NiO). No such drop is observed, so that XzZo,/XEio must be less than 0.03 in the ugandite at 1285°C in air. This conclusion is consistent with the measurement on NazO. 2Si02 glass by JOHNSTON( 1965). The quantity of trivalent nickel in lavas is therefore taken to be negligible over the range of oxygen fugacities observed in nature. Figure 2 shows the partition coefficients of Mn+l and Cae2 as a function of oxygen fugacity. Unlike Nit’, Mg”, and Fe+*, the partition coefficient of Ca+’ displays variation with oxygen fugacity. This dependence can be understood by examining the crystal chemistry of these cations in olivine. The pa~itioning of the cations Ca+2 and Mn+2, which have no crystal field stabilization energy (CFSE) in olivine, is governed by their size. Since the M-O bond distance in olivine decreases from 2.17 to 2.11 angstroms from fayalite to forsterite (SMYTH, 1975; HAZEN, 1976), the partition coefficient for

*

,

IW

P=laIm QFM

NNO

Air

FIG. 2. Experimentally measured partition coefficients between ohvine and liquid for manganese and calcium as a function of oxygen fugacity for an ugandite. Composition, pressure, and temperature are held constant. Error bars are 2s from the precision of the microprobe analyses. All data are in mol %.

308

D. A. Snyder and I. S. E. Carmichael

these large cations should, therefore, decrease with increasing oxygen fugacity (increasing X,,). Fig. 2 shows this type of variation. Dcao clearly decreases with increasing oxygen fugacity as the olivine composition changes from approximately Fo~~.~ in the reduced runs to Fog7.0 in air, as expected. JUREWICZand WATSON( 1988) have previously noted a similar correlation between DCaOand X$., DMvlnois also expected to decrease with increasing fo,both because of the changing olivine composition and because of the increasing concentration of Mnz03 in the liquid phase. As seen in Fig. 2, we are unable to resolve unambiguously any change within experimental resolution. WATSON (1977) was also unable to detect any variation in the partition coefficient of manganese in iron-free compositions with changing oxygen fugacity. Before discussing models for the olivine-liquid element partitioning, we turn to an analysis of the chemical activities which control these partition coefficients.

of the system are well studied and mixing has been found to be more ideal than the Pt-Fe system ( TOMISKAand NEWEL, 1985; RAMMENSEE and FRASER, 1981; CONARDet al., 1978; KUBASCHEWSKIet al., 1977; GRIMSEY and BISWAS, 1977; BELTONand FRUEHAN, 1967). Using this binary, we have calculated the activities of Fe 0.9470and NiO from the following reactions: Ni,,,,, +

‘/202

=

NiOsolld

(1)

0.947Fe,,,,, + Y202 = Fe0.9470sal,d.

(2)

For both reactions, we have used solid oxides as reference states. Fe0.94,0 was chosen as a standard state rather than estimated values for stoichiometric Fe0 because the latter yield ferrous iron activities in the melt which exceed unity (see e.g., DOYLE, 1988). Using these reactions

MONITORING OF Fe0 AND NiO ACTIVITIES Activity coefficients of some transition metal cations in silicate liquids can be determined by equilibrating silicate melts with simple metallic alloys. If the thermodynamic properties of the end member components and the mixing properties of the alloys are known sufficiently, the activities of the metallic components can be calculated in the liquid. The activity of NiO has been previously monitored in ironfree systems (DOYLE and NALDRETT, 1987) and in ironbearing liquids (CAMPBELL et al., 1979) by equilibrating samples on nickel wires at oxygen fugacities below the NNO buffer. Ferrous iron activities have similarly been monitored by equilibration with metallic iron at oxygen fugacities below the iron-wiistite buffer (IW; ROEDER, 1974; DOYLE and NALDRETT, 1986; DOYLE, 1988, 1989) and by equilibration with platinum (NOLAN, 1977; GUDMUNDSSON and HOLLOWAY,1989). Experiments employing equilibration with metallic iron are intrinsically restricted to the stability field of iron, which is at oxygen fugacities below that of nearly all natural lavas. Oxygen fugacities above the iron-wiistite buffer cannot be explored. The use of platinum avoids that difficulty; ironplatinum alloys are stable over a wide range of oxygen fugacities. Unfortunately, the mixing in the iron-platinum binary is, even at high temperature, very non-ideal (LARSON and CHIPMAN, 1954; TAYLOR and MUAN, 1962; HEALD, 1967; ALCOCKand KUBIK, 1969; GUDMUNDSSONand HOLLOWAY, 1989). The nature of this non-ideality creates three problems: ( 1) the technique is insensitive at small values of a:?; (2) due to a small analytical error in X2?, it can lead to large uncertainties in a$$ at high values of a$?; and (3) it necessitates detailed knowledge of the enthalpy of mixing to calculate the temperature dependence of the activity coefficients. The use of nickel-iron alloys reduces these problems. Nickel-iron alloys are stable from NNO to below IW. Because of multifarious industrial applications, the thermodynamics

* Relative to the uncertainty in In uFpo~94,0,&20’S, the difference we have between In uFeoMS and In a~& is quite small. Consequently, taken In aFeo 2 In aFeo.9,p in the subsequent calculations.

where the free energies ( AGR,) of reactions ( 1) and (2) were taken respectively from HEMINGWAY( 1990) and HOLMES et al. ( 1986), R, the gas constant, was taken to be 8.314510 J - mol-’ K-’ (COHEN and TAYLOR, 1987 ) and T is the absolute temperature. A simple Margules model (THOMPSON, 1967 ) was fitted to the thermodynamic data of TOMISKAand NECKEL( 1985) so that

(6) and In (a$:‘)( To) = In (X,i)

+-

RT

[( 1 - 2xN1)W$$Ni + (2xNi)w~iFel C7)

In ( a$py)( TO) = In (XF,) +

xk -

RT

[(

1 -

2xFe)WCFe

+

(2xFe)wLi]

(8)

and the excess enthalpy H’” = XNIX~WEIF~ + XhtXFe W&i

(9)

where To = 1623 K, W”.i.,,Fe = -5791.5 Jmmol-‘, w#,i = -12287.4 J. mol-‘, W{iFc = -5475.6 J. mol-’ and J - mol-’ . Using these equations, we have wh4i = -23839.7 calculated the activities of Ni, Fe, NiO, and Feo.94,0 and have listed them in Table 4. Estimated errors for the values of In azo and In a$,94,0 are believed to be 4% and 20%, respectively. The coexistence of olivine and alloy allows the calculation of the activities of MgO in the melt and NiSil,20Z (liebenbergite component, Lb) in olivine. Combining the known activities of ferrous iron* and nickel (II) oxide with a solution

Activities of metal oxides in silicate melts

309

Table 4. Calculated activities and activity coefficients. All activities are relative to a solid standard state at temperature. Activity coefficients (y’s) for NiO, FeO, MgO and FqO, are for the liquid phase and that of Lb (= NiSi,,O,) is for olivine. Run

aFaqnO 0.53

0.076

0.027

0.060

0.27

0.019

0.094

0.30

0.87

0.049

44-57

0.93

44-60

0.95

1.2

0.84

1.6

5.1

1.9

0.91

1.6

26.

0.091

29.

0.060

0.26

0.078

19.

4.1

1.1

0.81

1.3

0.33

0.094

25.

5.3

2.1

0.98

1.4

48-48

0.65

0.20

0.0034

0.13

0.058

9.8

1.6

0.05

0.32

2.3

48-56

0.87

0.057

0.016

0.13

0.072

9.2

2.2

0.13

0.38

1.6

48-57

0.93

0.024

0.060

0.24

0.084

22.

4.3

0.94

0.82

1.3

48-M)

0.95

0.017

0.095

0.27

0.095

33.

5.1

1.6

0.89

1.9

48-61A

0.95

0.021

0.069

0.21

0.099

13.

3.4

0.62

0.62

1.4

50-56

0.82

0.086

0.015

0.19

0.079

8.8

2.0

0.16

0.42

1.7

50-61A

0.94

0.026

0.068

0.25

0.099

8.7

2.7

0.58

0.55

1.3

77-52

0.93

0.027

0.061

0.25

0.10

22.

4.5

0.91

0.93

1.4

83-58

0.86

0.055

0.054

0.59

0.061

23.

3.5

3.1

1.0

1.3

&GO,(T)

(11)

by the relations

2

+ In agzo.

(12)

)

Ad% T) - A&d T) RT IN

aNiO i a%

1

+lna&.

(13)

A,G&,( T), A,GF,( T), and AfGtb( T) are, respectively, the standard state Gibbs free energies of formation of forsterite ( MgSi, ,202), fayalite ( FeSi , ,202), and liebenbergite (Nisi, ,2O2) from the oxides ( ROBIE et al., 1979; HEMINGWAY, 1990; ROBIE et al., 1984). Similarly, the activity of Fe203 was calculated from the reaction 2Fe(,,,,,,

+ 3/&~ = FeZO3(,,+

(14)

state free energy data for FezOs were taken from Estimated

uncertainties

in In a$03

are

+ 10%. Because of the error of 20% on the calculated activities of ferrous iron, we believe that the uncertainty culated activity coefficients

ANALYSIS

AND

DISCUSSION

Activities of FeO, NiO, Fe203, and MgO in Natural Basic Liquids Although several previous determinations of the activity of Fe0 in silicate melts have been made ( ROEDER, 1974; DOYLE and NALDRETT, 1986; DOYLE, 1988, 1989), all have

- &GO,,(T) RT

ROBIE et al. ( 1979).

4.4

0.081

0.094

+ln

Standard

1.5

0.026

and In a& were calculated

_ -

YLb

1.2

0.021

i uo, Lb

Ym@

3.0

0.93

+ In

,n

YF.203

4.9

0.94

Ni%,,) + FeSiIdb~ol) 5 FeOu,,, + Nisi ,,202(0,,.

=

YF+&

33.

46-57

Fe%,) + MgSi~~~%~)= MgOcliq)+ FeSil~~02~ol) (10)

In a$o

G.9

46-60

model for olivine (SACK and GHIORSO, 1989 ) , these activities are controlled by the reactions

In ~$o

YNio

k.J 0.055

+I

aNI

08-58

in these cal-

for Nisi, ,20z in olivine could be in error as much as +25%. Calculated values of ~,$o, liq liq yMso, yFelo,, and -r?,, are listed in Table 4.

been performed by equilibrating a silicate melt with metallic iron and consequently none have been reported for conditions more oxidizing than the IW buffer. This technique is an excellent one for calibrating the activity of Fe0 near the IW buffer, but predicting azo at higher oxygen fugacities based only on these data requires extrapolation. Further, it provides limited information on the activity of Fe203. The measurements reported here at higher oxygen fugacity, using NiFe alloys, permit the determination of both In a$& and the dependence of In ago on fo,. Using these new measurements, we can examine the variation of the activity of these two iron oxide components in natural basic liquids. From melt structure ( MYSEN, 1988 and references therein) and iron redox equilibrium (PAUL and DOUGLASS, 1965; THORNBER et al., 1980; SACK et al., 1980; KILINC et al., 1983 ), it has been suggested that the alkali metals complex with Fe+3 in silicate melts and therefore that total alkali content will influence the activities of Fe0 and Fez03. Previous observations on In a:‘&, ( ROEDER, 1974; DOYLE, 1988) indicate a strong positive correlation of In &!o with total alkali content, but because fo, was relatively constant in these experiments, it was not possible to examine the codependence of the activities on these parameters simultaneously. Figure 3 shows contour plots of RT In y$,94,o and RT In T/‘&~~as functions of log,, fo, and total alkali content ( 100(X~&o + X2Zo)). Although some of the fine scale structure in the plots may be spurious, overall patterns are clear. At high

310

D. A. Snyder and I. S. E. Carmichael

(kJ - mole-‘) RT1nY ;i.sa70 6.00

(a)

1 .oo

l%ofo2 RTlnyi$3

(kJ mole-‘) l

04

4.50

-13.50

-12.50

FIG.3. Contour plots of(a)Rl‘ln alkali

-11.50

y&&_+and f b) RT In content in mal 410.Boxes indicate locations of data.

oxygen fugacity, RT In+&o.9,~ is strongly a function of oxygen fugacity (and nearly independent of alkali content) but i3elow log,, fo, =

- 12 (near

the fW bu%r),

it is nearly

y!h&,

-10.50

(both in

kJ.

-9.50

-8.50

mol I’) as functions of log J;i, and

total

independent of oxygen fugacity and strongly a function of the total alkali content. RT In r$2s, on the other hand, varies to a much greater degree and shows its greatest cor-

Activities of metal

311

oxides in silicate melts

we do not offer a model for In aNio similar to that for

relation with total alkali content at higher oxygen fugacity, approximately in the range -5 < ANN0 < -3. In both cases, alkali content influences the activities of the iron components at all oxygen fugacities, but is overshadowed by the effects of fo, in regions of rapidly changing Fe203 /FeO. Since these activities vary in a relatively simple way with a few parameters, we can formulate empirical models to predict these variables. We have combined the measurements from this study with others on natural liquids ( ROEDER, 1974; CAMPBELLet al., 1979) to formulate empirical models for the chemical activities of ferrous and ferric iron as a function of temperature, oxygen fugacity, and composition in natural basic liquids using the equation

ln

aFeow70.

Fe-Mg Exchange Between Olivine and Liquid As mentioned above, the empirical activity models can be tested by using them to calculate the compositions of olivines precipitated from basic melts. From the FeO-MgO exchange reaction ( 10) and a solution model for olivine, we can write

(16)

+ z d, In X, i

In a y = a + : + c log,,f,,

(15) where W’ = 20.3 kJ.mol-’ (SACK and GHIORSO, 1989). For 174 experiments on natural basic liquids (both terrestrial and lunar) within the calibrated range of Eqn. ( 15; BENDER et al., 1978; GROVE and BRYAN, 1983; GROVE et al., 1982; JUSTER et al., 1989; KILINC et al., 1983; ROEDER, 1974; ROEDERand EMSLIE,1970; SACK et al., 1987;STOLPER,1977; TAKAHASHI, 1978; TORMEY et al., 1987; WALKER et al., 1976)) the ability of Eqn. ( 16) to predict olivine compositions (X&) is comparable to recent regressed fits. For example, the GEE and SACK (1988) and FORD et al. (1983) models both predict X$, with an average error of 1.O%and this model has an average error of 2.0%.

where X represents the mole fraction of oxide components in the melt. Regression estimates of these parameters, via singular value decomposition (SVD), are listed in Table 5 and Fig. 4 and illustrate the success of the models in fitting the data. These models are not intended to be substitutes for a thermodynamic mixing model for silicate melts, but are useful for petrologic calculations in much the same way as recent models by KRESS and CARMICHAEL( 199 1) and SACK et al. ( 1980) are for calculating Fe203/Fe0. In the next section, it is shown that these models successfully predict the Fe0 / MgO content of olivines in natural liquids. Because of their empirical nature, they should not be extrapolated outside of their calibrated ranges, listed in Table 6. In experiments with nickel wires, the activity of metallic nickel in the melt is near unity. By Eqn. (3)) at a constant temperature, the oxygen fugacity fixes the UNio. Since this acts as a buffer for NiO, there is no information regarding activities of NiO away from this aNio buffer, and hence

Crystal Chemistry of Minor Divalent Cation Exchange in Olivine Before developing models for divalent cation partitioning, a review of the relevant olivine crystal chemistry and thermodynamics is necessary. In olivine, divalent cations reside

Table 5. SVD

estimatesof parametersin equation (15). se. is the standard error of the fit parameter. n is the number of data used in each fit; mean dev is the mean of the absolute value of the percent deviation (residual/measured value); x2 is the chi-squared statistic; and SS/d.f. is the sum of squares of the residuals divided by the degrees of freedom.

Parameter

IM use Value

s.e.

-1.367

0.592

6176.

K

742.1

Value

s.e.

-7.033 27690.

1.572 K

1976.

0.2128

0.0086

0.6590

0.0279

-0.05926

0.0212

-0.1424

0.0452

1.7%

0.728

0.7433

Value

Units

s.e.

1.638 -2143.

1.121 K

2184.

0.2211

0.0097

0.1962

0.1779

0.06937

0.0251

0.0299

0.1337

0.0253

0.2258

0.0530

Regression statistics: n

74

74

33

mean dev

4.34

x2

0.70

3.17

0.19

SS1d.f.

0.010

0.047

0.0067

2.25

1.86

D. A. Snyder and 1. S. E. Carmichael

312

octahedral sites (designated M 1 and M2). Neither are perfectly octahedral. The M 1 site is slightly smaller and elongated along one of the tetrad axes relative to the M2 site which is a little larger and compressed (DEER et al., 1982 and references therein). These geometric differences affect the partitioning of cations between these sites. The trace cations in olivine (Ni +*, Ca+* , and Mn +‘) have appreciable site preferences. Nickel is expected to partition strongly into the M 1 site because of CFSE effects (BURNS, 1969/ 1970; WOOD, 1974). This preference has been verified in Fe-Ni (ANNERSTENet al., 1982), Mg-Ni (BOSTROM,1987; RAJAMANIet al., 1975; BISH, 198 1 ), and in Fe-Mg-Ni ( NORD et al., 1982) olivines. Neither Ca+2 nor Mn+* (in the high spin state in octahedral coordination) have finite CFSE (BURNS, 1969/ 1970). Both are relatively large, however, and therefore partition preferentially into the larger M2 site ( LUMPKINet al., 1983; AKAMATSUet al., 1988; ANNERSTEN et al., 1984). As calcium and nickel reside in different sites and are therefore strongly ordered, calcium and nickel do not substitute for one another. The partition coefficient for nickel will be independent of XFao and that of calcium will be independent of Xgio so that these partition coefficients are useful for natural compositions. Manganese and calcium do reside in the same site, however. The presence of one will to some degree affect the partitioning of the other. But, both calcium and manganese occur in low abundance relative to iron and magnesium in natural olivines ( SIMKINand SMITH, 1970). The M 1 and M2 sites are therefore dominantly populated by Fe+2 and Mg’* so that manganese and calcium substitute for iron and magnesium and negligibly for one another. For this reason, neither calcium nor manganese were doped into the liquids and the resulting partition coefficients for these cations will reflect closely those in natural systems. The models we have developed for partitioning of all of the elements are relevant, therefore, to natural basic magmas. Unlike the trace cations and despite slight differences in size and a finite CFSE for Fe+*, Mg+2 and Fe+* are distributed approximately randomly between the M 1 and M2 sites (e.g., MOTOYAMAand MATSUMOTO,1989; AIKAWAet al., 1985 ). This appears to continue to be the case even with substantial in two non-equivalent

-2.5

-5.0 -3.0

-2.5

-2.0

-1.5

-1.0

.5

-7.0 MM Fe203

-9.0

-2.5

m"

MS'

-3.0

FIG. 4. Diagram showing the predicted values of (a) In uk&,~,o, (b) In a$o,, and (c) In a$@ as functions of their measured values using Eqn. ( 15) and the coefficients in Table 5. The data for (a) and (b) are from this study, ROEDER ( 1974),and CAMPBELL et al. ( 1979),

and the data for (c) are from this study and ROEDER( 1974). All data are natural basic compositions.

Table 6. Ranges of temperature, oxygen fugacity, and liquid composition in the databases used for the activity models in equation (15).

Fe,,g,,O and Fe,O, Parameter T (Kehs)

Minimum 1395. -14.50

X Nl++Kp

MgO

Maximum 1579. -8.18

Minimum 1395. -14.11

Maximum 1579. -9.14

0.4212

0.8328

0.4270

0.5833

0.0024

0.0784

0.0051

0.0648

0.0508

0.1238

0.0613

0.1910

0.0003

0.0055

0.0006

0.0056

0.0080

0.2471

0.0538

0.2387

0.0063

0.1910

0.0613

0.1910

0.0159

0.1581

0.0899

0.1581

0.0016

0.0599

0.0016

0.0596

Activities of metal oxides in silicate melts

313

Ni+2 substitution (NORD et al., 1982). Since these two elements comprise most of natural olivines, the substitution of any divalent cation, whether it has a site preference or not, will substitute for Fe+* with a probability of X& and Mg+* with a probability of X& where X$ = X~~,si,,202/(X~~si,,202 + X”’ Mgsi,,*02) and X&is similarly defined. For example, Nii2 will substitute for Mg +* in pure forsterite and Fe+* in pure fayalite, but will substitute for Mg+2 and Fe+* with equal probability in an olivine of composition X& = 0.5. Thermodynamics of Minor Divalent Cation Exchange in Olivine

From the above discussion of olivine crystal chemistry, it is clear that any exchange reaction for minor divalent cations (e.g., Ni+2, Mn+*, and Ca+*) in olivine must reflect that these cations substitute for both iron and magnesium. This is described by X&FeSir,202(0r) + X%MgSir&(Or)

+ M+*Ocriq)

= X&FeGce,, + X%MgG~ri,, + Mf2Si,&(alJ

(17)

where X& and X$ denote the mole fractions of the components FeSi1,202 and MgSi,,202 projected onto the forsterite-fayalite binary so that X& + X& = 1. This reaction allows an evaluation of the relative contributions of temperature and composition on the partition coefficients. From the definition of the Gibbs free energy and the law of mass action

= %&GO,,(T)

+ %&A&,(T)

FIG. 6. Plot showing In KMnO [ from Eqn. ( 18)] vs. olivine composition. Lines indicate values for two different temperatures and squares are experimental data from this study. Notice that there is a negligible thermal dependence.

ted in Fig. 6, shows essentially no variation over 500 K and indicates that nearly all of the variation in In KMno is attributable to composition. In contrast to In KMno, temperature plays a significant role in the variation of In KcaO, as seen in Fig. 7. Even though In KNlo and In KMnodo not vary significantly with temperature, their corresponding measured values, In DNio and In DM~o, do. Figure 8 shows this variation in

- &G~+z,,,zo,(U

RT (18)

We have plotted In KNio, In KMnOand In Kcao as a function of X$, for two different temperatures in Figs. 5-7. Figure 5 shows that In KNio is strongly a function of composition, but less so of temperature. A variation of olivine composition of 13 mol% Fo produces a change in In KNio which thermal effects alone would require 500 K to produce. Ln KMnO,plot-

which is the partition coefficient adjusted for its explicit compositional dependence. Equation ( 19 ) indicates that the temperature dependence must reside in either a finite enthalpy change of the reactions or in a temperature dependence of one or more of the activity coefficients. But since In KMno has no temperature dependence and In KNio has a small one, the enthalpy changes of the exchange reactions ( 17 ) must be small for both of these cations and the temperature depen-

0’0° h

2.00

FIG. 5. Plot showing In ~~~~[from Eqn. ( 18)] vs. olivine composition. Lines indicate values for two different temperatures and squares are experimental data from this study. Notice that the compositional dependence is much greater than the thermal dependence.

,IIIIIIIII,,I ,,,,,,,,, 0.60 0.70

0.50

I I,,,, I ,,,,I, ‘ ,,,,,,,,,, 0.60

0.90

I,,, 1. 3

XFO

FIG. 7. Plot showing In Kc.,, [from Eqn. ( 18)] vs. olivine composition. Lines indicate values for two different temperatures and squares are experimental data from this study. Notice that unlike NiO and MnO, the thermal dependence is appreciable.

D. A.

314

Snyder and I. S. E. Carmichael

2.0 NiO

1

1.0 0 0.0

43

0 0 q 0

-1.0

Table 7 presents the results of weighted SVD estimates of parameters A and B for In DNlo using data from this study and results for In DMno using data from this study and LEEMAN ( 1974), ROEDER(1974), ARNDT (1977), TAKAHASHI (1978), LONGHI et al. (1978) and STOLPER(1977; Cobalt bearing runs were excluded). The coefficients for In DNio are calibrated for the temperature range 1395 to 1562 K and the composition range of the glasses and olivines reported in Tables 3 and 4 and those for In DMnO from 1395 to 1673 K. The partitioning of calcium is more complex since it is a rather large cation for the olivine octahedral sites. Its substitution is markedly non-ideal (ADAMS and BISHOP, 1985; DAVIDSONand MUKHOPADHYAY,1984; MUKHOPADHYAY and LINDSLEY, 1983; WARNER and LUTH, 1973) and consequently the activity coefficients in Eqn. ( 19) have significant compositional and thermal dependence. To accommodate this strong non-ideality, we have retained an additional fit parameter in Eqn. (20) so that the regression model equation for Dcao is

(a)

-2.0

, , , ( ( , , #, , , , 1, , , , , , ,

0.0 MnO

B

6.20

6.40

6.80

104iT (K-‘) FIG. 8. Diagrams showing the variation of the partition coefficients of (a) NiO, (b) MnO, and ( c) CaO (adjusted for explicit compositional variation) with temperature. See text for discussion.

dence of the partition coefficients must lie chiefly in the activity coefficient( s). Models of Minor Divalent Cation Exchange in Olivine

Reaction ( 17) and the thermodynamic relation of Eqn. ( 19) can be used to formulate models for divalent element partitioning in olivine. Since both the natural logarithm of the equilibrium constant of reaction ( 17) and the In y are proportional to 1/ T, the following regression model equation is suggested (at one bar) from Eqn. (19):

SVD estimates of A, B, and C for Dcao using the data from this study and 272 additional olivine-liquid pairs from experiments on natural basic liquids (BENDERet al., 1978; GEE and SACK, 1988; GROVE and BRYAN, 1983; GROVEand JusTER, 1989; GROVE et al., 1982; JUSTER et al., 1989; KILINC et al., 1983; ROEDER, 1974; SACK et al., 1987; STOLPER,1977: TAKAHASHI, 1978; TORMEY et al., 1987; WALKER et al., 1976; WALKER et al., 1979) are also listed in Table 7. Although there is reason to be concerned that not all of the analyses in this data set have considered the problems associated with secondary fluorescence of calcium (WATSON, 1979; JUREWICZand WATSON, 1988), we have included all of these data in order to increase the compositional span of the data to include very high values of Dcao, The resulting model fits the data of this study, where secondary calcium fluorescence was avoided (to within an average error of 22% ) , indicating that there is probably not a serious problem with these analyses. Because the data set is biased toward low values

Table 7. SVJI estimates of parameters in equations (20) and (21). se. is the standard parameter. n is the number of data in each fit. Oxide

A

S.C

B

n

it=

724.

21

0.93

521.

93

2.19

21

0.016

s.e.

NiO

-2.575

0.484

4592.

MnO

-3.449

0.345

2476. 12468

2332.

CaO

-11.32

1.25

C

0.3478

s.e.

0.255

error for each fit

Activities

-I

: 0 Amdt (1977) Han&Davis (1978) _ * Kinzler CI 01.(1990) 0 LeemaIl(1974) - A Takahashi (1978)

.

$

zo-

t( ‘e

I

S! Q :

lo-

o

I

0

10

20

30

measured

D,,,

315

of metal oxides in silicate melts

FIG. 9. Predicted &o using Eqn. (20) and the values in Table 6 are plotted for data from the literature as a function of their measured values. Cobalt bearing olivines and liquids with less than 250 ppm NiO were excluded. The plotted data were not used in the calibration. Open symbols are natural compositions and closed symbols are synthetic. All data are in mol %.

in that study differ from the natural compositions used here in being peraluminous. We are able to fit their data if we introduce a compositional term in Eqn. (20) for XA120J (&a20 + X,,o + J&o) to account for the peraluminous nature of their liquids. Such an additional term is not warranted in application to natural assemblages, however, since olivinebearing peraluminous lavas are unknown. The average relative deviation of all of the points in Fig. 9 is 13%. Figure 10 is a similar plot of DMnO for the data from this study and that of the six experimental studies listed above. Like nickel, the plot shows a satisfactory fit to the natural data at low values of DHnO (high temperature) with increasing spread at higher DMnO (lower temperatures) where the experimental uncertainty is higher. The average relative deviation of all of the points is 13%. The Dcao fit from Eqn. (2 1) is shown in Fig. 11 along with the models of kJREWlCZ and WATSON ( 1988 ) and FORD et al. ( 1983). All three models fit the data to within an average error of approximately 2 I%, but the earlier models

this studv

of DUO, we have weighted the high values of Dcao higher than lower values in the regression. The olivine solution of SACK and GHIORSO ( 1989) was used for all regressions. Note that, for the reasons outlined above, the regression coefficients A and B should not be interpreted as AS,, / R and AH,,/ R .

0.20

0.05 Evaluation of Models

The best test of a model is its success in predicting data on which it was not calibrated. Fig. 9 is a plot OfDNio predicted by Eqn. (20) vs. measured D,.,,o for five studies from the literature. None of the plotted data was used in the fit. The model predicts small values of DNio quite well and displays increasing scatter for higher values of DNlo, which are at lower temperatures, probably reflecting the increasing uncertainty in these measurements. The prediction of the HART and DAVIS ( 1978) data is excellent considering that nearly all of the runs in that study are at higher temperatures than this study and all are iron free. The only data in Fig. 9 which systematically deviate from the model are those of KINZLER et al. ( 1990). Eight of the ten synthetic compositions used

0.00 0.65

O.&l

o.ia

o.io

0.

Jurewicz & Watson (1988) 0.20 / 0.15 j

%o

0.10

/

4

/

0.05

0.00 0.00

0.05

0.10

0.15

0.

Ford et al. (1983) 0.20

0

0

-/

-I

2.50

/

0.15 l

LonghI

a Roe&r

2.00

et al

(19781 (1974)

tiCa

b Takahashi (1978) %

1.50

4 7J g

0.05 1.00

(c)

1

c z 0

0.10

O.“,

0.50

.

.

.

.

D cao 0.00 0.00

0.50

1 .oo

1.50

2.00

2. 0

D MnO measured

FIG. 10. Predicted &,,“o using Eqn. (20) and the values in Table 6 for published experimental data plotted against their measured values. See text for dtscusston. All data are in mol %.

FIG. 1 I. Predicted Dcao for published experimental data plotted against their measured values. (a) Model of Eqn. (2 1) and values in Table 6; data are in mole fraction. (b) Model of JUREWICZ and WATSON ( 1988); data are in mole fraction. (c) Model of FORD et al. ( 1983); data are in cation fraction. The datum in the legend of the x-axis of plot (a) is part of plot (c).

D. A. Snyder and 1. S. E. Carmichael

316

of JUREWICZ and WATSON ( 1988) and FORD et al. ( 1983) deviate systematically. Both fail to predict high values of&,,: the model of JUREWICZand WATSON never predicts values of Dcao over 0.06 (mole fraction) and that of FORD et al. ( 1983) overestimates DcaO above x0.08 (cation fraction). IMPLICATIONS FOR PRIMARY MANTLE MELTS Work over the past several decades has indicated that the upper mantle, believed to be the source region of most basic and ultrabasic magmas, is heterogeneous in oxygen fugacity. Estimates using a plethora of techniques indicate that the span of fo,may range from the iron-wiistite oxygen buffer to several orders of magnitude above the quartz-fayalitemagnetite buffer (e.g., CARMICHAEL, 1991 and references therein). Nevertheless, the use of Ni concentration in basic and ultrabasic liquids to discriminate primary mantle melts from those which have fractionated olivine has been based on DNIO data largely calibrated near the iron-wiistite buffer. The preliminary results of this study indicate that DNio is independent of oxygen fugacity from IW to air, a range of more than nine orders of magnitude and nearly the entire stability range of natural olivines ( NITSAN, 1974). Some basic liquids with high Ni contents (300-400 ppm) are now recognized to have erupted at high oxygen fugacities (near the hematite-magnetite buffer; LUHR and CARMICHAEL,198 1; LUHR et al., 1989). Since DNlo is independent of fo,, the criterion of SATO ( 1977) for these being (near) primary mantle melts still holds. However, the assumption ofthe SA~O ( 1977) model is that the NiO content in the upper mantle is homogeneous despite variations in fo,. No olivine-bearing nodules have been reported from these Ni-rich, oxidized basic lavas and the assumption that fertile mantle is homogeneous in NiO remains unverified. SUMMARY Experiments in which olivine, natural basic silicate melt, and NiFe alloy are equilibrated can be used to quantitatively constrain how the olivine-liquid partition coefficients vary with oxygen fugacity, temperature, and composition. The experiments in this study have confirmed that the FeO, MgO, NiO, and MnO partition coefficients do not vary with oxygen fugacity. Dcao changes with oxygen fugacity in accord with the variation in olivine composition. All of the divalent cations vary with both composition and temperature, although most of the thermal variation of DNio and DhlnO is due to the temperature dependence of the activities coefficients rather than a large enthalpy of the exchange reactions. Acknovvledgments-We thank Roger Nielsen and an anonymous reviewer for constructive comments on an earlier version ofthis manuscript. Discussions with Victor Kress and Paul Wallace are appreciated. We thank the Earth Science Division of the Lawrence Berkeley Laboratory for financial support. Editorial handling: B. J. Wood REFERENCES G. E. and BISHOPF. C. ( 1985) An experimental investigation of mixing properties and unit-cell parameters of forsterite-monticellite solid solutions. Amer. Mineral. 70, 714-722.

ADAMS

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