Ferric-ferrous equilibria in Na2O-FeO-Fe2O3-SiO2 melts: Effects of analytical techniques on derived partial molar volumes

0016-7037/89/$3.00

Geoehimrca n Cosmochlmrco Acla Vol. 53. PP. 2195-2204 Copyri&t 0 1989 Pcrgamon Rts pk.Printad inU.S.A.

+ .oO

Ferric-ferrous equilibria in Na20-FeO-Fe203 -Si02 melts: Effects of analytical techniques on derived partial molar volumes REBECCAA. LANGE* and IAN S. E. CARMICHAEL Department of Geology and Geophysics, University of California, Berkeley,CA 94720, U.S.A. (Received November 9, 1988; accepted in revisedform June 16, 1989) Abstract-A published comparison (MYSEN et al., 1985a) between Mossbauer spectroscopy and wet chemistry applied to silicate glasses containing large concentrations of total iron (> 14 wt% Fe209) indicates a large, systematic discrepancy in the determination of Fe0 between the two techniques, with Mossbauer results typically lower in the ferrous component. This may be accounted for by the common assumption that ferric and ferrous iron in silicate glasses have equivalent Mijssbauer absorption efficiencies at room temperature, which has been shown to be invalid for several crystalline materials (VAN LOEF, 1966; GRANT et al., 1967; SAWATZKYet al., 1969; ANDERSENet al., 1975). Although this assumption has been demonstrated to be valid for glasses with low concentrations of total iron (DYAR et al., 1987), the approximation breaks down when total iron concentrations approach 14 wt% FeZOJ. As a consequence, measurements of thermodynamic properties on iron-bearing silicate liquids may take quite different values if Miissbauer spectroscopy rather than wet chemistry is used to determine the ferric and ferrous concentrations in quenched iron-rich glasses. Accordingly, we have measured ferrous iron concentrations in 65 NarO-FeO-Fez03 -SiO;, glasses quenched from melts equilibrated in air between 926 and 1583°C using a calorimetric wet chemical method. These data were used to derive a symmetric, regular solution model for ferric-ferrous equilibria which has a standard error of 0.36 (2~) in the prediction of wt% FeO. Additional liquids with initial compositions close to the stoichiometry of acmite ( NaFe3+Siz06) but which crossed the perferruginous join due to sodium loss during high-temperature equilibration ( 1420- 1540°C) are significantly reduced relative to other NazO-FeO-Fez03 -Si02 liquids. A re-interpretation of the density data of DINGWELLet al. ( 1988) based upon these wet chemical ferric-ferrous data demonstrates that the partial molar volume of Fe203 is independent of composition in the NazO-FeO-Fe203 -SiOZ system with a derived value of 41.78 + 0.41 cc/mol at 1400°C. This is equivalent within error to the value presented by LANGE and CARMICHAEL( 1987) of 42.13 + 0.28 cc/mol derived from both 4-component synthetic and g-component natural melts and thereby indicates that the partial molar volume of Fe203 is independent of composition over a compositional range relevant to magmas. INTRODUCTION

ferrous ratios can be quenched and measured. However, if the samples achieve thermal equilibrium during the experimental runs, then independent determinations of equilibrium ferric-ferrous ratios as a function of temperature (via Pt-loop dropquench experiments) can be applied. The objective of this study is to develop a thermodynamic model of ferric-ferrous equilibria in liquids of the Na@-FeOFezOX-SiOz system and to demonstrate its utility in the derivation of precise partial molar liquid properties. The lowtemperature liquidus surface over much of the NarO-FeOFe203 -SiOZ system makes it ideal for measurements of liquid density ( DINGWELLet al., 1988 ) , viscosity ( DINGWELLand VIRGO, 1988), heat capacity and sound velocity, as well as Raman spectroscopy, since a wide temperature range in the liquid state can be accessed ( - 800- 16OO’C) by conventional Pt-wound or MoSir furnaces. This, in turn, allows precise temperature derivatives of the various partial molar properties of the ferric and ferrous liquid components in silicate melts to be determined. These data are essential for calculating magmatic crystallization sequences over a variety of temperatures, pressures and oxidation states ( GHIORSO and CARMICHAEL,1987 ) .

IN ORDERTO BERELEVANTto magmatic processes, thermodynamic descriptions of silicate melts must include precise information on both the ferric and ferrous components. However, despite an expanding body of thermodynamic data on silicate melts, the largest uncertainties are invariably associated with the iron components ( BOTTINGAet al., 1982; STEBBINSet al., 1984; LANGEand CARMICHAEL,1987 ). This can be attributed, in part, to the under-representation of ironbearing liquids in the data set, although uncertainties may also arise from the inherent difficulty of accurately characterizing ferric and ferrous concentrations in experimental liquids during measurements of thermodynamic properties. The difficulty resides in the strong temperature dependence of the ferric-ferrous ratio in silicate melts. This requires that the redox state of experimental melts be determined at each temperature of measurement. Unfortunately, this is not always easily achieved. For example, during measurements of enthalpy or ultrasonic velocity? it is not possible to directly sample the experimental liquids so that appropriate ferric-

l Present address: Department of Geological and Geophysical Sciences, Princeton University, Princeton, NJ 08544. t See STEBBINS et al. ( 1984) and RIVERSand CARMICHAEL C1987)

Redox state: M&sbauer vs. wet chemistry The calibration of a model of ferric-ferrous equilibria depends upon accurate measurements of their respective con-

for descriptions of experimental apparatus and procedures. 2195

R. A. Lange and I. S. E. Carmichael

2196 Table 1.

0.87

4.38

MOCOI

14.04 * 24

0.86 f .od

3.03 *

Morn2

34.12 z+35

O.% * .05

1.25 c 1.56

3 88

Fe-Albile

27.92 ct 28

0.82 t 04

4.52 * 1.03

624

004

14.24 + .14

0.65 * .03

4 48 z?0.38

5.05

010

32.04 * .32

O.% t .os

1 I5 f 144

3 22

‘Wet cbmicd ndyus

by I.S.E.C.

2Mcravsauulcorophysid~banlay ‘20 P 0.21 WI % Fe0

centrations in equilibrated melts. Therefore, we start with an analysis of the two most frequently used techniques for determining ferric-ferrous ratios in quenched glasses, wet chemistry and M&sbauer spectroscopy. It seems generally acknowledged that these two techniques, applied to the same samples, lead to similar results (MYSEN et al., 1985a), yet the reality is otherwise if the data are examined in detail. In Table 1 we present the results (taken from MYSEN et al., 1985a; Table 2) for five glasses which contain in excess of 14 wt% Fez03 (as total iron). A comparison of ferric-ferrous concentrations cast in terms of Fe3+/ C Fe suggests that the two techniques are in reasonable accord, with a bias for the M&sbauer results to indicate larger amounts of ferric iron. However, if these data are recast in terms of wt.% Fe0 and wt% Fez03, then the discrepancies between the two techniques are seen to be very large and again systematic with a strong correlation with total iron concentration (Table 1). In fact, the 1u errors in Fe3+/ 2 Fe obtained by the Miissbauer technique of 0.03-0.05 translate into significant errors in wt% Fe0 (Table 1) which are well outside the wet chemical precision in the analysis of Fe0 (20 = 0.21 wt%).$ There is, in addition, experimental and theoretical evidence (VAN LOEF, 1966;GOL'DANSUI, 1966; GRANT et al., 1967; SAWATZKY et al., 1969; GREENWOOD and GIBE, 1971; ANDERSEN et al., 1975; BOWKER, 1979; MARNNIN, 1979; DYAR, 1985) which demonstrates that Mossbauer spectroscopy overestimates the Fe3+ component in minerals and glasses unless corrections are made for variable absorption efficiencies of ferrous and ferric iron in different coordination sites. In principle, Mossbauer spectroscopy is based upon the recoihess emission and absorption of y-quanta for nuclei (i.e., 57Fe) within a crystalline lattice. The probability of recoilless absorption (or emission) of yquanta is commonly denoted as the&factor. This parameter describes the efficiency of absorption (or emission) of Mossbauer nuclei bounded differently in a crystalline lattice: f = exp[-6ERT/kt?,]

for

T > W4,

(1)

4 The magnitude of the lcr mars attached to the wet chemical Fe’+/C Fe values in MY~ENel al. ( 1985abl corresoonds to a 6% unc&tainty. This is a value taken f&m SACKer al. (1980). Uafortunately, this value was misapplied as it refers to a 2a error which reflects a combination of the errorin the wet chemical determination of wt% Fe0 as well as the ermr in the microprobe determination of total iron as FeO.

where En is the recoil energy of the free atom, k is the Boltzman constant, 6, is the Debye temperature and T is the temperatum ( K) of the sample. PCXLAKet al. ( 1962 ) were among the first investigators to demonstrate that glass is sufficiently rigid for recoilless absorption of y-rays to occur. Although the Debye model is an over-simplification for glasses, Debye temperatures are a convenient parameter for describing the strength with which an ion is bound to its equilibrium position within a lattice. As a consequence, those nuclei which are more tightly bound in a coordination site will have a greater efficiency of y-ray absorption leading to an enhancement of their absorption peaks in a spectra. As an example, in a study of Fe’+/Fe” ratios in arfvedsonite by M&sbauer spectmscopy, ANDERSEN et al. ( 1975 1 found that, at room temperature, Fe’* in octahedral M1 and M3 sites was detected with an efficiency of only about 85%, of that of Fe”+ in octahedral Mr sites. This result indicates that if the absorption efficiencies of ferric and ferrous iron are assumed to be equivalent, then the measured quantity 01 the ferric component from the M&sbauer spectra will be over-estimated. In another study, the ratio of f-factors for Fe3+ in octahedral (B) and tetmhedral (A) sites (f~/f~) was measured in magnetite and yttrium iron garnet by SAWATZKY et al. (1969) and reported to be 0.94 t 0.02 at room temperature and 0.99 + .Ol at 0 K. In the studies of VAN LOU; (1966)andG~etal.(1967),theratioofrecoiIlessfactors fdfA for ferric iron was found to be 0.85 at room temperature for BaFeirOlp and 0.96 + 0.02 at 5 K for GaFezQ. These studies demonstrate that the absorption efficiencies of ferric iron in octahedral and tetrahedral sites are significantly disparate at room temperature yet become increasingly similar with decreasing temperature From these M&sbauer studies on crystalline materials. there is every likelihood that ferric and ferrous iron in silicate glasses will also have different absorption efficiencies depending upon whether they occupy octahedral or tetrahedral sites (or any continuous distribution between the two coordination polyhedra). As a result, ferric-ferrous ratios in glasses containing large concentrations of iron may not simply bc determined from M&sbauer spectra at 298 K without making appropriate corrections for variable recoillessS_factors. However, these corrections prove to be extremely difficult for glasses (mWKER, 1979) due to the inherent width of the absorption peaks, As a consequence of these. difficulties, thermodynamic melt properties such as molar volume, which can only be derived from the density of the liquid if its gram formula weight is known (Vi = g.f.w./%), may take quite different values if Mizissbauer spectroscopy rather than wet chemistry is used to determine the ferric and ferrous concentrations of the quenched glasses. The results reported in this paper are intended to show how precise oxide partial molar volume derived from density measurements on hquids in the NarOFeG-Fe203-SiOz system (DINGWELL et al., 1988) can be if wet chemical ferric-ferrous ratios are used in preference to those obtained by the M&sbauer technique. The model of ferric-ferrous equilibria presented in this paper can be applied to measurements of viscosity ( DINGWELLand VIRGO, 19881, heat capacity and ultrasonic velocities as well.

2197

Fe)+-Fe’+ equilibria in Na-Fe silicate melts EXPERIMENTAL

METHODS

Eight compositions within the NarO-FeO-Fer03SiOz system plus the composition of the mineral acmite ( NaFeSiZOd) were prepared by mixing appropriate proportions of reagent grade SiOz, Fe203 and Na2C0, powders. Each mixture was initially decarbonated at 900°C and then fused at 1200°C. The samples were quenched to a glass, ground to a powder and re-fused. This procedure was repeated twice to ensure homogeneity. Each sample was equilibrated in air on 10 mil Bt90%-RhlO% wire loops at seven temperatures between 1050 and 1583°C. Samples 14 were also equilibrated at 926’C. The sample close to the stoichiometry of acmite (AC; Table 4) plus sample 002 from MO er al. ( 1982; approximately acmite composition) were botb ~uilib~ted at tem~mtu~ between 1420 and 154OY. In each experimental run, four samples (duplicated in two layers and fastened to a Pt cage) were suspended in the hot spot of a vertical quench MoSiz furnace. Temperature was measured with an S-type thermocouple placed immediately above the cage and corrected for a vertical thermal gradient of l.S”C/cm. The thermocouple was calibrated against the melting temperature of 99.99% gold ( 1064.43’C; accepted iPTS, 1969, value) twice during the course of the experiments. The measured melting temperatures of gold were 1063.6” (immediately prior to the experimentai runs) and 1063.2”C (toward the end of the runs). The samples were reacted for five hours between 1050 and 1450°C and for two and five hours at 1583°C before they were drop quenched into chilled, distilled water (an efficient quench media; DYAR and BIRNIE,1984). The quenched run products rarely spalled or fractured and typically formed hard, glassy beads of 40-60 mgms. Longer reaction times at 1050°C of eight and thirteen hours indicate that equilibrium had been achieved after five hours and possibIy sooner. The samples which were run at 926*C were equilibrated for ten hours. Iron-loss to the Pt loops was negligible since the experiments were run in air, although at temperatures above 1350°C the Pt loops were pre-equilibrated with separate aliquots of the samples as a precaution. The quenched charges were analyzed for SiOz, Na20 and total iron (as FeD) with an electron microprobe using an accelerating potentiai of I5 kV, a sample current of 0.03 PA and 10 s integration times on 20 snots per analysis. To minimize alkali loss, spot sizes on standards and samples were between 20 and 25 pm. The standard for Fe0 was NBS K-4 12 mineral glass, whereas the standard for both Nap and SiOr was albite glass (analyzed wet chemically by the second author). Either standard yielded similar results in the analyses of Siq. The data were reduced with an empirical non&mar correction scheme after BENCEand ALBEE( 1968). Standard deviations of the analyses range between 0.5 and 2.3% relative. FIame photometric analyses of NazO in the initial starting glasses of samples 1-8 are within 0.6% of the electron microprobe analyses of Na*O in the respective run products quenched from 105O’C. This indicates that ( 1) sodium loss during equiiibration was negligible at this Lowtemperature and (2) sodium loss under the electron beam during microprobe analysis was suffi~enUy minimized. A 3-8 mg sample of each glass charge was used for a calorimetric determination of wt% Fe0 as described by WUON ( 1960). A glassy mid-ocean ridge basalt, JDFD-2 (CARMICHAELand GHIORSO, 1986; Table 1), was used as a standard in each set of 24 measurements over the course of four months. The mean value of wt% Fe0 based upon the calorimetric technique is 10.93 + 0.21 (2a), whereas the mean value using a titrimetric method is 11.12 + 0.14 (2~) wt% FeO. Ahhouah these rest&s indicate a small systematic d&e&e between the two Seth& the respective mean values are equivalent within error. As the precision in the calorimetric technique is -0.21 wt% FeO, replicate measurements on the NazO-FeO-Fez03-SiOz glass charges which are significantly more discrepant probably indicate inhomogeneity in the samples with respect to FeO. As described below, all of the run products appear to be homogeneous based upon this criteria. The concentration of ferric iron was cafcuiated from the difference between total iron and iron in the ferrous state ( Fe203 wt% = 1.I 1I3 (FeO*FeO) wt%). Significant sodium volatilization occurred in the samples equilibrated at high temperatures (Table 2). However, two lines of evidence

indicate that this did not affect the achievement of ferric-ferrous equilibria. First, microprobe traverses of samples equilibrated at 1583°C after two and five hours, respectively, indicate no detectable compositional gradients. Second, measurements of Fe0 were duplicated on samples equilibrated at 1583°C to assess their homogeneity with respect to FeO. Since the amount of glass needed in the chemical analysis of Fe0 is ~5% of the inass of the charge, the excellent reproducibility of the analyses on these high-temperature samples (217 = 0.20 wt% FeO) indicates that they are homogeneous. Samples containing less than 0.5 wt% Fe0 in the presence of large concentrations of ferric iron (i.e., samples equilibrated at low temperatures) demonstrated a linear time dependence to the intensity of their absorptions during the calorimetric analysis. The absorptions of these samples were measured every 30 minutes over a three hour period and the reported values are the zero-time extrapolations. Duplicate measurements were made on these low-temperature sampIes (equilibrated at 926- 1ISOYZ)to assess the precision of the coiorimetric technique at low concentrations of Fe0 (~0.5 wt%). One sample with a total iron concentration of 38.27 wt% Fez03 (#I equilibrated at 926’C) was analyzed five separate times with resultant values of 0.27,O. 13,O. t 5,O. 18 and 0.15 wtgb Fe0 indicating a mean value of 0.18 f 0.11 (lo). These data indicate that the experimental reproducibility of -0.2 1 wt% ( 2~) is valid at low ferrous ~n~nt~tion~ although the uncertainty represents a large percentage of the Fe0 present. The essential point is that the magnitude of the experimental

error is uniform over a wide range of ferrous iron concentrations.

RESULTS

The data presented in Table 2 indicate that there is a significant increase in ferrous concentration with temperature for each composition. This is consistent with the following reaction which can be postulated to occur in the experimental melts: FeO,,$ (liq) = Fe0 (iiq) + 1/402(gas)

(2)

where temperature favors the high entropy side of the reaction. A quantitative examination of the effects of both temperature and composition can be made by evaluating the change in the free energy of the oxidation reaction. At equilibrium we have AC = AH0 - TM0 + RT In (~r~,.,/a~~Jr’~O~)

= 0 (3)

where &co,, and aFeo refer to the activities of the FeOl.5 and Fe0 liquid components and f 02 refers to the fugacity of oxygen in the system. AH@ and ASo refer to the standard state enthalpy and entropy of reaction, respectively, and are functions oftemperature. By rearranging the terms and using the relationship, ai = Xiri (where Xi and yi refer to the mole fraction and activity coefficient of component i, respectively), the following relationship is obtained: In (&&,.,/x&o)

= AH’/RT - A.S’/R + r/4Info2

+ In

(YFco/YFco,.,).

(4)

Values of In (Xr+o,,,/XM) for samples 1-8 at constant temperature ( 1050°C) are plotted within the NarO-SiOzFe24 ( total) ternary system (Fig. 1). Contours of constant In (XFa,.5/Xra) are approximately subparahe1 to the NazOSiOz binary, indicating that the ferric-ferrous ratio in these melts is a strong function of the total iron content. A plot of

R. A. Lange and I. S. E. Carmichael

2198

.I6

I

926.0

10

32.99

28.10

3x15

20

04

2

926.0

IO

42.25

29.79

28.09

,I4

.03

II

3

926.0

10

50.16

32.38

17.18

.?a

02

06

4

926.0

IO

4950

27.95

2w4

19

03

16

1

1051.0

5

32.99

28.70

37.99

14

.I8

2

1051.0

J

4225

29.79

27.85

.36

15

3

IO51.0

5

M.76

32.38

16.91

.32

10

4

lM1.0

5

49.60

27.95

22.84

.28

13

.I5

07

24

5

m9.5

5

62.43

26.53

II.12

6

1019.5

5

57.w

21.71

20.01

7

Pm.5

5

72.29

24.05

3.55

II

16 21 22

A3

.I2

31

.21

.06

.I5

8

I(u9.5

5

66.69

10.57

22.07

46

.14

-32

I

1145.0

5

33.91

2h49

38.93

49

-45

04

2

1145.0

5

43.2a

27.52

29.28

SI

38

2

1150.0

5

42.6?

28.&

28.50

.48

.34

13 tw

3

1145.0

5

51.95

30.67

17.37

.43

7.5

.I8

4

1145.0

5

50.04

26.90

23.13

.57

32

25

4

1150.0

5

50.14

27.28

22.67

.53

.33

20

5

1150.0

5

62.80

26.66

10.91

38

18

20

6

1150.0

5

58.41

21.51

20.01

.40

31

17

7

1150.0

5

72.54

24.M

21

.c%

8

1145.0

5

67.34

IO.04

21.87

.&a

34

.26

3.59

I5

I

1248.5

5

34.70

25.23

39.28

I.11

1 Ik

03

2

1248.5

5

43.51

2744

28.64

94

90

04

3

1248.5

5

52.36

30.36

17.05

.88

59

29

4

1248.5

5

5O.90

26.31

22.01

95

74

21

s

1249.5

5

62.31

26.44

10.98

61

41

2:

6

1249.5

5

58.27

21.49

19.73

97

70

27

7

1249.5

5

12.52

23.84

3.52

.a

14

09

8

1249.5

5

66.71

IO.59

21.45

1.02

79

.2'S

1

1yd.o

5

36.e

21.16

443.16

2.30

2.44

14

21%&O

5

45.46

24.81

28.73

i.84

t.91

-07

3

1346.0

5

54.32

28.02

16.76

147

122

4

1346.0

5

51.40

25.17

22.17

I.74

I.%

5

1346.0

5

63.40

25.54

IO.71

1.03

.82 I40

25 18 21 20

6

1346.0

5

59.04

21.38

19.03

1.60

7

1346.0

5

72.91

23.84

340

41

28

14

8

l346.O

5

66.72

IO.44

20.68

182

I57

25 I9

1394.0

39.04

3.19

1393.0

s

56.17

23.x?

17.70

I71

178

-07

1394.0

5

53.88

22.22

22.85

1.x3

2.23

-40

5

36.83

21.13

3.38

t 3 3 4

1393.0

5

52.41

22.30

2240

2.32

220

.12

4

1394.0

5

52.44

23.29

2l.M

2.25

2.21

M

5

1394.0

5

65.58

21.98

10.57

1.40

1.14

26

6

1394.0

5

60.94

IS.06

19.25

2.m

199

7

1393.0

5

75.69

20.19

3.51

46

.39

07

7

I3940

5

75.16

21.32

362

4d

4r

OS

8

1393.0

5

61.26

9.30

*0,,4

231

?.li

ix

8

lW4.0

5

66.78

19.87

2.53

213

40

I

1448,O

5

38.79

17.60

39%

474

507

29

1

1448.0

5

47.41

21.66

2766

3.74

479

05 09

1023

3

IU8.0

5

55.66

24.98

1708

2.36

2.45

1448.0

5

53.39

22.59

21.89

2.91

309

14

RT In yi = 2

Wt+)X, - % C 2

N’&X,,Xk

(5)

where ri is the activity coeffkient of oxide com~~eot i and Wi,j and Wik are temperature and pressure in&pendent bi* nary component interaction parameters which describe attractive or repulsive forces between unlike molecules (NJ’,,; = 0; .W’i,j = Wj,;i). U&g Eqn. (5) to define ~l;a,~ and -fFd)t

Ewe

(4)becomw:

where the Wjh parameters have cancelled. Note that the parameters in the last term modifying the mole fraction of each oxide component (Xi) do not define the m~itude and sign of ~nd~v~d~~ binary interactions, but rather the relative d$

I6

5

1448.0

S

65.05

23.83

IO.08

1.67

IS3

6

lU8.5

5

60.48

19.11

IR 17

2.69

2.6R

"I

7

1448.5

5

74.54

20.75

3 19

5x

10

08

8

1448.5

5

67.01

10.28

19.27

2.93

z.93

00

2

t542.0

6

57.02

6.47

2615

9.62

7.54

2.m

4

15490

3

57.11

16.23

20.98

3.50

574

~..?4

1

1583.0

2

4O.M

12.74

34.79

12.33

Ital

.32

2

1583.0

2

52.50

12.53

25.43

8.90

8.77

3

1583.0

2

62110

16.17

16.14

4.98

5.42

-44

4

IS83.0

2

56.68

IS.64

19.75

6.69

670

-01

5

1580.5

5

7166

15.39

939

3 03

3 IS

16.52

.I3

I2

7

I56cm

5

79.60

1.06

102

S

1580.0

5

68.94

8.54

16.59

5.m

f6B

-to

As

1422.0

5

52.72

12.26

29.50

5 02

163

i 79

02

a32

1422.0

5

53.05

12.64

29.23

506

361

i 45

002

1442.0

6

5518

8.38

28.58

7.op

4.28

z 76 1.68

14756

4

53.51

11.52

28.22

6.73

505

002

1474.0

4

53.85

11.33

28.20

6.S7

5.00

I57

&

1538.5

3

53.68

It.16

26.66

84)

7 18

125

oz

1538.5

3

53.99

10.81

26.37

854

714

140

AC

In (Xrfi,,JXra) versus 11 T for ail of the date is shown in Fig. 2. From Eqn. (4), it follows that the general slope of the data provides a measure of the enthalpy of the standard state reaction (~~~), whereas the scatter in the slope rekcts non-zero heats of mixing and can be modekd using regular solution theory. Thus, by definition (see C~To~soet al,, I983, pp. 110-111):

IO

4

3.01

FIG, I. A plot of In (Xr+,/X~) vahtes at E$WY’Cfor liquids within the NazO_Si~-FesOs (total) ternary system ( mol%1.

Y

%

5

l

Liquids l-8

2 4 x ‘io 23 e

. ii ;cc”2f’ z . - l- ,* 1 l

o!

.

‘

.

I

.

/

FIG. 2. A plot of In (Xpd),,,/Xfco) vs. 10000/T(K) for samples I-8 equilibrated at eight temperatures between 926 and 1583°C. The slope of the data corresponds to the enthaipy of the iron redox reaction (Eq. I ) whereas the scatter in the dope reflects non-zero heats of mixing.

Fe3+-Fe*+ equilibria in Na-Fe silicate melts

ferences between two. In fact, the only interaction parameter for which direct information can be extracted is WFa,F.+, since one of the two parameters within the parentheses in the last term will drop out when i is equal to either Fe0 or Fe&s. Equation (6) provides a linear regression equation whose residual &m-of-squares can be minimized using the method of least-squares. However, this form of the equation produces a bias in the regression as a result of the way that the experimental errors propagate during construction of the parameter, ln(X~~,,J.X,,). This point is illustrated in Fig. 3 where calculated values of In (X,,,,JX,) with one o error bars are plotted versus temperature for samples 1 and 7 which have initial iron concentrations of 37.7 and 3.5 wt% Fez03 (as total iron), respectively. The large error bars associated with In (XFd),,,/XFco) at low temperatures and low concentrations of total iron are due to the fact that the experimental error of -0.21 wt% Fe0 represents a large fraction of the amount present when X,, is smalf. This propagates into a large uncertainty in In (XFco,,JXF,). The inverse is true at high temperatures or at high concentrations of total iron where X,, is relatively large and the experimental uncertainty is proportionally small. The result is that the parameter, In (X,,,JXFd), is acutely sensitive to errors in XF, when XF, is small but becomes increasingly insensitive as XF, increases. As a consequence, a regression with In (X,,, $/ XF,) as the dependent variable effectively weights the low

FezOf

0 1000

= 3.5 wl 9%

I .,.,,l

.,.I.

1100

1200

1300

Temperature

1400

1500

1600

(“C)

FIG. 3. (a) A plot of In (XFcOl,/X~~) with one 4 error bars VS. T( “C) for sample 1 (initial total Fe203 = 37.7 wt%) equilibrated at seven temperatures between 1050 and 1583°C. The error increases with decreasing temperature as the ferrous component decreases. (b) A similar plot as in (a) for sample 7 (initial total Fe20, = 3.5 wt%). The errors increase on In (X,,,,,/X& relative to sample I due to the lower total iron concentration of sample 7.

2199

temperature experiments far more heavily than those at higher temperatures, despite the fact that the measurements of wt% Fe0 have equivalent uncertainties at all temperatures. A direct alternative is to simply use the measured parameter, wtR FeO, as the dependent variable in the regression equation because the errors in wt% Fe0 are ~~I~~. Equation (6) can be rearranged in the following way:

wt% Fe0 = M.W.(FeO)* nF&& *exp(-y)

(7)

where M.W.( FeO) is the molecular weight of FeO, &a,,s is the number of moles of FeOl,s and the argument in the exponential is the ant-hand side of Eqn. (6): y = AH’IRT - AS’,lR + ‘1’4 In f 02 + IIRT C &

(wi,FcO

-

f'&a,,$).

(7a)

Equation (7) provides a non-linear regression equation whose residual sum-of-squares can be minimized using a modified Marquardt procedure for a non-linear function (NASH, 1979; Algorithm 23) to extract the following unknowns from the data set: M’(T), WFCO,F~,., and w.FeO w,FcO,., (for i = NazO and SiOz). Since the binary interaction parameters in Eqn. (7a) describe non-zero heats of mixing relative to the heat of reaction involving only the pure standard state components, any physical inte~~tation of the derived interaction parameters regarding attractive or repulsive forces between components depends upon a reliable, independent estimate of AI!Z”(T). Unfortunately, pure FezOs liquid is unstable at high temperatures so that its heat capacity and the heat of fusion of hematite can only be estimated. Alternativeiy, the standard state reaction for Eqn. ( 2 ) can be chosen to involve the pure, solid components. This transfers the contribution of the “partial molar” heats of fusion of the Fe0 and FeO,.s components to the derived binary interaction parameters. The advantage, however, of this procedure is that experimental data, and not educated estimates, are used to calculate the free energy of the standard state reaction. The temperature dependence of the enthalpy and entropy of the solid standard state reaction can be written in terms of the heat capacity of the reaction where: AH’/RT

- AS”/R =

-

AHo{ Twf) + i

s

A@‘( T)dT

Ii

Ii

RT

A.!?‘( Tmf) + ACp’( Tf/TdT R. (8) s [ A reference temperature ( Tmf) of 1300°C was chosen as it represents the midpoint of the experimental temperature range. Using the calorimetric data presented in ROBIE et al. ( 1978, pp. 80, 164, f 65 ) for stoichiomet~c crystalline FeO, hematite and 02 gas, a value of 133.9 M/mol can be calculated for tiZ”( I;ef = 1300°C). The temperature dependence of the enthalpy of the solid standard state reaction, derived from the integrated heat capacity of the reaction, can also be calculated from the data of ROBIE et al. ( 1978). At 926 and 1583’C, the lowest and highest temperatures of our measurements, the heat capacity of the reaction contributes -0.16 kJ and - 1.37 kJ, respectively, to AH0 ( 13OO*C), each representing only 0.1 and 1.O% of AH0 ( 1300°C). In terms of the parameter, In (XFa,,,/XFa), this translates into 0.02

2200

R. A. Lange and 1. S. E. Ckmichacl

DISCUSSION

and 0.08 natural log units at 926 and 1583”C, resgactvely, neither of which can be resolved within our experimental precision. As a result, Eqn. (7) can be simplified to Eqn. (7’) by neglecting the heat capacity terms in Eqn. ( 8 ) : wt% Fe0 = M.W.(FeO)*

nrzo~,,~*exp(-y)

(7’1

WhXe

+ l/RT

c &(w,,

-

M/iFeO,.s).

(7a’)

In the mgression of E.qn. (7’), AH0 ( TEf = 13OO*C) was used as a constraint rather than as a variable, for which mgression results are presented in Table 3. At this point, we emphasize again that because AH0 ( 7’,r = 13OOV) refers to a solid standard state reaction, the regrea& binary interaction parameters reflect the partial molar heats of fusion of the Fe0 and Fe&s components as well as non-zero beats of mixing. As a consequence, the &ted values of the binary interaction parameters are essentially empirical constants for which physical interpretations are unwarranted. As demonstrated in Table 3, the quality of the fit is excellent with a two u error oi0.36 wt% FeO. This error is well within our combined experimental uncertainty in the calorimetric determination of FeQ (0.2 1 wt% ) and the microprobe errors on the analyses of Si02. Nat0 and Fe0 (as total iron) concentrations (OS-2.3% relative). Although all of the samples equilibrated at 2’ s 1346°C have positive residuals, this structure is not eliminated when the heat capacity terms are included in Eqn. (7’). Figure 4 presents the I (r residuals for this regression as a function of temperature. In the course of fitting the &ta, it was found that those liquids whose final compositions project beyond the Na&acmite join (Table 2) were characterized by large, positive residuals (open stars, Fig. 4). This indicates that these liquids are significantly redueed relative to the other 65 Na&-Fe&-SiO* liquids. As a muence, these samples were not used in the calibration of Eqn. (7’). The results for these liquids were verified by duplicate equilibraiian experiments and wet-chemical analyses. The significance of their reduced nature is explored in the following section.

§ The in&l composition of sample 2 lies on the join between acmitc and the Na& apex (Table 3 )

A plot of run products in the Na@-Si0~-Fe~03 (total) ternary system (Fig. Sa) provides an illustration of samples which have crossed the “nominally” perferruginous join during high temperature equilibrations. Nominaily perfer.~ ruginous liquids are defined as containing a mole fraction of NazO which is kz~ than their mole fraction of total iran east as Fe&. Sampleswhich have crossed into this region inch& liquids with initial compositions close to acmite (denoted by stars) as well as sample 2 equilibmted at 1542’C for six hour@ and sample 1 equilibmted at 1583°C for two hours. Of interest is the observation that samples which project directly beyond the Na@-acmite join across the nominally ~~e~no~~ join are signikantly more reduced than predicted by the model (A = 1.25-2.87 wt% FeO, Table 2 3I The explanation for this anomalous ferric-ferrous behavior may reside within their perferruginous nature, which distinguishes them due to an insu&ient concentration of sodium to charge balance alt of the iron cast in terms of the ferric com~nent. As a consequence, the speciation of f&c and ferrous iron may be quite distinct in perfkrruginous versus peralka&ine liquids since the stability of the ferric component depends, in part, on the char&&uGng role of sodium. These data suggest, therefore, that extrapolations of the model (calibrated predominantly upon peralkaline liquids) to ~~~~nous corn* sitions are not warranted. However, although sample 1 (equilibrated at 1583’C for two hours) also plots well within the nominally perferruginous field (Fig. 5a), its measured ferrous iron concentration is fitted well by the model ( A = .32 wtW FeO, Table 2 ) At this point it is necessary to di~~~i~ between nominally and truly perferruginous melts. Nomi~y ~e~~no~ liquids differ from their peraluminous anaiogues in that some of the total iron (cast entirely as ferric iron in Fig. 5a) is actually in the ferrous state. Therefore, truly perferruginous liquids can be plotted within the NazO-Fe&-SK& system only by projecting from the ferrous component. Such a diagram is presented in Fig. 5b, where the d~~~butio~ of the experi-

3,5 _’ z 2

P

5

d ;

2.5-

Liquids

Q

Acmitc

I.8

j

liquids

! I

**a

a.5-

_g 0 -1.5G! eF e2.5

I

h

1.5

-0.5 -

5

*

*

*

t

l

qx

i

*t

I I 1 i

-3.5 850

L 1050

1250

'1450

1650

Temperature (“0 FIG. 4. A plot of residuals from the regnsion of Eqn. (7’) as R function of temperature (“Cf. Ail residuals am less than 0.5 wt’% FeO, and their stand& deviation is 0. I8 WE&FeO.Sampleswhich pro* beyond the Na@-acmite join are significantoutliers ( Tabk 2; Fig. 5) and more reduced relative to the predicted values.

Fe’+-Fe2+ equilibria in Na-Fe silicate melts

2201

i0

Si102

\i

$ i

i i

I I

t ”

i 3j

I

i i i i

i i i i

i lb1 FIG. 5. (a) A plot of run products in the Na20, SiOl, and Fe*O, (total) ternary system (mol%). Stars denote liquids with initial compositions close to stoichiometric acmite. The pet-alkaline-“nominally” perferrugmous (see text for definition) boundary is marked by the dashed line. Labels 1 and 2 refer to the run products of samples 1 and 2 after their highest temperature equilibration (Table 2). Samples which do not fit the model of Table 3 are labelled by the stars and by the number 2 (see text and Table 2). Open squares denote the experimental liquids of DINGWELL etal.. ( 1988). (b) A similar plot of run products projected onto the Na20-Fe20s-SiG ternary system from the Fe0 component. The dashed line marks the ~~k~in~~~e~~nous boundary. Symbols are the same as in (a).

mental run products is also plotted. In this diagram, sample 1 has barely crossed the pemlkaline-perferruginous boundary whereas four of the eight samples characterized by large, positive residuals (Table 2) plot within the pera~kazine field. Although ferric-ferrous data on liquids within the perferruginous region are extremely limited, it appears that the outliers to the model presented in Table 3 are restricted to samples which project directly beyond the NazO-acmite join. This suggests that their reduced nature may be related to their proximity to the acmite composition. Mossbauer spectroscopic data on peralkaline NazO-FeO-FezOs -Si02 glasses quenched (in water) from liquids equilibrated in air ( GOSSELIN et al., 1967; HIRAO et al., 1980; VIRGO et al., 1982) indicate that Fe”’ cations are predominantly in a tetrahedral coordination whereas Fe’+ cations are confined to an octahedral coordination. The ferric-ferrous data in this study suggest that octahedral Fe’+ is energetically favored over tetrahedral Fe3+ in liquids with compositions close to acmite perhaps due to a prevalence of sites which mimic the Ml octahedron. This effect may be compounded as the sodium concentration decreases, further reducing the stability of the ferric component. Regardless of which mechanism controls ~~e~~nous ferric-ferrous equilibria in liquids that project beyond the NazO-acmite join, the model presented in Table 3 is noi applicable to these liquids. Therefore, an empirical equation of the form fn (-&~,.J&~)

= a + b/T +

CXN~~O

(10)

is presented in Table 4, which is based upon a linear leastsquares regression of ferric-ferrous data for these eight liquids.

Table 4 presents a comparison of measured values of wt% Fe0 with those predicted by Eqn. ( 10). The average deviation between predicted and measured values is 0.17 wt% FeO, which is within the experimentai precision. This equation is recommended for liquids with initial compositions close to acmite which have experienced variable sodium volatilization. Volumes of Na20-FeO-Fe20sSi02

liquids

In a recent study of NazO-FeO-Fe203-SiOz melt densities, DINGWELL etal. ( 1988) suggest that liquid volumes in this

system cannot be described by the simple equation biq(

T, =

C xiV(

T,

(11)

where Xi is the mole fraction of oxide component i and Vj is its partial molar volume, but require excess volume terms. This conclusion is based upon the observation that their vol-

R. A. Lange and I. S. E. Carmichael

2202 T&blC5. Mm

DBH

<@a Fe&1

I 2 3 4 5 6 7 9 10 II 12

wt % Fso of dulsily melts’ ____. ---_--

t&d2 ___

27.73

1.54 1.36

35.22 40.15 4275 34.63 25.93 17.66 25.98 M8S 44.36 5J.Y

1.53 1A9 2.03 0.78 0.49 0.45 0.31 0.31 0.51 0.30

card

DBD’ iuaw2 _.-__-. 2.62 3.02 2.61 3.w 1.56 1.06 0.92 087 0.93

1.91

1.15

I.71

1.21

----

Modct:

.-.--.---.. II 3 74 4 71

2.79

2.63’ 1.71 1.78 1.51 1.21 0.87 1.16 1.K1

T.”

-.... l54wC

MCWC

13oxI

Tovi id

sampa -

“8. prdmcd

4 49’ 3.43 3.57 3.01 2.39 1.70 2.29 3.01 3.45 1Yi

-.,._ “-_.-.----

s.33 7.18. 4 19 6.34 4.44 6.61 2.w 3.52 2.05 4.32 t.70 3.01 L.Y$ 4.16 240 5.%? 2.56 6.64 3 bl 7 64 ____ .“l._l

‘FromDtNGWELLoal.(1%38:Tabk 1)

ume data are poorly fitted by the linear model in Eqn. ( 11) which has a relative standard error of 0.83% (outside the experimental uncertainty ofO.558). These regression results of DINGWELL ez al. ( 1988) led to their suggestion that the poor quality ofthe Iinear fit is a reflection of ~~~~ changes in the melts. However, before structural interpretations can be accepted as unequivocal, it should first be demonstrated that the poor quality of DINGWELL ez d’s ( 1988) linear fit cannot be attributed to an incorrect assessment of ferric-ferrous ratios in the experimental melts. DINGWELL et al. ‘s ( 1988 ) m~u~ments of ferric and ferrous iron are based upon Mossbauer spectra and wet chemical analyses of glasses quenched from their experimental melts. However, as these liquids contain between 17.66 and 55.34 wt% FesOJ (as total iron), the results presented in Table 1 susest that DINGWELL et d’s ( 1988) M&sbauer measurements of Fe0 may also be subject to systematic errors. In light of the difficulties discussed earlier in quantitatively determining ferric and ferrous concentrations in iron-rich

DBD’ 13wC

Wmok f 1.~1

DBD2

--~

SiO,

ZchSS * 0.28

26.6oiO.lJ

26.92* 0.06

Wh

40.77f 0.77

41.39* 0.37

41.44* 0,31

&

2tl.90f 0.52

ma 13.61* f. 0.23 0.33

28.@2 13.35* rJ.18 0.12 --

14twC SiO,

26.67f 0.29

26.68f 0.16

26.90* 0.06

~

40.67fo.a~

41.78t 0.41

42.13* 0.28

&

29.66f 0.96

29.14 13.85ft 0.34 0.25

2%?8 13.65f* 0.15 0.10

SiO2

26.67* 0.37

26.74* 0.17

26.91* 0.06

FM+

40.46ZI1.16

42.46f 0.49

42.91* 0.29

z

M.64 * 0.71

29.80 14.12f* 0.37 0.26

29.51 13.97* 0.14 0.10

15ooT

‘FnnmDIMIWf&L 01 &. (19as:Tabk 4) ~ot~l(I~~~~aP~-f~n(fie~&) 3FramUNGfi rad s

ff9gl; T&bk8)

3.5 2.5

2

1.5

*

Liquids

-piDingwelt

I-a et II.

f 19881

850

FIG. 6. A cornparis~n of BILL ei d’s ( 1988) masuM vak~~ of wt% Fe0 by MWbauer spectroscopywith the values ptedictea by the models presented in this study calibrated on wet chemical results.

Also stmm are the residuals of Fig. 4. The discrepancy in wt% Fe0 between DINGWELLet al. ( 1988) and this study approaches 4.0 wtW Fe0 at 1500°C.

glasses by MasJbauer spectroscopy, it is appropriate to use the thermodynamic model presented in this study (calibrated upon wet chemical resuhs) to recalculate the ferrous concentrations in DING~ELL et al.‘s ( 1988 ) experimental melts. A comparison of the wt% Fe0 values reparted by DINGWELL ef al. ( 1988) and those recakuiated by our model of ferricferrous equilibria is given in Table 5 and illustrated in Fig. 6. Again, as was seen in Table 1, the discrepancies between the MWbauer results and the predictions of our model are significant and strongly correlated with total iron concentwtion. DINGWUL et d’s ( 1988 ) sample 2 is close to the composition of acmite, and, therefore, the linear regression equation presented in Table 4 was used to calculate its appropriate ferric-ferrous ratio at 1300, 1400 and 1500°C. The predicted ferric-ferrous values derived from the regular solution model were used to recalculate oxide mole fractions in DINGWELL et d’s ( 1988 ) experimenti liquids. These data. in turn, were used to recalculate molar volumes from DINGWELL et al.‘s ( 1988) density measurements using the relation

LC? --.--.^(cc/mole * la)

Wmok * lo)

8f

B

V,, = C Xi(M.w.)iI~l,,

( 1;:>‘)

where Xi is the mole fraction of oxide component i, (h&W.), is the moiecular weight of component i, ptiGis the measured density of the liquid and Vrisis its molar volume. These recalculated data were then used in a general regression to establish whether the linear model equation (Eqn. I 1) would fit the experimental data within the quoted errors. The only difference between this revised data set and that of DINGWELL eC ai.% ( 1988) is the inclusion of a liquid close to the stoichiometry of FeZSO3( Mr, ez ai., 1982; sample FS 1. Data for FeSiOs were inch&d as there is no controversy over its mdox state (its density was measured in equilibrium with metallic iron so that its ferric concentration was insignificant), and it contains a large fraction of the ferrous component which stabilizes VF,, in the regression and eliminates the necessity of fixing its value (I priori f LhNGwELL et ai., 1988 1. The resdts of this regression are reported in Table 6, which

Fe3+-Fe2+equilibria in Na-Fe silicate melts lists the derived values of the oxide partial molar volumes.

The average deviation between measured and predicted volumes at 1300, 1400 and 1500°C are 0.38,0.37 and 0.42%, respectively, which are comparable to DINGWELL et aI.% (1988) experimental uncertainty in volume of 0.55%. The volume of liquid acmite is fitted by the linear model within 0.43% at 1400°C and, hence, does not appear to be anomalous in volume due to its stoichiometric composition. Table 6 also lists the original regression results of DINGWELL et al. ( 1988 ) based upon the linear model equation for molar volumes (Eqn. 11) which are in marked contrast to the results of LANGE and CARMICHAEL ( 1987). However, the partial molar volumes derived from DINGWELL et al.% ( 1988) data set using our ferric-ferrous relations are equivalent (within error) to those reported by LANGE and CARMICHAEL ( 1987; based upon 4-component synthetic and g-component natural melts). The important implication of these results is that the density measurements of DINGWELL et al. ( 1988) are consistent with those of LANGE and CARMICHAEL ( 1987) as well as with those of STEIN ef al. ( 1986), EIOCKRISet al. ( 1956) and MO et al. ( 1982 ), all of which are based upon the Pt double-

bob Archimedean technique. However, due to the relationship between volume and density Viq = C Xt(M.W.)ilPriq

(12)

the discrepancy between the calculated volumes of DINGWELL el al. (1988) and those of LANGE and CARMICHAEL (1987) can be attributed entirely to differences in calculated compositions ( 2 Xr( M.W.),) arising from the bias between two

different methods of measuring ferric-ferrous ratios in glasses quenched from experimental melts. In summary, it has been demonstrated that the greater precision of the wet chemical method for characterizing the redox states of iron-rich glasses translates into a set of derived thermodynamic properties, namely the oxide partial molar volumes, which are themselves more precise and thus fully utilize recent experimental density data.

Acknowledgements-We

are grateful to Mark Ghiorso, who introduced us to the Marquardt procedure for minimizing non-linear functions. Constructive reviews by Drs. M. D. Dyar, R. 0. Sack and M. T. Naney are gratefully appreciated. This research was supported by EAR 8500813, a National Science Foundation grant to I. Carmichael. Editorial handling: R. G. Bums

REFERENCES ANDERSENE. B., FENGERJ. and ROSE-HANSENJ. ( 1975) Determinations of [ Fe2’]/[ Fe”]-ratios in arfvedsonite by Mbssbauer spectroscopy. Lithos 8, 237-246. BENCEA. E. and ALBEEA. L. ( 1968) Empirical correction factors for the electron microanalysis of silicates and oxides. J. Geol. 76, 382-403. BOCKRISJ. O’M., TOMLINSONJ. W. and WHITE J. L. ( 1956) The structure of the liquid silicates: partial molar volumes and expansivities. Faraday Sot. Trans. 52,299-3 10. BOTTINGAY., WEILLD. and RICHETP. ( 1982) Density calculations

2203

for silicate liquids. I. Revised method for aluminosilicate compositions. Geochim. Cosmochim. Acta 46,409-4 14. BOWKERJ. C. ( 1979) Statistical models and Mtissbauer spearoscopy of slags. Ph.D. dissertation, Carnegie-Mellon University, Pittsburgh, PA. CARMICHAEL I. S. E. and GHIORSOM. S. ( 1986) Oxidation-reduction relations in basic magma: a case for homogeneous equilibria. Earth Planet. Sci. Let?. 78,200-210.

DINGWELLD. B. and VIRGO D. ( 1988) Viscosities of melts in the Na20-FeO-Fe203 -Si02 system and factors controlling relative viscosities of fully polymerized melts. Geochim. Cosmochim. Acra 52,395-403.

DINGWELLD. B., BREARLEYM. and DICKINSONJ. E. ( 1988) Melt densities in the Na#-FeG-Fe203-Si02 system and the partial molar volume of tetrahedrallycoordinated ferric iron in silicate melts. Geochim. Cosmochim. Acta 52,2467-2475. DYAR M. D. ( 1985) A review of M&sbauer data on inorganic glasses: the effects of composition on iron valency and coordination. Amer. Mineral. 70, 304-3 17.

DYAR M. D. and BIRNIED. P. ( 1984) Quench media effects on iron partitioning and ordering in a lunar glass. J. Non-Cryst. Solids 67, 397-412.

DYAR M. D., NANEY M. T. and SWANSONS. E. ( 1987) Effects of quench methods on Fe3+/Fe2+ ratios: A Mossbauer and wetchemical study. Amer. Mineral. 72, 792-800. GHIO~LSO M. S. and CARMICHAEL I. S. E. ( 1987) Modeling magmatic systems: petrologic applications. In Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melts. (eds. 1. S. E. CARMICHAELand H. P. EUGSTER); Reviews in Mineralogy, 17, pp. 467-499. Mineralogical Society of America. GHIORSO M. S., CARMICHAELI. S. E., RIVERS M. L. and SACK R. 0. ( 1983) The Gibbs Free Energy of mixing of natural silicate liquids; an expanded regular solution approximation for the calculation of magmatic intensive variables. Contrib. Mineral. Petrol. 84, 107-145.

GOL’DANSKIIV. 1. ( 1966) The Miissbauer Effect and its Applications to Chemistry. Van Nostrand, 119~. GOSSELINJ. P., SHIMONVU., GRODZINSL. and COOPERA. R. ( 1967) Mossbauer studies on iron in sodium trisilicate glasses. Phys. Chem. Glasses 8, 56-6 1. GRANT R. W., WIEDERSICHH., GELLERS., GONSERU. and ESPINOSAG. P. ( 1967) Magnetic properties of substituted Ca2Fe10,. J. Appl. Physics 38, 1455-1456.

GREENWOODN. N. and GIBE T. C. ( 197 1) Miissbauer Specrroscop_v. Chapman and Hall, 659~. HIRAOK., KOMATSUT. and SOGAN. ( 1980) Mossbauer studies on some &sses and crystals in the Na20-Fe203 -SiOr system. J. NonCryst. Solids 40, 3 15-323. IPTS ( 1969) The International Practical Temperature Scale of 1968. Meteorologia 5, 35-44.

LANGER. A. and CARMICHAELI. S. E. (1987) Densities of Na20KrO-CaO-MgO-FeO-Fe203 -Al203-TiOz-SiOr liquids new measurements and derived partial molar properties. Geochim. Cosmochim. Acta 51,293 l-2946. MARFUNINA. S. ( 1979) Spectroscopy, Luminescence and Radiation Centers in Minerals. Springer-Verlag, 352~. MO X., CARMICHAELI. S. E., RIVERSM. and STEBBINSJ. ( 1982) The partial molar volume of Fe203 in multicomponent silicate liquids and the pressure dependence of oxygen fugacity in magmas. Mineral. Mug. 45, 237-245. MYSEN B. O., CARMICHAEL1.S. E. and VIRGO D.

( 1985a) A comparison of iron redox ratios in silicate glasses determined by wetchemical and “Fe Mossbauer resonant absorption methods. Contrib. Mineral. Petrol. 90, 101-106. MYSEN B. O., VIRGO D., NEUMANNE. and SEIFERTF. ( 1985b) Redox equilibria and the structural states of ferric and ferrous iron in melts in the system CaO-MgO-A1203-Si02-Fe-O: relationships between redox equilibria, melt structure and liquidus phase equilibria. Amer. Mineral. 70, 3 17-33 1. NASHJ. C. ( 1979 ) Compact Numerical Methodsfor Computers: Linear Algebra and Function Minimisation. J. Wiley & Sons, 227~.

2204

R. A. Lange and I. S. E. Carmichael

POLLAKH., DE COSTERM. and AMELINCKX S. ( 1962) Mossbauer effect in amorphous substances. In M&sbauer E$YI (4s. D. M. J. COMP~ONand D. SCHOEN), p. 2 12. J. Wiley Br Sons, 314p. FUVERS M. L. and CARMICHAEL1. S. E. ( 1987 1 Ultrasonic studies of silicate melts. J. Geophys. Res. 92,9f247-9!270. ROBIER. A., HEMINGWAYB. S. and FISHERJ. R. ( 1978) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar ( lo5 pas&s) pressure and at h&her temperatures. U. S. Geol. SUIV.Bull. 1452. SAWATZKYG. A., VAN DER WOUDEF. and MORRISHA. H. ( 1969) Recoilles&action ratios for Fe” in octahedral and tetrahedral sites of a spinet and a garnet. Phys. Rev. 183.383-386. STEBBINS J. F., CARMICHAEL I. S. E. and MORETL. K. ( 1984) Heat

capacities and entropies of silicate liquids and &lasses. (.,‘ornrib Mineral. Petrol. 86, 13 I- 148. STEIND. J., SIEBBINSJ. F. and CARMICHAEL1.S. E. ( 1986) Density of molten sodium aluminosiJicates. J. Amer. &ram. Sot. 69,396399. ___. WUON A. D. ( 1960) The micro-determination of ferrous iron 111 silicate minerals bv a volumetric and a calorimetric method. An., aIyst 85, 823-827.. VAN LOEF J. J. ( 1966) The s-electron chaqe and spin density and miylnetic moment of iron at different subtattice sites in ferrite5 and garnets. Physica 32,2 102-2 114. VIRGO D., MYSEN B. O., DANCKWERTHP. and SEIFERTF. ( 1982 ) Speciation of Fe3’ in I-atm Na@-SiOZ-F&-O melts. Carne& Inst. Wash. Yb. 81,349-353.