American Mineralogist, Volume 73, pages1267-1274, 1988 Stoichiometry of the iron oxidation reaction in silicate melts V. C. Knnss. I.S.E. Clnvtcrurr, Department of Geology and Geophysics, University of California at Berkeley,Berkeley,California 94720, U.S.A. Ansrnlcr Experimentshave been performed that calibratethe stoichiometry and thermodynamics of the iron oxidation reaction in natural silicate melts. A series of experimentswas carried out on six melt compositions covering a far larger range of oxygen fugacities than had been examined previously. Oxygen fugacitiesbetweenair and 5.2 log,ounits below those defined by the nickel-nickel oxide assemblage were investigatedat 1360 "C and 1460 "C. Results of theseexperimentsconfirm that ln(X..ro,/Xo"o) is a linear function of ln/o, over this entire range, and that this linear behavior is independent of composition over the range considered.These results are inconsistent with an ideal mixing between FeO and FerO. components.They are, however, entirely consistent with ideal mixing betweenFeO and FeO,464r0003 (FeO.6FerOr) components. A second seriesof experiments was per- formed on a single mid-oceanridge basaltcomposition (JDFD2) in order to better constrain the temperature dependence of the iron oxidation reaction in this simplified two-compo- nent subsystem. This serieswas carried out at temperaturesbetween 1299 "C and 1636 'C in air, COr, and 0.2 log,ounits below the fayalite-magnetite-quartz buffer assemblage. Resultsof both series of experiments were combined with the Sacket al. (1980) and Kilinc et al. (1983) databases to estimate thermodynamic parametersfor the iron oxidatron re- action expressed in terms of FeO and FeO,464 components. These coefficientsoffer the most precise method available for estimation of iron oxidation state in natural silicate melts as a function of ln /o, temperature,and composition. Our results support the con- clusion (Christie et at., 1986) that mid-ocean ridge basalts (MORBs) equilibrate as much as 3 log,ounits below that defined by the nickel-nickel oxide assemblage. INrnooucrroN Oy' : g-"rt. The equilibrium constant for Reaction I is Iron is unique among the major constituentsof natural defined by silicate melts in that it is present in significant portions in more than one oxidation state. The partitioning of iron x, = WL Q) between ferric and ferrous species caniubstantially influ- --r [af.:8]'[frj]' ence differentiation trends in crystallizing silicate mag- mas. Further, because the ferric and ferrous cations play where a denotes the activity and/denotes the fugacity of different structural roles in the melt, ferric-ferrous equi- the subscripted species in the superscripted phase. Adopt- librium may also have significant effect on silicate-melt ing a standard state consistingof the pure component at propertiessuch asdensity (Henderson et al., I 96 I ; Drick- P and T makesthe equilibrium constantK' a function of amer et al., 1969;Mo et al., 1982; Bottinga et al., 1982, pressure and temperature alone. If the ferric and ferrous 1983; Lange and Carmichael, 1987) and viscosity (Den- components mix ideally, then a plot of ln(Xr"ror/X1.o) sem and Turner, 1938; Cukierman and Uhlmann, 1974; (where ln refers to the natural logarithm and X, denotes Mysen et al., 1985b). Thus, the distribution of iron be- the mole fraction of the subscriptedspecies I in the melt tweenferric and ferrousspecies providesa means by which phase) againstln /o, should be linear, with a slope of one variations in the chemical potential of oxygen, a quite half. Deviations from such simple behavior will reflect mobile species, can profoundly influence the structure, nonideal mixing in ferric and/or ferrous components. rheology, and chemical composition of an evolving mag- The responseof the ferric/ferrous ratio of a silicate- ma. melt phase to variations in temperature,oxygenfugacity, The iron oxidation reaction in silicate melts is com- and composition has been investigatedby severalwork- monly expressed in terms of the reaction ers. Kennedy (1948) measured ferric and ferrous contents 2Feomdl+ yzoy": FezoT"',, (l) :^T_^t:l_,*"n Mountains basalt equilibrated in air at \r/ temperatures between 800 'C and 1400 "C. Johnston which is the sum of the homogeneous equilibrium 2FeO-.r, (1964, 1965) canied out similar experiments on simple + t/2}yeh : FerOf." and the heterogeneous equilibrium NarO'2SiO, glasses with less than 2 wto/o iron. Johnston 0003-004x/88 / rrr2-r267s02.00 1267
Transcript
American Mineralogist, Volume 73, pages 1267-1274, 1988
Stoichiometry of the iron oxidation reaction in silicate melts
V. C. Knnss. I.S.E. Clnvtcrurr,Department of Geology and Geophysics, University of California at Berkeley, Berkeley, California 94720, U.S.A.
Ansrnlcr
Experiments have been performed that calibrate the stoichiometry and thermodynamicsof the iron oxidation reaction in natural silicate melts. A series of experiments was carriedout on six melt compositions covering a far larger range of oxygen fugacities than hadbeen examined previously. Oxygen fugacities between air and 5.2 log,o units below thosedefined by the nickel-nickel oxide assemblage were investigated at 1360 "C and 1460 "C.Results of these experiments confirm that ln(X..ro,/Xo"o) is a linear function of ln/o, overthis entire range, and that this linear behavior is independent of composition over therange considered. These results are inconsistent with an ideal mixing between FeO andFerO. components. They are, however, entirely consistent with ideal mixing between FeOand FeO,464r0003 (FeO.6FerOr) components. A second series of experiments was per-
formed on a single mid-ocean ridge basalt composition (JDFD2) in order to better constrainthe temperature dependence of the iron oxidation reaction in this simplified two-compo-nent subsystem. This series was carried out at temperatures between 1299 "C and 1636'C in air, COr, and 0.2 log,o units below the fayalite-magnetite-quartz buffer assemblage.Results of both series of experiments were combined with the Sack et al. (1980) and Kilincet al. (1983) databases to estimate thermodynamic parameters for the iron oxidatron re-action expressed in terms of FeO and FeO,464 components. These coefficients offer themost precise method available for estimation of iron oxidation state in natural silicatemelts as a function of ln /o, temperature, and composition. Our results support the con-clusion (Christie et at., 1986) that mid-ocean ridge basalts (MORBs) equilibrate as muchas 3 log,o units below that defined by the nickel-nickel oxide assemblage.
INrnooucrroN Oy' : g-"rt. The equilibrium constant for Reaction I is
Iron is unique among the major constituents of natural defined by
silicate melts in that it is present in significant portionsin more than one oxidation state. The partitioning of iron x, = WL Q)between ferric and ferrous species caniubstantially influ-
--r [af.:8]'[frj]'
ence differentiation trends in crystallizing silicate mag-mas. Further, because the ferric and ferrous cations play where a denotes the activity and/denotes the fugacity ofdifferent structural roles in the melt, ferric-ferrous equi- the subscripted species in the superscripted phase. Adopt-librium may also have significant effect on silicate-melt ing a standard state consisting of the pure component atproperties such as density (Henderson et al., I 96 I ; Drick- P and T makes the equilibrium constant K' a function ofamer et al., 1969; Mo et al., 1982; Bottinga et al., 1982, pressure and temperature alone. If the ferric and ferrous1983; Lange and Carmichael, 1987) and viscosity (Den- components mix ideally, then a plot of ln(Xr"ror/X1.o)sem and Turner, 1938; Cukierman and Uhlmann, 1974; (where ln refers to the natural logarithm and X, denotesMysen et al., 1985b). Thus, the distribution of iron be- the mole fraction of the subscripted species I in the melttween ferric and ferrous species provides a means by which phase) against ln /o, should be linear, with a slope of onevariations in the chemical potential of oxygen, a quite half. Deviations from such simple behavior will reflectmobile species, can profoundly influence the structure, nonideal mixing in ferric and/or ferrous components.rheology, and chemical composition of an evolving mag- The response of the ferric/ferrous ratio of a silicate-ma. melt phase to variations in temperature, oxygen fugacity,
The iron oxidation reaction in silicate melts is com- and composition has been investigated by several work-monly expressed in terms of the reaction ers. Kennedy (1948) measured ferric and ferrous contents
2Feomdl + yzoy": FezoT"',, (l) :^T_^t:l_,*"n Mountains basalt equilibrated in air at
\r/ temperatures between 800 'C and 1400 "C. Johnstonwhich is the sum of the homogeneous equilibrium 2FeO-.r, (1964, 1965) canied out similar experiments on simple+ t/2}yeh : FerOf." and the heterogeneous equilibrium NarO'2SiO, glasses with less than 2 wto/o iron. Johnston
0003-004x/88 / rrr2-r267s02.00 1267
1268
(1964,1965) found that a plot of ln(Xu.,o,/X?r.) againstln /o, is linear with a slope of one half, consistent withthe ideal-mixing model postulated above.
Densem and Turner (1938) demonstrated that com-position plays a major role in determining ferric-ferrousequilibrium in silicate liquids. Paul and Douglas (1965)and Douglas et al. (1965) explored the effect of compo-sition on ferric-ferrous equilibrium in binary alkali-sili-cate glasses with less than 0.5 wto/o iron. They found thatincreased alkalis drove Equilibrium I to the right andthat the magnitude of this effect increased in the series Li< Na < K. Fudali (1965) examined the response of fer-riclferrous ratio to oxygen fugacity for a variety ofbasal-tic and andesitic rocks and confirmed that alkalis tend toincrease the ferric iron content of the melt. Fudali (1965)noted that the slope of ln(Xo.o, ,/Xr.") vs. ln rf, variesbetween 0.21 and 0.16 rather than the constant value of0.25 expected if mixing were ideal. Carmichael and Nich-olls (1967) observed that the oxidizing effect ofalkalis isevident in a wide variety of natural samples. Thornber etal. (1980) doped a tholeiitic basalt with varying amountsof oxide components in air in order to examine this effectdirectly. They confirmed that addition of NarO, KrO, andCaO increases the ferric/ferrous ratio of the melt sub-stantially. Thornber et al. (1980) also noted that increasesin Al,O. and SiO, decrease this ratio slightly.
Numerous models have been advanced that qualita-tively and quantitatively describe redox equilibria inquenched simple silicate melts (Toop and Samis, 1962a,1962b; Douglas et al., 1965; Masson, 1965, 1968, 1972Masson et al., 1970; Gaskell, 19771,Lauer, 1977;I-auerand Morris, 1977; Schreibner, 1986). Geologic applica-tions of these models have been discussed by Hess (1980).The first comprehensive calibration of iron redox state incomplex natural liquids as a function of oxygen fugacity,temperature, and bulk composition was given by Sack etal. (1980). Sack et al. (1980) performed alarge numberof Pt-loop experiments, primarily at oxygen fugacitiesclose to those defined by the fayalite-magnetite-quartz(FMQ) assemblage. These experiments were combinedwith the superliquidus ferric-ferrous equilibrium experi-ments of Kennedy (1948), Shibata (1967), and Thornberet al. (1980) in order to quantitatively establish the de-pendence offerric/ferrous ratio on oxygen fugacity, tem-perature, and the bulk composition of the melt. Regres-sion of these data suggested that a model in whichln(Xr,ror/ Xr.) is constrained to be linear in ln /o. resultsin a poor fit to the experimental data. Sack et al. (1980)found that a far better fit to observations could be ob-tained using a simple empirical expression of the form
[r",o _ I btn l# l :ah Io ,+ i+ c+ >d ,x , , (3 )L x i ? " 1
' t ;
where a, b, c, and d, are regression coefrcients and thesum is over the oxide components i. Kilinc et al. (1983)refined the compositional parameters d, by supplement-ing the data of Sack et al. (1980) with 46 additional ex-
KRESS AND CARMICHAEL: Fe OXIDATION IN SILICATE MELTS
periments, in air, on compositions ranging from nephe-linite to rhyolite.
Mysen (1987) recently proposed a far more complicat-ed model for estimation of ferric-ferrous equilibrium insilicate melts. This model differs from that proposed bySack et al. (1980) in that it is based on a regression ofinferred structural constituents in the melt. The data setemployed in the regression of Mysen (1987) also includesa large portion (>500/o) of simple three- and four-com-ponent compositions. With such an extreme range ofcompositions considered, it is not suprising that Mysen(1987) found that values for his regression coefficientswere quite dependent on variations in the input data set.
It has been suggested (Mysen et al., 1984; Mysen et al.,1985a; Virgo and Mysen, 1985), on the basis of Mdss-bauer data, that the ferric ion undergoes a coordinationchange from fourfold to sixfold as Fe3*/(Fe2* * Fe3*) isdecreased below one half. Because fourfold and sixfoldferric iron are expected to play diferent structural rolesin the melt, a progressive ferric coordination shift willalmost certainly be accompanied by a change in thechemical potential of the ferric component and its deriv-atives. Such a coordination shift would, therefore, be like-ly to be expressed macroscopically in a change in theslope of ln(Xo. ror/ Xr.o1 against ln /o,' Existence of such aslope break would suggest that it is incorrect to apply theregression ofKilinc et al. (1983) at oxygen fugacities be-low FMQ.
Recent high-precision determinations of the ferric-fer-rous distribution in mid-ocean ridge basalt (MORB)glasses (Christie et al., 1986) suggest that submarine ba-salts equilibrate under far more reducing conditions thanhad been previously believed. Using Reaction 3 with theregression coefficients of Kilinc et al. (1983), Christie etal. (1986) estimated quench oxygen fugacities up to 3log,o units below the nickel-nickel oxide (NNO) oxygenbuffer. These results suggest that MORBs are among themost reduced lavas on Earth. The most reduced experi-ments in the regression of Kilinc et al. (1983) were equil-ibrated at oxygen fugacities close to the fayalite-magne-tite-quarrz (FMQ) buffer (0.7 log,o units below NNO).The conclusions of Christie et al. (1986) are, therefore,based on an extrapolation of the regression of Kilinc etal. (1983) outside the range of experimental calibration.
In order to resolve these issues and to better define thestoichiometry of the iron oxidation reaction in silicatemelts, we have performed ferric-ferrous equilibrium ex-periments on a limited number of compositions spanninga much larger and more complete range of temperatureand fo, than had been examined previously.
ExpnnrurNTAL TECHNIeUE
Starting materials consisted ofground rock powders that werefirst fused at 1400'C in air, then broken into 1-g fragments.These fragments were welded onto 4-mm loops of 0.117-mmPte' Rhro wire with an oxyacetylene torch. In each experiment,l0 loops, comprising 5 duplicate pairs, were suspended in the
hot spot ofa vertical quench furnace. Oxygen fugacity was im-posed by a furnace atmosphere consisting of a CO-CO, gas mix-ture (Deines et a1., 1974). Gas-mixing ratios were controlled bycalibrated floating-ball flow meters. Temperatures were mea-sured by a Ptroo /Re' Rhro thermocouple placed roughly 3 mmabove the experiment cage. The thermocouple was isolated fromthe reducing furnace atmosphere by an alumina cement cap.Measurements of the melting point of 99.99o/o Au, both beforeand after the experiments, indicated temperatures of 1063.8 'C
and 1063.1 "C, respectively. These values compare favorablywith the accepted Au melting point of 1064.43 "C (IPTS, 1969).A 2'correction was added to adjust for measured temperaturegradients inside the furnace.
Oxygen fugacities imposed by furnace gas mixtures were cal-ibrated by measuring the temperature of iron-wiistite (Myers andEugster, I 983), nickel-nickel oxide (Chou, 1 978), and magnetite-hematite (Myers and Eugster, 1983) assemblages at the CO-CO,flow-rate combinations used in the experiments. These calibra-tion experiments indicated oxygen fugacities that were 0.01 to0.4 log,o units higher than those predicted by the Deines et al.(1974) calibration. Huebner (1975) noted a similar discrepancybetween observed and predicted oxygen fugacities in CO-CO,gas mixtures. His results differ somewhat from ours, however,in that the discrepancy observed by Huebner (1975) is largelyindependent of mixing ratio, whereas we found that the differ-ence between observed and predicted values was strongly cor-related with the propc.rtion of COr in the gas. Our results suggestthat the difference between the observed and predicted oxygenfugacities can be attributed to contamination of the CO, gas usedin our experiments. This conclusion was confirmed by duplicatecalibration experiments using 99.8 molo/o pure, bone-dry-gradeCO, gas instead of the commercial-grade CO, gas used in theferric-ferrous equilibration experiments. The calibration exper-iments performed with the higher-purity gas indicated less than0.1 log,o units discrepancy between -fo, values predicted fromDeines et al. (19'14) and those indicated by the magnetite-he-matite buffer curves ofMyers and Eugster (1983) or Chou (1978).On the basis ofthese results, calibration corrections were appliedto the individual experiments based on CO-CO, mixing ratio.Corrections ranged from +0.09 to *0.4 log,o units.
Duplicate runs of between 2 and I 2 h duration indicated thatexperiments of longer than about 5 h showed continued alkaliloss without significant change in the ferric/ferrous ratio. Shorterruns showed appreciable scatter in observed ferric/ferrous ratio.These results are consistent with those ofThornber et al. (1980)
and Kilinc et al. (1983). Experiment durations between 5 and 8h were considered an optimal compromise. Experiments werequenched by dropping into cold distilled H'O that had beenpreviously boiled. Though complete equilibration requires 5 to8 h, experiments indicate that the ferric/ferrous ratio can besubstantially altered in as little as 30 s. For this reason, ourapparatus was designed so that the quench could be carried outunder the reducing-furnace atmosphere. Experiments were per-formed at 1360 "C and 1460'C at oxygen fugacities between airand 5.21og,0 units below NNO at I to 3 logro unit invervals. Forthe experiments that were performed at higher oxygen fugacities,no efort was made to presaturate the loops in iron. Iron loss inthese runs was often found to be quite significant (20-30olo oftheamount present). Electron-microprobe traverses of quench glassbeads from these experiments revealed no detectable gradient intotal iron concentration. On the basis of this evidence, we as-sume that equilibrium saturation was closely approached duringthese experiments. For experiments at very low/o, and in com-positions with low initial total iron content, loops were used that
r269
had been previously saturated in an iron-rich melt and cleanedin 500/o HF solution.
All experiments were examined under a polarizing microscope
to verify the absence of a crystalline phase. Run products were
analyzed for major and minor elements on an eight-channelARL-sEMe electron microprobe using an accelerating potential of
15 kV, a sample current of 0.03 pA on brass, a spot size of
roughly 5 pm, and a l0-s integration time. Analyses made while
scanning the beam across the sample or using a defocused beamyielded no detectable difference in alkali content, but noticeably
decreased the analytical precision. For this reason, neither of
these techniques was employed. Data reduction was carried out
with the empirical correction scheme of Bence and Albee (1968)
using basaltic glass (USNM 113498) (Si, Al, Ti' Fe, and Mg)'
labradorite (Na and Ca), orthoclase (K), chlor-apatite (P)'
chromite (Cr), and V'O, (V) as standards. For each glass sample,
22-24 points were analyzed. The means of analyses for each
experiment are listed in Table l. Standard deviations of major-
element analyses are between 0.8 and 8.00/o relative. Ferrous iron
contents were determined using wet-chemical techniques. Ferriciron is calculated from the difference between total iron and ironin the ferrous state [FerOr: 1.1113(FeO* - FeO) where FeO*
is total iron as FeOl.Two series of experiments were performed. In the first series,
four compositions were equilibrated at 1360 "C and 1460'C at
I to 3 log,o unit intervals between air and 5.2 log units belowNNO. These experiments allow us to establish the response of
iron oxidation state to variations in oxygen fugacity, with tem-perature and all components except FeO and FerO. held con-
stant. In the second series, a single composition (JDFD2) was
equilibrated at roughly 50 "C intervals between 1299'C and1636'C at approximately 0.2 log,o units below FMQ (Table 1;
samples 103 and Blll-B120) in order to determine the tem-perature dependence ofthe iron oxidation reaction at nearly con-stant ferric/ferrous ratio.
Rpsurrs AND DISCUSSIoN
Figures la to ld are plots of ln(Xr.ror/X!"o) against In
/o, at approximately I 360 .C for four of the compositions
studied. The short lines at the upper right side of these
plots have a slope of 0.5 and are provided in order to
illustrate the slope expected if FeO-FerO. mixing were
ideal. The observed slopes are closer to 0.3 and are clearly
inconsistent with ideal mixing of these components. Sim-
ilar results were obtained in a series of experiments per-
formed on these same compositions at 1460 'C. It is, in
fact, quite remarkable that both the slope and curvature
of the plot of ln(Xr"ror/ )fo.o) vs. ln /o, seem to be largely
independent ofcomposition over the range considered.
Our data are consistent with earlier results (Sack et al.,
1980) that suggest that ln(X."ro r/Xr.o), rather than ln(Xr.ro'/
)fi"o), is linear in ln/or. Regressions in which the depen-
dent variable isln(Xr"ror/ Xzo.o show pronounced U-shaped
structure in a plot of residuals against predicted values.
Similar plots for regressions in which ln(X."rorlX."o) is
the dependent variable show no such structure. Linear
best-fiilines forln(Xr,ror/Xr"o) vs. ln/o, plots for the com-
positions considered have an average slope of0.2071 +
0.0012 (2o), which is somewhat lower than the value
0.2185 + 0.0044 obtained by Kilinc et al. (1983). The
slopes suggested by the plots of 780-U-105 composition
KRESS AND CARMICHAEL: FC OXIDATION IN SILICATE MELTS
1270 KRESS AND CARMICHAEL: Fe OXIDATION IN SILICATE MELTS
Teale 1. Compositions (in wt%) and conditions for individual experiments
7-l 74 79 83 86 89 91 100 101 102 103
Composition JDFD2 780-U-105 JDFD2rfc) 1461 1461 1459l og lo fo" -7 .17 -7 :7 -8 .21
. Totals for 780-U-1 05 and 20424 do not reflect contributions of SrO, BaO, and other minor elements that are significant in these compositions
are slightly higher than those suggested by the other com-positions, but this difference is within the analytical un-certainty.
The fact that the behavior observed in Figures la-ldis largely independent of bulk melt composition suggeststhat this effect must reside primarily in interactions be-tween the ferric and ferrous cations. This is consistentwith a suggestion made by Virgo and Mysen (1985) thatclusters with FerOo stoichiometry may be present in themelt at intermediate oxygen fugacities. An ideal-mixingmodel involving partial or complete association of ferricand ferrous components to a Fe,Oo cluster produc€s curves
TABLE 2, Coefficients for estimation of redox equilibria
CoefficientStandard
error
with the sort of overall slope observed in the experi-ments, but the shapes ofthe curves so produced are sig-nificantly convex upward. This is not in accord with ob-servations.
There is no indication of a slope break in any of theplots in Figure l, suggesting that there is probably no
-20 -15 -10 -5 0 -20 -15 -10 -5 0In(fe.)
Fig. l. Plot of ln(Xo.ror/)?r.") against ln/", for four composi-tions at 1360 "C. Error bars represent estimated 2o analyticalerror. Where error bars not present, error is smaller than datamarker. The curves in these plots are predicted using the modelin Table 2. The short lines at the upper right ofthe figures rep-resent the slope expected ifFeO-FerO, rnixing were ideal.
o
o -.8 "- ,x
8 ox
AHASL,Wauo.AW..oA W"."oAW*.oRStandard error
-95.93-46.05
49.04-48.87
- 106.04-110 .46
0.950.30
6.393.55
15.536.71
20 6419.52
KJJ/KKJKJKJKJ
I vrio I'"14*r#l : 0.2s2 tn ro" - # - * - I )or,,
r272
abrupt change in melt properties over the range of oxygenfugacities examined. This does not rule out a possibleferric ion coordination change within this range. A grad-ual coordination shift, distributed over a somewhat largerrange ofFe3*/(Fe,* * Fe3") could conceivably contributeto the unusual behavior displayed in Figure l.
A far simpler explanation becomes evident if one con-siders ferric-ferrous clusters of more arbitrary stoichi-ometry. It was found that the data can be remarkablywell represented by a model based on simple mixing be-tween FeO and a completely associated FeO, .uo.ooo. (€rp-proximately FeO.6FerO.) component. In terms of thesecomponents, the iron oxidation reaction takes the form
FeO + 0.23202: FeO,ouo. (4)
Analyses are easily recast in terms of this unusual com-ponent by first converting to mole fraction using FeO,,(molecular weight 79.849) rather than FerO. to representthe ferric component. Xr"o,ouo and Xo"o can then be esti-mated by the relations
KRESS AND CARMICHAEL: Fe OXIDATION IN SILICATE MELTS
Xr.o, ouo : 1 .077 6Xo"o, ,
Xr"o: Xo.o - 0.0776XF.ots.
A complete symmetric Margules formulation for Re-action 4 takes the form
(5)(6)
I f ' ac ' . _*nJ^ i d t
all" a^s. I r'rn(K.): -; i +; - uJ,, ^cpodr
I- u4T'Feor464
w'''"o)X'' (7)
where Aflo, ASo, and ACroare the enthalpy, entropy, andheat-capacity change ofReaction l, respectively, R is theuniversal gas constant, Z is in kelvins and T, is the ref-erence temperature in kelvins. In this formulation, thedeviation from ideality resides in the Margules mixingterms (W,, where W,, : W,, arrd W,, : 0). Wr,o;*,ouofsset equal to zero. The distribution coefrcient (K".) is de-fined as
Koo=-w (S)lx9:ElV",l'"''
Estimates can be made of the magnitudes of Aflo andAC"o using data from Stebbins et al. (1984) and Chase etal. (1985). These estimates suggest that, between 1230"Cand 1630 "C, the change in lnKo due to the ACr, terms isprobably less than 5olo of the contribution due to the A11,term. This corresponds to a contribution due to AC"o ofless than 0.25 ln units, significantly beneath the data res-olution. By adopting a reference temperature of 1673 K,a point that is interior to the data, we can justifiably ne-glect the AC"o terms, considerably simplifying Equa-tion 7.
The solid curves in Fisures la to ld are calculated froma model of the form
' A t fr"l4*,"1: o.ztzrnf", - #L xir3" -l
A.s I+?- uzAwxt (9)
(where LW, = W,,r.o,ouo - W,'.o) with coefficients fromTable 2. These coefficients were estimated by stepwiselinear regression of experimental results from this study,along with the database of Kilinc et al. (1983) and Sacket al. (1980). The most highly reduced experiments (log,of,less than -9.5) were omitted from this regression to pre-vent these less-certain data from exerting undue influenceon the regression. Plots such as those in Figures la-ldverify that this regression reproduces even the more re-duced data well within their analytical uncertainty. Oneof the data points from the Kilinc et al. (1983) data seton the 20424 composition is a serious outlier in bothregressions and is clearly inconsistent with results fromthis study on the same composition under nearly identi-cal conditions. Omission of this point substantially im-proved the precision ofthe regression. Equation 9 repro-duces the experimental data with a standard error of 0.3ln units. The estimated value for LHo is comparable toexperimentally determined A11 values for the FMQ solidbuffer (-86 kJ.mol I at 1723 K, recast in terms of anequivalent number of exchanged oxygens, O'Neil, 1987)but somewhat more negative than that measured for NNO(-54 kJ.mol I at 1723 K, similarly recast, Holms et al.,l 986) .
The positive sign of the LW^,rorterm is consistent withthe interpretation that tetrahedrally coordinated trivalentiron and aluminum compete for charge-balancing alkalisin peraluminous melts (Dickenson and Hess, l98l), thusleading to a positive enthalpy of mixing between thesespecies. The negative signs of the AW terms for CaO,NarO, and KrO are also in accord with the interpretationthat these cations play a charge-balancing role in the melt.The relative magnitudes of the CaO, NarO, and KrO termsare in agreement with the results of past workers (Pauland Douglas, 1965; Douglas et al., 1965; Thornber et al.,1980;Sack et al., 1980; Kil inc et al., 1983).
It should be emphasized that the postulated FeO, ouocomponent may not represent a discrete species existingin the melt. Rather, this unusual stoichiometry likely re-flects the most probable of a distribution of configura-tions, almost cenainly involving other cations in the melt.Nevertheless, regressions of various subsets of the totaldatabase result in nearly identical estimates of the stoi-chiometry of this component, suggesting that this prop-erty must reflect some fundamental aspect of the struc-ture of natural silicate melts. Our macroscopic data donot resolve this issue, but do provide hints ofpotentiallyprofitable lines of future inquiry. For now, the primaryadvantage of the formulation represented by Reaction 4
is that it allows a simple ferric/fenous mixing model tobe applied to natural silicate compositions. By castingcompositions in terms of FeO and FeO,464 components,ferric-ferrous mixing terms are avoided, resulting in sim-pler and more mathematically stable thermodynamic for-mulations (Ghiorso, I 985).
As a direct comparison of the regression presented inthis study with the best previously available calibration(Kilinc et a1., 1983), we rearranged Equations 9 and 3 toback-calculate ln(FerO./FeO), ln /"r, and T for each ofthe experiments in the entire data set. The mean of theresiduals (observed - calculated) for the Kilinc et al.(1983) regression for ln(Fe,Or/FeO) is -0.020 ln unitswith a standard deviation of 0.301. Back-calculation ofln(FerO./FeO) using the data in Table 2 results in resid-uals with a mean of 0.004 and a standard deviation of0.291 ln units. It is encouraging that Equation 9 repro-duces ln(FerO./FeO) better than the regression of Kilincet al. (1983) despite the fact that it contains one fewer fitparameters and was regressed on a different dependentvariable. Application of the Kilinc et al. regression toback-calculatelnfo, results in a residual mean of 0.039ln units and a standard deviation of 0.599. Our resultslead to a residual mean and standard deviation of -0.015
and 0.597 ln units, respectively. The mean and standarddeviation of the residuals for back-calculation of ?" are-4.1 'C and 62.8 oC, respectively, for the Kilinc et al.(1983) regression and -0.06 "C and 69.1 oC, respectively,for the regression presented in this study.
The results presented in this study confirm that Equa-tion 9 remains valid to oxygen fugacities as low as thosedefined by the iron-wiistite assemblage. Application ofthe coefficients in Table 2 to the ferric-ferrous determi-nations of Christie et al. (1986) yields estimated valuesof ln /o, between 0.09 and 0.24 log,o units lower thanthose predicted using the coefficients of Kilinc et al. (1983).This difference is quite small and does not challenge thevalidity of the conclusions reached by Christie et al.( l e86) .
CoNcr-usroNs
We have demonstrated that the iron oxidation reactionin silicate melts is well represented by a formulation in-volving oxidation of FeO to a completely associatedFeO, ouo component. Thermodynamic parameters arepresented that describe the iron oxidation reaction interms of these components. This regression is valid tooxygen fugacities as low as those defined by the iron-wiistite assemblage. The model presented in this study isa thermodynamically based calibration of the iron oxi-dation reaction in basic silicate melts and represents themost precise relation between ferric/ferrous ratio, oxygenfugacity, temperature, and bulk composition available.
Acrlqowr,BocMENTS
This text has benefited from discussions with D. Snyder andcareful reviews by J. Nicholls and an anonymous reviewer. M.Ghiorso suggested a clever method for determining the stoichi-
t273
ometry of ideally mixing components and provided valuable ad-vice regarding numerical methods. This work was supported, inpart, by National Science Foundation grants EAR 85-008 I 3 andOCE 86-13262 and, in part, by the Department of Energy con-tract DEACO3-76SF00098.
Rnrrnpucns crrrl
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