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Geochemistry International, Vol. 36, No. 1, 1998, pp. 15-23. Translated from Geokhimiya, No. 1, 1998, pp. 18-27. Original Russian Text Copyright ¿ 1998 by Ariskin. English Translation Copyright ¿ 1998 by åÄàä çÛÍ / Interperiodica Publishing (Russia).

Calculation of Titanomagnetite Stability on the Liquidus of Basalts and Andesites with Special Reference to Tholeiitic Magma Differentiation
A. A. Ariskin
Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, ul. Kosygina 19, Moscow, 117975 Russia
Received November 12, 1996

Abstract--A detailed review of experimental data on magnetite-melt equilibria in systems ranging from basalts to dacites is presented. This information (99 experiments) was processed statistically to yield the following equation relating the crystallization temperature of magnetite to melt composition and oxygen fugacity: 10 / T = ( b 0 + b 1 X
4 SiO
2

+ b2 X

TiO

2

+ b3 X

FeO tot

) log f

O

2

+ c + d1 X

SiO

2

+ d2 X

TiO

2

+ d3 X

FeO tot

+ d4 X

P2 O

5

.

For 90% of the data, this equation reproduces experimental temperatures to a precision of +15œC; the average deviation of the calculated temperatures from experimental ones is 9.3œC. The crystallization temperature of magnetite shows a complex dependence on oxygen fugacity: for ferrobasaltic and andesitic melts with moderate contents of Fe (up to ~15 wt %) and TiO2 (up to ~2 wt %), there is a fairly steep slope of the magnetite liquidus ~ 20œC/ log f O2 , whereas, for high-Ti (4-5 wt % TiO2) and Fe-rich (17-18 wt %) basalts, liquidus temperatures are virtually independent of oxygen fugacity and are near 1100œC. The equation for the magnetite liquidus can be used as an empirical basis for improving computer models of magma crystallization involving the separation of magnetite-bearing mineral assemblages.

THE PROBLEM OF THOLEIITIC DIFFERENTIATION TREND Titanomagnetite is one of the principal mineral phases that crystallize in the final evolutionary stages of basaltic magmas. This is indicated by its confinement to the most fractionated rocks of large layered complexes [1, 2] and differentiated sills [3, 4] and by the fact that the assemblages always contain phenocrysts, which represent the most evolved andesitic-dacitic members of tholeiitic [5, 6] and calc-alkaline [6-9] volcanic series. These observations attest to the important role played by magnetite crystallization in the formation of the main types of major-element trends; however, the validity of this inference for tholeiitic series has become the subject of debate. The main distinguishing feature of the tholeiitic differentiation trend is a stepwise enrichment of residual melts in iron oxides during the early and middle stages of fractionation and a strong depletion during the final stages. At present, most petrologists agree that this accumulation of total FeOtot (FeO + 0.9Fe2O3) is the result of low-pressure fractionation of basaltic magma when the crystallizing assemblages Ol-Pl and Ol-Pl-Px + Mt1 are dominated by plagioclase [10, 11].
1

Controversial topics include the highest possible degree of Fe enrichment, the direction of the SiO2 trend (enrichment or depletion), and the relative contributions of silicate phases and magnetite to these majorelement signatures. Differences of Tholeiitic Trends for Intrusive and Volcanic Rocks Using data on the relative volumes and average compositions of cumulates of the Skaergaard intrusion, Wager and et al. [1, 2] calculated the compositions of residual melts approximating the compositional evolution of the primary tholeiitic magma during intrachamber differentiation. According to these data, while the massif solidification F ranges from 0 to 88%, the calculated compositional series demonstrates a monotonic increase in the sum of iron oxides (FeOtot) from 9.6 to 18.2 wt %. The final crystallization stages 88 < F < 98% are characterized by a small increase in FeOtot to 21.7% and SiO2 to 49.8% followed by a decrease in the concentration of iron oxides and formation of very unusual ferroandesitic compositions: at F = 99.3%, the contents of FeOtot and SiO2 in the model differentiates are 18.5 and 55.0%, respectively (Fig. 1). The trend thus calculated became for many years the standard for the evolution of tholeiitic magmas with the maximum enrichment in Fe (Fenner's trend), and
15

The following abbreviations are used: Ol = olivine; Pl = plagioclase; Px = pyroxene (Cpx = clinopyroxene; Aug = augite; Pig = pigeonite; Opx = orthopyroxene); Sp = spinellid; Mt = titanomagnetite; and Ilm = ilmenite.


16 FeO 25
W& B

ARISKIN Al2O3 20 15 KT -39 5 10 MgO

EG4507

20
M

15

10

10 ag 0 ne COMA H&S tit ec ry GMA sta KT-39 lli T za model tio n EG4507 48 53 58 63

5 43

68

73 SiO2

Fig. 1. Model trends of Skaergaard magma evolution. Mass-balance calculations involving compositions of cumulate rocks: W&B [1, 2]; H&S [18]. Computer modeling of all fractional crystallization of chilled margin gabbros EG4507 [1, 2] and KT-39 [22] was conducted with the COMAGMAT program [21] for WM buffer with a nominal crystallization step (F) of 1 mol %.

analogous mass-balance calculations were conducted for some other intrusions (e.g. [12]). Paradoxically, although strongly Fe-enriched compositions (up to 18- 19 wt % FeOtot [13]) have been encountered in basalts and natural quenched glasses, no volcanic equivalents of the calculated ferroandesites (as the end products of magma differentiation at Skaergaard) have been found. It might also be noted that the majority of tholeiitic volcanic series display a moderate enrichment in FeOtot in the field of basaltic compositions, usually up to 13- 15% while exhibiting no decrease in SiO2 concentration [5, 14]. Effect of Redox Conditions Osborn [15] was the first to provide a physicochemical explanation for these facts. From experiments with the MgO-FeO-Fe2O3-SiO2 system, he established that the different directions of the evolutionary trends for crystallizing melts are due to the different conditions of magnetite separation, which, in turn, are controlled by redox conditions. He found that upon closed-system crystallization (with the bulk composition and FeO/Fe2O3 ratio being constant) the separation of magnetite does not cause the melt to deplete in FeOtot, and that in a system open with respect to oxygen ( P O2 = const), the content of Fe oxides in the melt rapidly drops after the onset of magnetite crystallization. An analysis of these chemical features led Osborn to infer that intrachamber differentiation of tholeiitic magmas, in particular at Skaergaard, can occur in a closed system, and that the fractionation of primary magmas of

volcanic series takes place at a certain oxygen pressure [15]. This conclusion was supported by additional experiments with the CaO-MgO-FeO-Fe2O3-SiO2 system [16] and by experimental melting of natural basalts (e.g., [17]). A new surge of interest in this problem was triggered by the British petrologists Hunter and Sparks [18], who offered a number of arguments that challenged the assumed evolutionary trend of Skaergaard magma composition [1, 2]. In their opinion, the principal contradiction of Wager's approach lies in the fact that the trend of Fe superenrichment accompanied by a monotonic decrease in the SiO2 content (determined from mass-balance calculations) is inconsistent with the available estimates of the primary Skaergaard magma composition and experimental data on basaltic phase equilibria. This inconsistency applies both to Fe accumulation and to the trend of decreasing silica content, which is difficult (if not impossible) to correlate with the low SiO2 content (44-46%) in the crystallization products of the "gabbroic assemblage" Ol-Pl-Px + Mt [18]. Another discrepancy with experimental data is that the calculated point of inflection at which Fe enrichment is replaced by silica enrichment does not coincide with the onset of titanomagnetite crystallization, which is known to appear quite early in the cumulate sequence when model solutions are depleted in SiO2 and enriched in FeOtot [1, 2]. Thus, it was suggested that the differentiation of Skaergaard magma is in fact an example of the tholeiitic-magma evolutionary line ferrobasalt-andesibasalt- icelandite (ferroandesite)-dacite, which is common for volcanic series. During the early and middle stages, this process is characterized by the Ol-Pl + Px assemblage, with the result that the melt is monotonously enriched in FeOtot, while the silica content in the melt is roughly constant; the appearance of Mt in the final fractionation stages causes the melt to be strongly depleted in FeO tot with a concomitant enrichment in SiO2 [18]. This interpretation implies that the major difference of the real Skaergaard series of melts (inaccessible to determination by direct analytical methods) from the typical assemblages of tholeiitic volcanics [5] is an elevated, but not anomalous, enrichment in Fe oxides (apparently to 17-18 wt % FeOtot), which is related to a relative delay in magnetite crystallization due to the more reducible conditions in the magma chamber. It should be noted that the method of estimating the compositions of the differentiation products based on successive subtraction of specified amounts of the gabbroic constituent from the primary magma [18] has the same drawback as Wager's method [1, 2]: when using the compositions of real intrusive rocks in mass-balance calculations, no allowance is made for the possible presence of trapped melt in the cumulates and the potential existence of suspended crystalline phases in the magma. For this reason, both of the trends presented in Fig. 1 [2, 18] are rather imprecise. It was, therefore, very important that the new interpretation of
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Skaergaard data [18] was further developed through numerical modeling of fractional crystallization of Skaergaard magma [11, 19] with the TOLEMAG program [20]. Computer Simulation of Skaergaard Magma Crystallization The TOLEMAG program was a precursor to the COMAGMAT software [20, 21]. COMAGMAT makes it possible to simulate the evolution of the phases (including their compositions) during the fractionation of basaltic magmas under specified pressure and oxygen fugacity. Figure 1 shows the results of COMAGMAT modeling of the fractional crystallization for two samples of chilled margin gabbro from Skaergaard; these samples (EG4507 [1, 2] and KT-39 [22]) were previously examined as possible analogues of the primary Skaergaard magma. Calculations were performed for 1 atm and oxygen fugacity defined by the wüstite-magnetite (WM) buffer; the nominal crystallization step was 1 mol %, with the most fractionated melts corresponding to 90% crystallization. According to these calculations, both samples are anchicotectic (Ol + Pl) compositions with liquidus temperatures of ~1240œC (EG4507) and 1170œC (KT-39). They are characterized by the appearance of high-Ca clinopyroxene as a third crystallizing phase, and, within a fairly wide crystallization range of the Ol + Pl + Cpx assemblage, there is indeed a trend of decreasing SiO 2 content with an increase in FeO in the melt (Fig. 1). However, in both cases, while the Ol + Pl cotectic crystallizes and before Cpx appears, there is a monotonic increase in the SiO2 content in the model solutions; after titanomagnetite (enriched in the ulvospinel component) appears, this trend becomes irreversible. The simulated phase equilibria of Skaergaard magma indicate that the compositional evolution of magmatic melt in the course of intrachamber differentiation can be of a much more complex nature than can be inferred from mass-balance recalculations based on cumulate compositions (Fig. 1). It should be kept in mind that the interpretation of the phases present in natural melts makes great demands on the accuracy of the crystallization models used. In particular, the COMAGMAT program was shown to be quite good in predicting the evolution of basaltic magmas where silica crystallization is concerned, but rather inadequate in simulating the separation of Fe-rich spinel [23]. In this paper, we will analyze the conditions for titanomagnetite stability on the liquidus of andesitic-basaltic systems--an important step in constructing an adequate computer model for crystallization of magnetite-bearing mineral assemblages.
GEOCHEMISTRY INTERNATIONAL Vol. 36 No. 1

EXPERIMENTAL STUDIES OF MAGNETITE STABILITY IN ANDESITIC-BASALTIC SYSTEMS An attempt to revise traditional views on the evolutionary trend of Skaergaard magma could not but provoke a controversy among petrologists who, to this day, have not resolved the contradictions between geological arguments put forward by opponents of the new interpretation [24] and the data on phase equilibria on which Hunter and Sparks [18, 25] based their work. It is clear that the key to this problem is estimating the conditions under which magnetite crystallized from ferrobasaltic melts and assessing the effect of the separation of magnetite-bearing mineral assemblages on the evolution of residual liquids. During the last 15 years, a considerable amount of experimental petrological data on these equilibria has become available. Using the INFOREX database [26, 27]2, we searched for melting experiments conducted on samples of terrestrial igneous rocks and synthetic basaltic mixtures in which the quenched products include Feand Ti-rich spinel. The query was formulated as follows: among experiments conducted at atmospheric pressure in the absence of volatile components, we needed to find runs with available data on the compositions of melts in equilibrium with titanomagnetite3. We retrieved 213 experiments from 22 studies (about half of the runs involved samples of alkaline basalts and nephelinites). For further analysis, this data set was narrowed to include only experiments in systems of low and moderate alkalinity by placing additional constraints on the compositions of quenched glasses (Na2O + K2O < 7 wt %) and the duration of melting (at least 48 h). The INFOREX database was found to contain 99 experiments that satisfy these criteria and represent 13 independent studies. Most of these experiments portrayed systems of ferrobasaltic and ferroandesitic-basaltic composition (10-18 wt % FeO, Fig. 2a), with the TiO2 content in residual melts varying from 1 to 5 wt %. All runs were performed in platinum capsules that controlled f O2 at 10-6 to 10-13 bars, near values defined by the IW- NNO+2 buffer (Fig. 3). The crystallization temperatures of titanomagnetite range from 1040 to 1160œC (Figs. 2b, 3). The phase assemblages obtained in these experiments usually include four or five minerals plus a quenched glass, and, with a few exceptions, the fourth or fifth phase to crystallize was magnetite. Plagioclase is present on the liquidus of all 99 compositions; femic phases consist of Ol, Aug, Pig, and Opx in various combinations. In 49 runs, ilmenite was found to be present; this
2

The most recent version of INFOREX (4.0, 1997) includes information from 235 works, in which the experimental conditions of 8660 runs and more than 11 370 glass compositions are reported. 3 When the spinel composition was present, we selected phases with a total content of Fe and Ti oxides of more than 85% and Cr2O3 concentration of less than 5%. When these data were not reported, spinel was classified as titanomagnetite based on descriptions provided by the authors. 1998


18 FeO 25 20 15 10 5 43

ARISKIN

Brief Review of Special Studies Snyder et al. (1993) presented the results of 53 experiments on ferrobasalt samples that are regarded, based on composition, as equivalents of the fractionation products of primary magmas for one of the layered complexes of Labrador and Skaergaard (Greenland) [28] (Table 1). With the exception of three cases, these runs were conducted at temperatures of 1060 to 1190 œC and at oxygen fugacities -12.9 < log f O2 < -8.5. The quench products of 18 experiments were found to contain magnetite; for 15 of these runs, the compositions of coexisting glasses were determined (see solid circles in Figs. 2 and 3). Note that all magnetite-bearing assemblages (Ol + Pl + Mt + Px + Ilm) were obtained in experiments more than 100 hours in duration, suggesting that the conditions were close to equilibrium. The results indicate that the crystallization temperatures of titanomagnetite are no higher than 1130œC and, with f O2 near the QFM buffer, strongly depend on the redox conditions (in Fig. 3, this range lies approximately midway between the IW and NNO lines). The separation of Mt causes the melts to be strongly depleted in FeO and enriched in SiO2 (Fig. 2). Nielsen et al. (1994) reported data from 16 experiments on 7 samples of basalts and andesites (the compositions of some of them are presented in Table 1). These runs were designed to study magnetite stability slightly above and below the NNO buffer; thus, Mt is present on the liquidus of all 16 compositions [29]. The experiments were conducted at temperatures of 1080 to 1129œC and at oxygen fugacities -9.3 < log f O2 < -7.6; run durations were at least 72 h. The data in Figs. 2 and 3 (solid squares) confirm that the crystallization temperature of Mt is a function of oxygen fugacity; both basaltic and andesitic melts display a depletion in FeO and enrichment in SiO2. Thy and Lofgren (1994) investigated the effect of melt composition on the crystallization temperature of magnetite along the QFM buffer (diamonds in Fig. 3). The starting materials in these runs were four samples of moderately alkaline ferrobasalts containing 13.5- 15.2 wt % FeO and 3.9-6.1 wt % Na2O + K2O (Table 1) [30]. For 15 out of the 46 runs, the end products contained magnetite (duration > 95 h). The crystallization temperatures of Mt in these experiments varied from 1051 to 1098œC, and there was a very distinct trend for the melts to be depleted in FeO and enriched in SiO 2 (Fig. 2). An important conclusion that can be drawn from this study is that, irrespective of the initial composition, the temperatures at which Mt begins to appear in the crystallization sequence are 1105 + 5œC--a fact that could greatly simplify the development of computer models involving the magnetite phase [30]. Toplis et al. (1994) reported the results of 34 isothermic experiments at T = 1072œC involving a sample of synthetic ferrobasalt (Table 1, column 11) with varying
Vol. 36 No. 1 1998

48

53

58

63

68

73 SiO2

Temperature, œC 1175
Snyder et al., 1993 Nielsen et al., 1994 Thy & Lofgren, 1994 Toplis et al., 1994 Toplis & Carroll, 1995 Others

1125

1075

1025 43

48

53

58

63

68

73 SiO2

Fig. 2. Characteristics of the experimental data set of glasses corresponding to magnetite-melt equilibrium.

Temperature, œC 1200 Snyder et

1150

al., 1993 Nielsen et al., 1994 Thy & Lofgren, 1994 Toplis et al., 1994 Toplis & Carroll, 1995 Others

1100

1050 -14 -12 -10 -8 log f -6
O2

Fig. 3. Temperature of magnetite-melt equilibrium vs. oxygen fugacity for the experimental data set of 99 glasses (see Fig. 2).

phase appears in experiments conducted under reducing conditions ( f O2 < 10-10). The most representative studies include five papers [28-32], which are worth discussing in greater detail.

IW

WM

NN O

GEOCHEMISTRY INTERNATIONAL


CALCULATION OF TITANOMAGNETITE STABILITY Table 1. Compositions of initial samples used in experimental studies of magnetite-melt equilibria Reference Sample SiO2 TiO2 Al2O3 FeO* MnO MgO CaO Na2O K2O P2O5 Snyder et al., 1993 4-3 48.63 2.33 14.57 14.71 0.21 6.29 9.27 3.05 0.72 0.23 4-83C 47.07 3.90 13.65 17.65 0.22 4.75 7.72 3.63 1.05 0.36 SK 50.28 2.56 13.69 13.28 0.26 6.58 10.22 2.62 0.51 0.00 Nielsen et al., 1994 T85-77 121492 45.87 4.14 15.16 12.54 0.18 5.16 11.04 3.53 1.87 0.50 50.64 2.96 15.05 14.23 0.23 4.57 8.46 2.39 0.95 0.52 V-31 63.83 0.74 15.09 8.31 0.20 0.36 4.27 4.13 2.87 0.19 9005 48.31 4.52 13.11 14.90 0.21 4.82 9.41 3.21 0.89 0.60 Thy, Logfren, 1994 7159V 48.37 4.01 13.80 14.26 0.19 3.31 9.04 4.87 1.28 0.88 8754 47.50 4.08 12.59 15.22 0.23 5.17 10.93 3.25 0.65 0.38 SAX2 46.18 3.80 15.23 13.59 0.23 5.47 10.43 3.29 1.06 0.72

19

Toplis et al., 1994-95 SC4 50.47 4.38 11.73 14.89 - 4.89 10.20 2.96 0.49 - SC1 48.75 2.90 14.89 13.09 - 6.49 10.89 2.70 0.30 - SC4a 49.45 4.37 11.68 16.45 - 4.67 9.85 3.05 0.50 -

Note: Compositions of samples are recalculated to 100 wt % dry substance; total Fe expressed as FeO.

amounts of P2O5. Although this study focused mainly on the effect of phosphorus on the phase equilibria of silicate phases, it includes the results from 15 experiments with magnetite as the liquidus phase (open diamonds in Figs. 2 and 3) [31]. These experiments were run for more than 149 hours, and the glass compositions encompassed a range from ferrobasalts to dacites. According to the experiments, magnetite crystallizes within the buffer range approximately from QFM-0.7 to QFM+1.9. Toplis and Carrol (1995) supplemented the results of the previous study with ten new experiments in the field of magnetite-melt equilibria. These runs were performed on samples of three synthetic ferrobasalts (Table 1, columns 11-13) at temperatures of 1057 to 1122œC and oxygen fugacities -11.2 < log f O2 < -8.1 [32]. Run durations were more than 115 hours: in Figs. 2 and 3, these data are represented by six-point stars. As in the experiments described above, the glass compositions show a systematic decrease in FeO content from basalts to dacites; in the field of andesitic- dacitic compositions, the crystallization temperatures of Mt were near 1070œC. Toplis and Carrol [32] presented the most complete analysis of phase relations and mineral-melt equilibria during the crystallization of tholeiitic magmas with the participation of magnetite and ilmenite. Here we focus on three results of that analysis. First, mass-balance calculations involving the compositions and proportions of the run products were used to establish that the percentage of titanomagnetite in assemblages that crystallize in systems open with respect to oxygen can reach as high as 15-22 wt %; this appears to be the principal factor that causes the residual melts to be enriched in SiO2 when magnetite-bearing assemblages separate. Second, within the buffer range from QFM-2 to QFM+1, the slope of the Mt liquidus temperature plotGEOCHEMISTRY INTERNATIONAL Vol. 36 No. 1

ted against f O2 is about 30œC/log f O2 . Third, a negative correlation between the inverse temperature and the content of Fe2O3 in the liquid was found to exist for magnetite-saturated melts (estimated from the equation of Kilinca et al. [33]), meaning that high temperatures of magnetite crystallization correspond to an elevated oxidation of Fe in magmatic melts. However, the authors [32] did not provide any consistent analysis of how the temperature of magnetite saturation depends on the melt composition and redox conditions. LIQUIDUS EQUATION FOR TITANOMAGNETITE: DEVELOPMENT AND ANALYSIS We set out to construct an internally consistent geothermometer with which the crystallization temperatures of titanomagnetite could be calculated within the widest possible range of melt compositions and oxygen fugacities. The aforementioned experimental data set of 99 compositions of glasses quenched at specified T and f O2 provides a good empirical basis for this. The experimental data were processed according to the following linear model: 10 / T = b log f
4 O
2

+c+



Xidi,

(1)

where T is the temperature (K); Xi denotes the mole fractions of the melt components; and b, c, and di are regression coefficients. In these calculations, we intentionally excluded Fe2O3 as an independent component and used only the total Fe concentrations (FeOtot). The intention was to minimize the errors in estimating the FeO/Fe2O3 ratio in melts; under the most reducing conditions, these relative errors may exceed 50% irrespective of the method adopted for the calculation [34]. Another motive was that the available equations for cal1998


20 Temperature, œC 1200 7.75 1150 1100 n=99 1050 1050

ARISKIN

7.50 104 / T( exp)

50% 40 30 20 10 0 - 60 - 20 20 60 í(exp)-í(calc )

1100

7.25 1150

geothermometer was the accuracy in solving the inverse problem, i.e., the statistical estimate of the extent to which the calculated temperatures deviate from experimental ones for the specified melt composition and oxygen fugacity. It was established that the strongest influence on magnetite stability is exerted by the following four components: SiO2, TiO2, FeOtot, and P2O5; the optimal equation that reproduces experimental temperature with an average accuracy of ~10œC has the form 10 / T = ( b 0 + b 1 X
4 SiO
2

+ b2 X
TiO
2

TiO

2

+ b3 X
FeO tot

FeO tot

) log f
P2 O
5

O

2

7.00

Snyder et al., 1993 Nielsen et al., 1994 Thy & Lofgren, 1994 Toplis et al., 1994 Toplis & Carroll, 1995 Others

+ c + d1 X

SiO

2

+ d2 X

+ d3 X

+ d4 X

. (2)

6.75 6.75

1200

7.00 104 T(calc)

7.25

7.50

7.75

Fig. 4. Comparison of experimental and calculated (by equation (2)) values of inverse temperature for the experimental data set of 99 glasses. The histogram portrays the distribution of deviations T(exp)-T(calc).

culating the ferric-ferrous ratio ignore the effect of phosphorus, which can be very significant, according to recent data [35]. Another fundamental distinction of this calibration consists in that we studied the possibility of varying the regression coefficient b of oxygen fugacity depending on the composition of the liquid phase. Borisov and Shapkin [36] were the first to notice the importance of this factor when dealing with elements of variable valence; as will be shown below, this approach enabled us to considerably increase our accuracy in calculating the liquidus temperature of magnetite. More than 30 variants of linear regression (1) involving varying sets and amounts of the melt components were analyzed. The criterion for finding the best
Table 2. Regression coefficients for equation (2) of magnetite liquidus Parameter b0 b1 b2 b3 c d1 d2 d3 d4 Coefficient - 0.6232 0.6826 4.0438 0.8251 0.0159 8.3626 35.9674 10.7347 12.4418 Standard deviation (1) 0.0205 0.0359 0.9327 0.2567 0.0686 0.2804 8.0819 2.1842 2.3521

The corresponding regression coefficients are presented in Table 2. Figure 4 compares the experimental and calculated values of the inverse temperature and a histogram of deviations = T(exp) - T(calc). In several cases, these deviations reach as high as 40-50œC, but, in general, about 90% of the data fall within the range +15œC; the absolute value of the average deviation is 9.3œC. Note that, in the studies [28-32], these deviations do not fall outside 30œC and, for the 25 experiments of longest duration [31, 32], = 3.6œC. The high reproducibility for the representative data set (n = 99) suggests that the form of the empirical relation obtained (2) reflects the real redox and structural-chemical equilibria in the liquid phase that involve the ions Fe3+ and Fe2+ and control stability on the titanomagnetite liquidus. The regression coefficients presented in Table 2 make it possible to specify the effect of each ith component selected. For this purpose, it is convenient to use partial derivatives of i (see equation (2)): i = ( 10 / T ) / X i = b i log f
4 O
2

+ di.

(3)

In the case of phosphorus, P2 O5 = d4 = 12.4418 > 0 (Table 2), i.e., an increase in the P2O5 concentration in the melt raises the inverse temperature or decreases the crystallization temperature of magnetite. This effect is by no means insignificant, because the addition of 1 mol % P2O5 can cause the crystallization temperature of magnetite to decrease by about 20œC. The causes of the destabilizing effect of P on magnetite stability have already been analyzed in the literature; the principal cause is the possibility of some of the ferric iron being bound to phosphate complexes [31] and the decrease in the overall ferric-ferrous ratio in the melts with increasing P2O5 [35] concentration. The increasing concentrations of SiO2 and FeOtot also have a destabilizing effect on magnetite: as can be inferred from Table 2 and equation (3), at log f O2 > -12, both derivatives of SiO2 and FeOtot are positive. With respect to SiO2, this result is quite natural, but it may appear somewhat surprising for FeOtot. It seems strange that the stability of the iron-ore phase is inversely proportional to the total content of Fe in the melt. Nevertheless,

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the low standard deviations for b3 and d3 (Table 2) indicate with certainty that this is a statistically based observation. An explanation for this fact should apparently be sought in structural-chemical and redox reactions involving Fe ions. For example, an analysis of experimental studies devoted to the dependence of the ferric-ferrous ratio on the composition of silica melts indicates that the percentage of ferric iron decreases with an increase in the total FeO concentration [36]. An analysis of equation (3) with parameters for TiO 2 shows that this component behaves ambivalently: at log f O2 > -9, the addition of Ti has a destabilizing effect and, under more reducing conditions, causes the crystallization temperature of titanomagnetite to increase, apparently owing to the enrichment of Ti-magnetite solution in the ulvospinel component. Calculation of Isopleths of Magnetite Stability in the T-log f O2 Coordinates Consider the dependence of the crystallization temperature of Mt on log f O2 . It follows from equation (2) that systems of different compositions will react differently to a change in redox conditions. The strongest dependence on log f O2 should be expected in ferrobasaltic compositions with low and moderate contents of TiO2 and FeO (approximately up to 2 and 15 wt %, respectively). For compositions enriched in TiO2 and FeO (such as Galapagos tholeiites [13]), this dependence may be fairly weak. This conclusion is illustrated by data shown in Fig. 5, in which the liquidus temperatures of titanomagnetite calculated for three model compositions (Table 3) are plotted against log f O2 . These compositions are approximate representations of low-Ti ferrobasalt (BAS-1), ferroandesite (AND), and high-Ti ferrobasalt (BAS-2). For each of these compositions, the liquidus temperatures were preliminarily estimated with the COMAGMAT [21]program; for basalts, these temperatures correspond to Ol-Pl cotectics (~1165 and ~1135œC); and for andesite, to a system slightly supersaturated in plagioclase with a liquidus temperature of about 1125œC (Table 3). Using equation (2) for the first two compositions BAS-1 and AND, we calculated the temperatures of magnetite stability above the silica liquidus. These data indicate that, for both melts, the slope of magnetite liquidus is about 20œC/log f O2 (Fig. 5). This value is about 1.5 times lower than that estimated in [32]; however, it should be borne in mind that, in contrast to the previous authors, our estimates were obtained for a constant composition of the melt. It is readily apparent that, according to calculations, the decrease in log f O2 from -6 to -7 in going from ferrobasalt BAS-1 to the ferroandesites is equivalent to a decrease of the magnetite liquidus by about 35œC (Fig. 5). Thus, our equation
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Temperature, œC 1200
-1

W M

1150

NN O

BAS

1100

1050 -12 - 10

fO2 og Ferrobasalt C /l œ esite 35 and rro Fe -2 Ferrobasalt BAS Compo- SiO TiO FeO* 2 2 sition BAS - 1 50.0 2.0 15.0 AND 60.0 0.5 10.0 BAS - 2 48.0 4.0 17.5

-8

-6

-4 log fO2

Fig. 5. Crystallization temperature of magnetite vs. oxygen fugacity according to equation (2) for two model compositions of ferrobasalts and ferroandesite (Table 3).

for magnetite stability realistically reproduces the pattern established with systems of variable compositions. In the case of high-Ti ferrobasalt BAS-2, the system is not saturated in titanomagnetite over a wide f O2 range because the calculated temperatures are near 1100œC, which is 25-30œC lower than the liquidus temperature of olivine and plagioclase. Apparently, when this type of crystallization takes place, the temperature at which Fe-spinellid begins to appear is buffered by the composition and will not deviate far from 1100œC if the melt is not substantially enriched in SiO2 or depleted in Ti.
Table 3. Compositions of model melts Sample SiO2 TiO2 Al2O3 FeO* MnO MgO CaO Na2O K2O P2O5 TPl, œC TOl, œC BAS-1 50.0 2.0 15.0 15.0 - 6.0 9.0 2.5 0.5 - 1164 1164 AND 60.0 0.5 16.0 10.0 - 3.0 5.5 3.5 1.5 - 1126 1094 BAS-2 48.0 4.0 13.5 17.5 - 5.0 9.0 2.5 0.5 - 1142 1133

Note: BAS-1 is low-Ti ferrobasalt; AND is ferroandesite; and BAS-2 is high-Ti ferrobasalt. Compositions of samples are recalculated to 100 wt % dry substance; total Fe expressed as FeO. The temperatures of Pl and Ol liquidus are calculated with the COMAGMAT model [21]. 1998


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CONCLUSIONS Statistical processing of data on magnetite-melt equilibria from 99 experiments in systems ranging from basalts to dacites was used to obtain an equation relating the crystallization temperature of magnetite to melt composition and oxygen fugacity. For 90% of the data, this equation (2) reproduces experimental temperatures to a precision of +15œC. SiO2, TiO2, FeOtot, and P2O5 are the components that have the strongest effect on the stability of magnetite. The crystallization temperature of Mt shows a complex dependence on oxygen fugacity: for ferrobasaltic and andesitic melts with a moderate Fe content (up to ~15 wt %) and TiO2 (up to ~2 wt %), there is a fairly steep slope of the magnetite liquidus ~20œC/log f O2 , whereas, for high-Ti (4-5 wt % TiO2) and Fe-rich (17- 18 wt %) basalts, these temperatures are virtually independent of oxygen fugacity and are near 1100œC. This equation for the magnetite liquidus can be used as an empirical basis for improving computer models of magma crystallization involving the separation of magnetite-bearing mineral assemblages. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, projects nos. 96-05-64231 and the 96-07-89054. REFERENCES
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