Journal of Petrology Advance Access originally published online on May 7, 2008
Journal of Petrology 2008 49(6):1161-1185; doi:10.1093/petrology/egn021
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The Titanomagnetite–Ilmenite Equilibrium: New Experimental Data and Thermo-oxybarometric Application to the Crystallization of Basic to Intermediate Rocks
Mineralogisches Institut, Ruprecht-Karls-Universität Heidelberg, INF 236, D-69120 Heidelberg, Germany
RECEIVED SEPTEMBER 10, 2007; ACCEPTED MARCH 27, 2008
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ABSTRACT |
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Although the titanomagnetite–ilmenite thermo-oxybarometer has been widely used to provide information on temperature and oxygen fugacity during magmatic and metamorphic processes, the available formulations yield unsatisfactory results; for example, at high temperature and low to moderate fO2 (i.e. in conditions relevant to crystallization in basic and intermediate rocks). We present a new version of this thermo-oxybarometer based on numerical fits of a large experimental dataset comprising new results in the Fe–Ti–Al–Mg–O system and those of literature studies. Our new subsolidus experimental results at temperatures in the range 1100–1300°C under low to moderate fO2 conditions show that the addition of Mg and/or Al in the concentration ranges that are usual in Fe–Ti oxides from basic magmatic rocks can be accommodated by simple projections. We have taken advantage of this fact and performed numerical fits to generate empirical formulations. With the resulting expressions we can retrieve temperature values from X'usp and X'ilm (projected mole fractions) of titanomagnetite–ilmenitess pairs and fO2 values from X'usp and T. The present thermo-oxybarometer model is designed for assemblages of titanomagnetite and hemoilmenite (with the
space group), with the usual low Al2O3, Cr2O3, MgO and MnO contents (less than about 6 wt %), which equilibrated at high temperatures (T 
800°C) and low to moderate oxygen fugacities (–4 < 
NNO < +2, where NNO is the nickel–nickel oxide buffer). Tests of our model by using the compositions of titanomagnetite–ilmenitess pairs in products of liquidus experiments conducted at known T–fO2 conditions (literature data and new results) show that the calculated values reproduce the experimental ones within ±70°C, and in most cases within ±50°C. The estimates of the oxygen fugacity are mostly within ±0·4 log units. This is a significant improvement compared with the previous models. KEY WORDS: Fe–Ti oxides; geothermometry; ilmenite; oxygen fugacity; titanomagnetite
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INTRODUCTION |
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The equilibrium between the iron–titanium oxide minerals titanomagnetite and ilmenite has been widely used to estimate both temperatures and oxygen fugacities in igneous and metamorphic rocks of the Earth, the Moon or other terrestrial planets. Buddington & Lindsley (1964
) introduced the titanomagnetite–ilmenite thermo-oxybarometer and provided the first calibration based on the experimental results of Lindsley (1962, 1963) in the Fe–Ti–O system. The thermometer is based on the temperature-dependent exchange of Fe2+ + Ti4+ for 2 Fe3+ between titanomagnetite (solid solution between the magnetite and the ulvöspinel endmembers) and ilmenite (solid solution between the hematite and the ilmenite endmembers) according to the reaction
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; Carmichael, 1967; Anderson, 1968; Lindsley & Spencer, 1982; Stormer, 1983). Numerous attempts were made to model the exchange and redox reactions that govern this thermo-oxybarometer (e.g. Rumble, 1970; Powell & Powell, 1977; Spencer & Lindsley, 1981; Andersen & Lindsley, 1988; Ghiorso & Sack, 1991a).
There are two current popular versions of the thermo-oxybarometer: one is included in the QUILF package (Frost & Lindsley, 1992; Lindsley & Frost, 1992; Andersen et al., 1993) and utilizes the solution models of Andersen & Lindsley (1988) and Andersen et al. (1991), and the other is the formulation of Ghiorso & Sack (1991a), which is based on the thermodynamic analysis of the same researchers and combines the solution models of Ghiorso (1990) and Sack & Ghiorso (1991a, 1991b). Lindsley & Frost (1992) have emphasized, however, that their formulation is not designed to be used for equilibria at oxygen fugacities higher than two log bar units above those of the fayalite–magnetite–quartz equilibrium (FMQ) (i.e. at FMQ > 2 or NNO > 1· 3). Unfortunately, the formulation of Ghiorso & Sack (1991a) also strongly overestimates both temperature and f O2 at such relatively high f O2 conditions. (Evans & Scaillet, 1997; Scaillet & Evans, 1999; see also Lattard et al., 2005, fig. 1). However, both formulations underestimate the temperature for conditions relevant to magmatic crystallization in basalts (see Lattard et al., 2005, fig. 1).
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cat, total number of cations; It has become clear that the shortcomings of the two thermo-oxybarometer models largely originate from the paucity of calibration data at high temperatures but also—for all temperatures—at oxygen fugacities far from those of the FMQ buffer. Two recent experimental studies (Lattard et al., 2005
; Evans et al., 2006) have now filled these gaps by providing a large set of experimental data in the critical T–fO2 ranges. Evans et al. (2006) have also considered the effect of additional components on the Fe–Ti oxide compositions at 800 and 900°C at relatively high oxygen fugacities.
In this paper we present new experimental data on the compositions of coexisting titanomagnetite and ilmenite solid solution in the Fe–Ti–O system at 950°C and on Mg-bearing and/or Al-bearing Fe–Ti oxide assemblages at 1100–1300°C. These new results complement our dataset at high temperatures (1000–1300°C) in the simple Fe–Ti–O system (Lattard et al., 2005) and the results of Evans et al. (2006) in the Fe–Ti–Al–Mg–Mn–O system at 800 and 900°C. We show that the addition of minor components in the concentration ranges that are usual in Fe–Ti oxides from basic magmatic rocks can be, to a first approximation, accommodated by simple projections. We have performed numerical fits to available experimental data with the aim of generating a simple empirical formulation of the titanomagnetite–ilmenite thermo-oxybarometer for temperatures in the range 800–1300°C, under reduced to moderately oxidized conditions. We have tested this empirical formulation both with synthetic and natural Fe–Ti oxide pairs and we shall show in the following that the results are encouraging.
We refer the readers to the review of Lindsley (1991) and to our recent paper (Lattard et al., 2005) for summaries of the experimental studies that unravelled the sub-solidus phase relations in the Fe–Ti–O system.
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EXPERIMENTAL AND ANALYTICAL TECHNIQUES |
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All experiments reported in the following discussion were designed to produce equilibrium pairs of titanomagnetite (Tmt) and ilmenite–hematite solid solution (Ilmss) at 1 bar pressure under various oxygen fugacity conditions. Three types of experiments were performed: (1) sub-solidus syntheses at 1100, 1200 or 1300°C from oxide mixtures in the Fe–Ti–Al–Mg–O system; (2) sub-solidus re-equilibration experiments at 950°C in evacuated silica-glass ampoules on products of previous syntheses in the Fe–Ti–O system; (3) crystallization experiments from a basic liquid at temperatures in the range 1050–1080°C.
All experiments were performed in vertical quench furnaces. The temperature was measured before and after the runs with a type S (Pt–Pt90Rh10) thermocouple calibrated against the melting point of silver (960·8°C) and gold (1064·18°C; ITS 90).
Sub-solidus syntheses in the Fe–Ti–Mg–Al–O system
The sub-solidus syntheses reported here were aimed at producing assemblages of Tmt and Ilmss with low Mg and/or Al contents comparable with those observed in magmatic Fe–Ti oxide minerals. The experiments were performed at 1100, 1200 or 1300°C, under a variety of oxygen fugacities (NNO range: +0·7 to –4·6), which were in most cases fixed by CO–CO2 gas mixtures. In a few experiments at 1100°C the oxygen fugacity was imposed by a solid-state oxygen buffer enclosed together with the sample in an evacuated SiO2 glass ampoule.
We chose a few bulk compositions in the two sub-systems Fe–Ti–Mg–O and Fe–Ti–Al–O with 2–4 wt % of either MgO or Al2O3, as well as two compositions with about 1 wt % of both minor components (Table 1). The starting mixtures were prepared from TiO2 (99·9%, Aldrich Chemical Comp. Inc.), Fe2O3 (99·9%, Alpha Products), metallic iron (99+%, Heraeus), MgO (99·5%, Ventron) and/or 
-Al2O3 (purest, Merck). Metallic iron was first employed in starting mixtures for experiments performed with solid-state oxygen buffers. In this case, the original oxygen content of the sample should be close to that of the run product because of the restricted buffer capacity. Starting mixtures with both Fe° and Fe2O3 also proved suitable for some gas mixing experiments because they yielded very homogeneous run products. The reagents were weighed in stoichiometric proportions, ground together and mixed under acetone in an agate mortar, pressed to pellets of 200–300 mg (about 5 mm diameter, 2–5 mm in length) and dried in air at 130°C.
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For the solid-state buffer experiments, pellets of sample and buffer material (iron–wüstite or wüstite–magnetite) were inserted in silica-glass tubes, which were evacuated with a rotary vane pump to a vacuum of the order of 10–2 mbar prior to sealing. A silica-glass filler rod was used to minimize the internal volume of the ampoule and to separate the sample from the buffer. At the end of the experiments, the silica-glass ampoules were pulled out of the furnace and quenched into water, a procedure that lasted less than 1 min. In all runs referred to in this paper all buffer phases were still present after termination of the experiments; that is, the desired oxygen fugacity was maintained during the whole experiment.
For the gas-mixing experiments, the sample pellets were placed on a grid of platinum wire. As sample and metal share only a very small surface and no melt ever occurs in the samples, negligible Fe loss to the wire but maximum contact of sample with gas mixture can be achieved. High-purity CO (CO >99·97 vol. %) and CO2 (CO2 >99·995 vol. %) gases were mixed with electronic valves (Millipore) and allowed to flow from the bottom to the top of the furnace tube (inner diameter 4 cm) at a rate of 200 cm3/min. The oxygen fugacity was measured after the experiments with an yttria-stabilized zirconia sensor (SIRO2) with air as the reference. The sensor was calibrated at 1300°C against the Ni–NiO (NNO) equilibrium (O’Neill & Pownceby, 1993). At the moderate to low oxygen fugacities reported in the present study (NNO < +1; CO > 1 vol. %), the accuracy of the experimental fO2 values are estimated at about ±0·2 log unit [for further details see Lattard et al. (2005)]. All fO2 values given for the gas-mixing experiments in the following are those measured with the zirconia sensor. As we also list the CO contents of the gas mixtures, the reader can easily retrieve the fO2 values from the tables of Deines et al. (1974) for comparison.
Run products were generally drop-quenched in water at the bottom of the furnace, a procedure that ensures a very fast cooling (within a few seconds). In a few cases, however, the gas flow was first turned off and the samples were pulled out of the furnace and quenched in water. The whole procedure usually took less than 1 min. In the following discussion this is referred to as ‘external quench’.
To approach equilibration as closely as possible in the synthesis products, total run durations were 18–60 h at 1300°C, but up to 330 h (14 days) at 1100°C. These run durations are longer than those applied in the Fe–Ti–O system (see Lattard et al., 2005) because the addition of magnesium and aluminium in the starting materials was expected to slow down the reaction kinetics, which could lead to inhomogeneous samples. Indeed, a few preliminary runs yielded products that contained a few grains of Fe–Al-rich spinel surrounded by zoned Tmt crystals with Al-bearing rims in contact with the Fe–Al spinel. Such Al-enriched regions disappeared if the samples were crushed, re-pelletized and re-run under the same T–fO2 conditions for at least another 24 h. Consequently, the gas-mixing runs at 1200°C and 1100°C reported here were interrupted through drop-quench after 1 or 2 days, the samples were ground to a powder under acetone, re-pressed to a new pellet and re-run under the same T–fO2 conditions for at least another 24 h.
Sub-solidus re-equilibration experiments at 950°C in vacuo (Fe–Ti–O system)
Our experiments at 950°C under low vacuum were originally designed to re-equilibrate under oxygen-conserving conditions Tmt–Ilmss assemblages previously synthesized in the Fe–Ti–O system at high temperatures (1100–1300°C) under various oxygen fugacities. The incentive was to estimate the original vacancy concentration of the high-temperature titanomagnetites from the amount of Ilmss exsolved from Tmt in correlation with the vacancy relaxation at 950°C (see Lattard, 1995; Sauerzapf, 2006). This aspect will not be considered here, but the run products are of interest for the present purpose because they yield data complementary to our series at 1300, 1200, 1100 and 1000°C in the Fe–Ti–O system (Lattard et al., 2005).
The starting samples were fragments (30–100 mg) of pellets synthesized in gas mixing experiments (procedure summarized in the section ‘Sub-solidus syntheses in the Fe–Ti–Mg–Al–O system’). These fragments were sealed in evacuated silica-glass ampoules (vacuum of the order of 10–2 mbar). The inner volume of the ampoules was minimized by using filling rods of silica-glass. The ampoules were kept in vertical tube furnaces at 950°C for durations (7–37 days), which should be long enough to approach re-equilibration. The samples were quenched by rapid immersion of the ampoules in cold water. Only dry samples were accepted for further investigation. Detailed investigations have shown that the silica-glass ampoules remain gas-tight and evacuated during the whole experiment and the quenching procedure, and that the sample systems can be considered to be closed for all elements including oxygen (Lattard, 1995; Lattard & Partzsch, 2001).
Crystallization experiments from a basic liquid
We have performed a few crystallization experiments to synthesize Tmt–Ilmss pairs of compositions relevant to Fe–Ti oxide crystallizing from natural basic magmas. These experiments are similar to those conducted by Toplis & Carroll (1995) and the reader is referred to that paper for more experimental details.
The starting material (SC47-P) was a synthetic eight-component glass with a composition corresponding to that of the residual liquid after 40–50% crystallization of a ferrobasaltic composition [near the SC1 composition of Toplis & Carroll (1995)]. The starting glass was synthesized from mixtures of oxides (SiO2, TiO2, Al2O3, Fe2O3 and MgO) and carbonates (CaCO3, Na2CO3 and K2CO3). The mixtures were decarbonated at 800°C in a Pt crucible for 0·5 h, fused at 1400°C in air for 5 h and poured for quenching into a steel mortar. The material was homogenized by repeated grinding and fusing. Its chemical composition is given in Table 1.
Aliquots of 40–60 mg starting material were loaded onto loops of platinum wire using polyvinyl alcohol as a binder. To minimize iron loss from the sample to the platinum wire (e.g. Ford, 1978; Johannes & Bode, 1978) the loops were ‘presaturated’ with iron by heating them in contact with some starting material at 1300°C under the required oxygen fugacities for 24 h, followed by cleaning in HF.
The samples were first heated at 1150°C or 1140°C; that is, well above the liquidus (see Toplis & Carroll, 1995) for 8–10 h to allow redox equilibration of the melt. They were subsequently cooled to the final temperature (near 1050 or 1082°C) at a constant rate of 3°C/h (to facilitate nucleation and growth of crystals large enough for microprobe analysis) and held at this temperature for 4–12 days to allow re-equilibration. During the whole procedure the CO–CO2 mixture was kept to the value corresponding to the oxygen fugacity at the end temperature. Runs were terminated by drop-quench into water. The run durations were of the same order as those of comparable subliquidus experiments in the literature (e.g. Toplis & Carroll, 1995) and should ensure at least a reasonable approach to equilibration at the final temperature.
Identification and chemical analysis of the run products
All run products were carefully characterized using optical microscopy, X-ray powder diffraction, back-scattered electron (BSE) images from a scanning electron microscope (SEM) and chemical analyses with the electron microprobe (EMP).
The EMP, a Cameca SX-51, was operated at an acceleration voltage of 15 kV and a beam current of 20 nA. Counting times were 20 s on peak and twice 10 s on background. The standards used were synthetic hematite (for Fe), rutile (for Ti), periclase (for Mg) and gahnite (for Al). The raw data were corrected with the ‘PAP’ software (Pouchou & Pichoir, 1985). To avoid possible instrumental drift, the standardization was checked at least every 2 h. If the measurements could not be reproduced within less than 1%, a new standardization was performed.
After recasting Fe to Fe2+ and Fe3+ or Ti to Ti4+ and Ti3+ on the basis of ideal stoichiometry (i.e. four oxygens and three cations for Tmt, but three oxygens and two cations for Ilmss), analysis totals range, with few exceptions, between 99 and 100·5 wt %. Repeated analyses on unzoned grains show that the precision of the analyses is excellent [1
standard deviations for the Ti/(Ti + Fe) values 
0·5% relative]. The accuracy is also satisfactory, as shown by analyses on a single-phase, very homogeneous ilmenite sample, which yielded Ti/(Ti + Fe) per cent values less than 0·35 at. % different from the bulk composition. As already reported by Lattard et al. (2005), analyses performed by D. H. Lindsley at Stony Brook (using a natural ilmenite standard) on two of our Ti-rich Tmt–Ilmss run products produced only slightly higher Ti/(Ti + Fe) per cent values (difference 0·5 at. %). Therefore we think it safe to estimate the accuracy for all compositions at ±0·005 for the Ti/(Ti + Fe) values, which translates into ±0·015 for Xusp and ±0·010 for Xilm.
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EXPERIMENTAL RESULTS |
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Products of sub-solidus re-equilibration experiments at 950°C in the Fe–Ti–O system
After annealing at 950°C the samples consist of polycrystalline, roughly equigranular aggregates of Tmt and Ilmss, with a grain size similar to that of the starting samples (i.e. around 10–50 µm). In nearly all annealed samples, however, the Tmt crystals display exsolution textures in the form of ilmenite lamellae oriented in the {111} planes of the spinel and of ilmenite rims around the spinel crystals. As discussed in detail by Lattard (1995
), such textures occur when the modal proportion of Ilmss in the sample increases during annealing under oxygen-conserving conditions, as a result of the shift of the Tmt composition towards stoichiometry (relaxation of the high-temperature cationic vacancies).
Careful EMP measurements on Ilmss lamellae and rims of suitable size have shown that they have the same chemical composition as the larger grains (Lattard, 1995; Sauerzapf, 2006). More generally speaking, in all samples both Ilmss and Tmt mineral phases have homogeneous chemical compositions within the crystals and over the whole sample. This is illustrated by the small standard deviations on the values of the mole fractions of the ulvöspinel (Xusp) and the ilmenite endmembers (Xilm), as listed in Table 2. These values are calculated from the Ti/(Ti + Fe) values (cation ratios) obtained from the EMP analyses, where
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In most cases, re-equilibration at 950°C of a Tmt–Ilmss assemblage synthesized at a higher temperature produces a clockwise rotation of the original steep tie-line to a flatter one, with a Ti-poorer spinel and a Ti-richer rhombohedral phase (compare dashed and continuous lines in Fig. 1). The flattening of the tie-lines with decreasing temperature reflects the exchange of Fe2+ + Ti4+ for 2 Fe3+ between titanomagnetite and ilmenite according to reaction (1) (see Introduction).
In some cases, however, the original high-temperature run product has been slightly oxidized because it was quenched outside the furnace, in contact with air (‘external quench’; see end of section ‘Sub-solidus syntheses in the Fe–Ti–Mg–Al–O system’). This oxidation affects only the surface of the sample pellet (depth <100 µm; see Lattard et al., 2006, fig. 3c) where it is manifested by oxy-exsolution textures in the sense of Buddington & Lindsley (1964). Such a spatially restricted oxidation (which cannot be documented by EMP analyses because of the small size of the exsolution textures) nevertheless changes the bulk oxygen content of the sample. Consequently, the re-equilibrated 950°C assemblage displays higher magnetite and hematite contents; that is, a tie-line shifted to the left in Fig. 1.
The positive slope of the tie-lines in Fig. 1 reflects the preferred partitioning of Fe2+ and Ti into the rhombohedral phase. At constant temperature, however, the tie-lines are not strictly parallel (Fig. 1). Instead, their slope continuously evolves with increasing Ti/(Ti + Fe) value of both Fe–Ti oxide phases, which means that the partitioning between the two phases is strongly controlled by their compositions, as already observed in previous experimental studies (e.g. Lindsley, 1962, 1963; Spencer & Lindsley, 1981; Andersen & Lindsley, 1988; Lattard et al., 2005; Evans et al., 2006).
Products of sub-solidus experiments in the Fe–Ti–Mg–Al–O system
The products of sub-solidus experiments in different sub-systems of the Fe–Ti–Mg–Al–O system are polycrystalline, roughly equigranular aggregates with grain sizes around 10–50 µm. They consist of Tmt–Ilmss assemblages. In six samples in the Mg-free sub-system pseudobrookite is the third phase (Psbss; solid solution between the endmembers Fe3+2TiO5 and Fe2+Ti2O5). The chemical compositions of the coexisting Tmt and Ilmss are listed in Tables 3 and 4, together with the run conditions. The compositions are plotted in Fig. 2a for the Fe–Ti–Mg–O sub-system, and in Fig. 2b for Al-bearing compositions (with or without Mg).
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space groups in the rhombohedral oxide (after Harrison et al., 2000
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The MgO contents of these synthetic Tmt and Ilmss range between 0·9 and 3·0 to 3·4 wt % respectively. The Al2O3 contents are low in Ilmss (maximum 1· 3 wt %) but vary between 1· 1 and 9·6 wt % in Tmt, with the highest content at 1100°C and relatively high contents at 1300°C in coexistence with Psbss (Tables 3 and 4). Natural Ilmss in gabbros or basalts may display higher MgO contents (up to 9 wt %; Fodor & Galar, 1997
), but otherwise the Mg and Al concentrations in the Fe–Ti oxides synthesized here are comparable with their natural counterparts in basic magmatic rocks (compare, for example, with values listed in the ‘GEOROC’ database, MPI Mainz, Germany, available at http://georoc.mpch-mainz.gwdg.de/georoc/Entry.html).
Because the runs were performed only at moderate to low oxygen fugacity conditions (0·7 NNO –4·5) the coexisting Fe–Ti oxides all have compositions poor in Fe3+-bearing end-members. In this compositional region, Mg preferentially enters the rhombohedral phase and the partitioning becomes more pronounced with decreasing temperature (Fig. 2a). This is in accordance with the experimental results of Pinckney & Lindsley (1976), Pownceby & Fisher-White (1999) and Evans et al. (2006). With increasing fO2, the Mg/Fe2+ distribution between rhombohedral and spinel phase becomes more equal (Fig. 2a) and, according to Speidel (1970), reverses between magnetite and hematite-rich Fe–Ti oxides. Such an fO2 dependence has also been observed by Evans et al. (2006, fig. 9a) at lower temperatures. In contrast, Al partitions into the spinel phase, especially at lower temperatures. The addition of Mg, however, counteracts this effect (Fig. 2b).
To better see how substituting magnesium and aluminium affect the temperature-dependent exchange equilibrium (1), we project the compositions of the Al and Mg-bearing Fe–Ti oxides onto the binaries in the simple Fe–Ti–O system, by using the same projection scheme as Evans et al. (2006). For Ilmss the projected mole fraction of the FeTiO3 endmember is calculated as X'ilm = Fe2+/(Fe2+ + Fe3+/2) (cation ratio). For Tmt, we assume equal partitioning of Fe2+ and Mg between titanate, aluminate and ferrite, which results in X'usp = Ti/(Ti + Fe3+/2). For both Tmt and Ilmss the Fe2+ and Fe3+ contents p.f.u. have been calculated by assuming stoichiometry; that is, four oxygens and three total cations for Tmt and three oxygens and two total cations for Ilmss (see Tables 3 and 4). At 1200 and 1300°C, however, Tmt in equilibrium with Ilmss may be cation deficient, particularly at low oxygen fugacities (e.g. Senderov et al., 1993; Lattard, 1995; Lattard et al., 2005). Calculated Ti3+ under the assumption of stoichiometry may, in fact, reflect non-stoichiometry in relation to the 
substitution. In such cases, our projection schemes are no longer adequate and no X'ilm and X'usp values are listed for the corresponding compositions in Tables 3 and 4.
As can be seen in the Roozeboom diagram of Fig. 3b, the projected compositions fit well within our dataset in the Fe–Ti–O system. They plot on or very near the isotherms defined by the simple system data. In particular, the Mg- and Al-bearing compositions from the 1100°C run products are in excellent agreement with those from the simple system, even in case of Al-rich Tmt. At 1200 and 1300°C the results scatter slightly more, but not as much as those in the Fe–Ti–O system of Andersen & Lindsley (1988).
Products of crystallization experiments from a basic liquid
The conditions and results of four crystallization experiments from the basic starting glass SC47-P are summarized in Table 5. The run products consist of mostly euhedral crystals embedded in glass (quenched melt phase). All samples contain Tmt, Ilmss and clinopyroxene, three of them plagioclase and two a few rounded crystals of olivine. Except for the run product devoid of plagioclase (apparently plagioclase did not nucleate during this run), our observations fully confirm those of Toplis & Carroll (1995) on the products of similar experiments. Plagioclase and olivine are the first phases that crystallize on the liquidus, followed at lower temperatures by clinopyroxene and Fe–Ti oxides. Plagioclase remains a liquidus phase down to 1050°C whereas olivine begins to resorb when the temperature falls below about 1100°C (Toplis & Carroll, 1995). Indeed, resorption is indicated by the rounded form of the rare olivine crystals in our run products, in contrast to the euhedral plagioclase and clinopyroxene crystals. Crystals of the Fe–Ti oxide phases are either embedded in glass or enclosed in plagioclase or clinopyroxene crystals. Titanomagnetite forms cubic–octahedral crystals, 5–40 µm in cross-section, but many of them have hollow cores. Ilmenitess forms long needles or strings of small rounded crystals, with a maximum width of about 10 µm. Because Fe–Ti oxides are abundant in all samples, there are enough crystals of desirable size for EMP analyses. There is, however, a clear correlation between the size of the crystals and the analysis totals after assignment of Fe to Fe2+ and Fe3+ based on ideal stoichiometry. Tmt with crystal sizes in the range 7–15 µm have totals between 96 and 99 wt %, whereas in the case of larger crystals the totals approach 100 wt %. Consistent with their small size, the analytical totals for the Ilmss crystals are generally around 98 wt %. As discussed by Evans et al. (2006), the low analysis totals can be attributed to ‘the minor loss of Fe and Ti counts that would have been fluorescence-induced by the continuum in larger crystals at distances from the electron-beam impact point greater than about 5 µm’. However, the cation proportions and the X'ilm and X'usp values are independent of the analytical totals.
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Whereas plagioclase and clinopyroxene are conspicuously zoned, the Fe–Ti oxide phases do not show any apparent zoning in BSE images. Indeed, the 1
values for the projected X'usp do not exceed 0·014 (3% relative), those for X'ilm are a maximum of 0·009 (1% relative; see Table 5). This means that these phases are essentially homogeneous within the single crystals and over the whole samples. As in the sub-solidus samples (preceding section), the Al partitioning between the Fe–Ti oxide phases is in favour of Tmt, whereas Mg prefers Ilmss. However, in contrast to the sub-solidus samples, the Al and Mg contents of the Fe–Ti oxide phases are significantly higher. As will be shown later, these higher Mg and Al contents do not disturb the Fe–Ti partitioning between Tmt and Ilmss. The projected X'ilm–X'usp pairs are in good agreement with values for the Mg- and Al-free system. They will be used to test our numerical version of the Tmt–Ilmss thermo-oxybarometer.
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NUMERICAL FITS TO EXPERIMENTAL DATA |
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 TOPABSTRACTINTRODUCTIONEXPERIMENTAL AND ANALYTICAL...EXPERIMENTAL RESULTS NUMERICAL FITS TO EXPERIMENTAL... TESTS OF THE NEW...APPLICATION TO NATURAL...CONCLUDING REMARKSSUPPLEMENTARY DATAAPPENDIXREFERENCES |
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We have performed numerical fits to the experimental results presented in the preceding sections, together with other published datasets, with the aim of deriving simple equations to estimate temperature and oxygen fugacity from the compositions of coexisting Tmt and Ilmss for a restricted T–fO2 realm. We take advantage of the fact that in our run products in the Fe–Ti–Al–Mg–O system, the projected compositions of the Fe–Ti oxides are in good agreement with those in the simple Fe–Ti–O system. Because this is also the case for the major part of the data of Evans et al. (2006
), we shall also include these results in our dataset.
Thermometry
The Roozeboom diagram of X'ilm vs X'usp (Fig. 3) is a very convenient basis for the numerical calibration of the Tmt–Ilmss thermometer based on an experimental dataset. The core of this dataset is the group of results in the Fe–Ti–O system that includes literature data (Lindsley, 1962, 1963; Spencer & Lindsley, 1981; Andersen & Lindsley, 1988; Senderov et al., 1993), our recently published results (Lattard et al., 2005) and the 950°C results presented in Table 2. The dataset also comprises the results of Evans et al. (2006) in the Fe–Ti–Al–Mg–Mn–O system, and the data listed in Tables 3 and 4, which were all projected into the simple system with the schemes described previously. Results from a few older experimental studies (in particular, Webster & Bright, 1961; Taylor, 1964; Speidel, 1970) were not included because the corresponding phase compositions are uncertain.
As can be seen from Fig. 3, we have plotted only those Tmt–Ilmss pairs that involve Ilmss with the long-range ordered ilmenite structure (space group 
). Following Harrison et al. (2000), the corresponding compositional fields are restricted to Xilm >0·875 at 1300°C, but gradually widen with decreasing temperatures (e.g. Xilm >0·575 at 800°C). There are several reasons for limiting our dataset to those Tmt–Ilmss pairs. The first is that the spacing of the isotherms is reasonably wide only on the ‘ side’ of the Roozeboom diagram (Fig. 3a). We see no chance to provide an acceptable numerical fit for the part of the Roozeboom diagram that involves Ilmss richer in the Fe2O3 endmember (disordered structure with space group 
), because the corresponding isotherms are too narrowly spaced (Fig. 3a). Moreover, our experimental results on Mg- and Al-bearing compositions essentially concern Ilmss rich in the FeTiO3 endmember and they provide very little information on the effect of minor components on hematite-rich compositions. The results of Evans et al. (2006) show that at 800 and 900°C the isotherms are not very sensitive to minor components on the ‘ side’ but strongly influenced by them on the ‘ side’. This would probably also hold for higher equilibration temperatures. On the whole, we shall restrict our numerical fits to the compositional realm indicated in Fig. 3c, with the aim of specifically addressing Fe–Ti oxide parageneses in basic and intermediate magmatic rocks that typically include Ti-rich Ilmss and Tmt of intermediate compositions.
Our first idea was to fit, through least-squares methods, X'ilm = f(X'usp, T) to a second- or third-order polynomial function, with the condition that X'ilm = 1 for X'usp = 1. However, we could not retrieve a satisfying, stable solution for temperatures in the range 700–1300°C. In particular, the high X'ilm and X'usp values at T 1000°C were badly reproduced. Therefore we turned to an expression derived by writing the law of mass action for reaction (1):
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and considering that Xilm = 1 – Xhem, we obtain
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We approximate through the polynomial (K1/ T) + K2 + (K3 /T2), with the constants K1, K2 and K3 and arrive at the following expression:
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| (3) |
usp and amag = Xmag mag and the activity coefficients, usp and mag are derived from expressions used for symmetrical solution models; that is, |
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| (4a) |
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| (4b) |
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| (4c) |
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| (4d) |
X'ilm = Xilm(calc) – X'ilm(meas). The squared X'ilm values are added up and the sum is minimized by using a GRG2 non-linear quadratic optimization algorithm (Lasdon & Waren, 1978) to determine the K1, K2, K3, WGusp and WGmag parameters.
One of the advantages of this optimization procedure is that it allows weighting of the X'ilm. Because our aim was to adequately fit the experimental data at high temperatures, we chose to weight all results gained from experiments at T 1000°C (Lindsley, 1962, 1963; Andersen & Lindsley, 1988; Senderov et al., 1993; Lattard et al., 2005; present data in Tables 3 and 4) with a factor of 500. Results from experiments performed at 800 T 950°C (Evans et al., 2006; present data in Table 2), which scatter much more in the Roozeboom diagram (Fig. 3c), were weighted with a factor of 100; those of experiments at lower temperatures (Lindsley, 1962, 1963; Spencer & Lindsley, 1981) with a factor of 10. The low weighting of the latter data was also chosen to account for the fact that the experiments at 600–750°C were reversals that did not yield equilibrium compositions but provided compositional brackets. This is also the case for two experimental brackets at 980°C (Spencer & Lindsley, 1981). A factor of 10 was also applied to the five data points at 800°C with X'ilm values between 0·70 and 0·58, which define a break in slope of the isotherm (Fig. 3c), possibly related to the solvus in the rhombohedral oxide series (Evans et al., 2006). On the whole, we have regressed the five parameters K1, K2, K3, WGusp and WGmag on the basis of 189 data points, whereby 83 X'ilm values were weighted with a factor of 500, 69 with a factor of 100 and 37 with a factor of 10. The regressed parameters are given in Table 6.
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Using these parameters one can easily calculate X'ilm as a function of X'usp at any given temperature and derive isotherms in the Roozeboom diagram, as depicted in Fig. 3b and c. As expected, these calculated isotherms fit the experimental data very well at temperatures in the range 1000–1300°C. They also reasonably match the experimental results at 950°C and those at 800°C, except for the values at X'ilm <0·75 discussed above. In contrast, the model isotherm at 900°C does not fit the experimental data points well. Its slope is somewhat too steep for 0·8 < X'ilm < 0·9 and the curvature is not strong enough towards lower X'ilm and X'usp (Fig. 3c). In fact, the curvature of all isotherms should ideally be slightly stronger to better account for the lowest X'ilm and X'usp values. Figure 4a confirms that the calculated X'ilm well approximates the measured values at temperatures between 1000 and 1300°C. With very few exceptions (less than 10% of the data), the difference is less than 0·01. But at T
900°C, where the experimental data scatter much more and the calculated isotherms do not perfectly match the experimental trends, the difference between experimental and modelled value can reach ±0·06. A close examination of the 800 and 900°C data of Evans et al. (2006) reveals that those with the strongest X'ilm all stem from very few experiments; that is, runs 13 and 26 at 900°C, and runs 9, 11 and 22 at 800°C, whereby the two last named belong to what Evans et al. (2006) called their ‘problem’ experiments. It is not clear whether these run products reached equilibrium.
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, Lindsley, 1962For any given X'ilm, X'usp pair we can calculate the corresponding equilibrium temperature by iteration nesting from equation (3) (a macro is given in a Supplementary Data Excel worksheet at http://www.petrology.oxfordjournals.org/). For X'ilm values up to 0·95 nearly all the calculated temperatures reproduce the experimental values within ±30°C. Even the 800 and 900°C results that show significant differences between experimental and modelled X'ilm values yield calculated temperatures that are at most ±35°C from the experimental values. Only one ‘problem’ experiment at 800°C (run 11-IV; Evans et al., 2006
) and two bracketing runs at 1200°C (Andersen & Lindsley, 1988) show stronger divergences (Fig. 4b), which may reflect a lack of equilibrium in the experimental products. For X'ilm values above 0·95 the discrepancies between experimental and calculated values increase considerably (Fig. 4b), which is a direct consequence of the narrow spacing of the isotherms at very high X'ilm and X'usp values (Fig. 3b and c). Such Ti-rich compositions are, however, of little significance for terrestrial magmatic rocks. We have checked the effect of weighting the results from experiments performed in the temperature range 800–950°C with the same high factor (500) as for the results at 1000–1300°C. This slightly improves the calculated X'ilm values for 800 and 900°C but worsens those for the higher temperature experiments. As the calculated temperatures are hardly influenced by the different weightings we have kept our original weighting factors.
Oxybarometry
The Tmt–Ilmss oxybarometer is based on iron redox equilibria [see reaction (2)] and the compositions of coexisting Tmt and Ilmss are unique at any given P–T–fO2 condition. With increasing fO2 both Fe–Ti oxide phases increase their Fe3+ contents; that is, decrease the proportions of their Ti-rich end-members. In the case of Tmt the compositional shift as a function of oxygen fugacity is small at low fO2 values (NNO < –2), but becomes strong at moderate fO2 values and decreases again at high values (NNO > 1). In a NNO vs X'usp plot this results in smooth, roughly parallel isotherms that can be fitted by a third-order polynomial function (Fig. 5). Similar behaviour might have been expected for the rhombohedral oxides; however, because of complications associated with long-range order and structural transitions, the isotherms have a complex shape and cross over (see Lattard et al., 2005, fig. 8); that is, they cannot be adequately fitted with simple functions. Consequently, we do not use the Ilmss isotherms to derive an expression for oxybarometry.
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Coming back to the effect of fO2 on titanomagnetite, we note that the projected compositions of the Tmt synthesized at 1100–1300°C in the Fe–Ti–Mg–Al–O system plot more or less on the same isotherms as the compositions in the simple system (Fig. 5). In contrast, Evans et al. (2006
) have shown that at T 900°C in the Fe–Ti–Mg–Mn–Al–O system, the X'usp values at any given NNO are systematically shifted as a function of their compositions. As can be seen in Fig. 5, the spread in the X'usp values at 900°C ranges up to 0·1 and is even stronger at 800°C. Consequently, the data at 800°C have not been used for our numerical fit.
The data used for the fit comprise the results of the present study for Mg- and/or Al-bearing Tmt under sub-solidus conditions at 1300–1100°C (Tables 3 and 4), those of Evans et al. (2006) at 900°C in the Fe–Ti–Al–Mg–Mn–O system, and those of Lattard et al. (2005) in the simple Fe–Ti–O system at 1000–1300°C. In contrast to the fitting of reaction (1), we have not restricted our database to Fe–Ti oxide pairs with Ilmss with the space group, which occur only at low NNO values. Instead, we have considered Tmt from all available pairs to better constrain the isotherms to high NNO values. We have fitted the data to a third-order polynomial function for NNO = f(X'Usp, T) with a standard least-squares algorithm for multiple linear regressions (RGP function of Microsoft ExcelTM). The NNO values for X'usp = 0 were fixed to those of the magnetite–hematite buffer using the data of Hemingway (1990). In fact, fits performed without this constraint lead to very similar results at X'usp = 0. The coefficients of the polynomial functions are listed in Table 6.
The calculated isotherms fit the experimental data reasonably well for temperatures in the range 900–1200°C (Fig. 5). At 1300°C, however, the calculated isotherm does not perfectly reproduce the experimental data. This may result partly from the effect of cation defects, which are undoutedly abundant in the Fe–Ti–O system at low oxygen fugacity values, but may have variable concentrations at higher NNO, depending on the redox state and the Al and Mg concentrations (Lattard et al., 2005; Sauerzapf, 2006). The calculated 900°C isotherm yields only mean NNO values, and the 800°C isotherm yields essentially maximum NNO values at any given X'usp (Fig. 5). As discussed by Evans et al. (2006), there is a systematic shift of X'usp with the bulk composition of the starting material. Interestingly, the strongest discrepancy between the experimental results and our 800°C isotherm is for bulk composition I, which is in the Fe–Ti–Al–O system. The best agreement is for bulk composition IV, which includes Al, Mg and Mn and is the most relevant for natural Fe–Ti oxide assemblages.
In the temperature range 900–1300°C, 95% of the NNO estimates with our fitted polynomial reproduce the experimental values within ±0·3, and 90% within ±0·2. This is a very good agreement, given that ±0·2 is the uncertainty of the e.m.f. measurements of the oxygen fugacity (Fig. 6). At 800°C or lower temperatures, however, our polynomial can yield overestimates in NNO of up to 1· 2 for Mg- and Mn-free compositions.
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TESTS OF THE NEW TITANOMAGNETITE–ILMENITE THERMO-OXYBAROMETER VERSION WITH INDEPENDENT EXPERIMENTAL DATA |
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On the basis of the numerical fits presented in the preceding sections, both temperature and oxygen fugacity can be calculated from the compositions of coexisting Tmt–Ilmss that are moderately substituted with Al, Mg and/or Mn. Our fits are based on experimental data in the temperature range 800–1300°C. Because they are not based on a rigorous thermodynamic model—in particular no solid-solution models for the Fe–Ti oxides—these fits should not be used for assemblages equilibrated at significantly lower temperatures. As shown in Fig. 5, the oxygen fugacity estimates yield only maximum values at temperatures below 900°C. It is also crucial not to use the thermometry fit for Ilmss with the long-range disordered hematite structure in the
space group. According to Harrison et al. (2000), this limits the application to compositions with Xilm > 0·59 at 800°C, but in excess of 0·70 at 1000°C and 0·82 at 1200°C. These values are only approximate because additional elements may shift the X'ilm value for the order–disorder transition. In any case, misuse of our fits for more Fe-rich ilmenite compositions would yield significant overestimates of the equilibration temperature.
In the following section we test our numerical expressions on independent experimental results relevant to the crystallization and differentiation of basic liquids. There are numerous experimental studies in which Fe–Ti oxide phases form part of the crystalline assemblages in equilibrium with the surrounding liquid. However, we have found only a few studies in the literature that report the compositions of coexisting Tmt and Ilmss equilibrated during experiments in the desired temperature and oxygen fugacity range. These are the data of Juster et al. (1989), Snyder et al. (1993), Toplis et al. (1994), Gardner et al. (1995b), Toplis & Carroll (1995), Scaillet & Evans (1999) and Prouteau & Scaillet (2003). Our own results (see section ‘Products of crystallization experiments from a basic liquid’) complement those of Toplis et al. (1994) and Toplis & Carroll (1995) because they were obtained from a starting material very similar to that used by those workers.
As can be seen from Table 7 and Figs 7 and 8, the temperature estimates obtained with our numerical model are encouraging. Eighty per cent of the 39 Tmt–Ilmss pairs yield temperatures that are within ±50°C of the experimental temperatures. The remaining values are within ±70°C of the experimental values, with the exception of those from one run (Fe-100; Toplis et al., 1994; Fig. 7a). At a first sight, there is an increasing tendency for calculated temperature to be underestimated with decreasing experimental temperatures (Fig. 7a). This could be attributed to the fact that our fits rely heavily on data obtained at T 1000°C. However, the question arises whether equilibrium was reached in all the experiments reported by Gardner et al. (1995b) or Prouteau & Scaillet (2003). The Fe–Ti oxide compositions given by Prouteau & Scaillet (2003) point to considerable inhomogeneities, at least in the titanomagnetites. The 1 values for X'usp are about 30% of the means of eight or nine single analyses and those researchers listed only single analyses of Ilmss which may not be representative (Table 7). Gardner et al. (1995b) provided only means of two to nine single analyses and did not give any standard deviation. The starting materials for their experiments were glass–crystals mixtures that were obtained by hydrothermal annealing of a powdered natural pumice sample at 2 kbar, 825 or 875°C. Although Gardner et al. (1995a) presented indications that Fe–Ti oxide re-equilibrate within the run durations of 4–5 days at 850°C, the detailed study of Venezky & Rutherford (1999) reveals that significant chemical heterogeneities may persist even after much longer runs. In particular, the latter workers observed that re-equilibration takes longer when PH2O is lower than the total pressure, which holds for all the runs of Gardner et al. (1995b) listed in Table 7, with one exception (G-3). Venezky & Rutherford (1999) showed that the temperatures calculated from partially re-equilibrated Fe–Ti oxide assemblages may be either lower or higher than the experimental values.
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As shown in Fig. 8, our model reproduces the experimental data of Toplis & Carroll (1995
) very well and yields much better results than the formulations of Andersen & Lindsley (1988) or Ghiorso & Sack (1991a), in particular for low oxygen fugacities. The strongest discrepancies between experimental and modelled temperatures concern the results of a single experiment performed by M. J. Toplis at 1072°C and NNO = 0·15 on six different bulk compositions [run products Fe-95 reported by Toplis & Carroll (1995), and Fe-95 to Fe-100 reported by Toplis et al. (1994)]. For all compositions the calculations yield underestimates by 40–100°C (Table 7). Interestingly, other models (Andersen & Lindsley, 1988; Ghiorso & Sack, 1991a) also consistently produce too low temperatures (Fig. 8), suggesting a possible error in the experimental temperature.
The oxygen fugacity values calculated from the X'usp values and the calculated temperatures generally agree within ±0·4 NNO with the experimental values (Fig. 7b). The values outside this range are essentially correlated with strong underestimates in temperature; that is, the one peculiar experiment of M. J. Toplis discussed above, the results of Gardner et al. (1995b) and those of Prouteau & Scaillet (2003). In fact, the NNO values reported by Gardner et al. (1995b) were not measured but, instead, are estimates based on the model of Andersen & Lindsley (1988) combined with the projection scheme of Stormer (1983). In the experiments of Prouteau & Scaillet (2003) problems arose with the monitoring of the oxygen fugacity (B. W. Evans & B. Scaillet, personal communication) with Ni–Pd–NiO and Co–Pd–CoO solid-state sensors (Taylor et al., 1992; Pownceby & O’Neill, 1994). The large compositional heterogeneities of the titanomagnetites (see above) translate into large uncertainties in the modelled T–NNO values and may well explain the discrepancies with the experimental values (Table 7, Fig. 7).
In fact, the temperature estimates are sensitive to compositional variations of the Fe–Ti oxide phases. In the products of our crystallization experiments, for example, numerous single EMP analyses (up to 49; see Tables 5 and 7) show variations of the order of only a few per cent, which suggest a reasonable approach to equilibrium (2 6% for all oxide concentrations in Tmt and for X'usp; 2 3% for all oxide concentrations in Ilmss and for X'ilm; see Tables 5 and 7). With a Monte-Carlo simulation program that generates a hypothetical set of some hundred thousand data points of coexisting titanomagnetite and ilmenite compositions by varying a pair of analyses within their statistical mean error (program ‘Oxytemp’, Burchard, in preparation), we can show that such small compositional variations induce variations in the estimated temperatures of up to ±60°C. The effect on the NNO estimates is a maximum of ±0·3 log units (Fig. 9).
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APPLICATION TO NATURAL ASSEMBLAGES |
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The thermo-oxybarometer model developed here is designed only for assemblages of titanomagnetite and hemoilmenite (with the
space group) that equilibrated at temperatures above about 700–800°C and low to moderate oxygen fugacities. These conditions restrict the applicability essentially to basic and intermediate magmatic rocks and a few high-temperature metamorphic assemblages. We do not intend here to extensively compare estimates from our model with those of previous formulations. We shall discuss only a few examples from the studies of Fodor et al. (1989), Feeley & Davidson (1994), Gardner et al. (1995a) and Fodor & Galar (1997). As shown in Fig. 10a, temperature estimates with our model are in some cases very similar to the values obtained from previous models, but may also differ by as much as 90°C. The discrepancies are related both to the model employed previously and to the temperature range. High Mg or Cr contents in the Fe–Ti oxides may also play a role.
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One of the datasets represented in Fig. 10 is that of Fodor et al. (1989
) on Eocene Ti-rich basalts and diabases from the Abrolhos Platform, offshore Brazil. Using the formulation of Buddington & Lindsley (1964), Fodor et al. derived temperatures that spread between 650 and 990°C. Our calculations yield similar values, except for the lowest estimate of Fodor et al. (650°C) for a core sample of a diabase, which our model shifts to 736°C (Fig. 10a). This value compares better with the other diabase core sample (T 
700°C with both models).
The temperature values retrieved by Feeley & Davidson (1994) from Andean andesites and dacites using the model of Ghiorso & Sack (1991a) are, with one exception, significantly higher than those obtained from our model (Fig. 10a). This reflects the stronger curvature of our isotherms compared with those of Ghiorso & Sack (1991). Consequently, the Ghiorso & Sack model yields temperature overestimates for pairs with X'ilm/X'usp in the range 0·75–0·80/0·15–0·50 (Feeley & Davidson, 1994), but underestimates for pairs with higher X'ilm/X'usp (e.g. Toplis & Carroll, 1995; see Fig. 8). As for the oxygen fugacity estimates, they are not strongly dependent on the model used (Fig. 10b).
Gardner et al. (1995a) reported analyses of 16 representative Fe–Ti oxide pairs from dacitic pumice clasts of Mount St. Helens. Using the model of Andersen & Lindsley (1988) together with the projection of Stormer (1983), they obtained temperatures in the range 801–912°C and NNO values between 0·8 and 2·0 [recalculated from their original log fO2 values with the NNO buffer values of O’Neill & Pownceby (1993)]. Gardner et al. (1995a), however, noted in accordance with Geschwind & Rutherford (1992) that among their temperature estimates those correlated with high fO2 values are too high by about 30°C. In fact, in this T–fO2 range the formulation of Andersen & Lindsley (1988) is being (mis)-used outside its calibration range and yields temperature overestimates [see discussion by Lattard et al. (2005, p. 750)]. Our model lowers these specific T values by 30–40°C, but it also yields lower temperatures by 4–43°C for the other samples of Gardner et al. (1995a) (Fig. 10a). Our estimated NNO values are in very good agreement—within ±0·2 log units—with those of Gardner et al. (1995a). At NNO <1· 5 our estimates are practically identical to those of the previous model; at higher oxygen fugacities our values are slightly higher (Fig. 10b).
Curiously, Gardner et al. (1995a) chose to use the formulation of Andersen & Lindsley (1988) on Fe–Ti oxide compositions projected with the scheme of Stormer (1983), although this combination (the so-called ‘ALS calibration’, e.g. Geschwind & Rutherford, 1992) generally produces higher temperature values than the combination of the Andersen & Lindsley formulation with the projection scheme of the same workers [see examples given by Lattard et al. (2005, Fig. 10b)]. Indeed, recalculations with the correct combination [QUILF software of Andersen et al. (1993)] give temperatures that are 20–40°C lower than those proposed by Gardner et al. (1995a) and (with only two exceptions) within ±15°C of our estimates. In any case, arbitrary combinations of thermometer formulations and projection schemes, as listed in the ‘ILMAT’ Excel worksheet of Lepage (2003), are not recommended.
As a final example, we would like to address the 15 temperature values calculated by Fodor & Galar (1997) for gabbroic xenoliths from Mauna Kea volcano (Hawaii) with an unspecified Fe–Ti oxide model. Fodor & Galar obtained two slightly overlapping temperature ranges correlating with their sampling sites. Cone-A and cone-B xenoliths yield 704–823°C, cone C xenoliths 801–890°C. Our estimates are in most cases higher (only three exceptions), and the strongest differences appear for samples with Cr-rich titanomagnetites (up to 15·5 wt % Cr2O3) that contain also appreciable Mg and Al contents. As we have no experimental data on Cr-rich spinels, it remains unclear whether our temperature estimates are valid for them. Putting the two assemblages with Cr-rich spinels aside, our estimates give more distinct temperature ranges for the two sampling groups: 749–823°C for cones A and B, but 853–944°C for cone C. Our estimates are nearer the values obtained from clinopyroxene–orthopyroxene pairs (953–1087°C) using the geothermometer of Wells (1977).
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CONCLUDING REMARKS |
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The formulation of the titanomagnetite–ilmenite thermo-oxybarometer presented here is based on numerical fits of the temperature and oxygen fugacity dependence of the compositions of coexisting Tmt and Ilmss of nearly 200 experiments. We considered essentially experiments performed at temperatures in the range 800–1300°C that produced Fe–Ti oxide assemblages with Ilmss in the space group
. Consequently, our formulation of the Tmt–Ilmss thermo-oxybarometer should definitely not be used if the X'ilm value of the rhombohedral oxide is below that marking the transition between the and structures [see values given by Harrison et al. (2000)]. Misuse would yield strong temperature overestimates. It is difficult to decide about the accuracy of our formulation for assemblages equilibrated at temperatures below 800°C because there are only few experimental results in this temperature range and their run products only approached equilibrium. Our calculated isotherms partially match the experimental brackets of Lindsley (1962, 1963) and Spencer & Lindsley (1981) at 600 and 700°C (Fig. 3c), which indicates that our formulation yields at least reasonable approximations for these temperatures.
In the proper T–fO2 range, tests on independent experimental results have shown that our model reproduces the experimental temperatures within ±70°C, and in most cases within ±50°C. The estimates of the oxygen fugacity are mostly within ±0·4 log units. Compared with the models of Andersen & Lindsley (1988) and Ghiorso & Sack (1991a), which yield strong temperature underestimates for assemblages equilibrated at temperatures above 950°C under moderate to low fO2 values (NNO 0), our formulation performs much better (Fig. 8). This is not surprising because it relies on a strong experimental database and because the effects of minor elements are slight in this T–fO2 range. This makes our formulation especially reliable for estimates of magmatic T–fO2 conditions of rapidly cooled intermediate to basic igneous systems. Temperature and oxygen fugacity estimates from Fe–Ti oxides with high contents of additional elements (Al2O3, MgO, MnO, Cr2O3 > 
6 wt %) and for those that equilibrated at relatively low temperatures would be better gained from models involving elaborate solid solution models.
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SUPPLEMENTARY DATA |
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Supplementary data for this paper are available at Journal of Petrology online.
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APPENDIX |
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As Supplementary Data to accompany this paper (available for downloading at http://www.petrology.oxfordjournals.org) we provide an Excel file to calculate temperature and oxygen fugacity values from the compositions of coexisting pairs of titanomagnetite and ilmenitess using our numerical model. Most calculations are performed with the help of macros written in Visual Basic.
The file contains nine worksheets. The first worksheet, ‘Analyses’, can be used to enter the compositions of both phases in term of weight per cent of oxides. The structural formulae (based on stoichiometric titanomagnetite and ilmenitess, with three cations and four oxygens for Tmt, but two cations and three oxygens for Ilmss) are automatically calculated and listed together with the projected mole fractions X'usp and X'ilm in the same column. The user should enter a pressure value and an accuracy for the temperature calculation, which is performed via iteration nesting. The program yields the temperature, NNO and log fO2 values calculated from the X'usp and X'ilm values. The other worksheets allow the user to set up tables and diagrams involving calculated temperature, NNO, X'usp or X'ilm values. As an example, we show in Fig. A1 a plot of X'usp and X'ilm isopleths as a function of temperature and NNO.
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It should be stressed that all calculations are valid only with the projection schemes used in the first worksheet [see equation (4a) and (4b) in subsection ‘Thermometry’]. The users are urged not to use any other projection! The permissible temperature range has been fixed to 600–1400°C. The permissible range of ilmenite compositions is restricted to those in the
space group, which, according to Harrison et al. (2000), corresponds to X'ilm > 0·0006 T + 0·095 (with T in°C). |
ACKNOWLEDGEMENTS |
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This study was funded by the Deutsche Forschungsgemeinschaft (Grant LA-1164/4-2 and LA-1164/5-3 to D.L.). We thank Hans-Peter Meyer for maintenance of the SEM and EMP laboratories in Heidelberg and for help during the measurements, and Georg Partzsch for preparing the starting glass SC47-P. We gratefully acknowledge helpful discussions with Bernard Evans (Seattle) and the constructive reviews of Hugh O’Neill and Tracy Rushmer. Geoffrey Clarke is thanked for his careful editorial handling.
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FOOTNOTES |
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This contribution is dedicated to the memory of Eduard Woermann (1929–2008), Professor at the University of Aachen (Germany), who generously shared with us his profound knowledge on oxide minerals and redox phase relations. 
*Corresponding author. Telephone: +49 6221 544810. Fax: +49 6221 544805. E-mail: dlattard{at}min.uni-heidelberg.de
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