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Composition of the core, II. Effect of high pressure on solubility of FeO in molten iron
94
Earth and Planetary Science Letters, 71 (1984) 94-103 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
[2]
Composition of the core, II. Effect of high pressure on solubility of FeO in molten iron E. Ohtani, A.E. Ringwood and W. Hibberson Research School of Earth Sciences, Australian National University, Canberra, A.C.T. (,4 ustralia)
Received May 30, 1984 Revised version received August 19, 1984
An experimental and theoretical investigation of the effect of pressure on the solubility of FeO in molten iron has been carried out. Analyses of shock-wave compression data on iron oxides combined with measurements of the Fe-O bond length in "metallic" oxides suggest that the partial molar volume of FeO (V*) dissolved in molten iron is substantially smaller than that of molten wiistite. Hence the effect of high pressure should be to increase the solubility of FeO in molten iron at a given temperature. This inference is confirmed by an experimental investigationof the effect of pressure on the position of the Fe-FeO eutectic. Thermodynamic calculations based on these experiments yield an estimate for V* which is in reasonable agreement with the theoretical estimates. The experimental value of V* is used to calculate the effect of high pressure upon the Fe-FeO phase diagram. Solubility of FeO in molten iron increases sharply with pressure, the liquid immiscibility region contracts and disappears around 20 GPa and it is predicted that the Fe-FeO phase diagram should resemble a simple eutectic system above about 20 GPa. Analogous calculations predict that the solubility of FeO in molten iron in equilibrium with magnesiow~tite (Mg0 sFe0.2)O at 2500°C increase from 14 mol.% (P = 0) to above 25 mol.% at 20 GPa. If the core formed by segregation of metallic iron originally dispersed throughout the earth, it seems inevitable that it would dissolved large amounts of FeO, thereby accounting for the observation that the density of the outer core is substantially smaller than that of pure iron under corresponding P, T conditions.
1. Introduction I n a c o m p a n i o n paper [1] we d e m o n s t r a t e d that at a m b i e n t pressures, m o l t e n iron dissolves a b o u t 35 mol.% of F e O at 2500°C a n d that complete miscibility between Fe and F e O is p r o b a b l y achieved above 2800°C. It was inferred from this behaviour that oxygen is likely to be the principal light element in the core. Before this conclusion can be accepted, it is necessary to examine the effect of high pressure on the solubility of F e O in m o l t e n Fe a n d on the d i s t r i b u t i o n of F e O between crystalline magnesiow~stite a n d m o l t e n iron. The effect of pressure will d e p e n d strongly u p o n the partial m o l a r volume of the F e O c o m p o n e n t which dissolves in m o l t e n iron. If this is smaller t h a n the m o l a r volume of pure FeO, high pressure will 0012-821X/84/$03.00
c(c)1984 Elsevier Science Publishers B,V.
increase the solubility of FeO in iron at a given temperature. W h e n F e O dissolves in m o l t e n iron, it is believed to form a metallic solution as discussed in [2] a n d also subsequently in this paper. It is possible to consider the metallic F e - O solutions as mixtures of pure Fe a n d of a hypothetical F e O e n d - m e m b e r possessing metallic b o n d i n g [2]. F o r convenience in s u b s e q u e n t discussion, we will denote this hypothetical metallic e n d - m e m b e r as FeO*. This comp o n e n t m a y be either liquid FeO~ or crystalline FeO*. I n 1977, R i n g w o o d [2] presented evidence that the partial molar volume of FeO* dissolved in m o l t e n iron was substantially smaller than that of wiastite, FeO, a n d estimated the m a g n i t u d e of the v o l u m e difference. He then calculated the effect of
95 pressure on the solubility of FeO* in iron in equilibrium with magnesiowi~stite (Mg0.ssFe0.12)O at 2500"C and concluded that this would be greatly increased by high pressure. For example, the metal phase at a pressure of 30 GPa was estimated to contain 52 wt.% FeO*. The purpose of this paper is firstly to obtain improved estimates of the partial molar volume of FeO* in molten iron using additional theoretical and experimental data, and secondly to recalculate the effect of high pressure on the solubility of FeO* in molten iron using this new evidence.
2. Indirect evidence bearing on the molar volume of FeO*
The chemical bonds in wi~stite are believed to be largely ionic in nature. Its melting point increases normally with pressure, implying that the density of liquid is smaller than that of the solid [3]. Thus, the chemical bonding in molten wi~stite is probably also essentially ionic. Many non-metals such as B, C, N, Si, P and S dissolve in crystalline a n d / o r liquid iron, and also form crystalline semi-metallic compounds with iron. The chemical bonds between non-metals and iron in these solutions and compounds are usually metallic or covalent-metallic (semi-metallic). It seems likely that when oxygen dissolves in molten iron it will behave analogously and form covalent-metallic bonds. Since the change from ionic to covalentmetallic bonding is accompanied by a substantial shortening of the metal-non-metal bond length [4], it is to be expected that the partial molar volume (V*) of FeO* in solution in Fe will be substantially smaller than the molar volume of wi~stite (V). The study of crystalline oxides, carbides and nitrides provides considerable insight into the chemical and physical principles involved. Carbon and nitrogen form extensive solid solutions in y-iron, in which the C and N atoms occupy interstitial sites in the close-packed metallic iron lattice because of their small sizes (atomic radii 0.77 and 0.70 A respectively [4]). These elements also form a series of metallic carbides and nitrides, e.g. Fe3C, Fe4N. The electronegativity of oxygen is greater
than those of C and N, hence it has a stronger tendency to form ionic bonds, as in wi~stite. However metallic oxide phases isostructural with corresponding metallic carbides and nitrides do exist (e.g. [5,6]). Of particular importance is a series of intermetallic compounds ABO where A = Mo, W and Re and B = Fe, Co, Ti, V, Cr, Mn [5]. In these compounds, the A and B atoms form a hexagonal close-packed lattice in which oxygen atoms are situated in the octahedral interstices. The F e - O bond length in these metallic compounds is 1.92 A, compared to 2.16 A for the F e - O bond length in wi~stite. This illustrates the rather spectacular decrease in bond length as the F e - O bond changes from ionic to covalent-metallic. The atomic radius of oxygen in these compounds is only 0.60 A [5]. If the F e - O bond length in wi~stite were reduced to 1.92 .~, its density would be 8.36 g / c m 3, as compared to 5.87 g / c m 3 for stoichiometric wi~stite. It seems likely that when oxygen dissolves in molten iron it would also enter interstitial positions, occupying "holes" in the disordered liquid structure. Accordingly, it can be expected that V* will be substantially smaller than F. When subjected to shock compression, magnetite (Fe304) with a density of 5.20 g / c m 3, and hematite (Fe203) with a density of 5.27 g / c m 3 transform to much denser phases possessing estimated zero pressure densities of 6.4 and 6.1 g / c m 3 [7]. Jackson and Ringwood [8] pointed out that these densities were too high to be caused by a lattice rearrangement of Fe 2+ and O a- ions, but implied, instead, a shortening of the F e - O bond length as would occur if the bond type changed from ionic to covalent-metallic. The observation of metallic electrical conductivity in the high-pressure form of Fe203 at 160 GPa [9] confirms this interpretation for hematite. Ringwood [2] predicted that wi~stite would also transform to a dense covalent-metallic phase at high pressures. Subsequent shock-wave compression studies on wiastite by Jeanloz and Ahrens [10] revealed a phase transformation near 70 GPa. The data are not sufficient to permit an unambiguous calculation of the density of the high-pressure phase. Jackson and Ringwood [8] showed that if the three highest-pressure measurements on the shock Hugoniot are considered, the density of the high-pressure phase is about
96
7.25 g / c m 3. However, if a fourth measurement at lower pressures is included, the density of the high-pressure phase falls to 6.7 g / c m 3. The former interpretation is preferred since the lowest pressure point may represent a state of incomplete transformation to the high-pressure phase. This interpretation is also favoured by the shock compression data on Fe203 and Fe304. If the Fe and O atoms were packed as densely as in the highpressure forms of Fe203 and Fe304, the density of high-pressure FeO* would be 7.1 g / c m 3, in good agreement with the higher of the two estimates by Jackson and Ringwood. It was suggested by these authors and also by Navrotsky and Davies [11] that the high-pressure phase of FeO* may be semi-metallic, with a crystal structure related to that of nickel arsenide. Liquids of this family of phases are usually completely miscible with those of the metallic end-member, e.g. Fe-FeS. Ringwood [2] suggested that the density dif-
ference between pure liquid wi~stite (FeOl) and the metallic FeO~ component which dissolves in molten iron is likely to be comparable to the density difference between crystalline wOstite and the high-pressure phase of wi~stite (FeO*) which was believed to be semi-metallic, on the basis of the evidence reviewed here. Alternatively, this density difference can be estimated from the difference in F e - O bond lengths as observed in crystalline wiistite and in ternary metallic oxides of the type MFeO where M = Mo, W or Re. Estimates of the densities and molar volumes of wi~stite and its high-pressure phase obtained by these approaches are given in Table 1. The estimated differences in molar volumes between those of normal wi~stite and the high-pressure phase FeO* are seen to cover a wide range, from 1.45 to 3.65 cm 3. Clearly, it would be desirable to determine the difference in molar volume AVl between FeOj and FeO~' by a more direct experimental procedure.
TABLE 1
3. Experimental
Zero-pressure densities and molar volumes of the high-pressure phase of FeO~¢) (and of wi~stite) obtained by several different methods Method
Density Molar volume AVc ~ (g/cm 3) V(cm 3) (cm3)
Hrftstite
Calculations based on extrapolation of lattice parameters of FexO
5.865 b
12.25
-
High - pressure phase of FeO*
Calculated from Fe-O bond length in metallic MFeO phases (1.92 ,~) Assume similar Fe-O atomic packing densities as in high pressure phases of Fe203 and Fe304 Extrapolation of shock compression data on high pressure phase of FeO (upper bound to density) Extrapolation of shock compression data on high pressure phase of FeO (lower bound to density)
8.36
8.60
3.65
7.1
10.12
2.05
7.25
9.91
2.26
6.7
10.72
1.45
AV~ ~ V(c)(wiastite) - V(*)(high-pressure FeO). b Hentschei [25].
An estimate of AV can be obtained from experimental measurements of the effect of pressure on the eutectic temperature in the system Fe-FeO. Relevant phase relationships at atmospheric pressure are well established [12,17] and are shown in Fig. 1. The temperature of the eutectic between molten iron and molten FeO occurs at 1523°C. The effect of pressure on the melting point of iron has been studied by Sterrett et al. [13] and by Boyd and England [14]. The former authors obtain an accurate melting point gradient of 28.5 o C / G P a . (Note that the absolute melting temperatures of iron in all of their experiments are slightly low, probably because of solution of some boron from the borosilicate glass (pyrex) in which their iron samples were suspended.) This gradient is in good agreement with the gradient of 2 7 . 5 ° C / G P a measured by Boyd and England [14] when the latter result is corrected for the effects of friction in their apparatus. The above investigations did not include corrections for the effects of pressure on thermocouple EMF's. Experiments to determine the eutectic temperatures at high pressures in the system F e - F e O were
97 1700 I I I
Fe-FeO*LiC,JO
TUBE
I I I
I
1650
THERMOCOL Fe-FeO*LIQUR)
I I
÷
I
FeO LJQLJE)
ALUMINA M~
"ER
I I I I
< 1600
I
1585°C
w
.q~m
PYROPHYLLITE iRON NITRIDE
3GPa
PUREIROt
m mu
1.73
0.82
[ GLASS
Fig. 2. High-pressure heating cell used in present experiments.
W
1550 1534
1
1523oc 5 Fe
0
0
I atm
~Fe (C), 0 FeO(L) " 6 1.0
2.0
2 3.0
F e O tool p e r c e n t Fig. 1. Iron-rich portion of the F e - F e O phase diagram at 1 atmosphere [12,17], and at 3 GPa. Phase relationships at 3 GPa are based on the present experiments.
carried out in a piston-cylinder apparatus using quenching techniques and differential thermal analysis. The pressure cell used in the former experiments is shown in Fig. 2. Molybdenum heaters were used to avoid the possibility of carbon contamination. All components of the pressure cell (except for the outermost talc sleeves) were carefully dried by calcination to eliminate the possibility of contamination of the sample by water or hydrogen. In addition, a separate set of runs was carried out at 4 GPa in which most of the magnesia inserts (Fig. 2) were replaced by fired pyrophyllite. To facilite comparison with the results of Sterrett et al. [13], corrections were not applied for the effect of pressure on thermocouple EMF's in our experiments. In the quenching experiments, the sample consisted of a 350-mg capsule of spec-pure iron containing about 40 mg of FeO. The capsule was closed with a tightly-fitting lid of spec-pure iron. Pressure was applied using the "piston-in" method, and a correction of minus 10% was made to total
pressure to allow for friction. In a typical run, full pressure was first applied. Temperature was then increased to 1000-1200°C and held for 5 minutes to allow the cell to densify and stabilize. Temperature was then increased to the desired value for the particular run and held constant for 5 minutes. After completion of the runs, the samples were quenched by terminating the power. Samples were then removed from the cell, polished, and examined by optical microscopy. In samples which had not melted, the sample of wbstite retained its original shape and remained fully enclosed within the iron capsule, which also displayed its original sharp cylindrical morphology. In samples which had melted, the wbstite migrated through the iron to form a black layer of FeO surrounding the exterior of the capsule. Negligible amounts of FeO remained included in the iron, which usually displayed rounded contours. In a few runs carried out close to the melting curve, one end or side of the capsule appeared to have melted, and displayed an external sheath of FeO over a rounded surface of iron whereas the other end or side of the iron capsule retained sharp contours and did not possess an FeO sheath. These are believed to represent partly melted runs arising from the presence of small temperature gradients across the sample. Results from these experiments are depicted in Fig. 3. A second set of experiments at 4 GPa in which most of the magnesia inserts of Fig. 3 were replaced by fired pyrophillite, showed identical textural relationships. It is seen from Fig. 3 that the increase of melting point of the F e - F e O eutectic with pressure is well defined by a straight
98
•
DTA Runs
• +} Quenching
X
X Runs
×
~/
16
oo Fe melting point dT m / d P ~ 2 8 . 5 °C/GPa
UJ rr ~.
/
• •/
16oo
UJ
O.
:E UJ Fe-FeOf eutectic d T e / d P ~ 2 0 . 5 °C/GPa
155o 1534
1500 t-
1
2
3
PRESSURE
4
5
GPa
Fig. 3. Lower line shows eutectic temperature of Fe-FeO system versus pressure determined by differential thermal analysis (solid circles) and by quenching techniques (squares). Open squares depict sub-solidus runs; solid squares depict melting. Half-filled squares show runs in which part of the charge is believed to have melted whilst another part appeared unmelted. The broken line depicts the melting of wi~stite contained in solid iron capsules, as determined by Lindsley [3]. The melting pointof pure iron versus pressure is shown in the upper line and is based upon the melting point gradient of 28.5°C/GPa determined by Sterrett et al. [13]. The melting point of iron at 4 GPa was also located in the present study using quenching experiments, depicted by crossed symbols.
The melting temperatures of the F e - F e O eutectic at pressures of 3 and 4 G P a were also determined by differential thermal analysis using the techniques described by Cohen et al. [15]. The sample consisted of a 350-mg capsule of spec-pure iron containing about 40 mg of FeO. The capsule was closed with a tightly-fitting lid of spec-pure iron. After mechanical and thermal stabilization of the pressure cell at full pressure and 1000°C, temperature was increased at 1 5 0 ° C / m i n u t e and the outputs from two closely spaced thermocouples [15] were displayed on an X-t recorder. The onset of melting was recorded by sharp D T A signals, as shown in Fig. 4. Eutectic temperatures determined by this technique are shown as solid circles in Fig. 3. They agree closely with the results obtained by the quenching technique. There are actually two separate D T A signals which can be generated during melting in the F e - F e O system. One can be caused by melting of wiastite in the iron container and the other arises from melting at the eutectic between iron and FeO. At pressures below about 3.3 GPa, FeO melts at a lower temperature than the F e - F e O eutectic. This creates the potential for confusion between the two D T A signals. To avoid this, the mass of FeO in the capsule was limited to a small proportion of the mass of metallic iron ( < 10%). The signal due to melting of FeO is thus smeared out by the thermal inertia of the surrounding metal and is too small to record. The major D T A signal observed (Fig. 4) records the eutectic close to metallic iron, where the entire capsule melts.
U o
line with a slope dTe/dP of 2 0 . 5 ° C / G P a . The variation of melting point with pressure of pure wbstite contained in iron capsules has been determined below the F e - F e O eutectic temperature by Lindsley [3]. His results are depicted as a broken line in Fig. 3. The curves intersect at a pressure of 3.3 G P a and a temperature of 1590°C. Theoretically, there should be an inflexion of the F e - F e O eutectic melting curve at this point, but this could not be resolved within the uncertainty limits of our experiments.
[5o IV
r
i
Fig. 4. Example of DTA signal showing melting of Fe-FeO mixture at 4 GPa beginning at 1605°C.
99 The melting curve of pure iron based upon its zero-pressure melting point of 1534°C [12] and the gradient of 28.5°C/GPa, carefully determined by Sterrett et al. [13], is also shown in Fig. 3. These results yield a melting point of 1648°C at 4 GPa. We have determined the melting point of pure iron at 4 GPa by a quenching method to check the consistency of our techniques with those employed by Sterrett et al. Chips of alumina were placed within a cylinder of pure iron, close to the base. Runs were carried out at 10 ° intervals between 1620 and 1670°C. Temperatures were measured using Pt-Pt 10% Rh and W5%Re-W25%Re thermocouples carried in 4-hole alundum tubing. (The additional W-Re thermocouple was employed because of contamination of Pt-Rh thermocouples which occurred in some runs.) In runs at 1620 and 1630°C, the alumina remained in position, whereas at 1660 and 1670°C the alumina floated to the top of the iron slug, immediately beneath the thermocouple. Iron in the former runs was evidently unmelted whereas the latter two had clearly melted. In two runs at 1640°C and in one run at 1650°C, the alumina rose to a level about 1 mm below the top of the iron. It appears that there was a temperature gradient within the sample caused by the relatively high conductivity of the thermocouple wire and its sheath. Hence the portion of the iron closest to the thermocouple was slightly cooler and apparently unmelted, preventing the chips from rising to the top. In a second run at 1650°C, chips did rise to the top of the iron sample. On the basis of these experiments, the melting temperature of iron as recorded by the thermocouples at the top of the iron capsule was taken at 1650 ___10°C. This result agrees well with the DTA measurement (Fig. 4) and with the results of Sterrett et al. [13].
4. Results
It is shown below that, to the first order, pressures of a few GPa do not significantly affect the relationship between depression of the melting point of iron and the quantity of dissolved FeO*. Thus, the slope of the liquidus joining the Fe melting point and the Fe-FeO~ eutectic at 3 GPa
will be similar to that at atmospheric pressure (Fig. 1). At 3 GPa, we located the F e - F e O eutectic at 1585°C whereas the melting point of pure iron at this pressure is 1620°C. These results, as shown in Fig. 1, demonstrate that the effect of high pressure is to increase the solubility of FeO* in Fe and that the partial molar volume V* of FeO* dissoloed in molten iron is smaller than that of molten w~4stite. This observation qualitatively confirms the conclusions reached earlier. The experimental measurements on the effect of pressure on the F e - F e O * eutectic can be used to obtain a quantitative estimate of the partial molar volume V* of FeO* in molten iron. The enthalpy change on melting of iron is 13,807 J / m o l [16], which yields an entropy change on melting (ASm) of 7.641 J / K mol. The effects of limited variations of pressure and temperature on AS m are relatively small and of opposite sign. Hence we can assume that ASm is approximately constant within the experimental range of pressures and temperatures. Raoult's Law implies that the activity coefficient of iron (~re) along the Fe solvus between p u r e Fe and the Fe-FeO~ eutectic is very close t o unity. (Note, however, that ~Feo on the FeO side of the eutectic is greater than unity owing to non-ideality of the system in this region.) Assuming that Yre 1.0, and ignoring the small pressure and temperature effects on ASm, the iron content at the eutectic temperature (1585°C) can be determined by applying the Van't Hoff equation for the depression of melting point of crystalline phases by solutes. The iron content at the eutectic (3 GPa and 1585°C) is thus found to be 98.27 mol.% (1.73 mol.% FeO*). If the observed slope for depression of melting point of Fe by FeO at atmospheric pressure (Fig. 1) had been assumed to be applicable at 3 GPa, the eutectic composition would have been similar at 2.0 mol.% FeO*. At 1585°C and one atmosphere, the solubility of FeO* is 0.82 mol.% [17]. At a given temperature T and pressure P, the free energy difference AG °, between liquid iron oxide and the FeO~ component of the liquid (Fe-FeO*) solution is given by: AG ° - PAV~ = R T In a l / a 2
(1)
where al is activity of FeO in the liquid iron oxide referred to pure liquid FeO as the standard state,
100 a 2 is the activity of FeO~ in molten iron and AV~ is the difference between the molar volume V1 of molten wiastite and the partial molar volume of FeO~' (V*). Since the composition of the iron oxide liquid is very close to that of pure wi~stite (Fig. 5), al can be taken as unity. Accordingly: AG ° - PAV] = - R r l n
a 2 = -RTln
YF¢oNzp
(2)
where N~ is the mole fraction of FeO~' dissolved in molten iron at pressure P and YF~ is the activity coefficient of the F e O t component. AG ° is related to the observed solubility N2° of FeO* in molten iron at temperature T and at atmospheric pressure by the expression: AG ° = - R T In ]tFeoN2°
(3)
In view of the small solubility range displayed by FeO* and the limited range of pressure conditions, it is reasonable to assume that the activity coefficient YFeO of FeO~ in molten iron is independent of pressure and of FeO~' content. Substituting (3) in (2) we have: PzXV, = R T In N z e / U ~
(4)
This equation may be solved for AVj using the experimentally determined values of P, T, N°2 and NzP. In this manner, AVI is found to be 3.8 cma/mol. This experimental value of AVI may be com-
Metal|lc(Fe-FeO ) liquid
1a t m ~
oo
.V? 2--0 cm3/mol
m~250(
\~ I
pared with estimates of the corresponding volume difference AVe between the high-pressure (covalent-metallic) polymorph of FeO* and crystalline wiastite FeO c, given in Table 1. It is seen to be very close to the corresponding A ~ value of 3.65 cm 3 calculated from the respective ionic bond lengths in wi~stite and the metallic F e - O bond lengths in M F e O compounds. This strongly suggests that oxygen occupies interstitial sites (holes) in molten iron and forms metallic F e - O bonds, as in the crystalline family of M F e O interstitial phases. Our experimental value of AVI (3.8 cm3/mol) is substantially higher than the preferred values of AV1 (2.05 and 2.26 cm3/mol) estimated from shockwave data (Table 1). This may reflect the fact that the shock wave data apply to phases possessing O / F e ratios greater than or equal to unity. The high-pressure phases of these oxides would be unable to accommodate all of their oxygen atoms in interstitial sites. A large proportion of the oxygens would occupy regular lattice sites, leading to a decrease in the packing density. These considerations suggest that AVI values in Fe-FeO* melts may decrease with increasing oxygen content. At relatively low FeO~ content, (e.g. O / F e < 0.5) the oxygen atoms mainly enter interstitial sites (holes) in the liquid. As the FeO* content increases, the available "holes" may become saturated and further solution may cause V~' to increase and AVj to decrease. The AVe values obtained from shock compression data may thus be indicative of AVI values appropriate to F e - O melts containing high oxygen contents ( O / F e >/1).
5. Effect of pressure on solubility of FeO* in Fe ,,X,200c F-
/ /
~
f /// /
'
u,o,d,~,.~,.,.,o.lo. (Fe-FeO~IL + FeO ILl
2'0
4'0
4o
FeO tool
go
1oo
%
Fig. 5. Calculated solubilities of FeO* in molten iron at l0 GPa based upon AVI values of 3.8 cm3/mol as determined in the present experiments(solid curve) and an arbitrary value of 2.0 cm3/mol (broken curve) representing a probable lower limit. The solubility of FeO* at ambient pressure [1] is also shown.
Calculations of the effect of a pressure of 10 G P a on the solubility of FeO* in molten iron have been carried out using the thermodynamic relationships described previously and the experimentally determined value of AVt (3.8 cm3). Results are shown in Fig. 5. A second set of calculations was carried out for an arbitrary value of AVj = 2.0 cm 3. This probably represents a conservative lower limit to AVI, allowing for the effects of differential compressibilities of molten wiastite and ( F e - F e O * )
101
liquid, and change of AVl with oxygen content, as discussed earlier. It is seen from Fig. 5 that, at constant temperature, high pressure causes the solubility of FeO* in Fe to increase in a rather spectacular manner. For example, at 2000°C, the solubility of FeO* in Fe is about 5 mol.% at atmospheric pressure. At 10 GPa, solubilities are increased to 14 and 40 mol.% FeO for AVI values of 2.0 and 3.8 cm3/mol respectively. High pressure also reduces the temperatures needed to achieve a given solubility of FeO* in Fe. For example, at atmospheric pressure, a solubility of 50 mol.% FeO* is reached at about 2650°C. At 10 GPa, this solubility is reached at 2340°C and 2060°C for AVj values of 2.0 and 3.8 cm 3 respectively. The effects of pressures up to 30 GPa on the F e - F e O phase diagram are shown schematically in Fig. 6. The calculations are based on the value of AVI 3.8 c m 3 determined earlier in this paper. The effects of pressure on the melting points of pure Fe and FeO are based on experimental measurements [3,13]. It is seen that the extent of the liquid immiscibility gap is reduced by high pressure. This effect is enhanced by the increase in melting temperatures of Fe and FeO with pressure, which cause the eutectic compositions to move inwards, away from these end-members [18]. It is estimated that the miscibility gap will disappear around 20 GPa, above which the F e - F e O system would resemble a simple eutectic, as in the F e - F e S system (see also Usselman [19]). As previously noted, it is possible that the effective value of AV] may be substantially smaller than the experimentally determined value of 3.8 cm 3. To a first approximation, this would cause a proportional increase in the pressures shown in Fig. 6. However, the essential features of the phase diagrams should remain intact. Finally, we consider the effect of pressure on the solubility of FeO* in iron in equilibrium with magnesiowiastite. The molar volume of molten wiastite can be estimated from Clapeyron-Clausius equation, dT/ dP A V m / A S m. The melting point gradient of whstite has been determined by Lindsley [3] whilst the entropy of melting is available from JANAF [20]. Thus, the volume change (AVm) on melting of FeO is found to be 1.3 cm3/mol. As =
=
3000
L1 L1
200G
i
Fe U O
3000
,
i
L2
Fe÷L2 , , ,
t
rl+
,
,
, FeO
LI+L2
i
L
i
Fe+FeO L i i
i
,
Fe
10 GPa
i FeO
15GPa
UJ nL1 re MJ
2000
2
~L2f
F 1e
¢
Fe.LI
L
L2]
~
i
O.
,
IIJ p-
~
, 7+LFeiO,
Fe
,
,
]
FeO
Fe+F.O . . . . . . Fe
5
0
0
,
, FeO
30 GPa
3s°°I 20 GPaL1 2
j
~
Fe*L1 Fe
20
40
60
' 8~0 F e O
Fe'
Fe*FoO 2'0 ' 4'0 ' 6'0 ' 8'0 ' F I O
COMPOSITION,mol % FeO
Fig. 6. Schematic diagrams depicting phase relationships in the F e - F e O system at pressures up to 30 GPa. The liquid immiscibility field is expected to disappear at pressures around 20 GPa.
the partial molar volume V~ of FeO in magnesiowiastite is essentially equal to that of wiastite, the effective value AVe_l (equivalent to V c - ~'~J) is 2.5 cm3/mol, based upon the value of 3.8 cm3/mol for AVl obtained from Fig. 1. For a probable "minimum" estimate of 2.0 cm3/mol for AVl, the value of AVe.1 would be 0.7 cm3/mol. Results of calculations using these values and the thermodynamic relationships described earlier are shown in Fig. 7. At 2500°C, and at atmospheric pressure, the solubility of FeO* in Fe in equilibrium with (Mg0.sFe0.2)O is 14 mol.% [1]. At this temperature for AV~.~= 2.5 cm 3, solubilities increase to 24 and 41 mol.% at pressures of 5 and 10 GPa respectively. For the assumed minimum value of AV~.1= 0.7 cm3, solubilities increase less rapidly with pressure, reaching 19 tool.% FeO* at 10 GPa and 25 mol.% FeO* at 20 GPa.
102
A
40
O E
°2500°C~-~: 2.5cm3/mol
C 4~ o
c 4)
3o
o E
.E
20
"O
@
>
O O (D
aVc-(: 0 . 7 cm3/mol 10
"O
*0
@ 0
10 PRESSURE
15
20
GPa
Fig. 7. The solubility of FeO* in molten iron in equilibrium with magnesiow~stite(Mg0.8Fe0.2)O calculatedas a functionof pressure at 2500°C. Valuesfor AVe.l ( - Vc- V~')of 2.5 cm3/mol and 0.7 cm3/mol were used in these calculations.
6. Composition of the earth's core
If the lower mantle has a similar bulk composition to the pyrolite model composition of the upper mantle, it would contain silicate perovskite and magnesiowi~stite as important phases. Experiments on the partition of FeO between these phases [21] imply that the magnesiowi)stite phase in the lower mantle would possess a composition close to (Mg0.sFeo.2)O. Most current estimates of the temperature near the core-mantle boundary lie between 2800 and 3700°C [22]. The results discussed in Part I show that at 2800°C, iron in equilibrium with (Mgo.8Feo.2)O would dissolve 40 mol.% FeO* [1] and that the solubility of FeO* rises still further with increasing temperature. Thus, considering only the effect of temperature, it follows that if the outer core formed by a process which permitted equilibrium with the lower mantle, it should contain at least 40 mol.% FeO*. High pressures present in the earth's interior have two distinct effects upon the distribution of
FeO between silicate oxide phases and metallic iron. McCammon et al. [18] showed that the highpressure phase (FeO*) formed under shock compression [10] would be exsolved from magnesiowi~stite at pressures exceeding 70 GPa, deep in the earth's interior. This phase is expected to dissolve in molten iron forming a simple eutectic system [18]. McCammon et al. developed a model of core formation based upon these phase relationships. The model was characterised by formation and segregation of F e - F e O * liquid alloys only at considerable depths, exceeding those corresponding to a pressure of 70 GPa. The results described in the present paper and in the companion paper [1] imply that solution of large amounts of FeO* in molten iron could occur at much smaller pressures than were considered by McCammon et al. [18]. We have described evidence that the partial molar volume V* of FeO* dissolved in molten iron is substantially smaller than that of the partial molar volume of FeO c in magnesiowi~stite. Accordingly, high pressures enhance the solubility of FeO* in iron. The magnitude of this effect is large, even for comparatively modest pressures in the vicinity of 20 GPa. Thus, if the core formed by segregation of metal originally dispersed throughout the earth, it seems inevitable that it would dissolve large amounts of FeO. Comparison of shock Hugoniots for pure Fe and FeO [10], indicate that the observed density of the outer core would be explained if it contained about 40 mol.% FeO* [10]. FeO contents of this order are readily explained by the experimental results described in this paper. These conclusions would remain valid even if the lower mantle consisted essentially of perovskite-type phases and contained only a small amount of magnesiowi~stite, as proposed, for example, by Anderson et al. [23]. In these models, density and elasticity constraints require the lower mantle to possess F e O / ( F e O + MgO) molar ratios greater than 0.05 [24]. The FeO would be accommodated principally in (Mg,Fe)SiO 3 perovskite. High-pressure partition experiments [21] demonstrate that magnesiowi~stite of composition (Mg0.sFe0.2)O would be in equilibrium with perovskite (Mg0.97Fe0.03)SiO 3. If the iron content of perovskite were increased, for example to
103 ( M g o . 9 5 F e o 0 5 ) S i O 3, t h e a c t i v i t y o f F e O w o u l d i n c r e a s e s u b s t a n t i a l l y as c o m p a r e d t o its a c t i v i t y i n (Mgo.sFeo.2)O. This would be accompanied by a corresponding increase in the solubility of FeO* in molten iron.
Acknowledgements T h e a u t h o r s a r e i n d e b t e d t o D r . H. O ' N e i l l , D r . I. J a c k s o n a n d D r . A. N a v r o t s k y f o r t h e b e n e f i t s of helpful comments and constructive criticisms.
References 1 E. Ohtani and A.E. Ringwood, Composition of the core, I. Solubility of oxygen in molten iron at high temperatures, Earth Planet. Sci. Lett. 71, 85-93, 1984 (this issue). 2 A.E. Ringwood, Composition of the the core and implications for the origin of the earth, Geochem. J. 11, 111-135, 1977. 3 D.H. Lindsley, Pressure-temperature relations in the system FeO-SiO2, Carnegie Inst. Washington Yearb. 65, 226-230, 1966. 4 L. Pauling, The Nature of the Chemical Bond, 3rd ed., 450 pp., Cornell, Ithaca, N.Y., 1948. 5 N. Sch6nberg, On the existence of metallic ternary oxides Me'Me"O with metal atoms in hexagonal close-packing, Acta Chem. Scand. 8, 630-632, 1954. 6 N. Sch6nberg, On the existence of ternary transition metal oxides, Acta Chem. Scand. 8, 932-936, 1954. 7 G.F. Davies and E. Gaffney, Identification of phases of rocks and minerals from Hugoniot data, Geophys. J.R. Astron. Soc. 33, 165-183, 1973. 8 I. Jackson and A.E. Ringwood, High pressure polymorphism of the iron oxides, Geophys. J.R. Astron. Soc. 64, 767-783, 1981. 9 S. Endo and K. Ito, Electrical resistance of aFe203 under ultrahigh static pressure, Solid State Commun. 36, 189-190, 1980. 10 R. Jeanloz and T.J. Ahrens, Equation of state of FeO and CaO, Geophys. J.R. Astron. Soc. 62, 505-528, 1980. 11 A. Navrotsky and P.C. Davies, Cesium chloride vs. nickel arsenide as possible structures for (Mg,Fe)O in the lower mantle, J. Geophys. Res. 86, 3689-3694, 1981.
12 L.S. Darken and R.W. Gurry, The system iron-oxygen, II. Equilibrium and thermodynamics of liquid oxide and other phases, J. Am. Chem. Soc. 68, 798-816, 1946. 13 K.F. Sterrett, W. Klement, Jr. and G.C. Kennedy, Effect of pressure on the melting of iron, J. Geophys. Res. 70, 1978-1984, 1965. 14 F.R. Boyd and J.L. England, The melting of iron at high pressures, Carnegie Inst. Washington Yearb. 62, 134-137, 1963. 15 L.H. Cohen, K. Klement, Jr. and G.C. Kennedy, Melting of copper, silver and gold at high pressures, Phys. Rev. 145, 519-525, 1966. 16 R.A. Robie, B.S. Hemingway and J.R. Fischer, Thermodynamic properties of minerals and related substances at 298.15 K and one bar (105 pascais) pressure and at high temperatures, U.S. Geol. Surv. Bull. 1259, 456 pp., 1978. 17 A. Fischer and J.F. Schumacher, Die S~ittingungslbslichkeit von Reineisen an Saurstoff vom Schmelzpunkt bis 2046°C ermittelt mit dem Schwebeschmelzverfahren, Arch. Eisenhuttenwes. 49, 431-435, 1978. 18 C.A. McCammon, A.E. Ringwood and I. Jackson, Thermodynamics of the system Fe-FeO-MgO at high pressure and temperature and a model for formation of the Earth's core, Geophys. J.R. Astron. Soc. 72, 577-595, 1983. 19 T.M. Usselman, Experimental Approach to the state of the core, I. The liquidus relations of the Fe-rich portion of Fe-Ni-S system from 30 to 100 kbar, Am. J. Sci. 275, 278-290, 1975. 20 JANAF, Thermochemical Tables, 2nd ed., 1141 pp., NSRDS-NBS37, Washington, D.C., 1971. 21 E. Ito, E. Takahashi and Y. Matsui, The mineralogy and chemistry of the lower mantle: An implication of the ultrahigh-pressure phase relations in the system MgO-FeO-SiO2, Earth Planet. Sci. Lett. 67, 238-248, 1984. 22 O.L. Anderson. The Earth's core and the phase diagram of iron, Philos. Trans. R. Soc. London, Ser. A 306, 21-35, 1982. 23 D.L. Anderson, C. Sammis and T. Jordan, Composition and evolution of the mantle and core, Science 171, 1103-1113, 1971. 24 I. Jackson, Some geophysical constraints on the chemical composition of the Earth's lower mantle, Earth Planet. Sci. Lett. 62, 91-103, 1983. 25 B. Hentschel, Stoichiometric FeO as metastable intermediate of the decomposition of wiistite at 225°C, Z. Naturforsch. 25a, 1996-1997, 1970.
Earth and Planetary Science Letters, 71 (1984) 94-103 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
[2]
Composition of the core, II. Effect of high pressure on solubility of FeO in molten iron E. Ohtani, A.E. Ringwood and W. Hibberson Research School of Earth Sciences, Australian National University, Canberra, A.C.T. (,4 ustralia)
Received May 30, 1984 Revised version received August 19, 1984
An experimental and theoretical investigation of the effect of pressure on the solubility of FeO in molten iron has been carried out. Analyses of shock-wave compression data on iron oxides combined with measurements of the Fe-O bond length in "metallic" oxides suggest that the partial molar volume of FeO (V*) dissolved in molten iron is substantially smaller than that of molten wiistite. Hence the effect of high pressure should be to increase the solubility of FeO in molten iron at a given temperature. This inference is confirmed by an experimental investigationof the effect of pressure on the position of the Fe-FeO eutectic. Thermodynamic calculations based on these experiments yield an estimate for V* which is in reasonable agreement with the theoretical estimates. The experimental value of V* is used to calculate the effect of high pressure upon the Fe-FeO phase diagram. Solubility of FeO in molten iron increases sharply with pressure, the liquid immiscibility region contracts and disappears around 20 GPa and it is predicted that the Fe-FeO phase diagram should resemble a simple eutectic system above about 20 GPa. Analogous calculations predict that the solubility of FeO in molten iron in equilibrium with magnesiow~tite (Mg0 sFe0.2)O at 2500°C increase from 14 mol.% (P = 0) to above 25 mol.% at 20 GPa. If the core formed by segregation of metallic iron originally dispersed throughout the earth, it seems inevitable that it would dissolved large amounts of FeO, thereby accounting for the observation that the density of the outer core is substantially smaller than that of pure iron under corresponding P, T conditions.
1. Introduction I n a c o m p a n i o n paper [1] we d e m o n s t r a t e d that at a m b i e n t pressures, m o l t e n iron dissolves a b o u t 35 mol.% of F e O at 2500°C a n d that complete miscibility between Fe and F e O is p r o b a b l y achieved above 2800°C. It was inferred from this behaviour that oxygen is likely to be the principal light element in the core. Before this conclusion can be accepted, it is necessary to examine the effect of high pressure on the solubility of F e O in m o l t e n Fe a n d on the d i s t r i b u t i o n of F e O between crystalline magnesiow~stite a n d m o l t e n iron. The effect of pressure will d e p e n d strongly u p o n the partial m o l a r volume of the F e O c o m p o n e n t which dissolves in m o l t e n iron. If this is smaller t h a n the m o l a r volume of pure FeO, high pressure will 0012-821X/84/$03.00
c(c)1984 Elsevier Science Publishers B,V.
increase the solubility of FeO in iron at a given temperature. W h e n F e O dissolves in m o l t e n iron, it is believed to form a metallic solution as discussed in [2] a n d also subsequently in this paper. It is possible to consider the metallic F e - O solutions as mixtures of pure Fe a n d of a hypothetical F e O e n d - m e m b e r possessing metallic b o n d i n g [2]. F o r convenience in s u b s e q u e n t discussion, we will denote this hypothetical metallic e n d - m e m b e r as FeO*. This comp o n e n t m a y be either liquid FeO~ or crystalline FeO*. I n 1977, R i n g w o o d [2] presented evidence that the partial molar volume of FeO* dissolved in m o l t e n iron was substantially smaller than that of wiastite, FeO, a n d estimated the m a g n i t u d e of the v o l u m e difference. He then calculated the effect of
95 pressure on the solubility of FeO* in iron in equilibrium with magnesiowi~stite (Mg0.ssFe0.12)O at 2500"C and concluded that this would be greatly increased by high pressure. For example, the metal phase at a pressure of 30 GPa was estimated to contain 52 wt.% FeO*. The purpose of this paper is firstly to obtain improved estimates of the partial molar volume of FeO* in molten iron using additional theoretical and experimental data, and secondly to recalculate the effect of high pressure on the solubility of FeO* in molten iron using this new evidence.
2. Indirect evidence bearing on the molar volume of FeO*
The chemical bonds in wi~stite are believed to be largely ionic in nature. Its melting point increases normally with pressure, implying that the density of liquid is smaller than that of the solid [3]. Thus, the chemical bonding in molten wi~stite is probably also essentially ionic. Many non-metals such as B, C, N, Si, P and S dissolve in crystalline a n d / o r liquid iron, and also form crystalline semi-metallic compounds with iron. The chemical bonds between non-metals and iron in these solutions and compounds are usually metallic or covalent-metallic (semi-metallic). It seems likely that when oxygen dissolves in molten iron it will behave analogously and form covalent-metallic bonds. Since the change from ionic to covalentmetallic bonding is accompanied by a substantial shortening of the metal-non-metal bond length [4], it is to be expected that the partial molar volume (V*) of FeO* in solution in Fe will be substantially smaller than the molar volume of wi~stite (V). The study of crystalline oxides, carbides and nitrides provides considerable insight into the chemical and physical principles involved. Carbon and nitrogen form extensive solid solutions in y-iron, in which the C and N atoms occupy interstitial sites in the close-packed metallic iron lattice because of their small sizes (atomic radii 0.77 and 0.70 A respectively [4]). These elements also form a series of metallic carbides and nitrides, e.g. Fe3C, Fe4N. The electronegativity of oxygen is greater
than those of C and N, hence it has a stronger tendency to form ionic bonds, as in wi~stite. However metallic oxide phases isostructural with corresponding metallic carbides and nitrides do exist (e.g. [5,6]). Of particular importance is a series of intermetallic compounds ABO where A = Mo, W and Re and B = Fe, Co, Ti, V, Cr, Mn [5]. In these compounds, the A and B atoms form a hexagonal close-packed lattice in which oxygen atoms are situated in the octahedral interstices. The F e - O bond length in these metallic compounds is 1.92 A, compared to 2.16 A for the F e - O bond length in wi~stite. This illustrates the rather spectacular decrease in bond length as the F e - O bond changes from ionic to covalent-metallic. The atomic radius of oxygen in these compounds is only 0.60 A [5]. If the F e - O bond length in wi~stite were reduced to 1.92 .~, its density would be 8.36 g / c m 3, as compared to 5.87 g / c m 3 for stoichiometric wi~stite. It seems likely that when oxygen dissolves in molten iron it would also enter interstitial positions, occupying "holes" in the disordered liquid structure. Accordingly, it can be expected that V* will be substantially smaller than F. When subjected to shock compression, magnetite (Fe304) with a density of 5.20 g / c m 3, and hematite (Fe203) with a density of 5.27 g / c m 3 transform to much denser phases possessing estimated zero pressure densities of 6.4 and 6.1 g / c m 3 [7]. Jackson and Ringwood [8] pointed out that these densities were too high to be caused by a lattice rearrangement of Fe 2+ and O a- ions, but implied, instead, a shortening of the F e - O bond length as would occur if the bond type changed from ionic to covalent-metallic. The observation of metallic electrical conductivity in the high-pressure form of Fe203 at 160 GPa [9] confirms this interpretation for hematite. Ringwood [2] predicted that wi~stite would also transform to a dense covalent-metallic phase at high pressures. Subsequent shock-wave compression studies on wiastite by Jeanloz and Ahrens [10] revealed a phase transformation near 70 GPa. The data are not sufficient to permit an unambiguous calculation of the density of the high-pressure phase. Jackson and Ringwood [8] showed that if the three highest-pressure measurements on the shock Hugoniot are considered, the density of the high-pressure phase is about
96
7.25 g / c m 3. However, if a fourth measurement at lower pressures is included, the density of the high-pressure phase falls to 6.7 g / c m 3. The former interpretation is preferred since the lowest pressure point may represent a state of incomplete transformation to the high-pressure phase. This interpretation is also favoured by the shock compression data on Fe203 and Fe304. If the Fe and O atoms were packed as densely as in the highpressure forms of Fe203 and Fe304, the density of high-pressure FeO* would be 7.1 g / c m 3, in good agreement with the higher of the two estimates by Jackson and Ringwood. It was suggested by these authors and also by Navrotsky and Davies [11] that the high-pressure phase of FeO* may be semi-metallic, with a crystal structure related to that of nickel arsenide. Liquids of this family of phases are usually completely miscible with those of the metallic end-member, e.g. Fe-FeS. Ringwood [2] suggested that the density dif-
ference between pure liquid wi~stite (FeOl) and the metallic FeO~ component which dissolves in molten iron is likely to be comparable to the density difference between crystalline wOstite and the high-pressure phase of wi~stite (FeO*) which was believed to be semi-metallic, on the basis of the evidence reviewed here. Alternatively, this density difference can be estimated from the difference in F e - O bond lengths as observed in crystalline wiistite and in ternary metallic oxides of the type MFeO where M = Mo, W or Re. Estimates of the densities and molar volumes of wi~stite and its high-pressure phase obtained by these approaches are given in Table 1. The estimated differences in molar volumes between those of normal wi~stite and the high-pressure phase FeO* are seen to cover a wide range, from 1.45 to 3.65 cm 3. Clearly, it would be desirable to determine the difference in molar volume AVl between FeOj and FeO~' by a more direct experimental procedure.
TABLE 1
3. Experimental
Zero-pressure densities and molar volumes of the high-pressure phase of FeO~¢) (and of wi~stite) obtained by several different methods Method
Density Molar volume AVc ~ (g/cm 3) V(cm 3) (cm3)
Hrftstite
Calculations based on extrapolation of lattice parameters of FexO
5.865 b
12.25
-
High - pressure phase of FeO*
Calculated from Fe-O bond length in metallic MFeO phases (1.92 ,~) Assume similar Fe-O atomic packing densities as in high pressure phases of Fe203 and Fe304 Extrapolation of shock compression data on high pressure phase of FeO (upper bound to density) Extrapolation of shock compression data on high pressure phase of FeO (lower bound to density)
8.36
8.60
3.65
7.1
10.12
2.05
7.25
9.91
2.26
6.7
10.72
1.45
AV~ ~ V(c)(wiastite) - V(*)(high-pressure FeO). b Hentschei [25].
An estimate of AV can be obtained from experimental measurements of the effect of pressure on the eutectic temperature in the system Fe-FeO. Relevant phase relationships at atmospheric pressure are well established [12,17] and are shown in Fig. 1. The temperature of the eutectic between molten iron and molten FeO occurs at 1523°C. The effect of pressure on the melting point of iron has been studied by Sterrett et al. [13] and by Boyd and England [14]. The former authors obtain an accurate melting point gradient of 28.5 o C / G P a . (Note that the absolute melting temperatures of iron in all of their experiments are slightly low, probably because of solution of some boron from the borosilicate glass (pyrex) in which their iron samples were suspended.) This gradient is in good agreement with the gradient of 2 7 . 5 ° C / G P a measured by Boyd and England [14] when the latter result is corrected for the effects of friction in their apparatus. The above investigations did not include corrections for the effects of pressure on thermocouple EMF's. Experiments to determine the eutectic temperatures at high pressures in the system F e - F e O were
97 1700 I I I
Fe-FeO*LiC,JO
TUBE
I I I
I
1650
THERMOCOL Fe-FeO*LIQUR)
I I
÷
I
FeO LJQLJE)
ALUMINA M~
"ER
I I I I
< 1600
I
1585°C
w
.q~m
PYROPHYLLITE iRON NITRIDE
3GPa
PUREIROt
m mu
1.73
0.82
[ GLASS
Fig. 2. High-pressure heating cell used in present experiments.
W
1550 1534
1
1523oc 5 Fe
0
0
I atm
~Fe (C), 0 FeO(L) " 6 1.0
2.0
2 3.0
F e O tool p e r c e n t Fig. 1. Iron-rich portion of the F e - F e O phase diagram at 1 atmosphere [12,17], and at 3 GPa. Phase relationships at 3 GPa are based on the present experiments.
carried out in a piston-cylinder apparatus using quenching techniques and differential thermal analysis. The pressure cell used in the former experiments is shown in Fig. 2. Molybdenum heaters were used to avoid the possibility of carbon contamination. All components of the pressure cell (except for the outermost talc sleeves) were carefully dried by calcination to eliminate the possibility of contamination of the sample by water or hydrogen. In addition, a separate set of runs was carried out at 4 GPa in which most of the magnesia inserts (Fig. 2) were replaced by fired pyrophyllite. To facilite comparison with the results of Sterrett et al. [13], corrections were not applied for the effect of pressure on thermocouple EMF's in our experiments. In the quenching experiments, the sample consisted of a 350-mg capsule of spec-pure iron containing about 40 mg of FeO. The capsule was closed with a tightly-fitting lid of spec-pure iron. Pressure was applied using the "piston-in" method, and a correction of minus 10% was made to total
pressure to allow for friction. In a typical run, full pressure was first applied. Temperature was then increased to 1000-1200°C and held for 5 minutes to allow the cell to densify and stabilize. Temperature was then increased to the desired value for the particular run and held constant for 5 minutes. After completion of the runs, the samples were quenched by terminating the power. Samples were then removed from the cell, polished, and examined by optical microscopy. In samples which had not melted, the sample of wbstite retained its original shape and remained fully enclosed within the iron capsule, which also displayed its original sharp cylindrical morphology. In samples which had melted, the wbstite migrated through the iron to form a black layer of FeO surrounding the exterior of the capsule. Negligible amounts of FeO remained included in the iron, which usually displayed rounded contours. In a few runs carried out close to the melting curve, one end or side of the capsule appeared to have melted, and displayed an external sheath of FeO over a rounded surface of iron whereas the other end or side of the iron capsule retained sharp contours and did not possess an FeO sheath. These are believed to represent partly melted runs arising from the presence of small temperature gradients across the sample. Results from these experiments are depicted in Fig. 3. A second set of experiments at 4 GPa in which most of the magnesia inserts of Fig. 3 were replaced by fired pyrophillite, showed identical textural relationships. It is seen from Fig. 3 that the increase of melting point of the F e - F e O eutectic with pressure is well defined by a straight
98
•
DTA Runs
• +} Quenching
X
X Runs
×
~/
16
oo Fe melting point dT m / d P ~ 2 8 . 5 °C/GPa
UJ rr ~.
/
• •/
16oo
UJ
O.
:E UJ Fe-FeOf eutectic d T e / d P ~ 2 0 . 5 °C/GPa
155o 1534
1500 t-
1
2
3
PRESSURE
4
5
GPa
Fig. 3. Lower line shows eutectic temperature of Fe-FeO system versus pressure determined by differential thermal analysis (solid circles) and by quenching techniques (squares). Open squares depict sub-solidus runs; solid squares depict melting. Half-filled squares show runs in which part of the charge is believed to have melted whilst another part appeared unmelted. The broken line depicts the melting of wi~stite contained in solid iron capsules, as determined by Lindsley [3]. The melting pointof pure iron versus pressure is shown in the upper line and is based upon the melting point gradient of 28.5°C/GPa determined by Sterrett et al. [13]. The melting point of iron at 4 GPa was also located in the present study using quenching experiments, depicted by crossed symbols.
The melting temperatures of the F e - F e O eutectic at pressures of 3 and 4 G P a were also determined by differential thermal analysis using the techniques described by Cohen et al. [15]. The sample consisted of a 350-mg capsule of spec-pure iron containing about 40 mg of FeO. The capsule was closed with a tightly-fitting lid of spec-pure iron. After mechanical and thermal stabilization of the pressure cell at full pressure and 1000°C, temperature was increased at 1 5 0 ° C / m i n u t e and the outputs from two closely spaced thermocouples [15] were displayed on an X-t recorder. The onset of melting was recorded by sharp D T A signals, as shown in Fig. 4. Eutectic temperatures determined by this technique are shown as solid circles in Fig. 3. They agree closely with the results obtained by the quenching technique. There are actually two separate D T A signals which can be generated during melting in the F e - F e O system. One can be caused by melting of wiastite in the iron container and the other arises from melting at the eutectic between iron and FeO. At pressures below about 3.3 GPa, FeO melts at a lower temperature than the F e - F e O eutectic. This creates the potential for confusion between the two D T A signals. To avoid this, the mass of FeO in the capsule was limited to a small proportion of the mass of metallic iron ( < 10%). The signal due to melting of FeO is thus smeared out by the thermal inertia of the surrounding metal and is too small to record. The major D T A signal observed (Fig. 4) records the eutectic close to metallic iron, where the entire capsule melts.
U o
line with a slope dTe/dP of 2 0 . 5 ° C / G P a . The variation of melting point with pressure of pure wbstite contained in iron capsules has been determined below the F e - F e O eutectic temperature by Lindsley [3]. His results are depicted as a broken line in Fig. 3. The curves intersect at a pressure of 3.3 G P a and a temperature of 1590°C. Theoretically, there should be an inflexion of the F e - F e O eutectic melting curve at this point, but this could not be resolved within the uncertainty limits of our experiments.
[5o IV
r
i
Fig. 4. Example of DTA signal showing melting of Fe-FeO mixture at 4 GPa beginning at 1605°C.
99 The melting curve of pure iron based upon its zero-pressure melting point of 1534°C [12] and the gradient of 28.5°C/GPa, carefully determined by Sterrett et al. [13], is also shown in Fig. 3. These results yield a melting point of 1648°C at 4 GPa. We have determined the melting point of pure iron at 4 GPa by a quenching method to check the consistency of our techniques with those employed by Sterrett et al. Chips of alumina were placed within a cylinder of pure iron, close to the base. Runs were carried out at 10 ° intervals between 1620 and 1670°C. Temperatures were measured using Pt-Pt 10% Rh and W5%Re-W25%Re thermocouples carried in 4-hole alundum tubing. (The additional W-Re thermocouple was employed because of contamination of Pt-Rh thermocouples which occurred in some runs.) In runs at 1620 and 1630°C, the alumina remained in position, whereas at 1660 and 1670°C the alumina floated to the top of the iron slug, immediately beneath the thermocouple. Iron in the former runs was evidently unmelted whereas the latter two had clearly melted. In two runs at 1640°C and in one run at 1650°C, the alumina rose to a level about 1 mm below the top of the iron. It appears that there was a temperature gradient within the sample caused by the relatively high conductivity of the thermocouple wire and its sheath. Hence the portion of the iron closest to the thermocouple was slightly cooler and apparently unmelted, preventing the chips from rising to the top. In a second run at 1650°C, chips did rise to the top of the iron sample. On the basis of these experiments, the melting temperature of iron as recorded by the thermocouples at the top of the iron capsule was taken at 1650 ___10°C. This result agrees well with the DTA measurement (Fig. 4) and with the results of Sterrett et al. [13].
4. Results
It is shown below that, to the first order, pressures of a few GPa do not significantly affect the relationship between depression of the melting point of iron and the quantity of dissolved FeO*. Thus, the slope of the liquidus joining the Fe melting point and the Fe-FeO~ eutectic at 3 GPa
will be similar to that at atmospheric pressure (Fig. 1). At 3 GPa, we located the F e - F e O eutectic at 1585°C whereas the melting point of pure iron at this pressure is 1620°C. These results, as shown in Fig. 1, demonstrate that the effect of high pressure is to increase the solubility of FeO* in Fe and that the partial molar volume V* of FeO* dissoloed in molten iron is smaller than that of molten w~4stite. This observation qualitatively confirms the conclusions reached earlier. The experimental measurements on the effect of pressure on the F e - F e O * eutectic can be used to obtain a quantitative estimate of the partial molar volume V* of FeO* in molten iron. The enthalpy change on melting of iron is 13,807 J / m o l [16], which yields an entropy change on melting (ASm) of 7.641 J / K mol. The effects of limited variations of pressure and temperature on AS m are relatively small and of opposite sign. Hence we can assume that ASm is approximately constant within the experimental range of pressures and temperatures. Raoult's Law implies that the activity coefficient of iron (~re) along the Fe solvus between p u r e Fe and the Fe-FeO~ eutectic is very close t o unity. (Note, however, that ~Feo on the FeO side of the eutectic is greater than unity owing to non-ideality of the system in this region.) Assuming that Yre 1.0, and ignoring the small pressure and temperature effects on ASm, the iron content at the eutectic temperature (1585°C) can be determined by applying the Van't Hoff equation for the depression of melting point of crystalline phases by solutes. The iron content at the eutectic (3 GPa and 1585°C) is thus found to be 98.27 mol.% (1.73 mol.% FeO*). If the observed slope for depression of melting point of Fe by FeO at atmospheric pressure (Fig. 1) had been assumed to be applicable at 3 GPa, the eutectic composition would have been similar at 2.0 mol.% FeO*. At 1585°C and one atmosphere, the solubility of FeO* is 0.82 mol.% [17]. At a given temperature T and pressure P, the free energy difference AG °, between liquid iron oxide and the FeO~ component of the liquid (Fe-FeO*) solution is given by: AG ° - PAV~ = R T In a l / a 2
(1)
where al is activity of FeO in the liquid iron oxide referred to pure liquid FeO as the standard state,
100 a 2 is the activity of FeO~ in molten iron and AV~ is the difference between the molar volume V1 of molten wiastite and the partial molar volume of FeO~' (V*). Since the composition of the iron oxide liquid is very close to that of pure wi~stite (Fig. 5), al can be taken as unity. Accordingly: AG ° - PAV] = - R r l n
a 2 = -RTln
YF¢oNzp
(2)
where N~ is the mole fraction of FeO~' dissolved in molten iron at pressure P and YF~ is the activity coefficient of the F e O t component. AG ° is related to the observed solubility N2° of FeO* in molten iron at temperature T and at atmospheric pressure by the expression: AG ° = - R T In ]tFeoN2°
(3)
In view of the small solubility range displayed by FeO* and the limited range of pressure conditions, it is reasonable to assume that the activity coefficient YFeO of FeO~ in molten iron is independent of pressure and of FeO~' content. Substituting (3) in (2) we have: PzXV, = R T In N z e / U ~
(4)
This equation may be solved for AVj using the experimentally determined values of P, T, N°2 and NzP. In this manner, AVI is found to be 3.8 cma/mol. This experimental value of AVI may be com-
Metal|lc(Fe-FeO ) liquid
1a t m ~
oo
.V? 2--0 cm3/mol
m~250(
\~ I
pared with estimates of the corresponding volume difference AVe between the high-pressure (covalent-metallic) polymorph of FeO* and crystalline wiastite FeO c, given in Table 1. It is seen to be very close to the corresponding A ~ value of 3.65 cm 3 calculated from the respective ionic bond lengths in wi~stite and the metallic F e - O bond lengths in M F e O compounds. This strongly suggests that oxygen occupies interstitial sites (holes) in molten iron and forms metallic F e - O bonds, as in the crystalline family of M F e O interstitial phases. Our experimental value of AVI (3.8 cm3/mol) is substantially higher than the preferred values of AV1 (2.05 and 2.26 cm3/mol) estimated from shockwave data (Table 1). This may reflect the fact that the shock wave data apply to phases possessing O / F e ratios greater than or equal to unity. The high-pressure phases of these oxides would be unable to accommodate all of their oxygen atoms in interstitial sites. A large proportion of the oxygens would occupy regular lattice sites, leading to a decrease in the packing density. These considerations suggest that AVI values in Fe-FeO* melts may decrease with increasing oxygen content. At relatively low FeO~ content, (e.g. O / F e < 0.5) the oxygen atoms mainly enter interstitial sites (holes) in the liquid. As the FeO* content increases, the available "holes" may become saturated and further solution may cause V~' to increase and AVj to decrease. The AVe values obtained from shock compression data may thus be indicative of AVI values appropriate to F e - O melts containing high oxygen contents ( O / F e >/1).
5. Effect of pressure on solubility of FeO* in Fe ,,X,200c F-
/ /
~
f /// /
'
u,o,d,~,.~,.,.,o.lo. (Fe-FeO~IL + FeO ILl
2'0
4'0
4o
FeO tool
go
1oo
%
Fig. 5. Calculated solubilities of FeO* in molten iron at l0 GPa based upon AVI values of 3.8 cm3/mol as determined in the present experiments(solid curve) and an arbitrary value of 2.0 cm3/mol (broken curve) representing a probable lower limit. The solubility of FeO* at ambient pressure [1] is also shown.
Calculations of the effect of a pressure of 10 G P a on the solubility of FeO* in molten iron have been carried out using the thermodynamic relationships described previously and the experimentally determined value of AVt (3.8 cm3). Results are shown in Fig. 5. A second set of calculations was carried out for an arbitrary value of AVj = 2.0 cm 3. This probably represents a conservative lower limit to AVI, allowing for the effects of differential compressibilities of molten wiastite and ( F e - F e O * )
101
liquid, and change of AVl with oxygen content, as discussed earlier. It is seen from Fig. 5 that, at constant temperature, high pressure causes the solubility of FeO* in Fe to increase in a rather spectacular manner. For example, at 2000°C, the solubility of FeO* in Fe is about 5 mol.% at atmospheric pressure. At 10 GPa, solubilities are increased to 14 and 40 mol.% FeO for AVI values of 2.0 and 3.8 cm3/mol respectively. High pressure also reduces the temperatures needed to achieve a given solubility of FeO* in Fe. For example, at atmospheric pressure, a solubility of 50 mol.% FeO* is reached at about 2650°C. At 10 GPa, this solubility is reached at 2340°C and 2060°C for AVj values of 2.0 and 3.8 cm 3 respectively. The effects of pressures up to 30 GPa on the F e - F e O phase diagram are shown schematically in Fig. 6. The calculations are based on the value of AVI 3.8 c m 3 determined earlier in this paper. The effects of pressure on the melting points of pure Fe and FeO are based on experimental measurements [3,13]. It is seen that the extent of the liquid immiscibility gap is reduced by high pressure. This effect is enhanced by the increase in melting temperatures of Fe and FeO with pressure, which cause the eutectic compositions to move inwards, away from these end-members [18]. It is estimated that the miscibility gap will disappear around 20 GPa, above which the F e - F e O system would resemble a simple eutectic, as in the F e - F e S system (see also Usselman [19]). As previously noted, it is possible that the effective value of AV] may be substantially smaller than the experimentally determined value of 3.8 cm 3. To a first approximation, this would cause a proportional increase in the pressures shown in Fig. 6. However, the essential features of the phase diagrams should remain intact. Finally, we consider the effect of pressure on the solubility of FeO* in iron in equilibrium with magnesiowiastite. The molar volume of molten wiastite can be estimated from Clapeyron-Clausius equation, dT/ dP A V m / A S m. The melting point gradient of whstite has been determined by Lindsley [3] whilst the entropy of melting is available from JANAF [20]. Thus, the volume change (AVm) on melting of FeO is found to be 1.3 cm3/mol. As =
=
3000
L1 L1
200G
i
Fe U O
3000
,
i
L2
Fe÷L2 , , ,
t
rl+
,
,
, FeO
LI+L2
i
L
i
Fe+FeO L i i
i
,
Fe
10 GPa
i FeO
15GPa
UJ nL1 re MJ
2000
2
~L2f
F 1e
¢
Fe.LI
L
L2]
~
i
O.
,
IIJ p-
~
, 7+LFeiO,
Fe
,
,
]
FeO
Fe+F.O . . . . . . Fe
5
0
0
,
, FeO
30 GPa
3s°°I 20 GPaL1 2
j
~
Fe*L1 Fe
20
40
60
' 8~0 F e O
Fe'
Fe*FoO 2'0 ' 4'0 ' 6'0 ' 8'0 ' F I O
COMPOSITION,mol % FeO
Fig. 6. Schematic diagrams depicting phase relationships in the F e - F e O system at pressures up to 30 GPa. The liquid immiscibility field is expected to disappear at pressures around 20 GPa.
the partial molar volume V~ of FeO in magnesiowiastite is essentially equal to that of wiastite, the effective value AVe_l (equivalent to V c - ~'~J) is 2.5 cm3/mol, based upon the value of 3.8 cm3/mol for AVl obtained from Fig. 1. For a probable "minimum" estimate of 2.0 cm3/mol for AVl, the value of AVe.1 would be 0.7 cm3/mol. Results of calculations using these values and the thermodynamic relationships described earlier are shown in Fig. 7. At 2500°C, and at atmospheric pressure, the solubility of FeO* in Fe in equilibrium with (Mg0.sFe0.2)O is 14 mol.% [1]. At this temperature for AV~.~= 2.5 cm 3, solubilities increase to 24 and 41 mol.% at pressures of 5 and 10 GPa respectively. For the assumed minimum value of AV~.1= 0.7 cm3, solubilities increase less rapidly with pressure, reaching 19 tool.% FeO* at 10 GPa and 25 mol.% FeO* at 20 GPa.
102
A
40
O E
°2500°C~-~: 2.5cm3/mol
C 4~ o
c 4)
3o
o E
.E
20
"O
@
>
O O (D
aVc-(: 0 . 7 cm3/mol 10
"O
*0
@ 0
10 PRESSURE
15
20
GPa
Fig. 7. The solubility of FeO* in molten iron in equilibrium with magnesiow~stite(Mg0.8Fe0.2)O calculatedas a functionof pressure at 2500°C. Valuesfor AVe.l ( - Vc- V~')of 2.5 cm3/mol and 0.7 cm3/mol were used in these calculations.
6. Composition of the earth's core
If the lower mantle has a similar bulk composition to the pyrolite model composition of the upper mantle, it would contain silicate perovskite and magnesiowi~stite as important phases. Experiments on the partition of FeO between these phases [21] imply that the magnesiowi)stite phase in the lower mantle would possess a composition close to (Mg0.sFeo.2)O. Most current estimates of the temperature near the core-mantle boundary lie between 2800 and 3700°C [22]. The results discussed in Part I show that at 2800°C, iron in equilibrium with (Mgo.8Feo.2)O would dissolve 40 mol.% FeO* [1] and that the solubility of FeO* rises still further with increasing temperature. Thus, considering only the effect of temperature, it follows that if the outer core formed by a process which permitted equilibrium with the lower mantle, it should contain at least 40 mol.% FeO*. High pressures present in the earth's interior have two distinct effects upon the distribution of
FeO between silicate oxide phases and metallic iron. McCammon et al. [18] showed that the highpressure phase (FeO*) formed under shock compression [10] would be exsolved from magnesiowi~stite at pressures exceeding 70 GPa, deep in the earth's interior. This phase is expected to dissolve in molten iron forming a simple eutectic system [18]. McCammon et al. developed a model of core formation based upon these phase relationships. The model was characterised by formation and segregation of F e - F e O * liquid alloys only at considerable depths, exceeding those corresponding to a pressure of 70 GPa. The results described in the present paper and in the companion paper [1] imply that solution of large amounts of FeO* in molten iron could occur at much smaller pressures than were considered by McCammon et al. [18]. We have described evidence that the partial molar volume V* of FeO* dissolved in molten iron is substantially smaller than that of the partial molar volume of FeO c in magnesiowi~stite. Accordingly, high pressures enhance the solubility of FeO* in iron. The magnitude of this effect is large, even for comparatively modest pressures in the vicinity of 20 GPa. Thus, if the core formed by segregation of metal originally dispersed throughout the earth, it seems inevitable that it would dissolve large amounts of FeO. Comparison of shock Hugoniots for pure Fe and FeO [10], indicate that the observed density of the outer core would be explained if it contained about 40 mol.% FeO* [10]. FeO contents of this order are readily explained by the experimental results described in this paper. These conclusions would remain valid even if the lower mantle consisted essentially of perovskite-type phases and contained only a small amount of magnesiowi~stite, as proposed, for example, by Anderson et al. [23]. In these models, density and elasticity constraints require the lower mantle to possess F e O / ( F e O + MgO) molar ratios greater than 0.05 [24]. The FeO would be accommodated principally in (Mg,Fe)SiO 3 perovskite. High-pressure partition experiments [21] demonstrate that magnesiowi~stite of composition (Mg0.sFe0.2)O would be in equilibrium with perovskite (Mg0.97Fe0.03)SiO 3. If the iron content of perovskite were increased, for example to
103 ( M g o . 9 5 F e o 0 5 ) S i O 3, t h e a c t i v i t y o f F e O w o u l d i n c r e a s e s u b s t a n t i a l l y as c o m p a r e d t o its a c t i v i t y i n (Mgo.sFeo.2)O. This would be accompanied by a corresponding increase in the solubility of FeO* in molten iron.
Acknowledgements T h e a u t h o r s a r e i n d e b t e d t o D r . H. O ' N e i l l , D r . I. J a c k s o n a n d D r . A. N a v r o t s k y f o r t h e b e n e f i t s of helpful comments and constructive criticisms.
References 1 E. Ohtani and A.E. Ringwood, Composition of the core, I. Solubility of oxygen in molten iron at high temperatures, Earth Planet. Sci. Lett. 71, 85-93, 1984 (this issue). 2 A.E. Ringwood, Composition of the the core and implications for the origin of the earth, Geochem. J. 11, 111-135, 1977. 3 D.H. Lindsley, Pressure-temperature relations in the system FeO-SiO2, Carnegie Inst. Washington Yearb. 65, 226-230, 1966. 4 L. Pauling, The Nature of the Chemical Bond, 3rd ed., 450 pp., Cornell, Ithaca, N.Y., 1948. 5 N. Sch6nberg, On the existence of metallic ternary oxides Me'Me"O with metal atoms in hexagonal close-packing, Acta Chem. Scand. 8, 630-632, 1954. 6 N. Sch6nberg, On the existence of ternary transition metal oxides, Acta Chem. Scand. 8, 932-936, 1954. 7 G.F. Davies and E. Gaffney, Identification of phases of rocks and minerals from Hugoniot data, Geophys. J.R. Astron. Soc. 33, 165-183, 1973. 8 I. Jackson and A.E. Ringwood, High pressure polymorphism of the iron oxides, Geophys. J.R. Astron. Soc. 64, 767-783, 1981. 9 S. Endo and K. Ito, Electrical resistance of aFe203 under ultrahigh static pressure, Solid State Commun. 36, 189-190, 1980. 10 R. Jeanloz and T.J. Ahrens, Equation of state of FeO and CaO, Geophys. J.R. Astron. Soc. 62, 505-528, 1980. 11 A. Navrotsky and P.C. Davies, Cesium chloride vs. nickel arsenide as possible structures for (Mg,Fe)O in the lower mantle, J. Geophys. Res. 86, 3689-3694, 1981.
12 L.S. Darken and R.W. Gurry, The system iron-oxygen, II. Equilibrium and thermodynamics of liquid oxide and other phases, J. Am. Chem. Soc. 68, 798-816, 1946. 13 K.F. Sterrett, W. Klement, Jr. and G.C. Kennedy, Effect of pressure on the melting of iron, J. Geophys. Res. 70, 1978-1984, 1965. 14 F.R. Boyd and J.L. England, The melting of iron at high pressures, Carnegie Inst. Washington Yearb. 62, 134-137, 1963. 15 L.H. Cohen, K. Klement, Jr. and G.C. Kennedy, Melting of copper, silver and gold at high pressures, Phys. Rev. 145, 519-525, 1966. 16 R.A. Robie, B.S. Hemingway and J.R. Fischer, Thermodynamic properties of minerals and related substances at 298.15 K and one bar (105 pascais) pressure and at high temperatures, U.S. Geol. Surv. Bull. 1259, 456 pp., 1978. 17 A. Fischer and J.F. Schumacher, Die S~ittingungslbslichkeit von Reineisen an Saurstoff vom Schmelzpunkt bis 2046°C ermittelt mit dem Schwebeschmelzverfahren, Arch. Eisenhuttenwes. 49, 431-435, 1978. 18 C.A. McCammon, A.E. Ringwood and I. Jackson, Thermodynamics of the system Fe-FeO-MgO at high pressure and temperature and a model for formation of the Earth's core, Geophys. J.R. Astron. Soc. 72, 577-595, 1983. 19 T.M. Usselman, Experimental Approach to the state of the core, I. The liquidus relations of the Fe-rich portion of Fe-Ni-S system from 30 to 100 kbar, Am. J. Sci. 275, 278-290, 1975. 20 JANAF, Thermochemical Tables, 2nd ed., 1141 pp., NSRDS-NBS37, Washington, D.C., 1971. 21 E. Ito, E. Takahashi and Y. Matsui, The mineralogy and chemistry of the lower mantle: An implication of the ultrahigh-pressure phase relations in the system MgO-FeO-SiO2, Earth Planet. Sci. Lett. 67, 238-248, 1984. 22 O.L. Anderson. The Earth's core and the phase diagram of iron, Philos. Trans. R. Soc. London, Ser. A 306, 21-35, 1982. 23 D.L. Anderson, C. Sammis and T. Jordan, Composition and evolution of the mantle and core, Science 171, 1103-1113, 1971. 24 I. Jackson, Some geophysical constraints on the chemical composition of the Earth's lower mantle, Earth Planet. Sci. Lett. 62, 91-103, 1983. 25 B. Hentschel, Stoichiometric FeO as metastable intermediate of the decomposition of wiistite at 225°C, Z. Naturforsch. 25a, 1996-1997, 1970.