Earth and Planetary Science Letters, 111 (1992) 217-227 Elsevier Science Publishers B.V., Amsterdam
217
[uc]
Melting of the Fe-FeO and the Fe-FeS systems at high pressure: Constraints on core temperatures R. Boehler Max-Planck-Institut fiir Chemie, Postfach 3060, W-6500 Mainz, Germany Received February 3, 1992; revision accepted April 12, 1992
ABSTRACT Melting temperatures of FeO, FeS and FeS 2 have been accurately determined in a hydrostatic, inert pressure environment up to about 0.5 Mbar using a new yttrium-lithium-fluoride (YLF) heating laser. The melting curve for FeO is in perfect agreement with data obtained from multi-anvil experiments at 160 kbar [1], but is in stark disagreement with previous laser heating experiments [2]. Preliminary measurements show strong melting depression on mixtures of Fe and FeS, whereas mixtures of Fe and FeO were observed to melt close to the melting curve of iron. The Kraut-Kennedy melting relationship [3], in which the melting temperature is a linear function of volume, is successfully tested in this study for Li, Na, K, Fe, FeS, FeS2 and FeO, to compressions up to > 30%. At 1.36 Mbar (core-mantle boundary, CMB) FeO, Fe, and FeS are estimated to melt at 3670, 3260 and 3060 (+ 100) K respectively. Assuming outer core compositions with about 60% Fe and about 40% FeO or FeS, and a solid solution system, the melting temperature at the CMB, on the core side, would be 3300 K ( + 200 K), compared to a temperature at the bottom of the mantle of 2650 + 100 K. If these systems exhibit eutectic behaviour, the melting gradient through the outer core would have to be substantially higher than the adiabatic gradient in order to maintain a thermal boundary at the CMB. The present melting data, and experimental constraints on the adiabatic gradient in the outer core suggest a temperature at the inner core-outer core boundary of nearly 4200 K.
I. Introduction C a l c u l a t i o n s of the t e m p e r a t u r e in the core a n d of the t e m p e r a t u r e rise, AT, across the c o r e - m a n t l e boundary (CMB) require knowledge of some highly u n c e r t a i n properties, such as the heat flux from the core, its chemical c o m p o s i t i o n a n d p h a s e b e h a v i o u r , adiabatic a n d m e l t i n g gradients, a n d t h e r m a l conductivity of the lower m a n t l e . Some e x p e r i m e n t a l c o n s t r a i n t s o n these p r o p e r t i e s c a n be a n d have b e e n p r o v i d e d from work o n p h a s e d i a g r a m s a n d melting, a n d from the m e a s u r e m e n t of e q u a t i o n s of state of candidate materials. However, the m e l t i n g b e h a v i o u r of a c a n d i d a t e core material, such as the F e - O - S system, is highly u n c e r t a i n . F o r example, serious controversies exist in the m e l t i n g data of the e n d m e m b e r s a n d discussions a b o u t w h e t h e r the FeO-S system above 1 M b a r b e h a v e s as a solid-solution system or a system with a eutectic m e l t i n g p o i n t d e p r e s s i o n are c o n t r a d i c t o r y [4,5]. T h e differences in m e l t i n g results o b t a i n e d from a vari-
ety of e x p e r i m e n t a l m e t h o d s , r a n g i n g from therm o d y n a m i c estimates of H u g o n i o t t e m p e r a t u r e s or emission m e a s u r e m e n t s d u r i n g shock or laser h e a t i n g in d i a m o n d cells, are over 1000 K. T h e difference b e t w e e n the m e l t i n g t e m p e r a t u r e s for eutectic a n d solid solution b e h a v i o u r is expected to be of the same order. R e c e n t estimates of the m e l t i n g curve of F e O [1,2] differ by as m u c h as 700 K at a pressure as low as 160 kbar. C o n t r o versies in r e c e n t estimates of the m e l t i n g curves of p u r e iron are now b e t t e r u n d e r s t o o d from new laser h e a t i n g m e a s u r e m e n t s to 1.2 M b a r [6], w h e r e m e l t i n g t e m p e r a t u r e s of 3000 + 100 K were measured at 1 Mbar, resulting in a E-y-liq. triple p o i n t at that pressure, which complicates the extrapolation of the m e l t i n g curve to higher pressures. While t e m p e r a t u r e m e a s u r e m e n t s d u r i n g shock c o m p r e s s i o n face p r o b l e m s such as u n k n o w n optical a n d t h e r m a l b e h a v i o u r of the window m a t e rials, data fit, a n d possibly t h e r m o d y n a m i c equilibrium, the m a i n e x p e r i m e n t a l difficulties in dia-
0012-821X/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
218
mond cells in the past have been the detection of melting, the measurement of temperature, and chemical reactions in the heated pressure chamber. The present study shows experimental techniques that solve these problems, resulting in well-constrained melting curves up to 500 kbar. New data on (1) FeO are reported that resolve the large discrepancies just mentioned and on (2) FeS and FeS 2, where new shock melting temperature measurements have become available [7]. Melting point depression is tested in a few runs with Fe-FeO and Fe-FeS mixtures. The present measurements incorporate the latest developments in temperature measurement such as very low P-T gradients, in-situ spot temperature measurement using fully corrected optics, and a new, very stable heating laser which allows in-situ detection of melting with greater precision. The simple relationship discovered by Kraut and Kennedy [3], in which the melting temperature, Tin, is presumed to be a linear function of the change in the volume, AV/Vo, is tested to compressions of over 30%, and is used to extrapolate the present data to core pressures (1.36 Mbar). This simple formula most likely yields more reliable estimates at high pressures than the Lindemann melting relationship in its form - d l n T m / d l n V = 23, - 2 / 3 , where 7 is the thermal GriJneisen parameter, which is not well known at high P-T conditions. The new measurements on the end members in the Fe-O-S system and the observed melting systematics provide a tight constraint on the meltir~g temperature in the outer core, in the case of solid solution with insignificant melting depression. For eutectic melting depression, an alternative solution for the melting behaviour of the outer core material is suggested on the basis of reasonable assumptions regarding the temperature rise across the CMB.
2. Experimental details 2.1. High-pressure cell The sample, randomly shaped discs and flakes of FeO, FeS and FeS2, with an approximate thickness of 20 ~ m and width of 50 /.tm, was loosely placed on the diamond flat without the use of bonding material. Several small ruby chips were distributed around the sample on the same
R. B O E H L E R
YLF- laser
ruby Fig. L Cross section of a laser-heated diamond anvil ceil.
diamond flat, which ranged in diameter from 250 to 300 /zm with a 7-10 ° bevel angle. Stainless steel gaskets (internal diameter 120-150 /zm, height 5 0 - 7 0 / z m ) were used. The cell was loaded with argon in a 3 kbar gas pressure vessel. A cross section of a typical high-pressure cell is shown in Fig. 1. It was necessary to keep the pressure for these melting experiments below 500 kbar, as above this pressure the molten sample frequently comes into contact with the upper diamond, resulting in chemical reaction and damage to the diamond. Pressures were measured before, during and after melting and showed deviations of less than 2 kbar.
2.2. YLF laser A significant improvement in laser stability was achieved by replacing the N d : Y A G rod with a Nd : Y L F (yttrium-lithium-fluoride) rod (Antares model, Coherent). A power stability of < 0 . 1 % rms with drastically improved beam pointing stability was achieved, which is due to the one order of magnitude smaller temperature dependence of the refractive index of this material compared to YAG. Temperature fluctuations of the heated samples were less than 10 K. The maximum power (cw, TEM00) is > 30 W at a wavelength of 1053 nm. Light from the krypton pump lamps could not exit the laser due to the folded laser cavity. The optical geometry for heating the sample is the same as that described in detail previously [6].
2.3. Measurement of Tm The optical geometry for measuring temperatures and temperature gradients of the laser
M E L T I N G OF Fe-FeO Fe-FeS SYSTEMS: C O N S T R A I N T S ON C O R E T E M P E R A T U R E S
heated spot is identical to that described for the iron melting measurement [6] using state-of-theart technology. Temperatures were measured from areas of 2 /xm in diameter, using fully corrected achromatic optics and a calibrated 1024 channel spectrometer for the wavelength range 600-900 nm. The reproducibility of temperature measurements at constant laser power was better than 10 K. Fits of the temperature spectra to the
219
Planck radiation function were nearly perfect with standard deviations of T of less than 3 K (X 2 < 0.02). Temperature profiles across the laserheated spot were identical to those reported earlier [6] and yielded perfect Gaussian fits with deviations of less than 20 K. When the material in the centre of the hot spot melted, vigorous convection in that area was observed. Figure 2a shows a sample during melting with a molten
(a)
Fig. 2. (a) Laser-heated sample during melting. The centre portion of the hot spot (about 15 ~ m in diameter) is convecting vigorously. (b) Sample after a melt experiment with an extremely defocussed laser beam.
220
region in the centre of the hot spot of about 15 Ixm in diameter. The reproducibility of the temperature measurement at the onset of this convection in most cases was less than + 60 K, which is the maximum variation of a minimum of four measurements at constant pressure. This high precision is a result of the high laser power stability and the large size of the hot spot which allowed reliable detection of the solid-liquid transition by visual observation. This method was checked by measurement of the change in optical reflection of an argon laser beam pointed at the centre of the hot spot [6]. In all the experiments the laser beam was defocussed to obtain molten areas of at least 10 ixm in diameter. Upon extreme defocussing the entire sample melted (see Fig. 2b). Temperatures were measured before and during the observed onset of melting and the laser power versus temperature was recorded. The visual observation of melting was accompanied by a strong discontinuity in the temperature-power function, a result of differing absorption of the melt. Melting was measured at pressures as low as 17 kbar to check the agreement between the melting curve and the 1 atm melting point.
R. BOEHLER
T
(K) 3500
///I/ 1$ /// /
3000
2500
iI
2000
/ d
"'~RH
? I
1500
100
~
I
I
i
i
300
400
500
600
P ( kbar ) Fig. 3. Melting of FeO. The vertical bars indicate the variation of at least four different measurements of the onset of melting; temperatures are measured during melting. The work by Ringwood and Hibberson [1] (cross) and the work by Knittle and Jeanloz [2] as also shown for comparison. The bars represent the temperature bounds for solid (s), and liquid (1).
3. Results
3.2. FeO 3.1. Fe
The melting curve of iron has been recently remeasured to 1.14 Mbar by Boehler et al. [6] using the state-of-the-art tech~fiques that have been used in the present study, fhe only experimental improvement is the increased laser stability using an YLF laser rod, which leads to more reproducible detection of the onset of melting, because the detection of the transition of a solid sample to a convecting, molten sample is not biased by temperature fluctuations. This previously published melting curve of iron was checked at 328 kbar, where melting was observed at 2450 + 50 K, which is in perfect agreement with the data reported earlier. There is also perfect agreement between the melting curve of Boehler et al. and a melting temperature of 2218 K measured at 160 kbar in a multi-anvil apparatus by Ringwood and Hibberson [1].
The samples were made by A.V. Wulf (MPI, Mainz) from Fe and Fe203, yielding a composition of Fe0.960 which was subsequently determined from the 1 atm X-ray pattern. A relatively large number of melting points was measured between 17 and 470 kbar to check the drastic disagreement between recently published melting data: one of the experiments resulting in the latter data is laser heating work performed in 1988 and published in 1991 by Knittle and Jeanloz [2], and the other is a melting experiment performed in a multi-anvil press in 1990 by Ringwood and Hibberson [1]. At 160 kbar, the difference between the two melting estimates is 700 K. Ringwood and Hibberson estimate their uncertainty to be +25 K, using thermocouples and textural changes in the molten sample after quenching. The bounds for liquid and solid in the work by Knitfle and Jeanloz at that pressure
MELTING OF Fe-FeO Fe-FeS SYSTEMS: CONSTRAINTSON CORE TEMPERATURES
these data and the present melting curve of FeS at 40 kbar is relatively poor, with deviations of about 100 K.
T
(K)
FeS2
25OO
5/t]
..," 3,4. f e S 2
////
Natural pyrite decomposes at temperatures above 1000 K, and the melting point is listed at 1444 K. Sharp [9] measured the decomposition temperature of pyrite to 65 kbar and the melting curve of pyrrhotite. They concluded that pyrite will start to melt congruently somewhere between 64 and 80 kbar. In the present experiment at four different pressures between 175 and 440 kbar the samples melted uniformly and the crossing of the melting curves of FeS and FeS 2 at a r o u n d 100 kbar is in qualitative agreement with Sharp's work.
1500
1000
221
100
200
300
400 '
500 '
600 '
P ( kbar ) Fig. 4. Melting of FeS and FeS z. Below about 70 kbar FeS 2 melts incongruently. The slopes of the melting curves are in agreement with qualitative work at low pressure by Sharp [9].
differ by as much as 1000 K (see Fig. 3), and this is mainly due to very large temperature gradients ( A i 2 0 3 pressure medium), indirect temperature measurement, indirect detection of melting, and strong temperature fluctuation (Knittle and Jeanloz's technique was the same as that used in the measurement of melting of pure iron by Williams et al. [8].) The present melting data are in perfect agreement with the work by Ringwood and Hibberson (shown by the cross in Fig. 3) and the 1 atm melting point at 1670 _+ 20 K.
3.3. FeS The sample was natural troilite, which is stoichiometric. Data were collected between 70 and 435 kbar and the melting curve extrapolates to the 1 atm melting point at 1469 K. Previous work on pyrrhotite (Fe8S 9) by Sharp [9] and by Ryzhenko and Kennedy [10], to 65 and 40 kbar respectively, was qualitative and the temperatures are poorly constrained. In Sharp's work the temperatures were not measured directly, and in Ryzhenko and Kennedy's work " n o particular effort was made to determine [the] curve with maximum precision". The agreement between
3.5. Mixtures of Fe-FeO and Fe-FeS Several difficulties arise in the melting experiments of multi-component systems in a diamond anvil cell: (1) the samples are non-uniform on a scale of several micrometres; (2) the absorption of the laser light is different for each component, leading to a non-uniform temperature distribution, even with flat laser beams profiles; and (3) the intrinsic, radial (Gaussian) and the axial temperature gradients can lead to unmixing during melting. Several reconnaissance experiments with mixtures of Fe with about 10-20 wt.% FeO or FeS were carried out over the pressure range 150-200 kbar to test the effect of eutectic mixing on the melting temperature of pure iron. For this purpose fine FeO or FeS powder was embedded in an iron foil using two diamond anvils and subsequently loaded into argon in the diamond cell. The samples were heated with a highly defocussed laser beam over an area of at least 50 ~ m in diameter. Temperatures were increased until convective motion was observed within the inhomogeneous sample, and temperatures were measured from the convecting regions. This process was repeated at the same and at other locations of the sample. At 176 kbar the Fe-FeS mixture starts to melt at 1650+ 50 K, which is 600 K below the melting temperature of pure iron, and 300 K below the melting temperature of pure FeS. This temperature is in good agreement with work reported on the pressure dependence of the
222
R. BOEHLER
eutectic t e m p e r a t u r e in the Fe-FeS system by Usselmann [11]. Several experiments on mixtures of Fe and F e O between 150 and 200 kbar yielded qualitatively similar results (e.g. a mixture of Fe and F e O at 190 kbar started to melt at 2160 + 60 K, which is only about 100 K below the melting curves of pure Fe and FeO). The mixture became homogeneous at 2350 + 50 K, about 100 K above the Fe and F e O melting curves. For comparison, note the melting t e m p e r a t u r e measured in a multi-anvil press [1] at 160 kbar for Fe: 10 wt.% F e O is 1943 + 20 K, which is about 200 K below the present estimate.
core, however, are highly uncertain. Although a large n u m b e r of experimental data on 3, exist at low pressure [14], frequently used formulas to extrapolate 3, to higher compressions, such as dln3'/dlnV = const., have been shown to be inadequate for the alkali metals over a large compression range [15]. In addition, 3' shows drastic changes across phase transitions [16]. Anderson [13] shows that above 1 Mbar the uncertainty in Tm of iron, using the Lindemann law, is over 1000 K, due to the uncertainty in 3'In 1966 Kraut and Kennedy [3] discovered a linear relationship between the melting temperature of a number of highly compressive metals and their compression A V / V o at room temperature. This relationship was later confirmed for measurements on gold, silver, copper and lead [17,18]. This formula, which has no theoretical basis (and does not work for Van der Waals solids and ionic compounds), is the most accurate and the most convenient for describing melting of metals, and the melting data of this study. For these reasons it is used to extrapolate the present melting temperatures to higher pressures, because the room t e m p e r a t u r e compression of the
4. D i s c u s s i o n
4.1. The Kraut-Kennedy melting relationship revisited No reliable formula to describe melting at high pressure has yet been found. In geophysics, the Lindemann melting relationship has been used in a variety of forms [12,13]. H e r e Tm is a function of the thermal Griineisen p a r a m e t e r 3'. Estimates on the value of 3" at the P-T conditions of the
'
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¢/ /I
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./
I
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i t
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e O ~ ~,,~F" /+'L-. Fe 1.5
t.i i
1.0 .9
.8
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.6
V/Vo Fig. 5. Melting versus compression. Data are taken from the smoothed curves shown in Figs. 3 and 4 and from previous measurements by Boehler [15] and Zha and Boehler [19]. CMB = core-mantle boundary.
223
M E L T I N G OF Fe-FeO Fe-FeS SYSTEMS: C O N S T R A I N T S ON C O R E T E M P E R A T U R E S
materials is accurately known. Using compression values along the melting curve would be more complicated, and is expected not to yield qualitatively different results, because for metals a • K is approximately constant, which yields linearity in both cases. In Fig. 5, T m/T o from this work and previous work on the alkali metals [15,19] is plotted versus compression. Values of Tm are taken from the smoothed curves shown in Figs. 3 and 4. Volumes are calculated from a third-order BirchMurnaghan equation of state. K and K', TO and the pressure range of the measurements are listed in Table 1. The dotted lines for Fe, FeO, FeS, and FeS 2 represent the extrapolation to pressures of the core-mantle boundary (1.36 Mbar). Iron undergoes a phase transition from bodycentred cubic (bcc) to hexagonal close packed (hcp) at 130 kbar at room temperature with a volume change of 0.35 cm3/mole. The KrautKennedy relationship works for most of the pressure range with a change in slope above 130 kbar. Many previous estimates on core temperatures are based on the Kraut-Kennedy relationship using a slope similar to that below 130 kbar, which yields core temperatures that are too high using this method. The melting point in the previous work at 1.14 Mbar [6] indicates a change in the slope of the melting curve which is most likely due to the e-y-liq, triple point at about 1 Mbar. For all the materials shown, the maximum deviation of Tm from a straight line is 20 K. This is remarkably low considering the large temperature and compression range. The values of Tm/Tmo at 1.36 Mbar are relatively insensitive to the values of K o and K~ used to calculate V / V o because both the slopes in Fig. 5 and the value of TABLE 1 Parameters and pressure range used in Fig. 5 Compound
Tm0 (K)
Ko
a-Fe e-Fe FeO FeS FeS 2 Li Na K
1809
1664 1650 1950 1178 1620 113 62 31
1680 + 10 1469 1444 * 454 371 336
* incongruent melting
Ref.
K~
Pm~x (kbar)
20 21 22 23 24 15 15 15
5.0 5.3 4.0 4.1 4.7 3.6 3.9 3.8
130 1100 470 430 440 30 110 70
(kbar)
4000
. . . .
,
T (K)
,
. . . .
FeO --,.........
3000
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'
.--
2
"
10000
. . . .
FeS
'
./
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~ 0.5
'
'
'
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t
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P ( Mbar ) Fig. 6. Melting of Fe [6], FeO and FeS versus pressure. The solid lines represent the experimental data range. The dashed curves are extrapolations to the C M B using the linear Tm vs V ~ Vo relationship shown in Fig. 5.
V / V o at 1.36 Mbar are affected. The melting curves of Fe, FeO and FeS are shown in P-T space in Fig. 6. The extrapolation of the melting temperature of FeO to 1.36 Mbar as shown in Fig. 5 may be affected by the phase change in FeO at about 700 kbar [2]. However, the nature of this phase transition with regard to the change in volume or compressibility is still unknown. The present extrapolations of the melting curves of FeS and FeS 2 yield temperatures that are about 600 K lower than new shock melting temperature estimates [7] at 1.25 and 1.42 Mbar respectively. The uncertainty in these measurements is reported as + 300 K. 4.2. Temperatures at the CMB The temperature at the bottom of a chemically homogeneous mantle is constrained by the transition temperature of (Mg,Fe)SiO3-perovskite at the 670 km depth [25] and estimates of the adiabatic gradient in the lower mantle, by both theory [26] and experiment [27]. From this Tc~ B should be between 2550 and 2750 K, the latter value including superadiabaticity above the CMB. It is generally believed that the CMB requires a thermal boundary layer due to core heat. AT across this layer depends on the heat flux from the core, and on the thermal conductivity of the lower mantle material. The thermal conductivity at 1.3 Mbar and /> 2500 K is unknown (e.g., nothing is known about the radiative term in the heat flow
224 equation at these conditions). Estimates of the core heat flux are based on the observed heat flux at the Earth's surface and depend strongly on assumptions on the magnitude of radioactive heating within the mantle and the core and on the heat of fusion at the inner core-outer core boundary. As a result, previous estimates of AT across the CMB relied on core temperatures derived from the highly uncertain melting properties of iron, and other unknown properties such as the effect of light (and other) elements on the melting temperature of iron and the assumption that the melting curve of this core material at the CMB is near the geotherm. In geodynamic arguments, including mantle convection and plumes, AT values between a few hundred and one thousand degrees are most frequently used. The melting of iron has been studied extensively, but both experimental and theoretical results show extreme variation. The most recent laser-heating diamond anvil cell work by Boehler et al. [6], supported by the present study, and measurements in a multi-anvil press [1], suggest that the melting temperature of iron at very high pressure has been mostly overestimated. Although the melting slope above 1 Mbar measured by laser heating [6] (shown in the Figs. 5 and 6) is not well constrained, an extrapolation to the shock melting point at 2.4 Mbar and 5600 + 500 K by Brown and McQueen [28] would require an extremely large melting gradient. Estimates of the melting point depression of iron due to light elements at high pressure have been scarce. Usselmann [11] reports eutectic temperatures of the Fe-Ni-S system to 100 kbar which are about 600 K below the melting temperatures of pure iron. Ringwood and Hibberson [1] report eutectic melting depression in the Fe-FeO system of 275 K at 160 kbar compared to pure iron. Knittle and Jeanloz [2] in a single experiment at about 800 kbar observe similar melting temperatures for a Fe-FeO mixture and for pure iron. Their uncertainty, however, is about 1000 K, due to experimental problems in the temperature measurement described above. The problems associated with laser heating of multi-component systems in a diamond cell (also described above) are enhanced in their experiment, due to tight focussing of the laser beam. Nevertheless, they interpret their observation of the Fe-FeO system
R. BOEHLER as behaving like a solid solution system at high pressure rather than a eutectic system at lower pressures [1]. Their main argument is that Fe and FeO are isostructural at high pressure. Indeed, both iron (above 50 kbar) and FeO have facecentred cubic (fcc) structures. At very high pressure FeO will most likely be in the bcc structure based on systematics observed on materials of the same class. Boehler and Zha [29, and unpublished data], have predicted that FeO undergoes a transition from B 1 to B2(bcc) at about 1.6 Mbar, from a new relationship between the volume changes of the Ba-B 2 transitions and the ionic radii of all alkali halides and metal oxides investigated so far. Ross et al. [30] suggest that, for iron, the high-pressure-high-temperature structure above about 1.5 Mbar is bcc, based on lattice dynamics and phase diagram systematics, and on the earlier melting study of iron by Boehler [31]. It is possible, therefore, from a structural point of view, that Fe-FeO represents a solid solution system over a very large pressure range, except for those pressures below 50 kbar. On the other hand, Boness and Brown [4] argue on the basis of electron band structure calculations, and on the basis of the atomic volumes of oxygen, sulphur, and iron at high pressures, that sulphur rather than oxygen will form solid solutions with iron. The above arguments are additionally complicated if metallization in FeO or FeS is considered. The present experiments on Fe-FeO mixtures qualitatively agree with the observation by Knittle and Jeanloz [2] in that the melting point of iron is not significantly lowered in the presence of oxygen. The experimental uncertainties in both experiments, however, are large due to the possibility of local changes in the chemical composition caused by temperature gradients. There is also the possibility that, on the FeO side of the Fe-FeO eutectic observed by Ringwood and Hibberson, convective motion will not be observed until temperatures of the two-liquid (Fe, FeO) region above about 2020 K are reached [Ringwood, pers. commun.]. Both theoretical and experimental arguments are still too weak to predict the behaviour of the Fe-O-S system at megabar pressures, and the subsequent discussion will therefore consider both cases, eutectic and solid solution. Possible solutions for geotherms through the
225
M E L T I N G OF Fe-FeO Fe-FeS SYSTEMS: C O N S T R A I N T S ON C O R E T E M P E R A T U R E S
lower mantle and the outer core are shown in Figs. 7a and 7b. The derivation of the mantle geotherms was described above. For the outer core to be liquid and its temperature to vary along an adiabat the melting gradient has to be slightly larger than the adiabatic gradient in order to freeze out a solid inner core. The adiabatic temperature rise across the outer core is taken as 700 K. This estimate is lower than previous estimates, but this value is constrained by new experimental results on the pressure dependence of the thermal expansion coefficient [6], and by direct m e a s u r e m e n t s of adiabatic gradients (OT/8P) s [14]. From the plot in Fig. 5 the melting temperatures of FeO, Fe and FeS at 1.36 Mbar (CMB) are 3670, 3260 and 3060 K respectively. In a solid solution system, the melting temperatures for compositions of 60% iron and 40% FeO or FeS, which would satisfy outer core densities, would
(a)
be about 3400 and 3200 K respectively. These temperatures would be lower bounds on the temperature of the outer core at the CMB, if it is near it's liquidus, and the temperature gradient across the CMB could be as small as 600 K (see Fig. 7a). The temperature at the inner c o r e - o u t e r core boundary would then be 4200 K. On the other hand, a eutectic melting point depression in the outer core of more than 600 K would result in a melting temperature at the CMB which is lower than the temperature at the bottom of the mantle (see Fig. 7b). In order to maintain a thermal boundary with a AT of a few hundred degrees, the temperature on the core side of the CMB would be significantly higher than the melting temperature. In order for the adiabat and the melting curve to intersect at the inner c o r e - o u t e r core boundary, the melting gradient of the outer core material has to be significantly higher than the adiabatic gradient through the outer core,
SOLIDSOLUTION
Tm 4ooo
T (K)
Fe,
"
~
3OOO
Fe
4000
AT
3000
FeO
solid
T
FeS
FeO F~
outm'core
FeFSFFeees..~SGO'BB~
....
2000 ~erms , I 1.0 CMB
, 2.0
, 3.0
I ICOCB
P ( Mbar ) Fig. 7. (a) Scheme of geotherms and melting behaviour in the outer core for the Fe-O-S system for solid solution behaviour (for explanation, see text). CMB = core-mantle boundary; ICOCB = inner c o r e - o u t e r core boundary.
226
R. BOEHLER
(b)
Tm40~O ~ EUTECTIC
T
(K)
Ft6
4000
3000
2000
fm ,ege0, e,ms ,
I
1.0 CMB
,
,
I
2.0
3.0
ICOCB
P ( Mbar ) Fig. 7. (b) Scheme of geotherms and melting behaviour in the outer core for the F e - O - S system for eutectic melting depression.
and the temperature at the inner c o r e - o u t e r core boundary could be as low as 3500 K. These estimates are significantly lower than those based on shock temperature estimates of iron by Brown and McQueen [28]. A discrepancy of this magnitude is not likely to be due to experimental error, or to an error in the thermodynamic calculation of shock temperatures, but could possibly be caused by non-equilibrium during shock melting. To solve this puzzle, static melting data at core pressures and accurate temperature measurements during shock compression are urgently needed.
solid solution system. This would result in a temperature gradient across the c o r e - m a n t l e boundary near or above 600 K and a temperature in the inner core near 4200 K. In the case of eutectic melting point depression in the outer core material, these values would be lower, unless the melting point gradient of the outer core material is very much larger than the adiabatic gradient.
5. Conclusions
References
The previous melting data on pure iron to 1.2 Mbar by Boehler et al. [6] and the present results on the Fe-O-S system suggest that, at the CMB, an outer core material consisting mainly of iron, oxygen and sulphur would melt between 3200 and 3400 K, if the outer core is near it's liquidus in a
Acknowledgements I thank A. Chopelas and D.A. Yuen for critical reviews of the manuscript, and H. Palme and A.V. Wolf for donation of samples for this study.
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