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S diffusivity in Fe–Ni–S–P melts
ELSEVIER
Earth and Planetary Science Letters 160 (1998) 823–830
S diffusivity in Fe–Ni–S–P melts E. Majewski Ł , D. Walker Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964, USA Received 5 January 1998; revised version received 19 May 1998; accepted 6 June 1998
Abstract Soret diffusion rise times were observed and resolved for Fe–Ni–S–P melts at 10 kbar in thermal gradients between 1300 and 1450ºC. A steady-state separation of S-rich components to the hot end of the ¾2 mm long liquid charges is achieved in about 20 minutes. Chemical diffusivities of about 10 5 cm2 =s are consistent with these observations and those of the compaction velocity of aggregates of crystalline Fe metal against the cold end of our experiments. These rapid diffusivities are not rapid enough for diffusion to be an important agent of bulk mass transfer in the addition or extraction of light elements in the Earth’s core. 1998 Elsevier Science B.V. All rights reserved. Keywords: thermal diffusivity; sulfur; core; melts
1. Introduction The formation and evolution of Earth’s core is a fundamental aspect of our planet’s evolution. The core is still internally active physically as recently demonstrated by Song and Richards [1]. Continuing chemical interaction between core and mantle or between inner and outer core may well have a role in this physical activity [2,3]. Diffusive and advective transport of light elements within liquid metal solutions should certainly play a role in core processes. For instance S and=or O rejected from the inner core during its solidification potentially contributes a buoyancy flux for outer core convection. Alternately S and=or O transfer into the core from the base of the mantle will gravitationally stabilize the upper part of the outer core. The time scale on which such stabilizing chemical fluxes might be dissipated throughout Ł Corresponding
author. On leave from the Institute of Geophysics. Polish Academy of Sciences, Warsaw, Poland.
the core depends upon the rate of chemical diffusion of the light components. That chemical diffusion in molten alloy systems is rapid compared to the sluggish diffusion behavior experienced in silicate solutions is evident in the crystallization behavior of alloys. Metallic glasses are rare enough to be curiosities. We measured the diffusivity of S in Fe–Ni–S–P liquid alloys at elevated pressures to provide some boundary conditions upon the chemical diffusivity of light elements into or out of the core.
2. Experimental There are many difficulties associated with chemical diffusivity measurements of very fluid alloy systems at elevated temperature and pressure. Many of these difficulties disappear if a gravitationally stable Soret separation can be induced in a temperature gradient in the fluid and if the rise time of the separation can be adequately resolved. Chemical diffusivity
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can be extracted from observation of the growth of a Soret separation as a function of time. Jones and Walker [4] demonstrated that Fe–Ni–S–P liquids were observably Soret active at 10 kbar and temperatures in the range of 1200–1500ºC. They found that S-rich alloy components segregate to the hot side of a temperature contrast, that the magnitude of the separation achievable at steady state increased with increasing S in the system, that the character of the separation and the ability to quantitatively predict the behavior of other tracers such as phosphorous on the basis of S could be understood with the Jones and Malvin [5] approach, and that the steady-state behavior was achieved in less than 18 hours for charges a few millimeters in length. Our approach to measuring diffusivity was to try resolving the rise time of the same sorts of Soret separations documented by Jones and Walker [4]. Fig. 1 shows a section through one of our 1=200 piston-cylinder assemblies which is the same as used by Jones and Walker [4]. Samples of Fe78 –Ni10 –S10 – P2 alloy mix prepared from Fe–Ni–P–FeS2 mixtures were placed in crushable MgO [Ozark Technical Ceramics, grade HP] and held at 800ºC and 10 kbar for 1–2 days to close the pores of the MgO before melting of the alloy. This sintering step keeps the alloy in one place rather than dissipating it throughout the MgO matrix by capillarity upon melting. It also produces coronal textures indicative of solid state reactions between pyrite grains and the metal powder matrix of the starting material. Once this necessary [4] presintering step was accomplished,
Fig. 1. Cross-section of experimental assembly inserted in piston-cylinder device, pressurized to 10 kbar and heated until thermocouple reached 1450ºC. Letters on left refer to positions measured after the experiment and recorded in Table 1. Experimental assemblies have initial length of 30 mm.
the heater temperature was raised so that the thermocouple temperature was 1450ºC. The rise of temperature from 800ºC to 1450ºC could be achieved in less than one minute with minimal overshoot. The W3Re=W25Re thermocouple was maintained at 1450ºC for times from 3 minutes to 27 hours and then the sample was quenched. Temperature fell to 500ºC, the effective crystallization threshold, in about 3 seconds by turning off the heater power. The sample–container–heater–pressure–medium assembly was extracted from the pressure vessel, potted whole in epoxy, and an axial section ground for optical and electron microprobe examination. The graphite heater configuration, sample placement, and thermocouple temperature used insures that there is an adequate thermal gradient across the sample to induce a Soret separation in the liquid alloy with the light S-rich component accumulating in a gravitationally stable configuration over the Fe-rich residue. We, like Jones and Walker [4], were able to induce a small amount of crystalline alloy growth at the cold end of the charge. This was an advantage for the experiments of Jones and Walker [4] because it provided an independent check on the temperature at the cold end of the charge and an opportunity to check the partitioning of tracers between crystalline Fe and Fe–S alloy liquid for local equilibrium and to evaluate the applicability of the Jones and Malvin [5] formalism in this new situation. In the present experiments, however, the crystallization of some Fe alloy at the cold end of the charge was a mixed blessing. The same advantages enjoyed by Jones and Walker were still of use here, but the crystallization of variable amounts of metal from experiment to experiment with the same bulk composition leads to variable composition of the liquid part of the system by fractional crystallization. Because of the variable compaction density along the length of the BaCO3 and MgO components in our assemblies there is some irreproducibility inherent a priori in where the charge winds up with respect to the thermocouple and the heater’s gradient of temperature. Thus for constant thermocouple temperature, some experiments recover more crystalline Fe than others. For Jones and Walker [4] this was interesting. But for us the Soret time series observed is for slightly different effective liquid compositions and slightly different charge lengths from experiment to exper-
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Table 1 Summary of experiments Experiment: Duration:
#14 3 min
#8 2h
#12 10 h
#6 27 h
Liquid phase compositions in atom% š standard error of the mean (D std. dev.=sqrt 10): Hot S 21.0 š 0.4 25.1 25.1 21.4 Hot P 1.4 š 0.03 1.3 1.4 1.5 Hot Ni 8.5 š 0.06 7.9 6.8 8.7 Hot Fe 69.0 š 0.2 65.7 66.7 68.4
20.8 2.2 8.4 68.6
24.9 2.3 8.9 63.9
22.8 1.9 8.2 67.1
Cold S Cold P Cold Ni Cold Fe
16.4 2.7 8.4 72.6
20.2 2.9 8.8 68.0
18.4 2.2 8.5 71.0
21.3 š 0.4 1.4 š 0.03 8.3 š 0.06 69.0 š 0.2
#16 6 min
23.8 1.5 8.0 66.7
#15 10 min
22.5 1.6 7.2 68.7
#13 15 min
17.5 1.6 8.7 72.1
Distances (mm) above base of assembly measured by vernier on translation stage to positions in Fig. 1: (a) Base of charge 8.1 8.0 8.0 8.1 7.5 6.9 7.7 (b) Top of metal 8.6 8.5=9.1 a 8.5 8.4 7.6 7.3 7.9 (c) Top of charge 10.4 10.8 10.3 10.2 9.8 9.0 10.1 (d) T.c. junction 13.5 14.2 12.9 12.9 13.2 11.5 13.0 (e) Whole charge 20.4 21.5 23.0 21.6 21.0 21.6 21.4 (∆X .S/ss from #8, 12, and 6 D 4.5 š 0.4% S } 0.3 1.3 2.6 3.9 4.4 4.7 4.4 X .S/hot X .S/cold š 0:8 log (t in min) 0.477 0.778 1 1.176 2.079 2.778 3.2095 (to D 3.5 minutes from Fig. 2) (t to ), s 30 150 390 690 6990 35790 96990 d, cm liquid b 0.194 0.178 0.177 ln[1 ∆X .S/t=∆X .S/ss ] 3.41E 00 8.62E 00 2.01EC01 .t to /³ 2 =d 2 3.93EC05 1.21EC06 2.17EC06 D Cerror, [EC06] 21 20 1 D, cm2 =s [EC06] 8.7 7.1 9.3 D error, [EC06] 2 3 4 a 8.5 b
mm to top of compacted metal=9.1 mm to top of metal C sulfide columns. Measured with micrometer eyepiece for extra precision.
iment. Fortunately these experimental perturbations can be measured and incorporated in a fairly harmless manner into the data manipulations leading to diffusivity extraction. Table 1 lists the experiments, their duration, the measured distance from the piston to the bottom of the charge, to the metal=liquid interface, to the top of the charge, to the thermocouple junction, and the overall length after recovery. The compositions of the hot and cold ends of the liquid portion of the charge are also recorded. Optical examination of the charges in reflected light showed that Fe–Ni–S–P liquids quenched to a dendritic intergrowth of skeletal alloy crystallites with a fine-grained matrix of metal, sulfide, and phosphide phase intergrowths. One contrast of our experiments with those of Jones and Walker [4], who used 1% P instead of the 2% P used here, is that
we stabilized an immiscible Fe–Mg phosphate liquid which depleted our recovered Fe–Ni–S–P liquids below the P content of our target composition. The phosphate liquid was typically found as a coating on the inside of the MgO container so that the Fe–Ni–S–P liquid had reduced direct contact with the container [(Mg,Fe)O after the experiment]. Jones and Walker [4], by contrast, lost P from their bulk composition to Ca impurities in their MgO, forming small amounts of crystalline Ca–Mg phosphate at the capsule margins. The crystalline metal phase at the cold end of the charge at durations greater than 10 minutes was a coarse–grained, featureless, fully compacted, S-free aggregate. Its evolution to this state during the first phase of the time series is of interest and will be discussed in detail below.
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The composition of the liquid phase at the hot end and the cold end of its extent was determined by electron microprobe analysis using the average of multiple rasters to reconstruct the local composition of the liquid phase before quench segregation into metal dendrites and matrix. Both standardizations and analyses were done in raster mode with a raster of about 100 µm2 . Standards used were FeS2 , GaP, and Ni; Kα lines were excited by a 15 kV beam at 50 nA beam current. Typically an array of 10 adjacent rasters was used to nearly completely cover a strip of the charge parallel and adjacent to the melt=metal interface or the hot end at the top of the charge. The compositional differences observed between the hot and cold ends of the charges are entirely consistent with the results reported by Jones and Walker [4]. S was concentrated towards the hot end, Fe and P to the cold end, with Ni showing no consistent segregation if any. All runs reported of longer than 15 minutes’ duration achieve the steady-state separation of S-rich material to the hot end which Jones and Walker [4] showed to take less than 18 hours. Evidently the experimental durations used by Jones and Walker [4] were approximately two orders of magnitude longer than necessary. The rise time of the separation is shown here to be fully captured in the first 15 minutes!
3. Results Fig. 2 shows the compositional separation between the hot and cold end of our charges as a function of experiment duration. ÐX .S/ is the compositional difference in S between different ends of the liquid. The two-hour experiment has long since achieved the steady state that also characterizes the 27-hour experiment. The rise time to this steady state is nicely demonstrated by the experiments covering the first 15 minutes of the series. Or is it? The experiment of 3 minutes’ duration shows a marginally negative ÐX .S/ implying S enrichment at the cold end of the charge. Certainly no noticeable effect of the Soret process is produced within a duration of 3 minutes. To understand this surprising result we must examine the petrography of the shortest duration experiment. Fig. 3A shows the charge run for 3 min-
Fig. 2. Compositional difference in atom% S between hot end of the liquid part of the charge and the cold end of the liquid adjacent to precipitated crystalline metal plotted against the log of the experiment duration in minutes. At durations longer than 15 minutes the Soret effect has produced a steady state compositional separation of 4.5 atom% S in this temperature gradient from 1450 to 1300ºC over a distance of about 2 mm. Contrary to expectation, the process has produced no separation, or a marginally negative one, after the first three minutes’ duration. The thermal migration process is competing with thermal diffusion during the first few minutes (see Fig. 3.) The time when the Soret process begins to produce an observable separation, to , is interpolated from this figure to be 3.5 minutes.
utes and 3B the one run for 10 hours. In contrast to the fully compacted metal masses of the runs from 15 minutes up to steady-state duration as in Fig. 3B, the cold end of the 3-minute charge has a very structured set of elongated crystalline metal blobs with interstitial elongated channels of sulfide melt. This elongate texture is highly characteristic of crystal=liquid aggregates with temperature-dependent solubility which are in the process of reorganizing themselves in a thermal gradient. This phenomenon has been previously documented for Fe alloy systems by Buchwald et al. [6] and given the name thermal migration. A theoretical and experimental treatment coupling the solubility and Soret dependencies as they apply to cumulate maturation in a temperature gradient has been given by Lesher and Walker [7] who showed that the elongation of the texture is a consequence of entropy production minimization considerations. Briefly, at the start of the experiment the cold end of the charge was below the liquidus for the bulk composition. This cold part of the charge partly crystallized to an aggregate of Fe metal and liquid alloy.
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Fig. 3. Photomicrographs in incident polarized light of sections through two experimental charges. Long dimension of each photograph is 2.3 mm. Dark horizontal structures are cracks which develop in the charge upon decompression from 10 kbar after quenching. These cracks become filled with epoxy during sample preparation. Liquid metal–sulfide alloy at the high temperature of the experiment is recovered upon quench as a dendritic intergrowth of skeletal metal blades and interstitial sulfide and phosphide phases. Metal is more highly reflective than sulfide and appears brighter in these photomicrographs. This dendritic texture is seen in the upper of each charge. The top of each photograph is the hot end of the charge compared to the colder bottom. The progress of the phase segregation and compaction process driven by the thermal gradient can be seen by comparison of these two photographs. A shows experiment #14 of 3 minutes duration. The cold base of the charge is a two-phase region of elongated crystalline alloy structures separated by channels of quenched metal–sulfide liquid which are in the process of being expelled into the warmer liquid region above the two-phase aggregate. B shows the steady-state completion of this expulsion process in experiment #12 of 10 hours duration. The metal at the cold base is liquid-free. The Soret effect, the rise time of which is the subject of this study, is monitored in the crystal-free liquid region by electron microprobe raster-mode analysis of the hot and cold ends of the thermal gradient. A shows areas of phosphate liquid collected at the interface between the MgO capsule and the charge at the hot end (giving sulfide liquid rounded corners in the square MgO container) and at the junction between the liquid and the two-phase region. After 10 hours these separate pools of phosphate liquid are much reduced by percolation into the (Mg,Fe)O capsule grain boundaries.
The proportion of metal and liquid varies in this region initially in response to the local temperature and the bulk composition. In this two-phase aggregate, temperature-dependent solubility will cause changes in the liquid composition along the temperature gradient. Fe is more soluble at the hot side and less at the cold. Therefore the liquid composition becomes more Fe-rich at the hot end and more Fe-poor at the cold end of the two-phase aggregate. [The liquid compositions in this region are of course all more
S-rich than the bulk composition by fractional crystallization of the Fe.] Diffusion in the liquid phase of the two-phase aggregate moves Fe down the compositional gradient from hot to cold. But this transfer can only be accomplished — while maintaining the composition along the aggregate constant, as it must because the compositions are pinned to particular values by the temperature-dependent solubility requirements — if crystalline Fe dissolves at the hot end and crystallizes at the cold end. This solubil-
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ity-driven diffusive transfer has the physical effect of compacting Fe against the cold end and expelling S-rich liquid into the overlying liquid alloy. While this process is in progress — as it still is at 3 and 6 minutes’ duration — the cold end of the all-liquid part of the charge receives S-rich liquid from the two-phase part of the charge below which must diffuse or convect away. Thus the Soret process is competing during the first few minutes with the thermal migration process at the cold end of the all-liquid part of the charge. Thermal migration pumps S-rich liquid from the two-phase aggregate into the cold end of the all-liquid-phase region while the Soret process depletes this region in S-rich components. The Soret process locally loses this competition at first because the length scale for moving material is larger (hence slower to show the cumulative effect for the same diffusivity) than for thermal migration, but it wins in the long run. The 6-minute experiment has a positive ∆X .S/ so that the Soret process has gained an observable level of control over the thermal migration process in the all-liquid region even though thermal migration is still injecting S-rich liquid into the all-liquid region from the two-phase region. Optical examination of the areas of the 6-minute charge bearing crystalline metal show the cold half of this region to be a fully compacted, S-free, aggregate while the hot half resembles the two-phase region of the 3-minute experiment of Fig. 3A. The rate of advance of the front of the fully compacted layer depends upon the chemical diffusivity. Observations of the advance of this compaction boundary through a charge in a time series has been used by Lesher and Walker [7] to extract diffusivities. However this compaction velocity also depends upon the magnitude of the solubility gradient, the Soret coefficients, and the magnitude of the thermal gradient and so is a more difficult route to the extraction of diffusivities from experimental measurements. It nevertheless provides a set of observations which may be useful for confirmation of the diffusivities extracted from the Soret analysis. For the purposes of a Soret analysis we take the interpolated time in our series where the curve of Fig. 2 intercepts ∆X .S/ D 0 as the effective start of the Soret experiment. Taking t0 D 3:5 minutes is a simplification because there is still a competition in progress between the Soret and thermal migration
processes. Picking t0 D 3:5 minutes at ∆X .S/ D 0 simply forms a convenient base line against which to start the Soret clock because by that time at least the ends of the liquid parts of the charge have achieved the same composition, a background against which Soret-induced separations will be easily recognized. Following deGroot [8] and Tyrrell [9], Lesher and Walker [10] analysed Soret rise time series for extracting silicate liquid diffusivities using: ln[1
∆X .S/t =∆X .S/ss] D [t³ 2 =d 2 ]D
with subscripts referring to time t and to the steady state. d is the length of the charge and D is the chemical diffusivity of the element undergoing separation, in this case S. The temperature and temperature difference is assumed constant from one experiment in the series to the next and D is assumed to be independent of T and liquid composition over the experimental range investigated. These assumptions are not strictly correct because of the inexactness of the reproducibility of charge placement relative to the thermal gradient and the implausibility of D actually being T - and composition-independent. However the assumptions are (necessarily) adequate for extracting diffusivities from these experiments and they yield values which are substantially more reliable than order of magnitude uncertainty. Because each of the experiments measured before steady state is achieved gives an independent calculation of D from observed ∆X .S/t , t, and d, the three D estimates can be compared. These calculations are listed in Table 1 for the 6, 10, and 15 minutes experiments. Their variation is š10% for t0 chosen to be 3.5 minutes. The appropriateness of this choice of t0 and the level of noise in the extraction of D from these 3 experiments can be judged by the extent to which a single line through the origin can be fit to the three separate experiments in the time series before steady state is achieved. Fig. 4 shows the l.h.s. of the equation plotted versus t ³ 2 =d 2 . The slope of such a line through the origin should be D; and a line for 8 ð 10 6 cm2 =s is shown for comparison to the data. Rough confirmation of the validity of this number as appropriate for D of S in Fe–Ni–S–P in this temperature range is afforded by comparison to information on the compaction velocity of Fe crystalline aggregates through the thermal migration process. In order to maximize the observability of
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4. Conclusions
Fig. 4. Normalized compositional separation before Soret process reaches steady state plotted versus time normalized to charge length. The slope of lines through the origin give values of D for the element undergoing compositional separation. The three experiments are all consistent with D of about 8 ð 10 6 cm2 =s. The large formal error bars reflect the strong leverage exerted by the compositional measurement uncertainties, which potentially could be uncorrelated, upon the ln[1 ∆X .S/t=∆X .S/ss ] function. Given the small spread in the calculated values using the mean compositions, these error bar are probably unrealistically large, suggesting correlation in the uncertainties.
thermal migration compaction, a new bulk composition was prepared by adding Fe to the original mix until S was reduced to 2.5%. Such a bulk composition will compact a much larger fraction of the charge as metal than our Soret time series composition. Two experiments in the same temperature range and experimental configuration as the Soret series were performed: one for 10 minutes and one for 20 minutes. In 10 minutes about 200 µm of clean metal had compacted against the cold end and about 200 µm of single phase liquid had been segregated from all metal at the hot end. After 20 minutes a complete separation of the charge into 60% S-free metal at the cold end had occurred. To complete the job, less than 20 minutes were required. So to a first approximation the observations of compaction rate give the same result as the Soret analysis. The chemical diffusivity is rapid enough to reorganize material on the length scale of a millimeter in about 1000 s; D is of order 10 5 cm2 =s.
Such diffusivities are up to several orders of magnitude faster than those found in silicates at comparable pressures and temperatures by comparable techniques, e.g. Lesher and Walker [10]. Although these experimental conditions are not those at the core–mantle boundary where diffusion might be even faster through higher temperature, it remains unlikely that any reasonable extrapolation of these diffusivities to core–mantle boundary conditions will change the conclusion that diffusion is not a major agent of mass transfer within the outer core. While our understanding of Soret diffusion has increased significantly over the past decade, our ability to incorporate this knowledge in large-scale geochemical processes in the vicinity of the D00 layer and the core–mantle boundary is still quite limited. We conclude with a list of some topics where advances in the near future might be expected. It would be interesting to extend the Soret study to 100 kbar to look for pressure effects on the diffusion coefficient. This would be interesting in its own right as well as being an aid to the extrapolation of the diffusion constant to core pressures. (It is less of a jump from 100 kbar to a megabar than it is from 10 kbar to a megabar!) Additional information on temperature effects and the effects of competing light elements would be desirable. Finally, we need to understand what processes at the microscopic level may be responsible for initiation and the steady state of Soret diffusion. In contrast to the base of knowledge for silicate liquids, we believe this study and the earlier work of Jones and Walker [4] are the only measurements of Soret coefficients in metal– sulfide liquids. Once these and other processes are better understood, we can more fully address such issues as how mass transfer across the CMB affects core chemistry and how diffusion processes near the CMB influence thermal convection in the lower mantle and in the core.
Acknowledgements One of the authors (E.M.) was supported by the Kosciuszko Foundation in New York City and by the National Science Foundation International Pro-
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gram through supplement to NSF grant EAR9417706 (to D.W.). This is LDEO contribution. D.W. thanks the Max Planck Institute, High Pressure Mineral Physics Group, Mainz for hospitality during manuscript preparation. We thank C.E. Lesher, A.J. Naldrett, and K. Righter for their constructive reviews. [FA]
References [1] X. Song, P.G. Richards, Seismological evidence for the differential rotation of the Earth’s inner core, Nature 382 (1996) 221–224. [2] E. Majewski, Thermodynamic model of the core–mantle boundary, Publ. Inst. Geophys. Polish Acad. Sci. A-25 (275) (1995) 1–61. [3] G.A. Glatzmaier, P.H. Roberts, A three-dimensional, self-consistent simulation of a geomagnetic field reversal,
Nature 377 (1995) 203–209. [4] J.H. Jones, D. Walker, Thermal diffusion in metal–sulfide liquids: early results, Proc. Lunar Planet. Sci. Conf. 21 (1991) 367–373. [5] J.H. Jones, D.J. Malvin, A nonmetal interaction model for segregation of trace metals during the solidification of Fe– Ni–S, Fe–Ni–P, and Fe–Ni–S–P alloys, Metall. Trans 21B (1990) 697–706. [6] V.F. Buchwald, T. Kjer, K.A. Thorsen, Thermal migration, I, Or how to transport iron sulfide in solid iron meteorites, Meteoritics 20 (1985) 617–618. [7] C.E. Lesher, D. Walker, Cumulate maturation and melt migration in a temperature gradient, J. Geophys. Res. 93 (1988) 10295–10311. [8] S.R. deGroot, L’Effect Soret, North-Holland, Amsterdam, 1947. [9] H.J.V. Tyrrell, Diffusion and Heat Flow in Liquids, Butterworths, London, 1961, 329 pp. [10] C.E. Lesher, D. Walker, Solution properties of silicate liquids from thermal diffusion experiments, Geochim. Cosmochim. Acta 50 (1986) 1397–1411.
Earth and Planetary Science Letters 160 (1998) 823–830
S diffusivity in Fe–Ni–S–P melts E. Majewski Ł , D. Walker Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964, USA Received 5 January 1998; revised version received 19 May 1998; accepted 6 June 1998
Abstract Soret diffusion rise times were observed and resolved for Fe–Ni–S–P melts at 10 kbar in thermal gradients between 1300 and 1450ºC. A steady-state separation of S-rich components to the hot end of the ¾2 mm long liquid charges is achieved in about 20 minutes. Chemical diffusivities of about 10 5 cm2 =s are consistent with these observations and those of the compaction velocity of aggregates of crystalline Fe metal against the cold end of our experiments. These rapid diffusivities are not rapid enough for diffusion to be an important agent of bulk mass transfer in the addition or extraction of light elements in the Earth’s core. 1998 Elsevier Science B.V. All rights reserved. Keywords: thermal diffusivity; sulfur; core; melts
1. Introduction The formation and evolution of Earth’s core is a fundamental aspect of our planet’s evolution. The core is still internally active physically as recently demonstrated by Song and Richards [1]. Continuing chemical interaction between core and mantle or between inner and outer core may well have a role in this physical activity [2,3]. Diffusive and advective transport of light elements within liquid metal solutions should certainly play a role in core processes. For instance S and=or O rejected from the inner core during its solidification potentially contributes a buoyancy flux for outer core convection. Alternately S and=or O transfer into the core from the base of the mantle will gravitationally stabilize the upper part of the outer core. The time scale on which such stabilizing chemical fluxes might be dissipated throughout Ł Corresponding
author. On leave from the Institute of Geophysics. Polish Academy of Sciences, Warsaw, Poland.
the core depends upon the rate of chemical diffusion of the light components. That chemical diffusion in molten alloy systems is rapid compared to the sluggish diffusion behavior experienced in silicate solutions is evident in the crystallization behavior of alloys. Metallic glasses are rare enough to be curiosities. We measured the diffusivity of S in Fe–Ni–S–P liquid alloys at elevated pressures to provide some boundary conditions upon the chemical diffusivity of light elements into or out of the core.
2. Experimental There are many difficulties associated with chemical diffusivity measurements of very fluid alloy systems at elevated temperature and pressure. Many of these difficulties disappear if a gravitationally stable Soret separation can be induced in a temperature gradient in the fluid and if the rise time of the separation can be adequately resolved. Chemical diffusivity
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can be extracted from observation of the growth of a Soret separation as a function of time. Jones and Walker [4] demonstrated that Fe–Ni–S–P liquids were observably Soret active at 10 kbar and temperatures in the range of 1200–1500ºC. They found that S-rich alloy components segregate to the hot side of a temperature contrast, that the magnitude of the separation achievable at steady state increased with increasing S in the system, that the character of the separation and the ability to quantitatively predict the behavior of other tracers such as phosphorous on the basis of S could be understood with the Jones and Malvin [5] approach, and that the steady-state behavior was achieved in less than 18 hours for charges a few millimeters in length. Our approach to measuring diffusivity was to try resolving the rise time of the same sorts of Soret separations documented by Jones and Walker [4]. Fig. 1 shows a section through one of our 1=200 piston-cylinder assemblies which is the same as used by Jones and Walker [4]. Samples of Fe78 –Ni10 –S10 – P2 alloy mix prepared from Fe–Ni–P–FeS2 mixtures were placed in crushable MgO [Ozark Technical Ceramics, grade HP] and held at 800ºC and 10 kbar for 1–2 days to close the pores of the MgO before melting of the alloy. This sintering step keeps the alloy in one place rather than dissipating it throughout the MgO matrix by capillarity upon melting. It also produces coronal textures indicative of solid state reactions between pyrite grains and the metal powder matrix of the starting material. Once this necessary [4] presintering step was accomplished,
Fig. 1. Cross-section of experimental assembly inserted in piston-cylinder device, pressurized to 10 kbar and heated until thermocouple reached 1450ºC. Letters on left refer to positions measured after the experiment and recorded in Table 1. Experimental assemblies have initial length of 30 mm.
the heater temperature was raised so that the thermocouple temperature was 1450ºC. The rise of temperature from 800ºC to 1450ºC could be achieved in less than one minute with minimal overshoot. The W3Re=W25Re thermocouple was maintained at 1450ºC for times from 3 minutes to 27 hours and then the sample was quenched. Temperature fell to 500ºC, the effective crystallization threshold, in about 3 seconds by turning off the heater power. The sample–container–heater–pressure–medium assembly was extracted from the pressure vessel, potted whole in epoxy, and an axial section ground for optical and electron microprobe examination. The graphite heater configuration, sample placement, and thermocouple temperature used insures that there is an adequate thermal gradient across the sample to induce a Soret separation in the liquid alloy with the light S-rich component accumulating in a gravitationally stable configuration over the Fe-rich residue. We, like Jones and Walker [4], were able to induce a small amount of crystalline alloy growth at the cold end of the charge. This was an advantage for the experiments of Jones and Walker [4] because it provided an independent check on the temperature at the cold end of the charge and an opportunity to check the partitioning of tracers between crystalline Fe and Fe–S alloy liquid for local equilibrium and to evaluate the applicability of the Jones and Malvin [5] formalism in this new situation. In the present experiments, however, the crystallization of some Fe alloy at the cold end of the charge was a mixed blessing. The same advantages enjoyed by Jones and Walker were still of use here, but the crystallization of variable amounts of metal from experiment to experiment with the same bulk composition leads to variable composition of the liquid part of the system by fractional crystallization. Because of the variable compaction density along the length of the BaCO3 and MgO components in our assemblies there is some irreproducibility inherent a priori in where the charge winds up with respect to the thermocouple and the heater’s gradient of temperature. Thus for constant thermocouple temperature, some experiments recover more crystalline Fe than others. For Jones and Walker [4] this was interesting. But for us the Soret time series observed is for slightly different effective liquid compositions and slightly different charge lengths from experiment to exper-
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Table 1 Summary of experiments Experiment: Duration:
#14 3 min
#8 2h
#12 10 h
#6 27 h
Liquid phase compositions in atom% š standard error of the mean (D std. dev.=sqrt 10): Hot S 21.0 š 0.4 25.1 25.1 21.4 Hot P 1.4 š 0.03 1.3 1.4 1.5 Hot Ni 8.5 š 0.06 7.9 6.8 8.7 Hot Fe 69.0 š 0.2 65.7 66.7 68.4
20.8 2.2 8.4 68.6
24.9 2.3 8.9 63.9
22.8 1.9 8.2 67.1
Cold S Cold P Cold Ni Cold Fe
16.4 2.7 8.4 72.6
20.2 2.9 8.8 68.0
18.4 2.2 8.5 71.0
21.3 š 0.4 1.4 š 0.03 8.3 š 0.06 69.0 š 0.2
#16 6 min
23.8 1.5 8.0 66.7
#15 10 min
22.5 1.6 7.2 68.7
#13 15 min
17.5 1.6 8.7 72.1
Distances (mm) above base of assembly measured by vernier on translation stage to positions in Fig. 1: (a) Base of charge 8.1 8.0 8.0 8.1 7.5 6.9 7.7 (b) Top of metal 8.6 8.5=9.1 a 8.5 8.4 7.6 7.3 7.9 (c) Top of charge 10.4 10.8 10.3 10.2 9.8 9.0 10.1 (d) T.c. junction 13.5 14.2 12.9 12.9 13.2 11.5 13.0 (e) Whole charge 20.4 21.5 23.0 21.6 21.0 21.6 21.4 (∆X .S/ss from #8, 12, and 6 D 4.5 š 0.4% S } 0.3 1.3 2.6 3.9 4.4 4.7 4.4 X .S/hot X .S/cold š 0:8 log (t in min) 0.477 0.778 1 1.176 2.079 2.778 3.2095 (to D 3.5 minutes from Fig. 2) (t to ), s 30 150 390 690 6990 35790 96990 d, cm liquid b 0.194 0.178 0.177 ln[1 ∆X .S/t=∆X .S/ss ] 3.41E 00 8.62E 00 2.01EC01 .t to /³ 2 =d 2 3.93EC05 1.21EC06 2.17EC06 D Cerror, [EC06] 21 20 1 D, cm2 =s [EC06] 8.7 7.1 9.3 D error, [EC06] 2 3 4 a 8.5 b
mm to top of compacted metal=9.1 mm to top of metal C sulfide columns. Measured with micrometer eyepiece for extra precision.
iment. Fortunately these experimental perturbations can be measured and incorporated in a fairly harmless manner into the data manipulations leading to diffusivity extraction. Table 1 lists the experiments, their duration, the measured distance from the piston to the bottom of the charge, to the metal=liquid interface, to the top of the charge, to the thermocouple junction, and the overall length after recovery. The compositions of the hot and cold ends of the liquid portion of the charge are also recorded. Optical examination of the charges in reflected light showed that Fe–Ni–S–P liquids quenched to a dendritic intergrowth of skeletal alloy crystallites with a fine-grained matrix of metal, sulfide, and phosphide phase intergrowths. One contrast of our experiments with those of Jones and Walker [4], who used 1% P instead of the 2% P used here, is that
we stabilized an immiscible Fe–Mg phosphate liquid which depleted our recovered Fe–Ni–S–P liquids below the P content of our target composition. The phosphate liquid was typically found as a coating on the inside of the MgO container so that the Fe–Ni–S–P liquid had reduced direct contact with the container [(Mg,Fe)O after the experiment]. Jones and Walker [4], by contrast, lost P from their bulk composition to Ca impurities in their MgO, forming small amounts of crystalline Ca–Mg phosphate at the capsule margins. The crystalline metal phase at the cold end of the charge at durations greater than 10 minutes was a coarse–grained, featureless, fully compacted, S-free aggregate. Its evolution to this state during the first phase of the time series is of interest and will be discussed in detail below.
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The composition of the liquid phase at the hot end and the cold end of its extent was determined by electron microprobe analysis using the average of multiple rasters to reconstruct the local composition of the liquid phase before quench segregation into metal dendrites and matrix. Both standardizations and analyses were done in raster mode with a raster of about 100 µm2 . Standards used were FeS2 , GaP, and Ni; Kα lines were excited by a 15 kV beam at 50 nA beam current. Typically an array of 10 adjacent rasters was used to nearly completely cover a strip of the charge parallel and adjacent to the melt=metal interface or the hot end at the top of the charge. The compositional differences observed between the hot and cold ends of the charges are entirely consistent with the results reported by Jones and Walker [4]. S was concentrated towards the hot end, Fe and P to the cold end, with Ni showing no consistent segregation if any. All runs reported of longer than 15 minutes’ duration achieve the steady-state separation of S-rich material to the hot end which Jones and Walker [4] showed to take less than 18 hours. Evidently the experimental durations used by Jones and Walker [4] were approximately two orders of magnitude longer than necessary. The rise time of the separation is shown here to be fully captured in the first 15 minutes!
3. Results Fig. 2 shows the compositional separation between the hot and cold end of our charges as a function of experiment duration. ÐX .S/ is the compositional difference in S between different ends of the liquid. The two-hour experiment has long since achieved the steady state that also characterizes the 27-hour experiment. The rise time to this steady state is nicely demonstrated by the experiments covering the first 15 minutes of the series. Or is it? The experiment of 3 minutes’ duration shows a marginally negative ÐX .S/ implying S enrichment at the cold end of the charge. Certainly no noticeable effect of the Soret process is produced within a duration of 3 minutes. To understand this surprising result we must examine the petrography of the shortest duration experiment. Fig. 3A shows the charge run for 3 min-
Fig. 2. Compositional difference in atom% S between hot end of the liquid part of the charge and the cold end of the liquid adjacent to precipitated crystalline metal plotted against the log of the experiment duration in minutes. At durations longer than 15 minutes the Soret effect has produced a steady state compositional separation of 4.5 atom% S in this temperature gradient from 1450 to 1300ºC over a distance of about 2 mm. Contrary to expectation, the process has produced no separation, or a marginally negative one, after the first three minutes’ duration. The thermal migration process is competing with thermal diffusion during the first few minutes (see Fig. 3.) The time when the Soret process begins to produce an observable separation, to , is interpolated from this figure to be 3.5 minutes.
utes and 3B the one run for 10 hours. In contrast to the fully compacted metal masses of the runs from 15 minutes up to steady-state duration as in Fig. 3B, the cold end of the 3-minute charge has a very structured set of elongated crystalline metal blobs with interstitial elongated channels of sulfide melt. This elongate texture is highly characteristic of crystal=liquid aggregates with temperature-dependent solubility which are in the process of reorganizing themselves in a thermal gradient. This phenomenon has been previously documented for Fe alloy systems by Buchwald et al. [6] and given the name thermal migration. A theoretical and experimental treatment coupling the solubility and Soret dependencies as they apply to cumulate maturation in a temperature gradient has been given by Lesher and Walker [7] who showed that the elongation of the texture is a consequence of entropy production minimization considerations. Briefly, at the start of the experiment the cold end of the charge was below the liquidus for the bulk composition. This cold part of the charge partly crystallized to an aggregate of Fe metal and liquid alloy.
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Fig. 3. Photomicrographs in incident polarized light of sections through two experimental charges. Long dimension of each photograph is 2.3 mm. Dark horizontal structures are cracks which develop in the charge upon decompression from 10 kbar after quenching. These cracks become filled with epoxy during sample preparation. Liquid metal–sulfide alloy at the high temperature of the experiment is recovered upon quench as a dendritic intergrowth of skeletal metal blades and interstitial sulfide and phosphide phases. Metal is more highly reflective than sulfide and appears brighter in these photomicrographs. This dendritic texture is seen in the upper of each charge. The top of each photograph is the hot end of the charge compared to the colder bottom. The progress of the phase segregation and compaction process driven by the thermal gradient can be seen by comparison of these two photographs. A shows experiment #14 of 3 minutes duration. The cold base of the charge is a two-phase region of elongated crystalline alloy structures separated by channels of quenched metal–sulfide liquid which are in the process of being expelled into the warmer liquid region above the two-phase aggregate. B shows the steady-state completion of this expulsion process in experiment #12 of 10 hours duration. The metal at the cold base is liquid-free. The Soret effect, the rise time of which is the subject of this study, is monitored in the crystal-free liquid region by electron microprobe raster-mode analysis of the hot and cold ends of the thermal gradient. A shows areas of phosphate liquid collected at the interface between the MgO capsule and the charge at the hot end (giving sulfide liquid rounded corners in the square MgO container) and at the junction between the liquid and the two-phase region. After 10 hours these separate pools of phosphate liquid are much reduced by percolation into the (Mg,Fe)O capsule grain boundaries.
The proportion of metal and liquid varies in this region initially in response to the local temperature and the bulk composition. In this two-phase aggregate, temperature-dependent solubility will cause changes in the liquid composition along the temperature gradient. Fe is more soluble at the hot side and less at the cold. Therefore the liquid composition becomes more Fe-rich at the hot end and more Fe-poor at the cold end of the two-phase aggregate. [The liquid compositions in this region are of course all more
S-rich than the bulk composition by fractional crystallization of the Fe.] Diffusion in the liquid phase of the two-phase aggregate moves Fe down the compositional gradient from hot to cold. But this transfer can only be accomplished — while maintaining the composition along the aggregate constant, as it must because the compositions are pinned to particular values by the temperature-dependent solubility requirements — if crystalline Fe dissolves at the hot end and crystallizes at the cold end. This solubil-
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ity-driven diffusive transfer has the physical effect of compacting Fe against the cold end and expelling S-rich liquid into the overlying liquid alloy. While this process is in progress — as it still is at 3 and 6 minutes’ duration — the cold end of the all-liquid part of the charge receives S-rich liquid from the two-phase part of the charge below which must diffuse or convect away. Thus the Soret process is competing during the first few minutes with the thermal migration process at the cold end of the all-liquid part of the charge. Thermal migration pumps S-rich liquid from the two-phase aggregate into the cold end of the all-liquid-phase region while the Soret process depletes this region in S-rich components. The Soret process locally loses this competition at first because the length scale for moving material is larger (hence slower to show the cumulative effect for the same diffusivity) than for thermal migration, but it wins in the long run. The 6-minute experiment has a positive ∆X .S/ so that the Soret process has gained an observable level of control over the thermal migration process in the all-liquid region even though thermal migration is still injecting S-rich liquid into the all-liquid region from the two-phase region. Optical examination of the areas of the 6-minute charge bearing crystalline metal show the cold half of this region to be a fully compacted, S-free, aggregate while the hot half resembles the two-phase region of the 3-minute experiment of Fig. 3A. The rate of advance of the front of the fully compacted layer depends upon the chemical diffusivity. Observations of the advance of this compaction boundary through a charge in a time series has been used by Lesher and Walker [7] to extract diffusivities. However this compaction velocity also depends upon the magnitude of the solubility gradient, the Soret coefficients, and the magnitude of the thermal gradient and so is a more difficult route to the extraction of diffusivities from experimental measurements. It nevertheless provides a set of observations which may be useful for confirmation of the diffusivities extracted from the Soret analysis. For the purposes of a Soret analysis we take the interpolated time in our series where the curve of Fig. 2 intercepts ∆X .S/ D 0 as the effective start of the Soret experiment. Taking t0 D 3:5 minutes is a simplification because there is still a competition in progress between the Soret and thermal migration
processes. Picking t0 D 3:5 minutes at ∆X .S/ D 0 simply forms a convenient base line against which to start the Soret clock because by that time at least the ends of the liquid parts of the charge have achieved the same composition, a background against which Soret-induced separations will be easily recognized. Following deGroot [8] and Tyrrell [9], Lesher and Walker [10] analysed Soret rise time series for extracting silicate liquid diffusivities using: ln[1
∆X .S/t =∆X .S/ss] D [t³ 2 =d 2 ]D
with subscripts referring to time t and to the steady state. d is the length of the charge and D is the chemical diffusivity of the element undergoing separation, in this case S. The temperature and temperature difference is assumed constant from one experiment in the series to the next and D is assumed to be independent of T and liquid composition over the experimental range investigated. These assumptions are not strictly correct because of the inexactness of the reproducibility of charge placement relative to the thermal gradient and the implausibility of D actually being T - and composition-independent. However the assumptions are (necessarily) adequate for extracting diffusivities from these experiments and they yield values which are substantially more reliable than order of magnitude uncertainty. Because each of the experiments measured before steady state is achieved gives an independent calculation of D from observed ∆X .S/t , t, and d, the three D estimates can be compared. These calculations are listed in Table 1 for the 6, 10, and 15 minutes experiments. Their variation is š10% for t0 chosen to be 3.5 minutes. The appropriateness of this choice of t0 and the level of noise in the extraction of D from these 3 experiments can be judged by the extent to which a single line through the origin can be fit to the three separate experiments in the time series before steady state is achieved. Fig. 4 shows the l.h.s. of the equation plotted versus t ³ 2 =d 2 . The slope of such a line through the origin should be D; and a line for 8 ð 10 6 cm2 =s is shown for comparison to the data. Rough confirmation of the validity of this number as appropriate for D of S in Fe–Ni–S–P in this temperature range is afforded by comparison to information on the compaction velocity of Fe crystalline aggregates through the thermal migration process. In order to maximize the observability of
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4. Conclusions
Fig. 4. Normalized compositional separation before Soret process reaches steady state plotted versus time normalized to charge length. The slope of lines through the origin give values of D for the element undergoing compositional separation. The three experiments are all consistent with D of about 8 ð 10 6 cm2 =s. The large formal error bars reflect the strong leverage exerted by the compositional measurement uncertainties, which potentially could be uncorrelated, upon the ln[1 ∆X .S/t=∆X .S/ss ] function. Given the small spread in the calculated values using the mean compositions, these error bar are probably unrealistically large, suggesting correlation in the uncertainties.
thermal migration compaction, a new bulk composition was prepared by adding Fe to the original mix until S was reduced to 2.5%. Such a bulk composition will compact a much larger fraction of the charge as metal than our Soret time series composition. Two experiments in the same temperature range and experimental configuration as the Soret series were performed: one for 10 minutes and one for 20 minutes. In 10 minutes about 200 µm of clean metal had compacted against the cold end and about 200 µm of single phase liquid had been segregated from all metal at the hot end. After 20 minutes a complete separation of the charge into 60% S-free metal at the cold end had occurred. To complete the job, less than 20 minutes were required. So to a first approximation the observations of compaction rate give the same result as the Soret analysis. The chemical diffusivity is rapid enough to reorganize material on the length scale of a millimeter in about 1000 s; D is of order 10 5 cm2 =s.
Such diffusivities are up to several orders of magnitude faster than those found in silicates at comparable pressures and temperatures by comparable techniques, e.g. Lesher and Walker [10]. Although these experimental conditions are not those at the core–mantle boundary where diffusion might be even faster through higher temperature, it remains unlikely that any reasonable extrapolation of these diffusivities to core–mantle boundary conditions will change the conclusion that diffusion is not a major agent of mass transfer within the outer core. While our understanding of Soret diffusion has increased significantly over the past decade, our ability to incorporate this knowledge in large-scale geochemical processes in the vicinity of the D00 layer and the core–mantle boundary is still quite limited. We conclude with a list of some topics where advances in the near future might be expected. It would be interesting to extend the Soret study to 100 kbar to look for pressure effects on the diffusion coefficient. This would be interesting in its own right as well as being an aid to the extrapolation of the diffusion constant to core pressures. (It is less of a jump from 100 kbar to a megabar than it is from 10 kbar to a megabar!) Additional information on temperature effects and the effects of competing light elements would be desirable. Finally, we need to understand what processes at the microscopic level may be responsible for initiation and the steady state of Soret diffusion. In contrast to the base of knowledge for silicate liquids, we believe this study and the earlier work of Jones and Walker [4] are the only measurements of Soret coefficients in metal– sulfide liquids. Once these and other processes are better understood, we can more fully address such issues as how mass transfer across the CMB affects core chemistry and how diffusion processes near the CMB influence thermal convection in the lower mantle and in the core.
Acknowledgements One of the authors (E.M.) was supported by the Kosciuszko Foundation in New York City and by the National Science Foundation International Pro-
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gram through supplement to NSF grant EAR9417706 (to D.W.). This is LDEO contribution. D.W. thanks the Max Planck Institute, High Pressure Mineral Physics Group, Mainz for hospitality during manuscript preparation. We thank C.E. Lesher, A.J. Naldrett, and K. Righter for their constructive reviews. [FA]
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