Physics and Chemistry of Minerals

, Volume 38, Issue 10, pp 767–776

Melting of Fe–Ni–Si and Fe–Ni–S alloys at megabar pressures: implications for the core–mantle boundary temperature

Authors

    • Institut de Minéralogie et de Physique des Milieux Condensés, UMR CNRS 7590, Institut de Physique du Globe de ParisUniversité Pierre et Marie Curie
  • Denis Andrault
    • Laboratoire Magmas et VolcansUniversité Blaise Pascal
  • Nicolas Guignot
    • Synchrotron SOLEIL
  • Julien Siebert
    • Institut de Minéralogie et de Physique des Milieux Condensés, UMR CNRS 7590, Institut de Physique du Globe de ParisUniversité Pierre et Marie Curie
  • Gaston Garbarino
    • European Synchrotron Radiation Facility
  • Daniele Antonangeli
    • Institut de Minéralogie et de Physique des Milieux Condensés, UMR CNRS 7590, Institut de Physique du Globe de ParisUniversité Pierre et Marie Curie
Original Paper

DOI: 10.1007/s00269-011-0449-9

Cite this article as:
Morard, G., Andrault, D., Guignot, N. et al. Phys Chem Minerals (2011) 38: 767. doi:10.1007/s00269-011-0449-9

Abstract

High pressure melting behavior of three Fe-alloys containing 5 wt% Ni and (1) 10 wt% Si, (2) 15 wt% Si or (3) 12 wt% S was investigated up to megabar pressures by in situ X-ray diffraction and laser-heated diamond anvil cell techniques. We observe a decrease in melting temperature with increasing Si content over the entire investigated pressure range. This trend is used to discuss the melting curve of pure Fe. Moreover, our measurements of eutectic melting in the Fe–Fe3S system show a change in slope around 50 GPa concomitant with the fcc–hcp phase transition in pure solid iron. Extrapolations of our melting curve up to the core–mantle boundary pressure yield values of 3,600–3,750 K for the freezing temperature of plausible outer core compositions.

Keywords

Iron alloys melting temperatureHigh pressureCore–mantle boundary

Introduction

It is well established that the Earth’s outer core is less dense than a pure Fe–Ni liquid alloy. The so-called core density deficit is currently estimated around 5–10 wt% (Anderson and Isaak 2002) and is attributed to the presence of light elements dissolved in an iron-rich liquid alloy. Among these light elements (Poirier 1994), cosmochemical abundances and geochemical models tend to favor Si and S (Allègre et al. 1995; Javoy 1995). It is, therefore, of primary importance to better constrain the melting properties of Fe–Ni–Si and Fe–Ni-S alloys at relevant P–T conditions to refine compositional and thermal models of the Earth as well as of terrestrial planets and satellites (Breuer et al. 2010).

The melting properties of pure Fe under Earth’s core conditions remain controversial despite a large amount and diverse types of studies on this subject. We can mention shock waves measurements, e.g., (Brown and McQueen 1986; Nguyen and Holmes 2004; Yoo et al. 1993), laser-heated diamond anvil cell studies, e.g., (Boehler 1993; Ma et al. 2004; Shen et al. 1998, 2004), and ab initio calculations, e.g., (Alfè et al. 2002b; Belonoshko et al. 2000; Morard et al. 2011). Thus, measurements of the melting properties of iron alloys under high pressure conditions not only have an intrinsic interest but could also bring important information on this controversial issue.

Sulfur and silicon have very different effects on the properties of iron alloys (Morard et al. 2008b). The large solubility of Si in Fe is related with a solid solution behavior (Kubaschewski 1982) that persists at high pressure (Kuwayama and Hirose 2004). On the contrary, Fe–S phase diagram evolves toward an eutectic system between Fe and Fe3S at 21 GPa (Fei et al. 2000), stable up to core conditions (Kamada et al. 2010). In both cases, melting temperatures need to be determined at megabar pressures, because of the direct consequences on thermal models and properties of the liquid outer core and the core–mantle boundary (CMB).

In this paper, we report investigations of the melting behavior of different Fe–Ni–Si and Fe–Ni–S alloys compressed in a laser-heated diamond anvil cell up to 113 GPa and 3,100 K. Our results are used to constrain the melting temperature depression associated with the presence of light elements at the CMB conditions and to discuss the melting curve of pure iron.

Experimental techniques

Two Fe–Ni–Si alloys and one Fe–Ni–S alloys were synthesized by an ultra-rapid quench method at the ICMPE (Institut de Chimie et des Matériaux de Paris-Est, Paris, France) starting from Fe (99.9%, GoodFellow), Ni (99.9%, GoodFellow), and either Si (99.9%, GoodFellow) or FeS (99.9%, Alfa Aesar). Homogeneous Fe-alloys were first obtained by induction melting in a water-cooled Cu crucible under He atmosphere. Ribbon specimens of ~25 μm thickness and 20–30 mm width were produced by the planar flow casting technique. The alloys were then remelted and ejected through a pressurized quartz nozzle on a rotating Cu-base wheel under 1 bar He atmosphere. Composition of the final products was studied using Cameca SX50 electronic microprobe at Camparis center, University Paris 6, and Zeiss Ultra 55 scanning electronic microscope at the IMPMC, Paris. Homogeneity of the samples was confirmed below 1 micron scale for Fe–Ni–Si alloys and below 2 microns scale for Fe–Ni–S alloys (due to a demixion between Fe and FeS end-members upon quenching). Measured composition of each alloy was, respectively, 85.20(±0.72) wt% Fe, 9.67(±0.14) wt% Si, 5.07(±0.26) wt% Ni; 81.14(±0.59) wt% Fe, 15.10(±0.28) wt% Si, 4.95(±0.33) wt% Ni; and 78.95(±0.53) wt% Fe, 12.42(±0.39) wt% S, 4.52(±0.33) wt% Ni. For convenience, these compositions will be referred hereafter as Fe-5 wt%Ni-10 wt%Si, Fe-5 wt%Ni-15 wt%Si, and Fe-5 wt%Ni-12 wt%S in close agreement with their measured chemical composition.

High pressures were generated with Le Toullec-type diamond anvil cells equipped with diamonds with 250, 300 μm flat or 150/300 μm bevelled diameter culets. Diamonds with conical supports (Boehler and De Hantsetters 2004) were used in order to collect X-ray diffraction over a wide 2-theta angle (70 degrees). The metallic foils were crushed in an agate mortar, and flakes with a thickness of ~10 μm and a diameter of ~50 μm were selected. These specimens were loaded between two dry KCl layers in 50–100-μm diameter holes drilled in a preindented rhenium gasket. KCl acts as a soft pressure medium at high temperature, insuring good hydrostatic conditions, with the further advantage of being chemically inert with the iron alloys (no reaction between KCl pressure medium and Fe liquid alloys has been noted from the analysis of quenched samples diffraction patterns). It also presents the property of trapping the melt, which enables the possibility of collecting a good X-ray diffraction signal.

Samples were heated on both sides by two continuous fibers YAG lasers (TEM 00) providing a maximum total power of 200 W. Temperatures were obtained from spectroradiometric method, using reflective collecting optics (Schultz et al. 2005). Laser spots were more than ~20 μm in diameter. Temperature was measured at the center of the hot spot by analyzing the pyrometric signal emitted by a 2 × 2 μm2 area. Heating power of the two lasers was tuned in order to obtain a same temperature on both sample sides. During acquisition of the X-ray pattern (10 s or 30 s), temperatures stability was checked by measurements on one sample side only.

Angle dispersive X-ray diffraction measurements were performed on the ID27 High Pressure beamline at ESRF (Grenoble, France). The 33 keV monochromatic X-ray beam (Iodine K edge: 0.3738 Å) was focused to a 4 × 4 μm size spot at the sample position. More details concerning the laser-heating experimental setup can be found elsewhere (Mezouar et al. 2005). Fluorescence (in the visible and UV range) induced by X-rays in the diamonds or the pressure medium was used to finalize the optical alignments. This allows the precise superposition between the X-ray beam, the center of the laser hot spot and the spectrometer entrance pinhole.

The experimental procedure was conceived to minimize thermal gradients in the laser-heated samples. The powerful fiber lasers were defocused over a sample area significantly larger than the X-ray spot. Also, good alignment of the optical system was always crosschecked after each heating cycle. Accordingly, radial temperature gradient is likely to be less then 50 K (Schultz et al. 2005). Axial gradients were recently reported to be nonnegligible irrespectively of the care in controlling the laser power on both side (Campbell et al. 2007). These simulations suggest a temperature gradient of ~100 K for our sample geometry. Finally, additional temperature uncertainty comes from the pressure evolution of the sample emissivity, which is generally neglected. A final source of error comes from the temperature fluctuation with time, which, however, was measured to remain lower than 50 K during X-ray acquisition. In summary, we assess the total temperature uncertainties in our experiment to be less than ±150 K.

At ambient temperature, sample pressure was derived from the equation of state of the KCl pressure medium (Walker et al. 2002). To evaluate the pressure change upon heating, we used the empirical law determined in a previous work (Andrault et al. 1998). This estimation is based on the value of αKT of the studied material which for pure Fe is of about 4 × 10−3 GPa/K, based on multi-anvil experiments (Funamori et al. 1996). It is expected that ~60% of the theoretical thermal pressure value (ΔP = αKTΔT corresponding to purely isochoric heating) contributes to the experimental pressure increase. Thus, we assumed a pressure increase of 2.5 × 10−3 GPa/K. This corresponds to 5–8 GPa, for the temperature range investigated in this study (2,300–3,500 K), in good agreement with the pressure increase of 7 GPa reported for the Fe–S system (Morard et al. 2008a). We estimate an overall pressure uncertainty of ±5 GPa at high temperature.

Results and discussion

Melting detection

Appearance of a diffuse X-ray scattering contribution has been recently used for in situ determination of high pressure melting in diamond anvil cell (Andrault et al. 2006; Dewaele et al. 2007; Morard et al. 2008a). This method requires short exposures and a careful monitoring of the temperature. In our systems, the transition between solid and liquid is quite obvious on the two-dimensional diffraction image (Fig. 1). Diffuse X-ray scattering coming from the liquid is observed as a continuous contribution all over the imaging plate, whereas diffraction spots coming from the solid portion of the sample appear as broad (but well-individualized) diffraction spots. In order to obtain the most accurate determination of the onset of melting, we integrated selected portions of the diffraction image with a minimum contribution from Fe-alloy crystals (Fig. 1). Upon temperature increase, diffuse contribution coming from the liquid appears at around 11° scattering angle. Our experimental protocol enables bracketing the melting temperature between two subsequent measurements, the first with and the second without the X-ray diffuse scattering contribution (Fig. 2; Tables 1, 2). To prevent the use of skewed area (melt percolation through the pressure medium, chemical diffusion…), samples were heated at different position after each heating ramp.
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Fig. 1

2D diffraction images of Fe-5 wt% Ni-15 wt% Si sample at temperatures just below the melting point, at the onset of partial melting and just above the melting point for a pressure of 77 GPa. The large diffraction spots can be associated with the presence of crystalline sample below the liquidus. Conversely, a diffuse ring from the liquid Fe-alloy is clearly visible above the solidus. By integrating a zone without any diffraction spots, the onset of melting can be optimally determined at the appearance of the diffuse signal

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Fig. 2

Melting temperature of Fe–Si and Fe–S alloys determined in this study: Square symbols represent data for Fe-5 wt% Ni-10 wt% Si, triangle up symbols for Fe-5 wt% Ni-15 wt% Si and round symbols for Fe-5%wt Ni-12 wt% S. Onset of melting occurs between solid and empty symbols. Melting temperature from previous studies of iron alloys is also reported (Asanuma et al. 2010; Fei et al. 1997; Morard et al. 2007, 2008a). Concerning the melting curve of pure Fe, solid lines and an open triangle show the diversity of experimental results (Boehler 1993; Ma et al. 2004; Williams et al. 1991) and theoretical calculations (Alfè et al. 2002b). The transition line between γ and ε structure in pure Fe is also indicated (Komabayashi et al. 2009)

Table 1

Experimental P–T conditions and phases indexed on the diffraction pattern at ambient temperature

Sample

Composition

Pressure (GPa)

Temperature (K)

Phases

#7–10

Fe-5 wt%Ni-10 wt% Si

28 ± 1

300

 

#7–19

34 ± 5

2,340 ± 150

Completely solid

#7–20

34 ± 5

2,440 ± 150

First liquid

#7–44

45 ± 1

300

 

#7–62

52 ± 5

2,880 ± 150

Completely solid

#7–63

52 ± 5

2,950 ± 150

First liquid

#3–2

Fe-5 wt%Ni-15 wt% Si

28 ± 1

300

 

#3–10

33 ± 5

2,170 ± 150

Completely solid

#3–11

34 ± 5

2,300 ± 150

First liquid

#3–34

40 ± 1

300

 

#3–40

46 ± 5

2,370 ± 150

Completely solid

#3–43

47 ± 5

2,730 ± 150

First liquid

#1–5

40 ± 1

300

 

#1–18

46 ± 5

2,540 ± 150

Completely solid

#1–19

47 ± 5

2,680 ± 150

First liquid

#3–59

49 ± 1

300

 

#3–68

56 ± 5

2,800 ± 150

Completely solid

#3–70

56 ± 5

2,830 ± 150

First liquid

#6–25

70 ± 1

300

 

#6–31

77 ± 5

2,970 ± 150

Completely solid

#6–32

78 ± 5

3,030 ± 150

First liquid

#6–44

72 ± 1

300

 

#6–60

80 ± 5

3,070 ± 150

Completely solid

#6–61

80 ± 5

3,110 ± 150

First liquid

The label “Completely solid” indicates the absence of diffuse signal from the liquid on the diffraction pattern. The label “First liquid” denotes the first appearance of a diffuse signal on the diffraction pattern. The melting sequence is illustrated on Fig. 1

Table 2

Experimental P–T conditions for Fe–S alloys

Sample

Composition

Pressure (Gpa)

Temperature (K)

 

#4–10

Fe-5%wtNi-12%wt S

23 ± 1

300

 

#4–32

 

27 ± 5

1,410 ± 150

Completely solid

#4–33

 

27 ± 5

1,460 ± 150

First liquid

#1–57

 

36 ± 1

300

 

#1–60

 

41 ± 5

1,660 ± 150

Completely solid

#1–61

 

41 ± 5

1,770 ± 150

First liquid

#3–46

 

39 ± 1

300

 

#3–49

 

44 ± 5

1,680 ± 150

Completely solid

#3–50

 

44 ± 5

1,790 ± 150

First liquid

#1–34

 

40 ± 1

300

 

#1–37

 

45 ± 5

1,700 ± 150

Completely solid

#1–38

 

45 ± 5

1,820 ± 150

First liquid

#1–13

 

50 ± 1

300

 

#1–23

 

54 ± 5

1,790 ± 150

Completely solid

#1–24

 

54 ± 5

1,880 ± 150

First liquid

#3–72

 

51 ± 1

300

 

#3–79

 

56 ± 5

1,900 ± 150

Completely solid

#3–80

 

57 ± 5

2,270 ± 150

First liquid

#3–87

 

56 ± 1

300

 

#3–90

 

61 ± 5

2,030 ± 150

Completely solid

#3–91

 

61 ± 5

2,320 ± 150

First liquid

#4–82

 

57 ± 1

300

 

#4–102

 

62 ± 5

2,120 ± 150

Completely solid

#4–103

 

62 ± 5

2,170 ± 150

First liquid

#4–121

 

61 ± 1

300

 

#4–140

 

67 ± 5

2,220 ± 150

Completely solid

#4–141

 

67 ± 5

2,270 ± 150

First liquid

#2–16

 

69 ± 1

300

 

#2–33

 

75 ± 5

2,270 ± 150

Completely solid

#2–34

 

75 ± 5

2,350 ± 150

First liquid

#N–7

 

73 ± 1

300

 

#N–22

 

79 ± 5

2,340 ± 150

Completely solid

#N–24

 

79 ± 5

2,440 ± 150

First liquid

#N–59

 

97 ± 1

300

 

#N–70

 

103 ± 5

2,570 ± 150

Completely solid

#N–71

 

104 ± 5

2,690 ± 150

First liquid

#N–80

 

106 ± 1

300

 

#N–70

 

113 ± 5

2,670 ± 150

Completely solid

#N–71

 

113 ± 5

2,700 ± 150

First liquid

The label “Completely solid” indicates the absence of diffuse signal from the liquid on the diffraction pattern. The label “First liquid” denotes the first appearance of a diffuse signal on the diffraction pattern. The melting sequence is illustrated on Fig. 1

Fe–Ni–Si ternary system

At ambient pressure, Fe–Si alloys present a bcc lattice with a A2 disordered structure or B2 or DO3 ordered structures in which Si atoms adopt well-defined positions (Raghavan 2003). In our measurements performed at 50–60 GPa, these three different bcc structures (hereafter called α-structure) have been indexed (Fig. 3). Actual phases depend upon specific historical P–T path encountered by the sample. For samples containing 10 wt% Si, hexagonal compact (hcp-ε) or face centered (fcc-γ) structures, similar to the structures of pure iron, were found in coexistence with bcc structure, with the ε-structure disappearing at the advantage of the γ-structure with increasing temperature (Fig. 4). This peculiar behavior, with reminiscence of α-structure at variable P–T conditions, has been already reported in the same Fe–Ni–Si ternary system at ambient (Raghavan 2003) and high pressures (Kuwayama et al. 2009). Also, in agreement with compression experiments performed at 300 K on Fe-17.8 wt% Si (Hirao et al. 2004), we observed only the bcc structure in the case of samples with 15 wt% Si (Fig. 3).
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Fig. 3

Selected diffraction patterns of studied iron alloys at high pressure and high temperature. The high quality of the starting material is confirmed by the absence of signals from impurities

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Fig. 4

The Fe–Si phase diagram reported for a pressure of 21 GPa (Brosh et al. 2009; Kuwayama and Hirose 2004) is used to draw a tentative phase diagram at ~50 GPa. Square symbols bracket the appearance of the γ phase in our diffraction patterns for the sample containing 10 wt% Si. We always observed the α phase for our sample containing 15 wt% Si. Melting temperatures of our study (crossed circles) are compatible with those reported previously (Asanuma et al. 2010; Kuwayama and Hirose 2004). It should be mentioned that the melting loops are not represented in the proposed phase diagrams. However, these loops might be relatively small, as indicated by experimental works at ambient pressure (60 K at the maximum) (Kubaschewski 1982) and at 21 GPa (lower than 100 K) (Kuwayama and Hirose 2004) and also from ab initio calculations at core pressures (Alfè et al. 2002a)

Our data set on Fe–Si solid alloys is insufficient to draw a precise phase diagram at the experimental pressure of ~50 GPa. However, the behavior appears very compatible with the Fe–Si phase diagram determined at 21 GPa on the basis of multi-anvil experiments (Kuwayama and Hirose 2004) and thermodynamic calculations (Brosh et al. 2009). As a matter of fact, changes from 21 to ~50 GPa appear to be limited to a slight increase in the stability field of hcp and fcc structures to higher Si contents (Fig. 4). Melting temperatures for samples with 10 wt% Si and 15 wt% Si have been measured up to 52 GPa and up to 80 GPa, respectively (Table 1; Fig. 2). The results obtained for 15 wt% Si are in good agreement with a previous report for a Fe-alloy with 18 wt% Si (Asanuma et al. 2010).

A very important observation is the increase in the melting temperature of Fe–Si alloys when reducing the Si content from 15 to 10 wt% Si, in agreement with multi-anvil experiments performed at 21 GPa (Kuwayama and Hirose 2004) (Fig. 3). The linear trend reported by Kuwayama and Hirose (2004) (decrease of ~15 K/wt%Si) reasonably fits our data, as well as previous measurement performed at higher pressures (Asanuma et al. 2010). According to this trend, we can extrapolate the melting temperature determined for Fe–Si alloys to that of pure Fe, obtaining a value of 3,000 K for pure Fe at 50 GPa (Fig. 4). Over the here-investigate pressure range, our data points, together with results from previous study (Asanuma et al. 2010), support a Fe melting curve at relatively high temperatures, comparable to that measured by Williams et al. (1991) or Ma et al. (2004) or that calculated by Alfe et al. (2002b), and strongly disagree with the experimental curve reported by Boehler (1993) (Fig. 2).

Fe–Ni–S ternary system

Eutectic melting temperature of Fe- 5 wt% Ni- 12 wt% S has been determined up to 113 GPa (Table 2, Fig. 2). The composition of the eutectic melt in the Fe–Fe3S system is assumed to be around 12 wt% S, as recently measured under megabar conditions (Kamada et al. 2010). At all pressures, we observed mixture of Fe and Fe3S phases up to the melting temperature (Fig. 3). Up to ~50 GPa, our data are in good agreement with previous experiments (Campbell et al. 2007; Chudinovskikh and Boehler 2007; Morard et al. 2008a; Stewart et al. 2007), showing (a) that 5 wt% Ni does not affect significantly the melting properties of Fe–S alloys and (b) that 12 wt% S induces a melting temperature depletion much more pronounced than for the same amount of Si. At about 55 GPa, the melting line shows a sudden change, with a difference of ~150 K between trends from lower pressure experiments (one point from this experiment and several points from previous experiments (Morard et al. 2008a, b; Campbell et al. 2007)) and our data at P > 60 GPa (Fig. 2). This discontinuity is supposed to reflect the γ–ε transition occurring in solid iron at comparable pressures (Komabayashi et al. 2009). This behavior is consistent with what observed at ~20 GPa, when the eutectic melting line changes from negative to positive slope, in relation with phase transition in the Fe–FeS system (Andrault et al. 2009; Fei et al. 2000). Furthermore, kinks in the melting curve are often observed when a solid–solid phase transition boundary crosses the melting curve (Brazhkin et al. 1997).

Geophysical implications

We used the Simon–Glatzel’s equation (Simon and Glatzel 1929) to extrapolate the melting curve of Fe–S and Fe–Si alloys up to 140 GPa:
$$ T_{M} = T_{0} \left( {\frac{{P_{M} - P_{0} }}{a} + 1} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 c}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$c$}}}} $$
(1)
In this expression, a and c are fitting parameters, TM and PM are the thermodynamic conditions of melting curve, and T0 and P0 are the coordinates of the initial point of the melting curve (Table 3). This formalism has been shown to represent adequately the melting curve of various metals (Asanuma et al. 2010; Errandonea 2010). We also obtained a very good fit to our data sets (Fig. 5). Concerning the Fe–S system, we only considered the data points recorded above 53 GPa and 1,800 K, in line with the previously discussed kink in the melting line at lower pressure (Fig. 2). At the pressure of 135 GPa, corresponding to the CMB, we obtain temperatures of 3,600 and 2,850 K for eutectic melting in the Fe–FeSi and Fe–Fe3S systems, respectively.
Table 3

Fit parameters of the Simon–Glatzel’s equation for Fe-5 wt%Ni-15 wt%Si and Fe–Fe3S eutectic melting

 

P0 (GPa)

T0 (K)

a

c

Fe-5 wt%Ni-15 wt%Si

0

1,478

10

3

Fe3S eutectic melting

53

1,800

5.5

6

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Fig. 5

Melting curve for Fe-5 wt% Ni-15 wt% Si and Fe–Fe3S extrapolated to the CMB (135 GPa), using the Simon–Glatzel’s equation (parameters from Table 3). These curves are compared with the melting curve of pure Fe from (Alfè et al. 2002b) and the lower mantle solidus temperature (Andrault et al. 2011; Fiquet et al. 2010). Inset: Ternary diagram Fe–S–Si representing the temperature at the CMB as a function of the light element content in the Earth’s core, from different geochemical models (Allègre et al. 1995; Javoy 1995). Dashed lines are isothermal melting points. Solid circle represent the Si content of the Fe–Si alloys studied here (15 wt% Si) and the S eutectic content in the Fe–Fe3S system at CMB pressure (Kamada et al. 2010)

About the melting curve of pure Fe, we already mentioned the good agreement between our data set and the ab initio calculations by (Alfè et al. 2002b). On the basis of this calculation, the melting temperature of pure iron is at about 4,400 K at CMB pressure. Therefore, the melting depressions at CMB conditions are estimated to be 800 K and 1,550 K, for the addition of 15 wt% Si and 12 wt% S, respectively (and neglecting the effect of 5 wt% Ni) (Fig. 5). This last assumption is validated by our experiments in the Ni-bearing Fe–Fe3S system, which plot in excellent agreement with previous work on samples without Ni (Fig. 2).

Assuming that the melting temperature depression is a linear function of the light element content seems to be realistic assumption for the FeSi system (Fig. 4). This behavior could be due to the structural property of this alloy that exhibits a solid solution behavior for Fe and Si atoms. For the Fe–S system, a nonideal melting behavior is observed at low pressures, but it has been suggested that this could disappear above 20 GPa (Chen et al. 2008). Accordingly, even the assumption of a linear relationship between melting temperature depression and S content seems reasonable under megabar conditions, as also suggested in a recent publication (Kamada et al. 2010). Under these assumptions, melting depressions at the CMB are the following: 124 K/wt% S and 53 K/wt% Si.

The composition of the outer core is still controversial, and in the following, we will only consider two standard geochemical models. The first propose an outer core containing 7.35 wt% Si and 2.30 wt% S (Model-A; Allègre et al. 1995), while the second suggest a larger amount of lighter elements: 10.36 wt% Si and 2.57 wt% S (Model-J; Javoy 1995). For these two compositions, the melting temperature or, looking at the problem with a different prospective, the crystallization temperature is calculated to be 3,600 or 3,750 K, for Model-A and Model-J, respectively (Fig. 5, inset).

To address the Earth’s outer core in a more complete manner, the consequences of the possible presence of oxygen should be discussed as well. Recent studies suggest the presence of up to 5–8%wt O in the liquid outer core (Badro et al. 2007; Ozawa et al. 2008). Given the observed core density, such high O content would require substitution with other light elements, preferentially sulfur (Badro et al. 2007). As oxygen has a smaller effect on pure Fe melting temperature than sulfur (Seagle et al. 2008), this would result in an overall increase in the crystallization temperature of the alloy at CMB conditions. However, more reliable data on melting properties in the Fe–FeO system at the CMB pressures are required to accurately address this point. Therefore, the temperature of 3,600–3,750 K can be looked at as a lower bound for the melting temperature of plausible outer core composition at the CMB pressure.

The core crystallizes from its center upon secular cooling of the Earth so that adiabatic and melting temperatures are equal at the inner core–outer core boundary pressure of 330 GPa, and the pressure gradient must be less for the adiabatic temperature than for its melting temperature profile over the entire liquid outer core. Consequently, the core temperature at the CMB is expected significantly higher than its crystallization temperature. How much the CMB core temperature is higher than crystallization temperature remains difficult to estimate, because extrapolations between 135 and 330 GPa of both adiabatic and melting temperature profiles are too imprecise. Our estimation of 3,600–3,750 K for temperatures at the CMB is compatible with a recent thermal model of deep Earth suggesting CMB temperature between 3,300 and 4,300 K (Lay et al. 2008).

On the basis of seismological heterogeneities observed in the D”-layer (Williams and Garnero 1996), the presence of a partially molten mantle in this region has been put forward. Solidus temperature of the lowermost mantle was recently reported to be around 4,100–4,200 K for both pyrolitic and chondritic compositions (Andrault et al. 2011; Fiquet et al. 2010) (Fig. 5). This temperature plots slightly higher than the outer core melting temperature of 3,600–3,750 K we propose. However, we argued above that the outer core temperature at the CMB must be significantly higher than its crystallization temperature. Therefore, the CMB temperature could range within a few hundreds K below, or above, the mantle solidus temperature. We also note that an increase concentration of fusible (incompatible) elements in the D”-layer would lower the solidus temperature below 4,100–4,200 K, which would even reduce the difference in melting temperature between the outer core and lowermost mantle. Finally, as the Earth’s temperature was higher in the past (with a core fully molten), partial melting in the D”-layer seems probable on the basis of our data set. The melting could have extended in a form of a basal magma ocean (Labrosse et al. 2007) and could reasonably still be present in some mantle regions nowadays (Lay et al. 2004).

Acknowledgments

GM acknowledges the SECHEL program of the Agence Nationale de la Recherche (Grant ANR-07-BLAN-185577) and the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 207467. The authors would like to thank the ESRF staff of the High Pressure Beamline ID27 (S. Bauchau) for the X-ray experiments. We would like also to thank G.Fiquet for fruitful discussions.

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© Springer-Verlag 2011