Geophysical Research Letters Supporting Information for Melting curve and phase relations of Fe-Ni alloys: implications for the Earth's core composition

1 Geophysical Research Letters

Supporting Information for

Melting curve and phase relations of Fe-Ni alloys: implications for the Earth's core composition

R. Torchio¹, S. Boccato¹, F. Miozzi², A.D. Rosa¹, N. Ishimatsu³, I. Kantor⁴, N. Sévelin-Radiguet¹, R. Briggs⁵, T. Irifune⁶ and G. Morard^2,7

1European Synchrotron Radiation Facility, Grenoble, France

2Institut de Minéralogie, de Physique des Matériaux, et de Cosmochimie (IMPMC), Sorbonne Université - UPMC, UMR CNRS 7590, Muséum National d’Histoire Naturelle, IRD UMR 206, F-75005, Paris, France

3Graduate School of Advanced Science and Engineering, Hiroshima Univ., Higashi-Hiroshima, Japan 4Institut for Fysik, Danmarks Tekniske Universitet, Kongens Lyngby, Denmark

5Lawrence Livermore National Laboratory, Livermore, CA, USA 6Geodynamics Research Center, Ehime University, Matsuyama, Japan

7Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre, 38000 Grenoble,

Contents of this file

Text S1 to S9 Figures S1 to S4 Table S1

Introduction

This file contains the following supporting information:

Text S1 to S4: further details on the experimental method and data analysis Text S5 and Fig. S1: Invar alloy data

Text S6: thermal pressure evaluation formula

Text S7: fitting parameters and error analysis for the different phase boundaries in the

Fe-20%wtNi phase diagram.

2

Text S8 and figure S2: discussion about chemical reactions

TextS9 and Figure S3: analysis of quenched samples spectra Table1: samples parameters

Text S1. Further details on the experimental method: fast detection

The energy dispersive geometry of the ID24 beamline allows for the simultaneous collection of the whole x-ray absorption spectrum. Such fast detection is particularly useful in online laser heating experiment where a long exposure to the heating laser is undesirable as it can lead to chemical reactions. In these experiment we averaged 8 XAS spectra acquired with 200 ms integration time for a total exposure of 1.6 s while the synchronized laser pulse was lasting 1.8 seconds.

Text S2. X-rays, IR lasers and temperature measurement alignment and radial thermal gradients

Before starting a heating run, the X-rays, IR lasers and optical path for the temperature measurement have to be carefully aligned. This is crucial in order to make sure that the x-rays probe exactly the center of the hotspot and that the temperature is measured at the same place.

This is made possible by the two side optical cameras that allow visualization of the laser and hot spot, the x-rays fluorescence on the salt and the spectrometer entrance. The x-ray position can be double checked by knife-edge scans at the gasket border or sample border. The IR lasers focal spot and the image of the spectrometer entrance for the temperature measurements can be moved independently (off-axis geometry) with sub-micrometric precision. The lasers spot is defocused to 15-20 µm so that the x-rays (4x5 µm FWHM) can be precisely aligned at the center of the hotspot.

Thanks to the independent movements and to the image quality and magnification, the full alignment can be performed with 1 µm precision, assuring that the x-rays and temperature measurement probe the hot spot center. The laser, x-ray and spectrometer entrance alignment is checked continuously during the heating run and adjusted if necessary. The detailed system parameters and alignment procedure is reported in (Kantor, RSI 2018).

The alignment capability is also crucial to cope with unavoidable radial thermal gradients, typically due to the Gaussian spatial profile of the laser spot or to the imperfect thermal insulation of the sample. In all our experiments, disks of KCl with known and homogeneous thickness were used, in order to get a homogeneous thermal insulation, so we believe that radial gradients are mainly related to the laser profile.

In order to roughly estimate radial thermal gradients we have measured the temperature in different positions moving away from the laser hot spot center. Our results show that an offset of few microns (≤2 microns) gives a negligible temperature error (<10%), below the average temperature error. Nevertheless, already at 5 µm away the temperature measured can be 500K lower than the temperature at the hotspot center. This is also in agreement with a simple simulation of thermal profile starting from a 2D Gaussian laser shape of 20 microns FWHM

3 (Giampaoli et al., HPR 2018, Fig.13). Therefore, our alignment capability described above assures that thermal radial gradients should not profoundly affect our measurements.

Text S3. Heating run

Once the desired pressure is reached and the alignment described in Text S2 has been performed, the heating run can start on a fresh portion of the sample. This is particularly important to determine the hcp to fcc phase boundary because, at low pressure, the laser power needed to visualize the hot spot for the alignment can be already enough to induce this transition.

Each heating run starts with a spectrum at room temperature and is followed by a sequence of alternating hot and quenched (to room temperature) spectra. The first ambient temperature spectrum is needed to check that a good portion of the sample has been chosen.

The quenches allow tracking of possible changes in the sample due to chemical reactions or distortions of the sample.

The heating run ends when melting has been detected or a problem, such as chemical reaction or sample distortion (hole formation) occurs, that leads to the discarding of the run. More details about the heating run procedure are reported in Boccato 2017.

Text S4. XANES data normalization

Since the XANES modifications both for the hcp to fcc and for the solid to liquid transition are quite small it is important to use a simple normalization procedure. Here the spectra were simply normalized by setting to 0 (zero) the absorption just before the edge (at E = 7096 eV) and to 1 the absorption just above the edge after the two bumps (E = 7148 eV). A standard normalization procedure, as typically used in EXAFS data processing, using a spline subtraction, would slightly deform the edge shape and lead to unreliable results.

Text S5. Fe-36%wtNi Invar alloy

The invar alloy with 36%wt of Ni was measured at the Ni K edge (8333 eV). This alloy was found in the fcc phase in the whole range of investigation up to the melting. Its behavior under high pressure and temperature as probed by XAS did not show any particular difference with respect to the Fe-20%wtNi alloy, showing similar XANES changes upon melting. This is not so surprising since Invar properties, such as absence of thermal expansion, are expected below the Curie temperature (417K) (i.e. Nataf 2006). An example of heating run is reported in Fig. S1

Text S6. Thermal pressure evaluation

The thermal pressure contribution was evaluated using the empirical formula already used for pure Fe in (Morard 2018):

4 𝑷 = 𝑷_{𝒃𝒆𝒇𝒐𝒓𝒆}+^{𝑷𝒂𝒇𝒕𝒆𝒓+∆𝑷−𝑷𝒃𝒆𝒇𝒐𝒓𝒆}

𝑻𝒎𝒂𝒙−𝟑𝟎𝟎 ∗ (𝑻 − 𝟑𝟎𝟎)

Where P

before

is the pressure measured before the heating run, P

after

is the pressure measured after the heating run, T

max

is the maximum temperature reached in the heating run and ΔP= 2 GPa.

This formula was obtained using XRD measurement, to determine the relationship between the pressure after the heating run and the pressure at the highest temperature during the run, following an approach previously proposed by (Lord 2014).

The obtained formula is only valid when

T

max exceeds 2000K, which is always the case in our experiments.

A detailed discussion about this method is reported in the SI of (Morard 2018).

Text S7. Fitting parameters for the different phase boundaries in the Fe-20%wtNi phase diagram and error analysis.

The melting curve of fcc Fe-20%wtNi was fitted using the Simon-Glatzel law (Simon and Glatzel 1929):

𝑇 = 𝑇₀(𝑃 − 𝑃₀ 𝑎 + 1)

1⁄𝑐

In this expression, a and c are fitting parameters, T and P are the thermodynamic conditions of the melting curve, and T0 and P0 are the coordinates of the initial point of the melting curve. The hcp/fcc boundary was fitted linearly: T=a+bP.

In order to evaluate the uncertainties on the fitting parameters from the errors on P and T, we have used a Montecarlo approach (N. Metropolis, Journal of Chemical Physics 1953). Standard uncertainties on P and T at the phase boundaries points were considered to be 10%.

We have generated 4000 independent boundary point data sets, in which Ti and Pi of each boundary point are randomly generated with a normal distribution around the experimental values Tiexp and Piexp with standard deviation  Tiexp) and  Piexp) of 10% for both Tiexp and Piexp.Each dataset has been fitted to the Simon-Glatzel equation for the melting boundary and to a straight line for the hcp/fcc boundary. From the distributions of the best fit parameters we calculated the expected values and standard deviation for the best fit parameters and we were able to calculate the phase boundary best fit curves with their ± and ±2 intervals as presented in the right panel of Fig. 4 in the main text.

For Fe-20%wtNi, with

T

0

= 1750 K and P

0

=0 GPa (O. Kubaschewski,

Iron binary phase diagrams, Springer Science 1982) we found:

a=8.1(5.2); c=3.7(1.2) for the Simon Glatzel

fit and

a= 590(130) K b= 19.9(1.8) for the linear one.

5 Text S8. Chemical reactions

An important experimental aspect in the technique of laser heating in the diamond anvil cell is the possible occurrence of chemical reactions between the sample and the diamond anvils, that can strongly modify the melting temperature. This has been previously observed in the study dedicated to the melting curve of pure iron (Morard, GRL 2018) and believed to be one of the main source of disagreement between Fe melting curves in the literature.

Chemical reactions with carbon and oxygen are anyway detectable in XANES modifications (Aprilis et al., 2019, Boccato et al., under review in Scientific Reports). In our heating runs, a quench (cold) spectrum is acquired in between each increase of laser power in order to monitor any undesired modifications in the sample. Fig.S1 shows an example of occurrence of chemical reactions with carbon that modifies the edge shoulder around 7118 eV.

We estimate that C or O can be detected in this way down to 1w% content. We show the example of FeC in fig. S2 right panel. When carbon enters in Fe it forms Fe3C, whose shape at the edge is quite different from that of pure Fe. By performing a linear combination of a pure Fe spectrum with one of Fe3C we estimate that we should be able to detect 10-15% of Fe3C corresponding to around 1w% of C. Upon melting of C contaminated samples, the hotspot can get enriched in carbon up to eutectic composition, around 3wt%C (Mashino, EPSL 2019).

Contamination is therefore detectable.

Text S9. The quench behavior

It is interesting to look at the behavior of the quench spectra as a function of applied temperature and induced transitions for Fe-20%Ni. This is shown in Fig.3S. Before the hcp to fcc transition, even after heating at 2420K, Fe-20%Ni quenches in the hcp structure (black line).

After the hcp-fcc transition (~2550 K) the quench exhibits a mixed hcp/fcc phase (blue line) that is re-transformed into hcp as temperature is further increased to 2960 K (violet line). Finally, after the liquid transition (~3450 K) the sample quenches in pure fcc structure. The same behavior is observed in all the investigated pressure range.

Therefore, the quench behavior is somehow reminiscent of the temperature induced transitions, and its analysis could thus be used as a further confirmation of T-induced transformations.

6

Alloy Goodfellow

catalog number

Thickness (µm)

Density (g/cm

³

)

Analysis (ppm)

Ambient structure

Ambient lattice parameter (Å)

Fe-

20wt\%Ni

FF090210 6 bcc 2.86(1)

Fe-

36wt\%Ni

FE020210 8 8 Ni 36%,

Mn + Si + C <1%, Fe balance.

fcc 3.601(1)

Table S1 : Available samples parameters. Thickness, density and analysis are furnished by Goodfellow. Ambient structure and lattice parameter are obtained from EXAFS analysis. In the case of Fe-36wt%Ni an EXAFS measurement of the foil at ambient conditions acquired on beamline BM23 was analysed. In the case of Fe-20wt%Ni there was no available ambient EXAFS spectrum. Therefore, high pressure spectra of bcc Fe-20wt%Ni from 2 to 12 GPa were analysed to obtain the compressed lattice parameter and volume and the ambient values have been derived through a Birch-Murnaghan fit.

Figure S1. Left: example of heating run for the Fe-36wt%Ni alloy at 50 GPa. Right: melting detection in the XANES region.

7 Figure S2. Left: modifications in the shape of the quench spectrum in Fe-20%Ni at 96 GPa indicating the occurrence of chemical reactions. Right: Linear combinations of a pure Fe spectrum with a Fe3C spectrum at the Fe Kedge.

Figure S3. Quenched sample spectra at 84 GPa and as a function of applied temperature along the different temperature-induced transitions.

7100 7120 7140

0.0 0.5 1.0

7130 7140

Normalized absorption (a.u.)

Energy(eV)

before hcp-fcc transition after hcp-fcc transition after heating at 2960K before melting

after melting

Fe_0.8Ni_0.2 at 84 GPa