Supplementary Materials
Methods
As starting materials we used samples of iron (99.999% purity), silicon
(99.999% purity), and amorphous silica (99.99% purity). Iron-silicon alloys were
synthesized by arc melting appropriate amounts of silicon and iron rod in an arc
furnace in a pure argon atmosphere. The samples were powdered by milling and then
homogenized in vacuum at 900°C for at least 120 hours.
Experiments in multianvil apparatus were performed in a 1200-tonne press.
The sample assembly consisted of an MgO (+5 wt% Cr2O3) octahedron (18 mm edge
length) containing a LaCrO3 heater. The octahedron was compressed using 32 mm
tungsten carbide anvils with a truncation edge length of 11 mm and pyrophyllite
gaskets. Temperature was monitored with a W3Re/W25Re thermocouple located
axially with respect to the heater and with a junction in a direct contact with the MgO
capsule. The P-T uncertainties are estimated to be 1 GPa and 50 K, respectively.
The sample (mixture of Fe (80 wt%), Si (5 wt%), and SiO2 (15 wt%)) was contained
in MgO capsule, which reacted during the experiments forming magnesiowüstite. In
each experiment the sample was first compressed to the desired pressure; the
temperature then raised with 100 K/min to the desired run temperature and was then
held there for 60 – 90 min. The sample was finally quenched by switching off the
power to the furnace and then slowly decompressed. After the completion of each
experiment, the entire sample assembly was mounted in epoxy, sectioned through the
centre of the sample and then polished. One part was used for the electron microprobe
analysis and another part served as a source of material for DACs experiments.
Chemical analysis was done with the CAMECA SX 50 electron microprobe.
The details of the experiments performed with electrically- and laser-heated
DAC are described in our earlier papers1–3. At ESRF powder diffraction experiments
were conducted at the beam lines BM01 and ID30. At the BM01 beam line the data
was collected with the MAR345 detector using an X-ray beam of 0.6996 Å
wavelengths and a size of 50x50 m (beam line BM01), and at ID30 we used
MAR345 or Bruker CCD area detectors and a highly focused beam of 10x15 m. The
detector-to-sample distance varied in different experiments from 170 to 350 mm.
Diamonds were mounted on seats made of B4C or cBN allowing us to collect the
complete Debye rings to 0.95 Å. The collected images were integrated using the
Fit2D program in order to obtain a conventional diffraction spectrum. Pressure was
determined from -Fe equation or NaCl equation of state2. All loadings of DAC were
made in inert atmosphere (Ar or He).
To study the tiny specimens recovered from diamond anvil experiments with
the transmission electron microscope (TEM) it was necessary to thin them to electron
transparency. The specimen foils were thin enough to be mounted directly onto
conventional Cu grids. They were subjected to Ar ion bombardment in a GATAN
DUOMILL milling machine (4.5 kV, 0.5 mA). To observe and characterise the
microstructures and structural state of ion-milled specimens, we used a PHILIPS
CM20 FEG analytical transmission electron microscope (ATEM), operating at 200
kV. Electron diffraction experiments on the polycrystalline, fine-grained specimens
were performed in selected area mode and generally yielded ring patterns; they were
scanned and evaluated in the same manner as X-ray diffraction patterns. To measure
the compositional variations, we employed a ThermoNoran Vantage energydispersive X-ray (EDX) spectrometer, which was attached to the ATEM. The
quantification of EDX spectra was done according to the Cliff-Lorimer thin film
technique4.
Ab initio electronic structure and total energy calculations were carried out in
the framework of the density functional theory5 using the generalized gradient
approximation for the exchange-correlation energy and one-electron potential. The
basis set of the so-called EMTO (exact muffin-tin orbitals) was employed, and the
complete technique is described in ref. 6. The all-electron calculations were carried
out. The 3p, 3d, and 4s electrons of Fe, as well as 3s and 3p electrons of Si were
treated as valence electrons. The core states were recalculated at each iteration within
the soft-core approximation. A sufficiently dense mesh was used for calculating
reciprocal space and energy integrals, so that the total energy was converged to within
0.1 meV. Dependences of the total energy on the volume for each system were fitted
using the Birch-Murnaghan equation, and theoretical values of pressure were
calculated from the fit.
Fig. S1 (Supplementary materials) Results of ab initio electronic structure and total
energy calculations for Fe-Si alloys at different compressions (see Methods). a.
Theoretically determined mixing enthalpies (in kJ/mole) of random hcp Fe0.9Si0.1
alloy (filled circles) and formation enthalpies (in kJ/mole) of B2 FeSi compound
(filled squares) at different pressures. b. Calculated density of states (DOS, per unit
cell) of the B2 FeSi as a function of energy E (in eV) at pressure 160 GPa. For the
mixing enthalpies, the hcp phase of Fe and the fcc phase of Si were chosen as
standard states at all pressures. Mixing enthalpies were also calculated for less
concentrated random hcp alloys, as well as for bcc random alloys (not shown in the
figure). The latter were found to transform into the former at pressures close to the
bcc-hcp transition pressure in the pure Fe. So-called ground state lines connect pure
Fe and points corresponding to the formation enthalpies of the B2 compound. The fact
that the mixing enthalpy of a random alloy at a given pressure is above the
corresponding ground state line indicates its instability with respect to the
decomposition into the Si poor hcp alloy and B2 FeSi. From the inset in a one can
clearly see that this tendency increases with increasing pressure. Note that at ambient
pressure the phase diagram of Fe-Si system is complicated with different intermediate
phases present. They were not considered in the present calculations because earlier
theoretical study for this system7 predicted the B20 to B2 structural transformation in
FeSi at relatively low pressure, and indicated that the latter should be the most stable
high-pressure phase for the compound with equatomic composition. The Fe3Si phase
in the DO3 structure is stabilized by the ferromagnetic order7, and therefore it is not
supposed to be stable at high pressure and temperature due to a suppression of
magnetism. A finite DOS at the Fermi level EF in b indicates that the compound
should be an electric conductor.
References
1.
Dubrovinsky, L. et al. Chemical interaction of iron and corundum as a source
of heterogeneity at the core-mantle boundary. Nature 412, 527–529 (2001).
2.
Dubrovinsky, L. S., Saxena, S. K., Tutti, F. & Le Bihan, T. X-ray study of
thermal expansion and phase transition of iron at multimegabar pressure. Phys. Rev.
Lett. 84, 1720–1723 (2000).
3.
Prokopenko, V. B., Dubrovinsky, L. S., Dmitriev, V. & Weber, H.-P. Raman
spectroscopy and X-ray diffraction in situ characterization of phase transitions in
cristobalite under high pressure. J. Alloys Compounds 327, 87–95 (2001).
4.
Cliff, G. & Lorimer, G. W. The quantitative analysis of thin samples. J.
Microsc. 103, 203 (1975).
5.
Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. B 136,
864–871 (1964).
6.
Vitos, L., Abrikosov, I. A. & Johansson, B. Anisotropic lattice distortions in
random alloys from first-principles theory. Phys. Rev. Lett. 87, 156401 (2001).
7.
Moroni, E. G., Wolf, W., Hafner, J. & Podloucky, R. Cohesive, structural, and
electronic properties of Fe-Si compounds. Phys. Rev. B 59, 12860–12871 (1999).
Fig. S1a (Supplementary Materials)
Fig. S1b (Supplementary Materials)