Research ArticlePLANETARY SCIENCE

Crystal structure and equation of state of Fe-Si alloys at super-Earth core conditions

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Science Advances  25 Apr 2018:
Vol. 4, no. 4, eaao5864
DOI: 10.1126/sciadv.aao5864
  • Fig. 1 Experimental setup for laser ramp-compression experiments.

    (A) The laser drive is focused to an 800-μm spot on the front diamond surface of C/Au/C/Fe-Si/C or C/Fe-Si/LiF target packages, which are centered over a 300-μm-diameter pinhole. (B) Ablation of the surface of the diamond pusher creates a rapidly expanding plasma that launches a pressure wave through the pusher/sample/window interfaces. For the thin samples used in this experiment, reverberations within the Fe-Si alloy layer due to impedance mismatches across the boundaries rapidly equilibrates the pressure. (C) Schematic of the PXRDIP diagnostic. Quasi-monochromatic x-rays emitted by a laser-generated plasma from a Cu, an Fe, or a Ge foil (left, recorded x-ray emission spectra) diffract from the target package and are recorded by image plates that line the box interior. A rear aperture provides access for velocity interferometry (VISAR).

  • Fig. 2 X-ray diffraction patterns of Fe-Si samples.

    (A and B) Examples of raw (unprocessed) image plate panels. Image plate positions were calibrated using ambient pressure W-pinhole diffraction lines (dashed blue lines). (C and D) Projection of the above image plates into d-spacing − φ coordinates. The one-dimensional (1D) x-ray diffraction patterns at top were integrated over the region between the blue horizontal lines. Diffracted peaks from Fe Hα radiation (6.963 keV) are also observed (gray arrows). Asterisks (*) in (B) and (D) denote an extended feature which has a d-spacing consistent with either hcp (100) or diamond (111), as discussed in the text.

  • Fig. 3 Measured diffraction peaks and density of Fe-Si alloys as a function of pressure.

    From measured (A) d-spacings of ramp-loaded Fe-7Si, we determine (B) the density of the hcp structure as a function of pressure. A Vinet equation of state fit to the data along the ramp-compression path is compared to measured and extrapolated diamond anvil cell experiments: *, green dash-dotted line = Fe-6.5Si (23); +, blue dashed line = Fe-8.7Si (11). (C) d-spacing and (D) density of ramp-loaded Fe-15Si interpreted as a bcc structure. Measured/extrapolated isotherms: +, red dashed line = Fe-17.8Si (11); purple dash-dotted line = Fe-16Si (14). For comparison, the pressure-density path of ramped Fe to 300 GPa (26) and the Fe-isentrope from Sesame EOS table 2150 (27) are shown.

  • Fig. 4 c/a ratio as a function of pressure for Fe-7Si.

    The unit cell ratios of hcp-structured Fe-7Si alloy were calculated from the x-ray diffraction patterns using all three observed hcp reflections (red squares) or only the two stronger reflections (blue circles). Low-pressure DAC data (gray symbols) predict a relatively modest increase in c/a ratio with increasing temperature (15, 23), approaching closer to the ideal hcp ratio of 1.633.

  • Fig. 5 Density difference between Fe and Fe-Si.

    Percent density difference for measured P − ρ of Fe-7Si (diamonds) and Fe-15Si alloys (circles) with respect to the Fe end-member isentrope from Sesame EOS table 2150 (27). Red and green curves represent Vinet EOS fits to our data with V0 fixed (filled 68% band) and V0, K′ fixed with K′ = 5 (dashed lines). Also shown are percent density differences with ramp EOS measurements on Fe (dashed gray) (26) and the Sesame EOS table 2150 300-K isotherm (blue trace) (27). We note that the Fe isentrope used here is in agreement with recent experimental results from laser-ramp experiments (29).

  • Fig. 6 Modeled interior profiles of Kepler-10b.

    Given the observational constraints on Kepler-10b (3.72 ME, 1.47 RE), end-member interior models can be compared to explore the impact of light-element substitution within the core. A simple two-layer planet, core + mantle, with substitution in the core of our measured P − ρ relationship for Fe-15Si (green trace) for that of pure iron (black trace) has a large effect on the modeled pressure and density profiles. CMB, core-mantle boundary; pv/ppv, perovksite-structured bridgmanite→post-perovskite; TZ, transition zone (olivine→bridgmanite + periclase).

  • Fig. 7 Timing and pressure determination of an Fe-15Si ramp-compression experiment (diamond window).

    (A) Composite laser drive for shot #78431 (1260 ± 20 GPa) (blue trace). X-rays are generated using a pair of square pulses (red trace). (B) A VISAR interferogram with extracted free-surface velocity history from two VISAR channels. (C) Calculated map of pressure distribution throughout the target package, where the horizontal dashed lines indicate material boundaries in Lagrangian coordinates. Shaded in light gray, predicted pressure release waves (see Materials and Methods). (D) Calculated pressure history of the Fe-Si sample, integrated over the x-ray probe time (vertical dashed lines).

  • Fig. 8 Timing and pressure determination of an Fe-15Si ramp-compression experiment (LiF window).

    (A) Composite laser drive for shot #77742 (277 ± 25 GPa) (blue trace). X-rays are generated using square pulses (red trace). (B) Raw interferogram from VISAR records sample-LiF particle velocity, which is reproduced by hydrocode simulations (red dashed curve) to determine (C) pressure history in the target package. The black rectangle represents the sample pressure conditions during the x-ray probe period (bounded by vertical dashed lines). (D) Calculated pressure history of the Fe-15Si sample.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaao5864/DC1

    fig. S1. Consideration of alternate structures for Fe-15Si.

    fig. S2. Constraints on the P-T phase diagram for Fe-7Si and Fe-15Si.

    fig. S3. Example of projected image plates, from shot s77742.

    fig. S4. X-ray diffraction patterns as a function of pressure.

    fig. S5. Equation of state models used for pressure determination.

    fig. S6. Summary of laser power, interface velocity, and sample pressure history for Fe-7Si and Fe-15Si ramp-compression experiments.

    table S1. Data summary.

    References (5760)

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Consideration of alternate structures for Fe-15Si.
    • fig. S2. Constraints on the P-T phase diagram for Fe-7Si and Fe-15Si.
    • fig. S3. Example of projected image plates, from shot s77742.
    • fig. S4. X-ray diffraction patterns as a function of pressure.
    • fig. S5. Equation of state models used for pressure determination.
    • fig. S6. Summary of laser power, interface velocity, and sample pressure history for Fe-7Si and Fe-15Si ramp-compression experiments.
    • table S1. Data summary.
    • References (57–60)

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