Author Affiliations
1Japan Synchrotron Radiation Research Institute (JASRI), Sayo, Sayo-gun, Hyogo 679-5198, Japan2Graduate School of Material Science, University of Hyogo, Kouto, Kamigohri, Hyogo 678-1297, Japanshow less
Fig. 1. Representative x-ray diffraction pattern (red crosses) and Rietveld simulation (green line) for hcp-Fe at 354 GPa. The blue line shows a residual. Lattice constants are calculated to be a = 2.1294(17) Å and c = 3.390(5) Å for hcp-Fe and a = 3.4049(11) Å for fcc-Pt.
Fig. 2. Compression curve of Fe up to a pressure of 354 GPa, together with curves from previous reports. Solid black, green, blue, and red curves correspond to the experimental results of the present study and those conducted by Mao et al.,3 Dubrovinsky et al.,4 and Dewaele et al.,5 respectively. ΔVa denotes the deviations of the atomic volume for each previous curve from the present one.
Fig. 3. Representative x-ray diffraction pattern (red crosses) and Rietveld simulation (blue line) for Ni at 368 GPa. The green line shows a residual. The estimated lattice constants a for fcc-Ni and fcc-Pt are 2.9521(10) and 3.3977(6) Å, respectively.
Fig. 4. Compression curve of Ni up to a pressure of 368 GPa, together with curves from previous reports. Solid black, green, and red curves are Vinet EOS fits to the experimental data from the present study, Kennedy and Keeler,14 and Dewaele et al.,6 respectively.
Fig. 5. Gamma plots constructed using (a) the fcc-Pt data at 354 GPa from Table II, (b) the fcc-Pt data at 368 GPa from Table IV, and (c) the fcc-Ni data at 368 GPa from Table IV.
Fig. 6. Densities of Fe, Ni, and Fe0.91Ni0.09 at 298 K as functions of pressure. The Preliminary Reference Earth Model (PREM)37 is also shown for comparison.
Run No. | Diamond anvil geometrya (μm) | PTMb | Scale | P range (GPa) |
---|
Fe 1 | 500 | He | Pt + ruby | 5–20 | Fe 2 | 350 | He | Ruby | 0–54 | Fe 3 | 35/250/350 | None | Pt | 0–296 | Fe 4 | 28/250/350 | None | Pt | 219–354 | Ni 1 | 500 | MEWc | Ruby | 0–10 | Ni 2 | 500 | He | Pt | 0–21 | Ni 3 | 100/300 | None | Pt | 2–179 | Ni 4 | 27/250/450 | None | Pt | 257–368 | Ni 5 | 50/230/450 | None | Pt | 163–202 |
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Table 1. Conditions of each experimental run.
2θ (deg) | do (Å) | hcp-Fe | fcc-Pt |
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a = 2.1294(17) (Å) | a = 3.4049(11) (Å) |
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c = 3.390(5) (Å) | |
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Index | dc (Å) | do − dc (Å) | Index | dc (Å) | do − dc (Å) |
---|
12.193 | 1.9661 | | | | 111 | 1.9658 | 0.0003 | 12.970 | 1.8487 | 010 | 1.8441 | 0.0046 | | | | 14.090 | 1.7024 | (002) | | | 200 | 1.7025 | −0.0001 | 14.833 | 1.6176 | 011 | 1.6200 | −0.0024 | | | | 19.290 | 1.2463 | 012 | 1.2480 | −0.0017 | | | | 20.004 | 1.2022 | | | | 220 | 1.2038 | −0.0016 | 22.639 | 1.0638 | 110 | 1.0647 | −0.0009 | | | | 23.451 | 1.0275 | | | | 311 | 1.0266 | 0.0008 | 24.518 | 0.9834 | | | | 222 | 0.9829 | 0.0005 | 25.003 | 0.9646 | 013 | 0.9636 | 0.0010 | | | | 26.808 | 0.9007 | 112 | 0.9016 | −0.0009 | | | | 27.113 | 0.8908 | 021 | 0.8897 | 0.0010 | | | | 28.406 | 0.8510 | | | | 400 | 0.8512 | −0.0002 |
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Table 2. 2θ and d-values (do) of the observed diffraction lines with λ = 0.4176 Å for the pattern at 354 GPa, indices for these lines, and calculated d-values (dc) for the hcp-Fe and fcc-Pt phases. Calculated lattice constants are also listed.
V0 (Å3) | K0 (GPa) | | P Range (GPa) | P Gauge | Formula | PTM | References |
---|
11.215(29) | 159.27(99) | 5.86(4) | 14–354 | Ruby or Pt | Vinet | He or none | Present | 11.176(17) | 164.8(3.6) | 5.33(9) | 35–300 | Pt | B-Ma | Ar or none | Mao et al.3 | 11.1780(2) | 160.67(5) | 5.36(1) | | | B-M | | Corrected EOS | 11.1989 | 156 | 5.81 | 20–200 | Pt | B-M | None (heating) | Dubrovinsky et al.4 | 11.2022(1) | 151.65(2) | 5.854(3) | | | B-M | | Corrected EOS | 11.214(49) | 163.4(7.9) | 5.38(16) | 17–197 | Ruby or W | Vinet | He | Dewaele et al.5 | 11.214 | 156.7(9) | 5.8(1.0) | | | Vinet | | Corrected EOS |
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Table 3. Parameters of the Vinet EOS obtained by a least-squares fit of the experimental compression data for hcp-Fe, together with those from previous reports. The parameters of these EOSs are the atomic volume V0, bulk modulus K0, and its pressure derivative under ambient conditions.
2θ (deg) | do (Å) | fcc-Ni | fcc-Pt |
---|
a = 2.9521(10) (Å) | a = 3.3977(6) (Å) |
---|
Index | dc (Å) | do − dc (Å) | Index | dc (Å) | do − dc (Å) |
---|
12.048 | 1.9614 | | | | 111 | 1.9616 | −0.0001 | 13.856 | 1.7065 | 111 | 1.7053 | 0.0011 | (200) | | | 16.008 | 1.4783 | 200 | 1.4769 | 0.0015 | | | | 19.722 | 1.2020 | | | | 220 | 1.2012 | 0.0008 | 22.757 | 1.0434 | 220 | 1.0443 | −0.0008 | | | | 23.186 | 1.0243 | | | | 311 | 1.0244 | −0.0001 | 24.244 | 0.9803 | | | | 222 | 0.9808 | −0.0005 | 26.746 | 0.8900 | 311 | 0.8906 | −0.0005 | | | | 27.969 | 0.8518 | 222 | 0.8527 | −0.0004 | (400) | | | 30.613 | 0.7798 | | | | 331 | 0.7794 | 0.0003 | 31.446 | 0.7596 | | | | 420 | 0.7597 | −0.0001 | 32.359 | 0.7387 | 400 | 0.7384 | 0.0001 | | | |
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Table 4. 2θ and d-values (do) of the observed diffraction lines with λ = 0.4134 Å for the pattern at 368 GPa and indices for these lines and calculated d-values (dc) for the fcc-Ni and fcc-Pt phases. Calculated lattice constants are also listed.
V0 (Å3) | K0 (GPa) | | Method | P Range (GPa) | Formula | References |
---|
10.9376(4) | 173.5(1.4) | 5.55(5) | DAC | 0–368 | Vinet | Present | ⋯ | 183(3) | ⋯ | Ultrasonic | ⋯ | ⋯ | Yamamoto15 | 10.940 | 176.7(2.5) | 5.23(9) | DAC | 0–156 | Vinet | Dewaele et al.6 | 10.940 | 169.3(8) | 5.67(18) | | | Vinet | Corrected EOS | 10.9376 | 187.8(5) | 4.89(4) | Shock wave | 0–120 | Vinet | Kennedy and Keeler14 |
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Table 5. Parameters of the Vinet EOS obtained by a least-squares fit of the experimental compression data for Ni, together with those from previous reports. The parameters of these EOSs are the atomic volume V0, bulk modulus K0, and its pressure derivative , under ambient conditions.