• Matter and Radiation at Extremes
  • Vol. 7, Issue 3, 038403 (2022)
Naohisa Hirao1, Yuichi Akahama2、a), and Yasuo Ohishi1
Author Affiliations
  • 1Japan Synchrotron Radiation Research Institute (JASRI), Sayo, Sayo-gun, Hyogo 679-5198, Japan
  • 2Graduate School of Material Science, University of Hyogo, Kouto, Kamigohri, Hyogo 678-1297, Japan
  • show less
    DOI: 10.1063/5.0074340 Cite this Article
    Naohisa Hirao, Yuichi Akahama, Yasuo Ohishi. Equations of state of iron and nickel to the pressure at the center of the Earth[J]. Matter and Radiation at Extremes, 2022, 7(3): 038403 Copy Citation Text show less
    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. 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.
    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. 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.
    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. 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.
    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. 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.
    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. 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.
    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.
    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)PTMbScaleP range (GPa)
    Fe 1500HePt + ruby5–20
    Fe 2350HeRuby0–54
    Fe 335/250/350NonePt0–296
    Fe 428/250/350NonePt219–354
    Ni 1500MEWcRuby0–10
    Ni 2500HePt0–21
    Ni 3100/300NonePt2–179
    Ni 427/250/450NonePt257–368
    Ni 550/230/450NonePt163–202
    Table 1. Conditions of each experimental run.
    2θ (deg)do (Å)hcp-Fefcc-Pt
    a = 2.1294(17) (Å)a = 3.4049(11) (Å)
    c = 3.390(5) (Å)
    Indexdc (Å)dodc (Å)Indexdc (Å)dodc (Å)
    12.1931.96611111.96580.0003
    12.9701.84870101.84410.0046
    14.0901.7024(002)2001.7025−0.0001
    14.8331.61760111.6200−0.0024
    19.2901.24630121.2480−0.0017
    20.0041.20222201.2038−0.0016
    22.6391.06381101.0647−0.0009
    23.4511.02753111.02660.0008
    24.5180.98342220.98290.0005
    25.0030.96460130.96360.0010
    26.8080.90071120.9016−0.0009
    27.1130.89080210.88970.0010
    28.4060.85104000.8512−0.0002
    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.
    V03)K0 (GPa)K0P Range (GPa)P GaugeFormulaPTMReferences
    11.215(29)159.27(99)5.86(4)14–354Ruby or PtVinetHe or nonePresent
    11.176(17)164.8(3.6)5.33(9)35–300PtB-MaAr or noneMao et al.3
    11.1780(2)160.67(5)5.36(1)B-MCorrected EOS
    11.19891565.8120–200PtB-MNone (heating)Dubrovinsky et al.4
    11.2022(1)151.65(2)5.854(3)B-MCorrected EOS
    11.214(49)163.4(7.9)5.38(16)17–197Ruby or WVinetHeDewaele et al.5
    11.214156.7(9)5.8(1.0)VinetCorrected EOS
    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 K0 under ambient conditions.
    2θ (deg)do (Å)fcc-Nifcc-Pt
    a = 2.9521(10) (Å)a = 3.3977(6) (Å)
    Indexdc (Å)dodc (Å)Indexdc (Å)dodc (Å)
    12.0481.96141111.9616−0.0001
    13.8561.70651111.70530.0011(200)
    16.0081.47832001.47690.0015
    19.7221.20202201.20120.0008
    22.7571.04342201.0443−0.0008
    23.1861.02433111.0244−0.0001
    24.2440.98032220.9808−0.0005
    26.7460.89003110.8906−0.0005
    27.9690.85182220.8527−0.0004(400)
    30.6130.77983310.77940.0003
    31.4460.75964200.7597−0.0001
    32.3590.73874000.73840.0001
    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.
    V03)K0 (GPa)K0MethodP Range (GPa)FormulaReferences
    10.9376(4)173.5(1.4)5.55(5)DAC0–368VinetPresent
    183(3)UltrasonicYamamoto15
    10.940176.7(2.5)5.23(9)DAC0–156VinetDewaele et al.6
    10.940169.3(8)5.67(18)VinetCorrected EOS
    10.9376187.8(5)4.89(4)Shock wave0–120VinetKennedy and Keeler14
    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 K0, under ambient conditions.
    Naohisa Hirao, Yuichi Akahama, Yasuo Ohishi. Equations of state of iron and nickel to the pressure at the center of the Earth[J]. Matter and Radiation at Extremes, 2022, 7(3): 038403
    Download Citation