Pressure measurements at high temperature: open issues and solutions

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Pressure measurements at high temperature open
issues and solutions

• Peter I. Dorogokupets
• Institute of the Earths Crust SB RAS, Irkutsk,
  Russia
• dor_at_crust.irk.ru

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Acknowledgments

• Artem R. Oganov Lab. of Crystallography, ETH
  Zurich, Switzerland a.oganov_at_mat.ethz.ch
• Agnes Dewaele CEA/DPTA Bruyeres-le-Chatel,
  France agnes.dewaele_at_cea.fr
• Paul Loubeyre CEA/DPTA Bruyeres-le-Chatel,
  France
• This work was supported by the Russian Foundation
  for Basic Research, Grant No. 05-05-64491.

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Outline

• Intro.
• Thermodynamics EoS formulation
• Best form of the ruby scale
• EoS and thermodynamic behavior of Au, C, MgO,
  NaCl B1, NaCl B2, e-Fe
• Cross-check of EoS
• Conclusion

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Intro

• Dorogokupets P.I., Oganov A.R. Ruby pressure
  scale revision and alternatives // in
  Proceedings Joint 20th AIRAPT 43th EHPRG Int.
  Conf. on High Pressure Science and Technology,
  June 27 to July 1, 2005, Karlsruhe, Germany
  (Forschungszentrum Karlsruhe, Karlsruhe, 2005).
• ??????????? ?.?., ?????? ?.?. ????????? ?????????
  Al, Au, Cu, Pt, Ta ? W ? ?????????????? ?????????
  ????? ???????? // ???. 2006. ?. 410. ? 2.
  239243. Dorogokupets P.I., Oganov A.R. Equations
  of State of Al, Au, Cu, Pt, Ta, and W and Revised
  Ruby Pressure Scale // Doklady Earth Scinces.
  2006. V. 410. 1091-1095.
• Dewaele A., Loubeyre P., Occelli F., Mezouar M.,
  Dorogokupets P.I., Torrent M. Quasihydrostatic
  equation of state of iron above 2 Mbar // Phys.
  Rev. Letters. 2006. V. 97. Art. No. 215504.
• Dorogokupets P.I., Oganov A.R. Ruby, metals, and
  MgO as alternative pressure scales A
  semiempirical description of shock-wave,
  ultrasonic, x-ray, and thermochemical data at
  high temperatures and pressures // Phys. Rev. B
  2007

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Thermodynamics

• Helmholtz free energy

• U0 is the reference energy
• E(V) is the cold part
• Eqh(V,T) is the quasiharmonic part
• Eanh(V,T) is the intrinsic anharmonicity
• Eel(V,T) is the electronic contribution
• Edef(V,T) is the thermal defects

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Cold energy (Vinet form)
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Kutin modelsee Kutin et al.Rus. J. Phys.
Chem. 72, 1567, 1998
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Intrinsic anharmonicity(Oganov, Dorogokupets,
2004)
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Electronic contribution(Zharkov, Kalinin, 1971)
Thermal defects contribution
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Thermodynamic functions

• S (?F/?T)V, EF TS,
• P (?F/?V)T, HEPV, GFPV,
• CV (?E/?T)V, KT V(?P/?V)T,
• (?P/?T)V aKT,
• CPCVa2TVKT, KSKTVT(aKT)2/CV,

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Hugoniot pressure
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We use input data are unbiased by calibration

• 22 parameters to fit!
• At zero pressure
• Heat capacity and enthalpy
• Thermal expansion coefficient or volume
• Adiabatic bulk modulus (from ultrasonic
  measurements)
• Temperature interval
• from 10 K to melting temperature
• At high P-T
• Shock wave data

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Room T isotherms obtained after fitting
Compared with static compression data with Mao 86
ruby calibration (A1904, B7.665)
Compared with static compression data with new
ruby calibration (A1885, B10.4)
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Best ruby pressure scale
Aleksandrov form
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Use of all available data

• At zero pressure
• Heat capacity and enthalpy
• Thermal expansion coefficient or volume
• Adiabatic bulk modulus (from ultrasonic
  measurements)
• Temperature interval
• from 10 K to melting temperature
• At high P-T
• Shock wave data
• PV and PVT measurements (at later stages of
  refinement)

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Results

• With our formalism we carry out a simultaneous
  processing of all the available measurements of
  the Cp, a, V, Ks and KT at zero pressure, static
  measurements of V on a room-temperature isotherm
  and at higher temperatures, shock-wave data, and
  calculate thermodynamic functions vs. T and P.
• Ag, Al, Au, Cu, Pt, Ta, W, Mo, Pb, Fe, MgO,
  diamond, NaCl EoS have been calculated.

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See Dorogokupets, Phys. Rev B, 2007
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Comparison of calculated EoS and thermodynamic
parameters with data
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Au, heat capacity
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Au, thermal expansion
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Au, bulk moduli
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Au, 300 KK0166.7 GPa, K'6
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Au, 300 KK0166.7 GPa, K'6
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Diamond, 300 K K0443.16 GPa, K'3.777
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Diamond, heat capacity
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Diamond, bulk moduli
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iron
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iron
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MgO, 300 K K0160.3 GPa, K'4.18
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MgO, bulk moduli
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MgO, bulk moduli
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MgO, K0160.3 GPa, K'4.18
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MgO, Zhang data fittedK0161 GPa, K'1.84
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NaCl B1, RT-isothermK023.9 GPa, K'5.13
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NaCl B1
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NaCl B1
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NaCl B1, bulk moduli
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NaCl B1, bulk moduli
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NaCl B2, RT-isothermK037.04 GPa, K'4.99
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NaCl B2, RT-isothermK037.04 GPa, K'4.99
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Cross-check between EoS at high T

• Two materials are compressed together in a high
  pressure/high temperature apparatus and their V
  is measured
• Pressure given by their EoS are compared
• If same pressure, validation of the EoS

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Comparison NaCl B2 and e-Fe
?Within 7GPa
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Au-MgO Inoue et al. (2006) Phys. Chem. Minerals
33, 106.
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K. Litasov et al. EPSL 238 (2005) 311
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Fei et al. (2004). PEPI, 143-144, 515
MgO and Au EoS are within 1 GPa at Plt30 GPa,
Tlt2200K
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Hirose et al. (2006). Geophys. Res. Lett. 33,
L01310.
MgO and Au EoS are within 3 GPa at Plt120 GPa,
Tlt2300K
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Conclusions

• We have proposed a ruby pressure scale based on
  precise measurements of Dewaele et al. 2004,
  2006.
• The obtained ruby pressure scale agrees within 2
  with the most recent ruby pressure scales.
• Our EoSs of Al, Au, Cu, Pt, Ta, W, MgO, C, NaCl
  are consistent with shock-wave and X-ray data and
  with numerous measurements of the heat capacity,
  volume, adiabatic bulk moduli, etc. at zero
  pressure.
• The EoSs of Au and Pt agree with the EoSs of Ag
  and MgO, constructed on independent measurements.
  
• The obtained P-V-T EoSs enable consistent
  pressure measurement using EoSs of any of the
  reference substances (Ag, Al, Au, Cu, Pt, Ta, W,
  MgO). This solves problems of inconsistency
  between different pressure scales and enables
  accurate pressure measurement at elevated
  temperatures, where the ruby scale cannot be
  used.

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