Pressure measurements at high temperature: open issues and solutions Peter I. Dorogokupets Institute of the Earth’s Crust SB RAS, Irkutsk, Russia

Acknowledgments Artem R. Oganov Lab. of Crystallography, ETH Zurich, Switzerland Agnes Dewaele CEA/DPTA Bruyeres-le-Chatel, France Paul Loubeyre CEA/DPTA Bruyeres-le-Chatel, France This work was supported by the Russian Foundation for Basic Research, Grant No

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

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). Дорогокупец П.И., Оганов А.Р. Уравнения состояния Al, Au, Cu, Pt, Ta и W и пересмотренная рубиновая шкала давлений // ДАН Т № –243. 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 V 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 V. 97. Art. No 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

Thermodynamics Helmholtz free energy U 0 is the reference energy E(V) is the cold part E qh (V,T) is the quasiharmonic part E anh (V,T) is the intrinsic anharmonicity E el (V,T) is the electronic contribution E def (V,T) is the thermal defects

Cold energy (Vinet form)

Total quasi-harmonic energy: Kut’in model Einstein model

Kut’in model: see Kut’in et al. Rus. J. Phys. Chem. 72, 1567, 1998

Intrinsic anharmonicity (Oganov, Dorogokupets, 2004)

Electronic contribution (Zharkov, Kalinin, 1971) Thermal defects contribution

Thermodynamic functions S = –(  F/  T) V, E=F + TS, P = –(  F/  V) T, H=E+PV, G=F+PV, C V = (  E/  T) V, K T = –V(  P/  V) T, (  P/  T) V =  K T, C P =C V +  2 TVK T, K S =K T +VT(  KT) 2 /C V,

Hugoniot pressure

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

Room T isotherms obtained after fitting: Compared with static compression data with Mao 86 ruby calibration (A=1904, B=7.665) Compared with static compression data with new ruby calibration (A=1885, B=10.4)

Best ruby pressure scale Aleksandrov form

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)

Results With our formalism we carry out a simultaneous processing of all the available measurements of the Cp, α, V, Ks and K T 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.

See Dorogokupets, Phys. Rev B, 2007

Comparison of calculated EoS and thermodynamic parameters with data

Au, heat capacity

Au, thermal expansion

Au, bulk moduli

Au, 300 K K 0 =166.7 GPa, K′=6

Diamond, 300 K K 0 = GPa, K′=3.777

Diamond, heat capacity

Diamond, bulk moduli

iron

MgO, 300 K K 0 =160.3 GPa, K′=4.18

MgO, bulk moduli

MgO, K 0 =160.3 GPa, K′=4.18

MgO, Zhang data fitted K 0 =161 GPa, K′=1.84

NaCl B1, RT-isotherm K 0 =23.9 GPa, K′=5.13

NaCl B1

NaCl B1, bulk moduli

NaCl B2, RT-isotherm K 0 =37.04 GPa, K′=4.99

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 Cross-check between EoS at high T

Comparison NaCl B2 and  -Fe  Within ~7GPa

Au-MgO: Inoue et al. (2006) Phys. Chem. Minerals 33, 106.

K. Litasov et al. EPSL 238 (2005) 311

Fei et al. (2004). PEPI, , 515 MgO and Au EoS are within ~1 GPa at P<30 GPa, T<2200K

Hirose et al. (2006). Geophys. Res. Lett. 33, L MgO and Au EoS are within ~3 GPa at P<120 GPa, T<2300K

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.