Pressure measurements at high temperature: open issues and solutions

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

2. Acknowledgments • Artem R. OganovLab. of Crystallography, ETH Zurich, Switzerland a.oganov@mat.ethz.ch • Agnes DewaeleCEA/DPTA Bruyeres-le-Chatel, Franceagnes.dewaele@cea.fr • Paul LoubeyreCEA/DPTA Bruyeres-le-Chatel, France • This work was supported by the Russian Foundation for Basic Research, Grant No. 05-05-64491.

9. 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

10. 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. 2006. Т. 410. № 2. 239–243.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. 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

11. Thermodynamics • 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 Helmholtz free energy

12. Cold energy (Vinet form)

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

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

15. Intrinsic anharmonicity(Oganov, Dorogokupets, 2004)

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

17. Thermodynamic functions S = –(F/T)V, E=F + TS, P = –(F/V)T, H=E+PV, G=F+PV, CV = (E/T)V, KT= –V(P/V)T, (P/T)V = aKT, CP=CV+a2TVKT, KS=KT+VT(aKT)2/CV,

18. Hugoniot pressure

19. 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

20. 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)

21. Best ruby pressure scale Aleksandrov form

22. 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)

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

24. See Dorogokupets, Phys. Rev B, 2007

25. Comparison of calculated EoS and thermodynamic parameters with data

26. Au, heat capacity

27. Au, thermal expansion

28. Au, bulk moduli

29. Au, 300 KK0=166.7 GPa, K′=6

30. Au, 300 KK0=166.7 GPa, K′=6

31. Diamond, 300 K K0=443.16 GPa, K′=3.777

32. Diamond, heat capacity

33. Diamond, bulk moduli

34. iron

35. iron

36. MgO, 300 K K0=160.3 GPa, K′=4.18

37. MgO, bulk moduli

38. MgO, bulk moduli

39. MgO, K0=160.3 GPa, K′=4.18

40. MgO, Zhang data fittedK0=161 GPa, K′=1.84

41. NaCl B1, RT-isothermK0=23.9 GPa, K′=5.13

42. NaCl B1

43. NaCl B1

44. NaCl B1, bulk moduli

45. NaCl B1, bulk moduli

46. NaCl B2, RT-isothermK0=37.04 GPa, K′=4.99

47. NaCl B2, RT-isothermK0=37.04 GPa, K′=4.99

48. 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

49. Comparison NaCl B2 and e-Fe Within ~7GPa

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