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Introduction

Introduction. 14 th ESRF User Meeting Phonons in Crystalline Materials Workshop 9. February 2004. Phonon DOS in oriented hcp iron and SnO from high-pressure NIS. Hubertus Giefers. Physics Department, University of Paderborn, D-33095 Paderborn, Germany. Survey.

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Introduction

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  1. Introduction 14th ESRF User Meeting Phonons in Crystalline MaterialsWorkshop 9. February 2004 Phonon DOS in oriented hcp iron and SnO from high-pressure NIS Hubertus Giefers Physics Department, University of Paderborn, D-33095 Paderborn, Germany

  2. Survey  Experimental setup and high-pressure cell for NIS (Nuclear Inelastic Scattering)  Iron under high pressure, texture in hcp iron  High pressure NIS-experiments with iron up to 130 GPa  Subtraction method: projected DOS of hcp iron  Sound velocity in hcp iron  SnO under pressure  Texture of SnO  Orientational dependent DOS-spectra of SnO  Phonon modes in SnO  Conclusion/Acknowledgment

  3. Experimental setup for NIS Kirkpatrick-Baez-mirror: Focusing essential for high pressure studies SR spot of 10x10µm2 at sample

  4. High-pressure cell for NIS • large openings for APD detector • diamonds without support ring → large scattering angle • Be-Gasket → transmission of Ka,b x-ray fluorescence • scattering geometry parallel and perpendicular to the HP-cell axis

  5. pressure ≈ 13 GPa e-phase hcp structure a-phase bcc structure e-Fe at 220 GPa pressure H.-R. Wenk et al., Nature 405, 1044 (2000). Iron under high pressure - a/e-phase transition at 13 GPa - after the a/e-phase transition e-Fe is preferentially oriented with the hcp c-axis along the load axis

  6. Iron in the Earth • Fe is of actual geophysical interest • the solid inner core consists mainly • of e-Fe • longitudinal sound velocity vp from • north to south is faster (3-4 %) than • from east to west • - assumption: e-Fe is textured in the • inner core

  7. High pressure NIS-experiments with iron APS Experiments 1999: DE = 2 meV ESRF Experiments 2003: DE = 3 meV H. Giefers et al., to be published. H.-K. Mao et al., Science 292, 914 (2001).

  8. Phonon density-of-state (DOS) of oriented hcp-iron

  9. 40 GPa Subtraction method: projected phonon DOS of iron e-Fe 40 GPa

  10. Comparison: theory ↔ experiment B1g E2g calculation: D. Alfè in Giefers et al., High Press. Res. 22, 501 (2002).

  11. projected DOS of iron

  12. gB1g=1.68(9) gE2g=1.44(3) [Merkel] gE2g=1.43(9) Mode-specific analysis of the phonon spectra

  13. Sound velocity in e-iron

  14. Sound velocity in e-iron

  15. Sound velocity vp and vs of e-Fe

  16. e-phase hcp structure Difference of sound velocities in hcp-iron Difference in sound velocities vp: from measured DOS-spectra at 130 GPa : 0°: 9.87(14) km/s 75°: 9.74(14) km/s difference: 1.3 % from subtracted DOS-spectra at 130 GPa : c-axis: 10.58(19) km/s a,b-plane: 9.55(19) km/s difference: 9.7 %

  17. Tin oxide SnO a = 3.800 Å c = 4.836 Å z(Sn) = 0.236 - layer structure - weak van der Waals binding between Sn-O-Sn layers Sn O Sn Sn O Sn Sn O Sn Sn O Sn

  18. XRD and EXAFS measurements Unit cell parameters of SnO under pressure • strong elastic anisotropy • no phase transition up to 50 GPa • Birch-EOS: K0=35(1) GPa, K0‘=6.1(2)

  19. Texture of SnO studied by EDXRD • SnO shows (001)-texture: • the c-axes of the • graphite-like • crystallites • are perpendicular to the • sample plane - texture occures even at ambient pressure - this texture is used for an orientation dependent NIS-study like in e-Fe

  20. Orientation dependent NIS-spectra of SnO

  21. Orientation dependent phonon-DOS of SnO the spectra resemble each other → SnO becomes more isotropic

  22. 1 acoustic 2 optic 3 optic 1 acoustic 2 acoustic/optic 3 optic Phonon modes in SnO: theory ↔ experiment ← S. Koval, Phys. Rev. B 54, 7151 (1996).

  23. Mode-Grüneisen parameter gi = 0.8 for 1 2 gi = 0.5 for 3 gi = 4.4 (0-1.3 GPa), 1.9 (1.3-6.1 GPa) for 1 Phonon modes in SnO

  24. Conclusion • - The new difference method for NIS-DOS-spectra from textured samples • allows a direction dependent analysis of the phonon DOS as demonstrated for • -Fe and SnO. • - This difference method delivers results similar to those obtained by single crystal • studies, for instance with INS or IXS; this method allows also, together with • theoretical calculations, for a mode selective analysis of the DOS-spectra. • Textured -Fe was investigated up to 130 GPa, the mode-specific analysis of • the E2g mode shows very good agreement with a Raman study, the sound • velocity is at 130 GPa faster along the c-axis by almost 10% than in the • a,b-plane. • - Application of the difference method to SnO reveal drastic differences in the • phonon DOS seen parallel and perpendicular to the c-axis; pressure reduces • this anisotropic behaviour, reflected in a soft mode, and makes the • phonon DOS more isotropic.

  25. Acknowledgment Paderborn group : G. Wortmann U. Ponkratz K. Rupprecht R. Lübbers iron at ESRF : A.I. Chumakov O. Leupold A. Barla SnO at APS : W. Sturhahn M.Y. Hu E.E. Alp SnO at HASYLAB : F. Porsch

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