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Introduction

Introduction. EHPRG-40 in Edinburgh 7. September 2002. Pressure and Temperature Dependence of the Phonon Density-of-States of Fe in the Invar Alloy Fe 65 Ni 35. Hubertus Giefers. Physics Department, University of Paderborn, D-33095 Paderborn, Germany. Survey. Introduction

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Introduction

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  1. Introduction EHPRG-40 in Edinburgh 7. September 2002 Pressure and Temperature Dependence of the Phonon Density-of-States of Fe in the Invar Alloy Fe65Ni35 Hubertus Giefers Physics Department, University of Paderborn, D-33095 Paderborn, Germany

  2. Survey • Introduction • •Nuclear Resonant Inelasic Scattering (NIS) • • HP cell and experimental setup • • some notes to Invar • Spectra of Fe65Ni35 • • NIS spectra T and p dependence • • phonon DOS spectra of Fe65Ni35 • • comparison: Fe65Ni35 / a-Fe • Derived parameters of Fe65Ni35 • • thermodyn./elastic properties of Fe65Ni35 • • sound velocity • • few notes to the Debye temperature • • Debye temperatures and Grüneisen parameters • Summary and Outlook • Acknowledgment

  3. Nuclear Resonant Inelastic Scattering (NIS) • energy scans around the Mössbauer resonance • counting of delayed photons • NIS: mostly secondary radiation (Fe Ka,b x-rays) Phonon density of states

  4. Experimental Details for NIS Sample: • 15 µg Invar • 200 µm Ø Pressure cell: • large opening for detectors • Be gasket for Ka,b fluorescence ID22N

  5. Invar • detected 1896 by Ch.-Ed. Guillaume • thermal expansion of aV  10-6 K-1for Fe65Ni35 compared to 10-5 K-1 for Fe • Nobel prize 1920 • Magnetism plays important role

  6. Normalized measured NIS spectra

  7. Derived Phonon Density-of-States

  8. Phonon DOS: Comparison of Fe65Ni35 with a-Fe

  9. Elastic / thermodyn. properties derived with g(E) fLM: Lamb-Mössbauer factor F vib: Helmholtz free energy D(s): mean force constant along direction s=k/k S vib: entropy D,HT: Debye temperature high-temperature limit cV: specific heat

  10. Elastic / thermodyn. properties: T / p dependence

  11. Average sound velocity vD in the Debye-model: • strong variation of vD under • pressure • “soft“ TA(110) mode hardens • strongly by pressure (known from • ultrasonic and neutron studies)

  12. Remark on the Debye-temperatures Dispersion relation (single crystal) high-energy region: low energy region: in the Debye-model: QD,LT QD,HT

  13. Debye-temperatures/Grüneisen parameters: HT vs. LT derived from g(E) in the region 0  E  45 meV derived from g(E) in the region 0  E  10 meV “Pressure and Temperature Dependence of the Fe Phonon Density of States in the Invar alloy Fe65Ni35“ H. Giefers, K. Rupprecht, O. Leupold and G. Wortmann (submitted)

  14. Summary and Outlook • The phonon DOS spectra of Fe65Ni35 as function of pressure and temperature reflect, when compared with normal metals, the “anomalous” Invar properties. • These “anomalous” properties are reflected in particular by the Debye temperatures QD,HT and QD,LT and Grüneisen parameters gHT and gLT, derived from the high-energy and low-energy part of the DOS; they disappear with the suppression of the Fe moment around 12 GPa (in agreement with an IXS study by Rueff et al., PRB 63, 132409 (2001)) Outlook: • Comparison of local phonon DOS at the Fe sites measured here with integral phonon DOS derived from IXS and neutron studies. • Similar 57Fe-NIS studies of (ordered and disordered) Fe72Pt28 Invar.

  15. Acknowledgments Co-workers: Paderborn group • Gerhard Wortmann • Kirsten Rupprecht • Ulrich Ponkratz Grenoble/ESRF • Olaf Leupold • Alexandr Chumakov • Bryan Doyle • Rudolf Rüffer Invar sample • Uwe van Brück • G.V. Smirnov This work was supported by a joint BMBF proposal of the Universities of Paderborn and Rostock (project 05 KS1PPB/3)

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