1. H. Giefers, University of Paderborn 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

2. H. Giefers, University of Paderborn Survey Introduction Nuclear Resonant Inelasic Scattering (NIS) HP cell and experimental setup some notes to Invar Spectra of Fe 65 Ni 35 NIS spectra T and p dependence phonon DOS spectra of Fe 65 Ni 35 comparison: Fe 65 Ni 35 /  -Fe Derived parameters of Fe 65 Ni 35 thermodyn./elastic properties of Fe 65 Ni 35 sound velocity few notes to the Debye temperature Debye temperatures and Grüneisen parameters Summary and Outlook Acknowledgment

3. H. Giefers, University of Paderborn Nuclear Resonant Inelastic Scattering (NIS) energy scans around the Mössbauer resonance counting of delayed photons NIS: mostly secondary radiation (Fe K  x-rays) Phonon density of states

4. H. Giefers, University of Paderborn Experimental Details for NIS Pressure cell: large opening for detectors Be gasket for K  fluorescence Sample: 15 µg Invar 200 µm Ø ID22N

5. H. Giefers, University of Paderborn Invar detected 1896 by Ch.-Ed. Guillaume thermal expansion of  V  10 -6 K -1 for Fe 65 Ni 35 compared to 10 -5 K -1 for Fe Nobel prize 1920 Magnetism plays important role

6. H. Giefers, University of Paderborn Normalized measured NIS spectra

7. H. Giefers, University of Paderborn Derived Phonon Density-of-States

8. H. Giefers, University of Paderborn Phonon DOS: Comparison of Fe 65 Ni 35 with  -Fe

9. H. Giefers, University of Paderborn f LM : Lamb-Mössbauer factor D(s): mean force constant along direction s=k/k  D,HT : Debye temperature high-temperature limit F vib : Helmholtz free energy S vib : entropy c V : specific heat Elastic / thermodyn. properties derived with g(E)

10. H. Giefers, University of Paderborn Elastic / thermodyn. properties: T / p dependence

11. H. Giefers, University of Paderborn Average sound velocity v D in the Debye-model: - strong variation of v D under pressure - “soft“ TA(110) mode hardens strongly by pressure (known from ultrasonic and neutron studies)

12. H. Giefers, University of Paderborn high-energy region: low energy region: in the Debye-model: Dispersion relation (single crystal) Remark on the Debye-temperatures  D,HT  D,LT

13. H. Giefers, University of Paderborn Debye-temperatures/Grüneisen parameters: HT vs. LT derived from g(E) in the region 0  E  10 meV derived from g(E) in the region 0  E  45 meV “Pressure and Temperature Dependence of the Fe Phonon Density of States in the Invar alloy Fe 65 Ni 35 “ H. Giefers, K. Rupprecht, O. Leupold and G. Wortmann (submitted)

14. H. Giefers, University of Paderborn Summary and Outlook The phonon DOS spectra of Fe 65 Ni 35 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  D,HT and  D,LT and Grüneisen parameters  HT and  LT, 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 57 Fe-NIS studies of (ordered and disordered) Fe 72 Pt 28 Invar.

15. H. Giefers, University of Paderborn 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)