Phononen in Fe65Ni35 Temperatur- und Druckabhängigkeit

Phononen in Fe65Ni35 Temperatur- und Druckabhängigkeit

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 H. Giefers, University of Paderborn 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 / -Fe Derived parameters of Fe65Ni35 thermodyn./elastic properties of Fe65Ni35 sound velocity few notes to the Debye temperature Debye temperatures and Grneisen parameters Summary and Outlook Acknowledgment H. Giefers, University of Paderborn Nuclear Resonant Inelastic Scattering (NIS) Counts prompt count rate from SR puls delayed count rate 57 from Fe Time energy scans around the Mssbauer resonance counting of delayed photons NIS: mostly secondary radiation (Fe K x-rays) Phonon density of states H. Giefers, University of Paderborn

Experimental Details for NIS Sample: 15 g Invar 200 m Pressure cell: large opening for detectors Be gasket for K fluorescence APD APD ID22N H. Giefers, University of Paderborn Invar detected 1896 by Ch.-Ed. Guillaume thermal expansion of V 10-6 K-1 for Fe65Ni35 compared to 10-5 K-1 for Fe Nobel prize 1920 Magnetism plays important role H. Giefers, University of Paderborn Normalized measured NIS spectra Absorption probability Inorm (1/eV) Temperature 12 Pressure Fe65Ni35 Fe65Ni35 660 K 450 K 295 K 150 K 5K 10 8 0.0 GPa 5.3 GPa

10.4 GPa 17.3 GPa 6 4 2 0 -60 -40 -20 0 20 40 rel. Energy (meV) 60 -60 -40 -20 0 20 40 60 rel. Energy (meV) H. Giefers, University of Paderborn Derived Phonon Density-of-States Temperature 60 Pressure phonon DOS g(E) (1/eV) 0.0 GPa 1.5 GPa 3.1 GPa

5.3 GPa 7.1 GPa 10.4 GPa 17.3 GPa 5K 150 K 309 K 350 K 400 K 450 K 480 K 500 K 600 K 660 K Fe65Ni35 50 40 30 Fe65Ni35 20 10 0 0 10 20 30 Energy (meV) 40 0 10 20 30 40 Energy (meV) H. Giefers, University of Paderborn Fe65Ni35

0.05 g(E) (1/meV) 0.05 0.04 0.03 0.02 0.01 0.00 0.05 0.04 0.03 0.02 0.01 0.00 0 5K 150 K 295 K 450 K 600 K 0.04 0.0 GPa 7.1 GPa 10.4 GPa 17.3 GPa 10 30 Energy (meV) 40 50 294 K 24 K 0.02 0.01 0.05 20 -Fe

0.03 0 g(E) (1/meV) g(E) (1/meV) g(E) (1/meV) Phonon DOS: Comparison of Fe65Ni35 with -Fe 0.04 10 20 30 40 Energy (meV) -Fe 0.0 GPa 6.9 GPa 0.03 0.02 0.01 0 10 20 30 40 Energy (meV) H. Giefers, University of Paderborn Elastic / thermodyn. properties derived with g(E) fLM: Lamb-Mssbauer factor f LM g E 1 e E k BT exp E R dE E k BT E 1 e 0

F vib: Helmholtz free energy Fvib 3 k B T g E ln e E 2 k BT e E 2 k BT dE 0 D(s): mean force constant S vib: entropy along direction s=k/k m D s 2 2 g E E dE 0 Svib 3 k B E g E 2k BT 0 D,HT: Debye temperature D ,HT g E E dE 0 dE

cV: specific heat high-temperature limit 4 3 kB E 2 kE T e E k BT 1 2 B E k BT ln e e k BT 1 e cV 3 k B 2 g E E k T e B 0 e E k BT E k BT 1 2 dE H. Giefers, University of Paderborn 0.9 0.8 0.7 0.6 0.5 0.4 200 180

160 140 120 100 400 380 360 340 320 300 0 0.85 Pressure 0.80 0.75 0.70 200 180 160 140 120 100 460 440 420 400 380 360 200 400 600 0 3 6 9 12 15 18 Temperature (K) Pressure (GPa) 50 0 -50 -100 -150 -200 cV (kB/atom) D (K) D (N/m) fLM

Temperature Svib(kB/atom) Fvib (meV/atom) Elastic / thermodyn. properties: T / p dependence Temperature 6 12 8 4 0 -4 -8 3.6 3.4 4 3.2 2 3.0 0 2.8 2.8 3 2 2.7 1 0 0 Pressure 2.6 200 400 600 Temperature (K) 0 3 6 9 12 15 18 Pressure (GPa) H. Giefers, University of Paderborn

Average sound velocity vD 25 g(E) (1/eV) 20 15 10 0.0 GPa 3.1 GPa 5.3 GPa 7.1 GPa 10.4 GPa 17.3 GPa g(E) = E in the Debye-model: 3 1 2 3 3 3 vD v p vs linear fit 2 5 4.00 0 0 50 100 2 150 2 200 - strong variation of vD under pressure - soft TA(110) mode hardens strongly by pressure (known from ultrasonic and neutron studies) vD (km/s)

Energy (meV ) 3.75 vD 3 3.50 V 2 2 3 3.25 3.00 2.75 2.50 0 3 6 9 12 p (GPa) 15 18 H. Giefers, University of Paderborn Remark on the Debye-temperatures Dispersion relation (single crystal) low energy region: g ( E ) E vD 3 2 D , HT V 2 2 3 in the Debye-model:

3 1 2 vD3 v 3p vs3 D , LT vD kB 3 high-energy region: 6 V 2 4 3 kB g E E dE 0 D,LT D,HT H. Giefers, University of Paderborn Debye-temperatures/Grneisen parameters: HT vs. LT 525 4 3 kB g E E dE 0 derived from g(E) in the region 0 E 45 meV D,HT D,LT

500 D (K) D , HT 475 450 425 400 375 vD kB 3 6 V derived from g(E) in the region 0 E 10 meV 350 5 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) D = - d ln D/d ln V 4 D D , LT 2 3 LT 2 1 0 1.00 HT 0.98

0.96 0.94 0.92 0.90 0.88 V/V0 H. Giefers, University of Paderborn 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 D,HT and D,LT and Grneisen 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 57Fe-NIS studies of (ordered and disordered) Fe72Pt28 Invar. 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 Rffer Invar sample Uwe van Brck G.V. Smirnov This work was supported by a joint BMBF proposal of the Universities of Paderborn and Rostock (project 05 KS1PPB/3) H. Giefers, University of Paderborn

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