Introduction

H. Giefers, University of Paderborn

Introduction

EHPRG-40 in Edinburgh7. 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


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 Grüneisen parameters

Summary and OutlookAcknowledgment


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

prompt count rate from SR puls

delayed count rate

from 57

Fe

Co

un

ts

Time


Experimental Details for NIS

APD APD

Pressure cell:• large opening for detectors• Be gasket for K fluorescence

Sample:• 15 µg Invar• 200 µm Ø

ID22N


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


Normalized measured NIS spectra

-60 -40 -20 0 20 40 600

2

4

6

8

10

12 Fe65

Ni35

Ab

sorp

tion

pro

ba

bili

ty I no

rm (

1/e

V)

rel. Energy (meV)

660 K 450 K 295 K 150 K 5 K

-60 -40 -20 0 20 40 60

Fe65

Ni35

PressureTemperature

rel. Energy (meV)

0.0 GPa 5.3 GPa 10.4 GPa 17.3 GPa


Derived Phonon Density-of-States

0 10 20 30 400

10

20

30

40

50

60

Fe65

Ni35

ph

on

on

DO

S

g(E

) (1

/eV

)

Energy (meV)

5 K 150 K 309 K 350 K 400 K 450 K 480 K 500 K 600 K 660 K

0 10 20 30 40

Fe65

Ni35

PressureTemperature

Energy (meV)

0.0 GPa 1.5 GPa 3.1 GPa 5.3 GPa 7.1 GPa10.4 GPa17.3 GPa


Phonon DOS: Comparison of Fe65Ni35 with -Fe

0 10 20 30 40 500.00

0.01

0.02

0.03

0.04

0.05

Energy (meV)

g(E

) (1

/meV

)

0.0 GPa 7.1 GPa10.4 GPa17.3 GPa

0.00

0.01

0.02

0.03

0.04

0.05

g(E

) (1

/meV

)

Fe65Ni35

5 K 150 K 295 K 450 K 600 K

0 10 20 30 40

0.01

0.02

0.03

0.04

0.05

-Fe 0.0 GPa 6.9 GPa

g(E

) (1

/meV

)

Energy (meV)

0 10 20 30 40

0.01

0.02

0.03

0.04

0.05

-Fe 294 K 24 K

g(E

) (1

/meV

)

Energy (meV)


0

TkE

TkE

RLM dEe1

e1

E

EgEf

B

B

exp

dEEEgm

sD

0

22

dEeeEgTk3F Tk2ETk2E

0

BvibBB

ln

dE1e

eTkEEgk3c 2TkE

TkE2

B

0

BVB

B

dEee1e

1e

Tk2

EEgk3S

0

Tk2

E

Tk2

E

TkE

TkE

BBvib

BB

B

B

ln

0B

HTD dEEEgk3

4,

fLM: 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

cV: specific heat

Elastic / thermodyn. properties derived with g(E)


Elastic / thermodyn. properties: T / p dependence

0.40.50.60.70.80.9

f LM

0.70

0.75

0.80

0.85

-200-150-100

-500

50

Fvi

b (m

eV

/ato

m)

-8-4048

12

100120140160180200

D (

N/m

)

100120140160180200

0

2

4

6

Svi

b(k B

/ato

m)

2.8

3.0

3.2

3.4

3.6

0 200 400 600300320340360380400

Temperature (K)

D (

K)

0 3 6 9 12 15 18360380400420440460

Pressure (GPa)0 200 400 600

0

1

2

3

Temperature (K)

c V (

k B/a

tom

)

0 3 6 9 12 15 18

2.6

2.7

2.8

Pressure (GPa)

PressureTemperaturePressureTemperature


Average sound velocity vD

3s

3p

3D v

2

v

1

v

3

in the Debye-model:

- strong variation of vD under pressure- “soft“ TA(110) mode hardens strongly by pressure (known from ultrasonic and neutron studies)

332D 2

Vv

0 50 100 150 200

0

5

10

15

20

25

g(E) = ·E2

linear fit

0.0 GPa 3.1 GPa 5.3 GPa 7.1 GPa10.4 GPa17.3 GPa

g(E

) (1

/eV

)

Energy2 (meV2)

0 3 6 9 12 15 18

2.50

2.75

3.00

3.25

3.50

3.75

4.00

v D (

km/s

)

p (GPa)


high-energy region:

0B

HTD dEEEgk3

4,

332D 2

Vv

3s

3p

3D v

2

v

1

v

3

3

2

B

DLTD V

6

k

v

,

2EEg )(low energy region:

in the Debye-model:

Dispersion relation (single crystal)

Remark on the Debye-temperatures

D,HT

D,LT


3

2

B

DLTD V

6

k

v

,

Debye-temperatures/Grüneisen parameters: HT vs. LT

0B

HTD dEEEgk3

4,

derived from g(E) in the region0 E 10 meV

derived from g(E) in the region0 E 45 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)

1.00 0.98 0.96 0.94 0.92 0.90 0.880

1

2

3

4

5

LT

HT

D = - d ln D/d ln V

V/V0

D

350

375

400

425

450

475

500

525

D,HT

D,LT

D

(K)


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 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 57Fe-NIS studies of (ordered and disordered) Fe72Pt28 Invar.


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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Introduction