Dynamics of - and -FeCr alloys as

seen by 57Fe NRIXS and theoretical

calculations

S. M. Dubiel1, E. E. Alp2, J. Zhao2, M. Y. Hu2, W. Sturhahn3, M. Sternik4,

P. Piekarz4, and J.Cieslak1

1AGH University of Science & Technology, Krakow, Poland, 2Advanced

Photon Source, Argonne National Laboratory, Argonne, Ill USA, 3California Institute of Technology, Pasadena, USA, 4Institute of

Nuclear Physics, PAN, Krakow, Poland

2

Global SS Production 1995-2010

0

5

10

15

20

25

30

35

years

mln

to

ns

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

3

Structure

Site

number

Site

code

ON CN <d>[nm]

1 A (2a) 2 12 0.2508

2 B (4f) 4 15 0.2701

3 C (8i) 8 14 0.2652

4 D (8i’) 8 12 0.2526

5 E (8j) 8 14 0.2638

-FeCr

4

Structure

5

StructureJ. Cieslak (2008) P. Blaha (2010)

6

Lattice Dynamics

Experimentally

1. Mössbauer Spectroscopy (MS) Debye temperature, D

2. Nucler Resonant Inelastic X-ray Scattering (NRIXS) Fe-

partial phonon density of states (PDOS)

Theoretically

1. Direct Method phonon dispersions and DOS

7

Lattice Dynamics - D

• Two spectral parameters viz. centre shift, CS, and the recoil-

free fraction, f, are related with lattice dynamics. The former

with the squared velocity of the vibrations, via the second-

order Doppler shift, the latter with the mean-squared

amplitude of vibrations. Both, via the Debye model, can be

used for determining D.

Example for Fe: D(CS) = 426 (14) K, D(f) = 358 (18) K

T

x

D

D

D

dxe

xT

TMc

kTISTCS

0

33

13

8

3

2

3)0()(

8

Lattice Dynamics - D

- D for -FeCr46 = 412 K

J. Cieslak et al., Intermetallics. 18 (2010) 1695

-FeCr

9

Lattice Dynamics - PDOS

NRIXS (295 K) Theory DM (0 K)

Quantity Experiment Theory

D [N/m] 157(2) 150.6

CV [k/atom] 2.748(7) 2.752

S [k/atom] 3.347(7) 3.412

D [K] 398 395

CCD

S. M. Dubiel et al., PRL, 104 (2010) 155503

10

Lattice Dynamics - PDOS

• Experiment (27 K) • Theory

E 1.5 meV (4%)E 0.15 meV (0.4%)

27 K295 K

11

Lattice Dynamics - PDOS

TC 38 K

12

Conclusions

57Fe-PDOS in Fe-Cr significantly depends on the structure

~ 40 meV peak in -PDOS shifts to ~41.5 meV at T < 40K

The ~1.5 meV shift is not due to lattice contraction

The ~1.5 meV shift is likely due to spin-phonon coupling

Thank you for your attention!

A and D sites are mostly responsible for the shift

13

H-T Phase Diagram -FeCr47