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