magnetic and dynamic properties of sigma-phase in fe-cr and fe-v
TRANSCRIPT
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Magnetic and dynamic properties
of sigma-phase in Fe-Cr and Fe-V
Stanisław M. Dubiel
Faculty of Physics & Applied
Computer Science, Kraków, Poland
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Structure
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Structure
Site
number
Site
code
ON CN <d>[nm]
1 A 2 12 0.2508
2 B 4 15 0.2701
3 C 8 14 0.2652
4 D 8 12 0.2526
5 E 8 14 0.2638
-FeCr
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Structure
Dubiel, J. Cieslak, Crit. Rev. Sol. Stat. Mater Sci., 36 (2011) 192
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StructureJ. Cieslak P. Blaha
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Structure
A: 1.66
B: 1.34
C: 1.34
D: 1.01
E: 2.16
Vzz
[1021 V/m2]
J. Cieslak, J. Tobola, S. M. Dubiel, Phys. Rev. B. 81 (2010) 174407
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Magnetism• Microscopic methods – Mössbauer spectroscopy
-FeCr
(b) 295 K
(a) 4.2 K
-Fe66V34 T=4.2 K
<H>=12.1 T
<H>=34 T
No chance for detecting magnetism
at the level of individual sites
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Magnetism• Mössbauer spectroscopy – Curie temperature, TC
-FeCr
-Fe66V34
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Magnetism• Mössbauer spectroscopy – Curie temperature, TC
-FeCr
RT
J. Cieslak et al., J. Magn. Magn. Mater., 321 (2009) 2160
-FeV
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Magnetism• Microscopic methods – Nuclear Magnetic Resonance V51
Dubiel, Tozoni, Cieslak et al., Phys. Rev. B. 81 (2010) 184407
-Fe100-xVx
x = 34.4 at% V
x = 39.9 at% V
x = 47.9 at% V
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Magnetism• Nuclear Magnetic Resonance V51
Fe
Dubiel, Tozoni, Cieslak et al., Phys. Rev. B. 81 (2010) 184407
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Magnetism• Macroscopic methods – Magnetometry
-FeV
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Magnetism• Macroscopic methods – magnetic moment,
-FeV
-FeCr
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Magnetism• Models
• Ferrimagnetism
1 = 2.0 2 = 1.8
B1 = 18 T B2 = 15 T
Bexp = 4 T
• Band-magnetism
)(
nnM B
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Magnetism
• Arguments in favour of band model
1. Lack of saturation 2. Rhodes-Wohlfarth plot
-FeCr
4K
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Magnetism• Theoretical calculations (KKR, LDA, Barth-Hedin exchange correlation)
1. FM ordering
2. APM ordering
Cieslak, Tobola, Dubiel, Intermetallics, 22 (2012) 7
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Magnetism
• Theoretical calculations – average magnetic moment
J. Cieslak, J. Tobola, S. M. Dubiel, Intermetallics, 22 (2012) 7
-FeV
V
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Magnetism• Non-colinear structure – re-entrant spin-glass in -Fe0.53 Cr0.47
R. Barco et al., J. Phys.: CM, 24 (2012) 046002
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Magnetism• Non-colinear structure – re-entrant spin-glass in -Fe0.52 V0.48
R. Barco et al., J. Phys.: CM, 24 (2012) 046002
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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
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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()(
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Lattice Dynamics - D
- D for -FeCr46 = 412 K
J. Cieslak et al., Intermetallics, 18 (2010) 1695
-FeCr
-FeV
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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
S. M. Dubiel et al., PRL, 104 (2010) 155503
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Lattice Dynamics – effect
of magnetism
There are anomalies both in <CS> and in f at T TC
Zero field results
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Lattice Dynamics - PDOS
E 1.5 meV (4%)
295 K 18 K
• Experiment
• Theory
E 0.1 meV (0.3%)
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Lattice Dynamics – effect
of magnetism In-field results
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Acknowledgement
• E. E. Alp • J. Zhao • M. Y. Hu •
W. Sturhahn
• R. Barco • P. Pureur
• G. L. F. Fraga
• J. Cieślak • S. M. Dubiel
• P. Piekarz • M. Sternik
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Conclusions
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