Magnetic and dynamic properties

of sigma-phase in Fe-Cr and Fe-V

Stanisław M. Dubiel

Faculty of Physics & Applied

Computer Science, Kraków, Poland

2

Structure

3

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

4

Structure

Dubiel, J. Cieslak, Crit. Rev. Sol. Stat. Mater Sci., 36 (2011) 192

5

StructureJ. Cieslak P. Blaha

6

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

7

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

8

Magnetism• Mössbauer spectroscopy – Curie temperature, TC

-FeCr

-Fe66V34

9

Magnetism• Mössbauer spectroscopy – Curie temperature, TC

-FeCr

RT

J. Cieslak et al., J. Magn. Magn. Mater., 321 (2009) 2160

-FeV

10

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

11

Magnetism• Nuclear Magnetic Resonance V51

Fe

Dubiel, Tozoni, Cieslak et al., Phys. Rev. B. 81 (2010) 184407

12

Magnetism• Macroscopic methods – Magnetometry

-FeV

13

Magnetism• Macroscopic methods – magnetic moment,

-FeV

-FeCr

14

Magnetism• Models

• Ferrimagnetism

1 = 2.0 2 = 1.8

B1 = 18 T B2 = 15 T

Bexp = 4 T

• Band-magnetism

)(

nnM B

15

Magnetism

• Arguments in favour of band model

1. Lack of saturation 2. Rhodes-Wohlfarth plot

-FeCr

4K

16

Magnetism• Theoretical calculations (KKR, LDA, Barth-Hedin exchange correlation)

1. FM ordering

2. APM ordering

Cieslak, Tobola, Dubiel, Intermetallics, 22 (2012) 7

17

Magnetism

• Theoretical calculations – average magnetic moment

J. Cieslak, J. Tobola, S. M. Dubiel, Intermetallics, 22 (2012) 7

-FeV

V

18

Magnetism• Non-colinear structure – re-entrant spin-glass in -Fe0.53 Cr0.47

R. Barco et al., J. Phys.: CM, 24 (2012) 046002

19

Magnetism• Non-colinear structure – re-entrant spin-glass in -Fe0.52 V0.48

R. Barco et al., J. Phys.: CM, 24 (2012) 046002

20

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

21

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()(

22

Lattice Dynamics - D

- D for -FeCr46 = 412 K

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

-FeCr

-FeV

23

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

24

Lattice Dynamics – effect

of magnetism

There are anomalies both in <CS> and in f at T TC

Zero field results

25

Lattice Dynamics - PDOS

E 1.5 meV (4%)

295 K 18 K

• Experiment

• Theory

E 0.1 meV (0.3%)

26

Lattice Dynamics – effect

of magnetism In-field results

27

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

28

Conclusions

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