1. -Phase in Fe-Cr and Fe-V Systems
Stanislaw M. Dubiel*
Faculty of Physics & Applied Computer Science, AGH University, Kraków

2. -Phase
The -phase (tetragonal structure, space group D144h – P42/mnm) is known to exist only in alloy systems. Among 53 members of the -phase family in binary alloys only two i.e. Fe-Cr and Fe-V have well documented magnetic properties [1]. The -FeCr seems to be the most known member of the family not only as the archetype, but also for technological reasons. The latter follows from a deteriorating effect of the phase precipitation on mechanical and corrosive properties of technologically important materials based on Fe-Cr alloys e. g. loss of corrosion resistance and reduction of ductility and toughness. Although the -FeCr and -FeV have been known since many years, their physical properties, and, in particular, magnetic ones, are not known satisfactorily, and the Debye temperature was determined for the first time only recently [2]. There are only very few theoretical papers on the issue available, which in a combination with a complex crystallographic structure (30 atoms distributed randomly over five different crystallographic sites with high coordination numbers) makes the interpretation of experimental results very difficult.
[1] E. O. Hall and S. H. Algie, Metall. Rev., 11 (1966) [2] J. Cieslak et al., Phys. Rev. B, 65 (2002)

3. Outline • Crystallographic structure and -phase family
• Short history of -FeCr
• Formation and identification of -FeCr
• Debye temperature, D
• Curie temperature, TC
• Hyperfine field, B
• Correlations between B and 
• Magnetism of -phase in Fe-Cr and Fe-V systems

4. Structure – Unit Cell A B C D E E

5. Structure – Sites Site number code CN ON <d>[nm] 1 A 12 2 0.250815 4
0.2701 3 C 14 8
0.2652 D
0.2526 5 E
0.2638
CN - coordination number; ON- occupation number; <d> -average nearest-neighbour distance

6. Structure – Sites A B D C E
The plot shows all 5 sites with all their NN-neighbours. The geometry of the NN-atoms is preserved. Note that atoms at B, D and E sites have all 5 different atoms as their NN-neighbours, but atoms at A miss A and C NN-atoms, and those at C sites miss A NN-atoms.

7. Structure – Site Occupancy
• Mössbauer spectroscopy (-FeCr)
Ba = 13.5 T; T = 4.2 K
Five different sites occupied by Fe atoms
J. Cieslak, M. Reissner, S. M. Dubiel, W. Steiner, 6th Seeheim Workshop on MS, 2006

8. Structure - Site Occupancy
• Neutron diffraction (---- FexV;  FexCr)
J. Cieslak et al., J. Alloys Comp., 460 (2008) 20

9. -Phase Family
• 53 cases in binary alloys e.g. FeV, FeNb, FeTa, FeCr, FeMo, FeTc, FeRe 

10. Phase Diagram - FeV System

11. History of -FeCr
• 1923: Bain observed hard, brittle and nonmagnetic phase (B-constituent) in FeCrNi alloy
• 1936: Jette & Foote gave the name „sigma”
• 1943: Cook & Jones recorded first XRD pattern
• 1954: Bergmann & Shoemaker established its crystal structure
• 1981: Yakel determined site occupancy
• 1995: Kawazoe et al. published first theoretical paper
E. O. Hall and S. H. Algie, Metall. Rev., 11 (1966) 61

12. Identification of -FeCr
• T = 295 K
XRD ME 
NEUTRONS    
The difference in the isomer shift between  and  amounts to ca mm/s
J. Cieslak et al.. J. Alloys Comp., 460 (2008) 20

13. Kinetics of Transformation
• -FeCr
• Isothermal annealing at ~ 530  T  ~ 830oC
Ta = 700oC
E = 196 ± 2 kJ/mol
A. Blachowski, S. M. Dubiel and J. Zukrowski, Intermetallics, 9 (2001) 493

14. Debye Temperature, ΘD
• -FeCr
T[K] 60 40 20
4.2

15. Debye Temperature, ΘD • -FeV + -FeCr
ΘD [K]
There is a linear increase of TD with x for x  45 for both V and Cr
J. Cieslak et al., J. Phys.: Condens. Matter., 17 (2005) 6889

16. Curie Temperature, Tc • Mössbauer effect (-FeCr) - from line width, G
(a) 4.2 K; (b) 295 K
(a) x = 45.0, (b) x = 46.2 and (c) x = 48.0
J. Cieslak et al., J. Magn. Magn. Mater., (2004) 534

17. Curie Temperature, Tc
• Mössbauer effect (-FeV34) - from average hf. field
TC = 323 K
J. Cieslak, B. F. O. Costa, S. M. Dubiel, M. Reissner, W. Steiner, ICAME2008

18. Curie Temperature, Tc • -FeV
-FeCr
There is a non-linear decrease of TC with vanadium content
J. Cieslak, B. F. O. Costa, S. M. Dubiel, M. Reissner, W. Steiner, ICAME2008

19. <B> -  Relationship
<B>  a 
<B> = a  + BCEP
Lack of linearily speaks for important contribution from conduction electrons
J. Cieslak, B. F. O. Costa, S. M. Dubiel, M. Reissner, W. Steiner, ICAME2008

20. Models of -FeCr Magnetism
Ferrimagnetism
1 = 2.0 B 2 = 1.5 B
B1 = 18 T B2 = 13 T
Bexp  4 T
• Band-magnetism

21. Models of -FeCr Magnetism
• Band-magnetism
Lack of saturation
Rhodes - Wohlfarth plot 4K
-FeCr
Both plots give evidence for itinerant magnetism in the -FeCr

22. Models of -FeCr Magnetism
Rhodes – Wohlfarth plot
Fe50.5Cr49.5
Fe53.8Cr46.2
µeff /µs
Systems for which eff/s > 1 have itinerant character of magnetism

23. Conclusions
 Mössbauer spectroscopy is very useful to study magnetic and dynamic properties of the -phase in Fe-Cr and Fe-V systems, as well as the kinetics of -to- transformation.
All measured quantities (TD, TC, and <B>) depend sensitively on Cr, V content, x);
• TD increases at the rate of ~15 K/at% (x 45) for both systems
• TC and <B> decrease non-linearly with x
• <B> is non-lineraly correlated with 
Magnetism of -FeCr (V) seems to obey itinerant model due to;
• lack of saturation
• Rhodes - Wohlfarth plot
• non-linear relationship <B> - .

24. More to read
• G. Bergman and D. P. Shoemaker, Acta Cryst., 7 (1954) • H. L. Yakel, Acta Cryst., B39 (1983) 20; ibid, B39 (1983) • H. H. Ettwig and W. Pepperhoff, Arch. Eisenhuttenwes., 43 (1972) • Y. Sumimoto et al., J. Phys. Soc. Jpn., 35 (1973) • A. M. van der Kraan et al., Phys. Stat. Sol. (a), 88 (1985) • R. Vilar and G. Cizeron, Acta Metall., 35 (1987) • A. Gupta et al., Hyper. Inter., 54 (1990) • B. F. O. Costa and S. M. Dubiel, Phys. Stat. Sol. (a), 139 (1993) • B. F. O. Costa et al., Phys. Stat. Sol. (a), 161 (1997) • J. Cieslak, S. M. Dubiel and B. Sepiol, Sol. Stat. Commun., 111 (1999) • J. Cieslak, S. M. Dubiel and B. Sepiol, Hyper. Inter., 126 (2000) • A. Blachowski et al., J. Alloys Comp., 308 (2000) 189; ibid, 313 (2000) • A. Blachowski et al., Intermetallics, 8 (2000) • J. Cieslak et al., J. Alloys Comp., 460 (2008) • J. Cieslak et al., J. Phys.: Condens Matter., 20 (2008)