1. Impurity effect on charge and spin density in α-Fe
– comparison between cellular model, ab initio calculations
and Mössbauer spectroscopy data
A. Błachowski1, U.D. Wdowik2, K. Ruebenbauer1
1 Mössbauer Spectroscopy Division, Institute of Physics,
Pedagogical University, Kraków, Poland
2 Applied Computer Science Division, Institute of Technology,

2. Impurities dissolved randomly on regular iron sites in BCC iron

3. magnetic hyperfine field B (electron spin density on Fe nucleus) and
Impurities modify
magnetic hyperfine field B
(electron spin density on Fe nucleus)
and
isomer shift S
(electron charge density  on Fe nucleus).
Electron charge and spin densities on Fe nucleus
are affected by volume effect
caused by solution of impurity
and
by conduction band modification.
Aim of this contribution is to separate
VOLUME EFFECT
and
BAND EFFECT
due to addition of impurity.

4. 1)
One can study
variation dB/dc of average magnetic hyperfine field B on Fe nucleus
versus particular impurity concentration c.
Similar variation d/dc of average electron density  on Fe nucleus
could be conveniently observed via isomer shift variation dS/dc ,
where S denotes a total shift versus total shift in pure -Fe.

5. Fe100-cPdc
Fe100-cMoc

6. References
[Be, Cu] I. Vincze and A. T. Aldred, Solid State Communications 17, 639 (1975).
[Al] S. M. Dubiel and W. Zinn, Phys. Rev. B 26, 1574 (1982).
[Si] S. M. Dubiel and W. Zinn, J. Magn. Magn. Mater. 28, 261 (1982).
[P] S. M. Dubiel, Phys. Rev. B 48, 4148 (1993).
[Ti] J. Cieślak and S. M. Dubiel, J. Alloys Comp. 350, 17 (2003).
[V] S. M. Dubiel and W. Zinn, J. Magn. Magn. Mater. 37, 237 (1983).
[Cr] S. M. Dubiel and J. Żukrowski, J. Magn. Magn. Mater. 23, 214 (1981).
[Mn, Ni] I. Vincze and I. A. Campbell, J. Phys. F, Metal Phys. 3, 647 (1973).
[Co] J. Chojcan, Hyperf. Interact. 156/157, 523 (2004).
[Zn] A. Laggoun, A. Hauet, and J. Teillet, Hyperf. Interact. 54, 825 (1990).
[Ga] A. Błachowski, K. Ruebenbauer, J. Żukrowski, and J. Przewoźnik, J. Alloys Compd. 455, 47 (2008).
[Ge] S. M. Dubiel and W. Zinn, Phys. Rev. B 28, 67 (1983).
[As, Sb] I. Vincze and A. T. Aldred, Phys. Rev. B 9, 3845 (1974).
[Nb] A. Błachowski, K. Ruebenbauer, and J. Żukrowski, Phys. Status Solidi B 242, 3201 (2005).
[Mo] A. Błachowski, K. Ruebenbauer, J. Żukrowski, and J. Przewoźnik, J. Alloys Compd. 482, 23 (2009).
[Ru] A. Błachowski, K. Ruebenbauer, and J. Żukrowski, Phys. Rev. B 73, (2006).
[Rh] A. Błachowski, K. Ruebenbauer, and J. Żukrowski, J. Alloys Compd. 477, 4 (2009).
[Pd] A. Błachowski, K. Ruebenbauer, and J. Żukrowski, Phys. Scr. 70, 368 (2004).
[Sn] S. M. Dubiel and W. Znamirowski, Hyperf. Interact. 9, 477 (1981).
[W] S. M. Dubiel and W. Zinn, Phys. Rev. B 30, 3783 (1984).
[Re] S.M. Dubiel, J. Magn. Magn. Mater. 69, 206 (1987).
[Os] A. Błachowski, K. Ruebenbauer, and J. Żukrowski, Nukleonika 49, S67 (2004).
[Ir] A. Błachowski, K. Ruebenbauer, and J. Żukrowski, J. Alloys Compd. 464, 13 (2008).
[Pt] S. M. Dubiel, Phys. Rev. B 37, 1429 (1988).
[Au] A. Błachowski, K. Ruebenbauer, J. Przewoźnik, and J. Żukrowski, J. Alloys Compd. 458, 96 (2008).

7. BAND EFFECT + VOLUME EFFECT
Correlation between electron spin density (dB/dc) and electron density (dS/dc) variations for various impurities
BAND EFFECT + VOLUME EFFECT
Isomer shift S could be transformed into electron density  on Fe nucleus
Calibration constant

8. VOLUME EFFECT and BAND EFFECT introduced by impurity? ANSWER 2)
QUESTION
How to separate
VOLUME EFFECT and BAND EFFECT
introduced by impurity?
ANSWER
VOLUME EFFECT can be calculated for pure -Fe
by using ab initio methods (Wien2k).
In order to do so one has to calculate
magnetic hyperfine field B and electron density 
on Fe nucleus for pure -Fe
varying lattice constant a.

9. Fe Variation of electron density -0 and
hyperfine field (contact field) B-B0
versus lattice constant a-a0

10. 3)
QUESTION
How impurities change lattice constant a?
ANSWER
X-ray diffraction data
Lattice constant a versus impurity concentration c
Å/at.%
Å/at.%
Fe100-cOsc
Fe100-cAuc

11. da/dc for all impurities studied
Ne - number of out of the core electrons donated by impurity

12. 1) 2) 3) 1) + 2) + 3) Mössbauer data ab initio calculations
- X-ray diffraction data 2) 3)
1) + 2) + 3)
Volume correction
for electron spin density (hyperfine field)
and
for electron charge density (isomer shift)
Pure BAND MODIFICATION EFFECT
i.e. volume effect due to impurity is removed.

13. Correlation between volume corrected (pure BAND EFFECT)
electron spin density (dB/dc)b and electron density (dS/dc)b
variations for various impurities
All d metals fall on single straight line with positive slope. Hence, the band effect
is almost the same regardless of principal quantum number of d shell of impurity.

14. for various impurities:
Correlation between electron spin density and electron density variations
for various impurities:
(a) – total; (b) – volume corrected, i.e., pure band effect.

15. Cellular atomic model (CAM) of Miedema and van der Woude
- isomer shift
of the alloy containing diluted impurity a in the matrix b
- electro-chemical potentials
of the pure element a and b forming binary alloy
- electron densities
- CAM parameters
[1] A. R. Miedema and F. van der Woude, Physica 100B, 145 (1980)
[2] A. R. Miedema, Physica B 182, 1 (1992)

16. Cellular atomic model (CAM) of Miedema and van der Woude
Correlation between experimental derivative
of the average isomer shift versus impurity concentration c
and corresponding derivative within CAM model

17. Cellular atomic model (CAM) of Miedema and van der Woude
(b) Correlation between
experiment and CAM for the first shell perturbations of isomer shift S1(E) and S1(M)
(c) Correlation between
ab initio calculated S1(C) and CAM S1(M)

18. Cellular atomic model (CAM) of Miedema and van der WoudeB
Dispersion
mm/(s∙V∙at.%) x102
mm/(s∙at.%)
x102
d<S>/dc
0.79
-2.11
0.20
mm/(sV) x102
mm/s x102
S1 exp
3.00
-11.18
2.60
S1 ab initio
4.86
-13.25
1.66

19. versus distance r from the impurity (co-ordination shell)
Variation of the electron density  (isomer shift S) and hyperfine field B
versus distance r from the impurity (co-ordination shell)

20. Mössbauer spectra for various concentrations of Ru and Os.
Red lines
- perturbations of the charge and spin density obtained from the ab initio calculations.