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Impurity effect on charge and spin density in
a-Fe comparison between cellular model, ab
initio calculations and Mössbauer spectroscopy
data A. Blachowski1, U.D. Wdowik2, K.
Ruebenbauer1 1 Mössbauer Spectroscopy
Division, Institute of Physics, Pedagogical
University, Kraków, Poland 2 Applied Computer
Science Division, Institute of Technology,
Pedagogical University, Kraków, Poland
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Impurities dissolved randomly on regular iron
sites in BCC iron
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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.
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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.
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Fe100-cPdc
Fe100-cMoc
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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. Cieslak 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.
Zukrowski, 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. Blachowski, K. Ruebenbauer, J. Zukrowski, and
J. Przewoznik, 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.
Blachowski, K. Ruebenbauer, and J. Zukrowski,
Phys. Status Solidi B 242, 3201 (2005). Mo A.
Blachowski, K. Ruebenbauer, J. Zukrowski, and J.
Przewoznik, J. Alloys Compd. 482, 23 (2009). Ru
A. Blachowski, K. Ruebenbauer, and J. Zukrowski,
Phys. Rev. B 73, 104423 (2006). Rh A.
Blachowski, K. Ruebenbauer, and J. Zukrowski, J.
Alloys Compd. 477, 4 (2009). Pd A. Blachowski,
K. Ruebenbauer, and J. Zukrowski, 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. Blachowski, K. Ruebenbauer, and
J. Zukrowski, Nukleonika 49, S67 (2004). Ir A.
Blachowski, K. Ruebenbauer, and J. Zukrowski, J.
Alloys Compd. 464, 13 (2008). Pt S. M. Dubiel,
Phys. Rev. B 37, 1429 (1988). Au A. Blachowski,
K. Ruebenbauer, J. Przewoznik, and J. Zukrowski,
J. Alloys Compd. 458, 96 (2008).
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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
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2) QUESTION How to separate VOLUME EFFECT and
BAND EFFECT introduced by impurity? ANSWER VOLU
ME 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.
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??Fe Variation of electron density ?-?0 and
hyperfine field (contact field) B-B0 versus
lattice constant a-a0
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3) QUESTION How impurities change lattice
constant a? ANSWER X-ray diffraction
data Lattice constant a versus impurity
concentration c
0.0028 Å/at.
0.0047 Å/at.
Fe100-cOsc
Fe100-cAuc
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da/dc for all impurities studied
Ne - number of out of the core electrons donated
by impurity
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1)

• 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.
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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.
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Correlation between electron spin density and
electron density variations for various
impurities (a) total (b) volume corrected,
i.e., pure band effect.
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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)
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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
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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)
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Cellular atomic model (CAM) of Miedema and van
der Woude
A B Dispersion
mm/(sVat.) x102 mm/(sat.) x102 mm/(sat.) x102
dltSgt/dc 0.79 -2.11 0.20
mm/(sV) x102 mm/s x102 mm/s x102
?S1 exp 3.00 -11.18 2.60
?S1 ab initio 4.86 -13.25 1.66
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Variation of the electron density ?? (isomer
shift ?S) and hyperfine field ?B versus distance
r from the impurity (co-ordination shell)
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Mössbauer spectra for various concentrations of
Ru and Os. Red lines - perturbations of the
charge and spin density obtained from the ab
initio calculations.