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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, Pedagogical University, Kraków, Poland
Impurities dissolved randomly on regular iron sites in BCC iron
Impurities modify magnetic hyperfine field B
(electron spin density on Fe nucleus)and
isomer shift S (electron charge density on Fe nucleus).
Aim of this contribution is to separate VOLUME EFFECT
and BAND EFFECT
due to addition of impurity.
Electron charge and spin densities on Fe nucleus are affected by volume effect
caused by solution of impurity and
by conduction band modification.
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.
Fe100-cPdc
Fe100-cMoc
dcdB
dcdS
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, 104423 (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).
Correlation between electron spin density (dB/dc) and electron density (dS/dc) variations for various impurities
BAND EFFECT + VOLUME EFFECT
S αρρ 10
13 s mm a.u. )1(29.0α
Isomer shift S could be transformed into electron density on Fe nucleus
Calibration constant
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.
FeVariation of electron density -0
and hyperfine field (contact field) B-B0
versus lattice constant a-a0
A a.u.el.
)1(2.5ρ
3 a
AT
(3)33 aB
a.u.el.
046.15322ρ 30
A 8311.20a
T 94.300 B
3)QUESTION
How impurities change lattice constant a?
ANSWERX-ray diffraction data
Lattice constant a versus impurity concentration c
Fe100-cOsc Fe100-cAuc
dcda
dcda
+0.0028 Å/at.% +0.0047 Å/at.%
da/dc for all impurities studied
Ne - number of out of the core electrons donated by impurity
Pure BAND MODIFICATION EFFECT
i.e. volume effect due to impurity is removed.
Volume correction for electron spin density (hyperfine field)
and for electron charge density (isomer shift)
A a.u.el.
)1(2.5ρ
3 a
AT
(3)33 aB
13 s mm a.u. )1(29.0α
. ρ
α
,
dcda
adcdS
dcdS
dcda
aB
dcdB
dcdB
b
b
1) + 2) + 3)
dcdS
dcdB
,
dcda
α , ρ
, aa
B
1) - Mössbauer data
- ab initio calculations
- X-ray diffraction data
2)
3)
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.
Correlation between electron spin density and electron density variations for various impurities:
(a) – total; (b) – volume corrected, i.e., pure band effect.
Cellular atomic model (CAM) of Miedema and van der Woude
bb
baba S
nnn
BAS
)Φ(Φ
aΦ bΦ
- 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
an bn
A B
S
[1] A. R. Miedema and F. van der Woude, Physica 100B, 145 (1980)[2] A. R. Miedema, Physica B 182, 1 (1992)
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
dcSd E /
dcSd M /
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)
A B Dispersion
mm/(s∙V∙at.%) x102
mm/(s∙at.%)x102
mm/(s∙at.%)x102
d<S>/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
Cellular atomic model (CAM) of Miedema and van der Woude
bb
baba S
nnn
BAS
)Φ(Φ
Variation of the electron density (isomer shift S) and hyperfine field B
versus distance r from the impurity (co-ordination shell)
Mössbauer spectra for various concentrations of Ru and Os.
Red lines - perturbations of the charge and spin density obtained from the ab initio calculations.