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.