Impurity effect on charge and spin density on the Fe nucleus in BCC iron

A. Błachowski 1, U.D. Wdowik 2, K. Ruebenbauer 1

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-cGacFe100-cOsc

dcdB

dcdS

Ga: -0.144 T/at.%Os: -0.254 T/at.%

Ga: +0.0063 mm/(s at.%)Os: +0.0028 mm/(s at.%)

Fe100-cRuc Fe100-cIrc

dcdB

dcdS

Ir: +0.010 T/at.%Ru: -0.104 T/at.%

Ir: +0.0052 mm/(s at.%)Ru: +0.0022 mm/(s at.%)

Fe100-cPdc

Fe100-cMoc

dcdB

dcdS

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 cVegard law

Fe100-cOsc Fe100-cAuc

dcda

dcda

+0.0028 Å/at.% +0.0047 Å/at.%

Vegard law 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.

Variation of volume corrected: hyperfine field (dB/dc)b, isomer shift (dS/dc)b and electron density (d/dc)b on Fe nucleus

versus number of out of the core electrons Ne donated by impurity

Addition of electrons by impurity leads to the lowering of electron density

on Fe nucleus.