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,

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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.

Fe 100-c Ga c Fe 100-c Os c Ga: T/at.% Os: T/at.% Ga: mm/(s at.%) Os: mm/(s at.%)

Fe 100-c Ru c Fe 100-c Ir c Ir: T/at.% Ru: T/at.% Ir: mm/(s at.%) Ru: mm/(s at.%)

Fe 100-c Pd c Fe 100-c Mo c

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

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.

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

3) QUESTION How impurities change lattice constant a? ANSWER X-ray diffraction data Lattice constant a versus impurity concentration c Vegard law Fe 100-c Os c Fe 100-c Au c Å/at.% Å/at.%

Vegard law for all impurities studied N e - 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) 1) + 2) + 3) 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 N e donated by impurity Addition of electrons by impurity leads to the lowering of electron density on Fe nucleus.