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

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,

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

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  1. Impurity effect on charge and spin density on the Fe nucleus in BCC iron A. Błachowski 1, U.D. Wdowik 2, K. Ruebenbauer 1 1Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, Kraków, Poland 2Applied Computer Science Division, Institute of Technology, Pedagogical University, Kraków, Poland

  2. Impurities dissolved randomly on regular iron sites in BCC iron

  3. 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.

  4. 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.

  5. Fe100-cOsc Fe100-cGac Ga: -0.144 T/at.% Os:-0.254 T/at.% Ga: +0.0063 mm/(s at.%) Os: +0.0028 mm/(s at.%)

  6. Fe100-cRuc Fe100-cIrc Ir: +0.010 T/at.% Ru: -0.104 T/at.% Ir: +0.0052mm/(s at.%) Ru:+0.0022 mm/(s at.%)

  7. Fe100-cPdc Fe100-cMoc

  8. Correlation betweenelectron spin density (dB/dc) and electron density (dS/dc) variations for various impurities BAND EFFECT + VOLUME EFFECT Isomer shiftS could be transformed into electron density on Fe nucleus Calibration constant

  9. 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.

  10. Fe Variation of electron density-0 and hyperfine field (contact field)B-B0 versus lattice constanta-a0

  11. 3) QUESTION How impurities change lattice constant a? ANSWER X-ray diffraction data Lattice constantaversusimpurity concentrationc Vegard law +0.0047Å/at.% +0.0028Å/at.% Fe100-cOsc Fe100-cAuc

  12. Vegard law for all impurities studied Ne - number of out of the core electrons donated by impurity

  13. 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.

  14. Correlation betweenvolume 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.

  15. Correlation between electron spin density and electron density variations for various impurities: (a) – total; (b) – volume corrected, i.e., pure band effect.

  16. 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.

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