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,

Impurities dissolved randomly on regular iron sites in BCC iron

magnetic hyperfine field B (electron spin density on Fe nucleus) and 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.

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

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).

BAND EFFECT + VOLUME EFFECT 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

VOLUME EFFECT and BAND EFFECT introduced by impurity? ANSWER 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-B0 versus lattice constant a-a0

3) QUESTION How impurities change lattice constant a? ANSWER X-ray diffraction data Lattice constant a versus impurity concentration c +0.0028 Å/at.% +0.0047 Å/at.% Fe100-cOsc Fe100-cAuc

da/dc for all impurities studied Ne - number of out of the core electrons donated by impurity

1) 2) 3) 1) + 2) + 3) 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.

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.

for various impurities: 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 - 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 [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

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)

Cellular atomic model (CAM) of Miedema and van der Woude B Dispersion mm/(s∙V∙at.%) x102 mm/(s∙at.%) x102 d<S>/dc 0.79 -2.11 0.20 mm/(sV) x102 mm/s x102 S1 exp 3.00 -11.18 2.60 S1 ab initio 4.86 -13.25 1.66

versus distance r from the impurity (co-ordination shell) 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.