Transcript Slajd 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
1
2
Mössbauer Spectroscopy Division, Institute of Physics,
Pedagogical University, Kraków, Poland
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).
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-cGac
dB
dc
Ga: -0.144 T/at.%
Os: -0.254 T/at.%
Ga: +0.0063 mm/(s at.%)
Os: +0.0028 mm/(s at.%)
dS
dc
Fe100-cOsc
Fe100-cRuc
Fe100-cIrc
dB
dc
Ir: +0.010 T/at.%
Ru: -0.104 T/at.%
Ir: +0.0052 mm/(s at.%)
Ru:+0.0022 mm/(s at.%)
dS
dc
Fe100-cPdc
dB
dc
dS
dc
Fe100-cMoc
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
ρ  ρ0  α 1 S
α  0.29(1) a.u.3 mm s 1
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
ρ
 5.2(1)
a
 el. 
 a.u.3 A
 
B
T
 33(3)  

a
A
el.
ρ 0  15322.046  3 
 a.u. 
B0  30.94 T 

a0  2.8311A
3)
QUESTION
How impurities change lattice constant a?
ANSWER
X-ray diffraction data
Lattice constant a versus impurity concentration c
Vegard law
da
+0.0028 Å/at.%
dc
Fe100-cOsc
da
+0.0047 Å/at.%
dc
Fe100-cAuc
Vegard law for all impurities studied
Ne - number of out of the core electrons donated by impurity
1)
dB dS
,
dc dc
- Mössbauer data
2)
B ρ
,
, α
a a
- ab initio calculations
3)
da
dc
- X-ray diffraction data
1) + 2) + 3)
Volume correction
for electron spin density (hyperfine field)
and
for electron charge density (isomer shift)
 dB    dB    B   da ,
      
 dc b  dc   a   dc 
 dS    dS   α  ρ  da  .
   
  
 dc b  dc 
 a  dc 
Pure BAND MODIFICATION EFFECT
i.e. volume effect due to impurity is removed.
B
 33(3)
a
T 
 A
 
ρ
 5.2(1)
a
 el. 
 a.u.3 A
 
α  0.29(1) a.u.3 mm s 1
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.