Transcript Slajd 1

Charge and spin density perturbation on iron nuclei
by non-magnetic impurities
substituted on the iron sites in -Fe
A. Błachowski 1, K. Ruebenbauer 1, J. Żukrowski 2, J. Przewoźnik 2
1
Mössbauer Spectroscopy Division, Institute of Physics,
Pedagogical University, Kraków, Poland
2
Solid State Physics Department,
Faculty of Physics and Applied Computer Science,
AGH University of Science and Technology, Kraków, Poland
Fe100-cXc
- arc melting
- ingots ~1.5 g
- rapid quench of the molten state
- metastable state
Lattice constant a and half-width of the <110> Bragg peak
versus impurity concentration c
Fe1-cOsc
Fe1-cAuc
Binomial distribution



 ks
ns !
 c (1  c) ns ks 
C (c | {ns k s })   
s 1  ( ns  k s )! k s ! 

0  c 1
s  1, 2, ..., 
ns
k s  0, 1, ..., ns
impurity concentration [at.%]
(  2 or   3)
n1  8 , n2  6 , n3  12
subsequent coordination shells around 57Fe
number of vortices in the s-th shell
number of impurities in the s-th shell
 2
 3
k1 k2 k 3 C (c | {ns k s })
k1 k2 C (c | {ns k s })
Example
Fe100-cXc
c  5 at.%
0
0
0
1
1
2
2
0
1
2
0
1
0
1
48.8
15.4
2.0
20.5
6.5
3.8
1.2
98.2
0
0
0
0
0
0
0
1
1
1
1
1
2
2
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
1
2
0
1
0
1
26.4
16.6
4.8
8.3
5.3
1.5
1.1
11.1
7.0
2.0
3.5
2.2
2.0
1.3
93.1
Hyperfine fields and isomer shifts for particular configuration
having the contribution
C (c | {ns k s })
( )
0
B ({ns k s })  B

  k s Bs
s 1
,
S ({ns k s })  S
( )
0

  k s S s
s 1
B0  , S0  hyperfine field and total shift for 57Fe atoms
surrounded entirely by Fe atoms up to the outermost shell 
Bs , S s contributions to the hyperfine field and isomer shift
due to a single impurity atom located in the s-th shell
Fe100-cGac
Fe100-cGac
c
B1
B2
B3
[at. %]
[T]
[T]
S1
S 2
S 3
[mm/s]
[mm/s]
[T]
[mm/s]
 0.1
 0.02
 0.02
 0.02
0
2
4
6
8
10
12
15
18
21
25
29
-1.97
-1.91
-1.88
-1.95
-1.97
-2.01
-2.08
-2.15
-2.23
-2.47
-2.66
-0.14
-0.06
-0.01
-0.04
-0.02
-0.01
-0.03
-0.02
0.01
-0.21
-0.19
0.44
0.43
0.44
0.46
0.46
0.45
0.43
0.45
0.44
0.48
0.55
FeGa
-2.02
-0.02
+0.44 +0.036 +0.076 -0.002
 0.002  0.002  0.002
0.045
0.041
0.036
0.036
0.035
0.035
0.033
0.034
0.034
0.032
0.036
0.082
0.073
0.071
0.072
0.076
0.073
0.081
0.075
0.081
0.075
0.072
0.006
0.002
-0.002
0.002
-0.003
-0.003
-0.006
-0.003
-0.010
0.004
0.002
Fe100-cIrc
Fe100-cIrc
ΔB1
ΔB2
ΔB3
ΔS1
(at.%)
 0.1
(T)
 0.03
(T)
 0.02
(T)
 0.03
(mm/s) (mm/s) (mm/s)
 0.003  0.002  0.002
0
1
3
5
7
9
11
0.78
0.68
0.64
0.67
0.64
0.81
-1.82
-1.81
-1.84
-1.89
-1.97
-2.04
0.75
0.72
0.66
0.68
0.73
0.65
-0.021
-0.023
-0.029
-0.034
-0.036
-0.030
FeIr
+0.66
-1.88
+0.70 -0.031 +0.003 +0.033
c
ΔS 2
0.004
0.005
0.003
0.001
0.002
0.000
ΔS 3
0.026
0.025
0.034
0.037
0.035
0.042
Correlation between
average hyperfine field change per at.% of impurity
and
average isomer shift change per at.% of impurity
[W] S.M. Dubiel, W. Zinn, Phys. Rev. B 30, 3783 (1984).
[Re] S.M. Dubiel, J. Magn. Magn. Mater. 69, 206 (1987).
[Pt] S.M. Dubiel, Phys. Rev. B 37, 1429 (1988).
Impurity ΔB ( ) ΔB ( ) ΔB( )
1
2
3
X
[T]
[T]
[T]
-3.55
-4.18
-1.99
+0.73
+1.38
-3.97
+0.66
+0.86
-2.02
Nb
Mo
Ru
Rh
Pd
Os
Ir
Au
Ga
δS 
σ
 [ΔS
s 1
-2.30
-2.30
-0.09
+0.70
+1.05
-1.11
-1.88
0
-0.02
( )
2
s
c
+0.51
+0.52
+0.43
+0.67
+0.70
+0.44
ΔS1( ) ΔS 2( ) ΔS3( )
[mm/s] [mm/s] [mm/s]
-0.033
-0.033
-0.019
-0.015
+0.010
-0.031
-0.031
+0.013
+0.036
 ] , δB 
σ
-0.015
-0.005
+0.072
-0.005
+0.008
+0.014
+0.003
+0.111
+0.076
+0.003
+0.005
+0.039
+0.003
+0.033
-0.002
( )
2
[

Δ
B

]
 s c .
s 1
Spin- and charge density oscillations
( )
( )
Average perturbations  S s  c and  Bs  c for Ru, Ir and Ga impurities
versus relative distance from the 57Fe nucleus r / a