Chemistry Reference
In-Depth Information
For a thick absorber specimen containing n multiple phases, the following
expression is frequently used for the analysis of the transmission spectra [
18
-
20
].
Z
þ1
s
ð
E
v
Þ
e
r
ð
E
Þ
dE
;
p
ð
v
Þ¼
N
0
ð
1
f
s
Þþ
N
b
þ
N
0
f
s
ð
1
:
21
Þ
1
where N
0
is counts from resonant radiation, N
b
counts from other radiation and f
s
recoilless fraction of source. Source has Lorentzian line shape as mentioned before
and is given by
s
ð
E
v
Þ¼
C
s
2p
1
ð
E
v
Þ
2
þð
C
s
=
2
Þ
2
:
Cross section r
ð
E
Þ
for the resonance absorption is usually expected to have the
form
r
ð
E
Þ¼
X
n
T
n
ð
C
n
=
2
Þ
2
ð
E
E
n
Þ
2
þð
C
n
=
2
Þ
2
:
ð
1
:
22
Þ
where T
¼
P
n
T
n
¼
n
a
af
a
r
0
t is a total effective thickness of the absorber. Other
notations are listed in Table
1.1
.
When the absorber thickness is thin, the (
1.21
) can be rewritten as follows;
¼
Z
þ1
c
ð
v
Þ
N
0
þ
N
b
p
ð
v
Þ
N
0
f
s
s
ð
E
v
Þð
1
e
r
ð
E
Þ
dE
:
ð
1
:
23
Þ
1
'
X
n
T
n
ðð
C
s
þ
C
n
Þ=
2
Þ
2
ð
v
E
n
Þ
2
þðð
C
s
þ
C
n
Þ=
2
Þ
2
C
n
C
s
þ
C
n
When the absorber is thin, the observed transmission Mössbauer spectrum is a
superposition of several Lorentz functions.
Table 1.1
List of the parameters used in Eq. (
1.22
) and T
C
s
Full width at half maximum (FWHM) of the source
C
n
FWHM of the absorption
E
n
Absorption line center
T
n
Effective thickness of nth atomic site
n
a
Number of atoms per cubic centimeter of absorber volume
f
a
Recoilless fraction of absorber
a
Fractional abundance of atoms which can absorb resonantly
r
a
Absorption cross section at resonance in square centimeter
t
Thickness of absorber in centimeter
a
r
0
¼
k
2
2p
2j
e
þ
1
2j
g
þ
1
1
1
þ
a
and a is the internal conversion coefficient of c transition
