242
C. McCammon
Table 5.2 Transmission of 14.4 keV radiation through selected materials as a function of physical
sample thickness (in mm)
Material
μ (cm 2 /g)
ρ (g/cm 3 )
Transmission (I /I 0 )
99%
50%
1%
Diamond (C)
0.87
3.5
0.033
2.3
15
Glass (SiO 2 )
6.97
2.2
0.007
0.45
3
Polycarbonate (C 16 H 18 O 5 )
1.2
1.2
0.070
4.8
32
Epoxy resin (C 21 H 25 ClO 5 )
2.84
1.2
0.028
2.0
13
Water (H 2 O)
2.00
1.9
0.050
3.5
23
I = I 0 e
−(lμ/ρ)
(5.8)
where I is the transmitted intensity, I 0 is the incident intensity, l is the length of the
sample in the direction of radiation (i.e., the physical thickness) and ρ is the sample
density.
Table 5.2 shows γ-ray transmission for selected materials calculated from Eq. 5.8
based on values of μ taken from [46]. More than 50% of 14.4 keV radiation is lost
to diamonds in diamond anvil cell experiments where diamond thickness exceeds
2.3 mm. This thickness is usually exceeded, especially since diamonds are used in
pairs. For preparation of small samples, glass is a poor choice of mounting substrate
due to its high absorption (Sect. 5.4.2). Instead a plastic such as polycarbonate should
be used. Epoxy resin can also be used, but the thickness of epoxy underlying the
sample should be minimised. Finally, Eq. 5.8 can be used to demonstrate the benefits
of
57 Fe enrichment. For an unenriched Fe 0.4 Mg 0.6 Si 0.63 Al 0.37 O 3 sample with physical
thickness of 232 μm (t a = 9.3), only 13% of the signal would be transmitted through
the sample, while a 90%
57 Fe enriched sample with 15 μm physical thickness (t a =
25.4) would transmit 88% of 14.4 keV radiation.
High values of t a cause internal resonance within the sample that manifests itself
differently in energy and time domain spectra. In the energy domain, linewidths
become broadened, lineshapes deviate from Lorentzian, and relative areas become
distorted from the relative abundance of their iron species. In the time domain, there
is a speed-up effect (intensity increases at short delay times) and dynamical beats are
superimposed over the quantum beats (Chap. 1, this volume). There are analytical
solutions for these thickness effects in both energy and time domain, but not all
cases yield comparable results to thinner samples. Such situations occur primarily
in energy domain measurements, where linewidths may be too broad to resolve
individual components and the overall intensity may be so saturated that information
is lost at velocities where absorption is highest.
C. McCammon
Table 5.2 Transmission of 14.4 keV radiation through selected materials as a function of physical
sample thickness (in mm)
Material
μ (cm 2 /g)
ρ (g/cm 3 )
Transmission (I /I 0 )
99%
50%
1%
Diamond (C)
0.87
3.5
0.033
2.3
15
Glass (SiO 2 )
6.97
2.2
0.007
0.45
3
Polycarbonate (C 16 H 18 O 5 )
1.2
1.2
0.070
4.8
32
Epoxy resin (C 21 H 25 ClO 5 )
2.84
1.2
0.028
2.0
13
Water (H 2 O)
2.00
1.9
0.050
3.5
23
I = I 0 e
−(lμ/ρ)
(5.8)
where I is the transmitted intensity, I 0 is the incident intensity, l is the length of the
sample in the direction of radiation (i.e., the physical thickness) and ρ is the sample
density.
Table 5.2 shows γ-ray transmission for selected materials calculated from Eq. 5.8
based on values of μ taken from [46]. More than 50% of 14.4 keV radiation is lost
to diamonds in diamond anvil cell experiments where diamond thickness exceeds
2.3 mm. This thickness is usually exceeded, especially since diamonds are used in
pairs. For preparation of small samples, glass is a poor choice of mounting substrate
due to its high absorption (Sect. 5.4.2). Instead a plastic such as polycarbonate should
be used. Epoxy resin can also be used, but the thickness of epoxy underlying the
sample should be minimised. Finally, Eq. 5.8 can be used to demonstrate the benefits
of
57 Fe enrichment. For an unenriched Fe 0.4 Mg 0.6 Si 0.63 Al 0.37 O 3 sample with physical
thickness of 232 μm (t a = 9.3), only 13% of the signal would be transmitted through
the sample, while a 90%
57 Fe enriched sample with 15 μm physical thickness (t a =
25.4) would transmit 88% of 14.4 keV radiation.
High values of t a cause internal resonance within the sample that manifests itself
differently in energy and time domain spectra. In the energy domain, linewidths
become broadened, lineshapes deviate from Lorentzian, and relative areas become
distorted from the relative abundance of their iron species. In the time domain, there
is a speed-up effect (intensity increases at short delay times) and dynamical beats are
superimposed over the quantum beats (Chap. 1, this volume). There are analytical
solutions for these thickness effects in both energy and time domain, but not all
cases yield comparable results to thinner samples. Such situations occur primarily
in energy domain measurements, where linewidths may be too broad to resolve
individual components and the overall intensity may be so saturated that information
is lost at velocities where absorption is highest.