236
C. McCammon
ments to be made with small beam size, even when using a conventional source,
while inattention to setting these distances can significantly reduce the quality of the
measurement.
There is a trade-off in choosing the optimum distance between source and sample.
A short distance increases the count rate due to a larger solid angle of radiation
(good), but at the same time increases distortion of the velocity (energy) scale (bad).
While the former effect can be compensated for by longer counting times, there is
no possibility to correct spectra for the latter effect after they have been collected (H.
Spiering, personal communication).
Distortion of the velocity scale occurs because γ-rays travelling at angle θ to the
horizontal have an energy shift given by:
E = E 0 (vcosθ )/c
( 5 . 4 )
which reduces to Eq. 5.3 when θ = 0. The cosθ term changes the energy distribution
of emitted γ-rays, which ultimately affects the shapes, widths and positions of the
absorption lines in the resulting Mössbauer spectrum. These effects have been calculated in detail [30] where, for example, line shift distortions are less than 1% at a
source velocity of 5 mm/s when θ < 10° (distortion increases at higher source velocities). This calculation assumes a point source (i.e., the source diameter is much less
than the beam size), but since conventional sources can be considered sheet emitters
when beam size is smaller (Fig. 5.10), the appropriate limit in this case is θ < 5° (see
also [1]).
The source to absorber distance (D 1 ) can be simply calculated from θ using the
following relation:
D 1 = d/(2 tanθ )
(5.5)
where d is the beam aperture diameter (Fig. 5.10).
Equation 5.5 can be used to calculate the appropriate source to sample distances for
the measurements shown in Fig. 5.3 (recall that the beam size for those measurements
was 2 mm diameter). For the conventional source measurement, θ should be less than
5°, so D 1 should be greater than 11 mm, and for the point source measurement, θ
should be less than 10°, so D 1 should be greater than 6 mm. Equation 5.5 is most
useful when measuring with small beam size using a conventional source, since in
this case the source to sample distance can be reduced to compensate for the smaller
beam size.
Equation 5.5 can also be used to calculate the appropriate source to sample distance
for the point source measurement shown in Fig. 5.4a. Here the beam size is 30 μm
diameter, which is considerably smaller than the point source diameter (500 μm).
To achieve θ = 5° would require a source to sample distance of only 100 μm, which
is not possible due to the thickness of the diamonds since the sample is inside a
diamond anvil cell. Indeed, Eq. 5.5 demonstrates that velocity scale distortion is
unlikely to cause problems in high-pressure experiments. Similarly, measurements
C. McCammon
ments to be made with small beam size, even when using a conventional source,
while inattention to setting these distances can significantly reduce the quality of the
measurement.
There is a trade-off in choosing the optimum distance between source and sample.
A short distance increases the count rate due to a larger solid angle of radiation
(good), but at the same time increases distortion of the velocity (energy) scale (bad).
While the former effect can be compensated for by longer counting times, there is
no possibility to correct spectra for the latter effect after they have been collected (H.
Spiering, personal communication).
Distortion of the velocity scale occurs because γ-rays travelling at angle θ to the
horizontal have an energy shift given by:
E = E 0 (vcosθ )/c
( 5 . 4 )
which reduces to Eq. 5.3 when θ = 0. The cosθ term changes the energy distribution
of emitted γ-rays, which ultimately affects the shapes, widths and positions of the
absorption lines in the resulting Mössbauer spectrum. These effects have been calculated in detail [30] where, for example, line shift distortions are less than 1% at a
source velocity of 5 mm/s when θ < 10° (distortion increases at higher source velocities). This calculation assumes a point source (i.e., the source diameter is much less
than the beam size), but since conventional sources can be considered sheet emitters
when beam size is smaller (Fig. 5.10), the appropriate limit in this case is θ < 5° (see
also [1]).
The source to absorber distance (D 1 ) can be simply calculated from θ using the
following relation:
D 1 = d/(2 tanθ )
(5.5)
where d is the beam aperture diameter (Fig. 5.10).
Equation 5.5 can be used to calculate the appropriate source to sample distances for
the measurements shown in Fig. 5.3 (recall that the beam size for those measurements
was 2 mm diameter). For the conventional source measurement, θ should be less than
5°, so D 1 should be greater than 11 mm, and for the point source measurement, θ
should be less than 10°, so D 1 should be greater than 6 mm. Equation 5.5 is most
useful when measuring with small beam size using a conventional source, since in
this case the source to sample distance can be reduced to compensate for the smaller
beam size.
Equation 5.5 can also be used to calculate the appropriate source to sample distance
for the point source measurement shown in Fig. 5.4a. Here the beam size is 30 μm
diameter, which is considerably smaller than the point source diameter (500 μm).
To achieve θ = 5° would require a source to sample distance of only 100 μm, which
is not possible due to the thickness of the diamonds since the sample is inside a
diamond anvil cell. Indeed, Eq. 5.5 demonstrates that velocity scale distortion is
unlikely to cause problems in high-pressure experiments. Similarly, measurements