9 Mössbauer Spectroscopic Studies on Atomic Diffusion in Materials
451
a Rh thin foil, and the strength will be selected from 0.37 to 3.7 GBq depending on
the
57 Fe concentration contained in the sample. The 14.4 keV γ-rays are transmitted
through the absorber with a thickness from 20 μm to 1 mm, depending on the sample.
We should choose the specimen thickness carefully [25] because a too-thick sample
would provide a spectrum shape strongly deviating from Lorentzian, and therefore,
a fitting analysis would be complicated using a superposition of Lorentz functions.
In the case of the iron sextet spectrum, an ideal thickness is 25 μm.
We count the transmitted γ-rays by using a gas proportional counter, or a scintillation counter, or a Si-PIN detector, and subsequently, record them on a multi-channel
scaler with 1024 channels typically as a function of Doppler velocity of the
57 Coin-Rh source. A transducer operates with a constant-acceleration mode, yielding a
triangular-Doppler-velocity function between −10 and 10 mms
−1 , for instance. In our
particular case for a “Mössbauer spectroscopic microscope” described in Sect. 9.5,
on the other hand, we use a linear actuator with a constant velocity operation to adjust
a resonance condition, to obtain the image corresponding to a spectrum component.
We draw a typical single Lorentz spectrum in the upper part of Fig. 9.7. To measure
such a very narrow absorption spectrum with a line width of an order of 10
−8 eV for
57 Fe nuclear probe, we use the Doppler effect to modulate the γ-ray energy. Since
the first-order Doppler shift, E D , is described by
E D =
v
c
E γ ,
(9.4)
where Eγ is the γ-ray energy of 14.4 keV, c the light velocity, and v the Doppler
velocity of the
57 Co source. Accordingly, v = 1 mms
−1 corresponds to an energy
shift of E D = 4.80766 × 10
−8 eV. One should notice that we cannot use a usual
spectroscopic detector for analyzing the γ-ray energy down to 10
−8 eV, but for
counting after selecting the 14.4 keV γ-rays by a single-channel analyzer within a
resolution from meV to keV range. We usually present the spectrum as a function of
Doppler velocity in Mössbauer spectroscopy.
Furthermore, the velocity is not the absolute value against the laboratory system,
but the relative one against the centre position of α-Fe sextet spectrum at room
temperature, as in the lower part of Fig. 9.7. If one uses
57 Co-in-Rh source, the zerovelocity for Fe-in-Rh absorber (δ = + 0.109 mms
−1 ) shifts to be + 0.109 mms
−1
against the centre of Fe sextet spectrum. One should notice, however, in a source
experiment, in which the source will be the sample, that the velocity scale is shown
converted in comparison to an absorber experiment.
A spectrum shape depends on the hyperfine interactions between the
57 Fe nuclear
probe and the electrons, i.e., electric monopole, electric quadrupole, and magnetic
dipole interactions. The monopole interaction affects the position of resonance
lines, leading to an “isomer shift (δ) in the Mössbauer spectrum, while the electric
quadrupole and magnetic dipole interaction remove the degeneracy of nuclear levels,
causing the electric quadrupole splitting (E q ) and the magnetic Zeeman splitting
(H m ), respectively. The electric monopole interaction energy, i.e., the Coulomb
interaction energy between the nucleus and the s-electrons penetrating, is given by
451
a Rh thin foil, and the strength will be selected from 0.37 to 3.7 GBq depending on
the
57 Fe concentration contained in the sample. The 14.4 keV γ-rays are transmitted
through the absorber with a thickness from 20 μm to 1 mm, depending on the sample.
We should choose the specimen thickness carefully [25] because a too-thick sample
would provide a spectrum shape strongly deviating from Lorentzian, and therefore,
a fitting analysis would be complicated using a superposition of Lorentz functions.
In the case of the iron sextet spectrum, an ideal thickness is 25 μm.
We count the transmitted γ-rays by using a gas proportional counter, or a scintillation counter, or a Si-PIN detector, and subsequently, record them on a multi-channel
scaler with 1024 channels typically as a function of Doppler velocity of the
57 Coin-Rh source. A transducer operates with a constant-acceleration mode, yielding a
triangular-Doppler-velocity function between −10 and 10 mms
−1 , for instance. In our
particular case for a “Mössbauer spectroscopic microscope” described in Sect. 9.5,
on the other hand, we use a linear actuator with a constant velocity operation to adjust
a resonance condition, to obtain the image corresponding to a spectrum component.
We draw a typical single Lorentz spectrum in the upper part of Fig. 9.7. To measure
such a very narrow absorption spectrum with a line width of an order of 10
−8 eV for
57 Fe nuclear probe, we use the Doppler effect to modulate the γ-ray energy. Since
the first-order Doppler shift, E D , is described by
E D =
v
c
E γ ,
(9.4)
where Eγ is the γ-ray energy of 14.4 keV, c the light velocity, and v the Doppler
velocity of the
57 Co source. Accordingly, v = 1 mms
−1 corresponds to an energy
shift of E D = 4.80766 × 10
−8 eV. One should notice that we cannot use a usual
spectroscopic detector for analyzing the γ-ray energy down to 10
−8 eV, but for
counting after selecting the 14.4 keV γ-rays by a single-channel analyzer within a
resolution from meV to keV range. We usually present the spectrum as a function of
Doppler velocity in Mössbauer spectroscopy.
Furthermore, the velocity is not the absolute value against the laboratory system,
but the relative one against the centre position of α-Fe sextet spectrum at room
temperature, as in the lower part of Fig. 9.7. If one uses
57 Co-in-Rh source, the zerovelocity for Fe-in-Rh absorber (δ = + 0.109 mms
−1 ) shifts to be + 0.109 mms
−1
against the centre of Fe sextet spectrum. One should notice, however, in a source
experiment, in which the source will be the sample, that the velocity scale is shown
converted in comparison to an absorber experiment.
A spectrum shape depends on the hyperfine interactions between the
57 Fe nuclear
probe and the electrons, i.e., electric monopole, electric quadrupole, and magnetic
dipole interactions. The monopole interaction affects the position of resonance
lines, leading to an “isomer shift (δ) in the Mössbauer spectrum, while the electric
quadrupole and magnetic dipole interaction remove the degeneracy of nuclear levels,
causing the electric quadrupole splitting (E q ) and the magnetic Zeeman splitting
(H m ), respectively. The electric monopole interaction energy, i.e., the Coulomb
interaction energy between the nucleus and the s-electrons penetrating, is given by