1 Historical Developments and Future Perspectives …
29
G 22 (t) ∝ e
−λ r t cos
2
Ωt
2
(1.29)
and in the fast approximation to
G 22 (t) ∝ e
−(Ω
2 /λ r )t
.
(1.30)
Combining both techniques the translational and rotational relaxation rates can be
separately extracted.
In both cases described above the sample has to contain the Mössbauer isotope.
For samples without Mössbauer isotopes a variant—time domain interferometry [69]
or Rayleigh scattering with Mössbauer radiation—may be utilized, see Sect. 1.3.5.
In the default TDI setup [69], with two identical single line resonance absorbers,
the interference of the probe and reference waves is described by
I (q, t) ∝ I NFS (t)(1 + f qe (q) · cos Ωt · S
n
(q, t)),
(1.31)
where I NFS (t) is the single line response of the two resonance absorbers, Ω is the frequency difference in the response of the two absorbers, f eq (q) is the elastic (including
the quasi-elastic part) fraction of scattering, and S
n
(q, t) is the normalized intermediate scattering function, i.e., the normalized Fourier transform of the dynamic structure
factor.
As described by Eq. 1.31 the TDI pattern displays an oscillating dependence,
where an envelope of the fading contrast is given by the intermediate scattering
function.
For more details on the TDI technique see in this book Seto et al. [60].
1.5.2 Phonon Density of States
Nuclear inelastic scattering measures the (partial) phonon density of states of the
Mössbauer element in the sample. As an example the intensity of nuclear inelastic scattering of synchrotron radiation in a polycrystalline α-iron sample at room
temperature is shown as a function of energy of the incident radiation (Fig. 1.10).
The central peak corresponds to elastic scattering. The structure beyond the central
peak shows the energy dependence of inelastic scattering (furtheron called “energy
spectrum”), accompanied either by creation (E > 0) or by annihilation (E < 0)
of phonons. At ambient temperature one may recognize various contributions to the
energy spectrum, which correspond to inelastic scattering accompanied by creation
or annihilation of a different number of phonons.
29
G 22 (t) ∝ e
−λ r t cos
2
Ωt
2
(1.29)
and in the fast approximation to
G 22 (t) ∝ e
−(Ω
2 /λ r )t
.
(1.30)
Combining both techniques the translational and rotational relaxation rates can be
separately extracted.
In both cases described above the sample has to contain the Mössbauer isotope.
For samples without Mössbauer isotopes a variant—time domain interferometry [69]
or Rayleigh scattering with Mössbauer radiation—may be utilized, see Sect. 1.3.5.
In the default TDI setup [69], with two identical single line resonance absorbers,
the interference of the probe and reference waves is described by
I (q, t) ∝ I NFS (t)(1 + f qe (q) · cos Ωt · S
n
(q, t)),
(1.31)
where I NFS (t) is the single line response of the two resonance absorbers, Ω is the frequency difference in the response of the two absorbers, f eq (q) is the elastic (including
the quasi-elastic part) fraction of scattering, and S
n
(q, t) is the normalized intermediate scattering function, i.e., the normalized Fourier transform of the dynamic structure
factor.
As described by Eq. 1.31 the TDI pattern displays an oscillating dependence,
where an envelope of the fading contrast is given by the intermediate scattering
function.
For more details on the TDI technique see in this book Seto et al. [60].
1.5.2 Phonon Density of States
Nuclear inelastic scattering measures the (partial) phonon density of states of the
Mössbauer element in the sample. As an example the intensity of nuclear inelastic scattering of synchrotron radiation in a polycrystalline α-iron sample at room
temperature is shown as a function of energy of the incident radiation (Fig. 1.10).
The central peak corresponds to elastic scattering. The structure beyond the central
peak shows the energy dependence of inelastic scattering (furtheron called “energy
spectrum”), accompanied either by creation (E > 0) or by annihilation (E < 0)
of phonons. At ambient temperature one may recognize various contributions to the
energy spectrum, which correspond to inelastic scattering accompanied by creation
or annihilation of a different number of phonons.