4 From Small Molecules to Complex Systems: A Survey of Chemical …
181
with concentrations up to the range of some mM. There is no need to create novel software for data analysis since both commercial software packages like e.g. NORMOS
[26], MOSWINN [27], WMOSS [28] and public domain software like VINDA [29]
are available. By means of computational fitting one obtains quite conveniently the
isomer shift δ, the quadrupole splitting ΔE Q , and the line width Γ with all parameters given in velocity units, mostly mms
−1 . In the case of magnetically split spectra
a further parameter, the magnetic hyperfine field at the nucleus B hf , can be obtained.
However, when it comes to samples which have higher concentration of
57 Fe, e.g.
57 Fe labelled chemical complexes in powder form, the thin absorber approximation
is not valid anymore and self-absorption of resonantly absorbed γ-quanta lead to
significant line broadening. In this case the transmission integral formalism should
be used. In order to account for self-absorption this analysis requires the knowledge
of the so called effective thickness which can be calculated from the density of
57 Fe
nuclei and the volume of the sample [30]. Furthermore, the effective thickness is
proportional to the Lamb-Mößbauer-factor f of the compound under study which
is often not known and thus is treated as a fit parameter in addition to δ, ΔE Q and
B hf . Note that the line width which goes into the transmission integral analysis is
not a free parameter anymore like in the lorentzian line shape analysis. Based on
the natural line width of a
57 Fe Mössbauer experiment which is 0.19 mms
−1 the
transmission integral formalism calculates the observed line width. It is obvious, but
might be overseen by new users of Mössbauer spectroscopy, that it is not possible to
have a line width which is lower or even equal to 0.19 mms
−1 . This value is actually
twice the natural line width of the 14.4 keV first excited nuclear state of
57 Fe since
in a Mössbauer spectrometer one has to regard the natural line width of the source
and of the absorber material. Typical experimental values of Γ are 0.24–0.36 mm
−1 .
If one observes higher linewidths some structural inhomogeneity may be present in
the sample which leads to distributions of the Mössbauer parameters. Common are
distributions of B hf in small particles with a high surface to volume ratio, but also in
amorphous metallic compounds [31]. Sometimes, also distributions of isomer shifts
and quadrupole splittings are reported. However, it should be noted that also vibrations of the experimental set-up due to vacuum pumps or cryogenic coolers in the
vicinity of the experiment can lead to significant line broadening effects. Therefore
special care has to be taken, if one wants to investigate phenomena which might be
related to line width broadening.
4.2.3 Mössbauer Spectroscopy of Iron in Molecules: The
Spin Hamiltonian Concept
Iron centers in proteins—with the exception of diamagnetic iron ions or magnetically
coupled diamagnetic clusters—are paramagnetic having a spin quantum number S.
An ideal isolated spin system S has a spin multiplicity of 2S + 1 and can be described
by its spin functions |S; m s > with m s being the magnetic spin quantum number which
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with concentrations up to the range of some mM. There is no need to create novel software for data analysis since both commercial software packages like e.g. NORMOS
[26], MOSWINN [27], WMOSS [28] and public domain software like VINDA [29]
are available. By means of computational fitting one obtains quite conveniently the
isomer shift δ, the quadrupole splitting ΔE Q , and the line width Γ with all parameters given in velocity units, mostly mms
−1 . In the case of magnetically split spectra
a further parameter, the magnetic hyperfine field at the nucleus B hf , can be obtained.
However, when it comes to samples which have higher concentration of
57 Fe, e.g.
57 Fe labelled chemical complexes in powder form, the thin absorber approximation
is not valid anymore and self-absorption of resonantly absorbed γ-quanta lead to
significant line broadening. In this case the transmission integral formalism should
be used. In order to account for self-absorption this analysis requires the knowledge
of the so called effective thickness which can be calculated from the density of
57 Fe
nuclei and the volume of the sample [30]. Furthermore, the effective thickness is
proportional to the Lamb-Mößbauer-factor f of the compound under study which
is often not known and thus is treated as a fit parameter in addition to δ, ΔE Q and
B hf . Note that the line width which goes into the transmission integral analysis is
not a free parameter anymore like in the lorentzian line shape analysis. Based on
the natural line width of a
57 Fe Mössbauer experiment which is 0.19 mms
−1 the
transmission integral formalism calculates the observed line width. It is obvious, but
might be overseen by new users of Mössbauer spectroscopy, that it is not possible to
have a line width which is lower or even equal to 0.19 mms
−1 . This value is actually
twice the natural line width of the 14.4 keV first excited nuclear state of
57 Fe since
in a Mössbauer spectrometer one has to regard the natural line width of the source
and of the absorber material. Typical experimental values of Γ are 0.24–0.36 mm
−1 .
If one observes higher linewidths some structural inhomogeneity may be present in
the sample which leads to distributions of the Mössbauer parameters. Common are
distributions of B hf in small particles with a high surface to volume ratio, but also in
amorphous metallic compounds [31]. Sometimes, also distributions of isomer shifts
and quadrupole splittings are reported. However, it should be noted that also vibrations of the experimental set-up due to vacuum pumps or cryogenic coolers in the
vicinity of the experiment can lead to significant line broadening effects. Therefore
special care has to be taken, if one wants to investigate phenomena which might be
related to line width broadening.
4.2.3 Mössbauer Spectroscopy of Iron in Molecules: The
Spin Hamiltonian Concept
Iron centers in proteins—with the exception of diamagnetic iron ions or magnetically
coupled diamagnetic clusters—are paramagnetic having a spin quantum number S.
An ideal isolated spin system S has a spin multiplicity of 2S + 1 and can be described
by its spin functions |S; m s > with m s being the magnetic spin quantum number which