Chemistry Reference
In-Depth Information
of the physical meaning of each hyperfine parameter is given in the chapter
' ' Application of Mössbauer Spectroscopy in Earth Sciences '') and their respective
proportions.
Additional information is given by the intensities and the shape of lines. In the
case of magnetic materials, the relative areas of the six lines sextet are correlated
to the Fe moment configuration respect to the c-beam direction. Indeed, the rel-
ative area ratios are given by 3:p:1:1:p:3, where p = 4 sin 2 h/(2 - sin 2 h) where h
represents the angle between the hyperfine field held by the nucleus probe and the
propagation direction of the c-beam. In the case of a powdered sample, i.e. random
distribution of the orientations of the Fe magnetic moments, one expects the
following relative ratio 3:2:1:1:2:3. When the magnetic moments are oriented
parallel to the c-beam, one obtains 3:0:1:1:0:3, i.e. the intermediate line disap-
pears: such a situation occurs in a perfect ferromagnetic or ferrimagnetic material
submitted to an applied field sufficiently large to saturate the magnetization. One
does obviously consider two magnetic components in the case of a ferrimagnetic
structure. In addition, it is important to check whether the hyperfine field is either
parallel or antiparallel to the magnetic moment, that remains unknown from the
zero-field sextet spectrum (one determines only the absolute value of the hyperfine
field!). When the effective field is smaller or larger than the hyperfine field, one
concludes that the hyperfine field is opposite or parallel to the magnetic moment,
respectively, because the magnetic moment is forced to be aligned parallel to the
external magnetic field. Consequently, the main contribution to the hyperfine field
corresponding to the Fermi or contact term is negative or positive. An other
situation occurs when the Fe moments are antiferromagnetically coupled: due to
the dominant antiferromagnetic interaction, they are rather oriented perpendicular
to the external field and the shape of the Zeeman sextet is 3:4:1:1:4:3 (maximal
intensities of intermediate lines) when the magnetic field is applied parallel to the
c-beam. But, the most commonly observed situation gives rise to intermediate
intensities values. As the total effective field at the nucleus results from the vec-
torial sum of the hyperfine field and the applied field, one can establish the
following expression
B hf ¼ B eff þ B app 2B eff B app cos h
ð 4 : 1 Þ
which allows the canting angle to be estimated. Figure 4.3 reports theoretical
Mössbauer spectra of different typical magnetic structures submitted to an external
magnetic field (see reviews [ 14 - 18 ]). In addition, the in-field Mössbauer theo-
retical spectra characteristics of non collinear static magnetic structures (spero-
magnetic SP, sperimagnetic SPi and asperomagnetic ASp) earlier evidenced by
Coey and Readmann are also illustrated [ 19 ]. Finally, one does notice when the
external field is applied perpendicular to the c-beam, the respective relative ratios
have to be inversed (3:4:1:1:4:3 becomes 3:0:1:1:0:3 and vice versa).
The natural Mössbauer line profile is lorentzian but the lattice tends to reduce the
lifetime of the excited state due to radiation less decay mechanisms originating thus
some broadening, in addition to instrumental effects. But some (in) homogeneous
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