distribution of only these electrons has an influence on the energy shift. Other
electrons (p, d, f, …) only play an indirect role changing by the so-called screening
effect the s-electrons density [2].
The energy shift of nuclear levels will be different for the ground state than for
the excited state due to the different radii of the nucleus in these states. The shift can
be expressed (in the non-relativistic) approximation as [7]:
IS ¼ C
dR
R
W A 0
ð Þ
j
j
2 À W S 0
ð Þ
j
j
2
ð9:3Þ
where C is a constant for a given isotope containing nuclear parameters, dR/R is the
relative change of nuclear radius between excited and ground states, and the term in
parenthesis represents the difference in the total electron density at the nucleus
between absorber and source. For the
57 Fe, the nuclear radius of the excited state is
smaller than the radius of the ground state, so dR has a negative sign and with
increasing s electron density the resonance line shift is decreasing. Electrons in 1s,
2s, 3s, … shells all contribute to W 0
ð Þ
j
j
2 but in decreasing amounts as the principal
quantum number rises. The inner shells are almost not affected by chemical bonding
and the principal influence on the isomer shift will by the outermost occupied
s-orbital [8].
A value of the isomer shift for a given material is given in relation to a substance
taken as the standard. In case of the
57 Fe, the most frequently used standard is
metallic iron (a-Fe) at room temperature.
Measurement of the isomer shift provides information about the effective selectrons density in the nucleus. It allows you to draw conclusions about the nature
of chemical bonds. It can be correlated with valence, spin state, coordination
number, and so on of the tested nucleus.
A good example of pure isomer shifted spectrum can be iron in MgO matrix
(Fig. 9.1). The sample was prepared by melting pure MgO powder with small
addition of iron [9].
The obtained spectrum is composed of only one single line (singlet) which
indicates only one iron site in the crystal lattice. The shape of the line is given be
Lorentz function and its center is shifted toward higher energies (higher velocities)
due to isomer shift effect. The IS value is approximately 1 mm/s. The IS values in
the range of 0.1–0.5 mm/s are characteristic for ferric iron and in the range of 0.6–
1.7 mm/s for ferrous iron in the high spin state [2, 7]. So, the value around 1 mm/s
can be ascribed to iron in the high spin ferrous state.
Isomer shift is also sensitive to iron coordination number but in this case, the
interpretation of the isomer shift should be more careful. Generally, in simple
oxides and silicates Fe
3+ in tetrahedral coordination adopt lower IS values (0.1–
0.35 mm/s) than in octahedral (0.35–0.5 mm/s) [2]. Similar behavior is characteristic for ferrous iron ions, and this division is below 1 mm/s.
9 Mössbauer Spectroscopy of Magnetoelectric Perovskite Oxides
277
electrons (p, d, f, …) only play an indirect role changing by the so-called screening
effect the s-electrons density [2].
The energy shift of nuclear levels will be different for the ground state than for
the excited state due to the different radii of the nucleus in these states. The shift can
be expressed (in the non-relativistic) approximation as [7]:
IS ¼ C
dR
R
W A 0
ð Þ
j
j
2 À W S 0
ð Þ
j
j
2
ð9:3Þ
where C is a constant for a given isotope containing nuclear parameters, dR/R is the
relative change of nuclear radius between excited and ground states, and the term in
parenthesis represents the difference in the total electron density at the nucleus
between absorber and source. For the
57 Fe, the nuclear radius of the excited state is
smaller than the radius of the ground state, so dR has a negative sign and with
increasing s electron density the resonance line shift is decreasing. Electrons in 1s,
2s, 3s, … shells all contribute to W 0
ð Þ
j
j
2 but in decreasing amounts as the principal
quantum number rises. The inner shells are almost not affected by chemical bonding
and the principal influence on the isomer shift will by the outermost occupied
s-orbital [8].
A value of the isomer shift for a given material is given in relation to a substance
taken as the standard. In case of the
57 Fe, the most frequently used standard is
metallic iron (a-Fe) at room temperature.
Measurement of the isomer shift provides information about the effective selectrons density in the nucleus. It allows you to draw conclusions about the nature
of chemical bonds. It can be correlated with valence, spin state, coordination
number, and so on of the tested nucleus.
A good example of pure isomer shifted spectrum can be iron in MgO matrix
(Fig. 9.1). The sample was prepared by melting pure MgO powder with small
addition of iron [9].
The obtained spectrum is composed of only one single line (singlet) which
indicates only one iron site in the crystal lattice. The shape of the line is given be
Lorentz function and its center is shifted toward higher energies (higher velocities)
due to isomer shift effect. The IS value is approximately 1 mm/s. The IS values in
the range of 0.1–0.5 mm/s are characteristic for ferric iron and in the range of 0.6–
1.7 mm/s for ferrous iron in the high spin state [2, 7]. So, the value around 1 mm/s
can be ascribed to iron in the high spin ferrous state.
Isomer shift is also sensitive to iron coordination number but in this case, the
interpretation of the isomer shift should be more careful. Generally, in simple
oxides and silicates Fe
3+ in tetrahedral coordination adopt lower IS values (0.1–
0.35 mm/s) than in octahedral (0.35–0.5 mm/s) [2]. Similar behavior is characteristic for ferrous iron ions, and this division is below 1 mm/s.
9 Mössbauer Spectroscopy of Magnetoelectric Perovskite Oxides
277