330
P.-E. Lippens
Fig. 7.3 Correlation
between the experimental
values of the 119 Sn isomer
shift, δ exp , relative to
BaSnO 3 and the theoretical
DFT-LAPW values of the
electronic density at the
nucleus ρ(0). The values
corresponding to Sn(IV),
Sn(0) and Sn(II)
compounds are shown in
blue, red and black,
respectively
30 40 50 60 70 80 90 100
-1
0
1
2
3
4
Sn
Sn(IV)
Sn(II)
FeSn 2
Sn
SnF 2
Sn(IV) 2 S 3
SnSe
SnS
SnCl 2
SnO
Sn(II) 2 S 3
SnSe 2
SnS 2
SnO 2
SnF 4
exp
(mm/s)
(0)-262100 a 0
-3
Sn(0)
α
β
β
ρ
δ
p-type or d-type valence electrons. It is possible to derive an approximate analytical
expression of ρ v (0) from the values obtained for different electron configurations of
a free atom [51, 52]. A simple expression was derived for Sn and used for the tightbinding interpretation of the isomer shifts of tin chalcogenides [54]. This expression
can be further simplified to qualitatively show the relative contributions of the Sn
valence electrons
ρ v (0) ∼ N 5s − 0.1N 5 p
(7.5)
where N 5s and N 5p are the Sn 5s and Sn 5p electron populations, respectively,
obtained by integration of the local densities of occupied states within the tightbinding approximation. The oversimplified expression (7.5) should only be used to
analyze some trends in the variations of the isomer shift and is just considered here
to show that ρ v (0), and therefore δ, strongly increases for the series N 5s = 0–1–2 and,
to a lesser extent, decreases with N 5p . This explains that the isomer shifts of Sn(IV),
Sn(0) and Sn(II) compounds are found in three distinct ranges of values as shown in
Fig. 7.3.
Interpretations based on Eq. (7.5) are rather qualitative but it is possible to relate
some trends in the variations of δ in terms of oxidation state or chemical bond.
A similar distinction can be made for
121 Sb but the isomer shift decreases for the
sequence Sb(V)-Sb(0)-Sb(III) because of the negative sign of α. The situation is
more complex for
57 Fe because there are overlaps between some ranges of isomer
P.-E. Lippens
Fig. 7.3 Correlation
between the experimental
values of the 119 Sn isomer
shift, δ exp , relative to
BaSnO 3 and the theoretical
DFT-LAPW values of the
electronic density at the
nucleus ρ(0). The values
corresponding to Sn(IV),
Sn(0) and Sn(II)
compounds are shown in
blue, red and black,
respectively
30 40 50 60 70 80 90 100
-1
0
1
2
3
4
Sn
Sn(IV)
Sn(II)
FeSn 2
Sn
SnF 2
Sn(IV) 2 S 3
SnSe
SnS
SnCl 2
SnO
Sn(II) 2 S 3
SnSe 2
SnS 2
SnO 2
SnF 4
exp
(mm/s)
(0)-262100 a 0
-3
Sn(0)
α
β
β
ρ
δ
p-type or d-type valence electrons. It is possible to derive an approximate analytical
expression of ρ v (0) from the values obtained for different electron configurations of
a free atom [51, 52]. A simple expression was derived for Sn and used for the tightbinding interpretation of the isomer shifts of tin chalcogenides [54]. This expression
can be further simplified to qualitatively show the relative contributions of the Sn
valence electrons
ρ v (0) ∼ N 5s − 0.1N 5 p
(7.5)
where N 5s and N 5p are the Sn 5s and Sn 5p electron populations, respectively,
obtained by integration of the local densities of occupied states within the tightbinding approximation. The oversimplified expression (7.5) should only be used to
analyze some trends in the variations of the isomer shift and is just considered here
to show that ρ v (0), and therefore δ, strongly increases for the series N 5s = 0–1–2 and,
to a lesser extent, decreases with N 5p . This explains that the isomer shifts of Sn(IV),
Sn(0) and Sn(II) compounds are found in three distinct ranges of values as shown in
Fig. 7.3.
Interpretations based on Eq. (7.5) are rather qualitative but it is possible to relate
some trends in the variations of δ in terms of oxidation state or chemical bond.
A similar distinction can be made for
121 Sb but the isomer shift decreases for the
sequence Sb(V)-Sb(0)-Sb(III) because of the negative sign of α. The situation is
more complex for
57 Fe because there are overlaps between some ranges of isomer