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H. Elnaggar et al.
Fig. 4.13 Conductivity tensor for a d 9 ion in an octahedral crystal field (10D q = 1.1 eV) calculated
using the symmetry adapted basis set
Five fundamental spectra come into play, namely, σ (0, 0), σ (2, 0), σ (4, 0),
σ (4, 4), and σ (4, −4) as shown in Fig. 4.14. The O h symmetry implies that R(2, 0) is
always equal to zero as confirmed by the calculation. In addition, R(4, 4) = R(4, −4)
and are proportional to R(4, 0) as can be seen from (4.75), (4.82), and (4.83). Therefore, as can be expected from group theory, only two fundamental spectra are required
to fully describe the system.
Let us investigate the angular dependence of a quadrupole transition in an O h
crystal field considering two scattering geometries. In the first geometry, the wave
vector (k) is aligned parallel to the [100] direction and the polarization () is rotated
in the z − y-plane as illustrated in the right panel of Fig. 4.16. Despite the presence of
non-isotropic fundamental spectra [σ (4, 0), σ (4, 4), and σ (4, −4)], the XAS crosssection is constant in these settings as shown in Fig. 4.16a. In the second geometry we
H. Elnaggar et al.
Fig. 4.13 Conductivity tensor for a d 9 ion in an octahedral crystal field (10D q = 1.1 eV) calculated
using the symmetry adapted basis set
Five fundamental spectra come into play, namely, σ (0, 0), σ (2, 0), σ (4, 0),
σ (4, 4), and σ (4, −4) as shown in Fig. 4.14. The O h symmetry implies that R(2, 0) is
always equal to zero as confirmed by the calculation. In addition, R(4, 4) = R(4, −4)
and are proportional to R(4, 0) as can be seen from (4.75), (4.82), and (4.83). Therefore, as can be expected from group theory, only two fundamental spectra are required
to fully describe the system.
Let us investigate the angular dependence of a quadrupole transition in an O h
crystal field considering two scattering geometries. In the first geometry, the wave
vector (k) is aligned parallel to the [100] direction and the polarization () is rotated
in the z − y-plane as illustrated in the right panel of Fig. 4.16. Despite the presence of
non-isotropic fundamental spectra [σ (4, 0), σ (4, 4), and σ (4, −4)], the XAS crosssection is constant in these settings as shown in Fig. 4.16a. In the second geometry we