Chapter 7
XANES and XMCD
In this chapter we will cover the features close to an absorption edge, often called
“XANES” (but sometimes NEXAFS). XANES is an acronym for X-ray Absorption
Near-Edge Structure. This is usually considered the region around the absorption
edge where there are dramatic changes in the density of states and/or individual
transition intensities, so that a simplistic EXAFS interpretation does not apply. As a
reminder, the absorption cross section will depend on both the density of states and
the transition matrix element for the given transition [254]:
μ / ψ f jb ε Á r
! e
i k
! Á r
! jψ i
D
E
2
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
dipoleþquadrupoleþ...
ρ E f À E i À ħω
À
Á
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
density of states
ð7:1Þ
For the EXAFS region, we were able to assume a smoothly varying density of
states, but this is not a good assumption at the edge. In the edge region, there is
usually a variety of discrete states, such as molecular orbitals and continuum
resonances, and each of these states can have a rather different cross section
(Fig. 7.1).
For K-edges, starting at a 1s level, the dipole Δ‘ ¼ Æ1 selection rule means that
transitions to states with p-symmetry are dipole-allowed. These edges are therefore
mostly 1s ! np transitions. In certain cases, one can also observe electric quadrupole
transitions, where the selection rule is Δ‘ ¼ 0, Æ2. For first transition element
K-edges, this can result in observable 1s! 3d features, while for the rare earth Lor M-edges, one can see weak 2p ! 5s or 3p ! 5s transitions.
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_7
165
XANES and XMCD
In this chapter we will cover the features close to an absorption edge, often called
“XANES” (but sometimes NEXAFS). XANES is an acronym for X-ray Absorption
Near-Edge Structure. This is usually considered the region around the absorption
edge where there are dramatic changes in the density of states and/or individual
transition intensities, so that a simplistic EXAFS interpretation does not apply. As a
reminder, the absorption cross section will depend on both the density of states and
the transition matrix element for the given transition [254]:
μ / ψ f jb ε Á r
! e
i k
! Á r
! jψ i
D
E
2
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
dipoleþquadrupoleþ...
ρ E f À E i À ħω
À
Á
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
density of states
ð7:1Þ
For the EXAFS region, we were able to assume a smoothly varying density of
states, but this is not a good assumption at the edge. In the edge region, there is
usually a variety of discrete states, such as molecular orbitals and continuum
resonances, and each of these states can have a rather different cross section
(Fig. 7.1).
For K-edges, starting at a 1s level, the dipole Δ‘ ¼ Æ1 selection rule means that
transitions to states with p-symmetry are dipole-allowed. These edges are therefore
mostly 1s ! np transitions. In certain cases, one can also observe electric quadrupole
transitions, where the selection rule is Δ‘ ¼ 0, Æ2. For first transition element
K-edges, this can result in observable 1s! 3d features, while for the rare earth Lor M-edges, one can see weak 2p ! 5s or 3p ! 5s transitions.
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_7
165