Electronic structure of RbBr during the phase transition: x-ray absorption near-edge structure analysis

In addition to the XANES region, at higher energies the extended X-ray absorption fine structure (EXAFS) region is found. The spectral shape in the near-edge region is determined by electronic density of states effects and gives mainly information about the electronic properties and the local geometry of the absorbing atom. The EXAFS region is dominated by single scattering events of the outgoing electron on the neighboring atoms, providing mainly information about the local geometric structure around the absorbing site. In this chapter we will focus on XANES. XANES SpectroscopyIn XPS the ground state (Ψ 0 ) is excited to the ground state plus a core hole (c), where the electron (ε) is excited to higher energy, while in XAS the ground state is excited with a coreto-valence excitation (cv). The XPS binding (E B ) is defined as the photon energy (Ω) minus the measured kinetic energy of the electron (E k ) and corrected for the work function (φ):The work function is the minimal energy to emit an electron from the material. In metals the XAS edge energy can be assumed to be equal to the XPS binding energy, because exactly at the XPS binding energy a transition is possible to the lowest empty state. Experimentally the XAS edge energy can be slightly higher than the XPS binding energy, for example if the transition to the lowest empty state is forbidden by selection rules. Single electron excitation approximation and selection rulesIn first approximation XANES can be described as the excitation of a core electron to an empty state. In the Fermi golden rule, the initial state wave function is rewritten as a core wave function and the final state wave function (ε) as a valence electron wave function (ν). This implicitly assumes that all other electrons do not participate in the X-ray induced transition. In this approximation, the Fermi golden rule can be written as:The X-ray absorption selection rules determine that the dipole matrix element is non-zero if the orbital quantum number of the final state differs by one from the initial state (∆L = ± 1, i.e., s → p, p → s or d, etc.) and the spin is conserved (∆S = 0). In the dipole approximation, the shape of the absorption spectrum should look like the partial density of the (∆L = ± 1) empty states projected on the absorbing site, convoluted with a Lorentzian. This Lorentzian broadening is due to the finite lifetime of the core-hole, leading to an uncertainty in its energy according to Heisenberg's principle. The single electron approximation gives an adequate simulation of the XANES spectral shape if the interactions between the electrons in the final state are relatively weak. This is the case for all excitations from 1s core states (K-edges).

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X-ray Absorption Near-Edge Structure (XANES) Spectroscopy

Henderson

Groot

Moulton

2014

Reviews in Mineralogy and Geochemistry

264

155

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Electronic structure of RbBr during the phase transition: x-ray absorption near-edge structure analysis

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X-ray Absorption Near-Edge Structure (XANES) Spectroscopy

X-ray Absorption Near-Edge Structure (XANES) Spectroscopy

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