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X-rays interact with matter in numerous ways, but the process which underpins XAS is the photoelectric effect. When an atom absorbs a sufficiently energetic photon a core electron is ejected into a continuum state. The loss of a core elec- tron leaves the absorbing atom in an excited state which can relax via several different mechanisms, the most significant of these being X-ray fluorescence and Auger electron emission (Figure 2.5). The probability of each decay mechanism is dependent on excitation energy; Auger emission is usually dominant at lower energies, but fluorescent X-ray yields approach 1 at higher energies i.e. those ap- propriate for excitation of K-shell electrons in elements withZ>40. Relaxation times are on the femtosecond scale. Both relaxation mechanisms begin with the transition of an electron from a more weakly bound shell to fill the core hole, but the subsequent process by which the resulting excess in energy is removed from the atom is different in each case.

If the atom relaxes via fluorescence, a photon is emitted with energy equal to the difference between the two electron energy levels involved in the transi- tion. The available transitions are determined by quantum mechanical selection

Figure 2.5:The core hole left behind after ejection of a photoelectron is filled when an electron from a higher shell ‘falls down’ to the core level. The excess energy from this transition is either converted into a photon (fluorescence) or transferred to another electron causing it too to be ejected from the atom (Auger emission).

rules for electric dipole radiation, namely ∆l = ±1; ∆s =0; ∆j =0,±1 (but

not 0→0), wherelandsare the orbital angular momentum and spin quantum

numbers respectively, and j is their vector sum i.e. j=l+s. Hence, for exam- ple, a transition from the 2sto 1s level isforbidden. The nomenclature for X-ray fluorescence emission is based on the initial and final states of the electron un- dergoing a transition. For example,K_αandK_β refer to transitions of the electron to the 1s state (n=1, l =0, s =±1/2) from the L and M shells respectively. With sufficiently high energy resolution, these can be further resolved to transi- tions from different split energy levels resulting from spin-orbit coupling. Since the electron energy levels (and their differences) are specific to each element, the fluorescence emission can be used for compositional analysis, as described in Section 1.3.

Fluorescence can be excited not only by X-rays, but also by energetic charged particles. In fact, the most common types of laboratory X-ray source produce photons by accelerating electrons into a metal anode to excite the core level transitions. The characteristic emission lines are observed, but they sit on a background of Bremsstrahlung (braking) radiation produced as the electrons rapidly decelerate inside the target material. The overall emission intensity is limited by the current which can be passed through the target i.e. by heat gener- ation. Rotating anodes improve this situation, but the brilliance of a laboratory

source is still many orders of magnitude lower than a synchrotron, and the pho- ton frequency is restricted by the source material used.

In contrast to fluorescence, Auger emission is a non-radiative process whereby the energy remaining from the initial outer shell electron relaxation is carried away by a second electron which is itself ejected from the atom. The excess energy is given by|E_c−E_n|, whereE_candE_nare the core- and outer-shell binding energies respectively. The ejected electron, assuming the excess energy is greater than its binding energy, then has kinetic energy|E_c−E_n−E0_m|, where

E_m is the binding energy of the Auger electron. The prime denotes that this

binding energy is slightly modified as the electron is originating from an already ionized atom[2].

Absorption Spectrum Characteristics

As described above, if the energy of an X-ray beam is swept across an absorption edge (easily achieved at a synchrotron) a sharp rise in absorption is observed. A typical absorption spectrum can be divided into four parts: the pre-edge, rising edge, near-edge and EXAFS (extended X-ray absorption fine structure) regions (illustrated in Figure 2.6). The precise boundaries between these regions are not well-defined in terms of X-ray energy, rather they represent the changing physical processes which occur as the probing X-ray energy passes through an absorption edge. In the pre-edge region, the incoming X-rays do not possess sufficient energy to eject an electron from the shell of interest. However, once the X-ray photons reach the threshold (binding) energy ionization of that shell can occur. After the rising edge, rather than returning to a smoothly decaying function, oscillations are observed which decay in amplitude as the X-ray en- ergy moves further beyond the edge itself. These arise from scattering of the photoelectron, which possesses kinetic energy equal to the difference between the X-ray photon energy and the core-level binding energy, with surrounding atoms. This modifies the photoelectric absorption cross-section of the absorb- ing atom, and the following details how this behaviour can be used to obtain information about the local atomic structure.

50 40 30 20 10 0

Normalized intensity / A.U.

9.4 9.2 9.0 8.8 Energy / keV EXAFS Pre-edge XANES

Figure 2.6: X-ray absorption spectrum of Cu obtained via fluorescence measure- ment (see Section 2.2.4) indicating the key regions where different physical pro- cesses occur.