X-ray is a form of electromagnetic wave with wavelength in range of 0.01~10 nm and energies in range of 0.12~120 keV, almost the same range for the core-level electron binding energy (0.1~100 keV).[1,2]

Therefore, X-rays can be used to determine the electronic structure of the material by monitor the absorptions of the X-ray with tunable photon energies, X-ray absorption spectroscopy (XAS). In XAS the final states of the elements, including the photoelectron emission, fluorescent and/or in-elastically scattered photoelectrons, can be measured and thus the electronic structure of the matter can be analyzed. In a X-ray absorption spectrum, there are three regions:

i) the rising edge which is refered to X-ray Absorption Near-Edge Structure (XANES) or Near-Edge X-ray Absorption Fine Structure (NEXAFS). This region shows the domain features of the XAS, indicating the photo absorptions when X-ray go through the sample. [3,4]

ii) the pre-edge region, which is sensitive to the valence of the elements, the site distortion, and the orbital mixing.[5] The energy of this region is lower than the rising edge.

iii) the Extended X-ray Absorption Fine Structure (EXAFS) region, which is corresponding to the interactions of the ejected photoelectrons from neighboring atoms. The energy range of EXAFS region is higher than XANES region and its signal at the high energy range is powerful tool for the analysis of atomic pair distribution.[6]

The peaks in XAS are related to the edge energy of the elements. For a single atom, the electrons are distributed at different energy levels according to Hund’s rules and Pauli Exclusion Principle with lowest system energy.[7] The energy levels named as K, L, M, N, O... are corresponding to the principle quantum number n=1, 2, 3, 4, 5... and there are 'sub-shell' orbitals in each energy level marked as s, p, d, f, g... corresponding to the angular momentum l=0, 1, 2, 3, 4...In each sub-shell the number of the electrons is limited by 4l+2, e.g., s-orbital can have 2 electrons, p-orbital can have 6 electrons and d-orbital can have 10 electrons.

The energies of these orbitals are different and one can sum up as: E1s < E2s < E2p < E3s < E3p < E4s < E3d < E4p < E5s < E4d < E5p < E6s... For example, Fe atom has 26 electrons and they distribute in orbitals as 1s2 2s2 2p6 3s2 3p6 4s2 3d6, Fe3+ has 23 electrons and distribute as 1s2 2s2 2p6 3s2 3p6 3d5 , and Fe2+ has 24 electrons and distribute as 1s2 2s2 2p6 3s2 3p6 3d6 to achieve the lowest system energy. The orbital state energy level can be expressed as En=(-hcRZ)/(n2) , which is related to the principal quantum number (n) and the atom number (Z). Here h, c and R in the expression are Planck’s constant, velocity of light and Rydberg constant. For instance, Hydrogen atom has its level energy of E1=-13.6 eV, E2=-3.4 eV, etc.

Because of the interactions between electrons for multi-electron atoms, the effective nuclear charge (Zeff) is used in the equation in which Zeff = Z-S where S is the number of non-valance electrons. The measured values of atomic energy levels of multi-electron atoms can be found in Bearden’s publications. [8,9] XAS can also be used in determining the magnetic properties of the materials, e.g., X-ray magnetic circular dichroism (XMCD) in which two XAS were taken in magnetic field, one was taken with left circularly polarized X-ray and the other was taken with right circularized X-ray.

The difference between the two indicates the atomic magnetic properties, such as its spin and orbital magnetic moment.

Refereces:

1 E. A. Merritt, (1996-2010), p. http://skuld.bmsc.washington.edu/scatter/AS_periodic.html.

2 Wikipedia, (2011), p. http://en.wikipedia.org/wiki/X-ray.

3 Wikipedia, (2011), p. http://en.wikipedia.org/wiki/X-ray_absorption_spectroscopy.

4 Wikipedia, (2011), p. http://en.wikipedia.org/wiki/XANES.

5 G. A. Waychunas, American Mineralogist 72, 89-101 (1987).

6 Wikipedia, (2011), p. http://en.wikipedia.org/wiki/EXAFS.

7 Wikipedia, (2011), p. http://en.wikipedia.org/wiki/Atomic_orbital.

8 J. A. Bearden, Reviews of Modern Physics 39, 78 (1967).

9 J. A. Bearden and A. F. Burr, Reviews of Modern Physics 39, 125 (1967).