The energies of the Al Auger KL 2,3L 2,3 transitions and the Al 2p photoelectron peak have been determined experimentally by AES, XPS and XAES for several Al compounds. The experimental results are compared with ab initio calculations based on a cluster model in which a central aluminum atom is surrounded by its first neighbours in the crystal. This model includes chemical, structural and relaxation effects and it allows the direct ab initio determination of the intra- and extra-atomic relaxation energies. These values are compared with the Wagner equation that relates the extra-atomic relaxation energy and the Auger parameter. The three approximations that support this equation are examined on the basis of the cluster results.
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