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Core electrons are the electrons in an atom that are not valence electrons and therefore do not participate in bonding. An example: the carbon atom has a total of 6 electrons, 4 of them being valence electrons. So the remaining 2 electrons must be core electrons.
They are so tightly bound to the nucleus as to be negligibly perturbed by the environment of the atom when in the solid state. Therefore on the contrary of the valence electrons, the core electrons usually play a secondary role on chemical bonding and reactions and their main role is to screen the positive charge of the atomic nucleus. In transition metals, however, the distinction between core and valence electrons is more subtle and it could be very important to consider the electrons in the highest d-shells as valence rather than core electrons.
A core electron can be removed from its core-level upon absorption of electromagnetic radiation (X-ray) and excited to an empty outer shell or emitted as photoelectron (photoelectric effect). The resulting atom with one of its core-level (a so-called core-hole) empty is in a metastable state and decays within 10−15 s by x-ray fluorescence or by the Auger effect.
By detecting the emitted photoelectrons (photoemission spectroscopy), the X-ray photons (XAS and fluorescence spectroscopy) or the Auger electrons (Auger electron spectroscopy) useful information on the electronic and the local lattice structures of a material can be obtained.
The atoms of such techniques results from the fact that since every atom has core-level electrons with well-defined binding energies, it is possible to select the element to probe by tuning the x-ray energy to the appropriate absorption edge. For the same reason the spectra of the radiation emitted (electrons or photons) can be used to determine the elemental composition of a material.