Binding interaction, surface relaxation

An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kp to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced effect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2A pr)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kp-value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1 /r5-decay is steeper than the monotonic 1 /r3-decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on. 

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