Statistical Model for the Trapping of Interstitials by Substitutional (Interstitial) Atoms in Solids

The distribution of noninteracting interstitial atoms in a lattice containing trapping centers is studied using Fermi-Dirac statistics. Assuming that the energies of free sites and trap sites are distributed according to density-of-states functions, the populations of the various types of clusters are calculated as a function of concentration and temperature; the only form of interaction between interstitials taken into account is represented by the inhibition of some types of clusters. The results are satisfactorily applied to internal friction to explain the anomalous relaxation observed in crystalline and amorphous metal-hydrogen (deuterium) systems.