Application of statistical mechanics to solid solutions of interstitial impurities in binary alloys

A statistical mechanical model has been developed for ternary interstitial alloys in the framework of the canonical ensemble. Short-range repulsive interactions among interstitials have been taken into account assuming a hard-sphere pair interaction potential. Sites of different geometrical kind (octahedral, tetrahedral, etc.) have been considered and further distinguished on the basis of either the chemical composition of their first shell of neighbouring metal atoms or of the distribution of the two metallic species within this shell. Analytical expressions for the thermodynamic functions of the system and for the occupancy probabilities of the different interstitial sites have been derived for a given alloy and assigned site energies. A general procedure for the evaluation of the blocking factors and the interstitial jump probabilities is proposed and applied to random f.c.c. and b.c.c. binary alloys containing H. The results are discussed in relation to diffusivity and anelastic relaxations associated with the interstitial impurity.