Theory of the snoek effect in ternary b.c.c. alloys

Abstract

A quantitative calculation is attempted for anelastic relaxation of interstitial atoms in the presence of substitutional atoms in body-centred cubic metals. A unit sphere is defined around a substitutional atom. Within the unit sphere the movement of interstitial atoms is affected by the substitutional atom, while interstitial atoms outside the sphere are assumed to behave independently. The octahedral interstices inside the unit sphere are classified into a number of shells according to their distance from the substitutional atom. General rate equations for the probability of occupation of various sites by interstitial atoms are derived for a crystal subjected to an applied stress. The equations are greatly simplified when an applied stress has no hydrostatic component because the number of interstitial atoms in each shell is conserved. Thus, a detailed treatment is given for the shear-stress case. The rate equations allow accurate computation of the damping spectrum if the anisotropy of the strain field, activation energies and attempt frequencies for the motion of interstitial atoms are known. The following conclusions of the theory are at variance with the interpretation of previous researchers. (1) For the appearance of a well-defined peak caused by the rotation of interstitial atoms around substitutional atoms, it is not necessary to assume direct next-nearest-neighbour jumps. (2) It is not correct to regard the damping spectrum as composed of separable components, each associated with a specific atomic jump. (3) The spectrum can be expressed as a sum of a number of Debye functions, but the individual peaks are not simply related to the rotation of interstitial atoms in a particular shell (e.g. nearest-neighbour sites of a substitutional atom). It is also shown that in the case of tensile stress a new type of relaxation (hydrostatic relaxation) may occur as interstitial atoms rearrange to different shells.