Anelastic relaxation of point defects in cubic crystals

Abstract. Point defects in solids can give rise to anelastic relaxation provided that the defects behave as elastic dipoles. Experiments with single crystals give information on the atomic configuration of the point defects. Measurements of the orientation dependence of the relaxation strength allow determination of the defect symmetry and the dipole shape factor 6h = I h,- A, I. This is demonstrated for two examples: (i) The Snoek relaxation of 0 and N in Nb and Ta single crystals: The 6h values for 0 and N are in the range of 0.6 to 0.7. The tetragonal defect symmetry is confirmed by experiments on Nb-0 crystals with various orientations. (ii) Defects in cubic, Y20,- or CaO-stabilized ZrO,: The oxygen vacancies created for charge compensation are associated with dopant cations thus forming elastic (and electric) dipoles. The dipoles exhibit trigonal symmetry. 1. THEORETICAL BACKGROUND Point defects in solids can give rise to anelastic relaxation provided that the defects behave as elastic dipo-les. Elastic dipoles represent atomic defects that produce an anisotropic local distortion of the crystal lat-tice. Application of elastic stress, as, e.g., in mechanical oscillations, leads to thermally activated reorien-tation of the dipoles, which manifests itself by the appearance of mechanical loss peaks. The most prominent example is the Snoek effect of heavy interstitial foreign atoms (C, N, 0) in bcc metals, which was originally discovered by Snoek [I] in iron containing carbon and nitrogen. The occurence of anelastic relaxation due to the presence of point defects is based on the following considerations [2,3,4]: (i) The defect exhibits a symmetry lower than that of the host crystal. (ii) The introduction of the defect produces anisotropic local elastic distortion which can be characterized by a second rank tensor, the h-tensor. The tensor describes the strain of a crystal by introduction of unit concentration of defects. The tensor can be expressed in the following form: fA, 0 0) h = O; h, O. (1