INTERNAL-FRICTION STUDIES ON OXYGEN-OXYGEN INTERACTION IN NIOBIUM .2. APPLICATION OF LONG-RANGE INTERACTION MODELS

The oxygen Snoek relaxation in niobium is studied under the assumption of a long-range interaction among interstitial atoms dissolved in b.c.c. metals. Two models describing this interaction in a mean field approximation (MFA), namely (i) the paraelastic and (ii) the random cooperative strain interaction (RCSI) model are discussed in detail. In the RCSI model the MFA treatment is modified by introducing the "Onsager correction", and a new formula for the internal friction peak of the Snoek effect is derived. Based on this modified RCSI model, a quantitative analysis of our experimental data from Nb with 0.12 to 0.85 at% 0 (presented in Part I) is performed by applying nonlinear regression. The model is able to account for all essential experimental results, (i) the shift of the Snoek maximum to higher temperatures with increasing 0 content, (ii) the broadening of the maximum increasing with 0 content, and (iii) a constant value of the activation enthalpy (H = 1.15 eV), independent of the oxygen content. The critical temperature characterizing the interaction of oxygen atoms increases from 1 10 K for 0.12 at% 0 to 280 K for 0.85 at% 0 and is, as predicted by the modified RCSI model, proportional to the square root of the oxygen concentration.