THEORY OF INTERNAL FRICTION IN A FACE-CENTRED CUBIC LATTICE

Abstract

It is now well-established that stress-induced micro-diffusion of carbon atoms in the interstitial lattice points will take place in body-centred cubic lattices such as in α-iron. This is the result of the lattice asymmetry introduced by an oscillating strain in the crystal. In a pure face-centred cubic metal, this phenomenon could not happen, namely, not in γ-iron. Nevertheless experimental evidences show to the contrary.The present note advances a criterion concerning the possible types of mechanisms which would give rise to internal friction in a face-centred cubic crystal. By the application of the general thermodynamical theory of internal friction, proposed by one of the present authors, we have calculated the relaxation strength for two important cases. If the asymmetry in the interstitial lattice points is to be ascribed to the presence of impurity or alloying atoms, then it can be shown that the relaxation strength will be proportional to the expression CxA (1-xA) , where xA. is the density in atom percentage of the impurity or alloying atoms and C is the density of the carbon atoms. However, recent experimental result of Ke and Tsien indicates that there is nothing like this sort of density dependence, i. e. it is rather structure insensitive. Hence, it is not likely that this micro-diffusion can be ascribed to the action of the alloying (substitutional) atoms.A second possible mechanism is proposed in the text. The asymmetry is due to the presence of the Schottky defects, in which a pair of carbon atoms settle down and orientates itself in accordance with the direction of external strain; the possible location of the pair may be such that one carbon atom is located in the centre of the hole while the other is in an interstitial point immediate to the hole. The calculated relaxation strength is proportional to the expression AC2/(B +C), where A and B are such constants that B is structure insensitive. A comparison of the calculated and the experimental curve for the internal friction strength is made in the text, which shows a remarkable agreement. Furthermore, one can thereby estimate the free energy evolved in trapping a carbon atom in a Schottky hole to about the order of 0.14 eV. It seems that the above proposed vacancy-induced asymmetry might be a possible correct explanation.The authors like to tend their appreciation to Dr. Ke Ting-sui and his collaborators for the kindness to communicate to us their results before publication and to their valuable discussions.