Lifshitz Abstract

Abstract The Lifshitz - Slezov theory is applied to study the metastable states of the matrix damage clusters, MA, and the copper enriched clusters, CEC, in neutron irradiated steels. It was found that under irradiation conditions the CE Cs are at the Ostwald stage for a neutron fluence of about 0.0002 dpa. The time dependence of number density, MDn, is determined by summarizing all differential equations of the master equation for MA with neglecting of dimmers concentration in comparison with concentration of the single vacancies and subtraction of the number CEC that replace the MA, namely vacancy clusters, due to the diffusivity of copper and other impurity atoms to them. For binary Fe-0.3wt%Cu under neutron irradiation with dose 0.026, 0.051, 0.10 and 0.19 dpa the volume content of the precipitates from the SANS experiment is found to be about 0.229, 0.280, 0.237 and 0.300 vol% respectively. The volume fraction of CEC, in these samples is 0.195 vol% and the calculated volume fraction ofMA is 0.034, 0.085, 0.042 and 0.105 vol% for doses 0.026, 0.051, 0.10 and 0.19 dpa respectively. 

T. O. Tiernan, B. M. Hughes, and C. Lifshitz, in Electronic and Atomic Collisions, Abstracts of Papers of the Vllth International Conference on the Physics of Electronic and Atomic Collisions, p. 808, North-Holland Publishing Co., Amsterdam, The Netherlands (1971). 

Near the Lifshitz line thermal composition fluctuations are expected to become strong over a larger temperature range because of the reduced smTace energy (c2 a I2 = 0), leading to a lower threshold force for thermal fluctuations. On a more abstract level this effect can also be interpreted in terms of a larger upper critical dimension Du = 8 beyond which thermal fluctuations become irrelevant, and Gi is twice as large as for ordinary binary polymer blends [86]. 

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