Modelling of Copper Precipitation in Fe-Cu Alloys Under Irradiation
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Modelling of Copper Precipitation in Fe-Cu Alloys Under Irradiation Alexander V. Barashev, Stanislav I. Golubov1 and David J. Bacon Materials Science and Engineering, Department of Engineering, The University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK. 1 Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong ABSTRACT Precipitation of copper-rich clusters is a major cause of in-service hardening of reactor pressure vessel steels and has attracted much attention. Experimental studies of microstructural changes in alloys under various conditions have revealed similarities and differences. It has been established that under ageing the precipitate ensemble experiences normal nucleation, growth and Ostwald ripening, a distinguishing feature of which is the bcc-9R-3R-fcc transformations the precipitates undergo during growth. The main effect of electron irradiation is believed to be enhancement of the diffusion of copper and hence acceleration of the kinetics. In the case of neutron irradiation, however, there are many aspects that are not clear. One is that at temperatures less than about 300oC the precipitate size is observed to be very small (~1-3 nm), i.e. the coarsening rate is very low. In this paper we study this phenomenon by computer simulations based on the “mean-field” approach for describing microstructural evolution. INTRODUCTION The precipitation of copper clusters has been studied both experimentally and theoretically in binary Fe-Cu alloys and steels under various conditions. Existing models of this phenomenon rest on the assumptions of the homogeneous nucleation of precipitates and migration of copper atoms via the vacancy mechanism [1-4]. The main difference between the models is in the functional form used for the binding energy of a copper atom with a precipitate containing x atoms, E b (x) . In the earliest model [1] the value E b (x ) = ∞ was adopted, whereas in [2] the capillary model was used, and in [3,4] a more complicated function was obtained by fitting the theory to the experimental data on precipitate evolution during ageing as measured by a combination of SANS and TEM [5]. An advantage of the latter approach is in the reproduction of the double-peak size distribution of precipitates observed at long ageing times (~10 hours at 550oC). This observation and features of the binding energy (see [3,4]) are associated with the bcc-9R-3R-fcc transformation of the precipitates during growth [6]. Not all aspects of this phenomenon are fully understood and extensive investigations have been carried out experimentally [6-9] and by molecular dynamics [10-12]. It has been found recently that the size at which a precipitate experiences transformation depends on the temperature and possibly some other conditions [7,10,12]. These features are yet to be included in the model of precipitate evolution, and mainly academic issues can be raised at this stage. In the present paper we study why under neutron irradiation the precipitates are observed to be ~1
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