Vacancy Cluster: Helium Synergy in Void Nucleation
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INTRODUCTION
RADIATION-INDUCED void swelling was first observed in the 1960s during materials development for fuel cladding and ducts for the fast breeder reactor.[1,2] High number densities of nanometer-micrometer diameter helium-containing voids (or cavities) were observed. The resulting volumetric swelling percentages were unacceptable in the reactor. There was a large international effort to understand the physical basis of the swelling and thereby to eliminate or at least control it. Theories for void nucleation from simultaneous supersaturations of vacancies and self-interstitials were derived simultaneously by Russell[3] and Katz and Wiedersich.[4] The resulting steady-state nucleation equations were much the same. Self-interstitial involvement was found to give a large, up to order of magnitude increase in the critical nucleus size. Self-interstitial involvement was found to reduce the nucleation rate by a few orders of magnitude, which is a relatively modest factor in the context of nucleation theory. Neutron irradiation produces helium through (n, a) transmutation reactions. Concentrations typically reach the parts per million (atomic) range in breeder reactor materials and may be several orders of magnitude higher under the high-energy neutron regimes of proposed thermonuclear reactors. Helium may also be introduced into the lattice by a-particle irradiation from an ion accelerator. Numerous experiments had shown that helium may give a major increase in void nucleation kinetics and the ensuing swelling rate. Prior to void formation, most helium atoms are trapped in vacant lattice sites. However, reaction with an impinging self-interstitial is energetically favorable and puts the helium atom into an interstitial site[5] where it can rapidly diffuse. KENNETH C. RUSSELL, Professor Emeritus of Metallurgy and Nuclear Engineering, is with the Departments of Materials Science and Engineering and Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA. Contact e-mail: [email protected] This article is based on a presentation given in the symposium entitled ‘‘Solid-State Nucleation and Critical Nuclei during First Order Diffusional Phase Transformations,’’ which occurred October 15–19, 2006 during the MS&T meeting in Cincinnati, Ohio under the auspices of the TMS/ASMI Phase Transformations Committee. Article published online November 1, 2007 956—VOLUME 39A, MAY 2008
Theories for the effect of helium on void nucleation were independently developed by Wiedersich et al.[6–9] and by Russell et al.[10–18] Two different approaches were taken to void nucleation in the presence of mobile helium. In the first,[7,8,12] difference equations were written to describe the movement of clusters in a phase space of void size and helium content and were numerically solved. Helium was predicted to significantly promote void nucleation under some conditions, in rough agreement with experiments. Unfortunately, the difference equations are slow to converge and tend to be unstable. In addition, the calculat
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