Theory of nucleation with cluster loss and injection: Application to plastic deformation and irradiation
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I.
INTRODUCTION
NUMEROUS materials processing and service environments may put a system susceptible to phase transformation into an unusual physical and chemical regime. For example, in high strain rate plastic deformation, as may occur in formation of nanostructures,tt,2,3~ intense, continual deformation produces large numbers of mobile point and line defects as well as thermal and stress pulses of significant magnitude. Any of these effects might destroy the small clusters of atoms which give rise to nucleation. The defect structure under fast reactor, fusion reactor, or light water reactor irradiation or ion mixing is markedly similart4] to that under high rate plastic deformation. In all cases, irradiation results in the formation of large numbers of isolated vacancies and self-interstitial atoms and sometimes vacancy-rich displacement cascades. The point defects may interfere with the nucleation process. The displacement cascades may disperse small clusters into single atoms but may also decay to two- or three-dimensional vacancy clusters which may serve as embryos for future nucleation. Phase selection in systems undergoing irradiation or plastic deformation is an extremely complex process and is certainly not explainable on the basis of formation of the minimum free energy phase, t3,a,SjFor example, under either plastic deformation or irradiation, solid solution phases, amorphous phases, and intermetallic compounds which are thermodynamically unstable sometimes form in place of the
KENNETH C. RUSSELL, Professor, is with the Department of Materials Science and Engineering and Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled "Atomistic Mechanisms of Nucleation and Growth in Solids," organized in honor of H.I. Aaronson's 70th Anniversary and given October 3-5, 1994, in Rosemont, Illinois. METALLURGICALAND MATERIALSTRANSACTIONS A
thermodynamically stable phases. The energy of the plastic deformation or irradiation is clearly being used in some way to cause the behavior of the system to deviate sharply from what would be observed thermally. Phase selection is most easily altered in the nucleation step, when typically only a few to a few tens of atoms are involved. This article analyzes the effects of destruction and creation of clusters of the new phase on the nucleation rate. Analytical expressions are derived for cases of both low and high cluster destruction rates. The theory was developed with solid state processes in mind but is applicable to nucleation processes involving fluid phases. Preliminary notes were published earlier.t5.6]
II.
CLASSICAL THEORY
Nucleation theory was first formulated by Farkas,t7] who was working from a suggestion by Szilard. Nucleation is represented as diffusion of a particle along a size coordinate, subjected to the potential gradient provided by the activation barrier to nucleus formation. Other workers modified the basic formul
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