Void ordering in metals during irradiation

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Abstract
Evans (1971) has reported that voids produced by irradiation could form into three-dimensional arrays. Since then void lattices have been observed in a number of metals, for example, Mo, W, Nb, Ta, Al and Ni. In all these metals the pattern of ordering shows many similarities. A number of theories have been proposed to explain the stability of the void lattice. Notable amongst these are the theories by Malen and Bullough (1971), Foreman (1972), Lucas (1973) and the work by Benoist and Martin (1975) and Imada (1978) who have viewed the void-lattice formation in terms of the spinodal decomposition involving point defects. On similar lines, Krishan (1981) has recently reported that the kinetics of void-lattice formation can be understood in terms of the bifurcation of the homogeneous state associated with point and extended defects. Detailed results are presented in this paper and it it shown that the bifurcation is induced by the coupling of the microstructural variables with point defects; the phase transition occurs when one of the modes in the coupled rate equation becomes soft at a critical value of the microstructural densities. Analysis is carried out for the first bifurcation and it is shown that vacancy-loop dynamics plays an important role in producing the phase transition. The analysis is consistent with many qualitative and quantitative experimental observations regarding the void-lattice formation which are discussed in detail. It is also shown that microstructure-induced ordering can occur under fairly general conditions and similar phase transitions could be induced by inert-gas vacancy complexes, evidence for which is available from some electron-irradiation results and bubble-lattice formation at low energies. The analysis establishes the void-lattice formation as a process of self-organization shown by open non-equilibrium dissipative systems.

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