Several past decades of intense research have resulted in a good understanding of the fundamental proper­ties of vacancies and self-interstitials in pure metals. We have reviewed this understanding from the following point of view: how do these fundamental properties affect radiation damage at elevated tem­peratures that exist in nuclear reactors. The key parameters that emerge from this perspective are the displacement energy of Frenkel pairs, the forma­tion and migration energies of vacancies and self­interstitials, and their relaxation volumes and elastic polarizabilities. While the physical basis for these key parameters is understood, obtaining precise values for them by experimental and theoretical means remains a formidable challenge. In particular, this is true for the type of alloys that are used for compo­nents in the core of nuclear reactors. In general, these are complex alloys. For example, the austenitic stain­less steels are composed of major alloy constituents, namely iron, nickel, and chromium, and many minor alloy elements such as molybdenum, titanium, man­ganese, carbon, and silicon. Therefore, many different types of vacancies and self-interstitials can exist in these alloys with potentially different properties. It is unlikely that all these different properties can actu­ally be measured. Rather, only effective average prop­erties, such as the self-diffusion coefficient, can be determined experimentally, and theoretical models must be employed to relate effective properties to the individual properties of the different vacancies.

At the present time, electronic structure method still require further development before effective properties of defects in complex alloys can be calcu­lated. In fact, only recently has it become possible to calculate, for example, accurate values for the forma­tion energies of mono — and divacancies in pure metals. Two advances have been responsible for the progress.

First, density functional theory requires different implementations when applied to bulk and to surface properties of metals. The uniform electron gas that serves as a starting point for the electron density functional in the bulk interior of solids is not suitable to formulate the corresponding functional for the ‘electron edge gas.’ As shown by Kohn and Mattsson,61,62 functionals must be developed that join the edge and the interior bulk regions, and Armiento and Mattsson63,64 have proposed and tested func­tionals for these two regions and how to join them. When applied to vacancies in metals,65,66 formation energies are predicted that are in much better agree­ment with experimental results. But there are also differences. For example, Carling et a/65 obtain a repulsive (positive) binding energy for divacancies in Al. However, this result may be due to the limited number of atoms employed in the calculations and the periodic boundary conditions.

This brings us to the second advance that has recently been made, namely the implementation of an orbital-free electron density functional theory based on finite-element methods.67 With this approach, much larger systems containing effectively millions of atoms can be treated; these systems are truly finite, and realistic boundary conditions can be applied to them.

Figures 28 and 29 reproduced from Gavini eta/.67 reveal a surprisingly large effect of the system size, that is, the effective number of atoms in a finite crystal into which one or two vacancies have been introduced. As demonstrated by these results, in order to obtain defect properties that are indepen­dent of the size of a finite system requires thousands of atoms as well as their full relaxation. In other words, electronic structure calculations need to be combined with continuum elasticity descriptions to predict radiation effects and to develop better alloys for nuclear power generation.