The cloud of vacancies and interstitial atoms produced by a neutron scattering event diffuses through the crystal lattice under the influence of thermal agitation. If the motion were entirely at random the density of vacancies and interstitials would rise until production was balanced by recombination at sinks such as grain boundaries and dislocations, where they would meet and annihilate each other. The motion is not entirely random, however. The stress field around a dislocation inter­acts with the stress fields around both interstitials and vacancies, and tends to attract them, but the interaction with an interstitial is stronger. As a result the interstitials tend to cluster together at dislocations and other defects in the crystals, leaving an excess of vacancies that also tend to form clusters rather than recombining. The normal form of

a cluster of vacancies is a flat mono-atomic layer that eventually col­lapses leaving an edge-dislocation ring, but if there is a nucleus, which may consist of a few atoms of an inert gas (helium), vacancies migrate to it and form a three-dimensional void.

Figure 3.11 is a series of electron micrographs of irradiated AISI type 316 stainless steel showing typical polyhedral voids about 0.1 ц-m in diameter. As these voids are formed and grow the mean density of the material falls and it swells. Most metals swell in this way when irradiated but the rate and extent of swelling vary widely from one to another.

Temperature has an important effect on swelling as may be seen in Figure 3.11. Figure 3.12 shows the ranges of values of void

density and mean diameter that are typically observed. The greater size of the voids at higher temperature is probably due to the increased mobility of vacancies at higher temperatures, but the corresponding reduction in the number of voids is not entirely understood because the mechanism of nucleation is uncertain. It may be that at high tem­perature the helium atoms migrate to existing voids and are not avail­able as nuclei of new ones. Alternatively nucleation may be connec­ted with the “spikes” of displaced atoms due to a neutron scattering event, the damage caused by which anneals out more readily at high temperature.

The result for many materials is that the swelling rate is high in a certain temperature range and low in others as shown in Figure 3.12. For 316 stainless steel there is little swelling below 350 °C. At high temperatures impurities may be very important, and above 600 °C the swelling is inhibited by the formation of very large voids on large grains

of carbide. This is strongly dependent on the carbon concentration, and one way to reduce swelling is to reduce the amount of carbon in the material.

Swelling is also reduced if there are many dislocations because they tend to attract the vacancies, although weakly, and if there are enough of them the number of vacancies left to form voids is small. This is shown by the much reduced swelling in 20% cold-worked 316 stainless steel as compared with annealed material, especially below 500 °C, as shown in Figure 3.13.

Finely dispersed precipitates within the grains also tend to reduce swelling because they attract both interstitials and vacancies and allow recombination. The nickel-rich alloy Nimonic PE16, in which the y’ phase is finely dispersed, is resistant to swelling for this reason. In a similar way the martensite crystals in ferritic-martensitic steels and the dispersions of nanometre-sized particles of oxide in oxide-disperse- strengthened or “ODS” steels have similar effects. For this reason these materials may be particularly attractive for the cladding and the structure of the core.

In most materials the amount of swelling increases with time and because it depends on the interaction between vacancies and nuclei the increase is nonlinear. Initially swelling accelerates as irradiation proceeds, but at very high doses there is some evidence that it may saturate.

318 Stainless Steel

Cold-Worked 316

Annea ed 316

Nimonic

Displacements per Atom

Figure 3.14 Irradiation creep in various materials.