3.3.1 Displacement of Atoms

The neutron irradiation to which the materials in the reactor are sub­ject alters their properties in several ways. The most important effects on the structural materials are to increase hardness and decrease ductility, to enhance creep rates at low temperatures, and, most import­ant, to reduce the density. These phenomena have to be taken into account in design of the reactor along with familiar effects such as thermal creep, fatigue and corrosion.

Irradiation affects the properties of non-fissile materials in two ways. Neutron scattering interactions displace atoms from their sites in the crystal lattice, creating vacancies and interstitial atoms in equal numbers, and neutron absorption by (n, a) and (n, p) interactions cre­ates atoms of helium, hydrogen and other transmutation products within the crystals. Helium has the greatest effect on the properties of the material.

A useful way to characterise the extent of the irradiation received by a piece of material is to specify the “displacement dose”, which is the average number of times an atom has been displaced from its lattice site. Each elastic scattering interaction imparts kinetic energy Ep to the target nucleus, where Ep is a random variable distributed uniformly (if the scattering is isotropic) in the range 0 — p. En, where En is the neutron energy, д = 4A/(1 + A)2, and A is the atomic weight of the target. For iron д = 0.069, so a 1 MeV neutron can impart up to 69 keV to an iron nucleus from which it is scattered elastically.

It requires only some 25 eV to displace an iron atom from its site in the crystal lattice, so the target nucleus may well have enough energy to displace several hundred atoms as it moves through the crystal. Some of the kinetic energy is however taken up by inelastic scattering interactions, and the number of atoms displaced by elastic scattering depends on the direction in which the target atom travels relative to the crystal lattice. Moreover some of the displaced atoms recombine with vacancies in the lattice. Various estimates of the relationship between Ep and nd, the number of atoms displaced, have been made. Figure 3.9 shows one such, that of Torrens, Robinson and Norgett (often called the “TRN”, or alternatively “NRT”, model), which is widely used.

It is possible to define a “displacement cross-section” for neutrons in group g, adg, by

r Eg-1 r Eg-1

odg ф(Е )dE = ae (E )n(E )ф(Е )dE, (3.12)

Eg Eg

where

(3.13)

ae(E) is the elastic scattering cross-section, and ф(Е) gives the vari­ation of flux within the group from, for example, a fundamental mode calculation. Figure 3.9 shows values of adg for iron.

The total number of displacements suffered by each atom, D, is then given by

(3.14)

where T is the length of time for which the irradiation continues. D is the average number of times each atom is displaced from its lattice site and is often referred to as “dpa” (displacements per atom).

The scattering cross-sections of chromium and nickel are quite similar to that of iron so it is often assumed that the displacement cross-section of iron as shown in Figure 3.9 can be used for all the constituent elements of the steel structural materials used in reactor cores, whatever their actual specifications.

Figure 3.9 shows that adg falls off rapidly at energies below about 0.1 MeV. For this reason an alternative way of characterising the extent
of irradiation, often used because it is easier to calculate, is the fast neutron fluence, Фf, defined by

(3.15)

The total flux above 0.1 Mev is sometimes called the “damage flux” and Фf is the “damage fluence”. If the power density Q in mixed-oxide fuel containing 20% plutonium is 2.5 GW m-2 (see section 3.2.1) and the neutron spectrum is similar to that shown in Figure 1.7 the damage flux is about 5 x 1019m-2s-1. If the fuel is irradiated to 20% burnup is about 1.4 x 1027m-2 and D is about 140 dpa. This irradiation takes about 5.4 x 107 s or 20 months at full power. These conditions are typical of the centre of the core and represent the full extent of the irradiation suffered by any of the structural material that is removed and replaced along with the fuel (i. e. cladding, subassembly wrappers, etc.). Any material in the core that is not replaced along with the fuel, such as the control rod guides, suffers a higher fluence. It is usual to design the core so that all of its structure can be replaced as necessary.