The NRT displacement model is most correct for irradiation such as 1 MeV electrons, which produce only low-energy recoils and, therefore, the FPs. At higher recoil energies, the damage is generated in the form of displacement cascades, which change both the production rate and the nature ofthe defects produced. Over the last two decades, the cascade process has been investigated extensively by molecu­lar dynamics (MD) and the relevant phenomenology is described in Chapter 1.11, Primary Radiation Damage Formation and recent publications.43,44 For the purpose of this chapter the most important findings are (see discussion in the Chapter 1.11, Primary Radiation Damage Formation):

• For energy above ^0.5 keV, the displacements are produced in cascades, which consist of a collision and recovery or cooling-down stage.

• A large fraction of defects generated during the collision stage of a cascade recombine during the cooling-down stage. The surviving fraction of defects decreases with increasing PKA energy up to ~10keV, when it saturates at a value of ^30% of the NRT value, which is similar in several metals and depends only slightly on the temperature.

• By the end of the cooling-down stage, both SIA and vacancy clusters can be formed. The frac­tion of defects in clusters increases when the PKA energy is increased and is somewhat higher in face-centered cubic (fcc) copper than in bcc iron.

• The SIA clusters produced may be either glissile or sessile. The glissile clusters of large enough size (e. g., >4 SIAs in iron) migrate 1D along close — packed crystallographic directions with a very low activation energy, practically a thermally, similar to the single crowdion.45,46 The SIA clus­ters produced in iron are mostly glissile, while in copper they are both sessile and glissile.

• The vacancy clusters produced may be either mobile or immobile vacancy loops, stacking-fault tetrahedra (SFTs) in fcc metals, or loosely corre­lated 3D arrays in bcc materials such as iron.

As compared to the FP production, the cascade damage has the following features.

• The generation rates of single vacancies and SIAs are not equal: Gv = Gi and both smaller than that given by the NRT standard, eqn. [2]: Gv, Gi <Gnrt.

• Mobile species consist of 3D migrating single vacancies and SIAs, and 1D migrating SIA and vacancy clusters.

• Sessile vacancy and SIA clusters, which can be sources/sinks for mobile defects, can be formed.

The rates of PD production in cascades are given by

Gv = Gnrt(1 — er)(1 — ev) [4]

Gi = Gnrt(1 — er)(1 — Єі) [5]

where er is the fraction of defects recombined in cascades relative to the NRT standard value, and ev and ei are the fractions of clustered vacancies and SIAs, respectively.

One also needs to introduce parameters describ­ing mobile and immobile vacancy and SIA-type clusters of different size. The production rate of the clusters containing x defects, G(x), depends on cluster type, PKA energy and material, and is connected with the fractions e as

^xGa(x)=eaGNRT(1 — er) [6]

x = 2

where a = v, i for the vacancy and SIA-type clusters, respectively. The total fractions ev and Єі of defects in clusters are given by the sums of those for mobile and immobile clusters,

ea = ea+ea [7]

where the superscripts ‘s’ and ‘g’ indicate sessile and glissile clusters, respectively. In the mean-size approximation

(x) = d(x — <x4» [8]

where j = s, g; 8(x) is the Kronecker delta and <xoj) is the mean cluster size and

G = <xa)-1GNRT(1 — er)ei [9]

Also note that although MD simulations46 show that small vacancy loops can be mobile, this has not been incorporated into the theory yet and we assume that they are sessile: evg = 0 and esv = ev.