particles. Light ions such as electrons and protons will produce damage as isolated FPs or in small clusters while heavy ions and neutrons produce dam­age in large clusters. For 1 MeV particle irradiation of copper, half the recoils for protons are produced with energies less than ^60 eV while the same number for Kr occurs at about 150 eV. Recoils are weighted toward lower energies because of the screened Coulomb potential that controls the interactions of charged particles. For an unscreened Coulomb inter­action, the probability of creating a recoil of energy T varies as 1/T2. However, neutrons interact as hard spheres and the probability of creating a recoil of energy T is independent of recoil energy.

In fact, a more important parameter describing the distribution of damage over the energy range is a combination of the fraction of defects of a particular energy and the damage energy. This is the weighted average recoil spectrum, W(E, T), which weights the primary recoil spectrum by the number of defects or the damage energy produced in each recoil:

Figure 6 Weighted recoil spectra for 1 MeV particles in copper. Curves representing protons and neutrons are calculated usingeqns[9]and [10], respectively. W(T) for other particles were calculated using Lindhard cross-sections and include electronic excitation. Reproduced from Averback, R. S. J. Nucl. Mater. 1994, 216, 49.

While heavy ions come closer to reproducing the energy distribution of recoils of neutrons than do light ions, neither is accurate in the tails of the distri­bution. This does not mean that ions are poor simu­lations of radiation damage, but it does mean that damage is produced differently and this difference will need to be considered when designing an irradi­ation program that is intended to produce microche­mical and microstructural changes that match those from neutron irradiation.

There is, of course, more to the description of radiation damage than just the number of dpa. There is the issue of the spatial distribution of damage production, which can influence the microchemistry and microstructure, particularly at temperatures where diffusion processes are important for micro­structural development. In fact, the ‘ballistically’ determined value of dpa calculated using such a displacement model is not the appropriate unit to be used for dose comparisons between particle types. The reason is the difference in the primary damage state among different particle types.

W(E, T)

[7]

Ed(E)

[8]

where Tt is the maximum recoil energy given by T = gEi = 4EiM1M2/(M1 + M2)2. Ignoring electron excitations and allowing ED(T) = T, then the weighted average recoil spectra for Coulomb and hard sphere collisions are

ln T — lnEd

[9]

ln T — lnEd

T2 e2

Whs(E, T)= d [10]

Equations [9] and [10] are graphed in Figure 6 for 1 MeV particle irradiations of copper. The character­istic energy, T1/2 is that recoil energy below which half of the recoils are produced. The Coulomb forces extend to infinity and slowly increase as the particle approaches the target; hence the slow increase with energy. In a hard sphere interaction, the particles and target do not interact until their separation reaches the hard sphere radius at which point the repulsive force goes to infinity. A screened Coulomb is most appropriate for heavy ion irradia­tion. Note the large difference in W(E, T) between the various types of irradiations at E = 1 MeV.