The creation of a stable FP requires that a lattice atom receives an energy greater than Tm, which is the minimum displacement energy. This value has been determined experimentally in many materials by measuring the change in some physical property, such as electrical resistivity or length change, as a function of maximum recoil energy of a target atom. Such experiments are practical only for electron irradiations for which recoil energies can be kept low, but with the irradiation particles still penetrating deeply into, or through, the specimen. Typical values are shown in Table 2.

As a crystal is not homogeneous, the threshold energy depends on the crystallographic direction in which the knock-on atom recoils. The anisotropy of the threshold energy surface has been mapped out in various crystals by measuring the production rate of defects as a function of both the electron energy, near threshold, and the orientation of single crystalline

specimens with respect to the electron beam direc­tion.15’16 The total cross-section for FP production rate is given by the expression

2p я/2

dff(g2; £1) df 2

d02 2p [19]

0 0

v(02, F2; T)dd2

where the subscripts 1 and 2 refer to incoming elec­tron and recoiling ion, respectively, and 0b F1, 02, F2 are the polar and azimuthal angles of the electron beam relative to the crystal axis; 02, f2, are these same angles relative to the beam direction; v is the anisotropic damage function. Near threshold, v = 1 for T> Tn, and 0 for T< Tm. By measuring the production rate for many sample orientations and energies, the damage function can be obtained using eqn [19], although various approximations are required in the deconvolution. The results are illustrated in Figure 10 for Cu.17 It is noteworthy that the minimum threshold energy is located in the vicinity of close-packed directions. This is also true for bcc metals. The anisotropy reflects the basic mechanism of defect production, viz., replacement collision sequences (RCSs), which had been identified by molecular dynamics simulations as early as 1960.1

(a)

The primary knock-on atom in an RCS recoils in the direction of its nearest neighbor, (110) in fcc crystals, and replaces it, with the neighbor recoiling also in the (110) and replacing its neighbor. A vacancy is left at the primary recoil site, and an interstitial is created at the end of the sequence. Replacement sequences are the most efficient way to separate the interstitial far enough from its vacancy, ^2-3 interatomic spacings, for the FP to be stable. While the lengths of these sequences are still debated, it is clear that the mechanism results in both defect pro­duction and atomic mixing. For neutron irradiations, higher energy recoils are numerous, and the average displacement energy, Ed, becomes more relevant for calculations of defect production (see eqn [1]). This value, which can be obtained by averaging over the threshold displacement energy surface, is usually dif­ficult to determine experimentally. A rough estimate, however, can be obtained from, Td ~ 1.4 Tm in fcc metals and 1.6ЕП in bcc metals.19