p. G. KLEMENS 



to remove a particular imperfection depends upon the nature of the imper- 

 fection, and by noting corresponding changes in the resistance as the anneal- 

 ing temperature is increased, it is possible to identify a number of recovery 

 stages, and to correlate the changes in resistance (and in other properties, 

 if they are also measured) with whatever imperfection has been removed. 

 In copper, five (or possibly six) such recovery stages have been observed, 

 and the problem is to identify the imperfections corresponding to each stage. 

 All but the last two stages occur at or below room temperature, and can 

 only be observed if deformation or irradiation is carried out at low tem- 

 peratures, otherwise annealing proceeds during the damaging process^"' i^- ^^^ 



In recent years great attention has been paid to the first annealing stage, 

 occurring at about 30"K for materials which have been irradiated at or near 

 liquid helium temperatures. It is now believed that this stage corresponds 

 to the removal of interstitial atoms, which are highly mobile except at the 

 lowest temperatures. Thus, in this temperature region, there is no annealing 

 of copper which was plastically deformed at helium temperatures i=^, when 

 one would not expect interstitials; however, it does occur after deuteron 

 irradiation^*. The quantitative interpretation is, however, somewhat 

 uncertain. 



The group under Koehler (University of Illinois), using high-energy 

 deuterons, has related changes in the electrical resistance to changes in 

 density and lattice spacing during that first recovery stage ^ 2, is Their 

 results generally support the interpretation of stage I in terms of the removal 

 of vacancy interstitial pairs, and allows an estimate of the electrical 

 resistivity due to such pairs. 



There is little uncertainty in the theoretical value of the electrical resis- 

 tivity due to vacancies in copper, for it arises mainly from their charge 

 defect^^'^^ and is about 1 [j.ohm-cm per atomic per cent. The resistivity of 

 interstitials, however, is governed largely by the lattice distortion around 

 them, and is much more difficult to calculate. Estimates of this resistance 

 range from 1 -5 [xohm-cm (Potter and Dexter^^) to 10 jxohm-cm (Overhauser 

 and Gorman 1^) per atomic per cent. From the relation between the electrical 

 resistivity increase and the lattice expansion, Simmons and Balluffi estimate 

 the resistivity of vacancy-interstitial pairs (Frenkel defects) to be about 

 4 [j.ohm-cm per atomic per cent, but the number of defects thus deduced is 

 only about one-sixth of the concentration calculated from the displacement 

 theory. ^ 



Corbett, Denney, Fiske and Walker^o bombarded copper with fast 

 electrons at liquid helium temperatures and studied changes in electrical 

 resistivity, as well as annealing behaviour. In this case there are single 

 displacements only, and very few displacement clusters or spikes, so that the 

 interpretation should be simple, and calculations of the number of displace- 

 ments relatively reliable. They found that 90 per cent of the resistance 

 increase disappeared during stage I, confirming that interstitials combine 

 with vacancies. However, they found the apparent change of resistivity to 

 be only 1 • 5 [aohm-cm per atomic per cent of Frenkel defects. 



Blewitt's group at Oak Ridge have now facilities for neutron irradiation 

 at liquid helium temperatures^^. Blewitt, Coltman, Klabunde and Noggle^^ 

 concluded from the annealing kinetics and the sensitivity of annealing rates 

 19 277 



