A. Sosin

Defect mobility and reaction: Diffusional and rate theory formulations in one and three dimensions

Abstract The migration of defects, leading to eventual reaction, is analyzed on the basis of diffusion theory and compared with chemical rate theory. A diffusional treatment is carried out in detail and in special cases of particular interest. Correlations between interstitials and vacancies, typical of metals following electron irradiation, are examined. Trapping by impurities and dislocations, thermal conversion, and high temperature bombardment are also treated. In each case, formulations are developed along both one- and three-dimensional diffusion models. These alternative results are compared with experiments, particularly annealing in copper irradiated by electrons at low temperature. The results support the conclusion that the defect which migrates in Stage I diffuses in three dimensions.

Analysis of the recovery of dilute alloys of gold and silver in copper after low temperature electron irradiation

Abstract The influence of dilute concentrations of both Au and Ag atoms on the stage I and stage I1 annealing structure in copper has been investigated using electrical resistivity measurements. An excellent agreement of the stage Id and I, experimental data with the theoretical predictions of the SimpsonJosin full diffusional theory is obtained; this analysis determines the capture radius of solute Au atoms in Cu to be 1.7 ± 0.1 I.c. and that of solute Ag atoms in Cu to be 1.8 ± 0.1 I.c. (in comparison with an interstitial-vacancy capture radius of 3.2 1.c.). Four well-defined recovery substages are observed in the dilute alloys during stage I1 recovery. An interpretation of each of these substages, consistent with experimental results, is presented. The following processes were observed to occur during stage 11: The release of trapped interstitial atoms from trapping centers formed by the proximity of a gold atom near a vacancy; the rearrangement of trapped interstitials to new trapping positions at imp...

THERMAL CONVERSION OF INTERSTITIALS.

Abstract Thompson and Buckc(l) have recently reported the results of experiments in pure copper which appear to have unusual significance with regard to providing a resolution of the long-standing problem of assignment of recovery stages in metals. Their major observations are summarized in Figure 1. The most notable characteristics which may be observed from this figure or otherwise reported by Thompson and are:

Defect retention in copper during electron irradiation at 80°K

Abstract Electron irradiation damage in copper at 80°K is analyzed by a reciprocal damage rate approach and by a method relating normalized damage and normalized fluence. The latter is more sensitive to changes in effective trapping concentrations: the unsaturable trap model has not been found to strictly hold for any sample irradiated here or described in the literature. More importantly, the increase in relative trapping radius with respect to the nucleation of interstitials varies at least by a factor of 30 according to sample pre-irradiation treatment. These results and those of stage II irradiations provide information regarding the relative size and nature of trapping centers. Trapping probabilities based upon interstitial diffusion in both the correlated and uncorrelated “stages” ID and IE, rather than IE alone, predict some nonlinear reciprocal damage rate curves-even for constant trapping radii-due to the increasing encroachment of stage IE into ID during irradiation. Values of initial damage rat...

ID-IE recovery in electron irradiated copper. II. Theory

Abstract A complete diffusional analysis of the low temperature, ID-IE post-irradiation recovery stages in copper is presented here. In applying this analysis to experiments, intrinsic defect characteristics are deduced by multi-parameter, minimum deviation fitting. The vacancy capture radius for interstitials is found to be 3.2 ± 0.3 lattice constants, for example. In addition, the shape of the initial interstitial-vacancy separation distribution function has been determined. A single distribution function describes this distribution for irradiation by electrons with energies greater than 0.6 MeV. At lower energies, the function is narrowed.

Low temperature electron-irradiation ofβ-tin

Abstract High purity polycrystalline wires of β-tin have been irradiated at 5 K by 0.7 to 2.0 MeV electrons. Damage was monitored by electrical resistance measurements taken at 4.2 K From a comparison of energy-dependent damage rate measurements with electron displacement cross section curves based on the calculations of O. S. Oen, a threshold displacement energy of 22 ± 2 eV was found. Isochronal anneals revealed three recovery substages below 12 K, accounting for 63% of the total, followed by rather constant recovery up to 180 K. Irradiation at 16 K indicated free interstitial migration below this temperature. A partial characterization of this stage suggests that the largest major substage (10.5 K) may be due to dose pair interstitial-vacancy annihilation, although a correlated recovery model cannot be ruled out completely.

The kinetics of an atom diffusing in one dimension: Hydrogen in quartz

Abstract The time dependence of frequency recovery at 306 K of pulse-irradiated quartz is analyzed and shown to be inconsistent with the diffusion of a specie in three dimensions, but follows well diffusion in one dimension. The main feature which distinguishes these cases is a t −1/2 time dependence of the recovery. No extended region for a t −1/2 dependence is possible in three-dimensional diffusion. An extensive t −1/2 dependence is predicted in one-dimensional diffusion, paralleling the observation that this holds for some three decades in time and over 80% of the recovery. Having established one-dimensional diffusion in frequency recovery, it is shown that acoustic relaxation found at 115 K and a long time component of conductivity recovery found near 300 K, as well as the frequency recovery, all appear to originate in a common mechanism—the diffusion of H+ in one dimension with an activation of approximately ¼ electron volt.

Simulated migration and reaction of correlated point defects

Abstract Monte Carlo techniques are applied to defect migration in the vicinity of a fixed reaction volume. Intended to simulate “stage ID ” annealing of correlated interstitials and vacancies in fcc metals, large reaction spheres of up to 720 atomic volume are employed, with mobile defects in the (100) split configuration symmetrically diffusing from maximum distances of more than twice the capture radius r 0 and for a maximum of 100 jumps. This discrete approach and continuum theory are judged to be equally valid. Random walk recovery probabilities are not a smooth function of initial distance r, but fQr large reaction volumes agree with continuum theory nearly as well for r ∼ r 0 as for r > 2r 0. Absolute agreement is improved as the “dumbbell” separation of the split defect is increased. Recovery due to an extended distribution of defects is obtained by weighting individual walks from distances < 3r 0: the resulting composite annealing curves disallow observation of structure and compare favorably wit...

ID-IE recovery in electron irradiated copper. I. Experimental

Abstract The ID-IE region (30 K–60 K) was studied using sequential isothermals following irradiation near 4.2 K, as a function of electron energy, Ee , and initial defect concentration, Ci. Resistivity was monitored almost continuously, and end point measurements were made at 4.2 K to correct for deviations from Matthiessens rule. Using temperature-compensated (equivalent) annealing times, obtained with the factor exp{−[(0.117 ± 0.003 eV)/kT]}, isothermal sections were joined to yield densely populated extended recovery profiles. The recovery is strongly Ee -dependent for Ee ∼ 0.5 MeV, only slightly between 0.6 and 1.4 MeV. The Ee -dependence is consistent with a model in which i-v pairs of large separations are produced in or near directions. I D is independent of Ci . The Ci -dependence of IE requires i-i and i-impurity interactions. A three-dimensional model is fit to the 0.6 MeV data at 2, 7, and 25 ppm point defect concentration, using a Gaussian separation distribution having a mean separation...

Extension of the dragging model to include elastic point defect-dislocation interactions

Abstract An extension of the Simpson-Sosin defect dragging model to include elastic interactions between point defects and dislocations is presented here. This model, which is compared with internal friction experiments using 99.999% pure Cu, aids in the explanation of: (i) data taken from a sample in which residual damage remain from a previous irradiation, (ii) the proportionality of the decrement (δ) and the modulus defect (M) after anneals in the 750°C to 800°C range, and (iii) the strain-dependence of the calculated value of the number of defects on an average dislocation line—determined for a fixed amount of damage inflicted for irradiation temperatures ranging from 100°K to 330°K. The model fails to correctly predict the frequency dependence of δ and M in the 100 Hz to 2200 Hz range. Use of the model must be made with the restriction that the “effective” dislocation damping term (B)is frequently dependent.