Point Defects In Copper Research Articles

The thermal conductivity of defected copper at finite temperatures

Copper-based materials have been selected as heat-sink materials in some nuclear fusion reactors, where a great number of structural defects will be created due to the irradiation of energetic particles. In the practice of fusion reactors, an important issue is how the defects in copper heat-sink material affect its thermal transport property. However, there is no systematic study on the relation between thermal conductivity and the concentrations of various point defects in copper up to now. Our theoretical calculations show that the thermal conductivity ($$ \kappa $$) of Cu is significantly reduced by the presence of vacancies, self-interstitial atoms, SIA–vacancy pairs and the doped impurity tungsten (W) at finite temperatures. Among these concerned point defects, the doped impurity W plays the strongest role in impeding the thermal transport of conduction electrons, and the presence of 4% W impurity in Cu leads to about 80% reduction in $$ \kappa $$ as compared to that of the defect-free Cu system ($$ \kappa_{0} $$). Furthermore, it is revealed that during the cascade, the thermal transport property of Cu changes as the structural defects evolve, and the thermal transport of electrons is impeded significantly in the initial stages of cascade. In addition, our calculations show that the Wiedemann–Franz law is still valid in defected copper systems.

Simulation of mechanical response of point defects in copper

A molecular dynamics simulation has been performed to investigate the dynamical nature and the mechanical response of self-interstitials in copper. The embedded-atom method potential developed by the present authors is adopted to express the atomic interaction in crystals. The static configuration and the interaction with the elastic vibration are simulated, and the internal friction by the interstitial is evaluated from the damping of elastic vibration. The motion of interstitial atoms in the vibrating crystal is analyzed through the trajectory of the motion of atoms. The trajectory for the thermal motion of interstitial atoms at elevated temperatures is also derived and the thermal migration of interstitials is investigated.

Effect of Coulomb explosion on track formation in metals irradiated by heavy ions

The existing descriptions of the process of track formation in metals bombarded with high-energy heavy ions are usually based on the T-spike model. However, this model fails to explain high temperatures developed in some target materials (e.g., in copper). We present a comparative analysis of track formation in metals under the action of heavy ion bombardment, as described using the Coulomb explosion model and the T-spike model in various modifications. Both models are used to calculate changes in the temperatures of the electron and ion subsystems in the track region in amorphous alloy Fe85B15) and copper targets bombarded with identical high-energy (E > 1 MeV/nucleon) heavy ions. The results show that the Coulomb explosion model predicts stronger heating of the ion subsystem in the track region (with the possible formation of a melt-through zone) as compared to the T-spike model. The formation of point defects in copper as a result of the ionization losses has been also described using the two models and compared to the available experimental data. The Coulomb explosion model provides for a more adequate description of track formation as compared to the T-spike model.

Agglomeration of point defects in copper after neutron irradiation at 4.6 K

Discussion of Huang scattering and the interstitial clusters in copper single crystals after neutron irradiation.

Influence of impurities on the de haas‐van alphen effect II. Application to point defects in copper

AbstractA recent theory for the effects of localized defects in metals on the amplitudes and the periods of the de Haas‐van Alphen oscillations is applied to point defects in copper. The parameters characterizing a defect in the employed model are fixed by means of the neutrality condition and the residual resistivity. The calculations of the Dingle temperatures and the changes in period are carried out for the most important extremal orbits on the Fermi surface of copper as given by Halse. The agreement with the available experimental data is satisfactory. The calculated changes in the de Haas‐van Alphen periods are shown to differ not very much from those obtained in the rigid‐band model.

On values of activation energy for migration of single vacancies in metals

Abstract New theoretical and experimental data on activation energies of migration of point defects in copper, cadmium, α-iron and tungsten have been analysed. Analysis revealed a close relationship between some activation processes in the crystalline metals and the phenomena of melting and polymorphic transformation and provided further confirmation that activation energies for migration of single vacancies for all pure metals can be calculated by eqns. (1) and (3) in the text.

Effect of Point Defects in Copper on the Anomalous Transmission of X Rays

Anomalous x-ray transmission (Borrmann) measurements were made at 4.2 \ifmmode^\circ\else\textdegree\fi{}K on nearly perfect copper single crystals before and after irradiation at 20 \ifmmode^\circ\else\textdegree\fi{}K with 3-MeV electrons (total integrated flux 0.87 \ifmmode\times\else\texttimes\fi{} ${10}^{18}$ ${\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{s}/\mathrm{c}\mathrm{m}}^{2}$). The intensity in the diffracted direction was measured for the (111), (222), (333), and (220) reflecting planes. The measured intensity changes were (1.2 \ifmmode\pm\else\textpm\fi{} 0.4)%, (4.5 \ifmmode\pm\else\textpm\fi{} 0.6)%, (8.9 \ifmmode\pm\else\textpm\fi{} 0.8)%, and (4.1 \ifmmode\pm\else\textpm\fi{} 0.8)%, respectively. The observed intensity changes are consistent with predictions if it is assumed that the damage consists of isolated interstitials and vacancies. Possible configurations of the interstitial are discussed. Measurements after annealing at 80 and 300 \ifmmode^\circ\else\textdegree\fi{}K were made. The measurements are consistent with small defect clusters forming when the irradiated crystals was heated to 80 \ifmmode^\circ\else\textdegree\fi{}K, and some clusters remaining after annealing at room temperature.

Elastic Field of a Point Defect in a Cubic Medium and its Interaction with Defects

Three equal orthogonal double forces without moment aligned along the cubic axes are used as a model for a point defect in a cubic medium. The method of Fourier transforms is used to obtain the solution for the displacement and stress fields. The solution is presented in a polynomial form. The elastic interaction between a point defect and an edge dislocation is computed for copper by making the displacement of the edge dislocation against the stress field of the defect. The interaction with the physically significant [112̄] edge dislocation on the (111) plane in copper is presented. The computer program was verified by the agreement of its results with those for the hypothetical [001] edge dislocation on the (010) plane, for which the stresses can be calculated in closed form. Near the slip plane, the calculated anisotropic interaction was almost twice that of a corresponding isotropic one. The elastic interaction between two point defects in copper is calculated, indicating regions of attraction of like defects along the cube axes and repulsion along the cube diagonals. Eshelby's perturbation analysis for materials with slight anisotropy predicts qualitatively similar effects, but the repulsion is much greater than that predicted by his approximate analysis.

Magnetoresistivity of metals II. Application to point defects in copper

The general theory given previously is applied to copper single crystals containing various kinds of point defects. The matrix elements of the scattering potential with Wannier functions, which determine the transition probability, are chosen such as to satisfy the charge neutrality condition (Friedel's sum rule) and to give a prescribed electrical resistivity in zero magnetic field. Numerical calculations are carried out for the Fermi surface due toShoenberg andRoaf. The computed Kohler and rotation diagrams for magnetoresistivity, transverse-even effect, and Hall effect at low temperatures are in satisfactory agreement with measurements. The influence of different anisotropic scattering mechanisms and of the anisotropic Fermi surface is discussed in terms of the Kohler diagrams and rotation diagrams.

Effect of Plastic Deformation on the Recovery of Stage I after Neutron Irradiation

AbstractThe recovery of point defects in copper after fast neutron irradiation at 15 °K was studied by measurements of residual resistivity. Especially, the effect of deformation before and after low‐temperature irradiation on the recovery spectrum was studied. The amount of stage I recovery was reduced by 20% by deformation after irradiation where the deformation was such that only 2% of atomic planes were swept by dislocations. This result suggests the transformation of some of stage I defects into more stable ones due to deformation and the fairly large distance between the interstitial and vacancy in a close pair of stage I. Also, the recovery spectra observed in the present experiments seem to show the annealing of interstitial clusters in stage II (≈︁ 130 °K recovery peak) in cold‐worked copper.

Point Defects in Copper

The atomic configurations and energies for point defects in copper have been studied theoretically using a classical model. The atoms near the defect are treated explicitly while the remainder of the crystal is treated as an elastic continuum with atoms imbedded in it. A Born-Mayer repulsive force law, $A{e}^{\ensuremath{-}\ensuremath{\alpha}r}$, is assumed to act between nearest neighbors. Vacancies, interstitials, di-vacancies, and di-interstitials have been considered. Configurations are found by choosing a starting configuration roughly approximating the situation under consideration, and an iterative process of successively adjusting the value of each variable occurring in the equation for energy such that the magnitude of the generalized force acting on it is minimized. The energy calculations include changes in bond energy in the discrete region, energy in the elastic field, and work done against cohesive forces, but neglect changes due to the redistribution of electrons. Various aspects of the model and method of calculation have been investigated, and the effects of electron redistribution are discussed. Predicted activation energies for motion of interstitials and vacancies are 0.05 and 0.43 eV, respectively. An upper limit of 0.26 eV has been found for the activation energy for migration of di-interstitials. The isolated interstitial has been thoroughly investigated, and eight well-defined equilibrium configurations have been found. Only one of these is stable, being the case in which two atoms are symmetrically split in the $〈100〉$ direction about a vacant normal lattice site. The configuration in which the interstitial is located at a body center is found to be a local maximum, but the saddle point configuration for migration of interstitials is quite close to it.

Gitterdeformationen um Zwischengitteratome, Leerstellen, Zwischengitteratom-Paare und Frenkel-Paare in Kupfer

The distortions of the lattice around a number of different point defects in copper are calculated with the help of the electronic digital computer Z 22 using a general method developed by TEWORDT 3. In the case of an interstitial which is sited at the center of an elementary cube about 500 atoms and in the case of a vacancy about 50 atoms are treated as discrete particles. The elastic solutions which are joined to the displacements of the discrete particles are determined for an anisotropic continuum. The changes in volume of the crystal arising from the interstitial are found to be 0.911, 1.219 and 1.441 atomic volumes respectively for the MORSE potential VM and the two BORN-MAYER potentials V1, V2 we have used [see Eqs. (25) — (27)]. The corresponding values for the vacancy are —0.441, — 0.378 and —0.321 atomic volumes. Further we caluclate the relaxation of the lattice around three configurations of interstitial pairs with axes in the (1,0,0), (1,1,0) and (1,1,1) directions considering about 100 atoms as movable in each case. The contributions to the binding energies arising from the potential V1 turn out to be 0.81, —0.18 and —0.26 eV respectively. This strongly indicates that interstitial pairs can attract one another. Finally the stability of the 10 closest interstitial-vacancy pairs (FRENKEL pairs) is examined. All pairs smaller than 1.5 lattice constants in diameter are found to be instable, the other pairs are stable and give a discrete spectrum of BORN-MAYER energies. The results are discussed in connection with recent experiments in the field of radiation damage.