Two-interstitial Model Research Articles

Irradiation-induced defects in thin aluminium films studied by 1/f noise

The paper reports on the recovery of irradiation-induced defects in thin aluminium films as studied by measurements of the electrical 1/f noise. The defects are produced by irradiation with 1 MeV electrons at 10 K, which results in a strong increase of the noise. Subsequent isochronal annealing at progressively higher temperatures causes the 1/f noise measured at 10 K to recover in discrete steps which occur at the same temperatures as the well-known recovery stages of the irradiation-induced electrical resistivity increase. In the noise measurements at 40 K, however, an additional recovery step without analogue in the recovery spectrum of the electrical resistivity is observed at 70 K. The temperature dependence and annealing behaviour of the 1/f noise may be understood in terms of thermally activated motion of defects in a distorted lattice potential. A microscopic explanation of the present observation as well as of earlier measurements on Cu by Pelz and Clarke within the framework of the two-interstitial model of radiation damage of metals is presented.

The nature of the C-defects in nickel and their r�le in the interpretation of radiation damage in metals

In previous Perturbed-Angular-Correlation (PAC) studies of the γ-γ emission of 111In probe nuclei in cold-worked or particle-irradiated nickel, it has been found that thermal annealing in the temperature regime of recovery stage III leads to the formation of so-called C-defects (Cubic defects). This is indicated by the occurrence of a new frequency of about 80 Mrad/s, in addition to the frequency (≈200 Mrad/s) that is due to 111In on substitutional sites. Obviously, the C-defects are complexes consisting of 111In and the intrinsic point-defect species that migrates freely in recovery stage III. Therefore, they have played an important role in the long-standing controversy on whether the recovery-stage-III defects are vacancies (one-interstitial model) or self-interstitials (two-interstitial model). The present paper reports on a novel experimental effort to reveal the nature of the C-defects by combining PAC studies on nickel samples differently pretreated in a systematic way, investigations of the Extended X-ray Absorption Fine Structure (EXAFS) on In-doped nickel, and measurements of the decay rate of 111In nuclei in the Electron-Capture-Induced Decay (ECID). On the basis of the results of these experiments it is concluded that the defects trapped by substitutional 111In atoms (Ins) in recovery stage III are self-interstitials (I), as expected according to the two-interstitial model. Moreover, there is evidence that the C-defects are In interstitials on tetrahedral sites (Ini) that form exclusively in the vicinity of the specimen surface from Ins − I pairs via the reaction Ins+I → Ini.

The Modified Two-Interstitial Model A Review

The Modified Two-Interstitial Model A Review

Investigation of Intrinsic Point Defects in Metals by Nuclear Quadrupole Double Resonance

Abstract The paper reviews the principal features of the Nuclear Quadrupole Double Resonance (NQDOR ) technique, with particular emphasis on its application to the investigation of imperfections in cubic metals. NQDOR permits measurements of the electric field gradients (EFG) at quadrupole-moment-carrying nuclei in the neighbourhood of point defects and thus to obtain “fingerprints” of these defects. An NQDOR facility set-up at the M ax-Planck-Institut für Metallforschung in Stuttgart is described. It has been used to study the intrinsic defects introduced into Cu and dilute Cu/Be alloys by low-temperature irradiation with electrons or protons or by cold-work. It is shown that all well-resolved irradiation-induced EFG observed in the present work are due to one kind of defect only, which is identified as the <100> dumbbell self-interstitial. When considered together with measurements of the electrical resistivity on the same specimens, the annealing behaviour of the NQDOR lines supports the so-called two-interstitial model of radiation damage in face-centred cubic metals rather than the one-interstitial model.

The Modified Two-Interstitial Model

The Modified Two-Interstitial Model

Rapid-pair-enhanced diffusion in α-Zr and its integration into the point-defect scenario in h.c.p. metals

Abstract After a brief review of our present knowledge on intrinsic point defects in h.c.p. metals, an interpretation of self-diffusion and foreign-atom diffusion in both the bulk and the grain boundaries of α-Zr is presented. It is demonstrated that rapidly diffusing foreign-atom–vacancy pairs play an outstanding role. In particular, Fe-atom–vacancy pairs control not only the bulk and grain-boundary diffusion of Fe but also the bulk self-diffusion in α-Zr. Atomistic models of the configurations, the formation and the diffusion of rapid foreign-atom–vacancy pairs are proposed. Finally, it is concluded that, on the one hand, α-Zr shows the anomaly of rapid-pairenhanced diffusion whereas, on the other hand, isolated monovacancies in α-Zr behave normally. For instance, they undergo long-range migration in the recovery stage IV (450–550 K) in accordance with the so-called two-interstitial model.

Injection of self-interstitials into a single crystal of nickel: One-interstitial vs. two-interstitial model

"In case the reader is not aware of it, it should be pointed out that there is, and has been, a long-standing controversy on the interpretation of the recovery stages in fcc metals. I suspect that after this conference there will still be a controversy!" Twenty years after these prophetic words were spoken by J.W. Corbett [i], Frank and Seeger [2] addressed the configuration of a cubic lattice defect in Ni that was discovered in a DPAC measurement on ~11In [3]. They argue that the defect must be a mixed interstitial, contrary to the original interpretation according to which the defect consists of an 111In atom at the centre of a tetrahedron of four nearest-neighbour vacancies. They further argue that, since the defect is formed in recovery stage III, its structure is a sensitive test of the existing defect models: the one-interstitial model according to which recovery stage III is associated with vacancy migration, and the two-interstitial model which denies any vacancy mobility in recovery stage III. In the following we report on the annihilation of C-defects by self-interstitial injection. We prepared a single crystal of Ni so that about 30% of the implanted *11In atoms were associated with the cubic defect, and bombarded it subsequently with i00 eV Xe ions to stepwise increasing doses ranging from 1.10'5-1.1017 cm -2. The Xe ions transfer at most 3.7 times the displacement energy to the host lattice atoms, and eventually initiate a displacement collision sequence leaving a vacancy at the surface. The self-interstitials injected in this way into the Ni lattice will move on

Identification of the C-defect in nickel found by means of PAC

The annihilation of C-defects in nickel by self-interstitials was observed in a γ-γ perturbed angular correlation experiment. The results corroborate the assigned vacancy character of the C-defect and, consequently, prove that recovery stage III in nickel is associated with vacancy migration. This conclusion has far-reaching consequences for the acceptability of either the one or two-interstitial model of defects in metals.

Proposal of an EXAFS experiment for the identification of the C-defect in nickel found by PAC

An EXAFS experiment is proposed that should permit an unambiguous decision between the two remaining alternatives for the configuration of the C-defect in nickel, a defect found by means of PAC studies using 111In probes. It is shown that such a decision is likely to have far-reaching consequences for the acceptability of either the one- or the two-interstitial model of defects in metals. Recent evidence from other techniques pertaining to this question is reviewed.

The influence of temperature on void-lattice formation and swelling

Abstract In two previous papers (see refs. [2] and [3]) the present authors have presented a theory of void lattices that is based on the two-interstitial model of point defects in metals and explains void-lattice formation in terms of a self-organization far from thermal equilibrium. Major features of the void lattices (e.g., the identity of the structure and orientation of void lattices and their host crystal lattices, the growth saturation and size uniformity of voids in a void lattice, the displacive stability of void lattices within a wide parameter range) are traced to a common cause—the existence of one-dimensionally migrating crowdion interstitials. In the present paper, the void-lattice theory is extended by including reactions among point defects (vacancy-interstitial recombination, athermal conversion of interstitials from the crowdion to the dumbbell configuration, and vice versa) as well as the evaporation of vacancies from dislocations and voids. It is shown that this extension accounts for the temperature dependences of swelling and void-lattice formation. For Mo and Ni it is demonstrated that, in accordance with observations, an optimum temperature for void-lattice formation exists which is located on the low-temperature side of the regime of strong swelling.

Rate‐Equation Treatment of PAC‐Monitored Defect Reactions in Irradiated Metals

AbstractThe variations of the fractions of defect‐occupied PAC probe atoms in low‐temperature electron‐irradiated metals during isochronal annealing up to the completion of recovery stage III are computer‐simulated within the framework of a rate‐equation approach. It is taken into account that the Stage‐IE interstitials migrate three‐dimensionally in the one‐interstitial model (OIM) but one‐dimensionally in the two‐interstitial model (TIM). The effect of the thermal conversion o crowdions and the existence of “caged” crowdion–PAC‐atom pairs, which are characteristic of the TIM, are investigated in detail. A comparison with experimental data shows that several observations may be understood in terms of the TIM but not of the OIM.

Simultaneous measurement of residual resistivity recovery and magnetic after-effect in high-purity ?-iron

Magnetic after-effect measurements were performed on high-purity α-iron after electron irradiation at 80 K. Using theLC-oscillator technique for measuring the magnetic after-effect we obtained simultaneously information about the recovery of the residual resistivity by analysing the permeability of the specimen at 4.2 K. The recovery in Stage IE and Stage III are briefly discussed in terms of the two-interstitial model.

Limited growth, displacive stability and size uniformity of voids in a void lattice

In a previous paper [J. Nucl. Mater. 137 (1985) 7], the present authors have shown that void-lattice formation in crystals under irradiation is a non-equilibrium disorder-order phase transition that is intimately related to the existence of a one-dimensionally diffusing, metastable excited self-interstitial state (crowdion), as assumed in the two-interstitial model. In contrast to all other models of void-lattice formation, this theory explains in a natural way why void lattices possess the same structure and orientation as the host crystal lattices. In the present work, the theory is extended to the evolution of void lattices after their formation. The three most characteristic features of void-lattice evolution, viz., the occurrence of void-growth saturation, the size uniformity of voids in a void lattice, and the displacive stability of void lattices within a wide range of the governing parameters, are not only predicted by the present theory but can be traced to a common cause — the existence of one-dimensionally migrating crowdions, previously shown to be the cause of void-lattice formation.

Interstitials in Copper-Zinc Alloys

In Cu-30 Zn alloys during irradiation with 2-MeV electrons from a Van de Graff generator, the electrical resistivity first decreases due to radiation-enhanced ordering and then increases due to the formation of very small interstitial clusters. The activation energy during irradiation for both processes is approximately Q/subirr/ = 0.3/sub 7/ eV and is interpreted as half of the migration energy of freely migrating interstitials. For irradiation temperatures below 75/sup 0/C, a second resistivity increase is found that is attributed to the formation of stable interstitial clusters. The observed radiation-enhanced diffusion rates below ambient temperature are many orders of magnitude smaller and larger than those predicted by the one- and two-interstitial models, respectively, and these rates are in agreement with the predictions of the modified two-interstitial model.

A theory of void-lattice formation

A theory of void-lattice formation in crystals under irradiation is presented that is based on the so-called two-interstitial model and makes use of no additional assumptions. It is shown that the formation of void lattices having the same crystallographic type and orientation as the host crystal lattices, as found by experiment, is intimately related to the existence of a one-dimensionally diffusing metastable excited self-interstitial state (crowdion). The transition from a random assembly of voids to a regular void lattice takes place if the void number density is so high that in their excited state self-interstitials can traverse the mean void distance before returning to their ground state. If the void density is lower and does not increase in the course of irradiation, the random void arrangement reaches a steady state. From the view-point of thermodynamics, void-lattice formation is a non-equilibrium phase transition in an open system. It is an example of self-organization of an ordered structure in a dissipative system in the sense of synergetics.

Has a neutrino-recoil experiment settled the controversy about radiation damage in metals?

Abstract The paper discusses recent perturbed γ-γ angular correlation (PAC) studies [Metzner and collaborators, Phys. Rev. Lett. 53, 290 (1984)] of the 111In/111Cd decay in Cu that had been damaged by the neutrino recoils associated with the decay of solute 111Sn atoms to the PAC mother nuclei 111In. It is argued that these experiments may settle a long-standing controversy on radiation damage in metals in favour of the so-called two-interstitial model.

Confirmation of the one-interstitial model for α-iron from positron annihilation experiments in thermal equilibrium on pure and carbon doped samples

The value of the vacancy migration enthalpy in α-iron has been the subject of a long standing controversy. In the one-interstitial model, the value of 0.55 eV has been put forward, whereas in the two-interstitial model a value of about 1.3 eV is given. In a review paper l, it was concluded that the majority of experimental data is in favour of the one-interstitial model. It was also pointed out that, if one accepts this model, an important problem remained to be solved: the vacancy migration enthalpy that can be obtained by subtracting the vacancy formation enthalpy from the self diffusion enthalpy (provided that self-diffusion is driven by a vacancy mechanism), was more than twice the vacancy migration enthalpy of the one-interstitial model. We report here on research we performed concerning this problem. The values of the enthalpies of vacancy formation and self diffusion were carefully re-investigated, taking into account: 1) the influence of ferromagnetic ordering, and 2) the influence of the strong interaction between residual carbon atoms and vacancies. To determine the ferromagnetic self diffusion enthalpy QS D,f, we used reliable literature data on self diffusion in iron. The main conclusion of our analysis is that only an upperlimit to QS D,f, can be given 2: QS D,f ⩽2.75 eV. We also performed positron annihilation measurements in thermal equilibrium on pure and carbon doped (50 and 750 appm) samples to determine the ferromagnetic vacancy formation enthalpy H V f,f. In very pure iron no trapping of positrons is observed below the Curie point, so that H V f,f cannot be determined. However in carbon-doped samples the carbon-vacancy pair can be used as a probe to determine H V f,f. We obtained: H V f,f = (2.0 ± 0.2) eV. This value is the first fully experimental determination of this parameter. By combining the data given above, we conclude that an upperlimit to the ferromagnetic vacancy migration enthalpy H V m,f is: H V m,f ⩽ 0.95 eV. On the other hand, it can be shown 3 that H V m,f ⩾ 0.16 eV. We therefore conclude that there is no longer an inconsistency between the one-interstitial model and the vacancy migration enthalpy derived from thermal equilibrium measurements.

Void growth and vacancy migration enthalpy in alpha-iron

Abstract The migration enthalpy of monovacancies in α-Fe, H1vm, is deduced from the growth of voids during electron irradiation as studied by Kitajima and co-workers in a high-voltage electron microscope. In this way H1vM = (1.3+0.1−0.3) eV is obtained, in excellent agreement with H1VM = (1.28±0.25) eV as deduced by Schaefer et al. from high-temperature equilibrium experiments. The disagreement between H1VM and H111= (0.55±0.05) eV, the activation enthalpy in recovery stage III of %aL-Fe after irradiation or cold-work, excludes the one-interstitial model but is in accordance with the two-interstitial model of point defects in metals.

Interpretation of damage-rate measurements on copper during long-time neutron irradiation at elevated temperatures

Electrical-resistivity measurements on copper performed during a 107-day irradiation with fission neutrons at 340 K by Chaplin and co-workers are compared with electron-irradiation damage curves measured at Stage II and Stage III temperatures, respectively. Though an interpretation of the data of Chaplin et al. in terms of the one-interstitial model is formally possible, serious contradictions appear if this interpretation is extended to the other experiments. By contrast, in the two-interstitial model all damage-rate experiments considered can be interpreted in a quantitatively consistent manner. This is an example that “interpretations” limited to isolated observations are meaningless and therefore not suitable to discriminate between current models of radiation damage in metals.

Hyperfine interaction evidence for the existence of two distinct types of self-interstitials in face-centred cubic metals

Recent perturbed-angular-correlation and Mössbauer-effect measurements have shown that self-interstitials that are mobile at low temperatures are not produced during low-temperature plastic deformation of A1. This result is in serious conflict with the so-called one-interstitial model of defects in metals and in full accordance with the two-interstitial model.