Immobile Vacancies Research Articles

Evolution of microstructure in nickel by low-energy deuterium ion irradiation

To understand the characteristics of damage in Ni by low-energy deuterium-ion irradiation, TEM observation and SIMS analysis have been carried out. Because of strong binding between an interstitial and a deuterium atom, nucleation of interstitial loops by deuterium-ion irradiation (0.5 to 5.0 keV) is enhanced. The density and the size of the loops increase with irradiation and the dislocation density exceeds 10 16/m 2 in the region where deuterium ions are injected. In the irradiation at room temperature, immobile vacancies, which act as good traps for deuterium atoms, are accumulated. At 300°C, however, dislocation loops and cavities are formed. Irradiation with 0.5 keV ions produces little displacement damage but platelet-like deuterium clusters are formed due to the localization of the injected deuterium atoms.

Low-temperature irradiation creep of fusion reactor structural materials

Irradiation creep has been investigated in the Oak Ridge Research Reactor in an assembly spectrally tailored to achieve a He : dpa ratio of 12–14:1 appm/dpa in austenitic stainless steels. Temperatures of 60–400°C were investigated to address the requirements of near term fusion devices. It was found that austenitic alloys, especially PCA, have higher creep rates at 60°C than at 330 and 400°C. Since this phenomenon could not be explained by existing theoretical models, a new mechanism was proposed and a corresponding theoretical model was developed. Since vacancy migration times can be a few orders of magnitude longer than the irradiation times in this temperature regime, the immobile vacancies do not cancel climb produced by mobile interstitials absorbed at dislocations. The result is a high climb rate independent of stress-induced preferred absorption (SIPA) mechanisms. Preliminary calculations indicate that this mechanism coupled with preferred-absorption-driven glide at higher temperatures predicts a high creep rate at low temperatures and a weak temperature dependence of irradiation creep over the entire temperature range investigated.

Vacancy-antistructure defect interaction diffusion in β-LiAl and β-LiIn

The lithium mass transport mechanisms of the NaTl-type intermetallic compounds β-LiAl and β-LiIn were studied by using the pulsed-field-gradient (PFG) nuclear magnetic resonance (NMR) spin-echo technique over a temperature range of 297–485 K. The lithium self-diffusion coefficients in β-LiAl alloys were found to follow Arrhenius behavior. The lithium diffusion coefficient and the associated diffusion constant D 0 (Li) and activation energy 〈E〉 decrease with increasing lithium content. The results can be interpreted if two types of vacancy point defects are considered: vacancies associated with immobile antistructure defects and vacancies which are otherwise free. A vacancy-diffusion mechanism based on two mean effective jump times, τ A and τ B τ B / τ A = 9.0), for these two types of vacancies yields a quantitative description of the dependence of the lithium diffusion rate on defect concentrations under a V Li − Li Al attractive interaction at a nearest neighbor distance. Very high values of lithium diffusivities (approximately 10 −6 cm 2 s −1 at room temperature) which increase with decreasing lithium content were observed in β-LiIn alloys. The lithium self-diffusion coefficient obeys the Arrhenius relation over the temperature range 300–400 K. The diffusion constant D 0 (Li) and activation energy 〈E〉 determined from the Arrhenius relation decrease with increasing lithium content. The results suggest that there is a repulsive interaction between the vacancy V Li and the antistructure atom Li In. Theoretical analyses based on a three-effective-jump-times diffusion model indicate that this V Li − Li In repulsive interaction is so strong that it extends well into the second nearest-neighbor distance.

Volume expansion of diamond during ion implantation at low temperatures

A type IIa diamond was implanted with fluorine ions while being maintained at liquid nitrogen temperature (77 K). After allowing the diamond to warm to room temperature the volume expansion caused by the ion implantation was measured using standard profilometry. No expansion could be detected up to an ion dose 6×10 15 ions/cm 2 . Above this ion dose, expansion, which could be ascribed to amorphization of the ion damaged layer towards a graphite phase, did occur. This result is in severe contrast to ion implantation carried out above room temperature where expansion occurs immediately with the onset of ion implantation, and can be explained in terms of the diffusion of interstitials out of the ion damaged layer leaving behind a high density of immobile vacancies.

Vacancies in HF-doped and in Irradiated Ice by Positron Annihilation Techniques

AbstractPositron annihilation techniques, which are specifically sensitive to vacancy-type defects have been used to study the effect on ice of irradiation and HF doping. Main conclusions are that immobile water-molecule vacancies can be created at low temperatures by either irradiation or HF doping. Upon heating, the vacancies become mobile at about 100 K. Some of them cluster into di- and multi-vacancies which grow in size with temperature up to at least 145 K. A vacancy migration energy of 0.34 ± 0.07 eV is deduced, about three times higher than previously assumed. Possible mechanisms for vacancy formation by HF doping are discussed. Out-diffusion of HF is followed at –26°C over several weeks. The diffusion constant derived agrees within uncertainty (a factor of two) with the large value obtained by Haltenorth and Klinger. In particular two results seem important for other parts of ice physics. One is that HF doping creates an appreciable increase in the vacancy concentration, the influence of which should be considered in models for other defects in ice. The other is that vacancies migrate at about 100 K, a fact which might be important for the interpretation of some of the many “anomalous” effects observed in ice at about that temperature.

Vacancies in HF-doped and in Irradiated Ice by Positron Annihilation Techniques

Abstract Positron annihilation techniques, which are specifically sensitive to vacancy-type defects have been used to study the effect on ice of irradiation and HF doping. Main conclusions are that immobile water-molecule vacancies can be created at low temperatures by either irradiation or HF doping. Upon heating, the vacancies become mobile at about 100 K. Some of them cluster into di- and multi-vacancies which grow in size with temperature up to at least 145 K. A vacancy migration energy of 0.34 ± 0.07 eV is deduced, about three times higher than previously assumed. Possible mechanisms for vacancy formation by HF doping are discussed. Out-diffusion of HF is followed at –26°C over several weeks. The diffusion constant derived agrees within uncertainty (a factor of two) with the large value obtained by Haltenorth and Klinger. In particular two results seem important for other parts of ice physics. One is that HF doping creates an appreciable increase in the vacancy concentration, the influence of which should be considered in models for other defects in ice. The other is that vacancies migrate at about 100 K, a fact which might be important for the interpretation of some of the many “anomalous” effects observed in ice at about that temperature.

Rate‐equation approach to stage II damage curves of metals in terms of the two‐interstitial model

AbstractA theoretical expression describing the increase of the electrical resistivity of metals as a result of irradiations at temperatures in the recovery stage II is derived within the frame‐work of the two‐interstitial model of radiation damage. The derivation is based on the use of rate equations taking into account the following processes: simultaneous production of mobile crowdions or immobile dumbbell interstitials, and of an equal number of immobile vacancies; trapping or athermal conversion of both off‐line and on‐line crowdions at impurities, dumbbells, trapped crowdions or nearby vacancies; annihilation of crowdions at vacancies. It is shown that, as a matter of principle, the information which may be obtained from stage II damage curves cannot suffice to exclude the two‐interstitial model. On the other hand, under favourable circumstances stage II damage curves may enable us to demonstrate the validity of the two‐interstitial model unambiguously and thus to rule out the one‐interstitial model.

Radiation-induced defect buildup and radiation-enhanced diffusion in a foil under energetic bombardment

Abstract The distribution of interstitials, monovacancies and vacancy aggregates containing two to six vacancies in a silver foil under irradiation was calculated as a function of both distance from the surface of the foil and irradiation time by numerically solving the rate equations for various temperatures (0–250°C) and internal sink concentrations (0,10 −5 and 10−3). The calculations would be useful in areas of high-voltage electron microscopy, radiation-enhanced diffusion and void formation. The mobile defects (interstitials, monovacancies, divacancies and trivacancies) were assumed to react with each other, to annihilate at fixed sinks and to diffuse to the surface. Vacancy clusters larger than trivacancies were considered to be immobile, able to grow, but not dissociate. Humps on the steady-state concentration profiles for monovacancies and immobile vacancy clusters were found near the surface of a foil, provided the irradiation temperature and sink density were low and/or the defect production rate was quite high. The radiation-enhanced diffusion coefficient, D rad , of the material was calculated from the diffusivities of mobile defects and their steady-state concentrations, as a function of temperature, sink concentration, and Frenkel-pair production rate.

Disorder in the crystal structures of paradichlorobenzene

A theory for certain molecular crystals of the relation of lattice vacancies to molecular orientational disorder is developed and applied to the case of para-dichlorobenzene. For a melt-grown or solution-grown crystal substantial molecular orientational disordering is predicted between 250 K and the melting point at 326 K. Comparison with experimental hydrogen atom Debye-Waller factors supports this conclusion. Such disorder may be common in molecular crystals, the requirements being (a) a high concentration of relatively immobile vacancies (> 10-3), (b) two other crystal structures close in free energy to the stable structure (differing in internal energies by less than 8 kJ mole-1).

Dynamics of Positive-Ion Vacancies in X-Irradiated NaCl by Positron Annihilation

A fraction of thermalized positrons in a NaCl crystal can be trapped in crystal defects to form annihilation or $A$ centers. This fraction is found to increase after x irradiation of the crystal. The increase is measured through the coincidence count rate of the two 0.51-MeV positron-electron-annihilation $\ensuremath{\gamma}$ quanta emerging from NaCl single crystals in exactly opposite directions. Isothermal annealing at various temperatures $T$ between 55 and 185 \ifmmode^\circ\else\textdegree\fi{}C always increases the count rate further, in time intervals ranging, respectively, from ${10}^{2}$ to 10 min. When $T>100$ \ifmmode^\circ\else\textdegree\fi{}C, the count rate as a function of time passes through a pronounced maximum and diminishes slowly (in ${10}^{3}$ to ${10}^{2}$ min) toward the count rate of the annealed crystal. The activation energy for the rate of increase is 0.4 eV, and for the decrease 1.2 eV. Both values coincide with the activation energies for the rise and decline of the ionic conductivity in isothermal anneals at $T\ensuremath{\ge}130$ \ifmmode^\circ\else\textdegree\fi{}C. To the extent that the dominant $A$ centers are positrons trapped in mobile or immobile positive-ion vacancies, and that the dominant charge carriers in ionic conductivity are the mobile positive-ion vacancies, our data support the long-held conjecture that x irradiation creates vacancies and that during incipient periods of annealing additional vacancies are released from radiation-induced vacancy aggregates. The positive-ion vacancy-diffusion constant is deduced to be 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{cm}}^{2}$/sec, corresponding to a mobility \ensuremath{\sim} ${10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{2}$/V sec, by Einstein's relation. The ubiquitous initial rise in our count rates implies that the initial drop in conductivity for isothermal anneals at moderate temperatures, $T\ensuremath{\lesssim}100$ \ifmmode^\circ\else\textdegree\fi{}C, is caused not by the neutralization of positive-ion vacancies but by their immobilization through complex formation. The decline at long anneal times in both our count rates and the conductivities, with identical activation energies, signifies the slow formation of positive-ion-vacancy sinks leading to the complete annealing of the radiation-induced defects so observed.

Fluence and temperature dependence of swelling in irradiated molybdenum

Volume changes have been analyzed in molybdenum which has been neutron irradiated to various fluences over the temperature range 50 to 1300°C. This data together with all previously reported data has been compiled into a three-dimensional plot of swelling versus temperature versus fluence. Significant low temperature swelling, < 400°C, is observed and is consistent with the presence of isolated immobile vacancies. Void swelling only becomes significant at temperatures > 400°C. The nature of the dislocation and void microstructure at high irradiation temperatures are analyzed quantitatively as a function of irradiation temperature and the results are reasonably consistent with a recent model of Brailsford and Bullough. The same model is also consistent with an observed trend towards saturation in the void swelling at high fluences at the low temperature end of the void region.

Neutron irradiation and defect recovery of tungsten

A detailed study of the recovery of defects in tungsten after fast neutron ( E m ⩾ 1 MeV) irradiation at about 70° C over a fast neutron fluence range from 8.5 × 10 17 n/cm 2 to 1.5 × 10 21 n/cm 2 has been completed. Three principal recovery regions have been observed at about 0.15 T m , 0.22 T m , and 0.31 T m where T m is the melting temperature of tungsten in °K. The 0.15 T m recovery involves an activation energy of about 1.7 eV and second-order kinetics. A shift of this recovery, with increasing neutron fluence, to lower temperatures is in keeping with second-order kinetics. These results are completely compatible with essentially a mobile self-interstitial, immobile vacancy, recovery process. The 0.22 T m recovery is suggested to be due to divacancy migration on the basis of its relative magnitude. The 0.31 T m recovery involves a first-order process with an activation energy of 3.3 eV in excellent agreement with other studies of monovacancy recovery. A non-annealing residual resistivity remaining after completion of the annealing studies has been shown to be due to rhenium. Rhenium is produced from the transmutation of tungsten by the β-decay of unstable isotopes of tungsten formed by thermal-neutron (n, γ) reactions. Rhenium appears to appreciably influence the migration energies for the various defects when its concentration is of the order of one atomic percent or greater. Small recoveries are also observed at about 0.27 T m and 0.35 T m . It is suggested that these recoveries may be due to the annealing of trivacancies and defect clusters or loops, respectively, with polygonization also contributing to the latter.

Vacancy Clusters inα-Iron

A mathematical lattice model was used to compute the kinetic and static aspects of vacancy-cluster nucleation, growth, and dissociation in $\ensuremath{\alpha}$-iron. Persistent attention is paid to the kinetics of changes among metastable configurations as well as the formation of stable configurations. The tetravacancy was the smallest immobile vacancy cluster and the mono-, di-, and trivacancy essentially share a common migration-energy value (0.65-0.70 eV). There exists a well-defined hierarchy of different types of stable clusters, the most stable structure being compact clusters, followed in order of decreasing stability by double layers, linear chains, tetravacancies, single layers, trivacancies, and divacancies. The gain in binding energy per additional vacancy increased as the cluster size increased from two to six vacancies. Between 6 and 10 vacancies this gain approached an upper limit of about 0.8 eV/vacancy and remained at this value for larger clusters.

A measurement of the charge on edge dislocations in a sodium chloride crystal

Abstract Single crystals of NaCl were plastically bent, and specimens were then cut from them in which the dislocations were almost entirely of the same mechanical sign. These specimens were subjected to a cyclic tensile and compressive stress such that the dislocations moved to produce a plastic strain and an electrical polarization. The charge on the dislocations was determined by measuring these quantities. On first testing it lay in the range—(6 to 12) × 10−-4 e.s.u./cm, but it was approximately doubled as a result of cyclic stressing at high amplitudes. The results are compared with two approximate models : one in which the dislocation acquires a charge by sweeping up otherwise immobile positive-ion vacancies, and another in which the dislocation is in thermal equilibrium with mobile positive-ion vacancies. Both models give results of the order of magnitude found experimentally.

Self diffusion in solid argon: The activation energy

Defect state features have been detected in second derivative O K edge spectra for thin films of nano-crystalline TiO2 and HfO2. Based on soft X-ray photoelectron band edge spectra, and the occurrence of occupied band edge 4f states in Gd(Sc,Ti)O3, complementary spectroscopic features have been confirmed in the pre-edge (<530 eV) and vacuum continuum (>545 eV) regimes of O K edge spectra. Qualitatively similar spectral features have been obtained for thin films of HfO2 and TiO2, and these have been assigned to defect states associated with vacancies. The two electrons/removed O-atom are not distributed uniformly over the TM atoms defining the vacancy geometry, but instead are localized in equivalent d-states: a d2 state for a Ti monovacancy and a d4 state for a Hf divacancy. This new model for electronic structure provides an unambiguous way to differentiate between monovacancy and divacancy arrangements, as well as immobile (or fixed) and mobile vacancies.

Analytical Study of Isochronal Annealing of Cold‐Worked Niobium

AbstractThe theoretical expressions derived in the preceding paper are applied to stage III isochronal annealing data for cold‐worked niobium. Close agreement between the experimental data and the theory is obtained by using the model based on uncorrelated bimolecular recombination of defects. This confirms an earlier proposed mechanism for stage III recovery in b.c.c. metals, namely recombination of randomly migrating interstitials with immobile vacancies.

Kinetics of the formation of anodic oxide films on tantalum

Theories of the growth of anodic oxide films are discussed and their predictions concerning the current and temperature-dependence of the field examined. New measurements of the mean field in (amorphous) Ta/sub 2/O/sub 5/ are used to test the predictions of the theories of oxide growth. Results obtained in 0.1 N H/sub 2/SO/sub 4/ and 100% H/sub 2/SO/sub 4/ as the form ing electrolyte are consistent with both the single carriersingle barrier theories and the theory in which a compensating space charge for the moving metal ions is provided by immobile cation vacancies. Formations in 40% H/sub 2/SO/sub 4/ over a wider temperature range (150 deg C) showed, however, significant departure from the predictions of the above theories. Instead they agree with Dewald's theory in which the rate of movement of metal ions is controlled by activation barriers located both at the metal-oxide interface and within the film. (auth)