On the theory of void formation during irradiation

A simple theory of the swelling of materials subjected to high energy particle irradiation is developed. Chemical reaction rate equations are used as a basis. Point defects, interstitials and vacancies, are assumed to be produced randomly throughout the solid. They move by random walk through the material until they cease to exist either by recombination with the opposite type of defect or by incorporation into the crystal at sinks such as dislocations, grain boundaries and voids. The rate equations for interstitials and for vacancies, which are coupled via the recombination term, are solved for steady state conditions under irradiation. Defect concentrations, supersaturations, recombination and total sink annihilation rates are obtained in terms of the production rate, sink annihilation probabilities, jump frequencies and thermal equilibrium concentrations of defects. The swelling rate is derived using sink annihilation probabilities at three principally different types of sinks, i.e. voids, sinks which have a bias with regard to the annihilation of interstitials and vacancies (such as dislocations), and sinks with no bias. The defect annihilation probabilities at void, precipitate, dislocation and grain boundary sinks are estimated by using a cellular model and solving the diffusion equation for geometries approximating that of the cells, e.g. a concentric sphere around a void. The relative effects of different types of sinks, i.e. the microstructure, on the swelling rate is discussed. The swelling rate is integrated to give swelling-time or swelling-dose relations, making some simplifying assumptions about the changes in the sink structure as the irradiation proceeds. It is shown that the relation obtained is rather sensitive to the type of assumptions made.     

Buildup of point-defect diffusion profiles in a foil during irradiation

The distribution of interstitials and vacancies in a foil under irradiation has been calculated as a function of both distance from the surface and irradiation time by solving the diffusion equation numerically on a computer. The defects were considered to annihilate at randomly distributed sinks, by mutual recombination, and by diffusion to the surface. Defect jump frequencies appropriate to silver at 125°C and foil thicknesses of 1 pm and 300 A were used. Large “humps” in the plot of vacancy concentration versus distance were found near the surface of the 1 pm foil at short irradiation times, unless the internal sink concentration was high. These humps may be responsible for some unusual void distributions observed near grain boundaries.     

Observation of a donor-acceptor pair recombination in the edge emission of ZnSe crystal by electro-luminescence

An injection type electro-luminescence in ZnSe crystal has been studied by using ZnSe-SnO₂ hetero-junction at 20°K. In the emission peak observed around 2·70 eV, a clear energy shift toward the higher energy side with increasing injection current density has been found at low temperatures, which could be associated with the D-A pair (donor-acceptor pair) recombination process. The energy sum of the donor and acceptor activation is estimated to be larger than 137 meV. In the higher temperature region, this emission line turns out due to the ‘free-to-bound’ recombination, and the related acceptor ionization energy is considered to be ～120 meV. By taking into consideration the energies of bound exciton emission, the exciton localization energies and the related donor and acceptor ionization energies are evaluated.     

Radiation enhanced silicon self-diffusion and the silicon vacancy at high temperatures

We report proton radiation enhanced self-diffusion (RESD) studies on Si-isotope heterostructures. Self-diffusion experiments under irradiation were performed at temperatures between 780 degrees C and 872 degrees C for various times and proton fluxes. Detailed modeling of RESD provides direct evidence that vacancies at high temperatures diffuse with a migration enthalpy of H(m)(V)=(1.8+/-0.5) eV significantly more slowly than expected from their diffusion at low temperatures, which is described by H(m)(V)<0.5 eV. We conclude that this diffusion behavior is a consequence of the microscopic configuration of the vacancy whose entropy and enthalpy of migration increase with increasing temperature.     

Low density approximation for diffusion annealing

The problem of annealing of Frenkel-pairs in electron irradiated fee metals due to diffusion of interstitials is treated starting from exact equations for single particle densities, pair densities, etc. The mobile interstitials are considered to interact with vacancies (leading to recombination), impurity atoms (leading to interstitial-impurity complexes) and with each other (leading to interstitial clusters).

By using the superposition approximation, i.e. replacing three-particle probabilities by products of two-particle probabilities we obtain generalized Waite equations. For low defect densities the annealing is at different times governed by different processes. For short times the important process is the recombination of an interstitial with the near-by correlated vacancy generated by the same electron impact event, the so-called correlated recovery. For long times the remaining interstitials undergo long range migration and interact with uncorrelated sinks. During this process interstitial impurity complexes and interstitial clusters are formed.

The time dependence of the defect densities, the remaining fraction of defects after completion of diffusion annealing and the size distribution of interstitial clusters are calculated. Detailed comparison with experiments in Cu and Pt will be made.     

Fe-Cr合金辐照空洞微结构演化的相场法模拟

Fe-Cr合金作为包壳材料在高温高辐照强度等极端环境下服役,产生空位和间隙原子等辐照缺陷,辐照缺陷簇聚诱发空洞、位错环等缺陷团簇,引起辐照肿胀、晶格畸变,导致辐照硬化或软化致使材料失效.理解辐照缺陷簇聚和长大过程的组织演化,能更有效调控组织获得稳定服役性能.本文采用相场法研究Fe-Cr合金中空洞的演化,模型考虑了温度效...     

The stability of homogeneous microstructure development under cascade-damage conditions

The development of microstructure, under cascade-damage conditions, in regions far away from any major sink is considered. Within the mean-field theory, a homogeneous distribution of point defects and their clusters is a pre-imposed artificial constraint on the kinetic system. The resulting excessive recombination of the vacancies and interstitials at a high density of accumulated point-defect clusters dictates a low rate of void growth. Considerations beyond the mean-field theory, by taking into account the concentration fluctuations of both the point defects and their clusters, relax the restriction of the homogeneous distribution. In this paper, we consider a system without pre-existing sinks, except the void nuclei, in which vacancies, interstitials and their clusters are continuously produced. Taking into account the mobility of small clusters and the stochastic fluctuations of the point-defect fluxes, a kinetic theory is formulated from first principles. It is rigorously shown that through the stochastic fluctuations, and the positive-feedback action of the mobility of the small clusters on the interstitial concentration, the homogeneous interstitial distribution is unstable at temperatures above stage V, leading to the formation of a spatially heterogeneous microstructure in pure metals at low irradiation doses. The characteristics of the microstructure evolution and void swelling, predicted from the theory, are found to be in good agreement with the experimental results. Received: 17 March 2000 / Accepted: 17 October 2000 / Published online: 25 July 2001     

Mn interstitial diffusion in (ga,mn)as

We present a combined theoretical and experimental study of the ferromagnetic semiconductor (Ga,Mn)As which explains the remarkably large changes observed on low-temperature annealing. Careful control of the annealing conditions allows us to obtain samples with ferromagnetic transition temperatures up to 159 K. Ab initio calculations, in situ Auger spectroscopy, and resistivity measurements during annealing show that the observed changes are due to out diffusion of Mn interstitials towards the surface, governed by an energy barrier of 0.7-0.8 eV. Electric fields induced by Mn acceptors have a significant effect on the diffusion.     

Quasielastic resonance absorption of57Fe in the hydrides and deuterides of vanadium and niobium

The anomalous temperature dependence ot the f-factor arising from the diffusion of interstitials has been studied for⁵⁷Fe in hydrides and deuterides of vanadium and niobium at temperatures between 6 and 500K. Isotope effects in both the diffusion rate of the interstitials and the magnitude of the displacements of the probes are observed. The centre shift and quadrupole splitting of the patterns provide further information on the hydrogen distribution near the probes and on phase transition temperatures.     

Reactions of COO− radical-ion with M+ and M3+ states produced in the radiolysis of aqueous solutions

Pure nickel and lithium-implanted nickel were irradiated with 1 MeV electrons at the Argonne HVEM-Tandem facility. The lithium-implanted nickel was not damaged as readily as the pure nickel under 1 MeV electron irradiation in the temperature range 20–600°C. The decreased damage accumulation in the lithiated nickel could arise from both the precipitated lithium and that in solution. The latter could slow down the nickel interstitials produced during irradiation by association, thus enhancing their recombination with vacancies. The interfaces of the precipitated lithium could also act as unbiased sinks for the vacancies and interstitials. Above 600°C, under electron irradiation, a melting process which created small irregular shaped regions occurred in the lithium-implanted nickel. Electron diffraction analysis showed that the compound Li₂NiO₂ was formed inside these regions.     

Metastable Frenkel pair defect in graphite: source of Wigner energy?

The atomic processes associated with energy storage and release in irradiated graphite have long been subject to untested speculation. We examine structures and recombination routes for interstitial-vacancy (I-V) pairs in graphite. Interaction results in the formation of a new metastable defect (an intimate I-V pair) or a Stone-Wales defect. The intimate I-V pair, although 2.9 eV more stable than its isolated constituents, still has a formation energy of 10.8 eV. The barrier to recombination to perfect graphite is calculated to be 1.3 eV, consistent with the experimental first Wigner energy release peak at 1.38 eV. We expect similar defects to form in carbon nanostructures such as nanotubes, nested fullerenes, and onions under irradiation.     

Influence of sintering conditions and laser radiation on the surface microstructure,chemical composition,and electrical conductivity of CuO/Ag ceramics

The influence of the third harmonic radiation of a YAG: Nd³⁺ laser on the microstructure, chemical composition, and electrical conductivity of CuO and CuO/Ag ceramic samples subjected to heat treatment under different conditions has been investigated. It has been found that the surface morphology is almost identical for all the samples sintered at the same temperatures. According to the X-ray microanalysis, the ratio of the copper and oxygen concentrations (Cu/O) increases with an increase in the sintering temperature and upon quenching cooling of the samples. It has been shown that laser irradiation changes the micro-structure of the samples, increases the concentration ratio Cu/O, and leads to the inclusion of silver atoms into the lattice of copper oxides. It has been revealed that the temperature dependence of electrical resistance of all the studied samples in the temperature range of 80–300 K has a semiconducting character, and the activation energy of electrical resistance varies in the range from 0.19 to 0.48 eV. The activation energy of electrical resistance decreases with an increase in the sintering temperature of the samples and increases upon their quenching, whereas the laser treatment leads to a weakening of the dependence of the activation energy on the sintering temperature. The deposition of a silver layer before the laser treatment has no noticeable influence on the activation energy. The obtained data can be used to purposefully change the physical properties of compounds formed in the Cu-O-Ag system.     

Activation energy of self-diffusion along symmetric tilt grain boundaries 〈111〉 in the Ni3Al intermetallic compound

Activation energy of self-diffusion along symmetric tilt grain boundaries 〈111〉 in the Ni₃Al inter-metallic compound has been calculated depending on the temperature and misorientation angle. For comparison, two types of potentials of interatomic interaction have been used: pair Morse potentials and multi-particle Cleri-Rosato potentials. It has been shown that the activation energy of grain-boundary diffusion increases with temperature on applying the additional diffusion mechanisms. Three temperature ranges with various activation energies have been found.     

On the mechanism of diffusion in sodium beta alumina

A microscopic interstitialcy-type diffusion mechanism for sodium beta-alumina involving three crystallographically different types of cation sites but only two equilibrium configurations of interstitialcy pairs is proposed. The resulting cation-site occupation probabilities are shown to agree with the experimental neutron-diffraction data of Roth et al. For various sizes of the associated regions around the charge-compensating oxygen interstitials (in which Na⁺ ions are not freely mobile), the ratio of the radiotracer diffusivity with respect to the charge diffusivity (the so-called Haven ratio, H_R)is determined. In agreement with the measurements of Kim et al.,H_R is found to increase with increasing temperature as a result of the decrease in the average size of the associated regions. It is concluded that, while at lower temperatures all excess Na⁺ ions are found in the associated regions around the oxygen interstitials, with increasing temperature more and more of them are freely mobile in the unassociated regions of the conduction plane. The formation enthalpy associated with the thermally activated creation of mobile “interstitials” is determined to be about 0.05 eV. The slope of the slightly curved Arrhenius plot associated with the proposed mechanism therefore consists of the sum of the energy of formation of freely mobile interstitials and the energies of migration of two types of interstitialcy pairs. The Raman and IR-conductivity results are found to be compatible with this emerging picture for the microscopic diffusion process in sodium β-alumina. Spectroscopic diffusion techniques (NMR, internal friction, dielectric loss) show more than one apparent activation energy E^A while, in the same temperature region, the d.c. ionic conductivity yields a unique value of E^A; reasons for this discrepancy are discussed.     

An acoustic study of the mixed-alkali-mixed phase β-aluminas. Part 1: Naβ″/βAl2O3, Kβ″/βAl2O3 and (Na0.6K0.4)β″/βAl2O3

The relative attenuation of compressional sound waves of frequencies 10–60 MHz in mixed alkali (Na/K) mixed phase (β″/β)-aluminas is reported for temperatures 80–550 K. The internal friction peaks shift to higher frequencies at higher temperatures and are attributed to Na⁺ interactions in Naβ″/β alumina and Na⁺ and K⁺ in NaK β″/β alumina. The broad attenuation peaks occuring at low temperatures (< 300 K) and at higher temperatures (> 400 K) suggest multi-relaxation processes giving a distribution of activation energies. The estimated average activation energy for Na⁺ diffusion in Naβ″/βAl₂ O₃ at low temperatures and high temperatures is 0.183 eV and 0.387 eV respectively. In the NaK β″/βAl₂o₃ samples, the Na ⁺ values were 0.239 eV and 0.386 eV, respectively. The estimated average activation energies for K⁺ diffusion at low and high temperatures in the Kβ″/β-alumina samples were 0.269 eV and 0.371 eV and for K⁺ in the NaK β″/β samples, 0252 eV and 0.339 eV, respectively. The low temperature attenuation peaks were interpreted in terms of ionic interaction in the bulk and the high temperature peaks were related to interactions in the grain boundaries. The measured activation energies confirmed these interpretations. A reversal of the temperature appearance of the Na⁺ and K⁺ high temperature peaks in the NaKβ″/βAl₂ O₃ is explained by the disorder at the grain boundaries.     

Size dependence of the activation energy of diffusion in multilayer Cu-Ni films

The results of studying the effect of the characteristic size on the rate of diffusion processes in nanometer Cu-Ni film systems have been reported. The film system has been prepared by sequential vacuum deposition of the components, and the activation energy of diffusion has been determined from a change in the electrical resistance of the film system in a heating-cooling cycle. It has been shown that the activation energy of grain-boundary diffusion decreases with decreasing characteristic size of the system and amounts to 0.25 eV for the film system with a characteristic size of 5 nm, which corresponds to an increase in the grain-boundary diffusion coefficient by 10 orders of magnitude with respect to massive samples.     

Charge-sensitive deep level transient spectroscopy of helium-ion-irradiated silicon, as-irradiated and after thermal annealing

Electrically active defects in the phosphor-doped single-crystal silicon, induced by helium-ion irradiation under thermal annealing, have been investigated. Isothermal charge-sensitive deep-level transient spectroscopy was employed to study the activation energy and capture cross-section of helium-induced defects in silicon samples. It was shown that the activation energy levels produced by helium-ion irradiation first increased with increasing annealing temperature, with the maximum value of the activation energy occurring at 873K, and reduced with further increase of the annealing temperature. The energy levels of defects in the samples annealed at 873 and 1073K are found to be located near the mid-forbidden energy gap level so that they can act as thermally stable carrier recombination centres.     

Nitrogen diffusion parameters in ion-implanted tungsten single crystals

Diffusion of nitrogen implanted in single-crystal tungsten was studied in the temperature range 700–820° C. Measurements were carried out using a method of nondestructive determination of diffusivities (developed by the authors) from the dynamics of variation in the surface impurity concentration. The initial distribution and diffusion profiles for various annealing times were determined by secondary ion mass spectrometry. The relative surface concentration of nitrogen was measured by Auger electron spectroscopy. Several fluxes of impurity atoms in the surface region of ion-doped tungsten were experimentally detected to exist. Under the assumption that the fluxes interact with each other, the temperature dependences of the nitrogen diffusivities in the flux associated with dislocations generated by ion implantation and in the flux associated with the bulk diffusion mechanism were determined. Nitrogen diffusion is characterized by a rather low activation energy, namely, 0.15 and 0.75 eV for dislocation and bulk mechanisms, respectively.     

Monte Carlo simulation of phosphorus diffusion in α-iron via the vacancy mechanism

Monte Carlo simulations of the vacancy and phosphorus (P) atom diffusion in body centred cubic (bcc) iron are presented. The input parameters for the calculations, namely the activation energies of atomic jumps, have been obtained using a potential set developed recently for a dilute Fe–P alloy using ab initio data. The diffusion coefficients entering equations for the fluxes of vacancies and solute atoms are evaluated. The results show that, in the temperature range of practical importance for P segregation, P atoms move down the vacancy gradient; hence, under irradiation conditions, vacancies should drag P atoms towards sinks of point defects. This is because of the high binding energy between a P atom and a vacancy in the first and second nearest neighbour sites from each other, which allows a vacancy to move around a P atom without loss of bonding and, hence, co-migrate with it.     

Influence of sintering conditions and laser irradiation on electroconductivity of CuO/Ag ceramics

We study the influence of different thermal treatments and pulsed laser irradiation on the temperature dependence of resistance and activation energy of ceramic samples of copper oxide. For studies of influence of impurity, thin film of silver was deposited on some samples prior to laser action. It is revealed that the temperature dependence of resistance of all samples has in the range 80–300 K a semiconductor nature and the activation energy of resistance varies within the limits 0.19–0.48 eV. It is established that the activation energy decreases with rise of the sintering temperature and quenching cooling increases the activation energy. Laser treatment reduces the dependence of activation energy on sintering temperature and deposition of silver upon the sample before laser treatment eliminates this dependence completely.