Experimental determination of the energy dependence of defect production

A knowledge of primary damage production as a function of recoil energy is essential for predicting defect production in radiation environments of practical interest. The damage function $\text{ν(T)}$, i.e., the number of Frenkel pairs as a function of recoil energy, is determined for Cu from electron and ion damage-rate measurements. $\text{ν(T)}$ shows a plateau at $\text{ν = 0.54}$ which extends up to ~ $\text{7T}{}_{\mathrm{d}}{}^{\min }$. Therefore, simple damage models, such as the modified Kinchin-Pease expression, are strongly deficient, not only at high recoil energies where stimulated recombination in cascades reduces defect production, but also in the single displacement regime. As a consequence, no simple relation between $\text{T}{}_{\mathrm{d}}{}^{\min }$ and $\text{T}{}_{\mathrm{d}}{}^{\mathrm{av}}$ is expected to exist. A procedure is suggested which uses anisotropy measurements in combination with polycrystal electron and ion irradiations to construct absolute damage functions in metals.     

Threshold energy surface and frenkel pair resistivity for Cu

In-situ electrical resistivity damage-rate measurements in the high voltage electron microscope have been used to study electron irradiation induced defect production in copper single crystals at $\text{T < 10 K}$. Analysis of the directional and energy dependence yields a threshold energy surface that is significantly different from those of previous investigations: two pockets of low threshold energy centered at 〈100〉 and 〈110〉 surrounded by regions of much higher threshold energy. The corresponding damage function exhibits a plateau at 0.6 Frenkel pairs. The present results imply a Frenkel pair resistivity for Cu of (2.75 ^+0.6_?0.2) × 10^?4 Ω cm.     

Autoirradiation d'un alliage cubique centre uranium-plutonium-molybdene

Measurements have been made of the length changes due to self-irradiation damage at 4.2 K for over 1300 h in a U-Pu-Mo bcc alloy (containing 20 at% plutonium and 15 at% molybdenum) stabilized by quenching. These are the first measurements of this type carried out on a bcc alloy. The initial rate of increase of δl/l was $\text{2,3 × 10}{}^{\mathrm{?7}}\text{h}{}^{\mathrm{?1}}$ If it is assumed that each α desintegration forms 1800 Frenkel pairs, it is found that Frenkel pairs have a formation volume equal to 0.5 atomic volume.     

Zum verhalten von tritium in reaktorgraphiten

An experimental investigation of the behaviour of tritium and hydrogen in HTR graphites is described. The diffusion and adsorption kinetic isotherms were measured using a specially developed vacuum apparatus with a variable temperature/time function. Hydrogen was estimated using a mass spectrometer. Tritium was analysed quantitatively after catalytic oxidation using a liquid scintillator. The diffusion coefficients for tritium in reactor graphite were found to be as follows: $\text{D = 0.024 cm}{}^2\text{/sec}\text{exp}\text{(?2.78 eV/kT)}$ and the desorption energies $\text{E}{}^{\mathrm{I}}{}_{\mathrm{des}}\text{= 1.38 ± 0.07 eV}$, $\text{E}{}^{\mathrm{II}}{}_{\mathrm{des}}\text{= 2.07 ± 0.13 eV}$, $\text{E}{}^{\mathrm{III}}{}_{\mathrm{des}}\text{= 3.27 ± 0.07 eV}$. The results indicated that the actual tritium inventory is largely determined by the buffering action of the graphite core. In the start-up phase of an HTR, the tritium concentration in the coolant gas remains relatively low, despite an increased rate of production because the tritium is being adsorbed by the graphite. In later stages of operation, after equilibrium has been reached, the tritium level will be supplemented by material from the hot core regions, so that the coolant activity is not determined by the production rate alone.     

Chemical states and thermal stability of hydrogen-implanted Ti and V studied by X-ray photoelectron spectroscopy

X-ray photoelectron spectroscopy (XPS) was applied to the chemical state studies of Ti and V metals bombarded with 8 keV hydrogen ions. The binding energies of the lines for the ion-implanted Ti and V shift from those for the metallic states by 0.3 eV, are consistent with the core-line shifts for the thermally synthesized hydrides such as TiH_1.97 and VH_0.55 The metal 3d-H1s bonding level for the hydrogen implanted Ti appears at ~ 3.5 eV below the Fermi level, which is lower by ~ 2.5 eV than the molecular-orbital energy previously calculated for TiH₂. In the case of the ion-implanted V, however, it appears at ~ 5.0 eV, which is almost equal to the molecular-orbital energy for VH₂. The photopeaks corresponding to the Ti-H and V-H bonds for the ion-implanted samples grew up on raising the annealing temperature up to 550°C and 150°C, respectively. The phenomena are interpreted by means of the thermal diffusion of the implanted hydrogen from bulk to surface.     

Molecular dynamics simulations of collision cascades in FeCrHe

Radiation damage due to 1 and 5 keV collision cascades in Fe₉₀Cr₁₀ in the presence of 0.1%, 0.5% and 1.0% He defects, relevant for fusion reactor steels, has been studied using molecular dynamics simulations. We show that with 0.1% interstitial He the effect on the damage production in the FeCr matrix is minor, while with 1.0% He, the number of Frenkel pairs is significantly increased in comparison to pure FeCr. The positions of the He interstitials and clusters depend on the Cr atoms and the amount of He inside the cascade region is increased by about 30% due to the cascade. With substitutional He less damage is formed in the FeCr matrix due to cascades.     

Energy distributions of charged and neutral hydrogen atoms backscattered from metal surfaces bombarded with 5 to 18 keV protons

Polycrystalline targets of Be, V, Nb, Mo and Ta have been bombarded with protons with primary energies in the range from 5 to 18 keV. The energy distributions of the charged and the neural particles backscattered at 135° with respect to the primary beam direction have been measured between 200 eV and 18 keV. The energy distribution of the neutrals has a pronounced maximum between 0.5 and 1 keV whose position does not depend on the primary energy or the target material, or the angle of emergence of the scattered particles. The energy distribution of the charged particles shows a less pronounced maximum between 1 and 1.5 keV. Only slight differences in the shape of the energy distributions have been observed for different target materials. The fractional number of charged backscattered particles increases from $\text{≈; 3\%}$ at 300 eV to $\text{≈; 40\%}$ at 18 keV.     

The characteristics of 15 MeV and fission neutron damage in niobium

Displacement damage by 15 MeV (d-Be source) and fission neutrons at 30°C in high purity niobium single crystals has been studied by transmission electron microscopy. The fluence of the 15 MeV neutrons was 1.8 × 10¹⁷n/cm² and the fluence of the fission neutrons (5 × 10¹⁷ n/cm²) was chosen so that samples from both types of irradiations had approximately the same damage energy. In both 15 MeV and fission neutron irradiated specimens, the loops were observed to be about $\text{2}\text{3}$ interstitial and $\text{1}\text{3}$ vacancy type. The analysis of Burgers vectors of the dislocation loops showed that more than $\text{2}\text{3}$ of the loops were perfect $\text{a}\text{2}\text{〈111〉}$ and that the rest were $\text{a}\text{2}\text{〈110〉}$ faulted. It is concluded that at equal damage energies, the detailed nature of the damage is the same for 15 MeV and fission neutron irradiated niobium.     

Simulation of displacement cascades in tungsten irradiated by fusion neutrons

Numerical calculations of damage in tungsten irradiated by fusion neutrons were performed using molecular dynamics simulations combined with an embedded atom method potential. The displacement cascade efficiency has been calculated using the ratio of the number of Frenkel pairs determined by molecular dynamics simulations to the number of Frenkel pairs derived from Norgett-Robinson-Torrens formula. The cascade efficiency decreases as the Primary Knock Atoms increases. The Norgett-Robinson-Torrens calculations overestimate the Frenkel pair defect production by a factor of 2. The changes in the cascades dimensions at the early stages after irradiation indicate that the tungsten interstitials are more mobile than the vacancies. We found that the most common types of defects are single vacancies, di-vacancies, vacancy-clusters, interstitials and small number of interstitial clusters containing more than three atoms.     

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations 2 ≤ Z ≤ 106

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wavefunctions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers 2 ≤ Z ≤ 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms with 2 ≤ Z ≤ 106. A self-energy correction is included for the 1s, 2s, and $\text{2p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.     

Modele elementaire sur les dommages radio-induits dans le graphite en pile: correlation entre temperature et flux

A model based on displacement spikes is examined (and confirmed) for the primary defects induced by neutron bombardment. It is shown that, before any random annealing takes place, these spikes consist of about 4 stably displaced atoms, either isolated or grouped as interstitials or vacancies. There are no vacancy-type defects with activation energies less than 4 eV. The effects of irradiation temperature on dimensional changes in graphite (as published in the literature) are readily described in terms of this model. In particular, this model permits one to account for the effect of dose rate on the defect concentration. At low temperatures ($\text{T}\text{\$}\text{?}\text{300°C}$), the theoretical treatment is equivalent to the currently accepted empirical treatment, and its extrapolates well to higher temperatures. A series of experiments is presented which helps to refine the model for high temperature and sets a lower limit of 4 eV for the vacancy activation energy in the displacement spike. Q = 4 eV is proposed for the purposes of temperature correction in the range 600–1400°C. More generally, as a first approximation, the model shows that a temperature rise of 7% (in degrees Kelvin) compensates for a 10-fold increase of flux, at constant fluence.     

The influence of cavitation damage upon high temperature creep under stationary and non-stationary loading conditions: Part III: Creep at steady increasing load and true stress

In this paper for ideally plastic materials the influence of high temperature cavitation damage upon creep at steady increasing loads is investigated. The damage function $\text{A(t)}$ enters a constitutive equation for plastíc flow through an effective stress σ_e. For given loading conditions the latter is derived from the solution of Hart's tensile test equation. In the present paper the case of time linear increase in load ($\text{F}$ = constant) and in true stress ($\text{/.s}$ = constant) is investigated. The creep equations for cavitating as well as for non-cavitating materials are derived and the volume change during creep at $\text{/.F}$ = constant are calculated.     

Molecular dynamics simulation of displacement cascades in Ni-Mo alloy

Molecular dynamics method is used to investigate the displacement cascades in Ni-Mo binary alloy. Effects of the irradiation temperature, energy of the primary knock-on atoms and concentration of solute Mo atoms are taken into consideration on radiation damage to the Ni-Mo alloy. It is found that Mo atoms reduce production of the Frenkel pairs at 100 K, while they enhance defect production at 300 K and 600 K. Size of the largest defect clusters decreases with increasing concentrations of Mo atoms(C_(Mo)) at 100 K, but it increases with CMo at 300 K and 600 K. Most of the point defects get clustered in cascades leaving only a few vacancies and interstitials isolated.     

A resistometric study of ageing in nimonic alloys (I). PE16

The Nimonic alloy PE16 is a candidate for use in a radiation environment in fast reactors. Williams and Fisher have investigated void-swelling in this alloy and have found it to be dependent upon the γ' precipitate present. In order to investigate the dependence of precipitation upon heat-treatment, the variation of the electrical resistivity with time on ageing PE16 at various temperatures between 580°C and 780°C has been measured. To account for the observed variation, a model based on nucleation and growth of γ' precipitates has been developed. This model allows for different scattering cross sections, and hence specific resistivities, of particles in small and large clusters. The rate constants for nucleation and growth are found to follow the usual Arrhenius behaviour with activation energies of 1.11 eV and 1.83 eV respectively. Specimens aged at different temperatures for varying times t, were viewed in the electron microscope. The observations have indicated that the precipitate diameter varies as $\text{(K}{}_2\text{t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where K₂ is the growth rate constant.     

Self-irradiation effects in 238Pu-substituted zirconolite: II. Effect of damage microstructure on recovery

Samples of ²³⁸Pu-substituted zirconolite (CaPuTi₂O₇) were stored near room temperature to allow accumulation of alpha recoil damage. Differential thermal analysis was employed to measure release of stored energy accompanying recrystallization, after damage had proceeded for times from 35 days ($\text{4.7 × 10}{}^{24}\text{alpha decays/m}{}^3$) to 1198 days ($\text{1.6 × 10}{}^{26}\text{α/m}{}^3$). It was found that three parameters related to energy release (amount of stored energy, transformation temperature, and abruptness of transformation) were dependent on damage dose. Results are interpreted in terms of the quantity and distribution of remanent crystallinity, and of the consequences of redamage to once-damaged material.     

Application of serpan's damage function to heavy-water moderated power reactors and its control with surveillance data of the karlsruhe power reactor,MZFR

For calculating $\text{ΔNDT}$, the irradiation-induced shift of the nil ductility transition temperature, for the design of pressurized water reactor vessels, literature data envelope curves are used. In the case of light-water moderated reactors no correction of different spectra influence is considered. Calculations with the damage functions, published by Serpan et al., demonstrate that neglecting spectrum influence yields conservative design data. For heavy-water moderated reactors an adjusting factor is calculated from Serpan's damage function. The $\text{ΔNDT}$ measured with samples of the ASTM reference steel A302-B, irradiated in the heavy-water reactor, MZFR, is compared to irradiation results of samples from the same steel plate irradiated in the Oak Ridge low intensity test reactor (LITR) which are published by NRL. From this comparison an experimental adjusting factor is derived. Both calculated damage function and experimental factors agree very well. This result demonstrates that Serpan's damage function is applicable also to MZFR. surveillance samples. The neutron spectrum in the MZFR surveillance location is extremely soft. Thermal neutron population is 900 times the fast flux ($\text{E > 0.9}\text{MeV}$). Its damage contribution, calculated with damage function, amounts to 73%.     

On the simulation of CTR neutron radiation damage by heavy ion irradiation

The primary recoil spectrum in nobium under 33 MeV self-ion bombardment is calculated and compared with a calculation by Logan et al. of the same spectrum under neutron irradiation in a controlled thermonuclear reactor. The two spectra are similar, which suggests that a close simulation of CTR neutron radiation damage by ion bombardment will be possible. The displacement rate per projectile is found to be $\text{3.7 × 10}{}^5$ times higher for ions than for neutrons, allowing very high neutron fluxes, up to about $\text{10}{}^{18}\text{cm}{}^{\mathrm{?2}}\text{· sec}{}^{\mathrm{?1}}$, to be simulated with existing accelerators.     

Simulation of collision cascades and thermal spikes in ceramics

Classical molecular dynamics simulations have been employed to examine defect production by energetic recoils in UO₂, Gd₂Ti₂O₇, Gd₂Zr₂O₇ and ZrSiO₄. These atomistic simulations provide details of the nature and size distribution of defect clusters produced in collision cascades. The accommodation of recoil damage by lower energy cation exchange and greater occupation of anion structural vacancies is a contributing factor for the greater radiation tolerance of Gd₂Zr₂O₇ relative to Gd₂Ti₂O₇. In addition, electronic energy loss processes in UO₂ has been modeled in the form of a thermal spike to study the details of track formation and track structure. For thermal spikes with energy deposition of 4 keV/nm in UO₂, a track was not formed and mainly isolated Frenkel pairs were produced.     

Can thermal spike calculations reproduce displacement cascades?

Molecular dynamics simulations are used to compare the defects created by full displacement cascades and thermal spikes. The spikes are designed from cascade simulations to be of the same energies and of comparable sizes. Quantitatively, one finds that spikes create much less Frenkel pairs than cascades. However qualitatively, the distinction that appears in cascade simulations, between direct impact amorphization and sole creation of point defects is reproduced by thermal spikes calculations.