The effect of irradiation on diffusion controlled creep processes

At temperatures below about half the melting point and under moderate stress, below the post-irradiated yield stress, a metal will, in a fairly high fast neutron flux ($\text{/}$ > 10¹³ n/cm² sec), suffer an enhanced creep compared to an unirradiated control held at the same temperature and state of stress. Ever since Schoeck's initial suggestion that the excess vacancies introduced by irradiation should cause an acceleration of the diffusion-controlled climb of edge dislocations over obstacles in their glide paths, there has been lively discussion on what conditions must exist (or indeed if there are any conditions) under which irradiation-accelerated diffusion will lead to an enhancement of the creep rate. It is shown here, considering both vacancies and interstitials, that for irradiation-accelerated climb of edge dislocations to enhance creep two basic conditions are necessary. First, the climb must be followed by glide and only that deformation produced by the glide is increased by irradiation. Second, there must exist a net difference in the flux of irradiation-produced interstitials and vacancies into the dislocations. This difference must be provided by other sinks which preferentially absorb one type of defect. This difference cannot be simply caused by the interaction of dislocations of differing orientations with the applied stress field or a preferential attraction between one type of defect and the dislocations. Creep rates computed using a diffusion-controlled climb model are compared with creep rates of a zirconium-base alloy at 300 °C, measured both during and following fast neutron bombardment. The model is shown to be reasonably consistent with such measurements.     

Atomistic Kinetic Monte Carlo studies of microchemical evolutions driven by diffusion processes under irradiation

Atomistic Kinetic Monte Carlo (AKMC) simulations are a powerful tool to study the microstructural and microchemical evolution of alloys controlled by diffusion processes, under irradiation and during thermal ageing. In the framework of the FP6 Perfect program, two main approaches have been applied to binary and multicomponent iron based alloys. The first one is based on a diffusion model which takes into account vacancy and self-interstitial jumps, using simple rigid lattice approximation and broken-bond models to compute the point-defect jump frequencies. The corresponding parameters are fitted on ab initio calculations of a few typical configurations and migration barriers. The second method uses empirical potentials to compute a much larger number of migration barriers, including atomic relaxations, and Artificial Intelligence regression methods to predict the other ones. It is somewhat less rapid than the first one, but significantly more than simulations using “on-the-fly” calculations of all the barriers. We review here the recent advances and perspectives concerning these techniques.     

Total cross sections for ionizing processes induced by proton impact on molecules of biological interest: A classical trajectory Monte Carlo approach

In the current work, we present a study of ionizing interactions between protons and molecular targets of biological interest like water vapour and DNA bases. Total cross sections for single and multiple ionizing processes are calculated in the independent electron model and compared to existing theoretical and experimental results for impact energies ranging from 10 keV/amu to 10 MeV/amu. The theoretical approach combines some characteristics of the classical trajectory Monte Carlo method with the classical over-barrier framework. In this “mixed” approach, all the particles are described in a classical way by assuming that the target electrons are involved in the collision only when their binding energy is greater than the maximum of the potential energy of the system projectile-target. We test our theoretical approach on the water molecule and the obtained results are compared to a large set of data and a reasonable agreement is generally observed specially for impact energies greater than 100 keV, except for the double ionization process for which large discrepancies are reported. Considering the DNA bases, the obtained results are given without any comparison since the literature is till now very poor in terms of cross section measurements.     

Effective Cadmium Cutoff Energies for Non-1/V Detectors

Effective cadmium cutoff energies were calculated for ²³⁹Pu, ²³⁵U, ¹¹⁵In, Au, ¹¹⁹Ir and ¹⁷⁶Lu as a function of the cadmium filter thickness, the mast probable energy of the Maxwellian flux and the epi-thermal index. An infinite slab geometry and isotropic flux were assumed in the calculations.

The calculated values of the cutoff energies are compared with those for 1/V detector, and are related to the resonance energies near the cutoff energy. If the resonance energy is lower than that of the 1/V detector, and the neutron spectrum and filter are same, the cutoff energy is lower than that of the 1/V detector. Such cases include ²³⁵U and ¹⁷⁶Lu with thin filter, ¹⁹¹Ir with thick filter, and ²³⁹Pu with either thin or thick filter. If the resonance energy is higher than the E _c of the 1/V detector, the cutoff energy is higher, such cases being ¹⁹¹Ir with thin filter, ¹⁷⁶Lu with thick filter and ¹¹⁵In with either thin or thick filter. And if the resonance energy is very much higher than the E _c of the 1/V detector, as in the case of Au with thin filter, the cutoff energy approaches the value of the 1/V detector.     

Analytical solution to a classical slowing-down problem

A classical spatially homogeneous, time-dependent, slowing-down problem for test particles, interacting like Maxwellian particles with a fixed background of field particles, is solved analytically. Curves representing the relevant distribution function, as a function of the speed for fixed times, are reported and illustrated on physical grounds.     

Beryllium diffusion in zirconium

The diffusion coefficients of ⁷Be in both α and β phases of Zr, are reported. The temperature dependence of the diffusion coefficient in the α phase may be expressed by $\text{D}{}^{\mathrm{Be}}{}_{\mathrm{\alpha -Zr}}\text{= 0.33 exp(?31900/RT) cm}{}^2\text{/s}$. The measured values in the β phase are in agreement with previously literature reported data, which give a temperature dependence expressed by $\text{D}{}^{\mathrm{Be}}{}_{\mathrm{\beta -Zr}}\text{= 8.33 × 10}{}^{\mathrm{?2}}\text{exp(?31800/RT) cm}{}^2\text{/s}$. Be diffusion in Zr, which is consistent with an interstitial-like behavior, is analyzed in terms of the Anthony and Turnbull conditions, and atomic size criteria. It is concluded that the latter is a very important parameter when assessing the possibility of significant interstitial-like dissolution.     

Silver diffusion in zirconium

The diffusion coefficients of Ag in both α and β phases of Zr are reported. The temperature dependence of the diffusion coefficients may be expressed by and and is strongly dependent on the phase transition. The general diffusion behaviour is analyzed in terms of the Hägg and the Anthony and Turnbull rules, indicating that Ag diffuses as substitutional in Zr.     

离子束混合中的扩散、热扩散与化学反应效应

离子束混合的理论研究目前集中在混合机制。已提出的机制主要有碰撞级联混合与辐射增强扩散混合。在文献[5、6]中我们给出了这两种机制统一处理的模型与数学表述。     

Ab initio-based diffusion theory and tracer diffusion in Ni-Cr and Ni-Fe alloys

In this paper, ab initio modeling is used to predict diffusion relevant thermodynamic and kinetic information for dilute Ni-Cr and Ni-Fe alloys. The modeling results are then used to determine the phenomenological coefficient matrices and the tracer diffusion coefficients for both vacancy and interstitial mediated diffusion. In addition to predicting diffusion coefficients, this ab initio-based approach provides information typically inaccessible to experiments, including the different contributions to diffusion (e.g., electronic excitation effects), the species dependence of interstitial diffusion, and the deviations from Arrhenius-type relations, which are often used to describe and extrapolate experimental diffusion data. It is found that: (1) Cr is the fastest diffusing species in Ni by both vacancy and interstitial diffusion, followed by Fe and then Ni. The enhanced diffusivity of Cr is primarily due to differences in migration barriers and binding energies, not pre-exponential factors. (2) Fe and Cr solutes in Ni have weak interactions with vacancies but Cr solutes bind strongly to interstitial defects. (3) Cr exhibits non-Arrhenius behavior in both vacancy and interstitial mediated diffusion. (4) Temperature dependent electronic contributions have a significant impact on the diffusion in some cases. (5) The vacancy diffusion mechanism in Ni-Cr changes as a function of temperature resulting in vacancy-solute drag below 460 K.     

Iterative methods in diffusion calculations

Typical problems arising in 2- or 3-D diffusion calculations of flux distributions in nuclear systems using iterative methods are illustrated. The problems of the initial guess, reliability of the converged solution and roundoff errors are considered. Examples of PWR core computations are given and discussed.     

Helium bubbles formation in aluminum: Bulk diffusion and near-surface diffusion using TEM observations

Experimental and analytical investigation of helium bubble formation and growth in aluminum is presented. A pure aluminum with 0.15 wt% of ¹⁰B was neutron-irradiated in the Soreq nuclear reactor to get homogeneous helium atoms in the metal according to the reaction . Formation and growth of helium bubbles was observed in situ by heating the post-irradiated metal to 470 °C in TEM with a hot stage holder. It was found that above 400 °C the change in the bubble shape takes less than a second. In other experiments the Al-¹⁰B was first heated in its bulk shape and then observed in TEM at room temperature. In this case the helium bubble formation takes hours. Analytical evaluation of the diffusion processes in both cases was done to explain the experimental results. The number of helium atoms in a bubble was calculated from the electron energy loss spectrum (EELS) measurements. These measurements confirmed the hard sphere equation of state (EOS) for inert gases that was used in the analytical diffusion calculations.     

Oxygen diffusion in β-Zircaloy

The diffusion of oxygen in β-Zircaloy-4 has been studied from 900 to 1500°C with survey measurements for β-zirconium and β-Zircaloy-2. The tracer diffusivity was measured over the entire temperature range and the chemical diffusivity from 1100 to 1450°C. The experiments were performed by using oxygen-18 as the tracer and activating it by proton bombardment. Some complementary measurements were made using Auger Electron Spectroscopy. The results indicated that the tracer and chemical diffusivity of oxygen in β-Zircaloy-4 are statistically identical, and that there is no oxygen concentration dependence over the oxygen concentration range studied, 0.1 to 0.6 wt.%. The temperature dependence of the diffusivity of ¹⁸O from 1000 to 1500°C is given by D = 2.48 × 10^?2 exp(?28200/RT) cm²/sec. The results for the β-zirconium and β-Zircaloy-2 indicated that the compositional differences between the three host materials exert no influence upon the oxygen diffusivity. An examination of the activation entropy, calculated assuming that Snoek's model describes the diffusion process, indicates that this model probably is not appropriate.     

Fission-enhanced diffusion in dispersion fuels

Irradiation-induced diffusion in finite, two-phase systems is analyzed and applied to the geometry of dispersion fuels of the type used in research and test reactors. A fissioning sphere irradiates the surrounding medium in which fission also takes place. In place of the fission rate used in conventional irradiation-induced diffusion coefficient (D^∗) correlations, the energy deposition rates due to electronic and nuclear stopping of the fission fragments are separated. The former is used to drive the point-defect contribution to D^∗ and the latter is the source of the thermal-spike component. This separation accounts for the preponderance of electronic energy loss early in the track of a fission-fragment and the dominance of nuclear stopping near the end of the range. This distinction accounts for the difference in the relative intensities of these two energy loss modes in a fission-fragment that exits one phase and deposits energy in an adjacent medium in which D^∗ is to be determined. Fission-fragment stopping powers and projected ranges are obtained from SRIM software, thereby permitting extraction of the two types of energy deposition rates from the fission rate. As expected, the ratio of nuclear stopping to electronic stopping in the medium surrounding a fissioning inclusion increases with distance from the interface. The effective irradiation-enhanced diffusivity for use in the diffusion equation depends upon two parameters: the fraction of D^∗ in an infinite, homogeneous solid attributable to nuclear stopping and the ratio of the volumetric fission rates in the dispersed and continuous phases.     

Averaging the neutron diffusion equation

This paper presents a general theoretical analysis of the neutron motion problem in a nuclear reactor, where large variations on neutron cross-sections normally preclude the use of the classical neutron diffusion equation. A volume-averaged neutron diffusion equation (VANDE) is derived which includes correction terms to diffusion and nuclear reaction effects. A method is presented to determine closure-relationships for the VANDE (e.g., effective diffusivity). In order to describe the distribution of neutrons in a highly heterogeneous configuration, it was necessary to extend the classical neutron diffusion equation. Thus, the averaged diffusion equation includes two correction factors: the first correction is related with the absorption process of the neutron and the second correction is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. As an example of the VANDE, the plane source in an infinite medium was considered to study the effects of the correction factors on the neutron flux, and the results were compared with classic solution.