辐照材料的肿胀理论(Ⅰ)——中性尾闾

本文从反应扩散方程出发,研究在辐照条件下,微洞和位错(无应力场)周围点缺陷的分布情况。对含有点缺陷复合项的定态的反应扩散方程,给出了一种近似求解的方法并分别得到了微洞和位错吸收点缺陷的汇强度。从所得结果与前人略去复合项的结果比较可知,微洞较大时,复合项对汇强度的影响变得重要;对于位错,当点缺陷产生率较大时,考虑了复合项后所得的汇强度可达前人结果的1.5倍以上。 关键词：     

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,模型考虑了温度效应对点缺陷的影响以及空位和间隙的产生和复合.选择400—800 K温度区间、0—16 dpa辐照剂量范围的Fe-Cr体系为对象,研究在不同服役温度和辐照剂量下的空位扩散、复合和簇聚形成空洞的过程.在400—800 K温度区间,随着温度的升高,Fe-Cr合金空洞团簇形核率呈现出先升高后下降的趋势.考虑空位与间隙的重新组合受温度的影响可以很好地解释空洞率随温度变化时出现先升高后降低的现象.由于温度的变化将影响Fe-Cr合金中原子离位阀能,从而影响产生空位和间隙原子.同一温度下,空洞半径和空洞的体积分数随辐照剂量的增大而增大.辐照剂量的增大,级联碰撞反应加强,空位与间隙原子大量产生,高温下空位迅速的扩散聚集在Fe-Cr合金中将形成更多数量以及更大尺寸的空洞.     

Dislocation vs. production bias revisited with account of radiation-induced emission bias. I. Void swelling under electron and light ion irradiation

Early experimental data on void swelling in electron-irradiated materials disagree with the dislocation bias models based on the dislocation-point defect elastic interactions. Later, this became one of the factors that prompted the development of models based on production bias (PBM) as the main driver for swelling, which assumed that the dislocation bias was much lower than that predicted by theoretical analyses of dislocation bias. However, the PBM in its present form fails to account for important and common observations, namely, the indefinite void growth often observed under cascade irradiation and the swelling saturation observed under high-dose irradiation and in void lattices. In this paper, we show that these contradictions can be naturally resolved in the framework of the rate theory that accounts for the radiation-induced vacancy emission from extended defects, such as voids, dislocations and grain boundaries. This modification introduces a new bias type in the theory, namely, the emission bias. This modified rate theory agrees well with the experimental data and demonstrates that the original dislocation bias should be used in rate theory models along with the emission bias in different irradiation environments. The modified theory predictions include, but are not limited to, the radiation-induced annealing of voids, swelling saturation under high-dose irradiation, generally, and in void lattices, in particular.     

Radiation enhanced diffusion in face centered cubic cu-zn alloys

The enhancement of diffusion by neutron irradiation has been investigated on a Cu-36 percent Zn alloy for various neutron fluxes and irradiation temperatures by means of in-pile measurements of electrical resistivity. For fresh samples the diffusion rate depends on temperature with an activation energy of 0.35 eV. During repeated irradiations the diffusion rate decreases and becomes nearly temperature independent. The variation of the concentration of interstitials and vacancies with irradiation time has been numerically calculated for various neutron fluxes, irradiation temperatures and sink concentrations. A comparison of the experimental and theoretical results shows that the point defects annihilate in fresh samples mainly by pair recombination and in samples which had been repeatedly cycled by pair recombination and at fixed sinks. Point defect clusters acting as sinks are created during the course of the irradiation as shown by electron microscope investigations. The radiation enhanced diffusion rate was found to depend on interstitials only, the activation energy of which was determined to 0.70 eV.     

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.     

The effect of phason defects on the radiation-induced swelling of quasicrystalline materials

The radiation-induced vacancy swelling of quasicrystals is considered. In quasicrystals, the dislocation kinetics involves the formation of phasons: vacancy- and interstitial-like localized topological defects. Phasons interact with radiation-induced point defects (PD; vacancies and interstitials) and influence the swelling behavior of quasicrystals. After absorption of vacancies, phasons of the interstitial type transform into phasons of the vacancy type and vice versa. In other words, phasons are the recombination centers of alternating polarity for PD. Assuming that (i) the production rate of phasons is proportional to the dislocation climbing rate and (ii) voids are the sinks for mobile phasons, the set of rate equations for PD and phasons is formulated and analyzed both analytically and numerically. It is shown that the swelling rate is lower in quasicrystals compared with crystals. Growth rates of loops and voids, as well as the swelling rate, strongly depend on the phason concentration which is controlled by phason diffusion to sinks.     

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     

Evolution pattern of collision cascades in bcc V with different grain boundary structures: an atomic scale study

Abstract

In this paper, by means of atomic-scale simulations, we investigate modifications of the evolution pattern of collision cascades in bcc vanadium (V) with different grain boundary (GB) structures on picosecond (ps) timescale. In primary damage state, in agreement with previous results of bcc and fcc bi-crystals, we find that the GBs in V are biased towards interstitials. The biased absorption of interstitials over vacancies reduces the in-cascade annihilation of vacancy-interstitial pairs and leads to aggregation of more number of vacancies in the grains interiors. The sessile vacancies accumulate in the bulk and form immobile vacancy clusters; in contrast, the glissile interstitials disperse in the damage zone and mostly diffuse in the form of single self-interstitial atoms (SIAs)/di-interstitials towards the GB region. Moreover, meanwhile, as we discuss the mechanisms that reduce (or increase) the concentration of defects in bi-crystal structures on picosecond timescale, we study the energetics of defects in close vicinity of pristine GBs, as an alternative driving force that facilitates formation and accumulation of defects in the GB regions. Finally, in a prolonged irradiation, we examine stability and sink properties of the damaged GBs. The results reveal that, irrespective of GB structure, the presence of grain boundaries leads to aggregation of more number of vacancies in the grain interiors in continuous bombardment. Overall, based on the results obtained in the primary damage event and the prolonged irradiation, we conclude that the GBs in bcc V act as efficient defect sinks on the simulated time frame.     

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.     

A study of void size growth in nonequilibrium stochastic systems of point defects

We study properties of voids growth dynamics in a stochastic system of point defects insolids under nonequilibrium conditions (sustained irradiation). It is shown thatfluctuations of defect production rate (external noise) increase the critical void radiuscomparing to a deterministic system. An automodel regime of void size growth in astochastic system is studied in detail. Considering a homogeneous system, it is found thatexternal noise does not change the universality of the void size distribution function;the mean void size evolves according to classical nucleation theory. The noise increasesthe mean void size and spreads the void size distribution. Studying dynamics of spatiallyextended systems it was shown that vacancies remaining in a matrix phase are able toorganize into vacancy enriched domains due to an instability caused by an elastic latticedeformation. It is shown that dynamics of voids growth is defined by void sinks strengthwith void size growth exponent varying from 1/3 up to 1/2.     

A phase-field modeling of void swelling in the Austenitic stainless steel

Two-dimensional phase-field simulations of void swelling in the Austenitic stainless steel were performed for irradiated materials. A numerical model was established for void swelling with an implementation of the elasticity effect, and we examined the roles of the applied stress and grain boundary sink strength and Frenkel defect recombination in determining the void swelling rate. The obtained results were compared with the existing experimental observations.     

Thermal evolution of defects produced by implantation of H, D and He in Silicon

Despite decades of study, voids in silicon produced by implantation of H or He followed by annealing continue to be a topic of interest. There are two key applications: gettering of heavy metal impurities, and “ion cutting” used in silicon-on-insulator fabrication. Positron annihilation is one of the few techniques that can probe the vacancies and vacancy clusters that are the precursors to void formation. Data from recent studies will be discussed, including (I) isotopic substitution, in which comparisons of H vs. D implantation permit examination of the impact of primary point defects vs. chemical effects. Remarkable differences exist between H and D in blistering of silicon - ion doses 2-3 times higher are required for blistering with D than with H, despite a higher rate of primary defect production for D; (II) the effect of annealing temperature ramp-rate, in which we show that ramp-rate has a significant impact on residual defects, despite which it is so disregarded as to often be omitted from published reports; and (III) comparisons with electron microscopy which suggest that positron annihilation can be insensitive to large voids. In these studies, positron annihilation augments data from techniques including ion channelling, Raman scattering and electron microscopy; the suite of techniques allows elucidation of the interplay between implanted impurities and the vacancies and interstitials created by implantation.     

孔洞和空位对单晶铝力学性能影响的分子动力学研究

采用分子动力学方法模拟含孔洞的单晶铝单轴拉伸过程,研究晶向、孔洞体积分数、空位体积分数等对孔洞生长的影响.结果表明：对于不同的晶向,决定孔洞生长变形的微观机制不同.[010]晶向单轴拉伸情况下,形变机制主要是｛111｝面位错引起的堆垛层错;[111]晶向单轴拉伸情况下,形变机制主要是位错的移动、堆积与发射.此外,孔洞及空位的体积分数对[010]、[111]晶向的孔洞生长过程也有着明显的影响.总的来说,随着孔洞或者空位体积分数的增加,材料的杨氏模量变小,屈服强度、屈服应变下降.     

Positron annihilation studies of vacancy-type defects

The annihilation radiation of low energy positrons gives information on the electronic and defect structure of solids. There are three conventionally measurable quantities: the positron lifetime, the angular correlation of 2 annihilation radiation and the Doppler-broadened annihilation line shape. In the presence of lattice defects the annihilation characteristics show considerable changes. This is due to positron trapping at defects like vacancies and their agglomerates, voids, dislocations and grain boundaries. The concentration of defects can be deduced from the ratio of trapped and free positrons.The annihilation characteristics are different for different defect configurations. Positrons reveal vacancy agglomeration and the lifetime of trapped positrons gives estimates on the size of microvoids in the range of 2–10 Å. Various examples on the study of equilibrium and non-equilibrium defects, radiation damage and defect annealing are presented. Special emphasis is given to vacancy recovery and vacancy-impurity interactions in electron and neutron irradiated bcc transition metals like Fe, Mo, Nb, Ta.     

Simulations of the effects of 1-d interstitial diffusion on void lattice formation during irradiation

This paper describes the use of simulation techniques to examine some of the processes involved in the alignment of voids under the influence of one-dimensional self interstitial atom (1-d SIA) transport. The work follows the paper of Heinisch and Singh on this topic but a different and simpler methodology is used. Besides repeating the scenarios studied by Heinisch and Singh, the effects of re-nucleation and the influence of vacancies have been introduced. One of the important processes that emerged from the results was the barrier to precise void alignment caused by the SIA-induced coalescence of aligned voids. This appears to prevent the formation of stable void lattices by any 1-d SIA transport mechanism, a point supported by the initial void alignment in the mechanism requiring swelling values well above those found experimentally. A full consideration of the void lattice phenomenon shows that the one-dimensional diffusion of self-interstitials central to the production bias model of irradiation damage cannot be the only mode of anisotropic diffusion available under irradiation.     

Defects in rutile and anatase polymorphs of TiO2: kinetics and thermodynamics near grain boundaries

The direct consequence of irradiation on a material is the creation of point defects-typically interstitials and vacancies, and their aggregates-but it is the ultimate fate of these defects that determines the material's radiation tolerance. Thus, understanding how defects migrate and interact with sinks, such as grain boundaries, is crucial for predicting the evolution of the material. We examine defect properties in two polymorphs of TiO(2)-rutile and anatase-to determine how these materials might respond differently to irradiation. Using molecular statics and temperature accelerated dynamics, we focus on two issues: how point defects interact with a representative grain boundary and how they migrate in the bulk phase. We find that grain boundaries in both polymorphs are strong sinks for all point defects, though somewhat stronger in rutile than anatase. Further, the defect kinetics are very different in the two polymorphs, with interstitial species diffusing quickly in rutile while oxygen defects-both interstitials and vacancies-are fast diffusers in anatase. These results allow us to speculate on how grain boundaries will modify the radiation tolerance of these materials. In particular, grain boundaries in rutile will lead to a space charge layer at the boundary and a vacancy-rich damage structure, while in anatase the damage structure would likely be more stoichiometric, but with larger defects consisting primarily of Ti ions.     

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.     

Defect concentration profiles near the surface in nickel irradiated with 2 MeV electrons

Abstract

In the next nearest surface region the vacancy concentration is constant and independent of the irradiation temperature between 750 and 300°C and decreases with increasing electron flux. The conentrations of interstitials and of vacancies in the sink-free bulk of the material are equal and depend on the irradiation temperature, and are almost independent of the irradiation flux. The activation migration energies of vacancies and of interstitials decrease with increasing irradiation flux.It is further shown that the dynamic steady state defect concentrations resulting from the rate equations are artificial concentrations, which will not be achieved in finite times.     

Modification of radiation damage microstructure by helium

Current experimental findings on the effects of helium on the evolution of radiation damage microstructure in metals at temperatures where vacancies are mobile are reviewed. It is shown that helium concentrations as low as a few parts per million promote the formation of cavities and dislocations, may increase or decrease swelling, and can alter the development of precipitate phases. Mechanisms underlying these processes are discussed in terms of the theory of radiation effects. Helium-vacancy trapping and the stabilization of cavities is seen as the unifying, underlying feature. Promotion of cavities is explained by reduction of critical cavity size by helium. This promotion, and the attendant increase in dislocations, changes the point-defect sink strengths and thereby modifies swelling. Correspondingly, solute segregation at sinks is changed, resulting in alteration of precipitate phases.