Void ordering in hexagonal close-packed metals

Voids occur in solids exposed to high-temperature particle irradiation. In hexagonal metals with lattice-parameter ratiosc/a which are smaller than for ideal close-packing, voids arranged in layers parallel to the basal plane have been observed after high-dose irradiation, whereas more perfect void ordering, e.g. the formation of void lattices like in cubic metals, has not been found. In this paper it is shown that it is the two-dimensional diffusion of self-interstitial atoms in the basal plane which gives rise to the layer-type arrangement of voids. The possibility of other void-ordering phenomena in hexagonal metals is investigated. It is demonstrated that, under certain circumstances, one-dimensional diffusion of a metastable self-interstitial configuration may lead to the arrangement of voids in columns perpendicular to the basal plane.     

Diffusion anisotropy and void development under cascade irradiation

Cascade irradiation of metals gives rise to swelling as a result of the creation of voids and the evolution of the void ensemble. Under suitable circumstances, the originally disordered void distribution transforms into to a void lattice. As demonstrated previously, the understanding of the evolution and the unique features of the void ensemble requires a difference in the anisotropy of the diffusion (DAD) of vacancies and self-interstitial atoms (SIAs), which is achieved by one-dimensional diffusion of the SIAs. On the other hand, void swelling has been successfully modeled in terms of three-dimensional diffusion of both vacancies and SIAs. In the present paper it is shown that these seemingly contradicting interpretations and all related observations can be quantitatively reconciled by a small DAD created by only ～1% of SIAs diffusing one-dimensionally. It is also demonstrated that at the initial stage of void-lattice formation, ordering occurs mainly on close-packed crystal planes, which is in contrast to the naïve expectation that one-dimensional diffusion of SIAs should result in a void ordering along close-packed directions. Finally it is found that, in the case of a small DAD, voids annihilate via stochastic shrinkage much faster than by coalescence. This falsifies the argument in the literature that one-dimensional diffusion of SIAs would necessarily lead to the coalescence of voids and destabilization of the void lattice.     

Self-organization of cavities under irradiation

In the present paper two examples of self-organization in solids under irradiation are considered on the basis of original mechanisms, namely, the ordering of voids in void lattices under high temperature irradiation and the alignment of gas bubbles in bubble lattices under low-temperature gas atom implantation. The ordering of cavities (i.e. voids or gas bubbles) is proposed to arise due to a dissipative interaction between cavities induced by the interstitial dislocation loop absorption and punching, respectively, which represent anisotropic mechanisms of atomic transport.     

Unlimited damage accumulation in metallic materials under cascade-damage conditions

Most experiments on neutron or heavy-ion cascade-produced irradiation of pure metals and metallic alloys demonstrate unlimited void growth as well as development of the dislocation structure. In contrast, the theory of radiation damage predicts saturation of void size at sufficiently high irradiation doses and, accordingly, termination of accumulation of interstitial-type defects. It is shown in the present paper that, under conditions of steady production of one-dimensionally (1-D) mobile clusters of self-interstitial atoms (SIAs) in displacement cascades, any one of the following three conditions can result in indefinite damage accumulation. First, if the fraction of SIAs generated in the clustered form is smaller than some finite value of the order of the dislocation bias factor. Second, if solute, impurity or transmuted atoms form atmospheres around voids and repel the SIA clusters. Third, if spatial correlations between voids and other defects, such as second-phase precipitates or dislocations, exist that provide shadowing of voids from the SIA clusters. The driving force for the development of such correlations is the same as for void lattice formation and is argued to be always present under cascade-damage conditions. It is emphasised that the mean-free path of 1-D migrating SIA clusters is typically at least an order of magnitude longer than the average distance between microstructural defects; hence, spatial correlations on the same scale should be taken into consideration. A way of developing a predictive theory is discussed. An interpretation of the steady-state swelling rate of ～1%/displacement per atom (dpa) observed in austenitic steels is proposed.     

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.     

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.     

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.     

One-dimensional migration of interstitial clusters in SUS316L and its model alloys at elevated temperatures

For self-interstitial atom (SIA) clusters in various concentrated alloys, one-dimensional (1D) migration is induced by electron irradiation around 300 K. But at elevated temperatures, the 1D migration frequency decreases to less than one-tenth of that around 300 K in iron-based bcc alloys. In this study, we examined mechanisms of 1D migration at elevated temperatures using in situ observation of SUS316L and its model alloys with high-voltage electron microscopy. First, for elevated temperatures, we examined the effects of annealing and short-term electron irradiation of SIA clusters on their subsequent 1D migration. In annealed SUS316L, 1D migration was suppressed and then recovered by prolonged irradiation at 300 K. In high-purity model alloy Fe-18Cr-13Ni, annealing or irradiation had no effect. Addition of carbon or oxygen to the model alloy suppressed 1D migration after annealing. Manganese and silicon did not suppress 1D migration after annealing but after short-term electron irradiation. The suppression was attributable to the pinning of SIA clusters by segregated solute elements, and the recovery was to the dissolution of the segregation by interatomic mixing under electron irradiation. Next, we examined 1D migration of SIA clusters in SUS316L under continuous electron irradiation at elevated temperatures. The 1D migration frequency at 673 K was proportional to the irradiation intensity. It was as high as half of that at 300 K. We proposed that 1D migration is controlled by the competition of two effects: induction of 1D migration by interatomic mixing and suppression by solute segregation.     

One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper

Atomic-scale computer simulation has been used to study the thermally activated atomic transport of self-interstitial atoms (SIAs) in the form of planar clusters in pure Cu and f-Fe. There is strong evidence that such clusters are commonly formed in metals during irradiation with high-energy particles and play an important role in accumulation and spatial distribution of surviving defects. An extensive study of the mobility of SIA clusters containing two to 331 interstitials has been carried out using the molecular dynamics simulation technique for the temperature range from 180 to 1200 K. The results obtained show that clusters larger than three to four SIAs are one-dimensionally mobile in both Cu and Fe. Large clusters of more than 100 SIAs in Cu and 300 SIAs in Fe have significantly reduced mobility. The problem of describing one-dimensional (1D) motion in three-dimensional space is discussed. An attempt is made to describe the mobility of SIA clusters within the approximation of 1D diffusion. For clusters in both metals the effective migration energy of 1D diffusion as estimated via the jump frequency of the cluster centre of mass is found to be independent of the number of SIAs in the clusters, although the cluster jump frequency decreases with increasing cluster size. Mechanisms of 1D mobility of interstitial clusters are discussed.     

Theory of dust voids in plasmas

Dusty plasmas in a gas discharge often feature a stable void, i.e., a dust-free region inside the dust cloud. This occurs under conditions relevant to both plasma processing discharges and plasma crystal experiments. The void results from a balance of the electrostatic and ion drag forces on a dust particle. The ion drag force is driven by a flow of ions outward from an ionization source and toward the surrounding dust cloud, which has a negative space charge. In equilibrium the force balance for dust particles requires that the boundary with the dust cloud be sharp, provided that the particles are cold and monodispersive. Numerical solutions of the one-dimensional nonlinear fluid equations are carried out including dust charging and dust-neutral collisions, but not ion-neutral collisions. The regions of parameter space that allow stable void equilibria are identified. There is a minimum ionization rate that can sustain a void. Spatial profiles of plasma parameters in the void are reported. In the absence of ion-neutral collisions, the ion flow enters the dust cloud's edge at Mach number M=1. Phase diagrams for expanding or contracting voids reveal a stationary point corresponding to a single stable equilibrium void size, provided the ionization rate is constant. Large voids contract and small voids expand until they attain this stationary void size. On the other hand, if the ionization rate is not constant, the void size can oscillate. Results are compared to recent laboratory and microgravity experiments.     

Local nonequilibrium mass transfer in a two-component system under external pulsed irradiation with energy fluxes

The nonisothermal mass transfer in metal materials under irradiation with concentrated energy fluxes is studied in the one-dimensional approximation. Local nonequilibrium equations of extended irreversible thermodynamics are used to describe the transfer phenomena. It is established that, for short times (on the order of the time required for relaxation of the diffusion flow to its local-equilibrium value), the wave mechanism for mass transfer is dominant over the diffusion one, ensuring that the impurity-concentration profiles have a nonmonotonous form. The degree of influence of the space-time nonlocality of the transfer processes on the formation of concentration profiles is estimated, and the model results are compared with the experimental data.     

Rates of diffusion controlled reactions for one-dimensionally-moving species in 3D space

ABSTRACT

The asymmetry in diffusion dimensionality between self-interstitial atom (SIA) clusters and vacancies is a fundamental feature of irradiation damage in crystals, leading to a defect buildup imbalance that manifests itself as measurable dimensional and mechanical property changes. It is well known that, while vacancies and mobile vacancy clusters diffuse in a three-dimensional (3D) fashion, SIA clusters perform one-dimensional motion along mostly rectilinear trajectories. Despite this, a complete set of kinetic coefficients, including coagulation reaction rates and sink strengths, does not exist for 1D-moving objects. In this paper, we derive analytical expressions for these coefficients from continuum diffusion theory particularised to 1D motion. Moreover, we carry out kinetic Monte Carlo simulations of numerical replicas of the geometry of diffusing particles and sinks to validate the proposed solutions. Our simulations, which are conducted entirely independently from the analytical derivations, reveal excellent agreement with the proposed expressions, adding confidence to their validity. We compare the 1D and 3D cases and discuss their relevance for kinetic codes for damage accumulation calculations.     

Vacancy effects on one-dimensional migration of interstitial clusters in iron under electron irradiation at low temperatures

We performed in situ observation of one-dimensional (1D) migration of self-interstitial atom (SIA) clusters in iron under electron irradiation at 110–300 K using high-voltage electron microscopy. Most 1D migration was stepwise positional changes of SIA clusters at irregular time intervals at all temperatures. The frequency of 1D migration did not depend on the irradiation temperature. It was directly proportional to the damage rate, suggesting that 1D migration was induced by electron irradiation. In contrast, the 1D migration distance depended on the temperature: distribution of the distance ranged over 100 nm above 250 K, decreased steeply between 250 and 150 K and was less than 20 nm below 150 K. The distance was independent of the damage rate at all temperatures. Next, we examined fluctuation in the interaction energy between an SIA cluster and vacancies of random distribution at concentrations 10^?4–10^?2, using molecular statics simulations. The fluctuation was found to trap SIA clusters of 4 nm diameter at vacancy concentrations higher than 10^?3. We proposed that 1D migration was interrupted by impurity atoms at temperatures higher than 250 K, and by vacancies accumulated at high concentration under electron irradiation at low temperatures where vacancies are not thermally mobile.     

Self-formation of void array in Al2O3 crystal by femtosecond laser irradiation

The femtosecond laser induced void array inside Al2O3 crystals was discussed.The void array was formed spontaneously under the irradiation of a single beam of infrared femtosecond laser which was focused at a fixed point inside the Al2O3 crystal sample.It was found that the regular voids only could be fabricated near the sample surface,which was different from the situation in CaF2 single crystal reported before.The possible mechanism of the phenomena was also discussed.     

Phase change and stress wave in picosecond laser–material interaction with shock wave formation

When background gas is present in pulsed laser–material interaction, a shock wave down to the nanoscale will emerge. The background gas will affect the phase change and explosion in the target. This study is focused on the void dynamics and stress wave in a model material (argon crystal) under picosecond pulsed laser irradiation. Our results show that existence of ambient gas and the shock wave significantly suppresses the void formation and their lifetime. Void dynamics, including their growing rate, lifetime, and size under the influence of ambient gas are studied in detail. All the voids undergo an accelerating and decelerating process in the growth. The collapsing process is almost symmetrical to the growing process. Higher laser fluence is found to induce an obvious foamy structure. Stress wave formation and propagation, temperature contour, and target and gas atom number densities are studied to reveal the underlying physical processes. Although the interaction of the plume with ambient gas significantly suppresses the void formation and phase explosion, no obvious effect is found on the stress wave within the target. Very interestingly, secondary stress waves resulting from re-deposition of ablated atoms and void collapse are observed, although their magnitude is much smaller than the directly laser-induced stress wave.     

冲击加载下孔洞贯通的微观机理研究

利用分子动力学方法计算模拟了沿〈100〉晶向冲击加载下单晶铜中双孔洞的贯通过程.发现孔洞周围发射剪切型位错环是孔洞塌缩和增长的原因.在拉伸阶段,孔洞首先分别独立增长,随后其周围塑性变形区开始交叠和相互作用,最后两个孔洞开始直接贯通.这种贯通模式和实验对延性材料中孔洞贯通过程的显微观察结果一致.对四种不同θ值（θ为两个孔洞中心连线与冲击加载方向之间的夹角）的模型分别进行了计算模拟,发现在相同的冲击加载强度下,θ＝0°和θ＝30°的孔洞之间没有相互贯通; 关键词： 纳米孔洞 分子动力学 冲击加载 贯通     

Photocarrier radiometry for noncontact evaluation of space monocrystalline silicon solar cell under low-energy electron irradiation

A space monocrystalline silicon(c-Si) solar cell under low-energy( 1 MeV) electron irradiation was investigated using noncontact photocarrier radiometry(PCR). Monte Carlo simulation(MCS) was employed to characterize the effect of different energy electron irradiation on the c-Si solar cell. The carrier transport parameters(carrier lifetime, diffusion coefficient, and surface recombination velocities) were obtained by best fitting the experimental results with a theoretical one-dimensional two-layer PCR model. The results showed that the increase of the irradiation electron energy caused a large reduction of the carrier lifetime and diffusion length. Furthermore, the rear surface recombination velocity of the Si:p base of the solar cell at the irradiation electron energy of 1 Me V was dramatically enhanced due to 1 MeV electron passing through the whole cell. Short-circuit current(I sc) degradation evaluated by PCR was in good agreement with that obtained by electrical measurement.     

Highly regular nanometer-sized hexagonal pipes in 6H-SiC(0001)

An array of troughs was prepared on a 6H-SiC(0001) surface using focused ion beam (FIB) patterning. Troughs were etched with various ion doses and close-to-circular voids of increasing depths for larger ion doses were obtained. The samples were then etched in a hot-wall reactor at a hydrogen partial pressure of 13 mbar at 1800 °C. The resulting morphological reorganizations have been studied by scanning electron and atomic force microscopy. Very regular hexagonal voids with facets oriented perpendicular to the surface were obtained after hydrogen etching. The voids were surrounded by regular secondary facets of lower inclination. Whereas the depth of the voids increases with ion dose, the void diameter and facet sizes stay constant. This effect is explained by surface diffusion during hydrogen etching. The FIB technique in combination with hydrogen etching allows the preparation of very regular surface patterns and highly ordered wells and tubes for nanometer-sized sieves and photonic crystals. PACS 47.70.Fw; 68.37.-d; 68.37.Hk; 68.37.Ps; 81.65.Cf     

Void formation in Nickel during high temperature proton irradiation

Pure Ni foils, doped with He from 0 to 28 appm, were irradiated with protons at temperatures in the range 0.3–0.6 T_m (T_m = melting point in °K) and void formation was studied. The influence of He doping, irradiation temperature and alloying were investigated. For constant He content and proton fluence, void number density and swelling are maximum at about 400°C, while the void size increases with temperature. Most voids are octahedral in shape with no sign of truncation. Helium is required to nucleate voids, and lowering the stacking fault energy by alloying suppresses void formation completely. Present results suggest that void nucleation is inhomogeneous. Some implications of these findings are discussed.