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 migration of interstitial clusters in SUS316L and its model alloys under electron irradiation

The one-dimensional (1D) migration of interstitial clusters in austenitic stainless steel SUS316L and its model alloys, namely, Fe–18Cr–13Ni, Fe–18Cr–13Ni–0.012C, and Fe–18Cr–13Ni–1.7Mn (mass %), was examined using in situ observation by high-voltage electron microscopy. Such 1D migration was confirmed to occur along the ?110? direction at irregular intervals in all these alloys under 1250-kV electron irradiation at room temperature. The frequency of 1D migration was found proportional to electron beam intensity, and was about 1/10 that in high-purity iron under the same irradiation intensity. The distance of 1D migration in the four alloys was less than 10?nm, which was much shorter than that in high-purity iron. No clear difference in the frequency or distance of 1D migration was observed among the four alloys, suggesting that minor solute/impurity elements have no apparent effect on 1D migration in SUS316L.     

Obstacles for one-dimensional migration of interstitial clusters in iron

Interstitial clusters are known to cause frequent one-dimensional (1D) jumps (stepwise positional changes) under electron irradiation around room temperature. The distance of 1D jumps in iron was examined in detail through in-situ observation using high-voltage electron microscopy. The 1D jump distance was found to be longer for smaller clusters in specimens of higher purity, although the distance did not depend on the irradiation beam intensity and electron energy. The distribution of the 1D jump distance was well described by the distribution of the free path of interstitial clusters migrating through randomly distributed impurity atoms. The 1D jump process is considered as fast 1D diffusion of interstitial clusters at low activation energy from the point where the cluster detrapped from an impurity atom to the point where the cluster was trapped again by another impurity. Electron irradiation provides a trigger for causing 1D migration by detrapping of clusters from impurity atoms.     

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.     

Effect of impurities on the growth of {113} interstitial clusters in silicon under electron irradiation

The growth and shrinkage of interstitial clusters on {113} planes were investigated in electron irradiated Czochralski grown silicon (Cz-Si), floating-zone silicon (Fz-Si), and impurity-doped Fz-Si (HT-Fz-Si) using a high voltage electron microscope. In Fz-Si, {113} interstitial clusters were formed only near the beam incident surface after a long incubation period, and shrank on subsequent irradiation from the backside of the specimen. In Cz-Si and HT-Fz-Si, {113} interstitial clusters nucleated uniformly throughout the specimen without incubation, and began to shrink under prolonged irradiation at higher electron beam intensity. At lower beam intensity, however, the {113} interstitial cluster grew stably. These results demonstrate that the {113} interstitial cluster cannot grow without a continuous supply of impurities during electron irradiation. Detailed kinetics of {113} interstitial cluster growth and shrinkage in silicon, including the effects of impurities, are proposed. Then, experimental results are analyzed using rate equations based on these kinetics.     

Multi-timescale investigation of radiation damage near TiO2 rutile grain boundaries

To understand the interactions between defects and grain boundaries (GBs) in oxides, two atomistic modeling methods were used to examine the role of GBs in a model system, rutile TiO₂, in modifying radiation-induced defect production and annealing. Molecular dynamics was used to investigate defect production near a symmetric tilt GB at both 300?K and 1000?K. The damage production is found to be sensitive to the initial distance of the primary knock-on atom from the GB. We find three distinct regimes in which GBs have different effects. Similar to GBs in metals, the GB absorbs more interstitials than vacancies at certain distances while this behavior of biased loading of interstitials diminishes at other distances. Further, we obtain the statistics of both interstitial and vacancy clusters produced in collision cascades in terms of their compositions at two temperatures. Perfectly stoichiometric defect clusters represent a small fraction of the total clusters produced. Moreover, a significant reduction in the number of interstitial clusters at 1000?K compared to 300?K is thought to be a consequence of enhanced migration of interstitials towards the GB. Finally, the kinetic properties of certain defect clusters were investigated with temperature accelerated dynamics, without any a priori assumptions of migration mechanisms. Small interstitial clusters become mobile at high temperatures while small vacancy clusters do not. Multiple migration pathways exist and are typically complex and non-intuitive. We use this kinetic information to explain experimental observations and predict their long-time migration behavior near GBs.     

Binding enthalpies of nitrogen-vacancy complexes in irradiated α-Fe

Abstract

Dilute iron-nitrogen alloys have been irradiated at low temperatures with electrons or neutrons to varying doses. In the temperature range above Stage III (T  200 K) a previously unknown family of small clusters composed of N interstitials and radiation-induced point defects, i.e. vacancies, could be resolved by means of a sensitive magnetic after-effect technique. Analysis of formation and dissociation kinetics of these clusters leads to nitrogen-vacancy binding energies between 0.08 and 0.5 eV, depending on cluster size. These relatively low values, together with further details of the precipitation kinetics, are shown to support the assumption of a two-interstitial recovery model.     

Non-collinear magnetic moments of seven-atom Cr, Mn and Fe clusters

The non-collinearity of magnetic moments of pentagonal bipyramid Cr₇, Mn₇ and Fe₇ clusters is discussed. The magnetic moments are calculated by the discrete variational non-collinear spin-density functional method. For the Cr₇ cluster, a coplanar magnetic arrangement appears at the large interatomic distance. With decreasing the interatomic distance, the coplanar arrangement changes to the parallel arrangement with a small absolute magnetic moment. For the Mn₇ cluster, the magnetic arrangement changes from coplanar to antiparallel with decreasing the interatomic distance. Also for the Fe₇ cluster, some coplanar magnetic moments appear at the interatomic distance of 2.23 ?. In these coplanar magnetic arrangements, the magnetic moment at the basal site of the pentagon rotates with a step of 144 degrees for the Cr₇ clusters and 72 degrees for the Mn₇ and Fe₇ clusters. Received 30 November 2000     

Dynamic behaviour of nanometre-sized defect clusters emitted from an atomic displacement cascade in Au at 50 K

Abstract

We demonstrate the emission of nanometre-sized defect clusters from an isolated displacement cascade formed by irradiation of high-energy self-ions and their subsequent 1-D motion in Au at 50 K, using in situ electron microscopy. The small defect clusters emitted from a displacement cascade exhibited correlated back-and-forth 1-D motion along the [?1 1 0] direction and coalescence which results in their growth and reduction of their mobility. From the analysis of the random 1-D motion, the diffusivity of the small cluster was evaluated. Correlated 1-D motion and coalescence of clusters were understood via elastic interaction between small clusters. These results provide direct experimental evidence of the migration of small defect clusters and defect cascade evolution at low temperature.     

Magnetism of small V clusters embedded in a Cu fcc matrix: an ab initio study

We present extensive first principles density functional theory (DFT) calculations dedicated to analyze the magnetic and electronic properties of small V _n clusters (n = 1, 2, 3, 4, 5, 6) embedded in a Cu fcc matrix. We consider different cluster structures such as: (i) a single V impurity, (ii) several V₂ dimers having different interatomic distance and varying local atomic environment, (iii) V₃ and (iv) V₄ clusters for which we assume compact as well as 2- and 1-dimensional atomic configurations and finally, in the case of the (v) V₅ and (vi) V₆ structures we consider a square pyramid and a square bipyramid together with linear arrays, respectively. In all cases, the V atoms are embedded as substitutional impurities in the Cu network. In general, and as in the free standing case, we have found that the V clusters tend to form compact atomic arrays within the cooper matrix. Our calculated non spin-polarized density of states at the V sites shows a complex peaked structure around the Fermi level that strongly changes as a function of both the interatomic distance and local atomic environment, a result that anticipates a non trivial magnetic behavior. In fact, our DFT calculations reveal, in each one of our clusters systems, the existence of different magnetic solutions (ferromagnetic, ferrimagnetic, and antiferromagnetic) with very small energy differences among them, a result that could lead to the existence of complex finite-temperature magnetic properties. Finally, we compare our results with recent experimental measurements.     

The non-Arrhenius migration of interstitial defects in bcc transition metals

Thermally activated migration of defects drives microstructural evolution of materials under irradiation. In the case of vacancies, the activation energy for migration is many times the absolute temperature, and the dependence of the diffusion coefficient on temperature is well approximated by the Arrhenius law. On the other hand the activation energy for the migration of self-interstitial defects, and particularly self-interstitial atom clusters, is very low. In this case a trajectory of a defect performing Brownian motion at or above room temperature does not follow the Arrhenius-like pattern of migration involving infrequent hops separated by the relatively long intervals of time during which a defect resides at a certain point in the crystal lattice. This article reviews recent atomistic simulations of migration of individual interstitial defects, as well as clusters of interstitial defects, and rationalizes the results of simulations on the basis of solutions of the multistring Frenkel–Kontorova model. The treatment developed in the paper shows that the origin of the non-Arrhenius migration of interstitial defects and interstitial defect clusters is associated with the interaction between a defect and the classical field of thermal phonons. To cite this article: S.L. Dudarev, C. R. Physique 9 (2008).     

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.     

Sub-nanometer distances and cluster shapes in dense hydrogen and in higher levels of hydrogen Rydberg matter by phase-delay spectroscopy

The inter-atomic distances in potassium clusters of Rydberg matter (RM) at excitation levels n _B = 4–8 were recently measured by phase-delay spectroscopy (Holmlid, J Nanopart Res 12: 273, 2010). Excitation levels n _B < 4 with shorter inter-atomic distances exist for hydrogen clusters, and distances down to 140 pm are now measured with this light-scattering method. The clusters studied have maximum dimensions from 0.3 nm up to several tens of nm, often being planar. A weak carbon dioxide laser beam interacts with the clusters in a tunable RM cavity. A strong fringe structure is observed as a function of the end-grating angular position. Delay lengths in the clusters are derived from the fringe structure, corresponding to twice the distance between rows or planes in the clusters. Good agreement with predicted and a few previously measured distances in excitation levels n _B = 1, 2, and 3 is found. Close-packing is the main structure both in planar and 3D clusters. Planar clusters are only observed for n _B = 1 and 3, while 3D clusters are found in excitation levels n _B = 1, 2 and 3. The cluster–cluster distance in stacks of planar clusters for n _B = 2 and 3 is now observed for the first time.     

Direct observation of local Mn-Mn distances in the paramagnetic compound CsMn(x)Mg(1-x)Br3

We introduce a novel method for local structure determination with a spatial resolution of the order of 0.01 ?. It can be applied to materials containing clusters of exchange-coupled magnetic atoms. We use neutron spectroscopy to probe the energies of the cluster excitations which are determined by the interatomic coupling strength J. Since for most materials J is related to the interatomic distance R through a linear relation dJ/dR=α (for dR/R?1), we can directly derive the local distance R from the observed excitation energies. This is exemplified for the mixed one-dimensional paramagnetic compound CsMn(x)Mg(1-x)Br3 (x=0.05,0.10) containing manganese dimers oriented along the hexagonal c axis. Surprisingly, the resulting Mn-Mn distances R do not vary continuously with increasing internal pressure but lock in at some discrete values.     

Structure and vibrational properties of cobalt clusters (n ≤ 20)

The binding energies and vibration frequencies of free small cobalt clusters containing up to twenty atoms inclusive have been calculated using the interatomic interaction potential obtained in the tight-binding approximation. The minimum frequency of the cluster vibrations has been shown to play the determining role in the evaluation of its dynamic stability. The analysis of the energy parameters and vibrations of clusters has demonstrated that the cobalt clusters in which the number of atoms is n = 4, 6, 13, and 19 are stable.     

3d系列 (TM)4 团簇的结构和磁性

基于第一性原理，在密度泛函理论下，用局域自旋密度近似(LSDA)和广义梯度近似(GGA)对(TM)₄团簇的所有几何构型进行优化、能量、频率和磁性计算.确定出3d系列(TM)₄团簇的基态构型，对其磁性、结合能和平均原子间距作了系统的研究，得出在3d系列(TM)₄团簇中，Mn₄的局域磁矩最大，V₄的局域磁矩最小，并且除Cr₄在LSDA和GGA均为反铁磁性耦合及GGA下的V_{关键词： 4}团簇')" href="#">(TM)₄团簇 基态构型 结合能 局域磁矩 平均原子间距     

原子模拟钛中微孔洞的结构及其失效行为

六角金属由于其各向异性等特点,在塑性变形等过程中容易产生形状和构型都相对复杂的点缺陷团簇.这些团簇之间及其与运动位错等缺陷的相互作用直接影响材料的物理和力学性能.然而对相关问题的原子尺度、尤其是空位团簇的演化和微孔洞的形成乃至裂纹形核扩展等的理解还不全面.本文采用激发弛豫算法结合第一原理及原子间作用势,系统考察了钛中的空位团簇构型及不同构型间的相互转变,给出了不同尺寸空位团簇的稳定和亚稳构型、空位团簇合并分解和迁移的激发能垒等关键参数,发现较小的空位团簇形成稳定构型,较大的空位团簇呈现出空间对称分布趋势进而形成微孔洞;采用高通量分子动力学模拟系统研究了不同尺寸的空位团簇在拉应力作用下对变形过程的影响,发现这些空位团簇可以形成层错,并对微裂纹的形核产生影响.     

Molecular dynamics simulations of displacement cascades in Feben 10%Cr systems

Molecular dynamics simulations of the displacement cascades in Fe-10%Cr systems are used to simulate the primary knocked-on atom events of the irradiation damage at temperatures 300, 600, and 750 K with primary knocked-on atom energies between 1 and 15 keV. The results indicate that the vacancies produced by the cascade are all in the central region of the displacement cascade. During the cascade, all recoil Fe and Cr atoms combine with each other to form Fe-Cr or Fe-Fe interstitial dumbbells as well as interstitial clusters. The number and the size of interstitial clusters increase with the energy of the primary knocked-on atom and the temperature. A few large clusters consist of a large number of Fe interstitials with a few Cr atoms, the rest are Fe-Cr clusters with small and medium sizes. The interstitial dumbbells of Fe-Fe and Fe-Cr are in the lan111ran and lan110ran series directions, respectively.