Simulation of nanostructure evolution under helium implantation in Fe–(2.5–12.5)at% Cr alloys at a temperature of 343 K

Characterization of helium-implanted Fe–(2.5–12.5)at% Cr alloys with the flux of 7?×?10^–6?dpa/s at a temperature of 343?K has been performed by means of cluster dynamics simulations. We have suggested a model for simulating an Fe–C–Cr system under helium implantation based on a selection of the latest data from atomistic studies and available experiments. Kinetics of carbon-vacancy and helium-vacancy complexes has been studied. Only one parameter is used to guarantee the best reproduction possible of experimental positron annihilation lifetime spectroscopy data for Fe–Cr alloys on dependences of vacancy cluster size on chromium content and irradiation dose via fitting. This is an effective binding energy of self-interstitial atoms to dislocation loops decorated by chromium atoms. It has a “snaky” dependence of chromium content with a minimum of about 9%Cr.     

Evidence from numerical modelling for 3D spreading of [001] screw dislocations in Mg2SiO4 forsterite

Computer simulations have previously been used to derive the atomic scale properties of the cores of screw dislocations in Mg₂SiO₄ forsterite by direct calculation using parameterized potentials and via the Peierls–Nabarro model using density functional theory. We show that, for the [001] screw dislocation, the parameterized potentials reproduce key features of generalized stacking fault energies when compared to the density functional theory results, but that the predicted structure of the dislocation core differs between direct simulation and the Peierls–Nabarro model. The [001] screw dislocation is shown to exhibit a low-energy non-planar core. It is suggested that for this dislocation to move its core may need to change structure and form a high-energy planar structure similar to that derived from the Peierls–Nabarro model. This could lead to dislocation motion via an unlocking–locking mechanism and explain the common experimental observation of long straight screw dislocation segments in deformed olivine.     

Heterogeneous precipitation on dislocations: effect of the elastic field on precipitate morphology

The shape of a coherent non-misfitting FeC precipitate formed from solute atoms that interact with a dislocation stress field was studied using kinetic Monte Carlo simulation on a rigid lattice. The system studied is a model for binary alloys with an interstitial alloying element similar to Fe–C. The interaction with the dislocation comprises both a short-range chemical term and a long-range deformation field. The effect of each of these terms on precipitate shapes for different C supersaturations was investigated. A simple analytical model is proposed to rationalize the results obtained in the atomistic simulations.     

Heavy-ion irradiations of Fe and Fe–Cr model alloys Part 1: Damage evolution in thin-foils at lower doses

The evolution of radiation damage in Fe and Fe–Cr alloys under heavy-ion irradiation was investigated using transmission electron microscopy. Thin foils were irradiated with 100 or 150 keV Fe⁺ and Xe⁺ ions at room temperature (RT) and 300°C. Dynamic observations followed the evolution of damage and the early stages in damage development are reported. Small (2–5 nm) dislocation loops first appeared at doses between 10¹⁶ and 10¹⁷ ions m^?2 in all materials. Loop number densities depended strongly on the foil orientation in pure Fe but not in Fe–Cr alloys. Number densities did not depend strongly on Cr content. For a given material, defect yields were higher for Xe⁺ ions than for Fe⁺ ions, and were higher at RT than at 300°C. Loops with both ?100? and ½?111? Burgers vectors were identified. The proportion of ?100? loops was larger, especially in pure Fe. Dynamic observations showed that: the contrast of some new loops developed over intervals as long as 0.2 s; hopping of ½?111? loops was induced by the ion and electron beams and was pronounced in ultra-pure iron; and many loops were lost during and after ion irradiation by glide to the foil surface. The number of loops retained was strongly dependent on the foil orientation in Fe, but less so in Fe–Cr alloys. This is due to lower loop mobility in Fe–Cr alloys, probably due to pinning by Cr atoms. Reduced loop loss probably explains the higher loop number densities in Fe–Cr alloys compared with pure Fe.     

Non-singular dislocation continuum theories: strain gradient elasticity vs. Peierls–Nabarro model

Abstract

Non-singular dislocation continuum theories are studied. A comparison between Peierls–Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analysed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realistic and physical than the corresponding fields of the Peierls–Nabarro model. Strain gradient elasticity of dislocations is a continuum dislocation theory including a weak non-locality within the dislocation core and predicting the size and shape of the dislocation core. The dislocation core is narrower in the strain gradient elasticity dislocation model than in the Peierls–Nabarro model and more evenly distributed in two dimensions. The present analysis shows that for the modelling of the dislocation core structure the non-singular dislocation fields of strain gradient elasticity are the suitable ones.     

Modelling the diffusion of self-interstitial atom clusters in Fe–Cr alloys

The results of molecular dynamics simulations of the diffusion of self-interstitial atom clusters in Fe–Cr alloys of different Cr content are presented. It is shown that, with increasing Cr concentration, the cluster diffusivity first decreases and then increases, in accordance with the predictions of a model developed recently and based on molecular static calculations. The minimum diffusivity is found at about 10 at% Cr for small clusters and it shifts towards lower concentration with increasing cluster size. The migration energy of SIA clusters is found to lie in between the binding energy of a Cr atom with a crowdion and half of it. This indicates that the mechanism of cluster migration is via the movement of individual crowdions from one Cr atom to another. The values obtained statically are much higher and are argued to be more reliable due to better sampling of different configurations in a bigger simulation box.     

Resistance of nanocrystalline vis-à-vis microcrystalline Fe–Cr alloys to environmental degradation and challenges to their synthesis

This paper presents a hypothesis and its experimental validation that a nanostructure can bring about dramatic improvements in the oxidation/corrosion resistance of iron–chromium alloys. More specifically, a nanocrystalline Fe–10 wt% Cr alloy was found to undergo oxidation at a rate that was an order of magnitude lower than its microcrystalline counterpart. Importantly, the oxidation resistance of nanocrystalline Fe–10 wt% Cr alloy was comparable with that of the common corrosion-resistant microcrystalline stainless steels (having 18–20 wt% chromium). The findings have the potential of leading to the next generation of oxidation-resistant alloys. However, due to poor thermal stability of nanocrystalline structure, synthesis/processing of such alloys is a challenge. Discs of nanocrystalline Fe–10% Cr alloy were produced by ball-milling of Fe and Cr powders and compaction of the powder without considerable grain growth by processing within a suitable time–temperature window. The paper also presents a theoretical treatise to arrive at the minimum chromium content required for establishing a protective layer of chromium oxide in an Fe–Cr alloy of a given nanometric grain size.     

Theory of hydrogen solubility in binary iron alloys based on ab initio calculation results

Interaction of hydrogen atoms with three substitutional impurities (X?=?Pd, Ti, Cr) in bcc iron base solid solution was modelled ab initio using the WIEN2k package. It was shown that in spite of attraction between H and X atoms, excess energy of the H atom in tetrahedral sites in the first sphere of coordination of the X atom has a significant positive value, while the lowest negative values are observed in the second (Pd, ?0.087?eV; Ti, ?0.091?eV) or the third (Cr, ?0.032?eV) sphere. A new thermodynamic theory of hydrogen solubility in dilute bcc Fe–X alloys was developed on the basis of these results. The resulting equation was used to analyze existing experimental data on H solubility in a number of Fe–X alloys, and X–H interaction energies were determined for each case. The energies determined from high-temperature solubility data for Fe–Pd, Fe–Ti and Fe–Cr are somewhat greater than those obtained in ab initio calculations. The theory gives a new basis for analyzing hydrogen behaviour in iron-base solid solutions.     

Relaxation method for constructing the interaction potentials of metal–nonmetal atomic pairs

An algorithm that employs the method of successive relaxation for determining the parameters of the pairwise interaction potential of iron and nonmetallic atoms that implicitly considers the redistribution of electron density between atoms is developed. The parameters of the interatomic interaction potential are calculated for ten pairs of elements: Fe–P, Fe–S, Fe–B, Fe–V, Fe–Mo, Fe–Cr, Fe–Mn, Fe–Si, Fe–Ni, and Fe–Al. The structural and thermodynamic properties of solid solutions based on iron and pure materials, and some pairwise interaction potentials constructed earlier in the Lennard–Jones form for identical metal atoms and homogeneous pairs of different metal–metal atoms, are used in these calculations.     

Temperature characteristics of the mechanical properties and of the dislocation structure of molybdenum-rhenium alloys

The temperature characteristics of the yield strength and of the dislocation structure of supersaturated molybdenum-rhenium alloys were studied over the 77–673°K temperature range. A lesser dependence of σ_0.1 on the temperature was found to result from twinning. The mobility of screw dislocations was found to become much lower due to alloying with rhenium. An analysis of the peculiarities in the dislocation structure of the alloys under consideration here (plane pileup, screw dipoles, singularities of interaction between glissile dislocations) has led to the conclusion that the lower mobility of screw dislocations is a consequence of the lower energy of the packing defect in molybdenum alloyed with rhenium. The lattice resistance to a movement of screw dislocations (τ_p) at room temperature has been estimated from the distance between dislocations in screw dipoles and found to be τ_p≥16 kgf/mm².     

Investigation of Cr-atom clustering in Fe‒Cr model alloys under irradiation

Irradiation-induced microstructure in Fe?Cr model alloys, 0.5 MeV-He ion-irradiated at room temperature, was investigated by atom probe tomography (APT). The APT results showed the formation of Cr-atom clustering depending on the ion-penetration depth. Although the Cr-atom clustering was observed in the irradiation damaged zone, this effect was not dominant in the less-damaged zone. In addition, we performed computer simulations using the Metropolis–Monte Carlo (MMC) method for investigating the tendency to form Cr-atom clustering in binary Fe?Cr alloys. The simulation results revealed the formation of Cr-atom clustering. The degree of Cr-atom clustering for the APT analysis and the MMC simulation was verified by plotting the Cr?Cr radiation distribution function. It was found that the number of Cr atoms, located in the first and second nearest-neighboring sites, increased significantly. Both results support the formation of Cr-clustering, which is believed to be a source of radiation hardening. The application of two techniques, APT and the MMC simulation, provided complementary information on the radiation-induced microstructure.     

镍晶格中的晶格格林函数

在含缺陷体系的模拟中，格林函数作为一种重要的多尺度耦合方法，可以将缺陷产生的局域应变场和长程应力场耦合起来.在镍基高温合金蠕变的初期阶段，位错主要分布在基体相中，通过格林函数的多尺度桥接模式，可得到基体相中位错芯的平衡构型，为位错-杂质复合体间相互作用提供计算基础.基于晶格动力学理论和声子谱计算中的力常数矩阵，通过第一布里渊区特殊k点取样以及傅里叶变换，计算完整镍晶格中晶格格林函数，可用于镍基材料的多尺度模拟计算.     

Magnetic cluster expansion simulation and experimental study of high temperature magnetic properties of Fe-Cr alloys

We present a combined experimental and computational study of high temperature magnetic properties of Fe-Cr alloys with chromium content up to about 20?at.%. The magnetic cluster expansion method is applied to model the magnetic properties of random Fe-Cr alloys, and in particular the Curie transition temperature, as a function of alloy composition. We find that at low (3-6?at.%) Cr content the Curie temperature increases with the increase of Cr concentration. It is maximum at approximately 6?at.% Cr and then decreases for higher Cr content. The same feature is found in thermo-magnetic measurements performed on model Fe-Cr alloys, where a 5?at.% Cr alloy has a higher Curie temperature than pure Fe. The Curie temperatures of 10 and 15?at.% Cr alloys are found to be lower than the Curie temperature of pure Fe.     

Density functional theory-based cluster expansion to simulate thermal annealing in FeCrW alloys

Abstract

In this work, we develop a rigid lattice cluster expansion as an ultimate goal to track the micro-structural evolution of Eurofer steel under neutron irradiation. The fact that all (defect) structures are mapped upon a rigid lattice allows a simplified computation and fitting procedure, thus enabling alloys of large chemical complexity to be modelled. As a first step towards the chemical complexity of Eurofer steels, we develop a cluster expansion (CE) for the FeCrW-vacancy system based on density functional theory (DFT) calculations in the dilute alloy limit. The DFT calculations suggest that only CrW clusters containing vacancies are stabilised. The cluster expansion was used to simulate thermal annealing in Fe–20Cr–xW alloys at 773 K. It is found that the addition of W to the alloy results in a non-linear decrease in the precipitation kinetics. The CE was found suitable to describe the energetics of the FeCrW-vacancy system in the Fe-rich limit.     

位错规范场对于位错芯区的应用

本文用位错连续分布方法分析了位错所产生的应变和应力场,用位错规范场表出了位错芯区的位错分布,并在一定规范条件下求解了位错规范场。得到了螺位错芯区内、外的应力场。在螺位错芯区外,其应力场与Volterra位错的应力场完全一样,而在芯区内,当ρ趋于零时,螺位错的应力场是有解的。最后计算了螺位错的能量。 关键词：     

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The analytical solutions to the elastic field and the electric field, the interfacial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interfacial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.     

Elastic energy of a straight dislocation and contribution from core tractions

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.     

Elastic interaction between a dilatation centre and split dislocations in b.c.c. metals

The elastic interaction energy between a dilatation centre and 1/2[111] dislocation split on {110} planes in b.c.c. metals is calculated for sessile and planar splittings of screw dislocation and for planar splitting of edge dislocation; the splitting is considered as a model of the dislocation core. It is concluded that the interstitial impurity atom has three or four possible minimum energy positions in the dislocation core. A hypothesis on the impurity jumps in the dislocation core is proposed.On leave from theInstitute of Physics, Hanoi, VDR.     

Difference approach to the analysis of resistivity recovery data for irradiated short-range ordered alloys

Electrical resistivity recovery (RR) data for irradiated concentrated alloys typically consist of two inseparable parts, one resulting from defect annihilation and the other from short-range order (SRO) effects. These parts exhibit different behaviour and often follow opposite trends. Therefore, in this case, analysis of RR data within the conventional method is too complicated. A new approach to data analysis of such a two-component RR is proposed. The approach involves a new quantity, the difference RR (DRR), which is composed of RR dependences of two similar samples irradiated to different defect concentrations. It is shown that the SRO formation proper and the stages corresponding to the onset of long-range migration of Frenkel pair defects, formed in each part of RR, can be clearly related to certain features of the DRR plots. This interrelationship allows detecting and identifying these stages in each part of RR separately. The validity of the approach is illustrated by analysis of the available pairwise RR data for Fe–16Cr–20Ni and Fe–4Cr alloys. It makes it possible to detect the small contribution from the SRO formation to RR in Fe–4Cr, which we failed to observe previously. It is shown that stage III of Fe–4Cr, which has a negligible contribution to the part of RR induced by defect annihilation, is clearly observed in the part induced by SRO formation.     

几何弯结与点缺陷的弹性交互作用位场

求得了各向同性弹性介质中直位错段的膨胀场的向量表示式。由此求出分段折线和光滑曲线组成的几何弯结与替代式溶质原子的弹性交互作用位场,并用数值计算了fcc晶体中各类位错上不同宽度的几何弯结的交互作用位沿位错管道的分布。分析了螺型位错和混合型位错上几何弯结与空位交互作用引起两种内耗的可能性。 关键词：