Atomic-scale study of dislocation–stacking fault tetrahedron interactions. Part I: mechanisms

Stacking fault tetrahedra (SFTs) are formed under irradiation in fcc metals and alloys. The high number density of SFTs observed suggests that they should contribute to radiation-induced hardening and, therefore, be taken into account when estimating mechanical property changes of irradiated materials. The key issue in this is to describe the interaction between a moving dislocation and an individual SFT, which is distinguished by a small physical size of the order of ～1–10?nm. We have performed atomistic simulations of edge and screw dislocations interacting with SFTs of different sizes at different temperatures and strain rates. Five possible interaction outcomes have been identified, involving either partial absorption, or shearing or restoration of SFTs. The mechanisms that give rise to these processes are described and their dependence on interaction parameters, such as SFT size, dislocation–SFT geometry, temperature and stress/strain rate are determined. Mechanisms that help to explain the formation of defect-free channels cleared by gliding dislocations, as observed experimentally, are also discussed. Hardening due to the various mechanisms and their dependence on loading conditions will be presented in a following paper (Part II).     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part I: interactions with screw dislocations

We present a comprehensive dislocation dynamics (DD) study of the strength of stacking fault tetrahedra (SFT) to screw dislocation glide in fcc Cu. Our methodology explicitly accounts for partial dislocation reactions in fcc crystals, which allows us to provide more detailed insights into the dislocation–SFT processes than previous DD studies. The resistance due to stacking fault surfaces to dislocation cutting has been computed using atomistic simulations and added in the form of a point stress to our DD methodology. We obtain a value of 1658.9 MPa, which translates into an extra force resolved on the glide plane that dislocations must overcome before they can penetrate SFTs. In fact, we see they do not, leading to two well differentiated regimes: (i) partial dislocation reactions, resulting in partial SFT damage, and (ii) impenetrable SFT resulting in the creation of Orowan loops. We obtain SFT strength maps as a function of dislocation glide plane-SFT intersection height, interaction orientation, and dislocation line length. In general SFTs are weaker obstacles the smaller the encountered triangular area is, which has allowed us to derive simple scaling laws with the slipped area as the only variable. These laws suffice to explain all strength curves and are used to derive a simple model of dislocation–SFT strength. The stresses required to break through obstacles in the 2.5–4.8-nm size range have been computed to be 100–300 MPa, in good agreement with some experimental estimations and molecular dynamics calculations.     

Mechanisms of stacking fault tetrahedra destruction by gliding dislocations in quenched gold

The destruction processes of stacking fault tetrahedra (SFTs) induced by gliding dislocations were examined by transmission electron microscopy (TEM) in situ straining experiments for SFTs with edge lengths ranging from 10 to 50 nm. At least four distinct SFT destruction processes were identified: (1) consistent with a Kimura–Maddin model for both screw and 60° dislocations, (2) stress-induced SFT collapse into a triangular Frank loop, (3) partial annihilation leaving an apex portion and (4) complete annihilation. Process (4) was observed at room temperature only for small SFTs (～10 nm); however, this process was also frequently observed for larger SFTs (～30 nm) at higher temperature (～853 K). When this process was induced, the dislocation always cross-slipped, indicating only screw dislocations can induce this process.     

Subsurface defect evolution and crystal-structure transformation of single-crystal copper in nanoscale combined machining

ABSTRACT

In the paper, molecular dynamics simulation is applied to study the evolution and distribution of subsurface defects during nanoscale machining process of single-crystal copper. The chip-removal mechanism and the machined-surface-generative mechanism are examined through analysis of the dislocation evolution and atomic migration of the workpieces. The findings show that under different stresses and temperatures, the difference of the binding energy leads to a zoned phenomenon in the chip. Owing to elastic deformation, some of the dislocations could be recovered and form surface steps; moreover, the work hardening of the workpiece can be achieved on account of generation of twin boundaries, Lomer-Cottrell dislocations, and stacking fault tetrahedra (SFT) by plastic deformation. A process of evolution of an immobile dislocation group containing stair-rod dislocations into SFT is discovered, which is different from the traditional Silcox-Hirsch mechanism. Furthermore, a growth oscillation phenomenon, which corresponding stacking fault planes growth and retraction during the formation of the stable SFT, is discussed.     

Dislocation and stacking fault core fields in fcc metals

Atomistic models were used to determine the properties of dislocation core fields and stacking fault fields in Al and Cu using embedded atom method (EAM) potentials. Long-range, linear elastic displacement fields due to nonlinear behaviour within dislocation cores, the core field, for relevant combinations of Shockley partial dislocations for edge, screw, and mixed (60° and 30°) geometries were obtained. Displacement fields of stacking faults were obtained separately and used to partition the core field of dissociated dislocations into core fields of partial dislocations and a stacking fault expansion field. Core field stresses were derived from which the total force, including the Volterra field plus core field, between dislocations for several dislocation configurations was determined. The Volterra field dominates when the distance between dislocations exceeds about 50b but forces due to core fields are important for smaller separation distances and were found to affect the equilibrium angle of edge dislocation dipoles and to contribute to the force between otherwise non-interacting edge and screw dislocations. Interactions among the components of a dissociated dislocation modify the equilibrium separation for Shockley partials suggesting that methods that determine stacking fault energies using measurements of separation distances should include core fields.     

Molecular dynamic studies of the interaction of a/6⟨112⟩ Shockley dislocations with stacking fault tetrahedra in copper. Part II: Intersection of stacking fault tetrahedra by moving twin boundaries

The interactions of moving twin boundaries with stacking fault tetrahedra (SFTs) have been studied by molecular dynamics. The results reveal a spectrum of processes occurring during these interactions. In general, they lead to damage of the parent SFT and formation of new defects in the twin lattice. The character of these defects depends on the nature of the twinning front, the size of the SFT and its orientation with respect to incoming dislocations. Typical structures that may be produced in the twin include product-SFTs, free vacancies, planar stacking faults bounded by partial dislocations, mutually linked stacking faults on non-coplanar {111} _T planes, small {111} _T tetrahedra and their partial forms. Dislocation mechanisms involved in the formation of these defects are being analyzed.     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part II: interactions with mixed and edge dislocations

In this paper we present the sequel to Part I and present a comprehensive dislocation dynamics study of the strength of stacking fault tetrahedra to mixed and edge dislocation glides in fcc Cu.     

强流脉冲电子束辐照诱发多晶纯铝中的空位缺陷簇结构

利用强流脉冲电子束（HCPEB）技术对多晶纯铝样品进行辐照,采用透射电子显微镜详细分析了辐照诱发的空位簇缺陷.HCPEP辐照后,在辐照表层内形成了大量的四方形空位胞,其间包含位错圈和堆垛层错四面体（SFT）等类型的空位簇缺陷.1次辐照后,空位胞内产生空位型位错圈,5次辐照则主要产生SFT;10次辐照后,空位胞内产生的空位簇缺陷主要是位错圈,局部区域也观察到了SFT缺陷,在产生SFT的附近区域具有很低的位错密度或者几乎无位错出现.HCPEB辐照产生的瞬间加热和冷却诱发了幅值极大且应变速率极高的应力,这一因素 关键词： 强流脉冲电子束 多晶纯铝 空位簇缺陷 堆垛层错四面体     

Atomic-scale plasticity in the presence of Frank loops

The different reactions between edge or screw dislocations and interstitial Frank loops were studied by means of molecular dynamics simulations. The calculations were performed at 600?K using an embedded atom method (EAM) potential describing a model FCC material with a low stacking fault energy. An interaction matrix that provides the corresponding interaction strength was determined. In an attempt to investigate the role of pile-ups, simulations with either one or two dislocations in the cell were performed. We find that screw and edge dislocations behave very differently. Edge dislocations shear Frank loops in two out of three cases, while screw dislocations systematically unfault Frank loops by mechanisms that involve cross-slip. After unfaulting, they are strongly pinned by the formation of extended helical turns. The simulations show an original unpinning effect that leads to clear band broadening. This process involves the junction of two screw dislocations around a helical turn (arm-exchange) and the transfer of a dislocation from its initial glide plane to an upper glide plane (elevator effect).     

面心立方晶体外延膜沉积生长中失配位错的结构与形成过程

用分子动力学方法对5%负失配条件下面心立方晶体铝薄膜的原子沉积外延生长进行了三维模拟.铝原子间的相互作用采用嵌入原子法(EAM)多体势计算.模拟结果再现了失配位错的形成现象.分析表明，失配位错在形成之初即呈现为Shockley扩展位错，即由两个伯格斯矢量为〈211〉/6的部分位错和其间的堆垛层错组成，两个部分位错的间距、即层错宽度为1.8 nm,与理论计算结果一致；外延晶体薄膜沉积生长中，位错对会发生滑移，但其间距保持稳定.进一步观察发现，该扩展位错产生于一种类似于“局部熔融-重结晶”的表层局部无序紊乱- 关键词： 失配位错 外延生长 薄膜 分子动力学 铝     

Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu

Performance degradation of structural steels in nuclear environments results from the formation of a high number density of nanometre-scale defects. The defects observed in copper-based alloys are composed of vacancy clusters in the form of stacking fault tetrahedra and/or prismatic dislocation loops that impede the motion of dislocations. The mechanical behaviour of irradiated copper alloys exhibits increased yield strength, decreased total strain to failure and decreased work hardening as compared to their unirradiated behaviour. Above certain critical defect concentrations (neutron doses), the mechanical behaviour exhibits distinct upper yield points. In this paper, we describe the formulation of an internal state variable model for the mechanical behaviour of such materials subject to these (irradiation) environments. This model has been developed within a multiscale materials-modelling framework, in which molecular dynamics simulations of dislocation–radiation defect interactions inform the final coarse-grained continuum model. The plasticity model includes mechanisms for dislocation density growth and multiplication and for irradiation defect density evolution with dislocation interaction. The general behaviour of the constitutive (homogeneous material point) model shows that as the defect density increases, the initial yield point increases and the initial strain hardening decreases. The final coarse-grained model is implemented into a finite element framework and used to simulate the behaviour of tensile specimens with varying levels of irradiation-induced material damage. The simulation results compare favourably with the experimentally observed mechanical behaviour of irradiated materials.     

Atomic simulations to evaluate effects of stacking fault energy on interactions between edge dislocation and spherical void in face-centred cubic metals

In this study, molecular dynamics simulations were performed to elucidate the effects of stacking fault energy (SFE) on the physical interactions between an edge dislocation and a spherical void in the crystal structure of face-centred cubic metals at various temperatures and for different void sizes. Four different types of interaction morphologies were observed, in which (1) two partial dislocations detached from the void separately, and the maximum stress corresponded to the detachment of the trailing partial; (2) two partial dislocations detached from the void separately, and the maximum stress corresponded to the detachment of the leading partial; (3) the partial dislocations detached from the void almost simultaneously without jog formation; and (4) the partial dislocations detached from the void almost simultaneously with jog formation. With an increase in void size or SFE, the interaction morphology changed in the above-mentioned order. It was observed that the magnitude of the critical resolved shear stress (CRSS) and its dependence on the SFE were determined by these interaction morphologies. The value of the CRSS in the case of interaction morphology (1) is almost equal to an analytical one based on the linear elasticity by employing the Burgers vector of a single partial dislocation. The maximum value of the CRSS is also obtained by the analytical model with the Burgers vector of the two partial dislocations.     

Explicit incorporation of cross-slip in a dislocation density-based crystal plasticity model

We present a crystal plasticity model that incorporates cross-slip of screw dislocations explicitly based on dislocation densities. The residence plane of screw dislocations is determined based on a probability function defined by activation energy and activation volume of cross-slip. This enables the redistribution of screw-dislocations and dislocation density patterning due to the effect of stacking fault energy. The formulation is employed for explaining the cross-slip phenomenon in aluminium during uniaxial tensile deformation of ?100? single crystal and a single slip orientation of single crystal, and compare the results with experimental observations. The effect of cross-slip on the stress–strain evolution is seen using this explicit treatment of cross-slip.     

Atomistic Simulations of the Effect of Helium on the Dissociation of Screw Dislocations in Nickel

The interactions of He with dissociated screw dislocations in face-centered-cubic(fcc) Ni are investigated by using molecular dynamics simulations based on an embedded-atom method model.The binding and formation energies of interstitial He in and near Shockley partial cores are calculated.The results show that interstitial He atoms at tetrahedral sites in the perfect fcc lattice and atoms occupying sites one plane above or below one of the two Shockley partial cores exhibit the strongest binding energy.The attractive or repulsive nature of the interaction between interstitial He and the screw dislocation depends on the relative position of He to these strong binding sites.In addition,the effect of He on the dissociation of screw dislocations are investigated.It is found that He atoms homogeneously distributed in the glide plane can reduce the stacking fault width.     

有限温度下位错环的脱体现象

在FCC单晶铜中构造了滑移面为（111）,伯格矢量为b=［112］/6的圆形不完全位错环．采用分子动力学方法模拟了该位错环在0—350 K温度区间内的自收缩过程．模拟结果发现：零温度下,位错不能跨越Peierls-Nabarro势垒运动,迁移速度为0;50　K温度下,螺型和刃型位错具有基本相同的迁移速度;随温度增加,刃型位错具有较大迁移速度;温度较高时,位错核宽度进一步增加;小位错环周围的局部应力,引起4个脱体位错环;脱体位错环在原位错的应力作用下逐渐生长,原位错消失后,在自相 关键词： 单晶铜 位错环 分子动力学 位错源     

Contrast analysis of Shockley partial dislocations in 4H-SiC observed by synchrotron Berg–Barrett X-ray topography

Shockley partial dislocations in 4H-SiC were observed using monochromatic synchrotron X-ray topography with a grazing-incidence Bragg-case geometry, that is, Berg–Barrett topography. The contrast of partial dislocations at the edges of Shockley-type stacking faults is discussed in terms of whether they have C- or Si-core edge components, or screw components. The dissociated state of basal-plane dislocation is discussed on a basis of the stacking sequence for basal-planes in the 4H-SiC crystal structure. It is expected that the results obtained in this study will be useful for characterizing Shockley-type stacking faults in Berg–Barrett topography.     

Closed and open-ended stacking fault tetrahedra formation along the interfaces of Cu–Al nanolayered metals

Stacking fault tetrahedra (SFTs) are volume defects that typically form by the clustering of vacancies in face-centred cubic (FCC) metals. Here, we report a dislocation-based mechanism of SFT formation initiated from the semi-coherent interfaces of Cu–Al nanoscale multilayered metals subjected to out-of-plane tension. Our molecular dynamics simulations show that Shockley partials are first emitted into the Cu interlayers from the dissociated misfit dislocations along the Cu–Al interface and interact to form SFTs above the triangular intrinsic stacking faults along the interface. Under further deformation, Shockley partials are also emitted into the Al interlayers and interact to form SFTs above the triangular FCC planes along the interface. The resulting dislocation structure comprises closed SFTs within the Cu interlayers which are tied across the Cu–Al interfaces to open-ended SFTs within the Al interlayers. This unique plastic deformation mechanism results in considerable strain hardening of the Cu–Al nanolayered metal, which achieves its highest tensile strength at a critical interlayer thickness of ~4 nm corresponding to the highest possible density of complete SFTs within the nanolayer structure.     

Cu刃型扩展位错附近局部应变场的原子模拟研究

通过结合virial应变分析技术的准连续介质多尺度模拟方法研究了金属Cu刃型扩展位错的局部应变场.结果表明在距离位错核心几十纳米的区域内晶体处于小变形状态,virial应变计算结果与弹性理论预测结果符合得相当好,当距离位错核心仅几纳米时,晶格畸变加剧,virial应变极大值出现在扩展位错两端的Shockley分位错芯部.进一步分析表明Shockley分位错芯部严重畸变区大致呈长轴7b1、短轴3b1的椭圆形,其中b1为分位错柏氏矢量的长度.