Elastic-energy relaxation in heterostructures with strained nanoinclusions

Elastic-energy relaxation in systems with nanoinclusions is considered. The relaxation is related to the formation of the following dislocation loops: a single misfit dislocation loop or a group of such loops on the matrix-nanoinclusion interface and/or a satellite dislocation loop near the inclusion. The critical inclusion sizes beginning from which misfit dislocation loops and satellite dislocation loops can nucleate are determined for various models of relaxation processes. The dependences of the satellite-dislocation-loop diameter on the inclusion size are calculated and compared with experimental data.     

Surface/interface effects on the formation of misfit dislocation in a core–shell nanowire

The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lamé constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit dislocation dipole is more expectable in the coarser ones.     

Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

外延生长薄膜中失配位错形成条件的分子动力学模拟研究

运用分子动力学方法对负失配条件下的外延铝簿膜中失配位错的形成进行了模拟研究.所采 用的原子间相互作用势为嵌入原子法(EAM)多体势.模拟结果显示：在500K下长时间静态弛豫 ，表面和内部结构完整的外延膜在9—80原子层厚度范围内(约为其热力学临界厚度的3—40 倍)均不形成失配位错，而在薄膜表面预置一个单原子层厚、三个原子直径大小的凸台或凹 坑时，失配位错则能够在15个原子层厚的外延膜上迅速形成：在动态沉积生长条件下，表面 自然形成凹凸，初始厚度为9个原子层厚的外延膜在沉积生长中迅速形成失配位错.在三种条 件下，所形成的位错均为伯格斯矢量与失配方向平行的全刃位错.分析发现：在压应力作用 下，表面微凸台诱发了其侧薄膜内部原子的挤出，造成位错形核；而表面微凹坑则直接因压 应力作用形成了一个表面半位错环核. 关键词： 外延薄膜 失配位错 分子动力学 铝     

Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity

A theoretical model is proposed for elastic stress relaxation of a buried strained cylindrical inhomogeneity, which assumes the edge misfit dislocation dipole formation in the soft matrix at some distance from the interface. The critical radius of the inhomogeneity for the formation of the edge misfit dislocation dipole is given and the influence of various parameters on the critical radius is evaluated. The result indicates that the critical radius decreases with increasing misfit strain and core radius of the misfit dislocation. It is also found that, compared to the edge misfit dislocation dipole formation in the interface, the critical radius of the inhomogeneity decreases when the location of an edge misfit dislocation dipole formation is in the soft matrix at some distance from the interface.     

温度对镍基单晶高温合金γ/γ'相界面上错配位错运动影响的分子动力学研究

用分子动力学方法研究了温度对镍基单晶高温合金γ/γ'相界面上错配位错运动的影响.研究结果表明:无论是在低温还是在高温下,错配位错的运动都是通过扭折的形核及扭折沿位错线的迁移来实现;在低温时错配位错的相互作用有利于错配位错的运动;然而在高温时错配位错的相互作用可以阻碍错配位错的运动,从而阻碍γ和γ'相界面的相对滑动,有利于提高镍基单晶高温合金的高温力学性能. 关键词： 镍基单晶高温合金 相界面 错配位错 分子动力学模拟     

Softening and hardening of yield stress by hydrogen–solute interactions

Abstract

Hydrogen atoms have a wide variety of effects on the mechanical performance of metals, and the underlying mechanisms associated with effects on plastic flow and embrittlement remain to be discovered or validated. Here, the reduction in the plastic flow stress (softening) due to hydrogen atoms in solute-strengthened metals, previously proposed by Sofronis et al. is demonstrated at the atomistic level. Glide of an edge dislocation through a field of solutes in a nickel matrix, both in the absence of hydrogen and in the presence of H bound to the solutes, is modelled. The ‘solutes’ here are represented by vacancies, enabling use of accurate binary Ni–H interatomic potentials. Since vacancies have a misfit strain tensor in the Ni matrix and also bind hydrogen atoms, they are excellent surrogates for study of the general phenomenon. The binding of H to the solute (vacancy) reduces the misfit volume to nearly zero but also creates a non-zero tetragonal distortion. Solute strengthening theory is used to establish the connection between strength and solute/hydrogen concentration and misfit strain tensor. Simulations show that when a dislocation moves through a field of random vacancy ‘solutes’, the glide stress is reduced (softening) when H is bound to the solutes. Trends in the simulations are consistent with theory predictions. Trends of softening or hardening by H in metal alloys can thus be made by computing the misfit strain tensor for a desired solute in the chosen matrix with and without bound hydrogen atoms. Pursuing this, density functional theory calculations of the interaction of H with carbon and sulphur solutes in a Ni matrix are presented. These solutes/impurities do not bind with H and the complexes have larger misfit strains, indicative of H-induced strengthening rather than softening for these cases. Nonetheless, H/solute interactions are the only mechanism, to date, that shows nanoscale evidence of plastic softening due to hydrogen associated with the hydrogen-enhanced localised plasticity concept in fcc metals.     

A study of the interphase boundary between ilmenite and hematite

The misfit dislocation network which forms between hematite and the ilmenite matrix from which it exsolves has been studied utilizing transmission electron microscopy techniques. It has been shown that the misfit dislocation network consists of a three-fold, symmetric dislocation configuration of half partial dislocations. The measured spacings between the misfit dislocations are in good agreement with those predicted from the postulated model of the network.     

Effect of H impurity on misfit dislocation in Ni-based single-crystal superalloy: molecular dynamic simulations

The effect of H impurity on the misfit dislocation in Ni-based single-crystal superalloy is investigated using the molecular dynamic simulation. It includes the site preferences of H impurity in single crystals Ni and Ni₃Al, the interaction between H impurity and the misfit dislocation and the effect of H impurity on the moving misfit dislocation. The calculated energies and simulation results show that the misfit dislocation attracts H impurity which is located at the γ/γ' interface and Ni₃Al and H impurity on the glide plane can obstruct the glide of misfit dislocation, which is beneficial to improving the mechanical properties of Ni based superalloys.     

Misfit dislocation loops in composite core-shell nanoparticles

The critical conditions have been calculated for the generation of circular prismatic loops of misfit dislocations at the interfaces in spherically symmetric composite core-shell nanoparticles. It has been shown that the formation of these loops becomes energetically favorable if the misfit parameter exceeds a critical value, which is determined by the geometry of the system. The most preferred position of the dislocation loop is in the equatorial plane of the nanoparticle. For a given radius of the nanoparticle, there is a minimum value of the critical misfit parameter below which the generation of a misfit dislocation is energetically unfavorable for any ratio of the core and shell radii. For a misfit parameter exceeding the minimum critical value, there are two critical values of the reduced radius of the particle core in the interval between which the generation of a dislocation loop is energetically favorable. This interval increases with increasing misfit parameter for a fixed particle size and decreases with decreasing particle size for a fixed misfit parameter.     

Misfit dislocation loops in composite nanowires

A new mechanism for relaxation of misfit stresses in composite nanowires (quantum wires) is suggested and theoretically examined, namely the formation of misfit dislocation loops. The stress field of a prismatic dislocation loop in a cylinder (nanowire) is calculated. The parameters of two-phase composite nanowires at which the formation of misfit dislocation loops is energetically favourable are estimated. The effect of stress fields of dislocation loops on the formation of compositionally modulated nanowires is discussed.     

Mechanism of formation of the interlamella dislocation network in polyethylene single crystals

It was found experimentally that bilayered polyethylene single crystals with an orientational misfit angle larger than the critical angle, θ*, show moire pattern and only those with an angle smaller than θ* show the interlamella dislocation network. The intermediate pattern, which could neither be classified into the typical moire pattern nor the typical interlamella dislocation network, was found in the vicinity of θ*. Criteria for discrimination between the moire pattern and the interlamella dislocation network are discussed. The crystal with a misfit angle a little larger than θ* also comes to show the feature of the dislocation network during long storage of the crystal in the mother solution at the crystallization temperature. θ* is, therefore, a function of the time of storage. A mechanism is presented such that crystal lattices near the interfacial boundary are distorted to form the dislocation network by intermolecular force between the overlying crystals when the misfit angle is smaller than θ*.     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

Positron annihilation in alpha- and beta-cyclodextrin

A new type of misfit dislocation multiplication is deduced from high-voltage electron micrographs of thin Ge layers on GaAs substrates. Two misfit dislocations with the same Burgers vectors on different glide planes cross and annihilate at the intersection point resulting in the formation of two angular dislocations. The tip of one of these dislocations may reach the growth surface by glide breaking into two separate dislocation segments. These segments may glide to form additional misfit dislocations, which may undergo the same multiplication process.     

Misfit dislocations in nanocomposites with quantum dots,nanowires and their ensembles

We review theoretical concepts and experimental results on the physics of misfit dislocations in nanocomposite solids with quantum dots (QDs) and nanowires (quantum wires). Special attention is paid to thermodynamic theoretical models of formation of misfit dislocations in QDs and nanowires, including composite core–shell nanowires. The effects of misfit dislocations on the film growth mode during heteroepitaxy and phase transitions in QD systems are analysed. Experimental results and theoretical models of the ordered spatial arrangement of QDs growing on composite substrates with misfit dislocation networks are discussed. The influence of subsurface dislocations in composite substrates on the nucleation of QDs and nanowires on the substrate surface is considered. Models of misfit strain relaxation and dislocation formation in nanofilms on compliant substrates are also reviewed.     

Strain analysis of misfit dislocations in α-Fe2O3/α-Al2O3 heterostructure interface by geometric phase analysis

The α-Fe₂O₃/α-Al₂O₃ heterostructure interfaces have been studied using transmission electron microscopy (TEM). The interface exhibited coherent regions separated by equally spaced misfit dislocations. The misfit dislocations were demonstrated to be edge dislocations with dislocation spacing of ∼4 nm. The strain fields around the misfit dislocation core were mapped using a combination of geometric phase analysis and high-resolution transmission electron microscopy images. The strain measurement results were compared with the Peierls–Nabarro dislocation model and the Foreman dislocation model. These comparisons show that the Foreman model (a = 2) is the most appropriate theoretical model to describe the strain fields of the dislocation core.     

Equilibrium critical thickness for a wurtzite InGaN/GaN heterostructure

We present a finite element model to simulate a combined strained In_xGa_1−xN/GaN heterostructure and an edge misfit dislocation on the basal {0001} slip plane, taking the anisotropic elasticity into account. The introduction of a misfit dislocation partially relaxes the misfit strain. The model directly gives the residual strain, which is the exact strain field stored in the system after relaxation. The critical thickness is then determined based on an overall energy minimization approach including the dislocation core contribution. Compared with the results from other methods and available experimental data, our approach is appropriate for describing the critical thickness of the wurtzite InGaN/GaN material system.     

The two-dimensional Peierls-Nabarro model for interfacial misfit dislocation networks of cubic lattice

A model is developed to investigate the two-dimensional interfacial misfit dislocation networks that follows the original Peierls-Nabarro idea. Structure and energies of heterophase interfaces are considered for the cubic lattice. To examine the energy contribution of misfit dislocations, where interactions between two dislocation arrays are concerned, a generalized stacking fault energy is proposed. Combined with first-principles calculations, we apply this model to a practical metal-ceramic example: the Ag/MgO(100) interface. An important correction to the adhesive energy is proposed in addition to its dislocation structure being confirmed.     

Low-density dislocation arrays at heteroepitaxial Ge/GaAs-interfaces investigated by high voltage electron microscopy

High-voltage electron microscopy in combination with a large-area thinning technique has been applied to thin epitaxial Ge layers on GaAs substrates. These layers exhibit 60° misfit dislocations along the 〈110〉 directions parallel to the interface. Various dislocation reactions are evaluated from the electron micrographs, e.g. the formation of non-glissile 90° dislocations from two nearly parallel 60° dislocations and the annihilation reaction of two crossing 60° dislocations with identical Burgers vectors. The latter reaction occasionally leads to a dislocation multiplication. The misfit dislocations in very thin layers (～0.5 μm thickness and a linear dislocation density of less than 100 dislocation lines/cm) tend to be arranged in groups rather than being equidistant. Consequences for the interpretation of x-ray topograms are discussed.     

Misfit dislocations in gold/Permalloy multilayers

Several groups have reported the misfit dislocation structures in Au/Ni_0.8Fe_0.2 multilayers where the lattice parameter misfit is very large. To explore the factors controlling such structures, molecular dynamics simulations have been used to simulate the vapour-phase growth of (111)-oriented Au/Ni_0.8Fe_0.2 multilayers. The simulations revealed the formation of misfit dislocations at both the gold-on-Ni_0.8Fe_0.2 and the Ni_0.8Fe_0.2-on-gold interfaces. The dislocation configuration and density were found to be in good agreement with previously reported high-resolution transmission electron microscopy observations. Additional atomic-scale simulations of a model nickel–gold system indicated that dislocations are nucleated as the first nickel layer is deposited on gold. These dislocations have an (a/6)?112? Burgers vector, typical of a Shockley partial dislocation. Each dislocation creates an extra {220} plane in the smaller lattice parameter nickel layer. These misfit-type dislocations effectively relieve misfit strain. The results also indicated that the dislocation structure is insensitive to the energy of the depositing atoms. Manipulation of the deposition processes is therefore unlikely to reduce this component of the defect population.