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.     

Generation of rectangular prismatic dislocation loops in shells and cores of composite nanoparticles

A theoretical model has been proposed for describing the relaxation of misfit stresses in a spherically symmetric composite core-shell nanoparticle due to the generation and expansion of rectangular prismatic dislocation loops at the internal and external interfaces. The critical conditions of the formation of these loops have been calculated for nanoparticles consisting of a relatively massive core and a thin shell. It has been shown that the generation of dislocation loops is possible when the misfit of the lattice parameters of the core and shell of the nanoparticle exceeds a critical value that depends on the nanoparticle radius, the shell thickness, the loop formation position, and the shape of loops. This condition holds for a loop in the shell when the shell thickness either lies in a specific range of small values or (for a larger misfit) is less than a critical value. For the generation of loops in the core, the shell thickness should exceed a critical value. The dislocation loops elongated along the core-shell interface are formed more readily. As the shell thickness increases at a fixed nanoparticle radius, the energetically more favorable generation of a dislocation loop occurs first from the free surface into the bulk of the shell, then from the interface into the shell, and finally from the interface into the core of the nanoparticle.     

Non-singular dislocation loops in gradient elasticity

Using gradient elasticity, we give in this Letter the non-singular fields produced by arbitrary dislocation loops in isotropic media. We present the ‘modified’ Mura, Peach–Koehler and Burgers formulae in the framework of gradient elasticity theory.     

Continuous distribution of dislocation loops

Formulae are derived for the displacement and stress in an unbounded continuous isotropic medium when the dislocation loops are continuously distributed. The physical interpretation of the tensor introduced for the dislocation loop density in the crystal is discussed and the relation to the theory of the continuous distribution of dislocations is pointed out.     

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.     

Cooperative nucleation of shear dislocation loops

The mean elastic interaction between randomly distributed transient subcritical shear loops of the same sign, formed in the presence of an applied shear stress, is the "image stress." This stress is proportional to the volume density of loops and has the same sign as the applied stress. The image stress promotes the cooperative nucleation of shear loops, and leads to an instability in which the number of loops and the image stress increase rapidly, leading to the generation of stable expanding loops. The critical stress at which the instability is predicted is relatively high.     

氢离子辐照纯钒中形成的位错环

钒合金作为聚变堆候选材料, 其辐照损伤行为一直是关注的重点. 研究辐照时形成的位错环的性质, 其意义在于揭示纯钒中辐照空洞的长大机理. 这种机理表现为不同类型位错环对点缺陷吸收的偏压不同, 从而影响金属的辐照肿胀. 本文利用加速器对纯钒薄膜样品进行氢离子辐照, 然后, 利用透射电镜的inside-outside方法分析氢离子辐照所形成的位错环的类型. 结果表明, 在氢离子辐照纯钒中没有发现柏氏矢量b=<110>的位错环, 只有柏氏矢量b=1/2<111>和b=<110>的位错环, 这两种位错环的惯性面处于{110}-{112}之间. 能确定性质的位错环全部为间隙型位错环, 未发现空位型位错环.     

Generation of dislocation loops in deformed nanocrystalline materials

A theoretical model is suggested which describes the generation of lattice perfect, lattice partial and grain boundary dislocation loops (DLs) at pre-existent DLs in mechanically loaded nanocrystalline materials (NCMs). The energy characteristics of various modes of the DL generation are calculated and compared. With these calculations and comparison, the two basic ranges of the grain size in NCMs are revealed each is characterized by its specific set of effectively operating modes of the DL generation and plastic deformation. The role of the DL generation in plastic and superplastic deformation processes in NCMs is discussed.     

Homogeneous nucleation of glide dislocation loops in nanoceramics

A theoretical model is proposed for the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics under deformation at low and high temperatures. The nucleation of a dislocation loop in a crystalline grain is considered an ideal nanoscopic shear whose magnitude (the Burgers vector of the dislocation) increases gradually as the loop is nucleating. The characteristics of the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics based on cubic silicon carbide are calculated. It is shown that, in general, the homogeneous nucleation of a dislocation loop in nanocrystalline ceramics at high temperatures proceeds in two stages, namely, the athermal nucleation of a loop of a “noncrystallographic” partial dislocation and its thermally activated transformation into an ordinary partial lattice dislocation loop.     

Instability of interstitial dislocation loops in electron-irradiated dielectrics

The experiments on electron irradiation of yttrium-stabilized zirconium oxide samples show the formation of strong elastic fields near interstitial dislocation loops. The fields increase with an increase in the loop radius and, when the loop radius reaches a certain critical value, the loops became unstable due to the beginning of plastic deformation and the formation of a dislocation network. The mechanism of the occurrence of this instability is suggested. It is based on the accumulation of charges at dislocation loops due to ionization processes in an electron-irradiated dielectric. It is shown that the accumulation of the electric charge at growing dislocation loops in dielectrics may be responsible for an increase in elastic stresses near dislocation loops and for their instability because of the beginning of plastic deformation near the loops when stresses at growing loops become close to the theoretical yield stress of the material.     

Precipitate assemblies formed on dislocation loops in aluminium-silver-copper alloys

The precipitation microstructure of the γ′ (AlAg₂) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-90at.Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ′ phase formed assemblies with a two-dimensional, open arrangement of precipitates. Each such assembly contained two variants of the γ′ phase alternately arranged to form a faceted elliptical unit. The θ′ (Al₂Cu) phase formed on these assemblies after further ageing. Each assembly was formed via repeated precipitation of the γ′ phase on dissociated segments of a single dislocation loop. This faceted elliptical assembly has not been previously reported for the γ′ precipitate. The difference between the precipitation behaviour of the γ′ phase in Al-Ag and Al-Ag-Cu alloys was attributed to copper modifying the as-quenched defect structure of the matrix. The formation of faceted elliptical γ′ phase assemblies clarifies earlier observations on the precipitate number density and mechanical properties of aluminium-silver-copper alloys.     

Steady-state diffusion of point defects to dislocation loops

Approximate formulae are given for the reaction constant of diffusion-controlled precipitation of point defects into dislocation loops. Simple results are derived for several cases of highly anisotropic uniaxial diffusion perpendicular to the loop area.     

Elastic interaction of dislocation loops and point defects

The elastic interaction energy of a circular dislocation loop with interstitial atoms and vacancies characterized as dilatation or relaxation centres is calculated. Further, the forces which the dislocation loops exert on point defects through elastic interaction are discussed.     

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor,dislocation key-formulas and dislocation loops

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.     

Formation of dislocation loops during He clustering in bcc Fe

The clustering of helium in bcc (body centered cubic) iron and the growth of a helium bubble are simulated at the atomistic level for the helium-rich vacancy-poor condition. It is shown that a ? 111 dislocation loop is formed as a sequential collection of 111 crowdions, the latter being the most stable self-interstitial atom configuration in the presence of a He cluster.     

Formation of helium bubbles and dislocation loops in tritium-charged vanadium

Dislocation loops and small He bubbles were observed by transmission electron microscopy in V samples which were tritium-charged to produce single α-phase and (α+ β) two-phase regions and subsequently aged up to 14 months at room temperature and at — 196°C. In the β-phase areas, large densities of He bubbles, 1–2 nm in diameter and dislocation loops were observed. Preliminary observations after 14 months of ageing showed that the loop pattern had coarsened into a dislocation network. In the α-phase areas, bubbles and tube-shaped cavities were found along dislocations and in dislocation tangles. Also, isolated bubbles which had grown by prismatic loop punching were observed. In low-angle grain boundaries bubbles were formed at dislocations. These results show that microstructures similar to those observed after energetic He implantation can form in the absence of irradiation-induced defects. It is concluded that He must be mobile at room temperature in both phases and precipitates by a mechanism which does not require He trapping in vacancies as a first step.