Dislocation motion in anisotropic multilayer materials

Line integral forms for the elastic field of dislocations in anisotropic, multilayer materials are developed and utilized in Parametric Dislocation Dynamics (PDD) computer simulations. Developed equations account for interface image forces on dislocations as a result of elastic modulus mismatch between adjacent layers. The method is applied to study dislocation motion in multilayer thin films. The operation of dislocation sources, dislocation pileups, confined layer slip (CLS), and the loss of layer confinement are demonstrated for a duplex Cu/Ni system. The strength of a thin film of alternating nanolayers is shown to increase with decreasing layer thickness, and that the maximum strength is determined by the Koehler barrier in the absence of coherency strains. For alternating Cu/Ni nanolayers, the dependence of the strength on the duplex layer thickness is found to be consistent with experimental results, down to a layer thickness of ≈10nm.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

Defect aggregates in neutron-irradiated β-Si3N4

Abstract

Microstructural analysis of the defect aggregates formed in bulk samples of polycrystalline β-Si₃N₄ neutron-irradiated to a dose of ～2.0 × 10²⁶n/m² at temperatures of 1100 K and 925 K has been carried out. This study has shown that the defect aggregates formed are faulted dislocation loops lying on the {1010} planes with a Burgers vector of b ? 1 /10<1125>. The vector is non-rational but corresponds to the insertion of an extra layer of [SiN4] tetrahedra on the {10l0} planes plus an additional shear in the loop plane. The formation of these loops is dependent upon the temperature of irradiation. In the sample irradiated at 1100 K their formation is additionally dependent upon whether or not a particular grain contains pre-existing c-axis dislocations. If no c-axis dislocations are present then independent nucleation of the loops is apparent; if there are pre-existing c-axis dislocations then the loops form from an apparent dissociation between the arcs of the irradiation-induced helical c-axis dislocation. In the sample irradiated at 925 K only independent nucleation of the loops occurs, regardless of whether or not there are any pre-existing c-axis dislocations in the grains.     

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.     

On the role of weak interfaces in blocking slip in nanoscale layered composites

Layered composites of Cu/Nb achieve very high strength levels when the individual layer thicknesses are 1–10?nm, attributable to the interfaces acting as barriers to slip. Atomistic models of Cu/Nb bilayers were used to explore the origins of this resistance. The models clearly show that dislocations placed near an interface experience an attraction toward the interface, regardless of the sign of the Burgers vector or the material in which it is placed. This attraction is caused by shear of the interface induced by the stress field of the dislocation. Furthermore, the dislocation, upon reaching the interface, is absorbed by it in the sense that the core spreads within the interface. We develop a model, using a fractional dislocation approach, which provides an estimate of the strength of the attraction as a function of distance from the interface and also the dependence of the interaction on the type of dislocation. A screw dislocation is much more effective in shearing the interface, and the resulting attractive forces on screws are larger than for edge dislocations.     

Role of interfaces in shock-induced plasticity in Cu/Nb nanolaminates

We investigate deformation of pure Cu, pure Nb and 30?nm Cu/30?nm Nb nanolaminates induced by high strain rate shock loading. Abundant dislocation activities are observed in shocked pure Cu and Nb. In addition, a few deformation twins are found in the shocked pure Cu. In contrast, in shocked Cu/Nb nanolaminates, abundant deformation twins are found in the Cu layers, but only dislocations in the Nb layers. High resolution transmission electron microscopy reveals that the deformation twins in the Cu layers preferentially nucleate from the Cu(112)//Nb(112) interface habit planes rather than the predominant Cu(111)//Nb(110) interface planes. Our comparative study on the shock-induced plastic deformation of the pure metals (Cu and Nb) and the Cu/Nb nanolaminates underscores the critical role of heterogeneous phase interfaces in the dynamic deformation of multilayer materials.     

The defect structure of AlGaN/GaN superlattices grown on sapphire by the MOCVD method

High-resolution x-ray diffractometry and electron microscopy are used to study the defect structure and relaxation mechanism of elastic stresses in AlGaN/GaN superlattices grown by the MOCVD method on sapphire covered with a preliminarily deposited GaN and AlGaN buffer layer. Based on an analysis of the half-widths of three-crystal scan modes of x-ray reflections measured in different diffraction geometries, the density of different dislocation families is determined. For all the dislocation families, the density is shown to increase with the Al concentration in the solid-solution layers and depend only weakly on the superlattice period. From the electron-microscopic patterns of planar and cross sections, the types of dislocations and their distribution in depth are determined. It is shown that, in addition to high-density vertical edge and screw dislocations, which nucleate in the buffer layer and propagate through the superlattice layers, there are sloped intergrowing dislocations with a large horizontal projection and bent mixed dislocations with a Burgers vector $\left\langle {11\overline 2 3} \right\rangle $ at the interface between individual superlattice layers. The former dislocations form at the interface between the buffer layer and the superlattice and remove misfit stresses between the buffer and the superlattice as a whole, and the latter dislocations favor partial relaxation of stresses between individual superlattice layers. In samples with a high Al concentration (greater than 0.4) in AlGaN layers, there are cracks surrounded by high-density chaotic horizontal dislocations.     

Dislocation and disclination loops in the virtual-defect method

A method of virtual circular defect loops is developed for determining the elastic fields produced by defects in a bounded medium in the case of an axially symmetric geometry. In this method, continuously distributed virtual circular Volterra and Somigliana dislocation loops are adjusted in such a way as to satisfy the boundary conditions imposed at free surfaces and interfaces. Original calculations of the elastic fields of circular defect loops of different types are carried out. The elastic fields are found for the case of straight dislocations and disclinations in a plate that are perpendicular to the plate plane and for the case of circular disclination loops parallel to the plate plane or to an interface.     

Dislocation transmission across the Cu/Ni interface: a hybrid atomistic–continuum study

The strengthening mechanisms in bimetallic Cu/Ni thin layers are investigated using a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The hybrid approach is an extension of the Peierls–Nabarro (PN) model to bimaterials, where the dislocation spreading over the interface is explicitly accounted for. The model takes into account all three components of atomic displacements of the dislocation and utilizes the entire generalized stacking fault energy surface (GSFS) to capture the essential features of dislocation core structure. Both coherent and incoherent interfaces are considered and the lattice resistance of dislocation motion is estimated through the ab initio-determined GSFS. The effects of the mismatch in the elastic properties, GSFS and lattice parameters on the spreading of the dislocation onto the interface and the transmission across the interface are studied in detail. The hybrid model shows that the dislocation dissociates into partials in both Cu and Ni, and the dislocation core is squeezed near the interface facilitating the spreading process, and leaving an interfacial ledge. The competition of dislocation spreading and transmission depends on the characteristics of the GSFS of the interface. The strength of the bimaterial can be greatly enhanced by the spreading of the glide dislocation, and also increased by the pre-existence of misfit dislocations. In contrast to other available PN models, dislocation core spreading in the two dissimilar materials and on their common interface must be simultaneously considered because of the significant effects on the transmission stress.     

Exponent for Hall–Petch behaviour of ultra-hard multilayers

Elastically inhomogeneous multilayer films are being exploited for use as ultra-hard coatings. These films exhibit a strong dependence between the compositional wavelength of the film, Λ, and the hardness, H=KΛ^?a+H₀ where the scaling exponent a depends on the elastic properties of the individual layers (shear moduli and Poisson ratios). The dislocation pileup model can explain this trend and form a bridge between the microscopic strength of multilayer interfaces and the macroscopic strength of the multilayer. A semianalytic solution to the pileup model of multilayer strength is presented. All parameter dependencies are solved analytically except a single dimensionless coefficient which is found from numerical simulation. The predictions are compared to data from a 2D discrete dislocation model and to experimental Cu/Ni data. Coefficients and exponents are given for some additional material systems.     

In situ TEM characterisation of dislocation interactions in α-titanium

In situ straining in the transmission electron microscope and diffraction-contrast electron tomography has been applied to investigate dislocation interactions in α-Ti. Dislocation debris, in the form of small loops, was seen to form from sequential cross-slip events. Electron tomography provided direct three-dimensional visualisation of the dislocation structures, allowing accurate identification of slip planes, dislocation line directions and spatial relations between dislocations.     

Molecular dynamics study of plastic deformation mechanism in Cu/Ag multilayers

The plastic deformation mechanism of Cu/Ag multilayers is investigated by molecular dynamics(MD) simulation in a nanoindentation process. The result shows that due to the interface barrier, the dislocations pile-up at the interface and then the plastic deformation of the Ag matrix occurs due to the nucleation and emission of dislocations from the interface and the dislocation propagation through the interface. In addition, it is found that the incipient plastic deformation of Cu/Ag multilayers is postponed, compared with that of bulk single-crystal Cu. The plastic deformation of Cu/Ag multilayers is affected by the lattice mismatch more than by the difference in stacking fault energy(SFE) between Cu and Ag. The dislocation pile-up at the interface is determined by the obstruction of the mismatch dislocation network and the attraction of the image force. Furthermore, this work provides a basis for further understanding and tailoring metal multilayers with good mechanical properties, which may facilitate the design and development of multilayer materials with low cost production strategies.     

晶体位错的离散弹性模型——位错中心结构和P-N力

在离散弹性模型中考虑了位错中心位错密度分布的影响,计算了fcc和bcc两种各向同性弹性介质中,不同中心结构的螺型位错的自能、等效内截半径与位错中心位置的关系,估算了不同滑移面上P-N力。讨论了原子热振动对P-N力的影响,比较了离散弹性方法与现有其它方法的结果,据信离散弹性方法是一种进一步进行更深入计算的有效方案。 关键词：     

Influence of layer thickness on the structure and the magnetic properties of Co/Pd epitaxial multilayer films

Co/Pd epitaxial multilayer films were prepared on Pd(111)_fcc underlayers hetero-epitaxially grown on MgO(111)_B1 single-crystal substrates at room temperature by ultra-high vacuum RF magnetron sputtering. In-situ reflection high energy electron diffraction shows that the in-plane lattice spacing of Co on Pd layer gradually decreases with increasing the Co layer thickness, whereas that of Pd on Co layer remains unchanged during the Pd layer formation. The CoPd alloy phase formation is observed around the Co/Pd interface. The atomic mixing is enhanced for thinner Co and Pd layers in multilayer structure. With decreasing the Co and the Pd layer thicknesses and increasing the repetition number of Co/Pd multilayer film, stronger perpendicular magnetic anisotropy is observed. The relationships between the film structure and the magnetic properties are discussed.     

Strain interactions and defect formation in stacked InGaAs quantum dot and dot-in-well structures

The growth of high-quality stacked quantum dot (QD) structures represents one of the key challenges for future device applications. Electronic coupling between QDs requires closely separated electronic levels and thin barrier layers, requiring near identical composition and shape, despite strong strain interactions. This paper presents a detailed characterization study of stacked InGaAs QD and InAs/InGaAs dot-in-well (DWELL) structures using cross-sectional transmission electron microscopy. For In_.5Ga_.5As/GaAs QD structures we have observed optimized stacking using a barrier thickness 12 nm.We also report studies of stacking in DWELL laser structures. Despite reports of very low threshold currents in such lasers, designed for 1.3 μm emission, performance is limited by gain saturation and thermal excitation effects. We have explored solutions to these problems by stacking multiple DWELL layers of three, five and 10 repeats. Initial attempts at stacked multilayer structures, particularly samples with a large number of repeats, produced variable results, with a number of the final devices characterized by poor emission and electrical characteristics. Analysis by transmission electron microscopy has identified the presence of large defective regions arising from the complex interaction of dots on several planes and propagating threading dislocations into the cladding layers. The origin of this defect is identified as the coalescence of QDs at very high density and the resulting dislocation propagating to higher dot planes. An effective modified method to reduce the defect density by growing the barrier layer at higher temperature will be discussed. Finally, we report the growth of a stacked 10-layer structure using relatively thin barriers, grown using this technique.     

Investigation of deformation instability of Au/Cu multilayers by indentation

Plastic deformation behavior of Au/Cu multilayers with individual layer thicknesses of 25–250 nm was investigated via microindentation experiments. It was found that plastic instability of the Au/Cu multilayer exhibits strong length scale (individual layer thickness and grain size) dependence. The smaller the length scale, the easier shear bands form. In other words, plastic deformation becomes unstable with decreasing length scale. Cross-sectional observation along with plan-view indicates that the occurrence of plastic deformation instability corresponds to transformation of the deformation mechanism associated with geometrical configuration and length scale of the material. At nanometer scale, buckling-assisted interface crossing of dislocations results in local shear band, while, at submicron scale or above, local dislocation pileup-induced interface offset leads to plastic instability. Theoretical analysis is conducted to understand the length scale-dependent plastic deformation behavior of the multilayer.     

Electronic states and vibration spectra of CdTe/ZnTe quantum dot superlattices

Electronic and vibrational states in CdTe/ZnTe quantum dot superlattices are studied using optical spectroscopy techniques (photoluminescence in a wide temperature range, IR reflection, and Raman scattering). The effect of the ZnTe barrier layer thickness on the luminescence spectra of the structures is discussed. The luminescence from electronically coupled islands is assumed to be due to spatially indirect excitons because of the specific features of the CdTe/ZnTe heterostructure band structure. A combination of quantum-dot vibrational modes, which has not been observed earlier, is detected in the Raman spectra. Analysis of the lattice IR reflection spectra shows that, in the case of large barrier thicknesses between the quantum-dot planes, elastic stresses are concentrated in the Zn_1?xCd_xTe layers, whereas in structures with lower barrier thicknesses the elastic-strain distribution exhibits a more complicated pattern.     

Specific features of plastic relaxation of a metastable Ge x Si1 − x layer buried between a silicon substrate and a relaxed germanium layer

Heterostructures Ge/Ge _x Si_{1 ? x} /Si(001) grown by molecular beam epitaxy have been investigated using atomic scale high-resolution electron microscopy. A germanium film (with a thickness of 0.5–1.0 μm) grown at a temperature of 500°C is completely relaxed. An intermediate Ge_0.5Si_0.5 layer remains in a strained metastable state, even though its thickness is 2–4 times larger than the critical value for the introduction of 60° misfit dislocations. It is assumed that the Ge/GeSi interface is a barrier for the penetration of dislocations from a relaxed Ge layer into the GeSi layer. This barrier is overcome during annealing of the heterostructures for 30 min at a temperature of 700°C, after which dislocation networks having different degrees of ordering and consisting predominantly of edge misfit dislocations are observed in the Ge/GeSi and GeSi/Si(001) heteroboundaries.     

Computed epitaxial monolayer structures: I. One-dimensional model: Comparison of computed and analytical results

An exact computational procedure is developed which, when applied to Frank and van der Merwe's one-dimensional dislocation model, yields the equilibrium structures of a one-dimensional atom chain with elastic interatomic forces and sinusoidal substrate potential. This forms the first part of the development of a general procedure for calculating the equilibrium structures of two-dimensional monolayers with elastic interatomic forces and substrate potentials of more complex character. The minimum energy principle is applied to distinguish the stable structures from the computed equilibrium ones. The results aie in close agreement with the analytical approximate solutions of Frank and van der Merwe. The atomic displacements and limiting misfits agree almost perfectly. The curves of lowest energy against misfit are likewise in excellent agreement for long chains. For relatively short chains, containing only few dislocations, the curves are composed of segments, one segment for each additional dislocation. The discreteness of dislocations in finite chains is also borne out in other properties. The calculations further show (i) that, for a finite chain with odd numbers of dislocations and atoms, the stable configuration is one with the central atom on a potential crest and (ii) that the cusped minima present in the interfacial energy curve of thick bicrystals disappear when complete or partial accommodation of lattice parameters is energetically possible as in thin films.     

A parametric simulation method for discrete dislocation dynamics

A new computer simulation method employed in discrete dislocation dynamics is presented. The article summarizes results of an application of the method to elementary interactions among glide dislocations and dipolar dislocation loops. The glide dislocations are represented by parametrically described curves moving in glide planes whereas the dipolar loops are treated as rigid objects. All mutual force interactions are considered in the models. As a consequence, the computational complexity rapidly increases with the number of objects considered. This difficulty is treated by advanced computational techniques such as suitable accurate numerical methods and parallel implementation of the algorithms. Therefore the method is able to simulate particular phenomena of dislocation dynamics which occur in crystalline solids deformed by single slip: generation of glide dislocations from the Frank-Read source, interaction of glide dislocations with obstacles, their encounters in channels of the bands, sweeping of dipolar loops by glide dislocations and a loop clustering.