Monazite (monoclinic LaPO4) slip systems at room temperature

Polycrystalline monazite (monoclinic LaPO₄) was deformed by spherical indentation at room temperature. Slip systems were identified using TEM of thin sections prepared parallel and close to the indented surface. Dislocation Burgers vectors (b) were identified by Burgers circuit closure in high resolution TEM images, supplemented by diffraction contrast where possible. A total of 441 b determinations were made in 97 grains. The most common slip systems were [001]/(010), [100]/(010) and [010]/(100). Slip on (001) was less common. Many other less common slip systems and Burgers vectors were also identified, including b = [101], [101], [011], [110] and [111]. b = [101] dislocations dissociate into ½[101] partials, and b = [101] dislocations are inferred to dissociate to ½[101] partials, with a low energy stacking fault of ～30 mJ/m². b = [100] dislocations may dissociate into ¼[210] + ¼[210] partials. b = [010] may sometimes dissociate to ½[010] + ½[010] partials. Other types of partial dislocations were also observed and discussed. All partial dislocations were climb dissociated. The line energies of monazite dislocations and their partials were calculated, and stacking fault structures for partial dislocations are analyzed. Satisfaction of the Von Mises criterion for full ductility most likely involves [101]/(111) and ?011?/{011} or {111} slip, but other combinations that require both b = [101] and ?011? or ?110? are possible. If deformation twinning is active, slip systems with b = ?011? or ?110? may not be necessary for full ductility.     

Analysis of contrasts and identifications of Burgers vectors for basal-plane dislocations and threading edge dislocations in 4H-SiC crystals observed by monochromatic synchrotron X-ray topography in grazing-incidence Bragg-case geometry

Contrasts of dislocations in the sub-surface region of the Si-face of a 4H-SiC wafer were observed by monochromatic synchrotron X-ray topography in grazing-incidence Bragg-case geometry. Basal-plane dislocations show very characteristic contrast depending on their Burgers vectors, running directions, and types of dislocations, whether they are screw dislocations, C-core edge dislocations, or Si-core edge dislocations. The rules for contrasts of basal-plane dislocations are summarized. It is shown that by observing those contrasts at fixed diffraction conditions, Burgers vectors of the basal-plane dislocation can be identified without performing a g?·?b analysis in some cases. Threading edge dislocations also have very characteristic contrasts depending on the angles between the projected g and their Burgers vectors. It is shown that Burgers vectors of threading edge dislocations can be determined uniquely by observing their characteristic contrasts without performing g?·?b analysis. Contrast mechanisms for these dislocations in grazing-incidence X-ray topography are discussed.     

The influence of strain rate on the visibility of dislocations in transmission electron microscopy images of deformed Ti–6 wt% Al–4 wt% V and in Timet 550

Samples of Ti–6?wt%?Al–4?wt%?V and Timet 550 (Ti–4?wt%?Al–4?wt%?Mo–2?wt%?Sn–0.5?wt%?Si) have been subjected to strain rates between 10^?1 and 10³?s^?1and detailed examination of the dislocation structure in the α grains has been carried out using transmission electron microscopy (TEM). For samples deformed to a strain of 0.1 at 10^?1?s^?1, detailed analysis of the defects can be carried out using all diffracting vectors and the presence of (c +?a) dislocations and a dislocations thus confirmed. In contrast, for samples strained to the same strain of 0.1 but at 5?s^?1, it is not possible to obtain images of dislocations when using any diffracting vectors other than 0002. Thus the presence of dislocations which have a Burgers vector containing a c component can be confirmed in the samples strained at 5?s^?1 but the presence of a-component dislocations can only be inferred from TEM of these samples because of the difficulty of obtaining images with diffracting vectors other than 0002. Limited observations on samples strained at 10³?s^?1 show that similar difficulties are found in imaging dislocations as are found in samples deformed at 5?s^?1 but at this strain rate, the highest used, the difficulties are reduced since images can be obtained in some grains using diffracting vectors other than 0002. These results are discussed in terms of the nature of damage as a function of strain rate and the factors that influence contrast from dislocations in crystals.     

On the glide of [100] dislocation and the origin of ‘pencil glide’ in Mg2SiO4 olivine

ABSTRACT

Olivine with chemical composition (Mg,Fe)₂SiO₄ is a silicate which is supposed to strongly constrain the flow of the Earth’s upper mantle under thermal convection. Its mechanical properties are thus of primary importance. Slip systems in olivine involve two types of dislocations with [100] and [001] Burgers vectors. In this study, we report atomistic modelling of screw dislocations with [100] Burgers vector and their intrinsic properties. We show that the [100] screw dislocation core exhibits several configurations corresponding to spreading in different planes and different relative stabilities. At low pressure, we identify a clear tendency for core spreading in (010). At higher pressure, relevant for the Earth’s mantle, we show that pressure promotes a change in core configuration with spreading into equivalent {021} planes. Based on the systematic investigation of the minimum energy path between the different configurations, we show that the variability of core structures allows complex glide paths which has been described at the macroscopic level as ‘pencil glide’. Our results suggest that the pencil glide is more efficient at high pressure.     

The nucleation of faulted dipoles at intersection jogs in γ-TiAl

Single crystal samples of n-(Ti-54.7 at.% Al) deformed to a permanent strain of 2% at room temperature under multiple-slip conditions contain faulted dipoles (FDs) whose density exhibits some dependence on load orientation. Although FDs are hard to observe after compression along [210], they are profuse and congregated in places in the [1 1 8.6] load orientation. They exhibit most of the topological characteristics of FDs formed under single slip as reported by Grégori and Veyssière such as elongation in the screw direction of the primary d011] slip direction and a noticeable shape asymmetry. It is shown further that, in the [1 1 8.6] samples, bundles of FDs originate at jogs that result from intersection with forest dislocations of appropriate Burgers vectors. A mechanism for FD nucleation is proposed on the basis of asymmetrical dissociation of the parent d011] dislocation and specific impingements between the various partials on two adjacent octahedral planes. Implications of the FD nucleation at jogs on the load orientation dependence of the FD density are discussed.     

Characterization of dislocation interactions in olivine using electron tomography

We have investigated by electron tomography, in a transmission electronic microscope, the interactions between dislocations in olivine single crystals and polycrystals deformed in axial compression at T < 1000 °C (T < 0.5T_m). Dislocations are mostly of the [0?0?1] type, except in the polycrystal where [1?0?0] and [0?0?1] dislocations have been activated. A few 〈1?0?1〉 junctions have been found and characterized. Many collinear interactions have been identified either involving direct interactions between crossing dislocations of opposite Burgers vectors or indirect interactions between dislocations gliding in parallel planes and sessile dislocation loops. We suggest that collinear interaction, already identified as the primary source of strain hardening in FCC metals, is the main dislocation interaction mechanism in olivine deformed at temperatures below 1000 °C.     

The character of micropipes in silicon carbide crystals

There has been some question as whether micropipes in SiC crystals, giant dislocations that possess hollow cores and lie roughly along the hexagonal c-direction, are screw dislocations with Burgers vectors of nc, where n is an integer, or are dislocations of mixed character, with Burgers vector nc?+?ma, where m is equal to n or possibly different from n. X-ray topographs of the basal faces of PVT-grown 4H-SiC wafers containing micropipes taken in both back-reflection and grazing-incidence geometries are compared with computer simulations of micropipe images. The deviation from circular symmetry of micropipe images in such topographs may be explained as well by the micropipe's tilt from the c-direction as by an nc?+?ma nature. The contrast of micropipes in electron micrographs comprises of a pair of light and dark lobes consisting of a detailed system of subsidiary fringes. These are comparable with micropipe image computer simulations for Burgers vector nc. When an na edge component is introduced to the simulation, a small feature, a few hundred nm wide, appears, which is absent from the micrographs.     

On the measurement of dislocation core distributions in a GaAs/ZnTe/CdTe heterostructure by high-resolution transmission electron microscopy

Tensorial maps of misfit dislocations at the strained GaAs-ZnTe-CdTe interfacial zone are reconstructed by use of digital processing of high-resolution transmission electron micrographs. Large distortions of the crystal lattice around Lomer dislocations are measured using the geometric phase technique. The integration of the dislocation distribution tensor field over a dislocation core region gives the in-plane components of their Burgers vectors. The accuracy of the method for the dislocation map reconstruction is tested by comparing the theoretical values of the so-called true Burgers vectors with those obtained from the integration of tensorial maps.     

Section images of dislocations normal to the surface of a 6H-SiC single crystal

Section topographs of edge and screw dislocations with an axis along [0001] in 6H-SiC are taken and interpreted, and the image formation is explained for this case. The contrast induced by various arrangements of dislocations within the Borrmann triangle is experimentally studied. The sign of the Burgers vector of an edge or screw dislocation normal to the crystal surface is shown to be unambiguously determined from the section-topograph image of this dislocation. The sign of the Burgers vector of a screw dislocation can also be determined from its image taken with Lang projection topography. The contribution of a long-range strain field to the section images of edge and screw dislocations normal to the crystal surface is revealed. The experimental contrasts recorded using section topography and Borrmann-effect-based topography are compared.     

Refined Prediction and Observation of Dislocation Structures in Low Σ Symmetric Grain Boundaries

The grain boundary dislocation structures of three Fe–4at.% Si bicrystals with an additional misorientation of the order of 2° were studied by transmission electron microscopy (TEM), one S5 [001] (310) and two S9 [110] (1 [`1]\overline 1 4). It was found that in the S5 case two Burgers vectors of the structure are not simple basic complete displacement shift lattice (DSC) vectors and are larger than any one of them. This enabled formation of the preferred grain boundary dislocation (GBD) structure with a hexagonal net composed of three screw dislocations and an independent set of parallel edge dislocations. In the S9 case the GBD structure comprises three apparently independent sets of parallel dislocations. The Burgers vectors of two sets could be established as basic DSC vectors in screw and edge orientation, respectively, with respect to the GB plane. For the third set formed by separated groups of four dislocations no corresponding basic DSC vector exists. This case needs further investigation. The previously published table of predicted GBD structures for symmetrical coincidence boundaries up to S11 was refined according to the new results.     

LiNbO3晶体中包裹物和位错的X射线形貌研究

用X射线透射扫描形貌方法研究了LiNb0₃晶体中的包裹物和位错。在实验中发现了包裹物的相应于不同衍射矢量的X射线形貌与基于各向同性理论预言的形貌之间存在分歧,这被解释为弹性各向异性效应。同时还观察到Burgers矢量为最短点阵平移矢量1/3的纯刃型位错和次短点阵平移矢量1/3<0111>的纯螺型位错,以及由该螺型位错组成的纯扭转晶界。 关键词：     

Secondary dislocation structures in a Ni–TiN system from the GMS and O-lattice theory

The preferred state in an interface is the key to evaluating misfit strain, especially for the interphase interfaces in secondary preferred state. The structure of good matching site (GMS) in a GMS clusters offers a guidance for the preferred state, especially for identifying the coincidence site lattice in two dimension for secondary preferred state and the Burgers vectors in a large misfit system. Here, we combine the GMS with O-lattice theory to calculate the secondary dislocation structure in the habit planes of the type II and III TiN precipitates in a Ni–TiN system. We find that under a slight elastic strain, the type III habit plane contains a single set of secondary dislocations, consistent with the experimental observation. The type II habit plane contains three sets of secondary dislocations, two of which can be relaxed to be nearly parallel and another of which may be invisible in diffraction contrast due to its short Burgers vector. The present study provides a reasonable interpretation to the observed interfacial dislocations, and also suggests Burgers vectors for the dislocations that are not determined experimentally.     

Frenkel model of pair of dislocations

The graphical method of solution given in the paper [1] is used to study a pair of dislocations with opposite signs of the Burgers vectors in the Frenkel model of a crystal. The dependence of the force between the dislocations on their mutual distance is determined.     

Formation of Ge self-assembled quantum dots on a SixGe1−x buffer layer

Ge self-assembled quantum dots (SAQDs) grown on a relaxed Si_0.75Ge_0.25 buffer layer were observed using an atomic force microscopy (AFM) and a transmission electron microscopy (TEM). The effect of buried misfit dislocations on the formation and the distribution of Ge SAQDs was extensively investigated. The Burgers vector determination of each buried dislocation using the g·b = 0 invisibility criterion with plane-view TEM micrographs shows that Ge SAQDs grow at specific positions related to the Burgers vectors of buried dislocations. The measurement of the lateral distance between a SAQD and the corresponding misfit dislocation with plane-view and cross-sectional TEM images reveals that SAQDs form at the intersections of the top surface with the slip planes of misfit dislocations. The stress field on the top surface due to misfit dislocations is computed, and it is found that the strain energy of the misfit dislocations provides the preferential formation sites for Ge SAQDs nucleation.     

Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al

The interaction of dislocations with grain boundaries (GBs) determines a number of important aspects of the mechanical performance of materials, including strengthening and fatigue resistance. Here, the coupled atomistic/discrete-dislocation (CADD) multiscale method, which couples a discrete dislocation continuum region to a fully atomistic region, is used to study screw-dislocations interacting with Σ3, Σ11, and Σ9 symmetric tilt boundaries in Al. The low-energy Σ3 and Σ11 boundaries absorb lattice dislocations and generate extrinsic grain boundary dislocations (GBDs). As multiple screw dislocations impinge on the GB, the GBDs form a pile-up along the GB and provide a back stress that requires increasing applied load to push the lattice dislocations into the GB. Dislocation transmission is never observed, even with large GBD pile-ups near the dislocation/GB intersection. Results are compared with experiments and previous, related simulations. The Σ9 grain boundary, composed from a more complex set of structural units, absorbs screw dislocations that remain localized, with no GBD formation. With increasing applied stress, new screw dislocations are then nucleated into the opposite grain from structural units in the GB that are nearby but not at the location where the original dislocation intersected the boundary. The detailed behaviour depends on the precise location of the incident dislocations and the extent of the pile-up. Transmission can occur on both Schmid and non-Schmid planes and can depend on the shear stresses on the GB plane. A continuum yield locus for transmission is formulated. In general, the overall dissociation and/or transmission behaviour is also determined by the Burgers vectors and associated steps of the primitive vectors of the grain boundary, and the criteria for dislocation transmission formulated by Lee et al . [Scripta Metall. 23 799 (1989); Phil. Mag. A 62 131 (1990); Metall. Trans. A 21 2437 (1990)] are extended to account for these factors.     

Intralamellar dislocation networks formed by glide in γ-TiAl I. The mechanism of formation

In a lamellar TiAl alloy deformed at room temperature under an orientation that activates slip parallel to the interfaces, the nphase exhibits intralamellar dislocation networks parallel to the primary slip plane and entirely glissile in their habit plane. Their meshes are mainly rectangular with branches all coplanar, screw or near-screw in character and with Burgers vector of and types. Dislocation organization at and in the near-vicinity of these intralamellar networks suggests a reaction between a family of primary coplanar d011] dislocations that slip in the network habit plane and a family of dislocations that cross-slip from a plane inclined to the lamellae into the network. The reactions result in junctions with Burgers vector that subsequently transform into rectangular units. The presence of these networks is consistent with that of a residual elastic twist between adjacent nlamellae.     

Reprise: partial chemical strain dislocations and their role in pinning dislocations to their atmospheres

A correct solution for a dislocation atmosphere is provided using Hirth's Standard Model, confirming the errors in Hirth and Lothe. Contrary to what is given there, concentration changes in Cottrell atmospheres reduce an edge dislocation's stress and its elastic energy, thereby reducing the magnitude of the concentration changes. The chemical and elastic strain fields from Cottrell atmospheres are again shown to behave as partial dislocations with variable Burgers vectors that are not crystal translation vectors. The reality of partial dislocations provides a simpler explanation for pinning of dislocations by atmospheres. Much of the literature on dislocation properties in solid solutions should be re-examined.     

Structure of dislocations and stacking faults in the complex intermetallic ξ′-(Al–Pd–Mn) phase

We present the results of an electron microscopy study of defects in plastically deformed single crystals of the intermetallic ξ^′-(Al–Pd–Mn) phase. Pure edge dislocations with two different Burgers vector directions and four different Burgers vector magnitudes were found. All Burgers vector magnitudes observed can be described in terms of irrational fractions of the unit-cell parameters, and we have observed Burgers vector directions that can be indexed using irrational indices. The stacking faults observed have displacement vectors whose magnitudes and directions are incompatible with the unit cell of the ξ^′ phase. A comparison of the Burgers vectors observed in this study with those reported for the corresponding icosahedral quasicrystal shows that they are equivalent with respect to their directions and lengths. This leads to the conclusion that local order rather than long-range periodic (or quasiperiodic) order governs the structure of defects in these materials.