Burgers Vector Component Research Articles

Phase composition and morphology development in WE-type alloys modified by high Zn content

Abstract Quasicrystalline icosahedral equilibrium phase was found in Mg – Y – Nd (WE43) alloys with the addition of 12 wt.% and 25 wt.% Zn constituting grain boundary eutectic phases. In response to the isochronal annealing, morphologically similar precipitates of phases with the same structure as those developing during heat treatment of binary Mg-8 wt.% Zn alloy at temperatures higher than 150 °C were observed, namely β (b-centered monoclinic crystal structure a = 2.596 nm, b = 1.428 nm, c = 0.524 nm, = 102.5°) and β (hexagonal MgZn2). The evolution of the resistivity and microhardness during isochronal annealing corresponds to the phase transformations and the morphology changes of the phases observed. Dislocations with the c Burgers vector component generated due to the presence of icosahedral phase are responsible for the improved formability as compared to the WE43 alloy.

Effect of Extrinsic Grain Boundary Dislocations on Mechanical Properties of Ultrafine-Grained Metals by Molecular Dynamics Simulations

The effect of extrinsic grain boundary dislocations (EGBDs) in nonequilibrium grain boundaries on the mechanical properties of ultrafine-grained metals is investigated by molecular dynamics simulations. Aluminum bicrystal models containing cracks and EGBDs impinged from the crack tips are prepared. First, the dependence of the local grain boundary structure on the accommodation mechanism of EGBDs, and on its stress field is studied. Then, the shielding effect of EGBDs on the emissions of dislocations from crack tips is investigated, and the effect of nonequilibrium grain boundaries on the intragranular deformation is discussed. Finally, to investigate the relationship between EGBDs and intergranular deformations, shear loading is applied to the bicrystal models. It is found that extrinsic grain boundaries function as the intergranular deformation source, and the Burgers vector components of the EGBDs lead to anisotropic grain boundary sliding.

Formation of La 2Zr 2O 7 on yttria-stabilized ZrO 2(110) single crystals during vapour–solid reaction

La 2Zr 2O 7 (LZO) islands were grown on yttria-stabilized ZrO 2 (YSZ) (110) single crystals by reaction between La 2O 3-vapour and the heated YSZ single crystal. The samples were investigated by AFM, XRD and TEM. The pole figure of the LZO(440) plane shows that LZO islands on YSZ(110) are slightly tilted around [11¯0] with maxima at tilt angles of ± 0.6° and by ± 0.9° around [001]. We explain this behaviour by interfacial dislocations with a Burgers vector component perpendicular to the interface, which causes the tilt, and a component parallel to the interface which accommodates the LZO/YSZ lattice misfit of + 5%. The shape of the LZO islands can be explained by the assumption that {111} planes are energetically preferred.

Synthesis and characterization of ZnGeN 2 grown from elemental Zn and Ge sources

Polycrystalline ZnGeN 2 was synthesized by a new method, via vapor growth from Zn and Ge with thermal cracking of NH 3. Measured lattice parameters indicate a monoclinic structure with a= b=0.3157±0.0024 nm, c=0.5137±0.0021 nm, and γ=119°30′±22′, consistent with previous reports. Planar stacking faults lying on the (0 0 1) plane were identified by transmission electron microscopy. Analysis indicates that these stacking faults are bound by a prismatic dislocation loop having in-plane and out-of-plane Burgers vector components of ( a/3[1 1¯ 0]) and ( c/2[0 0 1]), respectively. Photoluminescence spectroscopy at low temperature (∼4 K) showed broad “yellow-band” impurity luminescence centered around 2.6 eV and a narrower near-band-edge luminescence peak at 3.40±0.01 eV. The near-band-edge luminescence peak is higher in energy by approximately 50 meV, and higher in efficiency by at least two orders of magnitude than any previously reported. These observations indicate that this material has superior optical quality than previously obtained by other growth methods. The temperature dependence of the near-band-edge luminescence efficiency is consistent with excitons bound to a shallow donor band.

High-geometrical-resolution imaging of dislocations in SiC using monochromatic synchrotron topography

We demonstrate high-geometrical-resolution imaging of dislocations in 4H-SiC by monochromatic synchrotron topography (but still under the “integrated wave” condition). In back-reflection topographs, 1c screw dislocation images are “magnified” to appear as well-defined circular white spots, while basal plane dislocations with opposite edge Burgers vector components exhibit two distinct kinds of contrast features. All the dislocation images are precisely described by ray-tracing simulations. This imaging technique provides an accurate, comprehensive, and nondestructive characterization tool, which is needed by current SiC researchers is used for industrial applications. It also provides a simple picture for understanding the mechanisms underlying synchrotron diffraction imaging of defects.

Topographic study of dislocation structure in hexagonal SiC single crystals with low dislocation density

We have investigated hexagonal silicon carbide with low dislocation density to reveal inherent dislocation types and structures using the bulk-sensitive synchrotron X-ray topography. This topographic study reveals that: (1) Basal-plane dislocations with the Burgers vector of 1 3 〈1 1 2 ¯ 0〉 preferred to be screw dislocations along 〈1 1 2 ¯ 0〉 in straight shape. (2) Threading dislocations containing the Burgers vector component of 〈0 0 0 1〉 are mostly mixed dislocations containing that of 1 3 〈1 1 2 ¯ 0〉. (3) Threading edge dislocations with the Burgers vector of 1 3 〈1 1 2 ¯ 0〉 are of short lengths, about 30–100 μm. (4) All these dislocations are connected to convert, combine and dissociate to each other. We discuss the dislocation types and structures in terms of both the Peierls energy and elastic interaction. Moreover, we propose that the source of dislocations with the Burgers vector of 1 3 〈1 1 2 ¯ 0〉 is due to the propagation from a seed crystal rather than due to the Frank–Read mechanism.

Atomic structures of dislocations in BaF2/CaF2 strained multilayers

The atomic structures of dislocations in BaF2/CaF2 (111) multilayers grown on Al2O3 were studied by high-resolution transmission electron microscopy on ( ) and ( ) cross-sections. It was found that dislocations generated in these multilayers have structures significantly different from those observed in bulk materials, and that the dislocation structure depends on the morphology of the multilayer. Most dislocations are misfit dislocations along and have Burgers vectors of a/2 on the (111) interfaces. Interface dislocations with a Burgers vector of a/2⟨ 110 ⟩ on (11 ) planes are also observed in multilayers of medium layer thickness l with wavy interfaces. Occasionally, edge dislocations with Burgers vectors a/2⟨ 110 ⟩ and a/2⟨ 001 ⟩ are observed along [1 0]. Edge dislocations with Burgers vectors a/2[ 10] are found dissociated into two partials with an in-plane Burgers vector component of a/4[ 10], and form low-angle boundaries. The influence of these crystal defects on the chemistry of point defects in these multilayers must be taken into account when the ionic conductivity of the multilayer is predicted by space charge theory.

Strain-relaxation mechanisms of SiGe layers formed by two-step growth on Si(0 0 1) substrates

We have investigated the relationship between strain-relaxation behaviors and dislocation structures in SiGe layers on Si(0 0 1) substrates grown by the two-step stain-relaxation procedure. From the plan-view transmission electron microscopy (TEM) observation, three kinds of dislocation structures at the SiGe/Si interface can be observed, reflecting the propagation process of 60° dislocations in the SiGe layer. Threading dislocations in the strain-relaxed SiGe layer observed in the plan-view TEM image show the correspondence to pit morphologies formed on the surface detected by atomic force microscopy. In samples after the two-step growth, the degree of strain-relaxation measured by X-ray diffraction is found to be larger than that estimated from dislocation separations at the SiGe/Si interface measured from the TEM images and the [1 1 0] edge component of Burgers vector of the 60° dislocation. This indicates that additional factors other than the [1 1 0] edge component of Burgers vector of the 60° dislocation also play a role in relaxing the strain along the [1 1 0] direction in the SiGe buffer layer.

Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling

Recent advances in 3-D dislocation dynamics include the proper treatment of free surfaces in the simulations. Dislocation interaction and slip is treated as a boundary-value problem for which a zero-traction condition is enforced at the external surfaces of the simulation box. Here, a new rigorous method is presented to handle such a treatment. The method is semi-analytical/numerical in nature in which we enforce a zero traction condition at select collocation points on a surface. The accuracy can be improved by increasing the number of collocation points. In this method, the image stress-field of a subsurface dislocation segment near a free surface is obtained by an image segment and by a distribution of prismatic rectangular dislocation loops padding the surface. The loop centers are chosen to be the collocation points of the problem. The image segment, with proper selection of its Burgers vector components, annuls the undesired shear stresses on the surface. The distributed loops annul the undesired normal stress component at the collocation points, and in the process create no undesirable shear stresses. The method derives from crack theory and falls under “generalized image stress analysis” whereby a distribution of dislocation geometries or entities (in this case closed rectangular loops), and not just simple mirror images, are used to satisfy the problem’s boundary conditions (BCs). Such BCs can, in a very general treatment, concern either stress traction or displacements.

The displacement field of a rectangular Volterra dislocation loop

The displacement field of a rectangular Volterra dislocation loop having three non-zero Burgers vector components is obtained in an analytical closed form. The solution is obtained via integrating the Burgers equation for the displacement field of any closed dislocation curve and is expressed in a relatively compact form. The current solution has utility in a number of problems including dislocation-particle interaction problems, where the boundary condition involved imposes certain restrictions on the displacements in the medium, and modelling of cracks of arbitrary shapes. The solution is also useful in benchmarking newly emerging dislocation dynamics codes which discretize a curved dislocation line in some form or another. Several verification steps of the solution correctness are made including a comparison with the displacement and stress fields of a circular Volterra dislocation loop of equal Burgers vector and comparable size.

The treatment of traction-free boundary condition in three-dimensional dislocation dynamics using generalized image stress analysis

Recent attention has been given to the proper treatment of the planar traction-free surfaces which typically bound a computational box in three-dimensional dislocation dynamics. This paper presents an alternative to the use of the finite-element method for this purpose. Here, to annul the tractions produced by a sub-surface dislocation segment on a finite-area free surface S, a combination of an image dislocation segment, and a distribution of N prismatic rectangular Volterra dislocation loops meshing S is utilized. The image dislocation segment, with the proper sign selection of the Burgers vector components, annuls the shear stresses, and the normal stress component is annulled discretely at N collocation points representing the centers of the loops. The unknowns in this problem are the magnitudes of the N Burgers vectors for the loops. Once these are determined, one can back calculate the Peach–Koehler force acting on the sub-surface segment and representing the effect of the free surface. As expected, the accuracy of the method improves as the loops continuously decrease in size.

Plasticity study of deformed materials by in situ atomic force microscopy

The emerging of a single dislocation at a surface creates a step with a height equal to the Burgers vector component normal to the surface. By coupling an atomic force microscope with a tensile tester, the fine slip line structure can be analyzed. This equipment is particularly suitable to follow the course of plastic flow from the emergence of the first few dislocations from bulk crystal to the stages of work hardening. The motivations, instrumentation and results on LiF single crystal are described.

Glissile non-coplanar superdislocations, and mechanisms of faulted-dipole formation in γ-TiAl

Abstract 〈101] and ½〈2] non-coplanar C-type and S-type dislocation core structures, where partial dislocations lie on two parallel {111} slip planes, are proposed. Such cores involve three parallel partial dislocations, one of which is delocalized on two {111} planes, delineating two regions of stacking fault. The distinction is made between glissile and sessile C-type and S-type superdislocation cores. Glissile cores can enable 〈101] and ½〈112] superdislocations to glide in low-energy complexes with small Burgers vector components and no high-energy antiphase boundary, whilst sessile cores can give rise to dipole formation. The mechanisms of faulted dipole formation and destruction are proposed which involve the glissile ⌆ sessile transformation of C-and S-type superdislocation cores. The glissile ⌆ sessile transition simply requires the rearrangement of the core of the partial dislocation which is delocalized over two parallel {111} planes. Such a transition cannot be detected by weak-beam (WB) transmission electron microscopy (TEM). The possibilities of erroneous interpretation of WB TEM experimental data are discussed.

Glissile non-coplanar superdislocations, and mechanisms of faulted-dipole formation in gamma-TiAl

Abstract 〈101] and ½〈2] non-coplanar C-type and S-type dislocation core structures, where partial dislocations lie on two parallel {111} slip planes, are proposed. Such cores involve three parallel partial dislocations, one of which is delocalized on two {111} planes, delineating two regions of stacking fault. The distinction is made between glissile and sessile C-type and S-type superdislocation cores. Glissile cores can enable 〈101] and ½〈112] superdislocations to glide in low-energy complexes with small Burgers vector components and no high-energy antiphase boundary, whilst sessile cores can give rise to dipole formation. The mechanisms of faulted dipole formation and destruction are proposed which involve the glissile ⌆ sessile transformation of C-and S-type superdislocation cores. The glissile ⌆ sessile transition simply requires the rearrangement of the core of the partial dislocation which is delocalized over two parallel {111} planes. Such a transition cannot be detected by weak-beam (WB) transmission electron microscopy (TEM). The possibilities of erroneous interpretation of WB TEM experimental data are discussed.

Relaxation mechanisms in single InxGa1−xAs epilayers grown on misoriented GaAs(111¯)B substrates

Transmission electron microscopy (TEM) has been used to investigate the mechanisms of misfit strain relaxation in InxGa1−xAs epilayers grown on GaAs(111¯)B substrates misoriented 2° towards [211¯]. It was found that the relaxation was brought about by a triangular network of misfit dislocations lying along the three 〈11̄0〉 directions near the interface. However, the dislocation distribution was anisotropic with a much higher density of dislocations lying parallel to the [01̄1] direction. A second relaxation mechanism was also observed which involved the formation of deformation twins. These had nucleated at the epilayer surface and grown down into the epilayer, sometimes entering the underlying buffer layer. Twin formation was also anisotropic with twins forming on the (1̄11)[211] system only. The dislocation and twin anisotropy may not be explained using the Schmid Factor considerations but is thought to be associated with heterogeneous nucleation of dislocations at the [01̄1] surface steps caused by the misorientation. The critical layer thickness for the observation of misfit dislocations by TEM in In0.25Ga0.75As (111¯)B epilayers was found to be between 15 and 25 nm. This is the same range as that observed for (001) epilayers of the same composition. This is as expected from theoretical considerations of the effects of orientation on the elastic modulus and the strain relieving component of the misfit dislocation Burgers vector.

Deformation mechanisms in a binary Ti-48 at.%Al alloy with lamellar microstructure

The deformation mechanisms active in the eta- and alpha-lamellae of a Ti2 48 at.%Al alloy during room-temperature and 800 C tensile loading have been determined by transmission electron microscopy. A marked change in the plastic behaviour of the alpha-phase has been detected between room and elevated temperature, whereas the deformation mechanisms active in the eta-phase remained the same at both temperatures. At room temperature, plasticity in the alpha-phase occurred only locally by prism plane slip of dislocations with Burgers vectors parallel to 1120 where cross-lamellar twins in the eta-plane impinged on the eta alpha-interface. At 800 C more homogeneous plastic behaviour of the alpha/ phase resulted from slip and climb activity of dislocations with Burgers vector components parallel to 1120 and parallel to both 1120 and [0001]. The increased contribution to strain accommodation at 800 C by the alpha-lamellae coincided with a change in predominant fracture mode.

Study of residual strains in wafer crystals by means of lattice tilt mapping

A high-resolution X-ray diffractometer equipped with an accurateX-Y translation stage has been used to obtain Bragg angle maps of large-area crystal wafers. It is found that the Bragg angle shifts observed by this method in conventional reflection geometries are mainly due to the local lattice tilts rather than to the lattice parameter changes. The formula to calculate from the lattice tilt maps the displacement of the crystal lattice sites with respect to the ideal unperturbed lattice is obtained. It is shown that such lattice displacement is quantitatively correlated to the wafer dislocation density and to the distribution of the Burgers vectors of the dislocations in the crystal. Semi-insulating Czochraslki-grown GaAs wafers with dislocation densities ranging from 104 to 105cm−2 have been analysed by this technique and by double-crystal X-ray topography. From the lattice tilt maps the dislocation density evaluated appeared similar to those determined by topography and etch pit density in this material. It is concluded that the majority of dislocations in the wafer have the same Burgers-vector component along the (100) growth axis. Finally the method is proposed as a new tool for characterizing large-area wafer crystals.

Topographical development and misfit relief in laser-ablated heteroepitaxial YBa 2Cu 3O 7− δ thin films

Epitaxial YBa 2Cu 3O 7− δ thin films of various thicknesses have been deposited on single crystal substrates of MgO and SrTiO 3 with nominal (001) surface orientations. These films have been examined using scanning tunnelling and atomic force microscopies to reveal the development of the surface topography. It has been shown that films on MgO exhibit Volmer-Weber island growth but those on SrTiO 3 grow in the two-dimensional Frank-van der Merwe mode. For both systems, spiral growth features are apparent only for films above a certain deposit thickness indicating that they are formed at the emergent threading segments of dislocation half-loops introduced in response to the misfit. For films on SrTiO 3, the thickness at which this occurs corresponds well with the critical thickness for dislocation half-loop introduction given by Matthews' model. For films on MgO, the first spirals arise at a similar thickness indicating that the residual misfit is similar to the total misfit for YBCO SrTiO 3 . The spiral density increases with deposit thickness to a peak value before falling to a background level in both systems. The form of the variation corresponds well to the variation in threading dislocation density that would be expected for dislocation half-loop introduction followed by mutual annihilation of adjacent threading segments with Burgers vector components parallel to [001] of opposite sense.

Observation and analysis of extended dislocations in an Al–Pd–Mn icosahedral quasicrystal by transmission electron microscopy

Extended dislocations including partial dislocations and a stacking fault in Al70Pd20Mn10 icosahedral quasicrystal have been observed and identified for the first time. The diffraction contrast and defocus convergent-beam electron diffraction experiments show that the dissociation of the extended dislocations is of the form 1/2<1 −2 0 0 −2 1> → 1/4<1 −3 1 −1 −1 1>+ 1/4<1 −1 −1 1 −xs3 1> with a stacking fault between these two partial dislocations. For the partial dislocations, the Burgers vector components in physical space b¶part are along different fivefold axes with a magnitude of 0.17 nm, which is about one seventh of that in complementary space. For the perfect dislocation, the Burgers vector component in physical subspace b¶perf is along a twofold axis with a magnitude of 0.183 nm, which is about an eleventh of that in complementary space.

Deformation of two C36 laves phases by microhardness indentation at room temperature

Microhardness indentation and electron microscopy were used to study the room-temperature deformation behavior of two Laves phases, ZrFe2 and MgNi2, in two-phase alloys. Evidence of extensive plastic deformation was found around the indentations. Activation of basal and nonbasal slip systems forms a distinctive cell structure in both Laves phases. Slip on planes nearly normal to the basal plane occurs in the lamellar form of ZrFe2. Burgers vectors of the dislocations and resulting shear displacements are studied using high-resolution transmission electron microscopy (TEM). Curved or zigzag nonbasal slip surfaces in atomic scale were observed. Each slip plane can be considered to be composed of a series of small facets of high atomic density. A common Burgers vector and displacement vector component of 1/4 [0001] was found on many different slip planes. The “zonal glide” concept for slip on prismatic planes is discussed.