Angular Misorientation Research Articles

Changes in the grain structure of metallic materials upon plastic treatment

Experimental data on structural changes in the process of plastic deformation of polycrystalline copper and stainless steel have been reviewed. It has been shown that the mechanisms of the formation of a new grain structure, i.e., dynamic recrystallization, depend on the conditions of treatment or flow stresses at the steady-state stage, which are determined unambiguously by the temperature and strain rate. Upon hot deformation (low flow stresses), it is local migration (bulging) of grain boundaries and subsequent growth of these bulgings that seem to be the main mechanism of formation of new grains. Since the nucleation of new grains in this case is of a heterogeneous character, the microstructure evolution can be classified as a discontinuous dynamic recrystallization. Upon worm or cold deformation (high flow stresses), we deal with a dynamically recrystallized structure only after very high degrees of deformation. The new grain structure is formed due to the growth of angular misorientation between subgrains with an increase in the total degree of deformation, which can be considered as a continuous dynamic recrystallization. Changes in the mechanisms of dynamic recrystallization with changes in the conditions of treatment lead to a bimodal dependence of the size of dynamically recrystallized grains on the flow stresses.

Diffuse scattering from large-angle, thermally induced, orientational disorder in molecular crystals

Large-angle rotational motion (libration) characteristic of molecular solids has not been properly included in many scattering calculations because of the need to develop scattering theory through small-angle approximations. A simple but effective approach to calculating the influence of large-angle librations on the thermal disorder scattering given by molecular solids is to treat the molecules as independent librators, each in a harmonic potential well, using the mathematics appropriate for large-angle rotations. The resulting probability distribution for angular misorientations is Gaussian and this distribution can be used to smear the molecular form factor, enabling the librational influence on the scattering to be calculated. It is shown how to apply this direct approach quite generally and by way of examples the technique is used with the molecular solids sulfur hexafluoride (SF(6)), adamantane (C(10)H(16)) and buckminsterfullerene (C(60)). For these materials, the molecular Fourier transform (i.e. the molecular form factor) have been calculated in selected planes in reciprocal space, followed by the separate effects of librational and translational smearing. It is found that the librational smearing produces a large effect on the form factor, particularly at larger scattering vectors, that is not sensitive to approximations in the argument. Additionally, the Debye-Waller effect of vibrational motion is included in the calculations, showing quantitatively the decreasing influence of vibrations on the scattering with increasing scattering vector. Both effects illustrate with pedagogic clarity how different processes modify the basic molecular scattering.

Crystallographic Orientation Analyses of Magnetite Thin Films Using Electron Backscatter Diffraction (EBSD)

The crystallographic orientation of magnetite (Fe3O4) thin films was measured using electron backscatter diffraction (EBSD). Misorientation boundaries appear in maps of angular misorientation data. The distribution of misorientation angles changes after annealing the samples in air at 250degC. Most small-angle misorientations (<5deg) are removed after one minute of annealing, whereas larger misorientations (as high as 60deg) continue to persist

Geometric aspects of lattice contrast visibility in nanocrystalline materials using HAADF STEM

In conventional high-resolution transmission electron microscopy (HRTEM) imaging on nanopolycrystalline materials , the surprising abundance of lattice fringe contrast has been readily explained by the geometric relationship between the Ewald sphere and the streaking of reciprocal lattice spots from small crystals. However, in high-angle annular dark field (HAADF) imaging in scanning transmission electron microscopy (STEM) the same interference considerations do not apply. We present a new method to quantify the probability of seeing lattice contrast from a set of random crystals by estimating as a function of instrumental resolution, the range of angular misorientations from each crystallographic pole, which can give rise to lattice contrast. The maximum angular deviation for common HAADF imaging conditions has been experimentally determined by tilting perfect silicon off pole. The visibility of single and multiple sets of fringes has been successfully predicted for a range of microscope resolutions and for two materials of different unit cell sizes. As many as 70% of randomly oriented nanocrystals can be expected to show fringes in an aberration-corrected STEM.

X-Ray Diffraction Analysis of GaN and AlGaN

ABSTRACTIn this paper, threading dislocation densities in GaN and AlGaN epitaxial layers have been evaluated using two different X-ray analysis techniques; a Williamson Hall (WH) plot and reciprocal space mapping (RSM). GaN and AlGaN have crystalline growth composed of columnar structures that can be estimated by coherence length and angular misorientation measured by X-ray. A WH plot can provide information about coherence length and tilt angle from a linear fit to the linewidth of the triple axis rocking curve (000l) symmetric reflections. RSM is typically used to obtain this data, but it is more involved in technique. The two dominant components of threading dislocation densities (screw and edge types) in the GaN and AlGaN epitaxial layers were found to be similar by both techniques. The treading dislocation density correlates to the size of columnar structure as determined by coherence length, tilt angle, and twist angle. The effect of Al composition in AlGaN alloys on these dislocation densities was investigated and found to depend on strongly on the type of nucleation layer, GaN or AlN.

Preferential dissolution along misoriented boundaries in heterogenite

ABSTRACTHigh-Resolution Transmission Electron Microscopy (HRTEM) results show a strong crystal-chemical and defect dependence on the mode of dissolution of synthetic heterogenite (CoOOH) particles. As-synthesized heterogenite particles are micron-size plates (aspect ratio ∼ 1/30) constructed of crystallographically oriented ∼ 3-nm primary particles or are single ∼ 21-nm unattached heterogenite platelets (aspect ratio ∼1/7). Reductive dissolution, using hydroquinone, was examined in order to evaluate morphology evolution as a function of reductant concentration. Two end-member modes of dissolution were observed: 1) non-specific dissolution of macroparticles and 2) preferential dissolution along misoriented boundaries. In the case of non-specific dissolution, average macrocrystal size and morphology are not altered as building block crystals are consumed. The result is web-like particles with similar breadth and shape as undissolved particles. Preferential dissolution involves the formation of channels or holes along boundaries of angular misorientation. Such boundaries involve only a few degrees of tilt, but dissolution occurs almost exclusively at such sites. Energy-Filtered TEM thickness maps show that the thickness of surrounding material is not significantly different from that of undissolved particles. Finally, natural heterogenite from Goodsprings, Nevada, shows morphology and microstructure similar to those of this synthetic heterogenite.

Problems in determining the misorientation axes, for small angular misorientations, using electron backscatter diffraction in the SEM.

The errors associated with calculating misorientation axes from electron backscatter diffraction (EBSD) data have been assessed experimentally. EBSD measurements were made on the same grains after imposed rotations of 2 degrees, 5 degrees, 7 degrees, 10 degrees, 12 degrees, 17 degrees, 27 degrees and 180 degrees around the normal to the specimen surface. The misorientation magnitudes and the misorientation axes associated with the imposed rotations have been calculated from the EBSD data. Individual measurements of misorientation axes are precise for misorientation magnitudes greater than approximately 20 degrees. The errors must be appreciated when assessing misorientation data at lower misorientation magnitudes and particularly at magnitudes less than 5 degrees. Where misorientation axes can be characterized by the distribution of axes from a number of individual measurements, current EBSD techniques are satisfactory, for data sets of 30 measurements, as long as misorientation magnitudes are 10 degrees or more. With larger data sets it may be possible to extend this approach to smaller misorientation magnitudes. For characterization of individual misorientations less than 5 degrees, new EBSD techniques need to be developed.

Electron Microscopy of Nanoledges at the (001)InAs/(001)GaAs Interface for an Approximate Orientation Relationship

The structure of the InAs/GaAs(001) epitaxial heterointerface is observed by high resolution electron microscopy (HREM) along [110] when there is a slight long range angular misorientation between the two crystals around the common observation direction. The lattice misfit and the local misorientation (η = 6.9%, Δθ = 1.5°) are simultaneously accommodated via a non planar and non pseudoperiodic distribution of defects involving usual 90° and 60° dislocation cores and yet unreported nanoledges with exotic Burgers vector contents. One of these nanoledges is five (001) planes high and has a total Burgers vector content equal to (1/6)[33-1]. Its local elastic field has been analysed in terms of ribbon-like Somigliana dislocations. It depends on η, Δθ and its nanoledge height. Comparisons between the experimental and calculated tunnel positions between atom columns are given to appreciate the validity of the model.

Effect of grain orientation on deformation structure in cold-rolled polycrystalline aluminium

Pure (99.996%) polycrystalline aluminium (grain size about 300μm) has been cold-rolled to reductions in the range from 5 to 50% (εvm=0.06–0.80) and the deformation microstructure has been analysed by TEM in a large number of grains. The deformation microstructure is subdivided by dislocation boundaries having different characteristics depending on the orientation of the deformed grain. An analysis of the dislocation boundaries based on Frank's formula shows that the majority of the dislocations in the boundaries originate from active slip systems predicted by a Schmid factor analysis. Thereby a link is created between the microstructural evolution and the macroscopic plastic behaviour. The boundary parameters have also been used in a calculation of the dislocation density and the stored energy for grains of different orientations. These calculations together with measurements of the angular misorientation distribution shows that microstructural differences caused by differences in grain orientation are enhanced as the strain is increased.

Microstructure development during equal channel angular drawing of Al at room temperature

In this study 3004 aluminum alloy can-stock remelt (composition 99.9% Al) was subjected to Equal Channel Angular Drawing (ECAD) at room temperature. Tests were conducted to an applied true strain of 2.95. Mechanical properties like tensile strength, ductility at fracture, and microhardness were measured. The development of the substructure was studied using optical and transmission electron microscopy. Subgrain sizes and their angular misorientations were measured as a function of the applied strain. In general, a substructure that consists of cells and subgrains was seen to evolve, as is expected for the case of high SFE fcc metals.

Geometrically necessary boundaries and incidental dislocation boundaries formed during cold deformation

The evolution of microstructure during plastic deformation has recently been described in terms of grain subdivision involving the formation of rotated volume elements. These elements are ordinary dislocation cells and cell blocks where a cell block contains from one to several cells. The cell blocks are bounded by dislocation boundaries which accommodate the lattice misorientation between neighboring cell blocks which deform with different slip system combinations and/or by different amount of shear. The boundaries which accommodate these lattice misorientations are called geometrically necessary boundaries or GNBs. The ordinary cells are also bounded by dislocation boundaries which, however, form as a result of statistical trapping of glide dislocations supplemented by unpredicted dislocations. These boundaries have been called incidental dislocation boundaries of IDBs. The formation and characteristics of the two types of boundaries was discussed and it was suggested that: (i) the misorientation across GNBs should typically be much larger than across IDBs and should rise faster with increasing strain, and (ii) the influence on the flow stress should be different for the two types of boundaries. The present study was initiated to examine the validity of the first suggestion by characterizing the deformation structure in terms of boundary type and bymore » analyzing the boundaries by measuring their spacing and their angular misorientation as a function of the plastic strain. Pure aluminum rolled at room temperature has been used by way of example.« less

X-ray diffraction of bent crystals in Bragg geometry. II. Non-ideally imperfect crystals, modelling and results

An earlier model for finite curved perfect crystals is extended to the non-ideally imperfect regime, allowing for mosaic structure from dislocations, vacancies or phase boundaries. Effects of Johann crystal mounting and depth penetration in the Bragg geometry are included. The model estimates diffraction shifts for mosaic crystals with regular local structure. Integrated reflectivities, diffraction widths, shifts and profiles against several parameters demonstrate agreement with the earlier model as an extreme and hence agreement with the literature. The theory is applied to first- and fourth-order spectra in differential quantum electrodynamic (QED) measurements and to pentaerythritol 002 crystals. A study of widths, reflectivities and shifts shows that comparison of profiles from wavelengths differing by large factors can yield the mean mosaic block thickness, angular misorientation half-width, incident polarization and beam divergence and can provide sensitive experimental tests of theory and modelling. Results for ammonium dihydrogen phosphate 101 and silicon 111 crystals agree with experiment for parameters investigated. Qualitative contributions to shifts and other parameters are identified. Results for precision QED measurements of iron and germanium Lyman αand Balmer β radiation are presented. Uncertainties in shifts due to input parameters are provided for each crystal. Crystal thickness can be a major variable in the determination of diffraction shifts, and differences between perfect and mosaic crystals are reduced for curved crystals.

The 45° grain boundaries in YBa2Cu3O7−δ

High-angle grain boundaries in YBa2Cu3O7−δthin films are of technological interest because of the weak coupling observed between the grains; however, not all high-angle grain boundaries show this weak-link behavior. The microstructure of both these boundaries is not understood, nor is the reason for the differing electrical transport properties. High-angle grain boundaries in YBa2Cu3O7−δthin films on MgO, where the angular misorientation between the grains is ∼45°, have been examined using high-resolution electron microscopy. The results show that the boundary structure can appear quite different even when the angular misorientation between the two grains is the same. The stability of the grain boundaries under the electron irradiation in the electron microscope was found to be a function of the accelerating voltage—400 kV leads to rapid disordering of the boundary region.

Misorientation of grains and critical current of high-Jc epitaxial YBCO films

Factors which control Jc values and spread in thin epitaxial YBCO/SrTiO3 films are studied systematically by precision analysis of X-ray diffraction, voltage-current, VCC, and Jc (B) characteristics (B=0/30 mT). It is shown that there is no direct correlation between the Jc values of (0.3/5).106 A/cm2 and the creep activation energy U:c U(78 K) approximately=0.35 eV approximately=const (Jc) in contrast to the creep model. The direct correlation is obtained between the angular misorientation ( Delta ) of the c-axis oriented grains and Jc value of films. A new model of nonuniform critical current distribution is suggested, which describes absolute values of Jc and Jc(B) dependences completely as a function Jc(B,U, Delta ).

Limits to the accuracy of lidar measurements of hydrooptical parameters

The specific manifestation of the amplification of backscattering due to surface waves, caused by angular misorientation of the optic axes of the lidar transmitter and detector, was investigated theoretically and in model experiments. This effect limits the accuracy of the internal reference method with normalization to the spontaneous Raman scattering signal, widely used in lidar experiments. Measurement errors may also arise as a result of nonlinear optical interactions caused by random focusing of the probe beam by surface waves.

Clean grain boundaries and weak links in high T c superconducting YBa2Cu3O7−x thin films

It is demonstrated that polycrystalline thin films of high Tc superconducting YBa2Cu3O7−x can be grown with clean grain boundaries, i.e., without a boundary layer of segregation or different phase. In clean stoichiometric samples, angular misorientations of grains may be the origin of weak link behavior. High-resolution scanning transmission electron microscope images of films grown on ZrO2 and MgO by reactive evaporation, reactive sputtering, and laser ablation show atomic lattice images of clean grain boundaries. X-ray microanalysis with a 10 Å spatial resolution also indicates no composition deviation at the grain boundaries. Grain sizes and epitaxial relations of samples prepared by different methods are characterized.

Inter-relationships between disclinations, surface dislocations and grain boundaries

Abstract It has been shown that the disclination dipole description of a grain boundary is equivalent to the surface dislocation model in the limit of low angular misorientations. Neither model is compatible with the classical formulation of Burgers, which is shown to be incomplete. For larger angles, on the other hand, the situation becomes more complex, and the surface dislocation approach is seen to be the most desirable.

E-beam melted icosahedral Al–Mn surface layers: Microstructures and phason defects

The microstructure of icosahedral Al(Mn) in melt-quenched surface alloys has been characterized with TEM. Single-phase alloys with 20 at. % Mn show angular misorientations (up to ∼7°) across internal boundaries radiating from the nucleation centers of grains. Lowering the Mn content results in fcc Al at grain boundaries and between branches of the icosahedral grains; the presence of Al-rich liquid around growing grains apparently eliminates the misorientations seen with 20 at. % Mn. The grains have a dense distribution of dislocation-like defects, but have sufficient orientational order to exhibit well-defined diffraction contours. Weak reflections in diffraction patterns from small areas (0.7 μm) of grains exhibit deviations from exact icosahedral symmetry positions which were analyzed to evaluate a phason strain tensor and characterize misordering defects in the quasicrystalline structure. A negative matrix element (m ≍–0.05) for a tensor axis along a twofold icosahedral axis accounts for most of the distortions in these patterns and those from other melt-quenched icosahedral Al(Mn) and Al(Mn, Si) alloys; this dominant element lowers the symmetry to D2. This axis is nearly perpendicular to the growth direction, which suggests that the misordering is due to rapid growth during the quench; however, the D2 distortion may also result from an elastic instability predicted for icosahedral phases. Distortions in Al(Cr, Ru) can be fit with a similar tensor but with m&gt;0. Thus the phason character identified here may apply to other aluminum-transition metal icosahedral phases as well.

Substrate orientation and processing effects on GaAs/Si misorientation in GaAs-on-Si grown by MBE

The angular misorientation of GaAs epitaxial layers grown on silicon substrates by molecular beam epitaxy has been measured using x-ray diffraction. A significant misorientation, or tilt, between the epitaxial layer and the substrate has been observed. The magnitude of the tilt depends on the initial substrate orientation, the silicon substrate type (float zone or Czochralski), postgrowth annealing, and epitaxial layer thickness. In almost all cases, the sense of the tilt is such that the GaAs 〈001〉 lies between the surface normal and the silicon 〈001〉. While the presence of interfacial dislocations with Burgers vectors that are approximately parallel to the heterointerface does predict a tilt between the substrate and the epitaxial layer, the sense of the tilt that arises from these dislocations is opposite to that observed experimentally. A model, based on the relief of misfit by dislocations inclined approximately 45 degrees to the interface, is proposed that correctly describes the observed tilt.

Influence of angular misorientation of thin Sn/SnTe bilayers of the fine structure of electron diffraction patterns

The peculiar electron diffraction patterns of Sn/SnTe specimens grown by evaporation on a NaCl substrate were studied. The streaks formed by doubly diffracted beams could be explained by simple rotations of the lattices. It is shown that the pattern of the streaks allows one to determine more reliably which of the layers is more misoriented than the arcing of the basic reflections. In most of the investigated specimens the rotational misorientation of the SnTe layer is found to be larger than that of the deposited Sn islands. The possible origins of moiré fringe irregularities observed in the coalescence stage of Sn islands are discussed.