Sample Coordinate System Research Articles

Comparative Study of Methods to Present the Results of Texture Analysis of Polycrystalline Materials

It is necessary to use various methods of texture analysis at all stages of the technological processing of metals and alloys in order to select the optimal parameters for processing materials and obtain the necessary properties of final products. The article deals with the methods of presenting the results of texture analysis. Usually, the texture of a material is described by several preferred texture components, where the way of representation depends on the given task. The textural components combine the orientations of crystals having similar position in the sample volume. The results of texture analysis are the distribution of orientations relative to the base coordinate system. Orientation is described by four parameters: three coordinates in space and intensity, which is defined as the probability of occurrence of this orientation in the sample. Methods for representing the orientation of a single crystal by several descriptors: Euler angles, Miller indices, Rodrigues vectors, etc., each describing the rotation of the crystal coordinate system relative to the selected sample coordinate system, are given in the article. The formulae for the transition from one descriptor to another are given. The texture calculation algorithms depend on the way orientations are represented. Some representations are more convenient to use for calculations, others - for visualization and data processing. In particular, the use of the Rodrigue space allows not only to visualize the orientation cloud, but also to form textural components in it with a given accuracy by clustering. Variants of the analysis result presentation are shown in a model example. The textural components computed with high accuracy are displayed in the spaces of Euler angles and Rodrigues vectors. The orientation distributions are shown as a histogram and a pole figure {001}.

The evolution of main textures and the formation of P orientation with nanoprecipitates after friction stir processing

Textures, significantly affecting the anisotropy and the related key properties, are often used as variables for industrial control. However, compared with many technological studies, the texture-related mechanisms during friction stir processing (FSP) are insufficient, including P orientation associated with precipitation. These knowledges are useful for understanding the nature of materials and achieving control of properties. In this experiment, FSP was used to obtain a nearly defect-free processing zone in Al-Mg-Sc alloy, and the changes in orientation of stirring zone were discussed to determine main texture types and the causes of their formation. In addition, after FSP, the P orientation decreased monotonically as the distance from the top increased, regardless of how the main texture changed. The orientation of crystallographic coordinates of all P oriented grains in the sample coordinate system indicated that P oriented grains came from two parts, one was the growth of P cores mainly formed by the shoulder, the other was the transformation of non-P oriented grains due to the dominant direction of 45° ~ 52°〈111〉. Finally, the effect of nanoscale Al3Sc precipitates on texture, especially P orientation, was analyzed. As the distance from the top increased, the density of Al3Sc precipitates on grain boundaries increased, which limited the preferred growth required by the texture including P orientation, and the texture tended to be random.

Monte Carlo modelling of recrystallization in alpha Zirconium

A Monte Carlo based modelling framework combined with experimental EBSD microstructures was used in order to simulate partial recrystallization taking place during short annealing of moderately deformed hexagonal Zirconium and discuss the role played by Strain Induced Boundary Migration (SIBM). The experimental part started from low alloyed Zr702α which was channel-die-compressed along two different compression directions (Normal Direction - ND and Transverse Direction – TD of initial sample coordinate system) until 17% of strain was reached. As a result, two different microstructure and texture evolutions were witnessed and characterized using EBSD measurements. In particular mechanism of accumulation of local misorientations as well as formation of grain boundaries is analysed. Textures of grain boundary areas also provides important information about the way how new recrystallization grains are formed. Based on EBSD results, a SIBM model of recrystallization is proposed and compared with classical nucleation using Monte Carlo simulations. It is concluded that only simulations performed using the SIBM model provide results which are in a very good agreement with experimental data in terms of texture as well as microstructural evolution.

Experimental and simulation analysis of residual topography dominated deformation mechanism of nanoindentation: a case study of Inconel 625 superalloy

The microscopic deformation behavior of Inconel 625 superalloy has been investigated by means of nanoindentation experiments and crystal plasticity finite element simulations. Based on the electron backscattered diffraction characterizations, the nanoindentation simulations were performed on grains with various orientations. The simulated load–displacement curves match well with those of experiment and the maximum difference in materials hardness between the experimental and the simulation result is about 6.86%, which is within the accuracy of the model. Moreover, surface Schmid factor (SSF) and interior Schmid factor (ISF) were proposed out and the scanning electron microscope and atomic force microscope characterizations were carried out. The results show that the pile-up tends to occur at the locations with a large SSF. Subsequently, the simulations of nanoindentation on [001]-, [011]-, and [111]-oriented grains were performed by the established model. It is revealed that the residual topography changes periodically when the indenter is fixed and the crystal only rotates around the Z-axis of the sample coordinate system. Combining with the analysis of the ISF, this periodicity of residual topography reflects the superimposed effect of the slip systems, and a large ISF promotes the in-plane displacement of the interior material which inhibiting the evolution of pile-up, while a small ISF leads to a high pile-up.

A novel approach to index site-specific grain boundary plane

A novel approach using focused ion beam (FIB) and electron backscatter diffraction (EBSD) or transmission Kikuchi diffraction (TKD) was developed to characterize all five parameters of the individual grain boundary. With this approach, the grain orientations and the grain boundary trace angles on two perpendicular surfaces can be measured. Then the grain boundary plane normal in the sample coordinate system can be determined and transformed to plane indices in the two crystal coordinate systems. FIB-TKD is a viable alternative to FIB-EBSD when EBSD measurement can't be conducted on the sample surface which is degraded by oxidation or corrosion. This approach was verified on a coherent twin boundary in alloy 690. The accuracy of the present FIB-EBSD method is better than 3°. This approach provides a convenient and efficient solution for measuring all five parameters of a site-specific grain boundary during FIB sample preparation.

Research on milling hole of AFRP based on cryogenic cooling processing

The aramid fiber–reinforced composite (AFRP) has special the structure and physical properties. Although, the dry helical milling hole method could improve the machining precision and reduce the cutting force for AFRP. There were still some problems such as hole defects, limited hole depth, and low machining efficiency. In this paper, the tool cutting point trajectory model based on sample and tool coordinate system was established. The cutting force model of milling hole considering fiber orientation was constructed. A series of cryogenic cooling milling hole tests were carried out using liquid nitrogen internal jet cutting equipment. The results show that the cutting path and cutting force are mainly related to axial feed, tangential feed, and center distance between tool and hole axis. Similarly, type I and II defects are serious at low-speed dry milling hole, as well as obvious type III ablative defects at high speed. Compared with dry milling hole, the cutting force in cryogenic cooling is greater at the same cutting speed. And the influence of tool axial feed on axial force and tangential force is larger than that of tangential feed. Meanwhile, the property changes of resin base and composite in cryogenic are the main reasons for inhibiting type I and II milling hole defects. Furthermore, the cryogenic medium cooling is the reasons for inhibiting type III defects, as well as passivation and adhesion of tool side edge and flank. So the cryogenic cooling milling method can improve milling hole effect and restrict machining defects for AFRP.

Molecular Order in Cold Drawn, Strain-Recrystallized Poly(ε-caprolactone)

Biaxial order in free-standing films of poly(e-caprolactone) (PCL), induced by plastic deformation and fibrillation, is studied by infrared transition moment orientational analysis (IR-TMOA) and X-ray diffraction (pole figures). This enables one to determine the order parameter tensor for the different molecular moieties with respect to the sample coordinate system. The main chains of the polymers are aligned with the stretching direction (x), leading to a strong order of the crystallites (Hermans orientation function, Sxx = 0.9 ± 0.1), and less ordered, amorphous regions (Sxx = 0.34 ± 0.1). The microscopic biaxiality of the system, |Syy – Szz| ≈ 0.1, is caused by the macroscopically asymmetric deformation perpendicular to the stretching direction. Cold drawing leads to a reduction in crystallinity and distorted crystallites in the fibrils, indicating the absence of “melting and recrystallization” or “fine slip” processes.

Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer.

The IR-based method of infrared transition moment orientational analysis (IR-TMOA) is employed to unravel molecular order in thin layers of the semiconducting polymer poly[N,N'-bis(2-octyldodecyl)-1,4,5,8-naphthalenediimide-2,6-diyl]-alt-5,5'-(2,2'-bithiophene) (P(NDI2OD-T2)). Structure-specific vibrational bands are analyzed in dependence on polarization and inclination of the sample with respect to the optical axis. By that the molecular order parameter tensor for the respective molecular moieties with regard to the sample coordinate system is deduced. Making use of the specificity of the IR spectral range, we are able to determine separately the orientation of atomistic planes defined through the naphthalenediimide (NDI) and bithiophene (T2) units relative to the substrate, and hence, relative to each other. A pronounced solvent effect is observed: While chlorobenzene causes the T2 planes to align preferentially parallel to the substrate at an angle of 29°, using a 1:1 chloronaphthalene:xylene mixture results in a reorientation of the T2 units from a face on into an edge on arrangement. In contrast the NDI unit remains unaffected. Additionally, for both solvents evidence is observed for the aggregation of chains in accord with recently published results obtained by UV-vis absorption spectroscopy.

Arbitrary tip orientation in STM simulations: 3D WKB theory and application to W(110)

We extend the orbital-dependent electron tunnelling model implemented within the three-dimensional (3D) Wentzel–Kramers–Brillouin (WKB) atom-superposition approach for simulating scanning tunnelling microscopy (STM) by including arbitrary tip orientations. The orientation of the tip is characterized by a local coordinate system centred on the tip apex atom obtained by a rotation with respect to the sample coordinate system. The rotation is described by the Euler angles. Applying our method, we highlight the role of the real-space shape of the electron orbitals involved in the tunnelling, and analyse the convergence and the orbital contributions of the tunnelling current above the W(110) surface depending on the orientation of a model tungsten tip. We also simulate STM images at constant-current condition, and find that their quality depends very much on the tip orientation. Some orientations result in protrusions on the images that do not occur above W atoms. The presence of such apparent atom positions makes it difficult to identify the exact position of surface atoms. It is suggested that this tip orientation effect should be considered in the evaluation of experimental STM images on other surfaces as well. The presented computationally efficient tunnelling model could prove to be useful for obtaining more information on the local tip geometry and orientation by comparing STM experiments to a large number of simulations with systematically varied tip orientations.

Effect of pulsed magnetic field annealing on the microstructure and texture of grain-oriented silicon steel

The effect of pulsed magnetic primary annealing on the microstructure and texture of two-stage cold-rolled silicon steel is investigated. Specimens are annealed at 700°C for 1h under a 1T pulsed magnetic field along different directions with respect to the sample coordinate system. Crystallographic orientation and grain size are identified by analyzing electron backscattered diffraction pattern. The effects of magnetic field treatment are related to the magnetic field direction. Based on the anisotropy energy of ferromagnetic material during magnetic annealing, a hypothesis is proposed. All of the experimental results in this work support the proposed model.

IR transition moment orientational analysis on semi-crystalline polyethylene films

The recently developed approach of Transition Moment Orientation Analysis is employed to determine the three dimensional orientation and order of the different molecular moieties in semi-crystalline polyolefins. Based on IR transmission spectra for varying polarisation and inclination the quadratically averaged orientation distribution of the different IR transition moments is deduced. By that, the full order parameter tensor and its orientation with respect to the sample coordinate system is obtained.

Three-dimensional small-angle neutron scattering of shear-induced phase separation in a dynamically asymmetric polymer mixture

A polymer mixture of polystyrene (PS)/poly(vinyl methyl ether) (PVME) has been investigated by using a three-dimensional small-angle neutron scattering (3D-SANS) method. PS and PVME exhibit a large difference in the glass transition temperatureTg. Therefore, dynamical asymmetry is strongly enhanced in an intermediate temperature region between theTgvalues of neat PS and PVME. In the intermediate temperature region, a shear deformation was imposed on the polymer mixture to enhance the concentration fluctuations,i.e.shear-induced phase separation. By rotating the film specimen, which was rapidly quenched after deformation, 3D-SANS due to shear-induced phase separation was observed successfully. In theqx=qyplane of the sample coordinate system, whereqis a component of scattering vectorq, it was possible to observe SANS of `double-lobe' shape, with the minor axes of the lobes inclined towardsqx=qy, whereqx,qyandqz, denote the shear, velocity gradient and vorticity directions in reciprocal space, respectively. Abnormal `butterfly' scattering was observed in a section cut through the 3D-SANS in theqxqzplane. The 3D-SANS thus obtained is discussed in comparison with a model of dynamical coupling between stress and diffusion.

Experimental verification of the 1/v law for the absorption cross section of ultracold neutrons in natural gadolinium

The results of a new experiment on the transmission of ultracold neutrons through a natural gadolinium film are reported. The results indicate that the transmission of the sample is unchanged when the sample moves parallel to its surface. The neutron velocity in the sample coordinate system varies in a range of 6–35 m/s. It follows from the constancy of the sample transmission that the imaginary part of the scattering length is constant; i.e., the law 1/v is valid for the capture cross section of the free nucleus with an accuracy of about 0.5%.

Determination of Real Space Residual Stress Distributions σ<sub>ij</sub>(z) of Surface Treated Materials with Diffraction Methods Part II: Energy Dispersive Approach

The detection of near surface residual stress gradients in real space requires high depth resolution for any orientation of the diffraction vector with respect to the sample co-ordinate system. In order to meet this demand, the slits are no longer being fixed in the laboratory co-ordinate system as in strain scanning experiments but directly coupled with the sample. Hence, the gauge volume orientation within the sample remains constant and allows performing depth-resolved sin2ψ measurements in real space. The method’s accuracy is determined by the gauge volume definition, which is investigated in detail. Apart from the evaluation of the σ(τ) versus σ(z) relation, which is of fundamental interest in X-ray residual stress gradient analysis, the method will be shown to have a unique applicability in rather delicate sample geometries such as multilayer systems.

Precise Alignment of Workpieces Using Speckle Patterns as Optical Fingerprints

Engineering process chains sometimes require a precise repositioning method of workpieces within production machines and measuring devices. This causes difficulties, however, if the workpiece may not be marked permanently in order to set up a sample coordinate system. This paper presents a repositioning method based on the unique statistical properties of monochromatic speckle patterns emerging from a specific spot of a rough workpiece surface. The speckle pattern could be regarded as an individual “fingerprint” of this specific surface spot. The influence of the experimental parameters (laser wavelength, beam diameter, wavefront curvature) on the uncertainty of relocation is discussed.

A virtual laboratory for neutron and synchrotron strain scanning

The new generation of dedicated Engineering Strain Scanners at neutron and synchrotron facilities offer considerable improvements in both counting time and spatial resolution. In order to make full use of these advances in instrumentation, the routine tasks associated with setting up measurement runs and analysing the data need to be made as efficient as possible. Such tasks include the planning of the experiment, the alignment and positioning of the specimen, the least-squares refinement of diffraction spectra, the definition of strain in the sample coordinate system, and its visualization within a 3D model of the specimen. With this aim in mind, we have written a software providing support for most of these operations. The approach is based on a virtual lab consisting of 3D models of the sample and laboratory equipment. The system has been developed for ENGIN-X, the new engineering strain scanner recently commissioned at ISIS, but it is flexible enough to be ported to other neutron or synchrotron strain scanners. The software has been designed with visiting industrial and academic researchers in mind, users who need to be able to control the instrument after only a short period of training.

Second-harmonic imaging of the absolute polar molecular orientation at interfaces

Interface specific second-harmonic (SH) and sum-frequency microscopes have been developed recently. In these microscopes, the two-dimensional intensity distribution of the nonlinear signal is used to create an image of the interface structure. In the intensity measurements, however, the phases of the nonlinear signals become obscured. The phases provide information on the absolute molecular orientation, which is not accessible in a corresponding linear optical experiment. Here we describe two homodyne techniques for the quantitative measurement of the absolute phases and their two-dimensional distribution. The data can be transformed into the polar molecular orientation field of an interface. As a model example, a Langmuir monolayer of organic molecules, 2-docosylamino-5-nitropyridine, is investigated. The SH and laser light are off resonance with the molecular dipole oscillators. In this case, the electromagnetic theory predicts a signal phase of 90\ifmmode^\circ\else\textdegree\fi{} relative to the laser light. Intensity and homodyne images are taken. Dendritic features are observed in the monolayers. Any local feature which is clearly resolved in the images we consider as an individual sample whose local symmetry and polar order we determine. For the description of the features, it is important to introduce local sample coordinates. As we have shown recently, the point group of the local objects and the axial orientation of their molecules (orientation with an uncertainty of 180\ifmmode^\circ\else\textdegree\fi{}) can be determined from a series of intensity images taken with different polarizer orientations. We may then fix a sample coordinate system at any local feature. One coordinate axis may correspond to the preferential molecular orientation of the feature. Since the absolute orientation of the molecules is not known at this state of the investigations, we may assume an arbitrary polar sign of this coordinate axis as a first hypothesis. If this sign agrees with the real sign of the molecular dipoles, we expect a phase of the SH signal of +90\ifmmode^\circ\else\textdegree\fi{}. Since the inversion of a dipole's absolute orientation corresponds with a phase shift of 180\ifmmode^\circ\else\textdegree\fi{} in the SH signal, we expect a phase of -90\ifmmode^\circ\else\textdegree\fi{} if the real dipole orientation is opposite to the local coordinate axis. In the homodyne experiments, the intensity image of the interface is then coherently mixed with a spatially homogeneous SH signal from a reference sample. From the local homodyne intensities and the known phase of the reference signal, the local features' signal phase is calculated. The results (+90\ifmmode^\circ\else\textdegree\fi{}, -90\ifmmode^\circ\else\textdegree\fi{}) agree with the theory. Thus we can determine the absolute orientation of any local feature. In experiments, carried out near or in resonance, additional phases contribute to the SH signal. We show that the absolute dipole orientation can also be measured in these cases without ambiguity.

Analysis of local strain in aluminium interconnects by energy filtered CBED

Energy filtered convergent beam electron diffraction (CBED) was used to investigate localised strain in aluminium interconnects. The quantitative analysis of the experimental patterns is based on a multi-step evaluation procedure which is the main subject of the present paper. The improvements which were made to the analysis method aim at increasing both the automation and the accuracy. The detection of the higher order Laue zone (HOLZ) line positions is performed by means of the Hough transform. The required sub-pixel resolution can be achieved routinely and the achievable accuracy is only limited by the line width and the amount of noise in the patterns. The determination of the strain state is performed via a refinement algorithm which is based on varying the strain state in the sample coordinate system and simulating the patterns for the individual grains until a best fit with the experiment is obtained. For the simulation we have developed a new correction scheme in which the dynamical effects are treated separately for each individual HOLZ line. The results show that the main source of the observed strains is the difference in thermal expansion coefficients. The strain is substantially reduced underneath a hillock in the interconnect. Asymmetries in the strain distribution around the hillock show that the unidirectional diffusion during electromigration tests causes peak strains in areas next to the hillock which may be possible failure sites.

Yield stress increase in a W/Cu composite observed by neutron diffraction

Ceramic matrix composites with a ductile reinforcement phase can be produced by infiltrating a metal melt into a porous ceramic preform [1, 2]. Due to the thermal expansion mismatch, residual stresses of opposite signs develop in the ceramic and metal phase. For alumina/aluminum composites, the tensile stresses of the metal phase can exceed several times its bulk yield stress [3, 4]. This phenomenon may be called “yield stress increase” and was first observed in mechanically constrained metal wires by Ashby et al. [5]. The magnitude of the yield strength increase depends on the diameter of the ductile ligaments, their shape and connectivity [3]. In this study, exceptionally high residual stresses have been observed in the copper phase of a tungsten/copper composite with a graded interpenetrating network microstructure. These stresses are about 16 times larger than the yield stress of bulk, age-hardened copper. The graded W/Cu composite was produced from tungsten powder containing 2 wt % Ni. From this powder, a body of 57% relative density and an average grain size of 14 μm was produced by partial sintering. The porosity was locally increased by anodic oxidation in 2 M NaOH at 8.5 mA cm−2 for 165 h [6]. The resulting tungsten preform with a graded porosity was infiltrated with molten electrolyte copper at 1250 ◦C in a hydrogen atmosphere for 1/2 h. After cooling to room temperature, a composite with a gradient in the copper content along one direction (called depth) was obtained (see Fig. 1). The composite was dense. Determination of Young’s modulus of the composites and phase contrast acoustic microscopy both indicate that no microcracks were present at the tungsten/copper interfaces. Image analysis of optical micrographs showed a gradient in copper content from 49 to 66 vol % (Fig. 2). The electrochemical process also introduces a gradient in the specific interface area into the composite.1 The specific interface area is a measure of the thickness of the average copper ligaments and hence the mechanical constraint exerted on the copper phase. The copper-rich region of the graded composite had a specific interface area of 0.13 μm−1 whereas the region of low copper content had a specific interface area of 0.33 μm−1. Assuming cylindrical copper ligaments of uniform diameter, one calculates copper ligament diameters between 30 and 12 μm. Neutron diffraction allows one to determine the stress tensor in the tungsten and copper phase σ = σ (z) as a function of depth z by selecting the probe volume using appropriate beam collimators. The present measurements were done using the D1A diffractometer at the Institute Laue-Langevin (ILL), Grenoble. D1A is equipped with a long scattered beam collimator resulting in a probe volume of ≈1 mm3 [7]. The measured strain 2= 2(h k l, φ, ω, z) depends on the measurement direction (φ, ω) with respect to the sample coordinate system. Furthermore, 2 depends on z because of the copper concentration gradient. Copper is an elastically anisotropic material, therefore 2= 2(h k l, φ, ω, z) also depends on the lattice plane indices (h k l). To account for the anisotropy, we measured the Cu(1 1 1)and the Cu(3 1 1)-reflection of copper. The diffraction experiments on three samples showed that the copper phase is textured and can be regarded as one single crystal. This texture results from the solidification process, when the solidification front takes on one single crystallographic orientation. Because of the texture, we had to search for suitable sets of tilting angles (φ, ω) to record measurable intensities [8]. Because tungsten is elastically isotropic, we worked with the W(1 1 1)-reflection only. From the measured 2(h k l, φ, ω), the stress tensor σ (z) was calculated at all selected z-values according to Hooke’s law [9]. Single-crystal elastic compliances were used, because the probed volume consisted essentially of a single crystal.2 Fig. 3 shows for both phases the three components σ11, σ22 and σ33 of σ (z) expressed in the principal axes system. For copper, the stress is relaxed at the surface where the copper concentration is highest. At great depths (z<−3 mm), where the copper concentration goes to zero, tensile stress exists, and in the intermediate region compressive stress is present. The tungsten phase has stresses with opposite depth dependence. At the free surface, where the tungsten concentration was low, tensile stress is found. In the intermediate region, tensile stress still exists, which drops to zero at great depths, where the tungsten concentration rises to 100%. This observed depth dependence can be qualitatively explained by the mechanical equilibrium conditions and the lever rule for stresses in a two-phase material.3 At any depth z, the concentration-weighted stresses in both phases balance each other (as long as no interface failure occurs). Stresses at different depths z

Preliminary results of chemical remagnetization under uniaxial compression

Studies of the influence of uniaxial compression on the direction of remanent magnetization acquired during chemical changes were carried out on rocks containing goethite, siderite and pyrrhotite. One of a pair essentially identical samples was heated to 400 ° C, the second sample was heated to the same temperature (T) and compressed (P) along the Z direction of the sample coordinate system during heating and cooling. Remanence was acquired in an ambient, laboratory field which was nearly vertical. Remanence acquired under compression has a lower inclination than remanence acquired without compression. Deviation of the direction of CRM(T,P) from the direction of compression depends on the degree of anisotropy.