Volume Fractions Of Texture Components Research Articles

The influence of microstructure and texture on the hardening by annealing effect in cold-rolled titanium

The purpose of this study was to compare the influence of microstructural and textural changes on the hardening by annealing effect in cold-rolled titanium. Ultrafine-grained (UFG) Ti Grade 2 was produced by multi-pass cold rolling (or warm rolling at 400 °C at the final stage) to different thickness reductions (90%, 95% and 97%) aimed at varying both the microstructural features of the material (dislocation density, grain size distribution and grain boundary characteristics) and its texture (the intensity and volume fraction of texture components). The hardening effect of UFG Ti Grade 2 sheets was obtained by a short-time annealing at 250 °C for 15 min. The highest strengthening, of about 4–5%, was observed for the UFG Ti Grade 2 sheet rolled to 90%; the strengthening gradually decreased for higher thickness reductions (down to ∼ 2% for 97%). The texture intensity and volume fractions of texture components for the annealed UFG Ti Grade 2 sheets were very close to their as-rolled counterparts, so this did not demonstrate any clear reason for the hardening effect. Instead, the dislocation substructure recovered during annealing at 250 °C, i.e. the dislocation density declined significantly, the remaining dislocations became rearranged, and it was easier to differentiate more nanosized subgrains of about 50–150 nm. The hardening by annealing effect was a result of the annihilation of mobile dislocations and the ordering of the dislocation substructure, mostly within coarse grains (>500 nm). The level of strengthening by low-temperature annealing was mainly affected by the fraction of coarse grains with a tangled-dislocation substructure in the as-rolled state, i.e. a higher fraction of coarse grains favored more pronounced strengthening. These observations seem to be very promising for optimizing the cold rolling process and short-time annealing of the UFG Ti Grade 2 sheets, which could be a simple and cost-effective way of enhancing their mechanical properties.

Rapid measurement scheme for texture in cubic metallic materials using time-of-flight neutron diffraction at iMATERIA

A rapid texture measurement system has been developed on the time-of-flight neutron diffractometer iMATERIA (beamline BL20, MLF/J-PARC, Japan). Quantitative Rietveld texture analysis with a neutron beam exposure of several minutes without sample rotation was investigated using a duplex stainless steel, and the minimum number of diffraction spectra required for the analysis was determined experimentally. The rapid measurement scheme employs 132 spectra, and by this scheme the quantitative determination of volume fractions of texture components in ferrite and austenite cubic phases in a duplex stainless steel can be made in a short time. This quantitative and rapid measurement scheme is based on the salient features of iMATERIA as a powder diffractometer, i.e. a fairly high resolution in d spacing and numerous detectors covering a wide range of scattering angle.

Nullifying the extinction effect in XRD characterization of fibre textures

To gain accuracy and, hence, physical reality of the data acquired by XRD measurements of fibre textures, a technique is elaborated to achieve experimental values, which are free of extinction effects. Its elaboration is based on combining basic definitions of the extinction theory and texture analysis. This technique is applicable to characterization of metal coatings that appear infinitely thick for X-rays. A nickel sample representing <100> + <221> texture components is used as a model. Resultant derived series of data on pole-density distribution of the {200} diffraction pole figure shows that the data corresponding to the main <100> texture component are strongly affected by extinction. On the contrary, due to definitions that require reduction of the intensity distribution to multiples of random density, the extinction-free values of the volume fraction of texture components do not differ substantially from those calculated by standard methods. Evidently, any of the standard methods for volume fraction measurements provides reasonable data if secondary extinction is even disregarded.

Decomposing textures of hexagonal magnesium alloys with fiber component

The orientation distribution function (ODF) calculated from measured pole figures with series expansion method is decomposed into texture components of Gauss type distribution and the volume fraction of texture components can be calculated with the model distribution function. Firstly, as fiber texture components are often found in magnesium alloy, the series expansion coefficients for Gauss type fiber components are derived. Secondly, as the textures of magnesium is very complicated, the group decomposing method, i.e., a major component accompanied by several minor components with trivial misorientation from the major one, is proposed to ensure better fitting or decomposing results. Finally, the group decomposing method is used to calculate the texture volume fraction of two typical experimental ODFs.

Comparison of textures determined by X-ray and electron backscatter diffraction in aluminium alloy AA 6111 sheets with different levels of cube texture

The crystallographic textures in five AA 6111 aluminium alloy sheets, having an increasing cube ({001}<100>) texture component, were determined by X-ray diffraction and electron backscatter diffraction (EBSD) techniques. It has been demonstrated that the two techniques yield very similar results in regard to pole figures, but they may give different volume fractions of texture components. The difference is limited when the specimen is weakly textured, but it increases with increasing dominant texture component. The EBSD technique gives a sharper dominant texture component than the X-ray technique. This could be attributed to the fact that the two methods apply different mathematics in data analyses. The different levels of systematic error and instrumental broadening may also be critical.

On the Calculation of Volume Fraction of Texture Components in AA5754 Sheet Materials

There is currently no general agreement on how to extract the volume fraction of texture components for aluminum alloy sheets based on X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) techniques. In order to clarify this problem, grain orientation data of AA5754 sheet material in the O-temper were acquired using XRD and EBSD. The volume fractions of 10 selected texture components were calculated using the MTM FHM software package for XRD and EDAX-TSL OIM Analysis for EBSD. The measured grain orientation data from EBSD were then processed again using MTM FHM. The results show that there are no significant differences in the constructed pole figures using different measuring techniques when the same analysis system is used. Thus, the differences in volume fractions of texture components are mainly related to the deviation angle used in the two different software packages. The differences in the deviation angle used lead to potential overlaps between the selected texture components. A suitable deviation angle for the volume fraction calculation can be selected using the concept of misorientation.

Determination of volume fraction of the texture components in the Rodrigues fundamental region

The fundamental region of Rodrigues space was discretized with finite elements as Euler space was discretized with 5° cell structures. Texture components were modeled with Gaussian distributions in the Rodrigues fundamental region. Spherical texture components are described by a sphere with a Gaussian distribution centered at its ideal position. Ideal fiber orientations are represented by a straight line or a skeleton line in Rodrigues space. The usual fiber textures are represented by a tube with a Gaussian distribution centered along a fiber line in Rodrigues space. The volume fractions of typical texture components can be collected by misorientation approach. The volume collections of spherical components of interest begin with the calculation of misorientation angles between the ideal components and their adjacent orientations. The radius of the orientation sphere is an angular distance. Adjacent components with smaller misorientation angles than a given criterion or a cut-off value locate inside the sphere and contribute to the volume fraction of the spherical component. For fibers, angular distances between the orientations along a skeleton line and adjacent orientations are compared with a cut-off. In addition, discretization effects of the Rodrigues fundamental region on the ODF and texture analysis were investigated. The volume fractions of texture components measured from a cold-rolled gold sheet and bonding wire were analyzed using the misorientation approach proposed.

Determination of volume fractions of texture components with standard distributions in Euler space

The intensities of texture components are modeled by Gaussian distribution functions in Euler space. The multiplicities depend on the relation between the texture component and the crystal and sample symmetry elements. Higher multiplicities are associated with higher maximum values in the orientation distribution function (ODF). The ODF generated by Gaussian function shows that the S component has a multiplicity of 1, the brass and copper components, 2, and the Goss and cube components, 4 in the cubic crystal and orthorhombic sample symmetry. Typical texture components were modeled using standard distributions in Euler space to calculate a discrete ODF, and their volume fractions were collected and verified against the volume used to generate the ODF. The volume fraction of a texture component that has a standard spherical distribution can be collected using the misorientation approach. The misorientation approach means integrating the volume-weighted intensity that is located within a specified cut-off misorientation angle from the ideal orientation. The volume fraction of a sharply peaked texture component can be collected exactly with a small cut-off value, but textures with broad distributions (large full-width at half-maximum (FWHM) need a larger cut-off value. Larger cut-off values require Euler space to be partitioned between texture components in order to avoid overlapping regions. The misorientation approach can be used for texture’s volume in Euler space in a general manner. Fiber texture is also modeled with Gaussian distribution, and it is produced by rotation of a crystal located at g 0, around a sample axis. The volume of fiber texture in wire drawing or extrusion also can be calculated easily in the unit triangle with the angle distance approach.

Determination of volume fractions of texture components with standard distributions in euler space

Determination of volume fractions of texture components with standard distributions in euler space

Textures of Cu and Dilute Binary Cu(Ti) and Cu(In) Thin Films

The development of texture in thin Cu and dilute binary Cu(Ti) and Cu(In) films has been investigated as a function of annealing history. The textures are comprised of , and fiber in different proportions for the three films. Annealing strengthens the texture for all films. For the annealed films, alloying with Ti strengthens the component, whereas alloying with In weakens it compared to pure copper. Two different approaches were used to derive volume fractions of texture components, namely fiber plots and orientation distributions. For strong mono-textured films of materials such as aluminum, fiber plots are most effective. For weaker, poly-textured films such as the copper alloys studied here, orientation distributions derived from pole figures provide the most reliable basis for quantitative characterization. Introduction As dimensions of very narrow copper interconnections reach the 100 nm range, the control of microstructural features such as texture and grain size becomes increasingly important. In a recent study we addressed the impact of alloying elements on the decomposition and resistivity of a series of dilute binary Cu alloy films annealed at a constant heating rate up to 950 C [1]. In this work, we focus on the impact of isothermal annealing at 400 C on the texture of pure Cu and dilute binary Cu(Ti) and Cu(In) films. In addition to the detailed behavior of the films, we briefly discuss the advantages and disadvantages of various x-ray based methods for the analysis of the texture of Cubased films. Experiment Pure Cu and dilute binary Cu(Ti) and Cu(In) alloy films were electron beam evaporated onto thermally oxidized silicon wafers. The composition and thickness of the films are listed in Table 1. X-ray diffraction (XRD) experiments were conducted using Cu Kα radiation in a Rigaku powder diffractometer with a curved graphite monochromator. These patterns were used to give a qualitative indication of the texture in the films. For the quantitative analysis of film texture, fiber plots and pole figures were used. Pole figures and fiber plots were obtained in a Philips X’Pert Pro diffractometer, utilizing an X-ray lens and 0.27 Soller slits in the path of the incident beam and a flat graphite monochromator in the path of the diffracted beam. The fiber plots were measured in 0.1 intervals per second as is commonly done in texture studies of Al films [2], while the pole figures were determined at 5 intervals every two seconds. Three pole figures {111}, {200} and {220} were obtained for each sample. In order to ensure that the use of 5 intervals for the collection of pole figures did not affect the resolution of intensity data used for the calculation of the orientation distribution functions (ODFs), sections through the pole figures were compared with 2 Title of Publication (to be inserted by the publisher) the fiber plots. Three such sections for the annealed Cu film have been overlaid on their respective fiber plots in Fig. 1 and show no discernible difference. Table 1 Composition and thickness of the films. Sample Solute [at%] Thickness [nm] Cu(Ti) 3.0 488 Cu(In) 2.6 520 Cu 420 0 20 40 60 80 0 500

Texture and Resistivity of Cu and Dilute Cu Alloy Films

AbstractAnnealing of dilute binary Cu(Ti), Cu(In), Cu(Al), Cu(Sn), Cu(Mg), Cu(Nb), Cu(B), Cu(Co) and Cu(Ag) alloy films resulted in the strongest &lt;111&gt; fiber texture for Cu(Ti) and the lowest resistivity for Cu(Ag). The behavior of the alloy films was compared and contrasted with that for a pure evaporated Cu film. Electron beam evaporated films with compositions in the range of 2.0-4.2 at% and thicknesses in the range of 420-560 nm were annealed at 400°C for 5 hours. Two different approaches were used to derive volume fractions of texture components, namely fiber plots and orientation distributions. It is argued that for polytextured films such as the copper alloys studied here, orientation distributions derived from pole figures provide the most reliable basis for quantitative characterization.

The development of a computer software system for the prediction of formability parameters of sheet metals form X-ray diffraction data

A computer software for the prediction of formability parameters of sheet metals from X-ray diffraction data has been developed. There are two functional parts in the software system. One of them is to complete the calculation and analysis of the crystallographic texture, and the another is to predict the formability parameters such as the plastic strain ratios, yield loci and Taylor factor from the experimental textures. A new algorithm using Fast Fourier Transform to calculate the crystallite orientation distribution function is used, and the volume fraction of texture components are determined automatically. A conception of cubic equivalent spreading width is proposed to describe the degree of texture spreading and is used for the prediction of the plastic anisotropy of sheet metals. The prediction results agree well with experimental data obtained from an AlCu alloy. The software will be useful for engineers in the quality control and testing of sheet metals in industry.

A Computer Program for Determining Volume Fractions of Texture Components in Cubic Materials

A Computer Program for Determining Volume Fractions of Texture Components in Cubic Materials

Volume fractions of texture components in polycrystalline materials

The orientation distribution of crystallites has until now been interpreted by a small number of texture components. In the frame of the harmonic formalism, an analytical method for the accurate determination of the volume fractions of peak-type components in restricted regions is developed without recourse to additional assumptions. Its validity and feasibility are demonstrated through two numerical examples.

An Assessment on Reliability of Quantitative Calculation Method for Obtaining Volume Fractions of Texture Components With the Reduced ODF

The reliability and the accuracy of a quantitative calculation method for obtaining volume fractions of texture components of cubic materials were verified for the reduced ODFs terminated at l max = 22 and at l max = 16. It is concluded that an integrated width of r = ±10° around selected ideal orientations may be used in quantitative analysis of texture components. It is also shown that the conventional peak height method, which does not consider volume fractions, can only roughly give informations about texture components.

Volume Fractions of Texture Components of Cubic Materials

A method for obtaining volume fractions in regions about ideal texture components of cubic materials by integration of the orientation distribution function is described. Illustrative examples of the application of the method are given for the primary-recrystallized textures of a 3.15% Si-Fe alloy and several low-carbon steels.