【正文】 rce of significant waste in can production if sheet texture is not controlled, as this excess material is unusable and is cut away.Figure 2 – Deep drawn aluminium cups, showing the effects of, left, weak rolling texture and, right, strong rolling texture on the deformation observed.How is Texture Measured?In modern materials science texture is normally measured by a diffraction of xrays, electrons or neutrons from the crystallographic planes.XRaysThe most mon method of measuring texture uses xray diffraction and is known as the “Schultz reflection method”. The apparatus used is known as a fourangle diffractometer or a Eulerian cradle, see figure 3.The source of xrays and the detector are oriented so that a particular value of 2θ (the angle between the source and the detector) is specified. This means that only diffraction from a single set of planes, with a particular spacing will be measured. The sample is tilted and rotated systematically, so that all angular orientations are investigated. When the lattice plane specified by the 2θ value is in the right orientation, it will diffract and the detector will record the reflection. For a polycrystalline material, the intensity of detected xrays will increase when there are more grains in that specific orientation, and the intensity for any angle is proportional to the volume fraction of crystallites with that orientation. Areas of high and low intensity suggest a preferred orientation, while constant intensity at all angles would occur in a random polycrystalline aggregate.Figure 3 – A schematic diagram of a four angle diffractometer for texture determination.In some materials the bulk and surface textures may be different。 for example after rolling. It is therefore, important to identify which texture is of interest, and which is being measured. Different sources of radiation can lead to different degrees of penetration, and hence allow the measurement of either bulk or surface textures.Electrons – EBSDAn alternative method of texture determination is that of electron backscattered diffraction, EBSD, which uses a scanning electron microscope. At each single beam position (each spot on the image), the electron beam is rocked about a fixed point on the surface. At particular angles, where the diffraction conditions for particular planes are satisfied, the beam is diffracted, so that there is a change in the intensity of the reflection measured. This leads to the formation of a channelling pattern made up of Kikuchi lines, Figure 4.Figure 4 – Kikuchi lines formed during EBSD of a born doped (001) oriented Si wafer, with lines indicating the reflections identified. Image from DoITPoMS ().The symmetry of the channelling pattern, and vector addition of the different reflections allows the planes generating specific bands to be identified (usually done using mercially available software). This gives the orientation of the material under the beam at that spot, and so it is possible to build up a 2D map of the orientation of grains on the surface of a polycrystalline sample.Neutron DiffractionNeutron diffraction can be used in a similar way to xray diffraction. There is a large reduction in absorption but a much higher angular resolution in neutron diffraction in parison with xray diffraction. This means that neutrons are suitable for situations where a large depth of penetration is required, and are relatively rapid, meaning that they can be used to measure insitu texture changes due to environmental factors (. temperature changes and stress). However, beams of sufficient intensity are difficult to generate and usually require a beamline on a nuclear reactor.R Goodall, October 2010 15Quantification of Microstructure and Texture Analysis of TextureQuantification of Microstructure and Texture11. Analysis of TextureRepresentation of TextureThe term crystallographic orientation, which we seek to represent when we are trying to define the texture of a material in some way, refers to the 3dimensional orientation of the lattice, and therefore has three independent variables. Defining the orientation of a certain plane (requiring 2 independent variables) is not sufficient to fully specify the texture.Pole FiguresThe normal way to represent such an orientation on a 2D page is to use a construction known as a pole figure. A pole figure is based on the stereographic projection method of representing crystal shapes. This imagines a reference sphere, Figure 1, with the crystal at the centre. Lines normal to the faces of this crystal are extended to the surface of the sphere. Lines are then projected from the intersection with the surface back to the “South pole” of the sphere, Figure 1. Where these lines intersect the equatorial plane a spot is marked. A picture of the equatorial plane constitutes the stereographic projection. An animated demonstration of this may be found on: Figure 1 – a) A reference sphere with a cubic crystal at the centre, with lines normal to the crystal planes extended to the sphere, and b) the projection of these lines back to the south pole through the equatorial plane to give c) the stereographic projection.Stereographic projections can be used for representing crystal shapes. A pole figure is simply a stereographic projection where the crystal is known, and a particular (specified) set of planes is projected showing their orientation relative to a reference set of directions. These reference directions are usually the rolling, transverse and normal directions, or other names representing the three principal axes of the specimen. See the example pole figures in Figure 2.As well as showing the orientation of a single crystal or grain, a pole figure can build up a representation of a polycrystalline specimen by adding a point for each additional orientation present. This allows areas of particular intensity, re