【正文】 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, repre。 that is, the underlying atomic structure of the grains is more likely to be of a certain spatial orientation, or close to a certain orientation, than any other.Sometimes a distinction is drawn between macrotexture and microtexture.MacrotextureSometimes this term is used to denote the general macroscopic texture associated with a ponent or large sample, often resulting from the processing history of the part, and represented as a certain most probable orientation for any grain in the material. This is of great important when considering the processing of many real metallic materials, and their use in a wide range of applications.MicrotextureThis is used to refer to the determination and study of the orientation of single grains in a material, paying attention to the spatial location of the grains studied within the sample. It is thus a bination of the study of texture and microstructure. This type of study is particularly useful in probing grain boundary structure, phase relationships (including before and after transformation), and sub grain dislocation structures, amongst others.Origin of TextureAny process that affects a material in an anisotropic way can give rise to texture. This can include solidification (where the direction of greatest heat extraction will be the direction of solidification, leading to texture in materials where crystals grow more easily along certain directions, see Figure 1), deformation (as materials may deform more easily in certain directions).Figure 1 – A solidification microstructure, showing anisotropic grain shapes. Note that, although this material does show texture, this cannot be concluded from the image. All we can say for certain is t