Measurement and representation of grain-boundary texture
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INTRODUCTION
FROM a pragmatic viewpoint, the modern crystallographic texture analysis t~'zJ has proven useful because it establishes a representation of microstructure with successful connections to modeling anisotropic physical properties of polycrystaUine materials and their processing. This utility is not particularly surprising, since material behavior is clearly rooted in the underlying arrangement of interatomic bonding, and the principal representation of the modern texture analysis, the crystallite orientation distribution function (CODF), gives substantial information about the spatial distribution of bonding. It is also evident, however, that the CODF (or any other known representation of microstructure) does not provide complete microstructural information, and some properties and processes will require other representations which emphasize other features of internal structure. This is certainly true for phenomena which are sensitive to grain-boundary structure. In this case, a minimum description of the local bonding structure now depends upon the relative orientation between grain lattices and the crystallographic orientation of the boundary separating them. An even more complete description (beyond the scope of this article) may require additional information about such features as local boundary curvature, chemical segregation, jump discontinuities in lattice curvature, and other microstructural details. In this article, we take up the general topic of grainboundary texture in polycrystalline materials. By the term "grain-boundary texture," we mean the distribution or probability of occurrence of grain boundaries with specified local structure. The word "texture" derives from BRENT L. ADAMS, Associate Professor, is with the Department of Mechanical Engineering, Yale University, New Haven, CT 065202157. DAVID P. FIELD, formerly Graduate Student, Yale University, is Engineer, Fabricating Technology Division, Alcoa Technical Center, Alcoa Center, PA 15069-0001. Manuscript submitted November 20, 1991. METALLURGICAL TRANSACTIONS A
the Latin root textura, which connotes the arrangement of the particles or components of a material. In the subject of grain-boundary textures, we are specifically interested in the grain-boundary component of microstructure and not the grain interiors. This component consists of a three-dimensional network of intercrystalline boundaries of variable local structure. Local structure at any point lying upon the network is here assumed to be fully defined by the lattice orientation of two grains which come together to form the boundary and the orientation of the boundary relative to the two lattices. We shall not concern ourselves with triple lines or quadruple p o i n t s . . , only with the two-dimensional surfaces. This description is fully developed in Section II. From an experimental point of view, although it is possible to directly measure local structure of grain boundaries (e.g., through a two-surface analysis or thin foil techniques), it is often more practical to r
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