Analysis of Complex Microstructures: Serial Sectioning and Phase-Field Simulations
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Introduction The morphology and topology of interfaces determine the properties of many multiphase materials. The processing conditions of a material, in turn, determine to a great extent its interfacial morphology and therefore its nano- or microstructure. Thus, controlling the properties of a material requires that the link between processing and nano- or microstructure be understood with great precision. Once achievable, such an ability to completely examine and characterize a structure and compute its evolution in three dimensions will permit the design of new materials for a wide range of applications. It has been clear for some time that three-dimensional measurements and computation of materials microstructures are essential. The need for threedimensional information to evaluate microstructures was discussed in detail by DeHoff1 in 1983. Some microstructural properties, such as the volume fraction or interfacial area of a phase, can be directly derived from the images of two-
dimensional sections of a bulk sample, and others, such as the particle size distribution or the degree of interfacial anisotropy, can be obtained through planar sections with the help of simplifying assumptions. However, there is another group of parameters that can be determined only from a three-dimensional representation of the microstructure. This group includes the number of features per unit volume (such as particles or cells, without assumptions about feature morphology and spatial arrangement), the connectivity of features (as in dendritic structures, for example), size distributions (without assumptions about particle morphology), spatial distribution information, and interfacial curvature and topology. This lack of three-dimensional information has also made it difficult to connect the processing, structure, and properties of a material. Models that predict material properties or structure without a priori knowledge of the size, morphology, and spatial distribution of phases within
MRS BULLETIN • VOLUME 33 • JUNE 2008 • www.mrs.org/bulletin
a microstructure often, by necessity, employ broad and general assumptions. Some recent progress, however, has been made using computational algorithms to evolve three-dimensional microstructures from two-dimensional micrographs.2 The importance of relating the threedimensional structure of a material and its mechanical properties has already been emphasized.3,4 This topic is also discussed in detail in the article by Spanos et al. in this issue. Here, we describe the important approach of making a similar connection between the processing of a material and its structure. A classical method for obtaining threedimensional information on micrometersized microstructures is serial sectioning where material is removed layer by layer, typically through machining or metallographic polishing. Serial sectioning has been used successfully in several cases,5–8 but it has the disadvantage of being extremely tedious when performed manually. In order to acquire meaningful microstructural information,
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