Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning
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6/8/04
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Characterization of Three-Dimensional Grain Structure in Polycrystalline Iron by Serial Sectioning C. ZHANG, A. SUZUKI, T. ISHIMARU, and M. ENOMOTO The face number, the volume, and the surface area (boundary area) of grains are measured in recrystallized -iron by serial sectioning coupled with quantitative microstructural analysis on twodimensional (2-D) sections. The sampling volume contained approximately 1000 grains whose mean grain size was 15 m. The grain volume distribution decreased monotonously with increasing grain volume, whereas the surface area had a peak around one-half of the average. The distribution of the sphere equivalent radii significantly deviated from the log-normal distribution and distributions predicted from mean field theories. The peak and the mean of the face number distribution were f 11 and 12.1, respectively. The linear relationship between the face number of a central grain and the mean face number of surrounding grains, known as the Aboav–Weaire law, was observed in three dimensions. The mean radius of f-faced grains was not proportional to the face number (perimeter law in 3-D), but appeared to be related by a curve convex upward. I. INTRODUCTION
THE size and the shape of grains and their spatial correlation are considered to have an important influence on the properties of polycrystalline materials. They are likely to play a key role in the evolution of microstructures as well. Accordingly, the prediction and control of grain structure is one of the major objectives in materials science. The experimental methods so far used for the observation of three-dimensional (3-D) grain structure include intergranular corrosion,[1,2] stereoscopic microradiography,[3] and serial sectioning.[4,5] The alloy systems to which these techniques are applicable are limited, and the experimental procedures are often very tedium. Thus, efforts are being made to correlate the distributions in 2-D sections to those in 3-D.[2,6] For the same reason, computer simulation has become a very popular means of studying the evolution of microstructure in polycrystalline solids.[7–10] In this article, serial sectioning is employed to characterize the grain structure in cold-rolled and recrystallized -iron. Coupled with quantitative microstructural analysis on 2-D sections, not only the face number, but also the grain volume and the surface area were measured. One of the advantages of serial sectioning may be that one can measure the spatial correlation of the grain size and shape within neighbors without special contrivance. Measured results are compared with various rules in grain growth so far proposed. II. EXPERIMENTAL PROCEDURE A. Alloy Specimen Electrolytic iron was vacuum induction melted under argon with carbon deoxidation. The chemical composition is shown
in Table I.* The ingot was forged at 1200 °C into a bar of *The carbon deoxidation was not very successful. The alloy contained quite a large amount of oxygen.
the cross section of 30 50 mm2. The coupons cut from the
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