On the analysis of grain size in bulk nanocrystalline materials via x-ray diffraction
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On the Analysis of Grain Size in Bulk Nanocrystalline Materials via X-Ray Diffraction Z. ZHANG, F. ZHOU, and E.J. LAVERNIA The Warren–Averbach (WA) analysis and other simplified methods that are commonly used to determine the grain size of nanocrystalline materials are discussed in terms of accuracy and applicabilities. The nanocrystalline materials used in the present study are prepared by cryomilling of A1 powders and subsequent consolidation (hot isostatic pressing and extrusion). Transmission electron microscopy observations of the as-extruded nanocrystalline A1 reveal a bimodal distribution of grain sizes centered around 50 to 100 nm and 250 to 300 nm. It is shown that the grain size determined by the WA analysis agrees with the lower bound grain size (e.g., 50 to 100 nm) observed experimentally. In the case of the integral method, it is useful to use a parabolic (Cauchy–Gaussian (CG)) relationship to approximate instrumental broadening and separate the intrinsic broadening. Compared to the Cauchy–Cauchy (CC) and Gaussian–Gaussian (GG) approximations, this is shown to give the best results. In addition, the reliability of the Scherrer equation is also discussed.
I. INTRODUCTION
II. EXPERIMENTAL PROCEDURES
IN recent years, nanocrystalline (nc) materials, defined hereafter as having characteristic spatial dimensions within the 100 nm regime, have gained increasing attention due to their unique properties and behavior.[1] It is of interest to characterize the grain size of nc materials both from the fundamental and performance standpoints because their behavior is intrinsically size dependent. Transmission electron microscopy (TEM) and X-ray diffraction (XRD) are two basic methods for the grain size evaluation. Transmission electron microscopy can provide a direct image of the grain size distribution. However, grain overlapping will lead to uncertainty and the reliability also depends on whether the thin area is a representative of the original microstructure of the entire sample. In contrast, the indirect methods based on XRD line broadening have the advantage of averaging over a much larger area of the sample and ease of sample preparation. As various techniques, such as gas condensation and compaction,[2,3] ball milling,[4,5,6] severe plastic deformation,[7,8] have been developed to synthesize nc materials, variations in microstructural characteristics (e.g., crystallite size, crystallographic texture, faults, etc.) of these materials are anticipated. Accordingly, there is a need to ascertain the accuracy of existing characterization methods, as well as to determine their self-consistency and applications to nc materials produced by using various synthesis methods. In this study, XRD and TEM are employed to determine the grain size in a bulk nc A1 fabricated via cryomilling and consolidation.
The bulk nc A1 was prepared by a four-step procedure: cryomilling, degassing, hot isostatic pressing (HIP’ing), and extrusion: (1) cryomilling for 16 hours in a liquid nitrogen ambient with 0.2 wt pct stearic acid and
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