Department of Chemical Engineering and Materials ScienceMike MeierUniversity of California, DavisFebruary 22, 2005Figure 1.FEG-SEM image of nanosized aluminum oxide powder. Note themagnification and the size of the micron bar. Also note how the smaller particlesand the edges of the larger particles appear to be somewhat transparent. This isbecause much of the 5 kV electron beam can pass through these thinner parts of theparticles.MEASURING CRYSTALLITE SIZE USING X-RAYDIFFRACTION,THE WILLIAMSON-HALL TECHNIQUE(DRAFT)IntroductionPhase identification using x-ray diffraction relies mainly on the positions of the peaks in a diffraction profileand to some extent on the relative intensities of these peaks. The shapes of the peaks, however, containadditional and often valuable information. For instance, the width of the peaks increases as the size of thecrystalline domains (crystallites) that diffract the x-rays, decreases. In addition, the whole shape of thediffraction peaks can be analyzed, using Fourier techniques, to obtain the distribution of crystallite sizes.Finally, microstrain, short range lattice strains caused by crystalline defects (not macroscopic stresses) alsocauses peak broadening. X-ray diffraction can be used to measure all three, but the fact that microstrain andcrystallite size both lead to peak broadening means that either both size and strain must somehow bemeasured, or a way to eliminate the effect of one or the other must be found. In this experiment bothcrystallite size and microstrain are measured where the Scherrer method (which yields the size based onmeasurements of any one peak when strain is not present) is applied to all diffraction peaks and the variationin size is used to measure the microstrain. This experiment is based on the one described in Suryanarayanaand Norton‘s book  and the specific technique, called the Williamson-Hall method , has manyapplications in nano-technology, including characterizing nano-powders (see figure 1) and studyingcrystallization in glasses.
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