Substructure Measurements by Statistical Fluctuations in X-Ray Diffraction Intensity
The substructures of a beta-quenched and a recrystallized form of high-purity uranium were measured by a method based on statistical fluctuations in X-ray diffraction intensity. For these measurements, Warren’s1 statistical equation for determining grain size was modified to make the equation applicable to materials with high absorption coefficients or moderate-to-large grain size (> 20 microns) or both, since many metals fall into this category, and to allow for defocusing of the X-ray beam which occurs as a natural consequence of the experiment.
The beta-quenched uranium was found to have numerous subgrains with a range of misorientation angles that was smaller and larger than the limits of the X-ray measurements (Ω = 10−4 to 10−2 steradians). The presence of the large subgrains was corroborated by optical microscopy. The presence of very small subgrains was corroborated by transmission electron microscopy which showed 0.1- to 1-micron subgrains relatively free of dislocations bounded by dense dislocation networks, and by micro Laue diffraction patterns (30-micron beam diameter) which showed partial rings similar to a powder pattern.
The recrystallized uranium had no misorientation within the grains greater than 5.5 × 10−3 steradians. In contrast to the beta-quenched case, no subgrains were found either by transmission electron microscopy (TEM) or micro Laue diffraction patterns. The TEM micrographs showed a uniform distribution of dislocation networks. Since no other substructural elements were observed, the dislocations are believed to be the cause of the misorientation within the grains for solid angles of less than 5 × 10−3 steradians.
These preliminary experiments show that the statistical method may be used in conjunction with transmission electron microscopy and micro Laue diffraction for the study of substructure. The statistical method gives quantitative data on “bulk” specimens that can be given a meaningful interpretation with the aid of the other techniques.
KeywordsSolid Angle Statistical Fluctuation Substructural Element Beam Area Laue Pattern
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