A method is described which assigns indices to a set of
single-crystal reflections recorded by the rotation-oscillation
technique using a fixed X-ray wavelength. It is assumed that the space
group and approximate unit-cell parameters are known. The unknown
crystal orientation is determined directly from the observed diffraction
pattern of one or several oscillation data records. A local indexing
procedure is described which tolerates large initial errors in the
parameters controlling the diffraction pattern. These parameters are
refined subsequently, thereby satisfying the constraints imposed by the
space-group symmetry.
Diffraction bending of waves around the edge of an obstacle. When light strikes an opaque body, for instance, a shadow forms on the side of the body that is shielded from the light source. Ordinarily light travels in straight lines through a uniform, transparent medium, but those light waves that just pass the edges of the opaque body are bent, or deflected. This diffraction produces a fuzzy border region between the shadow area and the lighted area. Upon close examination it can be seen that this border region is actually a series of alternate dark and light lines extending both slightly into the shadow area and slightly into the lighted area. If the observer looks for these patterns, he will find that they are not always sharp. However a sharp pattern can be produced if a single, distant light source, or a point light source, is used to cast a shadow behind an opaque body.
The radiation diffraction pattern for amorphous materials requires special analysis for information on atomic groupings. Powdered crystalline material may also give diffuse patterns requiring this type of analysis. Absence of a sharp diffraction pattern does not necessarily indicate absence of the material. Examples are given for chrysotile and powdered chrysotile.
If the diffraction pattern of the hyperbolic umbilical diffraction catastrophe is produced by an optical system of increasing aperture, it passes continuously from the two-dimensional system of Airy rings in the focal plane, made by a very small aperture, to the full three-dimensional pattern corresponding to infinite aperture. The paper studies this transition by examining the truncated diffraction integral and following the evolution of the wave dislocation lines (phase singularities) on which the pattern is based. The seed of the evolution from a two-dimensional to a three-dimensional pattern turns out to be already present asymptotically even for the smallest aperture: namely, a column of small dislocation rings very close to the axis that stream in procession towards the focal plane, and become dislocations lying in the Airy fringe surfaces that run parallel to the main fold caustic, only to disappear ultimately by retreat to infinity. The evolution into the final dislocation pattern takes place by a sequence of primitive local topological events, such as reconnection (hyperbolic interchange) and ring creation.
Diffraction bending of waves around the edge of an obstacle. When light strikes an opaque body, for instance, a shadow forms on the side of the body that is shielded from the light source. Ordinarily light travels in straight lines through a uniform, transparent medium, but those light waves that just pass the edges of the opaque body are bent, or deflected. This diffraction produces a fuzzy border region between the shadow area and the lighted area. Upon close examination it can be seen that this border region is actually a series of alternate dark and light lines extending both slightly into the shadow area and slightly into the lighted area. If the observer looks for these patterns, he will find that they are not always sharp. However a sharp pattern can be produced if a single, distant light source, or a point light source, is used to cast a shadow behind an opaque body.
The radiation diffraction pattern for amorphous materials requires special analysis for information on atomic groupings. Powdered crystalline material may also give diffuse patterns requiring this type of analysis. Absence of a sharp diffraction pattern does not necessarily indicate absence of the material. Examples are given for chrysotile and powdered chrysotile.
If the diffraction pattern of the hyperbolic umbilical diffraction catastrophe is produced by an optical system of increasing aperture, it passes continuously from the two-dimensional system of Airy rings in the focal plane, made by a very small aperture, to the full three-dimensional pattern corresponding to infinite aperture. The paper studies this transition by examining the truncated diffraction integral and following the evolution of the wave dislocation lines (phase singularities) on which the pattern is based. The seed of the evolution from a two-dimensional to a three-dimensional pattern turns out to be already present asymptotically even for the smallest aperture: namely, a column of small dislocation rings very close to the axis that stream in procession towards the focal plane, and become dislocations lying in the Airy fringe surfaces that run parallel to the main fold caustic, only to disappear ultimately by retreat to infinity. The evolution into the final dislocation pattern takes place by a sequence of primitive local topological events, such as reconnection (hyperbolic interchange) and ring creation.
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