![]() The generation of multiple spots is also illustrated in Figure 8.1, where the reciprocal lattice points 2 to 5 from the indicated reciprocal lattice line produce a multiple Laue spot on the detector. If a spot is multiple, its integrated intensity is the sum of the integrated intensities of each component. The directions of reflected beams lie on the surface of the cone.ġ/dmin, a Laue spot may be single, arising from only one reciprocal lattice point, wavelength, and structure factor, or multiple, arising from several points. The projection of this circle from the center M of the largest Ewald sphere reveals a cone with cone axis. The expansion is illustrated by four rays and the expanded circle, which cuts the largest sphere, as shown. (b) Expansion of a circle resulting from the intersection of a reciprocal lattice plane passing through origin O with the smallestĮwald sphere. (a) Expansion of reciprocal lattice by rays along the lines between the origin of the reciprocal lattice O and the respective reciprocal lattice points. 8.2 Explanation of the geometry of Laue diffraction patterns. Because a ray may contain only one reciprocal lattice point H with indices (h k l) or several (hkl, 2h 2k 2l., nhnknl) between the origin andįig. This means that Laue spots arise from mapping of rays (lines emanating from the origin in reciprocal space) onto the detector, in contrast to spots in a monochromatic pattern that arise from mapping of individual reciprocal lattice points. Each point H between the spheres for Xmin and Xmax and no other point intersects the largest sphere in a point S, and MS indicates the direction of the reflected beam whose indices coincide with those of H for its wavelength, the following relationship holds, This is carried out in Figure 8.2 a for the points H1 to H3. Each lattice point H moves on the line OH to the point H with a distance from O of (Eq. The generation of multiple spots is illustrated.Īpproach is illustrated in Figure 8.2. Reciprocal lattice points lying in the hatched area give rise to reflections. The resolution sphere exhibits a radius of 1/dmin. The largest sphere has a radius of 1 /Xmin and the smallest one a radius of 1/Xmax. 8.1 Ewald construction for the Laue diffraction technique. However, it is more advisable to stretch the reciprocal lattice because the mutual position of the sphere and the lattice is essential to determine the direction of the reflected beam. A Laue pattern may be thought of as the superposition of a series of monochromatic still diffraction patterns, each taken at a different wavelength of X-rays - that is, a contraction of the Ewald spheres with radii from 1 /Xmin to 1 /Xmax. A reciprocal lattice point that lies in the hatched area (the region between the limiting Ewald spheres of radii 1 /Amin and 1 /Xmax and within a sphere of radius 1/dmin, the limiting resolution of the crystal) is in diffraction position for the wavelength X and will contribute to a spot on the Laue diffraction pattern. Figure 8.1 shows the Ewald construction for the Laue technique. A Laue diffraction pattern is obtained when a stationary crystal is illuminated by a polychromatic X-ray beam spanning the wavelength range from Xmin to Xmax, the so-called band pass. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |