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Learn how to apply the selection rules for X-ray diffraction to different crystal structures and symmetries in this recitation module from Chemistry LibreTexts. This module covers the basics of X-ray diffraction, the Bragg's law, the Laue equation, and some examples of diffraction patterns and intensity calculations.
hkl for Face Centered Cubic • Substitute in a few values of hkl and you will find the following: – When h,k,l are unmixed (i.e. all even or all odd), then F hkl = 4f. [NOTE: zero is considered even] – F hkl = 0 for mixed indices (i.e., a combination of odd and even). Ffe e e 1 ih k ih l ik l() ( ) ( ) hkl Selection rules for hkl reflections
Cubic m3 23 m3 m 3m 432 43 m m 3m You should be able to convince yourself that the diffraction pattern for a crystal in I4 1cd will have 4=mmmpoint symmetry; likewise, that of a crystal in P6 2 will have 6=mpoint symmetry. Having established the effect of point symmetry on the diffraction pattern, we now proceed
Example: Body-centered cubic lattice The sc lattice is not the only one with cubic symmetry. Sometimes extra lattice points can be identified within the unit cell that have the same symmetry as those at the corners. These lattices are called “centered”. The body-centered cubic (bcc) lattice occurs when there is an extra lattice point at the ...
Table 1.1 summarizes the selection rules (or extinction conditions as they are also known) for cubic lattices. According to these selection rules, the h2 + J<2 + [2 values for the different cubic lattices follow the sequence Primitive I, 2, 3,4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, ... Body-centered 2,4, 6, 8, 10, 12, 14, 16, ...
Body-Centered Cubic Cells. Some metals crystallize in an arrangement that has a cubic unit cell with atoms at all of the corners and an atom in the center, as shown in Figure 2. This is called a body-centered cubic (BCC) solid. Atoms in the corners of a BCC unit cell do not contact each other but contact the atom in the center.
