513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
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Structure Factor

What is the structure factor for a body-centered cubic lattice? For which reciprocal lattice indices hkl is there an extinction of the diffracted beam due to destructive interference?

The labeling of the reciprocal lattice vectors depends on the choice of unit cell. If you have an bcc crystal with one atom per primitive unit cell, and you choose to work with the primitive unit cell there can be no interference between the reflections from atoms in a unit cell so the structure factor is 1. However, to index the reflections in a diffraction experiment, crystalographers use a conventional cubic unit cell for cubic crystals. This unit cell is a cube that is typically bigger than a primitive unit cell and contains more atoms. There are two atoms in a bcc conventional unit cell. The advantage of doing this is the [100] reflection is the x direction and the [010] reflection is in the y direction etc. In this question, calculate the structure factor for the conventional cubic unit cell.