5 Order/disorder

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So far we've looked only at "perfect crystals." The remaining presets address several issues concerning imperfect crystals.

Here is a perfect "diatomic crystal" with equally spaced atoms of equal size but different atomic number (electronic charge). From the ratio of the intensities of the strong to weak lines of 4/1 you should be able to conclude that the ratio of atomic numbers of the two crystals is 3/1.

"laue" can mix up the crystal, putting one kind of atom where the other kind is supposed to be and vice versa. The order parameter p describes the amount of mixing. (p=1 is the ordered crystal; p=0 gives a random assignment of atoms to sites.)

Calculate for three different values of p: 0, 1, and 0.5, and copy diffraction for each of these. (It's probably easier to compare if they're separate: you could try steal data to put them on a single plot.) There are three features to note:

  1. a set of lines whose intensity is (roughly) the same for all three plots. What is the lattice constant of the crystal that would give this line spacing?
  2. a set of lines whose intensities depend upon p. These are called superlattice lines. What is the lattice constant of a crystal which would give, in its diffraction pattern, both sets of lines?
  3. a collection of garbage which becomes evident when you zoom in to low intensities, and which also depends upon p. This is diffuse disorder scattering.