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3 ``laue'' - x-ray scattering in one dimension in perfect and imperfect crystals

``laue'' computes the diffraction pattern of a one dimensional crystal. It is designed to illustrate a number of important ideas in x-ray diffraction: atomic form factor, structure factor, extinction, diffraction from a periodically perturbed crystal (phonon sidebands), thermal diffuse scattering, diffraction analysis of the order-disorder transition, quasicrystal diffraction, and short range versus long range coherence.

"laue" was programmed by Joerg Draeger with much of the original code from Jim Sethna.




It is easy to set simple problems to check understanding of the physics. On the left below is the electron density in two successive cells of a diatomic (one-dimensional) crystal. The two atoms have different widths of the electron distribution. On the right is the corresponding diffraction pattern (Fourier transform of the electron density). How many different features of the diffraction patern can you interpret? What can you say about the relative number of electrons in each of the two kinds of atoms?




``laue'' can also compute the diffraction patterns for non-periodic arrays of atoms. In the example on the left there is a periodic modulation of the atomic positions. The result is the presence of first and higher order satellite peaks (phonon sidebands) associated with each of the main Bragg peaks. On the right is the diffraction pattern of a quasicrystal.
. . . .


Here are two diffraction patterns from a diatomic 50/50 alloy. On the left, the two kinds of atoms are ordered in an ...ABABAB... structure. On the right the order is partially destroyed (an order parameter of 0.5). You see both the loss of intensity in the superlattice lines and the presence of disorder diffuse scattering.
. . . .


Table of contents for Chapter 3 of Simulations for Solid State Physics
  1. Introduction
  2. Bragg condition
  3. Atomic form factor
    1. Atomic scattering
    2. Envelope of diffraction pattern
    3. Other atomic shapes
  4. Structure factor
    1. Identical atoms
    2. Different atomic numbers
    3. Different sizes
  5. Order-disorder
  6. Atomic displacements and thermal disorder
    1. Periodic distortion
    2. Thermal motion
    3. Long range crystalline order
  7. Quasicrystals
  8. Summary
  9. Appendix: "laue" -- the program

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