Reciprocal Lattices and Diffraction

Many physical properties of crystals as well as the geometry of the three as the geometry of the three -dimensional dimensional patterns resulting from a diffraction event are most easily represented using the are most easily represented using the concept of the reciprocal lattice !

Diffraction occurs in inverse proportion to the spacin g between ob jects causin g diffraction.

Importance of Reciprocal Space

When a diffraction event occurs, the diffracted waves/pattern will waves/pattern will “match ” the reciprocal lattice. the reciprocal lattice.

►Radiation Radiation ‘scatters scatters’ in inverse proportion to the in inverse proportion to the spacings between diffraction centers (i.e., planes in crystals).

We make the use of this fact in x-ra y diffraction and transmission electron microscopy.

Reference: http://bama.ua.edu/~mweaver/courses/MTE583/MTE%20583_Class_17a.pdf

 Reference: http://phy.ntnu.edu.tw/~changmc/Teach/SS/SS_note/chap02.pdf

Surface Diffraction and the Reciprocal Lattice

The diffraction of either photons or electrons (sometimes neutrons) is one of the most powerful techniques for surface structure determination. Unfortunately, the diffraction pattern is not a direct representation of the real-space arrangement of the atoms in a solid or on a surface. The most convenient way to link the real structure of the material to it's diffraction pattern is through the reciprocal lattice.

Reference: http://www.cem.msu.edu/~cem924sg/Reciprocal.html

Basic diffraction: waves, interference and reciprocal space

Outline

• Waves
  • Describing waves
  • Waves as vectors
  • Adding waves as vectors
• Diffraction
  • When do waves scatter in phase?
  • When do we see diffraction from a crystal?
• Reciprocal space
  • The Ewald sphere
  • Diffraction from a real crystal
• Quantum mechanics and diffraction
• Other resources