Submitted by Maggie Geselbracht / Reed College on Sat, 11/17/2007 - 16:53
My Notes
­This activity introduces students to the symmetries of 2-D repeating patterns and X-ray diffraction. Using small lasers and Optical Transform slides (available from the Institute for Chemical Education), students qualitatively and quantitatively investigate the relationships between the sizes and symmetries of unit cells and the effects observed in diffraction patterns.
Learning Goals

After exploring the diffraction of visible light from a variety of 2-D crystalline patterns, a student should be able to qualitatively and/or quantitatively describe:

  • The effect of changing the wavelength of the diffracted light on the diffraction pattern
  • The effect of changing the crystal spacing on the diffraction pattern
  • The effect of changing the crystal symmetry (i.e. 2-fold, 4-fold, 6-fold) on the diffraction pattern
  • The diffraction signatures of lattice centering and the presence of glide symmetry in the crystalline pattern
  • The determination of the unit cell size of the crystalline pattern from diffraction measurements

Equipment needs
Optical Transform slides (available from the Institute for Chemical Education), HeNe lasers
Implementation Notes
See the attached document below for helpful hints and tips for the instructor.
Time Required
2-3 hours
Evaluation Methods

In their lab notebooks, students are asked to qualitatively and quantitatively analyze all of the diffraction patterns and relate these to the unit cells of the crystal dot patterns on the optical transform slide.  This report in their notebook is graded and is the first of several "notebook reports." 

In years when all of the students in the lecture portion of the course are also in the lab, I follow-up with a problem set question such as the one linked above under Related Activities (viewable to VIPEr users with approved Faculty status).

Evaluation Results

Students easily grasp the concept that distances in the diffraction pattern are inversely related to distances in the crystal. They also readily see that the rotational symmetry of the crystal is also observed in the diffraction pattern.

 Understanding systematic absences due to centering and glide plane symmetries is a more difficult concept for them to grasp.  In particular, they are often confused when I ask them to draw centered vs. primitive unit cells for a particular crystalline pattern and that this refers to the periodic array that is the "crystal" and not the diffraction pattern.  This is a case where asking a follow-up question on centered lattices and the effects on diffraction patterns can be particularly useful. 

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Elizabeth Jensen / Aquinas College

I used this as an in-class activity before a crystallography lab experience. I gave a short (60 minute) overview of x-ray crystallography, then had the students work through the activity together. I didn't have a laser, so I used red and green laser pointers held by a clamp on a ring stand. It was a little shaky, but it worked. In about 90 minutes or 2 hours, they finished measuring at least the first three patterns and then they calculated the lattice spacings of those. They were really impressed by being able to do that.

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