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Materials Science 142
Applications of Diffraction Techniques

Laboratory Exercises 1: Point Group Symmetry

Assigned: 1/11/12
Due:1/18/12, 5pm

Goal: Identify the point group and crystal system of a high symmetry object. Seven objects are to be analyzed.

  1. List and identify the symmetry elements in each. For example, when describing the cube, state "mirror plane in (110)", or make drawings of the faces of the cube with the symmetry elements shown.
  2. Identify the point group of each object.
  3. Identify to which crystal system each of the models must belong.


Turn in a description of the symmetry elements in each object, the point group of the object, and the appropriate crystal system. Make sure your drawings are relatively neat and legible. A formal lab write-up is not required. If you were not in lab, or would like to get additional copies of the cut-out patterns for the 3-d objects, you can download them here (see below).

Textbook Problems:

Chapter 2: #1, #5, #6 (reproduced below)

1. Consider two mirror planes that intersect at f = 90°. Using a geometrical representation of two planes, establish which symmetry element(s) appear(s) as the result of this combination of mirror planes. What is(are) the location(s) of new symmetry element(s)? Name the point gorup symmetry formed by this combination of symmetry elements.
5. Determine both the crystal systems and point group symmetry of an ideal brick in which a =/= b =/= c and a = b = g = 90°.
6. Determine both the crystal system and point group symmetry of the benzene molecule, C6H6. Treat atoms as spheres, not dimensionless points.

Preparation for X-ray Data Analysis:

Install Origin Software. It can be downloaded from the company website A one-year student license can be purchased for $50. A sample ascii data file of diffraction data is available here. Plot this using properly label axes and provide a meaningful figure caption: “Figure 1. X-ray powder diffraction pattern collected from xxxx at xxx C using CuKa radiation (Panalytical X’Pert Pro) over the two-theta range xxx to xxx.” The material examined is Rb5H3(SO4)4, and data were collected at 190C.

Crystal Models (pdf files)

cube (gold)
cubo-octahedron (salmon)
pyritohedron (blue)
tetrahedron (green)
rhombohedron (purple)
bipyramidal crystal (rose)
dodecahedron - irregular (yellow)

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Last modified: January 11, 2012