Rotation Matrices and Translation Vectors in Crystallography

S. Hovmöller

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• 1. Rotation Matrices and Translation Vectors
• 2. The Structure Factor
• 3. Special Reflections
• 4. Phase Restrictions
• 5. Systematic Absences
• 6. Systematic Enhancement, Epsilon
• 7. Phase Shifts
• Suggestions for Further Reading

Teaching Aims

To show how rotation matrices and translation vectors can make a useful contribution to the understanding of symmetry in real space and its implications in reciprocal space.

Level

This approach would be most useful for students who already have some acquaintance with crystallography in undergraduate courses.

Background

The text is self-contained but assumes familiarity with complex numbers and some knowledge of vectors and matrices, e.g. multiplication of row and column vectors or of two matrices.

Practical Resources

No specific practical resources are required.

Time Required for Teaching

This text could be worked through on a self-teaching basis in perhaps four or five hours.

Copyright © 1981, 1998 International Union of Crystallography