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Rotations, reflections, translations for Diamond Structure

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Please help with the following problems.

The Bravais lattice of the diamond structure is fcc with two carbon atoms per primitive unit cell. If one of the two basis atoms is at (0,0,0), then the other is at (1/4,1/4,1/4).

(a) Illustrate that a reflection through the (100) plane followed by a non-primitive translation through [1/4,1/4,1/4] is a glide-plane operator for the diamond structure.

(b) Illustrate that a fourfold rotation about an axis in diamond parallel to the x-axis passing through the point (1,1/4,0) (the screw axis) followed by the translation [1/4,0,0] parallel to the screw axis is a screw operation for the diamond structure.

Please explain as clearly as possible.

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Solution Summary

This solution discusses rotations, reflections and translations for a diamond structure. It helps illustrate a reflection through a plane followed by a non-primitive translation and a fourfold rotation about an axis. Step by step explanations with diagrams are provided.

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