Question

Problem 3.1 Prove that in two-dimensional Bravais lattices an $n$-fold rotation axis with $n = 5$ or $n \ge 7$ does not exist. Show first that the axis can be chosen to pass through a lattice point. Then argue by \"reductio ad absurdum\" using the set of points into which the nearest neighbor of the fixed point is taken by the $n$ rotations to construct a point closer to the fixed point than its nearest neighbor.

Name: Problem 3.1 Prove that in two-dimensional Bravais lattices an n-fold rotation axis with n = 5 or n ≥ 7 does not exist. Show first that the axis can be chosen to pass through a lattice point. Then argue by r̈eductio ad absurdumüsing the set of points into which the nearest neighbor of the fixed point is taken by the n rotations to construct a point closer to the fixed point than its nearest neighbor.
Uploaded: 2023-04-25T06:22:34-08:00
Duration: 2 min 18 s
Channel: Sri K

          Problem 3.1 Prove that in two-dimensional Bravais lattices an $n$-fold rotation axis with $n = 5$ or $n \ge 7$ does not exist. Show first that the axis can be chosen to pass through a lattice point. Then argue by \"reductio ad absurdum\" using the set of points into which the nearest neighbor of the fixed point is taken by the $n$ rotations to construct a point closer to the fixed point than its nearest neighbor.

Problem 3.1 Prove that in two-dimensional Bravais lattices an n-fold rotation axis with n = 5 or n ≥ 7 does not exist. Show first that the axis can be chosen to pass through a lattice point. Then argue by r̈eductio ad absurdumüsing the set of points into which the nearest neighbor of the fixed point is taken by the n rotations to construct a point closer to the fixed point than its nearest neighbor.

Added by Lisa M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

04/25/2023

Step 1

Step 1: Assume that there exists an n-fold rotation axis with n = 5 or n > 7 in a two-dimensional Bravais lattice. Show more…

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Problem 3.1 Prove that in two-dimensional Bravais lattices an n-fold rotation axis with n = 5 or n > 7 does not exist. Show first that the axis can be chosen to pass through a lattice point. Then argue by "reductio ad absurdum" using the set of points into which the nearest neighbor of the fixed point is taken by the n rotations to construct a point closer to the fixed point than its nearest neighbor.