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Unformatted text preview: x,y ) about an axis through the origin that forms an angle with the xaxis. Show that the matrix form of this operation is cos(2 ) sin(2 ) sin(2 )cos(2 ) ! Hint: An ecient way of nding the matrix consists in rotating the lattice such that the reection axis coincides with the xaxis, performing the reection, and rotating back! Problem 3: Allowed rotation axes (15 points, Marder  Problem 1.4) Prove that the only allowed rotation axis in a twodimensional Bravais lattice are twofold, threefold, fourfold, and sixfold! To this end, consider the images of the lattice point ( a, 0) under rotations around the origin by angles and . Both must be in the Bravais lattice! From these conditions derive a simple expression that implicitly species all possible ....
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This note was uploaded on 10/04/2011 for the course PHYSICS 481 taught by Professor Thomasvojta during the Spring '11 term at Missouri S&T.
 Spring '11
 ThomasVojta
 Physics, Work

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