Consider A 2d Crystal Having A Square Lattice And One Atom Per Basis The Edge Length Of The Primitive Unit Cell Is A T 1 (61.79 KiB) Viewed 44 times
Consider A 2d Crystal Having A Square Lattice And One Atom Per Basis The Edge Length Of The Primitive Unit Cell Is A T 2 (67.4 KiB) Viewed 44 times
Consider a 2D crystal having a square lattice and one atom per basis. The edge length of the primitive unit cell is a. The sample size is A = L?, where L = Na is the sample length, and N » 1. (a) Sketch the reciprocal lattice and construct the first Brillouin zone. (b) What are the allowed values of q? If N (note that this is different from N) is the total number of unit cells in the crystal sample, how many allowed q's are there in the 1st B.Z.?
(c) Find the area in the reciprocal space that each allowed q occupies. (d) In a unit area of the reciprocal space, how many allowed q's are there? (e) Assume the atoms can only move within the plane of the lattice, how many branches do you expect in the phonon dispersion relation and what type of branches are they? Show how you arrive at your answer. (You don't need to solve the equations of motion.)
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