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lecture_8c notes

We know about brillouin zones the points a and b

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Unformatted text preview: es the points A and B (related by a reciprocal lattice vector) must be identical This implies that the wave form of the vibrating atoms must also be identical. Strain in a Discrete Lattice Strain Example of Nearest Neighbor Interactions ω A: k=-0.7π/a κ=-2π/a κ=-π/a A n-5 κ=π/a n-4 n-3 B B: k=1.3π/a κ=2π/a κ n-2 n-1 n n+1 n+2 n+3 n+4 n+5 But: note that point B represents a wave travelling right, and point A one travelling left Strain in a Discrete Lattice Strain Example of Nearest Neighbor Interactions ω κ=-2π/a κ=-π/a c κ=π/a Consider point C at the zone boundary When k=π/a, λ=2a, and motion becomes that of a standing wave (the atoms are bouncing backward and forward against each other κ=2π/a κ λ=2a n-5 n-4 n-3 n-2 n-1 n n+1 n+2 n+3 n+4 n+5 Strain in a Discrete Lattice Strain Example of Nearest Neighbor Interactions In the limit of long-wavelength, we should recover the continuum model… Linear dispersion, just like the sound waves for the continuum solid...
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