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 n5 κ=π/a n4 n3 B B: k=1.3π/a κ=2π/a κ n2 n1 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 n5 n4 n3 n2 n1 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 longwavelength, we should recover the continuum model… Linear dispersion, just like the sound waves for the continuum solid...
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 Spring '03
 TerryOrlando
 Reciprocal lattice, Brillouin zone, nearest neighbor interactions, discrete lattice

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