This preview shows page 1. Sign up to view the full content.
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...
View
Full
Document
This document was uploaded on 03/19/2014 for the course EECS 6.730 at MIT.
 Spring '03
 TerryOrlando

Click to edit the document details