Nanotechnology-Enabled Sensors

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Chapter 6: Inorganic Nanotechnology Enabled Sensors
The dispersion equation of a diatomic lattice has two roots (Fig. 6.34).
It has an acoustic branch and an optical branch. The frequency gap between
the acoustic branch and the optical branch is forbidden as the lattice
cannot transmit them. Therefore, a diatomic lattice can operate as a bandpass
mechanical filter.
-2π/a
n-1
-π/a
n n+1
Segment of a one-dimensional diatomic lattice
[2α(1/M1+1/M2)] 1/2
(4α/M2) 1/2
0 π/a 2π/a
Fig. 6.34 Segment of a one-dimensional diatomic lattice (top) and the dispersion
curve for a diatomic one-dimensional lattice (bottom). The curve is periodic. Mass
of one atom is different from the other (M1 < M2).
This upper branch in the dispersion curve is classified optical as the frequencies
of this branch can be approximated by (2α/M) 1/2 , which is approximately
3×10 13 s -1 which falls in infrared range.
Optical phonons occur in crystals with more than one type of atom in
the unit cell and are excited by infrared radiation. Optical phonons that interact
in this way with light are called infrared active. Optical phonons
which are Raman active can also interact indirectly with light, through
Raman scattering.
ω
a
(4α/M1) 1/2
k