Week 5 Lattice Vibrations Flashcards
what are the two main dynamics of a solid
vibrational motion
motion of valence electrons
what is the Einstein model of lattice vibrations
vibrational motion of a lattice as many independent simple harmonic oscillators
what is unique of vibrations in solids
the lattice has both transverse and longitudinal vibrations
what is the longitudinal vibration relation in 1D chain equation
mω^2 = 4k(sin(ka/2))^2
what is the general rule for dealing with longitudinal vibrations of a diatomic chain
focus on the basis
view from perspective of both atoms
what is the dispersion (square) relation for a diatomic chain
ω^2 = K(M+m)/Mm +- K[μ^2 - 4Mm * (sin(ka/2))^2]^1/2
what are the small k conditions for the diatomic chain
for small k
ω^2 –> K(M+m)/Mm +- K(M+m)/Mm
ω = SQRT[2K/M] for + and 0 for -
what are the boundary conditions for the diatomic chain
as k –> π/a
ω^2 –> K(M+m)/Mm +- K(M-m)/Mm
ω = SQRT[2K/m] for + and SQRT[2K/M] for -
what do the +- solutions of diatomic chain lead to
+ upper band is optical
- lower band is acoustic
why is the upper band referred to as the optical band
optical band because it is the only one that responds to optical light
how many different vibrational modes are there in a single brillouin zone and where are they
4 different modes 1 peak of optical band 2 trough of acoustic band 3 at boundary of optical 4 at boundary of acoustic
what is true of transverse oscillations and what is the difference between acoustic and optical
vibrations are perpendicular to propagation
acoustic both atoms oscillate in phase
optical different classes of atoms vibrate out of phase
what is a phonon
quasi-particles corresponding to quantum states of vibrations
what is true of the energy of a normal mode of a lattice vibration and its equation
the energy is discrete
E(k) = (n + 1/2)ħω(k)
