Lecture 8 Flashcards
Classically, what values can the amplitude and energy of a vibrational mode take?
Any value
Quantum mechanically, what values can the energy of a vibrational mode with angular frequency, ω, take?
n = positive integer
What is a phonon?
A quantum of vibrational energy.
Are phonons bosons or fermions?
Bosons
How can the energy of a mode occupied by n phonons of energy ℏω change?
It can change by integer multiples of ℏω
What momentum do phonons behave like they have?
p = ℏk
Give the equation for the change in wavevector when a particle is elastically scattered into a new state by absorbing or emitting a phonon
k’ = new state wavevector
k = wavevector
G = reciprocal lattice vector
Give the equation for the change in wavevector when a particle is inelastically scattered into a new state by absorbing or emitting a phonon
k’ = new state wavevector
k = wavevector
K = phonon wavevector
G = reciprocal lattice vector
Give the equation for the change in energy due to x-ray photon diffraction
k = photon wavevector
k’ = new state photon wavevector
K = phonon wavevector
How does inelastic scattering of an x-ray photon occur?
The x-ray is diffracted and scatters which either absorbs or emits a photon.
What is a thermal neutron?
A neutron whose energy is ~kT
Give the equation for the energy of a neutron
Give the equation for the energy of a phonon
Give the equation for the total thermal energy of a solid consisting of N atoms acting as independent classical harmonic oscillators.
U = total thermal energy
Give the equation for the specific heat of a solid containing N atoms acting as independent classical harmonic oscillators
Describe the change in the measured specific heat of copper with temperature
State the Bose-Einstein distribution
Give the equation for the total thermal energy for a crystal
Describe the shape of the curve for the Debye model for specific heat
Give the equation for the specific heat using the Debye model
