Part 2 (Phonons)

Question 1

Why is there a maximum energy in phonon dispersion relation?

Answer 1

Phonons have no maximum wavelength but minimum is set by lattice spacing a

Question 2

What is the Brillouin zone?

Answer 2

It represents Bragg planes which reflect (diffract) waves having particular wave vectors so that they cause constructive interference.

Question 3

How can any k vector be mapped back into the Brillouin zone?

Answer 3

By adding or subtracting integer multiples of 2pi/a (aliasing)

Question 4

What does Einstein’s model of specific heat assume?

Answer 4

A solid is formed by N atoms, each an independent quantum oscillator

Question 5

How is the Debye model of specific heat different to Einstein’s?

Answer 5

Debye included the interactions that Einstein left out

Question 6

What does the speed of sound and Debye temperature relate to?

Answer 6

How stiff a lattice is (higher the Debye temp the stiffer the lattice)

Question 7

What assumption can be made about phonon scattering?

Answer 7

Above the Debye temperature, number of number density of phonons will be roughly the same as number density of atoms