1.3 Crystal Dynamics

Question 1

How do we model a crystal?

Answer 1

As masses on a spring

Question 2

What is significant about the pattern of the BZ?

Answer 2

It is periodic in k space

Question 3

What is the relation about the period of real space and space?

Answer 3

A system which is periodic in real space will be periodic in k space with a period of 2pi/a

Question 4

Define the BZ

Answer 4

A periodic unit in k space

Question 5

Define the reciprocal lattice

Answer 5

A set of points in k space which are equivalent to k = a

Question 6

What is a phonon?

Answer 6

A discrete quantum of vibration (similar to photon for light)

Question 7

How can we define the crystal momentum in an atom?

Answer 7

By using p = hbar k

k is the crystal momentum as k -> k+ 2pi/a, so the momentum is defined within the first BZ

Question 8

Describe how we can make a simple model for an ionic crystal

Answer 8

Have a periodic arrangement of two different atoms on chains, with “a” being the separation between them

Question 9

When can a phonon absorb a photon?

Answer 9

When photons have a very small k (w = ck) and phonons have a finite w
Acoustic phonons have low energy for a small k, so therefore must excite an optical phonon

Question 10

For n atoms in a primitive unit cell, how many modes do we get for each value of k?

Answer 10

• 1 acoustic mode where masses move in the same direction

- n-1 optical modes

Question 11

In d dimensions, how many modes do we get for each value of k in a primitive unit cell?

Answer 11

• d acoustic modes

- d(n-1) optical modes