Crystals, lattices, phonons

Question 1

What is a crystal?

Answer 1

Crystal is a material consisting of atoms or molecules arranged in a regular lattice
extending in all three dimensions

Question 2

What are the types of crystals?

Answer 2

Body centred cubic
Face centred cubic
Diamond structure
Perovskites
Layered materials

Question 3

How can we predict crystals structures?

Answer 3

Approximate atoms as hard spheres

A plane of spheres naturally packs in a hexagonal array

Two planes can fit nearly on top of each other neatly

There are two non-identical way of placing the third plane this leads to either ent crystal structures:
Hexagonal close packing (HCP) or
Face centred cubic packing (FCC)

Question 4

What is the HCP structure?

Answer 4

Regular alternation
of planes
Unique threefold
symmetry axis and basal
plane

Question 5

What is the FCC Structure ?

Answer 5

Regular alternation
of planes
Cube with an atom at
each corner, and at the centre of each face

Question 6

How to calculate the packing fraction?

Answer 6

Use the hard sphere approximation

Packing fraction = volume of atoms/total volume of the crystal