Body centered cubic

Note that each corner atom is in eight cubes so only 1/8 of the corner atom is in this cell

Number of atoms = 1 center + 8 x 1/8 corners = 2

in the unit cell

Face centered cubic

Eight atoms at the corners

Six atoms at the face centers

Each face atom is in two cubes

Number of atoms =

6 x ½ faces + 8 x 1/8 corners = 4

in the unit cell

Hexagonal close packed

This unit cell has the same packing as the fcc – WHY?

Stacking of hexagonal planes

First layer is labeled A

Two ways of placing 2nd layer:

Can use only 3 of the 6 “holes”, so have two sets:

Sites B or Sites C

Stacking of hexagonal planes (2)

Alternating sites A with sites B

leads to

Hexagonal close packed

Stacking of hexagonal planes (3)

Stacking of the sequence ABC

leads to

FCC

An oblique plane shows the hexagonal planes

Scattering of radiationRadiation absorbed by atoms is re-emitted in all directions

In-phase rays reinforce

Out-of phase rays annihilate each other

Rays out of phase by an exact number of wavelengths reinforce each other

Xray Diffraction

For certain specific angles of incidence rays re-emitted from two parallel planes of a crystal are out of phase by exactly multiple wavelengths (n)

Path difference between two rays shown is SQT. If SQT equals nλ reinforcement occurs and a diffracted beam is found. SQT = 2d sin where d is separation of planes