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 radiation Radiation 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