Lesson 1, Topic 1
In Progress

# Atomic Packing Factor

##### Abdulaziz July 26, 2020

Maximum fraction of the volume in a unit cell occupied by the atoms.

• Assume that the atoms are closely packed and that they can be treated as hard spheres.
• This fraction is called atomic packing factor (APF) or packing density.

Eg. Calculate APF for the fcc (cubic closed packed) structure.

• Number of atoms per cell: 4
• Volume of each atom: 4/3 π R3
• Unit cell volume: a3 = (22R)3

number of atoms x volume of each atom / unit cell volume

## Atomic Packing factor for different structures

As expected, fcc has the highest apf since it is essentially a close packed structure which has the most efficient packing

## Crystal structure vs material properties

• Previous egs:
• carbon (CNT, graphite, diamond, C60)
• Si (amorphous, single crystal, polycrystalline)
• Fe (α, β, γ, δ, ε):
• ferrite (alpha iron) -forms below 770 °C (Curie point TC); becomes magnetic; BCC
• beta forms below 912°C ; BCC crystal structure
• gamma -forms below 1394 °C; FCC
• delta –forms from cooling down molten iron below 1538°C; BCC crystal structure
• epsilon –forms at high pressures
• Others: boron, Ge, tin all exist in different structures