Definitions and Equations

Crystalline materials:

• materials that have atoms that are situated in a repeating or periodic array over large atomic distances

• long-range order exists, such that upon solidification, the atoms will position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest neighbour atoms.

• Schematic of Crystalline material:

Metallic crystal structures

• Bonding is metallic and non-directional

  • Therefore, the nearest neighbour distances tend to be small in order to lower bond-energy

  • Sea of negative electrons hold together the positive metal ions

  • Shielding essentially blocks the repulsive Coulomb forces between the positive charges

  • Metal atoms pack together to maximise the shielding effect

  • Metallic structures have the simplest crystal structures and dense atomic packing

Atomic Packing Factor (APF)

• • The fraction of solid volume within 1 unit cell

Theoretical Density

• • The density taken by ideal atom/material with no cracks or impurities (this is a maximum)

Number of atoms for a cube unit cell (e.g FCC, BCC)

Number of atoms for a HCP unit cell

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