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Crystal structures and packing

Most metals are crystalline, with atoms arranged in a regular lattice. The most common structures are BCC (body-centered cubic, like iron at room temperature), FCC (face-centered cubic, like aluminum), and HCP (hexagonal close-packed, like titanium). The atomic packing factor (APF) shows how much of the volume is filled by atoms.

APF=volume of atoms in the cellvolume of the unit cell\text{APF} = \frac{\text{volume of atoms in the cell}}{\text{volume of the unit cell}}atomic packing factor

Symbols

BCC\text{BCC}body-centered cubic, 2 atoms/cell, APF =0.68= 0.68
FCC\text{FCC}face-centered cubic, 4 atoms/cell, APF =0.74= 0.74
HCP\text{HCP}hexagonal close-packed, few slip systems

Example

3 unit cells of FCC structure (4 atoms/cell) contain 3⋅4=123\cdot 4 = 12 atoms in total.

FCC and HCP have the highest packing factor (0.740.74), but FCC has more slip systems and thus better ductility.
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Grain size and Hall–Petch →

Part of Materials Technology: Structure.