Close-Packed Structures

Hexagonal Close Packing (HCP):

• Layer stacking: ABAB...
• Every third layer is directly above the first
• Unit cell has 6 atoms (full hexagonal cell)
• CN = 12, PE = 74%, c/a = 1.633 (ideal)
• Examples: Mg, Zn, Ti, Be

Cubic Close Packing (CCP = FCC):

• Layer stacking: ABCABC...
• Third layer is offset from both A and B layers
• Unit cell has Z = 4 atoms (cubic)
• CN = 12, PE = 74%
• Examples: Cu, Ag, Au, Al, Pt

Voids in Close-Packed Structures

For n close-packed atoms:

$\text{Octahedral voids} = n \quad \text{(one per atom)}$

$\text{Tetrahedral voids} = 2n \quad \text{(two per atom)}$

$\text{Total voids} = 3n$

Geometry of voids:

• Tetrahedral void: formed between 3 atoms in one layer and 1 atom in adjacent layer (or vice versa); 4-coordinate; radius ratio $r^{+}$/$r^{-}$ = 0.225
• Octahedral void: formed between 3 atoms in lower layer and 3 atoms in upper layer; 6-coordinate; radius ratio $r^{+}$/$r^{-}$ = 0.414

Mnemonic: "One-Oct, Two-Tet"

• n atoms → n octahedral + 2n tetrahedral