Lattice Structures Part 1

Lattice types

Simple cubic (SC)

• Atoms at the eight cube corners.
• Corner atoms contribute 1/8 each → 8 × (1/8) = 1 atom per unit cell.
• Atoms touch along cube edges.
• Coordination number: 6.

Body-centered cubic (BCC)

• Atoms at the eight corners plus one atom at the cube center.
• Equivalent atoms per unit cell: 8 × (1/8) + 1 = 2.
• Atoms touch along the body (cube) diagonal; the center atom contacts the corner atoms.
• Coordination number: 8.

Face-centered cubic (FCC)

• Atoms at the eight corners plus one atom centered on each of the six faces.
• Equivalent atoms per unit cell: 8 × (1/8) + 6 × (1/2) = 4.
• Atoms touch along the face (side) diagonal.
• Coordination number: 12.

Fractional atom contributions in unit cells

• Corner atom: 1/8 of that atom lies inside a given unit cell.
• Face-centered atom: 1/2 of that atom lies inside a given unit cell.
• Body-centered atom: 1 (entire atom) lies inside the unit cell.

Coordination number

The coordination number is the number of atoms that a given atom touches in the lattice. In an ideal lattice, this number is the same for any atom of the same type.

Close-packed structures

• In a single close-packed layer, each atom is surrounded by six neighbors.
• No two close-packed layers lie directly on top of one another; atoms in an upper layer occupy the dimples formed by three atoms in the layer beneath.

Hexagonal close-packed (HCP)

• Stacking: ABAB… (every other layer is identical).
• Each atom sits in a dimple formed by three atoms in the previous layer.

Cubic close-packed (CCP / FCC)

• Stacking: ABCABC… (every third layer is identical).
• CCP stacking produces the same arrangement as the FCC lattice.
• Occupancy and coordination are the same as FCC: 4 atoms per unit cell and coordination number 12.

Geometric contact directions

• SC: contact along cube edges.
• BCC: contact along cube (body) diagonals (corner ↔ center).
• FCC/CCP: contact along face (side) diagonals.

Researchers / sources featured

• None mentioned.