Summary of "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.
Category
Science and Nature
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