Crystal Structures of Metals (Face-Centered Cubic)

Description

Metals are crystallized in four crystal structures: simple cubic (sc); body-centered cubic (bcc); face-centered cubic (fcc) or cubic-close-packing (ccp); and hexagonal-close-packing (hcp).
Face-centered cubic (fcc) system (or cubic close-packed or ccp) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell (1⁄8 × 8 from the corners plus 1⁄2 × 6 from the faces). The lattice is not a primitive one since there are 4 lattice points (atoms) per unit cell, one at the vertices (one eighth at each vertex) and three other on the 6 faces. The lattice constant can be calculated by the radius of the atom. Lattice constants have the dimension of length, their SI unit is the meter. Lattice constants are typically on the order of several angstroms (i.e. tenths of a nano-metre).
For face-centered cubic and body-centered cubic lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions. For face-centered (fcc) cubic crystals, the primitive cell is a parallelepiped or rhombohedron, respectively, but the conventional unit cell used to describe these structures is a simple-cubic supercell.

Related formulas

Variables

αLattice constant (Å)
rAtomic radius (Å)