Face-Centered Cubic (fcc) Crystal Structures
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Face-centered cubic (fcc) crystals are common among metals at low temperatures because the atoms pack well. Steels are body-centered cubic at low temperatures and face-centered cubic at high temperatures. For FCC and HCP systems, the coordination numbers are 12, while for BCC it’s 8. Assuming a hard sphere model, atomic packing factor is defined as the ratio of atomic sphere volume to unit cell volume, which is 74% for both FCC and HCP and 68% for BCC. In general, ~90% elemental metals crystallize into three crystal structures which are BCC, FCC, and HCP.

Table 2872a. Some normalized surface energies of low-index surfaces of fcc.


Table 2872b lists the characteristics of the three cubic Bravais lattices.

Table 2872b. The only three cubic Bravais lattices.

Number of
lattice points
per unit cell
Number of
atoms per unit cell
Nearest distance
between lattice points
Maximum packing
Maximum packing condition
Density (or fraction of packing, Vatom/Vcell)
1 1 Nearest distance When the adjacent atoms touch each other along the edge
of the cube
2 2 Nearest distance When the adjacent atoms touch each other along the body diagonal of the cubic cell 68.0%
4 4 Nearest distance When the adjacent atoms touch each other along the face diagonal of the cubic cell 74.0%
4 8 Nearest distance 34 %

For FCC and BCC structures, the lattice constants are given by, (For FCC, you can download the excel file for your own calculations)

         Phase Identification with XRD and its Procedure ----------------- [2872]

Table 2872c. Other characteristics of FCC structures.

Close packed planes and directions page3029
Atomic packing factor page3030
Number of lattice points (atoms) per unit cell page3032
Lattice point (or called Motif or basis) page3076
Coordination number of atoms page3031
Space groups Fm-3m (225), F4-3m (216), Fd-3m (227), Pm-3m (221)
d-spacing ratios of allowed Bragg reflections 1, √3, √4, √8, √11, √12, √16, √19, √20, √24, √27, ...
Tables of Burgers vectors of dislocations and g·b page1995
Dominating slip planes, slip directions and stable Burgers vector for common crystal structures page3557
Digital Micrograph script to compute reflection angle Script link

Atomic structure of FCC

Figure 2872a. Atomic structure of FCC.