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Face-Centered Cubic (FCC)

Reviewed by Raghvendra GopalCheckmark | Last updated: June 16, 2022

What Does Face-Centered Cubic (FCC) Mean?

Face-centered cubic (also known as FCC, cF, cubic close-packed or CCP) is the name given to a type of atom arrangement found in nature. A face-centered cubic unit cell structure consists of atoms arranged in a cube where each corner of the cube has a fraction of an atom with six additional full atoms positioned at the center of each cube face.

The atoms at the corner of the cube are shared with eight other unit cells. As such, each corner atom represents one-eighth of an atom.

The atoms at each face of the unit cell are shared with adjacent unit cells; therefore, each face atom represents half of an atom.

Using this concept, the total number of atoms in the FCC unit cell structure is four: six halves at each of the faces plus eight one-eighth atoms at the corners. This is illustrated in the equation below:

(1/2 atoms x 6 faces) + (1/8 atoms x 8 corners) = 4 atoms

The atoms in the FCC unit cell arrangement are packed closer than other cell arrangements (such as the body-centered cubic [BCC], which is the simple unit cell arrangement). Due to their packing arrangement, FCC metals are typically softer and more ductile than their BCC counterparts, which may be an important factor when selecting materials for a given application.

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Corrosionpedia Explains Face-Centered Cubic (FCC)

Metal atoms naturally pack themselves in a close arrangement to form the strongest metallic bond possible. In nature, several packing arrangements are possible, including the face-centered cubic arrangement.

One of FCC's defining features is that atoms are packed as close together as theoretically possible; the atoms from one layer nest themselves snugly into the empty space of each adjacent layer.

This close packing arrangement is quantified in FCC’s packing density.

Some metals that possess this crystalline structure include aluminum, gold, lead, platinum, iridium and silver.

Packing Density

The packing density, also known as the atomic packing factor (APF), is essentially the fraction of the volume of atoms that occupy a crystal structure.

An FCC structure's APF is equal to the volume of the atoms in the unit cell divided by the volume of the unit cell.

Therefore:

APFFCC = Vatoms/Vunit cell

Because each atom is represented as a sphere and the unit cell is a cube:

APFFCC = n·Vsphere/Vcube (where n = number of atoms calculated previously)

APFFCC = (4 x 4/3πr3)/a3

To further break this down, we can express “a” in term of “r”.

Using the Pythagorean Theorem: a2 + a2 = (4r)2

Solving for “a” we get, a = 2√2.r

Taking this result for “a” and putting it back into the formula for APF, the equation becomes:

APFFCC = (4 x 4/3πr3)/ (2√2.r)3

Cancelling common terms, we get APFFCC = 0.74. In other words, 74% of the volume of the unit cell is occupied by atoms. This value is referred to as close-packed because it is not possible to pack the atoms any closer to achieve a higher APF. Some metals that possess face-centered cubic structure include copper, aluminum, silver, and gold.

For iron, the lattice arrangement is a unit cube with eight iron atoms at its corners. Allotropy of iron is important in steels—that is, its existence in two crystalline forms. In case of body-centred cubic (BCC) arrangement, there is an additional iron atom in the centre of each cube. In the face-centred cubic (FCC) arrangement, there is one additional iron atom at the centre of each of the six faces of the unit cube.

It is noteworthy that the sides of the face-centred cube, or the distances between neighbouring lattices in case of FCC structure, are about 25% larger than in the BCC arrangement. This means there is more space in the FCC than in the BCC structure to keep foreign (i.e., alloying) atoms in solid solution.

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Synonyms

cF, Cubic Close-Packed (ccp), FCC, CCP

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FabricatorsMaterials SelectionScientific PropertiesPhysical Property Chemical Property Metals

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