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Face Centered Cubic


The face-centered cubic unit cell is a cube (all sides of the same length and all face perpendicular to each other) with an atom at each corner of the unit cell and an atom situated in the middle of each face of the unit cell.
The unit cell completely describes the structure of the solid, which can be regarded as an almost endless repetition of the unit cell.

The volume of the unit cell is readily calculated from its shape and dimensions. This calculation is particularly easy for a unit cell that is cubic. In the case of the face-centered cubic unit cell, the atoms lying along the diagonal of each face are in c
ontact with each other. Thus the diagonal of each face has a length of 4 r, where r is the radius of an atom.


Atoms, of course, do not have well-defined bounds, and the radius of an atom is somewhat ambiguous. In the context of crystal stru
ctures, the diameter (2 r) of an atom can be defined as the center-to-center distance between two atoms packed as tightly together as possible. This provides an effective radius for the atom and is sometime called the atomic radius.

A more challenging task is to determine the number of atoms that lie in the unit cell. As described above, an atom is centered
on each corner and in the middle of each face of the unit cell. None of these atoms lies completely within the unit cell. Each atom exists partially inside the unit cell and partially outside the unit cell. In determining the number of atoms inside the unit cell, one must count only that portion of an atom that actually lies within the unit cell.

The density of a solid is the
mass of all the atoms in the unit cell divided by the volume of the unit cell.

Number of
Atoms in FCC Unit Cell















Packing Efficiency of FCC

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