Question

What is the edge length of a face-centred cubic unit cell if the radius of the atom is r?

Answer 1

In a face-centered cubic unit cell (FCC), atoms are located at the eight corners of the cube and the centres of all six faces.

In this structure, the atoms touch each other along the face diagonal of the cube. Let the edge length of the unit cell be aaa, and the atomic radius be r.

∴ The face diagonal of the cube = `sqrt 2 a`

Along this face diagonal, there are 2 atomic radii from each face atom and 1 atomic diameter (2r) in between, so

`sqrt 2 a` = 4 r

⇒ a = `(4 r)/sqrt 2`

= `2 sqrt 2r`

∴ The edge length a of a face-centred cubic unit cell in terms of the atomic radius r is a = `2 sqrt 2r`.