What is the characteristic of a face-centered unit cell?

A face-centered unit cell is a type of crystal lattice structure where atoms are located at each of the corners and at the centers of each of its faces. To understand why it contains four lattice points per unit cell, we can analyze how the lattice points are counted.

In a face-centered cubic (FCC) unit cell, there are atoms at the eight corners of the cube. Each corner atom is shared among eight neighboring unit cells, contributing 1/8 of an atom to the unit cell. Thus, the contribution from the corner atoms is:

8 corners x (1/8) = 1 atom.

Additionally, there are six faces, and each face has one atom that is shared between two unit cells, contributing 1/2 of an atom per face to the unit cell. Therefore, the contribution from the face-centered atoms is:

6 faces x (1/2) = 3 atoms.

When you add these contributions together, the total number of lattice points in a face-centered cubic unit cell is:

1 (from corners) + 3 (from faces) = 4 lattice points.

This combined counting helps clarify why the face-centered unit cell is characterized by having four lattice points, confirming that the answer provided is indeed correct.