In an edge-centered cubic unit cell, also known as a face-centered cubic (FCC) unit cell, there are a total of four atoms. This arrangement consists of atoms at the eight corners of the unit cell and an additional atom centered in each face of the unit cell.
Let's break it down:
Corners: Each corner atom is shared among eight adjacent unit cells, so the contribution of each corner atom to the unit cell is 1/8. Since there are eight corners in total, the total contribution of corner atoms is 8 * (1/8) = 1 atom.
Faces: Each face atom is shared among two adjacent unit cells, so the contribution of each face atom to the unit cell is 1/2. Since there are six faces in total, the total contribution of face atoms is 6 * (1/2) = 3 atoms.
Adding the contributions from corners and faces together, we get 1 atom from corners + 3 atoms from faces = 4 atoms in total in an edge-centered cubic unit cell.