Which unit cell type has atoms at the corners and centers of all faces?

Which unit cell type has atoms at the corners and centers of all faces?

• A. Simple Cubic
• B. Body-Centered Cubic
• C. Hexagonal Close-Packed
• D. Face-Centered Cubic

Answer: (D)

This arrangement has atoms at the corners and on the centers of all faces, which identifies it as the face-centered cubic lattice. In this structure, each corner atom is shared among eight neighboring unit cells, contributing 1/8 of an atom per corner, so 8 corners give 1 total. Each of the six faces has an atom centered on it, and that atom is shared by two cells, contributing 1/2 of an atom per face, so 6 faces give 3 total. Altogether, there are 4 atoms per unit cell. This configuration leads to a very high packing efficiency (about 74%) and a coordination number of 12, reflecting its dense, tightly packed nature. Other lattices place atoms differently: a simple cubic lattice has atoms only at corners, a body-centered lattice adds a single atom in the center but not on face centers, and hexagonal close-packed is not a cubic arrangement and uses a different stacking pattern.

This arrangement has atoms at the corners and on the centers of all faces, which identifies it as the face-centered cubic lattice. In this structure, each corner atom is shared among eight neighboring unit cells, contributing 1/8 of an atom per corner, so 8 corners give 1 total. Each of the six faces has an atom centered on it, and that atom is shared by two cells, contributing 1/2 of an atom per face, so 6 faces give 3 total. Altogether, there are 4 atoms per unit cell.

This configuration leads to a very high packing efficiency (about 74%) and a coordination number of 12, reflecting its dense, tightly packed nature. Other lattices place atoms differently: a simple cubic lattice has atoms only at corners, a body-centered lattice adds a single atom in the center but not on face centers, and hexagonal close-packed is not a cubic arrangement and uses a different stacking pattern.