An FCC unit cell has 8 corner atoms and 6 face-center atoms. How many atoms does one FCC unit cell contain?
A14 — count all corner and face atoms directly
B2 — 8×(1/8) + 6×(1/2) is incorrect; it should be 1
C4 — 8×(1/8) + 6×(1/2) = 1 + 3 = 4
D6 — only face atoms are counted since they are shared between two cells
Each corner atom is shared among 8 unit cells, contributing 1/8 per cell. Each face-center atom is shared between 2 unit cells, contributing 1/2 per cell. Total = 8×(1/8) + 6×(1/2) = 1 + 3 = 4 atoms per unit cell. This is the correct count for FCC, and it feeds directly into calculating atomic packing factor and theoretical density.
Question 2 True / False
HCP (hexagonal close-packed) is one of the 14 Bravais lattices.
TTrue
FFalse
Answer: False
HCP is NOT one of the 14 Bravais lattices. It is a hexagonal Bravais lattice with a two-atom basis — one atom at the corner/face positions and one offset inside the cell. The distinction matters: a Bravais lattice is a set of translation vectors describing periodicity, while a crystal structure is a Bravais lattice plus a basis (the pattern of atoms placed at each lattice point). HCP has hexagonal symmetry but requires two atoms per lattice point to describe the actual arrangement.
Question 3 Short Answer
What does the coordination number of an atom in a crystal structure tell you, and how does it differ between BCC and FCC?
Think about your answer, then reveal below.
Model answer: Coordination number is the number of nearest-neighbor atoms surrounding a given atom. In BCC, each atom has 8 nearest neighbors (the 8 corners surrounding the body-center atom). In FCC, each atom has 12 nearest neighbors. Higher coordination number means more nearest neighbors and generally a higher atomic packing factor.
Coordination number describes the local geometry around each atom — how many atoms it directly touches. FCC (coordination 12) is more densely packed than BCC (coordination 8), which is why FCC has a higher atomic packing factor (0.74 vs 0.68). Coordination number influences physical properties like ductility, diffusion rates, and how easily atoms can slip past each other during deformation.