Crystal structures describe the repeating 3D arrangement of atoms inside solid materials, especially metals, ceramics, and semiconductors. Engineers care about crystal structure because it strongly affects strength, ductility, density, melting behavior, and how a material fails. The three common metal structures are body-centered cubic, face-centered cubic, and hexagonal close-packed.
Learning to compare BCC, FCC, and HCP helps connect atomic-scale geometry to real material performance.
A unit cell is the smallest repeating block that builds the crystal, and its geometry determines how tightly atoms pack and how many neighbors each atom touches. Atomic packing factor measures the fraction of the unit cell volume filled by atoms, while coordination number counts nearest neighbors. FCC and HCP both pack atoms very efficiently, but their different stacking patterns affect slip and ductility.
BCC is less densely packed, yet many BCC metals are strong and useful because their crystal structure influences dislocation motion.
Key Facts
- BCC has atoms at 8 corners plus 1 atom at the body center, giving 2 atoms per unit cell.
- FCC has atoms at 8 corners plus 6 face-centered atoms, giving 4 atoms per unit cell.
- HCP has a hexagonal unit cell with close-packed layers in an ABAB stacking sequence.
- Atomic packing factor: APF = volume of atoms in unit cell / total unit cell volume.
- Typical APF values: BCC = 0.68, FCC = 0.74, HCP = 0.74.
- Coordination numbers: BCC = 8, FCC = 12, HCP = 12.
Vocabulary
- Unit cell
- The smallest repeating 3D block that represents the pattern of atoms in a crystal.
- Body-centered cubic
- A cubic crystal structure with atoms at the corners and one atom at the center of the cube.
- Face-centered cubic
- A cubic crystal structure with atoms at the corners and at the centers of each cube face.
- Atomic packing factor
- The fraction of a unit cell's volume that is occupied by atoms modeled as hard spheres.
- Slip system
- A combination of a slip plane and slip direction along which dislocations can move in a crystal.
Common Mistakes to Avoid
- Counting each corner atom as one full atom, which is wrong because a corner atom is shared by 8 neighboring unit cells and contributes only 1/8 to one cell.
- Assuming FCC and HCP are identical because both have APF = 0.74, which is wrong because their stacking sequences and available slip systems differ.
- Confusing coordination number with atoms per unit cell, which is wrong because coordination number counts nearest neighbors around one atom, not the atoms contained in one cell.
- Saying higher packing always means higher strength, which is wrong because strength also depends on bonding, defects, grain size, temperature, and dislocation motion.
Practice Questions
- 1 A BCC unit cell has 8 corner atoms and 1 body-center atom. Using 1/8 contribution for each corner atom, calculate the total number of atoms per BCC unit cell.
- 2 An FCC unit cell has 8 corner atoms and 6 face-centered atoms. Using 1/8 contribution for each corner atom and 1/2 contribution for each face atom, calculate the total number of atoms per FCC unit cell.
- 3 FCC metals such as aluminum and copper are often very ductile at room temperature, while many HCP metals are less ductile. Explain how slip systems and crystal geometry help account for this difference.