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Crystalline solids are characterized by long-range periodic atomic arrangements described by a unit cell — the smallest repeating unit of the lattice. The 14 Bravais lattices classify all possible 3D periodic arrangements, with metals commonly adopting FCC, BCC, or HCP structures. Knowing a crystal structure allows calculation of atomic packing factor, theoretical density, and coordination number. These structural details directly determine many physical and mechanical properties of the material.
Build physical or digital models of FCC, BCC, and HCP unit cells and calculate the number of atoms per cell, coordination number, and packing factor for each. Reinforce by working backward from density measurements to confirm crystal structure.
You already know from atomic structure that atoms bond through electron interactions, and from bonding theory that the bond type (metallic, ionic, covalent) determines many of a material's properties. In crystalline solids, those atoms are not randomly arranged — they settle into highly ordered, periodic patterns that repeat in all three dimensions. The unit cell is the fundamental repeating unit: a small box that, when stacked together filling all of space, recreates the entire crystal. Every property derivable from a crystal structure — density, packing efficiency, slip planes for plastic deformation — comes from understanding the unit cell.
The three structures you will encounter most in metals are BCC (body-centered cubic), FCC (face-centered cubic), and HCP (hexagonal close-packed). BCC has one atom at each corner and one at the center of the cube. FCC has one at each corner and one at the center of each face. HCP stacks hexagonal layers with an offset middle layer. A critical skill is counting atoms per unit cell correctly: corner atoms are shared among 8 unit cells (count 1/8 each), edge atoms among 4 (count 1/4), face atoms between 2 (count 1/2), and body-center atoms belong entirely to one cell (count 1). For FCC: 8×(1/8) + 6×(1/2) = 4 atoms per cell.
The atomic packing factor (APF) measures what fraction of the unit cell volume is occupied by atoms, treating atoms as hard spheres touching at the closest approach. FCC achieves APF = 0.74, which is the theoretical maximum for equal sphere packing. BCC achieves 0.68. Both FCC and HCP achieve 0.74 — they are both "close-packed" structures, just with different stacking sequences (ABCABC for FCC, ABABAB for HCP). Materials with higher APF are denser and typically harder to compress.
One of the most important conceptual distinctions is between the lattice and the basis. The lattice is an abstract set of geometric points — it has no chemistry, just spatial repetition. The basis is the atom (or group of atoms) placed at each lattice point. The crystal structure = lattice + basis. For most simple metals, the basis is a single atom and the distinction is trivial. But for HCP, the basis is two atoms, which is why HCP is not itself a Bravais lattice — the hexagonal Bravais lattice plus a two-atom basis generates the HCP arrangement. Getting this distinction right is essential when you encounter more complex structures like ceramics or intermetallics.
These structural details directly drive material properties. FCC metals (aluminum, copper, gold) are generally more ductile than BCC metals (iron at room temperature, tungsten) because their close-packed planes can slide more easily — there are more equivalent slip systems. Coordination number affects bond strength and melting point. Theoretical density calculated from the unit cell (density = nA / VₙNₐ, where n is atoms per cell, A is atomic mass, Vₙ is cell volume, Nₐ is Avogadro's number) is a quick experimental check of crystal structure — if your measured density matches the FCC calculation but not BCC, you have evidence for the structure.