A unit cell is the smallest repeating arrangement of atoms that, when stacked in three dimensions, builds the entire crystal. It is defined by edge lengths and angles (lattice parameters). The three most common metallic unit cells are body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP).

What is the atomic packing factor?

The atomic packing factor (APF) is the fraction of a unit cell's volume occupied by atoms, treating them as hard spheres. FCC and HCP are close-packed with an APF of 0.74 (the densest possible packing of equal spheres), while BCC has an APF of 0.68. A higher APF generally means a denser, often more ductile metal.

Why are FCC metals usually more ductile than HCP metals?

Ductility depends on the number of slip systems — combinations of close-packed planes and directions on which dislocations can move. FCC metals have 12 slip systems, giving abundant ways to deform plastically, so they are very ductile. HCP metals have far fewer active slip systems, so they tend to be less ductile and more prone to cracking.

What are Miller indices used for?

Miller indices are a notation for identifying planes and directions within a crystal. Directions are written in square brackets [hkl] and planes in parentheses (hkl), derived from the reciprocals of where the plane intercepts the axes. They let engineers specify exactly which crystallographic plane slip, cleavage, or growth occurs on.

What is a dislocation and why does it matter?

A dislocation is a line defect — an extra half-plane of atoms (edge dislocation) or a spiral ramp of atoms (screw dislocation) within the crystal. Dislocations are crucial because plastic deformation happens by dislocations gliding through the lattice. Their motion explains why real metals yield at stresses thousands of times lower than a perfect crystal would, and blocking their motion is how we strengthen metals.

Engineering·12 min read·February 18, 2025

🧊 Crystal Structures: BCC, FCC, HCP & Defects

Understand crystal structures in materials science — unit cells, BCC, FCC and HCP geometry, atomic packing factor and coordination number, Miller indices, and point, line and planar defects.

📖Materials Science & Metallurgy Handbook (Full Access)

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Why Atomic Arrangement Matters

The properties of a metal — its strength, ductility, density, and how it deforms — trace directly to how its atoms are arranged. Most engineering metals are crystalline: their atoms sit in a regular, repeating three-dimensional pattern. Understanding that pattern, and the defects within it, is the foundation of physical metallurgy.

Topics covered

crystal structureunit cellBCCFCCHCPatomic packing factorcoordination numberMiller indicescrystallographydislocationspoint defectsline defectsgrain boundaryvacancy