Are FCC and HCP equally densely packed?

Yes for hard spheres: both reach η ≈ 0.74 with twelve nearest neighbors. They differ in stacking — ABCABC… (FCC) versus ABAB… (HCP) — which changes symmetry and slip systems, not the ideal packing fraction.

Why include BCC if it is not close-packed?

BCC is common in metals yet has lower packing fraction and coordination 8. Comparing it next to FCC/HCP prevents the misconception that all cubic metals are close-packed and clarifies what ‘close-packed’ specifically means.

Do real crystals match these hard-sphere η values?

Hard-sphere η is an ideal geometric limit. Real atomic radii, directional bonding, and temperature-dependent lattice parameters shift densities; the schematic still correctly ranks FCC/HCP above BCC for sphere packing.

Close Packing FCC / BCC / HCP

Coordination numbers, maximal packing η, schematic ABC vs AB stacking beside a BCC cubic cell.

About this model

This simulator compares close-packed crystal structures: face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC). It highlights coordination numbers, the maximal packing fraction η, and schematic ABC versus AB layer stacking beside a BCC cubic cell. FCC and HCP both achieve η = π/(3√2) ≈ 0.74 with coordination 12 but differ in stacking sequence; BCC is more open (coordination 8, lower η). The view is geometric and pedagogical: atoms are hard spheres, thermal vibrations and real bonding anisotropy are ignored. You switch among lattices to contrast stacking and packing efficiency — core solid-state and materials-chemistry intuition.

Who it's for: Introductory solid-state chemistry, materials science, and crystallography courses on metallic and ionic packing.

Key terms

Close packing
FCC
HCP
BCC
Coordination number
Packing fraction

How it works

FCC and HCP are two ways to stack close-packed planes with the same coordination (12) and maximal packing fraction η = π√2/6. BCC is denser than simple cubic but not close-packed (η = π√3/8, CN = 8).

Key equations

ABC stacking of hexagonal close-packed planes (…ABCABC…).

Frequently asked questions

Are FCC and HCP equally densely packed?: Yes for hard spheres: both reach η ≈ 0.74 with twelve nearest neighbors. They differ in stacking — ABCABC… (FCC) versus ABAB… (HCP) — which changes symmetry and slip systems, not the ideal packing fraction.
Why include BCC if it is not close-packed?: BCC is common in metals yet has lower packing fraction and coordination 8. Comparing it next to FCC/HCP prevents the misconception that all cubic metals are close-packed and clarifies what ‘close-packed’ specifically means.
Do real crystals match these hard-sphere η values?: Hard-sphere η is an ideal geometric limit. Real atomic radii, directional bonding, and temperature-dependent lattice parameters shift densities; the schematic still correctly ranks FCC/HCP above BCC for sphere packing.

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