Crystal Structures — BCC, FCC, HCP & Unit Cells

The short answer: BCC, FCC, and HCP differ in where their atoms sit and how tightly they pack — FCC and HCP are both close-packed in the hard-sphere model, while BCC is not.

BCC vs FCC vs HCP at a Glance

For most introductory questions, this table separates the three structures quickly.

Reading Each Row

BCC (body-centered cubic): atoms at the eight cube corners plus one at the cube center. It is more open than a close-packed structure, so it does not pack spheres as tightly as FCC or HCP.

FCC (face-centered cubic): atoms at the eight corners plus one at the center of each of the six faces. It is close-packed in the hard-sphere model, with close-packed layers following an $ABCABC$ stacking sequence.

HCP (hexagonal close-packed): also close-packed, but built from hexagonal layers stacked $ABAB$ instead of $ABCABC$. So FCC and HCP can share the same ideal packing efficiency and coordination number even though their repeating cells differ in shape.

First, though, recall what a unit cell is: the repeating block that generates the full crystal by translation. It is not a private box of atoms. Atoms drawn on corners, faces, or edges are usually shared with neighboring cells, so a unit-cell picture shows the pattern, not a count of whole atoms — which is exactly what the next example relies on.

When to Reach for Each Structure

• Identify BCC when a diagram shows a single atom dead-center in a cube and you are told the structure is not close-packed.
• Identify FCC when atoms decorate the cube faces and the layers stack $ABCABC$.
• Identify HCP when the cell is hexagonal and the layers alternate $ABAB$.

The cleanest discriminator between the two close-packed structures is not density — both reach an atomic packing factor near $0.74$ — but the stacking sequence.

Worked Example: Atoms in an FCC Unit Cell

FCC makes atom sharing obvious, so it is the best example. The cell contains $8$ corner atoms and $6$ face-centered atoms, but those are shared.

Each corner atom belongs to $8$ neighboring cells, so corners contribute

Each face-centered atom is shared by $2$ cells, so faces contribute

Total atoms in one FCC unit cell:

The usual error is counting every drawn atom as fully inside the box, which overcounts badly because most atoms are shared.

Apply the Counting Method Yourself

Run the same fractional count for BCC. The corners contribute $8 \times \frac{1}{8} = 1$, and the single body-center atom is unshared, contributing $1$, for a total of $2$ atoms per cell — matching the table. Once shared atoms make sense, most unit-cell questions become much easier to read.

Common Mistakes in Crystal Structure Questions

Counting Drawn Atoms Instead of Shared Fractions

Corner and face-centered atoms are shared with neighbors. A unit-cell diagram is not a count of whole atoms.

Calling BCC Close-Packed

BCC is an important cubic structure, but it is not close-packed like FCC or HCP.

Mixing FCC and HCP Because Both Are Dense

Both are close-packed, but they are not the same structure. The stacking sequence is the cleanest way to tell them apart.

Confusing Unit-Cell Shape With the Whole Crystal

The unit cell is only the repeating block; the actual crystal is its large three-dimensional repetition.

Where Crystal Structure Matters

Crystal structure helps explain why solids differ in density, diffusion, and mechanical behavior — one of the main links between atomic arrangement and bulk properties. For metals, the structure affects how planes of atoms slide past each other, one reason different metals behave differently even though all are atoms packed into a solid.

A memory hook for each: BCC is a cube with a center atom, FCC is a cube with atoms on the faces, and HCP is hexagonal layers stacked $ABAB$.