Crystal Structures — BCC, FCC, HCP & Unit Cells

Crystal structures are the repeating three-dimensional arrangements of particles in a solid. If you are comparing BCC, FCC, and HCP, the key questions are simple: what the unit cell looks like, whether the structure is close-packed, and how many atoms belong to one unit cell after sharing is taken into account.

BCC has an atom at the center of a cube, FCC has atoms at the centers of the cube faces, and HCP is built from hexagonal layers. FCC and HCP are both close-packed in the hard-sphere model; BCC is not.

What Is a Unit Cell?

A unit cell is the repeating block that generates the full crystal by translation. It is not a separate little chunk floating on its own. It is a convenient way to describe the pattern.

This matters because the atoms drawn on corners, faces, or edges are usually shared with neighboring cells. A unit-cell picture shows the pattern, not a box full of private atoms.

BCC vs FCC vs HCP

BCC: Body-Centered Cubic

In body-centered cubic, atoms sit at the eight corners of a cube and one atom sits at the center of the cube.

BCC appears in some metals under the right conditions. 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

In face-centered cubic, atoms sit at the eight corners and at the center of each of the six faces.

FCC is close-packed in the hard-sphere model. Its close-packed layers follow an $ABCABC$ stacking sequence.

HCP: Hexagonal Close-Packed

HCP is also close-packed, but the stacking sequence is different. Instead of $ABCABC$, it follows an $ABAB$ pattern.

So FCC and HCP can have the same ideal packing efficiency and the same coordination number, even though their repeating cells are not the same shape.

Quick Comparison Table

Structure	Unit-cell picture	Close-packed?	Typical coordination number
BCC	corners + 1 body center	no	8
FCC	corners + 6 face centers	yes	12
HCP	hexagonal layered cell	yes	12

For most introductory chemistry questions, this table is enough to separate the three structures quickly.

Worked Example: How Many Atoms Are in an FCC Unit Cell?

FCC is the best first example because it makes atom sharing obvious.

An FCC unit cell contains:

• $8$ corner atoms
• $6$ face-centered atoms

But those atoms are shared.

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

$$8 \times \frac{1}{8} = 1$$

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

$$6 \times \frac{1}{2} = 3$$

So the total number of atoms in one FCC unit cell is

$$1 + 3 = 4$$

The usual mistake is to count every drawn atom as fully inside the box. That overcounts badly because most of the atoms are shared.

Why FCC and HCP Are Often Grouped Together

FCC and HCP are often taught together because both are close-packed arrangements of equal spheres. In that idealized model, both have an atomic packing factor of about $0.74$.

The main difference is not density. It is layer stacking: FCC uses $ABCABC$, while HCP uses $ABAB$.

Common Mistakes in Crystal Structure Questions

Counting drawn atoms instead of shared fractions

Corner atoms and face-centered atoms are shared with neighboring cells. 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

FCC and HCP are both 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 the large three-dimensional repetition of that block.

Where Crystal Structures Matter

Crystal structure helps explain why solids can differ in density, diffusion, and mechanical behavior. In chemistry and materials science, it is one of the main links between atomic arrangement and bulk properties.

For metals, the structure affects how planes of atoms can move past each other. That is one reason different metals can behave differently even when they are all made of atoms packed into a solid.

A Simple Way to Remember BCC, FCC, and HCP

Use one mental hook for each structure:

• BCC: cube with a center atom
• FCC: cube with atoms on the faces
• HCP: hexagonal layers stacked $ABAB$

If you want a next step, try your own version of the counting method for BCC. Once shared atoms make sense, most unit-cell questions become much easier to read.