Face-centered cubic, or FCC, is a crystal structure in which atoms sit at the corners and the centers of all six faces of a cube. In Principles of Physics III, it shows how atomic packing shapes metal properties.
Face-centered cubic, or FCC, is a crystal lattice used to describe how atoms are arranged in some solids, especially metals. In this structure, atoms occupy the 8 cube corners and the centers of all 6 faces of the cube. When you count the shared atoms correctly, each unit cell contains the equivalent of 4 atoms total.
The FCC structure is one of the closest-packed arrangements you will see in an introductory materials context. Its packing efficiency is about 74 percent, which means a large fraction of the space in the crystal is filled by atoms rather than empty gaps. That close packing is why FCC metals often have relatively high density compared with less tightly packed structures.
A useful number for FCC is the coordination number, which is 12. That means each atom touches 12 nearest neighbors. In other words, the lattice gives atoms many contact points, and that geometry affects how the solid behaves when force is applied.
In the cubic unit cell, the edge length and atomic radius are linked by a simple geometry relation, a = 2\u221a2r. That comes from the fact that atoms touch along the face diagonal, not along the cube edge. If you ever need to find radius, unit-cell length, or density, this geometric relationship is the starting point.
In a physics course, FCC is not just a picture of a cube. It is a model for why metals like aluminum, copper, silver, nickel, and gold tend to be dense, metallic, and relatively ductile. The arrangement leaves enough symmetry and slip options for layers of atoms to shift past one another without the crystal breaking immediately.
That is the big idea: FCC is a compact way to connect atomic arrangement with real material behavior. When you see it, think structure first, then packing, then physical properties.
Face-centered cubic shows up whenever the course moves from single atoms to bulk matter. It gives you a concrete way to connect geometry to measurable properties like density, atomic spacing, and how a metal deforms under stress.
This term also bridges several ideas in modern physics and materials. If you know the FCC arrangement, you can reason about why some metals are dense, why the coordination number is high, and why close packing matters for slip and ductility. That is the kind of link professors like to test in short answer questions and problem sets, because it shows you are not just memorizing a shape.
FCC also gives you a setup for using formulas. You may need to relate atomic radius to unit-cell edge length, count atoms per unit cell, or compare FCC with other lattice types. Those tasks show up in density calculations, crystal-structure identification, and questions where you match a diagram to a structure name.
If your class discusses real materials, FCC is a common example because it fits many familiar metals. That makes it a good reference point when you are trying to explain how microscopic arrangement affects macroscopic behavior such as strength, density, and ductility.
Keep studying Principles of Physics III Unit 11
Visual cheatsheet
view galleryCoordination Number
FCC has a coordination number of 12, so each atom touches 12 nearest neighbors. That number is one reason FCC metals pack efficiently and often deform in a ductile way. When you compare crystal structures, coordination number is the quickest way to see how crowded the local atomic environment is.
Packing Efficiency
FCC is a classic close-packed structure with a packing efficiency of about 74 percent. That means very little empty space compared with looser arrangements. In physics problems, packing efficiency connects directly to density and to why different lattice types can give different material properties.
Body-Centered Cubic
Body-centered cubic looks similar at first glance, but it puts one atom in the cube center instead of the face centers. That changes the number of neighbors, the packing efficiency, and usually the mechanical behavior. Comparing FCC and BCC is a common way to test whether you can read a lattice diagram correctly.
x-ray diffraction
X-ray diffraction is how physicists and materials scientists identify crystal structures like FCC in real samples. The pattern of scattered X-rays depends on the spacing and symmetry of the lattice. If a metal is FCC, its diffraction peaks appear in a specific arrangement that can confirm the unit cell.
A quiz or problem set may ask you to identify an FCC lattice from a diagram, count the atoms in the unit cell, or use the geometry relation a = 2\u221a2r. You might also compare FCC with BCC or HCP and explain which one is more tightly packed. In a lab, you could connect an FCC model to density or diffraction data, then justify why a metal sample matches that structure. The task is usually not just naming the lattice, but using the arrangement to predict a property.
FCC and body-centered cubic are both cubic lattices, so they can look similar on a diagram. The difference is where the atoms sit and how many neighbors each atom has. FCC has face-centered atoms, 12 neighbors, and higher packing efficiency, while BCC has one atom in the center of the cube and lower packing efficiency.
Face-centered cubic is a crystal structure with atoms at the cube corners and face centers.
FCC has a coordination number of 12 and a packing efficiency of about 74 percent, so it is a close-packed lattice.
The geometry of FCC gives the relation a = 2\u221a2r, which is useful for unit-cell calculations.
Many common metals, including aluminum, copper, silver, nickel, and gold, adopt FCC structures.
When you see FCC in physics, connect the atomic arrangement to density, ductility, and diffraction patterns.
Face-centered cubic is a crystal lattice where atoms sit at the corners and the centers of all six faces of a cube. In Physics III, it is a standard model for how atoms pack in metals and how that packing affects density and ductility.
FCC puts atoms on the faces as well as the corners, while BCC puts one atom in the center of the cube plus atoms at the corners. FCC is more tightly packed, with 12 nearest neighbors, while BCC is less densely packed.
FCC is close-packed because the atoms are arranged so that spheres fit together with very little empty space. The face-diagonal geometry lets atoms touch efficiently, which is why the packing efficiency reaches about 74 percent.
Common FCC metals include aluminum, copper, silver, gold, nickel, and lead. In class, these examples often show up when you are linking crystal structure to real material properties like density and malleability.