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Metal Unit Cells in 3D – Simple Cubic, BCC, FCC and HCP

ChemistryChemical BondingAges 17–18

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A rotatable 3D model of one unit cell: simple cubic, body-centred cubic, face-centred cubic and hexagonal close-packed. Cut and exploded views show the fraction of each atom inside the cell (corner 1/8, face 1/2, inside 1; hexagonal corner 1/6), and a counting table gives the number of atoms per cell Z, the coordination number, the link between edge length a and atomic radius r, the packing efficiency and the density of example metals (Po, Na, Fe, W, Cu, Al, Au, Mg, Zn, Ti…).

Lesson: Metallic crystal structures: simple cubic, body-centred cubic, face-centred cubic and hexagonal close-packed unit cells; atoms per cell, coordination number, packing efficiency

What it shows

A unit cell is the smallest repeating box of a crystal. Atoms on its corners, edges and faces are shared with neighbouring cells, so only 1/8, 1/4 or 1/2 of each belongs to the cell, and 1/6 at the corner of a hexagonal cell. This 3D model cuts the atoms at the cell walls or pulls the pieces apart so you can count them: simple cubic 1, body-centred cubic 2, face-centred cubic 4 and hexagonal close-packed 6 atoms per cell. It shows where the atoms touch, links edge length a to radius r, and uses measured lattice constants to calculate packing efficiency and density.

How to use

Choose a structure, then switch the display between Cut to the cell, Exploded pieces, Whole atoms and Small atoms to count the fractions and check the table below. Tick Contact line to see where the atoms touch and derive a from r, and Nearest neighbours to count the coordination number, including atoms in neighbouring cells. Pick a metal and ask students to calculate its density from a before reading the result.

Parameters you can change

  • Crystal structure Simple cubic (SC), Body-centred cubic (BCC), Face-centred cubic (FCC), Hexagonal close-packed (HCP)
  • Example metal (if it has another structure, the first metal of the chosen structure is used) α-Polonium (Po) – simple cubic, Sodium (Na) – BCC, Potassium (K) – BCC, α-Iron (Fe) – BCC, Chromium (Cr) – BCC, Tungsten (W) – BCC, Copper (Cu) – FCC, Aluminium (Al) – FCC, Silver (Ag) – FCC, Gold (Au) – FCC, Nickel (Ni) – FCC, Magnesium (Mg) – HCP, Zinc (Zn) – HCP, α-Titanium (Ti) – HCP
  • Display Cut to the cell, Whole atoms, Exploded pieces, Small atoms
  • Show coordination number
  • Show contact line

Questions to explore

  1. Why does a face-centred cubic cell contain only 4 atoms although 14 atoms touch the cell?
  2. Along which direction do the atoms touch in a body-centred cubic cell, and what does that give for a in terms of r?
  3. Why does body-centred cubic pack less efficiently than face-centred cubic and hexagonal close packing?

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