Close Packing, Unit Cells and Ionic Lattice Types
A crystal is one small block repeated. Choosing that block, counting what it contains and finding where the holes are explains structure types, densities and why a given pair of ions adopts one arrangement rather than another.
What a learner can do afterwards
- Counts atoms per unit cell for the cubic types and calculates a density from cell dimensions
- Distinguishes hexagonal from cubic close packing by their stacking sequence
- Locates tetrahedral and octahedral holes and links occupancy to a named structure type
- Uses a radius ratio to predict a coordination number and states where the prediction fails
1 · Read
Most solids are crystalline: their atoms stack in a pattern that repeats in three directions. The smallest repeating block is the unit cell. Counting its contents needs care, because shared atoms count only in part: a corner atom belongs to eight cells, so it counts as one eighth, while a face atom is shared by two cells, so it counts as one half. An atom buried in the cell centre belongs to that cell alone.
Apply the sharing rules to the cubic cells. Simple cubic holds 1 atom, body-centred cubic holds 2, and face-centred cubic holds 4. Where ions touch along an edge or a face diagonal, the cell edge fixes the ionic radius. Density then follows: the mass of the atoms in one cell divided by the volume of that cell. X-ray diffraction reveals the spacing between layers, which is how the hidden arrangement is measured.
Close packing stacks layers of spheres, and hexagonal and cubic close packing use different repeating orders of those layers. Between the packed atoms sit small gaps of two shapes, and which gaps get filled decides the named structure type. Comparing the sizes of the two ions predicts how many neighbours each ion gets, but the prediction fails where bonding is far from purely ionic.
Count what one cell holds, then scale up: that count sets the density and the structure.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.