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Crystal Structures

High schoolChemistryExact cubic site-sharing geometry for SC, BCC, FCC, rock-salt ions and a hypothetical molecular-centre lattice

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About this experiment

Rotate and expand a unit cell to inspect corners, faces, edges and body sites. Count shared particles, calculate packing and density, and distinguish a lattice of ions from a lattice of molecular centres.

Learning goals

  • Count fractional contributions of boundary particles to one unit cell.
  • Relate hard-sphere contact to cubic lattice parameter.
  • Distinguish particle count from formula-unit count in an ionic crystal.

How to use it

  1. 1Select an FCC corner and face site and compare their shared fractions.
  2. 2Expose hidden sites and verify four effective particles in the FCC cell.
  3. 3Switch to BCC and compare packing with the FCC result.
  4. 4Inspect the rock-salt cell and distinguish eight effective ions from four formula units.

The model

Corners, edges, faces and interior sites have different sharing factors.
These contact relations apply to monatomic hard-sphere cells.
Density uses formula units per cell and molar mass per formula unit.

Assumptions

  • Monatomic structures use hard spheres. The rock-salt cell uses two FCC sublattices; its size prevents anion-anion overlap as well as unlike-ion overlap.
  • The molecular option is a hypothetical simple-cubic lattice of dimer centres, not a claim about the structure of a real molecular solid. Its hard-sphere packing value is intentionally omitted.
  • Visual expansion only separates the drawing. Density and contact geometry always use the unexpanded model cell. Thermal motion and lattice energies are omitted.

Try this in class

  1. Q1Why does one corner sphere contribute only one eighth?
  2. Q2Why are there four formula units but eight ions in a rock-salt conventional cell?

Frequently asked questions

Does FCC always mean the same chemical bonding?

No. FCC names a geometric arrangement. The sites can represent atoms or one sublattice of ions; chemistry requires additional information.

Why can the rock-salt lattice parameter stop changing when the cation is very small?

At sufficiently small cation radius, the anion FCC framework reaches anion-anion contact before unlike-ion contact. The model takes the larger of those two minimum cell sizes.