Undergraduate · 20 min

Crystal structures explorer: metals and salts

Rotate SC, BCC, FCC, NaCl, CsCl and diamond-type cells, count atoms and compare packing of real materials.

Goal

Connect each structure type to real substances and compute $Z$ , coordination number and packing fraction.

Apparatus and reagents

Interactive lattice viewer only. Atom radii follow the nearest-neighbour distance; the ionic structures use two different radii.

Procedure

Cycle through structures 0–2 (simple cubic, BCC, FCC) and count atoms: corners weigh $1/8$ , body centre $1$ , faces $1/2$ .
Now compare NaCl and CsCl: how many of each ion per cell, and what is each ion’s coordination number?
Increase to 2–3 cells per edge and shrink the spheres to see long-range order; then set size to 1 to see atoms touching.

What to observe

$Z$ = 1 (SC), 2 (BCC), 4 (FCC); NaCl has 4 + 4 ions with 6 : 6 coordination, CsCl has 1 + 1 with 8 : 8, diamond has 8 atoms with 4-coordination.
Packing climbs from 52 % (SC) to 68 % (BCC) to 74 % (FCC, the densest possible for equal spheres); diamond is open at 34 %.

Explanation

Metals adopt the packings that minimise energy: alkali and $\alpha$ -Fe are BCC, $\ce{Cu}$ , $\ce{Ag}$ , $\ce{Au}$ , $\ce{Al}$ are FCC. Ionic solids pack ions of unequal size: NaCl is two interpenetrating FCC sublattices (6 : 6), CsCl a simple-cubic anion lattice with the cation in the cube centre (8 : 8). The packing fraction $f = Z\cdot\frac{4}{3}\pi r^3/a^3$ measures space usage: 74 % for close packing, only 52 % for SC — which is why almost no element crystallises SC (polonium is the exception). Directional bonding, not packing, governs diamond’s open structure.

Chemists behind it

Dorothy Crowfoot Hodgkin Rosalind Franklin