Why salt forms cubes: crystal structure and unit cells

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1 / 15 One cell of saltThis cube, 0.564 nm on a side, is the unit cell of rock salt. Sodium (purple) and chlorine (green) alternate along every edge, and the labels show which is which.

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One cell of salt
This cube, 0.564 nm on a side, is the unit cell of rock salt. Sodium (purple) and chlorine (green) alternate along every edge, and the labels show which is which.
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Stacking cells into a block
Four cells along each edge make 64 cells. The Block zoom goes up to 10 × 10 × 10 for small cells, thousands of ions drawn at once.
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Why salt breaks into cubes
The block comes apart along a {100} plane, one of three at right angles. Each piece is again a box with flat faces, which is why crushed salt still looks like tiny cubes.
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From cells to a grain
The Shape zoom shows the crystal a cell grows into. A salt grain 1 mm wide holds about 5.6 × 10¹⁸ cells, all lined up the same way.
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Diamond: four bonds per atom
Each carbon holds four neighbours 0.154 nm away. The blue tetrahedron joins them. The cubic cell is 0.357 nm wide and contains 8 atoms.
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Graphite: sheets 0.335 nm apart
The same carbon laid out as flat sheets of hexagons: 3 neighbours each, 0.142 nm apart, with the sheets 0.3355 nm apart.
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Ice: held by hydrogen bonds
Each water molecule points its two hydrogens at two neighbours and receives a hydrogen from two more. The open rings these blue bonds make are why ice floats.
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Metals pack balls tightly
Copper is face-centred cubic: each atom touches 12 others, and the balls fill 74% of the space, the most that equal balls can.
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Fourteen ways to repeat a point
Every crystal is built on one of 14 Bravais lattices. Here is body-centred cubic: corners plus one point in the middle. The lab below lists all 14.
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Cutting a (111) plane
Miller indices name planes. With h = k = l = 1 the planes cut the cube corners off; on each plane copper atoms sit in a pattern of triangles, the densest plane there is.
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X-rays reflect off planes
Bragg’s law, n λ = 2 d sin θ: the (2 0 0) planes of salt are 0.282 nm apart, so Cu Kα X-rays at 1.5406 Å reflect at 2θ = 31.70°. The pattern in the corner lists every reflection.
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Iron changes at 912 °C
Heat α-iron past 912 °C and it turns face-centred cubic. This change, and the carbon that dissolves in the new lattice, is what heat treatment of steel uses.
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A dislocation
Seen end-on, an extra half plane of copper atoms ends at the ⊥. Metals bend at low stress because such lines move one row at a time.
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Quartz grows hexagonal
Quartz is trigonal: a six-sided prism capped by rhombohedron faces. Steno found in 1669 that the angles between these faces never change.
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Weighing one cell
Density is the mass of one cell over its volume, ρ = Z·M / (N_A·V). For salt that gives 2.163 g/cm³ against 2.168 measured. Counting every drawn ion gives too much, because ions on the faces are shared with the next cell.

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