Diamond and NaCl Crystal Structures: Units Cells Compared

Diamond and table salt look nothing alike, yet both crystals are built on the same face-centred cubic (FCC) scaffolding. Diamond is an FCC lattice with a two-atom basis, one at the corner position and one a quarter of the way along the body diagonal. Sodium chloride (NaCl) is two interpenetrating FCC lattices, one of sodium ions and one of chloride ions, shifted by half a cell edge. The shared FCC backbone gives both cubic symmetry, while the different bases give them totally different properties.

This comparison matters because it shows how the same lattice can host very different materials. Silicon and germanium, the heart of all electronics, use the diamond structure. Salt, potassium chloride and magnesium oxide use the rock-salt structure. Knowing the unit cell lets scientists predict bond lengths, density and even why diamond is the hardest known material.

Key Concepts

• Basis: the group of atoms attached to each lattice point. Diamond has a 2-atom basis at (0,0,0) and (1/4,1/4,1/4); NaCl has Na⁺ and Cl⁻ as its basis.
• Coordination number: each carbon in diamond touches 4 neighbours in a tetrahedron; each ion in NaCl touches 6 neighbours of the opposite charge in an octahedron.
• Nearest-neighbour distance: diamond: √3·a/4; NaCl: a/2.
• Atoms per conventional cell: diamond: 8 (8 corners × 1/8 + 6 faces × 1/2 + 4 inside); NaCl: 4 Na⁺ and 4 Cl⁻.
• Atomic packing factor: diamond ≈ 0.34 (very open, because of the tetrahedral bonds); NaCl ≈ 0.67 if ions are treated as touching spheres.

Formulas

• Diamond nearest-neighbour distance: d = √3·a/4. For diamond a = 3.567 Å and for silicon a = 5.431 Å, giving d = 1.545 Å and 2.352 Å respectively.
• NaCl nearest-neighbour distance: d = a/2. With a = 5.64 Å for NaCl, the Na⁺–Cl⁻ separation is 2.82 Å.
• Density: ρ = (atoms per cell × atomic mass) / (N_A × a³). For diamond: 8 × 12.01 g/mol ÷ (6.022×10²³ × (3.567×10⁻⁸ cm)³) = 3.51 g/cm³, matching the measured value.

Worked Example

Silicon has the diamond structure with a = 5.431 Å. Find the Si–Si bond length.

1. In the diamond structure, each atom's nearest neighbour sits at 1/4 of the body diagonal.
2. Body diagonal of the cube = √3·a = 1.732 × 5.431 Å = 9.406 Å.
3. One quarter of this: 9.406 / 4 = 2.352 Å.
4. So the Si–Si bond length is about 2.35 Å, the accepted value used in chip design.

Common Misconceptions

• "Diamond is just tightly packed carbon." Diamond is actually open (APF 0.34); its hardness comes from strong directional covalent bonds, not from tight packing.
• "NaCl has molecules of NaCl." There are no discrete NaCl molecules in the crystal; every Na⁺ is shared by six Cl⁻ and vice versa, forming one giant ionic network.
• "Graphite and diamond differ only in density." Graphite is layered hexagonal sheets while diamond is tetrahedral 3D — the bonding geometry, not just the packing, changes everything.

Real-World Applications

• Semiconductors: silicon and germanium chips are diamond-structure crystals; the tetrahedral bonds create the band gap that makes transistors possible.
• Cutting tools: diamond's tetrahedral network makes it the hardest material known, used in drill bits and cutting wheels.
• Table salt and ceramics: the rock-salt structure appears in MgO crucibles and refractory bricks that survive furnace temperatures.

Diamond and NaCl share an FCC backbone but differ in basis and bonding: diamond is an open tetrahedral network of 8 atoms per cell, while rock salt is two interlocked FCC ion lattices of 4 + 4 ions per cell. Comparing them shows how the basis, not just the lattice, decides a crystal's behaviour.