Crystal Structures: NaCl, CsCl, ZnS, Diamond, Graphite

The five classic crystal structures — NaCl (rock salt), CsCl, ZnS (zinc blende), diamond and graphite — show how the same idea (ions or atoms arranged in a lattice with filled voids) produces wildly different materials. Table salt, a semiconductor, the hardest natural substance and a lubricant are all explained by these five patterns.

They matter because each is a prototype for thousands of compounds: MgO copies NaCl, CsBr copies CsCl, and silicon copies diamond. Learn these five and you can predict the structure — and many properties — of a huge number of solids.

Key Concepts

• NaCl (rock-salt) structure: Cl⁻ ions in FCC; Na⁺ occupies ALL octahedral voids. Coordination 6:6. 4 NaCl units per cell. Radius-ratio range 0.414–0.732.
• CsCl structure: Cl⁻ in simple cubic arrangement with Cs⁺ at the body centre — coordination 8:8. 1 CsCl unit per cell. Needs a large cation (ratio above 0.732).
• ZnS (zinc blende): S²⁻ in FCC; Zn²⁺ occupies HALF the tetrahedral voids (alternate ones). Coordination 4:4. 4 ZnS units per cell. Ratio 0.225–0.414.
• Diamond: carbon in FCC with half the tetrahedral voids filled by carbon — each C bonded tetrahedrally to 4 others. Extremely hard, electrical insulator.
• Graphite: hexagonal layers of carbon (each C bonded to 3 neighbours in-plane); layers held by weak forces, 3.35 Å apart. Soft, slippery, conducts electricity along layers.

How It Works

1. Start with the anion close packing: Cl⁻/S²⁻ form an FCC array (NaCl, ZnS) or a simple-cubic array (CsCl).
2. Count the voids: each FCC cell has 4 octahedral and 8 tetrahedral voids.
3. Fill them by stoichiometry: NaCl needs equal numbers → all 4 octahedral voids get Na⁺. ZnS needs 1:1 with tetrahedral preference → 4 of the 8 tetrahedral voids get Zn²⁺.
4. For diamond, the "anion" and "cation" are both carbon: FCC carbon plus carbon in half the tetrahedral voids gives the tetrahedral network.
5. Graphite breaks the 3D pattern entirely — strong covalent bonds within flat hexagonal sheets, weak attraction between sheets.

Worked Example

Predict the structure of MgO: r(Mg²⁺) = 72 pm, r(O²⁻) = 140 pm.

1. Radius ratio = 72/140 = 0.514, which lies in the octahedral range (0.414–0.732).
2. So O²⁻ forms an FCC array and Mg²⁺ fills all octahedral voids → NaCl-type (rock-salt) structure, coordination 6:6.
3. Check stoichiometry: 4 O²⁻ per FCC cell, 4 octahedral voids all filled → 4 MgO units per cell. Correct 1:1 ratio.

Common Misconceptions

• "NaCl has molecules of NaCl." No — the crystal is one giant lattice; "4 NaCl per unit cell" is just the repeating formula count, not discrete molecules.
• "Diamond and graphite differ because of impurities." Both are pure carbon. The difference is purely structural: 3D tetrahedral network versus stacked sheets.
• "CsCl has a BCC structure." It looks like BCC, but BCC has identical atoms at corners and centre. In CsCl the corner and centre ions differ, so it is a simple-cubic anion array with the cation at the body centre — coordination 8:8.

Real-World Applications

• Semiconductors: silicon and germanium use the diamond structure; GaAs and many LED materials use zinc blende.
• Abrasives and cutting: diamond's tetrahedral network makes it the hardest known natural material — used in drill bits and cutting tools.
• Lubricants and pencils: graphite's sliding layers make it a dry lubricant and the "lead" in pencils.

In short, NaCl fills all octahedral voids of FCC (6:6), CsCl puts the cation at a cube's body centre (8:8), ZnS fills half the tetrahedral voids (4:4), diamond is a tetrahedral carbon network, and graphite is stacked hexagonal sheets.