Crystal lattice structures

IB Chemistry HL· 2.4 Bonding & structure· 45 min read

1. Core concepts: Lattices and unit cells★★☆☆☆⏱ 15 min

All crystalline solids are made of particles arranged in a regular, repeating 3D pattern. This pattern is called a crystal lattice, and the smallest repeating unit that preserves the symmetry of the full lattice is called a unit cell.

📘 Definition

Crystal lattice

A regular, repeating three-dimensional arrangement of atoms, ions, or molecules extending throughout a crystalline solid

Example:

Alternating sodium and chloride ions in table salt

Coordination number describes how many nearest neighbouring particles a given particle has in the lattice. Higher coordination numbers usually correspond to stronger inter-particle attractions in ionic and metallic lattices.

📐 Worked Example

State the coordination number of both Na⁺ and Cl⁻ in a sodium chloride lattice, given that each Na⁺ is surrounded by 6 Cl⁻ ions

1
By definition, coordination number counts the nearest neighbouring oppositely charged ions for each ion in an ionic lattice.
2
Each Na⁺ ion has 6 Cl⁻ nearest neighbours, so the coordination number of Na⁺ is 6.
3
The lattice is symmetric and electrically neutral, so the coordination number of Cl⁻ must also be 6.

Exam tip:

Always state the coordination number for both ion types in ionic lattices, not just one.

2. Ionic crystal lattice structures★★★☆☆⏱ 20 min

Ionic lattices consist of alternating cations and anions held together by strong electrostatic attractions. The structure of the lattice is primarily determined by the ratio of the cation radius to the anion radius ( $\frac{r ^{+}}{r ^{-}}$ ), and the charge ratio of the ions.

- Sodium chloride (rock salt): Coordination number 6:6, face-centered cubic unit cell, forms when $0.414 < \frac{r ^{+}}{r ^{-}} < 0.732$
- Cesium chloride: Coordination number 8:8, cubic unit cell, forms when $0.732 < \frac{r ^{+}}{r ^{-}} < 1.0$
- Fluorite (CaF₂): Coordination number 8:4, matches the 1:2 charge ratio of Ca²⁺ to F⁻

📐 Worked Example

Use radius ratio rules to explain why MgO has the same 6:6 coordination structure as NaCl, given $r_{M g^{2 +}}^{+} = 72$ pm, $r_{O^{2 -}}^{-} = 140$ pm

1
Calculate the radius ratio of cation to anion:
2
$\frac{r^+}{r^-} = \frac{72}{140} \approx 0.51$
3
Radius ratios between 0.414 and 0.732 correspond to 6-coordinate geometry, the same range that NaCl falls into.
4
Therefore MgO adopts the same 6:6 rock salt structure as NaCl.

✓ Quick check

Test your understanding of radius ratio rules:

What coordination number would you predict for a compound with $\frac{r ^{+}}{r ^{-}} = 0.3$ ?
- 4
- 6
- 8
- 12
Reveal answer
4 —
Correct. The range 0.225 – 0.414 corresponds to coordination number 4.

3. Metallic and covalent network lattices★★★☆☆⏱ 18 min

Crystal lattices are not exclusive to ionic compounds. Two other common lattice types are metallic lattices and covalent network lattices, each with distinct structures and properties.

📘 Definition

Covalent network lattice

A continuous crystalline structure where all atoms are connected by strong covalent bonds, with no discrete molecules

Example:

Diamond, silicon, silicon(IV) oxide

- Metallic lattices: Made of positive metal ions in a delocalized electron sea. Common close-packed structures (CCP/HCP) have coordination number 12 and 74% packing efficiency.
- Diamond (covalent network): Each carbon atom is covalently bonded to 4 other carbon atoms in a tetrahedral 3D network.
- Graphite (covalent network): Layered structure, each carbon is bonded to 3 others in planar hexagonal layers, with weak London dispersion forces between layers.

📐 Worked Example

Explain why graphite conducts electricity but diamond does not, using their lattice structures.

1
In graphite's layered lattice, each carbon atom bonds to 3 other carbons, leaving one delocalized valence electron per carbon atom.
2
These delocalized electrons are free to move through the lattice, so graphite can conduct electricity.
3
In diamond's lattice, every carbon atom uses all 4 valence electrons to form covalent bonds to 4 neighbouring carbons.
4
No free delocalized electrons are available to carry charge, so diamond cannot conduct electricity.

4. Lattice structure and physical properties★★☆☆☆⏱ 12 min

The structure of a crystal lattice directly determines all key physical properties of the solid. The table below summarises the relationships between lattice type and common properties:

Lattice Type	Melting Point	Electrical Conductivity	Solubility in Water
Ionic	High	Solid: No / Molten/Aqueous: Yes	Most soluble
Metallic	High	Yes (solid and liquid)	Insoluble
Covalent Network	Very High	Most no (graphite yes)	Insoluble
Molecular	Low	No	Variable

5. Common Pitfalls

Wrong move:

Claiming graphite is a molecular solid because it is soft

Why:

Graphite is a covalent network solid, it is only soft because weak forces exist between its layers, not because it is made of discrete molecules

Correct move:

Identify graphite as a layered covalent network solid, with weak intermolecular interactions between layers that allow sliding

Wrong move:

Assuming cation and anion coordination numbers are always equal in ionic lattices

Why:

Coordination numbers adjust to maintain charge neutrality for 1:2 or 2:1 ionic compounds

Correct move:

For CaF₂, the 1 Ca²⁺ : 2 F⁻ ratio gives coordination numbers of 8 for Ca²⁺ and 4 for F⁻

Wrong move:

Confusing a crystal lattice with a unit cell in definition questions

Why:

These terms have distinct meanings, and examiners penalise mixing them up

Correct move:

Remember the unit cell is the smallest repeating unit of the larger full crystal lattice

Wrong move:

Stating all covalent network solids are non-conductive

Why:

Graphite and graphene are covalent network solids that have delocalised electrons and conduct electricity

Correct move:

Specify that most covalent network solids are non-conductive, with graphite being a key exception

6. Quick Reference Cheatsheet

Lattice Type	Examples	Coordination	Key Property
Ionic (Rock salt)	NaCl, MgO	6:6	High MP, conducts molten
Ionic (CsCl)	CsCl	8:8	High cation:anion radius ratio
Ionic (Fluorite)	CaF₂	8:4	Matches 1:2 charge ratio
Metallic (Close packed)	Cu, Ag	12	High packing efficiency
Covalent (Diamond)	Diamond, Si	4	Very high MP, non-conductive
Covalent (Graphite)	Graphite	3 (per layer)	Conductive, soft

7. Frequently Asked

What is the difference between a crystal lattice and a unit cell?

A crystal lattice is the repeating 3D arrangement of particles across the entire solid crystal. A unit cell is the smallest repeating unit that can be extended to form the full lattice.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · 1
Identify NaCl lattice coordination number
2024 · 2
Compare diamond and graphite structure
2023 · 1
Radius ratio prediction for ionic lattices

Going deeper

syllabusOfficial IB Chemistry HL SyllabusFull syllabus for this topic

What's Next

Understanding crystal lattice structures is the foundation for explaining the physical properties of all solids, a core assessment objective for IB Chemistry HL. This knowledge also underpins the calculation of lattice energy in thermodynamics, and the study of materials chemistry for optional topics. Extending your understanding of lattices will help you answer structure-property questions, which make up a large portion of exam marks in this unit.