# Crystal lattice structures

> IB Chemistry HL · S2: Models of bonding and structure
> Source: https://www.owlsprep.com/study/ib-chemistry-hl-u2-crystal-lattice-structures/

This sub-topic explores regular repeating 3D arrangements of particles in crystalline solids. We examine common lattice types for ionic, metallic and covalent network solids, and connect structure to physical properties.

**Prerequisites:** [Ionic bonding](https://www.owlsprep.com/study/ib-chemistry-hl-u2-ionic-bonding/); [Covalent bonding](https://www.owlsprep.com/study/ib-chemistry-hl-u2-covalent-bonding/)

## Learning objectives

- Describe the structure of ionic, metallic and covalent network crystal lattices
- Relate lattice coordination and structure to physical properties of solids
- Use radius ratio rules to predict ionic lattice coordination numbers
- Distinguish between unit cells and full crystal lattices

## Core concepts: Lattices and unit cells

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.

**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.

## Ionic crystal lattice structures

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 $r^+_{Mg^{2+}} = 72$ 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.

**Check your understanding**

Test your understanding of radius ratio rules:

1. What coordination number would you predict for a compound with $\frac{r^+}{r^-} = 0.3$?

   - 4
   - 6
   - 8
   - 12

   *Why:* Correct. The range 0.225 – 0.414 corresponds to coordination number 4.

## Metallic and covalent network lattices

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.

**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.

## Lattice structure and physical properties

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 |

**Exam command terms**

- **Compare** — State both similarities and differences between two lattice structures or their properties *(Compare the structure of diamond and graphite)*

- **Relate** — Connect the microscopic structure of the lattice to macroscopic observable properties *(Relate metallic lattice structure to electrical conductivity)*

## Common pitfalls

- **Wrong:** Claiming graphite is a molecular solid because it is soft
  - Why it fails: 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: Identify graphite as a layered covalent network solid, with weak intermolecular interactions between layers that allow sliding
- **Wrong:** Assuming cation and anion coordination numbers are always equal in ionic lattices
  - Why it fails: Coordination numbers adjust to maintain charge neutrality for 1:2 or 2:1 ionic compounds
  - Correct: For CaF₂, the 1 Ca²⁺ : 2 F⁻ ratio gives coordination numbers of 8 for Ca²⁺ and 4 for F⁻
- **Wrong:** Confusing a crystal lattice with a unit cell in definition questions
  - Why it fails: These terms have distinct meanings, and examiners penalise mixing them up
  - Correct: Remember the unit cell is the smallest repeating unit of the larger full crystal lattice
- **Wrong:** Stating all covalent network solids are non-conductive
  - Why it fails: Graphite and graphene are covalent network solids that have delocalised electrons and conduct electricity
  - Correct: Specify that most covalent network solids are non-conductive, with graphite being a key exception

## 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 |

## 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.

- [AHL: Covalent bond order and electron delocalization](https://www.owlsprep.com/study/ib-chemistry-hl-u2-ahl-covalent-bond-order-and/)
- [AHL: Advanced hybridization and delocalized pi systems](https://www.owlsprep.com/study/ib-chemistry-hl-u2-ahl-advanced-hybridization-and-delocalized/)

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