Bravais Lattice (original) (raw)
Last Updated : 23 Jul, 2025
**Bravais lattice is a framework in which the points or atoms are arranged in a three-dimensional configuration. Bravais Lattice is named after Auguste Bravais. There are a total of 14 Bravais Lattices across 7 Crystal Systems. This helps us to understand the structure of the particles within a crystal.
In this article, we'll explore the world of Bravais lattices. Let's dive deep to learn the definition of bravais lattice, its types, unit cells & lattice systems while solving some great examples.
Table of Content
- What is a Bravais Lattice?
- What is a Unit Cell?
- Types of Lattice System
- 14 Bravais Lattices
- Bravais Lattice Table
- Examples of Bravais Lattice
What is a Bravais Lattice?
Bravais Lattice is a system of arrangement of atoms inside a unit cell observed by Auguste Bravais. There are a total of 7 Crystal System which has different possible combinations leading to 14 possible Bravais lattices.
Bravais Lattice Definition
A bravais lattice is the uniform arrangement of atoms, molecules or ions which builds a 3-dimensional structure of a crystal.
What is a Unit Cell?
Unit Cell is the smallest point which when kept together repeatedly, forms an entire lattice. It is the building element of a crystal lattice.
For example, when puzzle pieces are assembled together, they make an elegant structure. In the same way, a unit cell is the foundational unit which completes a lattice structure. Each bravais lattice has its specific unit cell.
Types of Unit Cell
Unit cells are mainly categorized into 2 parts:
- Primitive
- Centered
**Primitive Unit Cell
Primitive unit cells are those which contain points at the corners of a cubic structure. It has only 1 type
**Simple Lattice
Simple lattice which is also called primitive lattice is the most fundamental lattice. In this lattice, particles are located around the corners of a unit cell structure. It's the least dense lattice. Think of it as an organized array of modules or units. Example- Polonium.
**Centered Unit Cell
There are 3 main categories of centered unit cells. Each type has its own unique properties.
- Body Centered Cell
- Face Centered Cell
- Edge Centered Cell
**Body-Centered Lattice
Body-Centered lattice consists of an additional point in the middle of a cubic structure. In this BCC lattice, an extra particle is present in the center which makes it slightly denser as compared to Primitive lattice. Example - Tungsten.
**Face-Centered Lattice
Face-Centered lattice is a step further in the crystal world. In Face Centered, the particles are situated at each face of the unit cell which increases its density more than primitive and Body Centered lattice. Here, the points are present at the center as well as corners of each face of the cube. Example - Aluminum, Copper etc.
**Edge-Centered Lattice
In Edge-Centered Lattice, it's clearly evident from its name that the particles are present at the edges of the unit cell. It consists of an open structure like a primitive lattice while having a denseness similar to Body Centered Lattice.
Types of Lattice System
Now, let's understand the broader perspective of lattice systems which gives a different view of Bravais lattice world. These are 7 bravais lattice systems which are given below:
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Cubic Lattice System
Cubic lattice system is a combination of three lattice categories. It's a collection of simple cubic lattice, BCC and FCC. Example- Copper, Silver etc.
Hexagonal Lattice System (HCP)
Hexagonal lattice system contains a unit cell which has a hexagonal base. The HCP contains only one type of Bravais lattice which is simple or primitive lattice. Example- Graphite.
Tetragonal Lattice System
Tetragonal lattice system contains a unit cell which has a square base. The tetragonal lattice system contains 2 types of Bravais lattice which are simple cubic lattice & BCC. It is more like a stretchable cube. Example- SnO2
Orthorhombic Lattice System
Orthogonal lattice system contains a unit cell which has a rectangular base. The orthogonal lattice system contains 4 types of Bravais lattice which are simple cubic lattice, BCC, FCC & edge centered cubic lattice. Example- K2SO4
Monoclinic Lattice System
Monoclinic lattice system contains a unit cell which has a parallelogram base. The unit cell is tilted in this lattice system. The monoclinic lattice system contains 2 types of lattice system which are simple and BCC lattice. Example- Gypsum
Triclinic Lattice System
Triclinic lattice system consists of an irregular unit cell which has no right angles. The triclinic lattice system contains only 1 type of lattice system which is a simple cubic lattice. Example- k2Cr2O7
Rhombohedral Lattice
Rhombohedral lattice system contains a unit cell which has a rhombus base. The rhombohedral lattice system contains 1 type of lattice system which is simple or primitive lattice. Example- Sb, As.
14 Bravais Lattices
These 7 crystal systems are further divided into 14 possible Bravais lattices which we have discussed below:
Cubic Lattice System
- **Simple Cubic Lattice: This lattice contains particles only at the corners of a cubic structure.
- **Body-centered Cubic Lattice(BCC): In this lattice, one extra particle is situated at the center of a cubic structure.
- **Face-centered Cubic Lattice(FCC): This lattice contains points at the each face of a cubic structure as well as the corners.
Hexagonal Lattice System (HCP)
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- **Simple Hexagonal Lattice: In this lattice, there is 1 lattice point at each corner of the cubic structure.
Tetragonal Lattice System
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- **Simple Tetragonal Lattice: In this lattice, points are located at the corners while containing 1 lattice point per unit cell.
- **Body-centered Tetragonal Lattice: The BCT includes 1 additional lattice point at the center.
Orthorhombic Lattice System
- **Simple orthorhombic lattice: This lattice includes 1 lattice point at every corner of a cubic structure.
- **Base-centered orthorhombic lattice: In BCO lattice, each pair of opposite faces contain an extra point at the center.
- **Face-centered orthorhombic lattice: As it is clear from the name itself that FCO lattice contains an extra point at the face of a unit cell.
- **Body-centered orthorhombic lattice: In this lattice, each unit cell has a lattice point at the center of cubic structure.
Monoclinic Lattice System
- **Simple monoclinic lattice: SMC lattice has 1 lattice point per unit cell and its differentiated by 90° angle among their three edges.
- **Base-centered monoclinic lattice: At the center of 1 pair of opposite faces, an additional point is present in BCM lattice.
Triclinic Lattice System
- **Simple-triclinic lattice: This lattice has 1 lattice point per unit cell. It has no equal edges and angles.
Rhombohedral Lattice
- **Primitive or Simple Rhombohedral lattice: This lattice includes 1 lattice point situated at a rhombus shaped unit cell.
Bravais Lattice Table
Let's make it more simple by understanding its parameters to distinguish these 7 lattice systems:
| Lattice System Name | Lattice Type | Angles between faces | Edge length |
|---|---|---|---|
| Cubic Lattice System | Primitive, BCC, FCC | a = b = c= 90° | x=y=z |
| Hexagonal Lattice System | Primitive | a= 120°, b= c= 90° | x=y ≠ z |
| Tetragonal Lattice System | Primitive, BCC | a = b= c = 90° | x=y ≠ z |
| Orthorhombic Lattice System | Primitive, BCC, FCC, Edge centered | a = b = c = 90° | x ≠ y ≠ z |
| Monoclinic Lattice System | Primitive, edge centered | a ≠ 90°, b = c = 90° | x = y ≠ z |
| Triclinic Lattice System | Primitive | a ≠ b ≠ c = 90° | x ≠ y ≠ z |
| Rhombohedral Lattice | Primitive | a= b= c ≠ 90° | x=y=z |
Examples of Bravais Lattice
Now, as we have understood, what is Bravais lattice and its types as well as categories of lattice systems. It is high time, we see some real life examples of these Bravais lattice systems. Here are some common examples of lattice system:
Sodium Chloride (NaCl) Crystal Structure
Sodium chloride which you also called table salt is a great example of Face-Centered cubic lattice. In this Crystal structure, sodium ions (Na) and Chlorine ions (Cl) are neatly present in a cubic structure.
NiAs Crystal Structure
NiAs crystal structure shows a hexagonal lattice system. The arrangement of NiAs crystal structure is done in such a way that it resembles a beehive.
**Also, Check
Sample Questions on Bravais Lattice
**Question 1: Identify the types of Bravais lattice for the below crystal structures:
****(i) Iron(Fe) (ii) Diamond**
**Answer:
(i) Iron (Fe): Body-Centered Cubic (BCC)
(ii) Diamond: Face-Centered Cubic (FCC)
**Question 2: Write the angles between faces for following Lattice system:
****(a) Hexagonal Lattice System (b) Tetragonal Lattice System**
**Answer:
(a) Hexagonal Lattice System: a= 120°, b= c= 90°
(b) Tetragonal Lattice System: a = b= c = 90°
**Question 3: Choose the correct lattice type of rhombohedral lattice system:
****(a) BCC (b) Primitive (c) Edge-centered**
**Answer:
The correct lattice type of rhombohedral lattice system is (b) Primitive.
**Question 4: Choose the correct edge length of monoclinic lattice system:
****(a) x ≠ y ≠ z (b) x = y ≠ z (c) x=y ≠ z**
**Answer:
The correct edge length of monoclinic lattice system is (b) x = y ≠ z.
**Question 5: Identify the Bravais Lattice that shows each of the following descriptions:
**a) A lattice where points are located only at the corners of a cube.
**b) A lattice with points at the corners and center of each face of a cube.
**c) A lattice with points on the edges of a cube, but not on the faces or center.
**Answer:
a) A lattice where points are located only at the corners of a cube= Simple Cubic
b) A lattice with points at the corners and center of each face of a cube= Face-Centered Cubic (FCC)
c) A lattice with points on the edges of a cube, but not on the faces or center= Body-Centered Cubic (BCC)