Bravais Lattice

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.

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:

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)

• Simple Hexagonal Lattice: In this lattice, there is 1 lattice point at each corner of the cubic structure.

Tetragonal Lattice System

• 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.

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)

Bravais Lattice – FAQs

1. What is Bravais Lattice?

Bravais Lattice is systematic arrangement of atoms in a Crystal. This system was named after Auguste Bravais

2. Why is the Bravais Lattice used?

Bravais lattice is used to showcase the systematic arrangement of particles such as atoms, molecules or ions in a crystal lattice structure in the field of crystallography.

3. How can we identify the type of Bravais lattice in a Crystal Structure?

A bravais lattice can be identified by its position of particles in a crystal structure. You can look at the placement of particles at corners, edges and centers of a crystal structure to know the type of lattice system.

4. How many types of Bravais Lattices are present in nature?

There are mainly 14 types of bravais lattice present in nature which we have further divided into 7 lattice systems.

5. How many Bravais Lattices are present in a Cubic Crystal?

There are 3 main types of Bravais lattice which are located in a cubic crystal. They are simple cubic lattice, Body-centered cubic lattice and Face-Centered cubic lattice.

6. Name the lattice system which consists of more than 1 Bravais Lattice.

There are a total of 4 lattice systems which have more than one bravais lattice. They are tetragonal, cubic, orthorhombic and monoclinic lattice systems.

7. Which Lattice System contains only One Bravais Lattice?

The Hexagonal, Rhombohedral and triclinic lattice systems have only 1 bravais lattice.

8. ZnO and CdS are the Prime Examples of which type of Lattice System?

ZnO and CdS are examples of hexagonal lattice systems (HCP).

9. Which is the most common Example of Face-Centered Cubic Lattice?

The most common example of Face-Centered Cubic lattice is diamond.

10. What is the Importance of Unit Cells in Crystal Lattice?

The unit cell is the most crucial and smallest unit for building a lattice structure completely. Unit cells help to identify the types of lattice system by understanding the symmetry of lattice structure.