The concept of lattice comes along with the concept of crystals. Crystalline solids have definite patterns which arise due to the definite patterns in which the different atoms of the crystals are placed. The definite geometric shapes of crystals are possible due to the formation of a lattice with a series of atoms arranged in that specific pattern to give a well-designed three-dimensional structure. The repetitive pattern of the lattice units forms the actual crystal. The atoms can also be substituted with ions or molecules. Lattice points are the points of finding the constituent atoms of the crystal.
Now when we can understand what is a lattice in a crystal, we can also understand what is braves lattice. Bravais lattice actually denotes all the 14 types of three-dimensional patterns in which the atoms can arrange themselves to form a crystal named after the great physicist Auguste Bravais of France. His work including Bravais laws is an important breakthrough in the field of crystallography.
Bravais lattices are possible both in two-dimensional and three-dimensional spaces where the lattices are filled without any gaps.
In three-dimensional space, 14 Bravais lattices are there into which constituent particles of the crystal can be arranged. These 14 Bravais lattices are obtained by combining lattice systems with centering types.
A Lattice system is a class of lattices with the same set of lattice point groups, which are subgroups of the arithmetic crystal classes. 14 Bravais lattices can be divided into 7 lattice systems -
Cubic
Tetragonal
Orthorhombic
Hexagonal
Rhombohedral
Monoclinic
Triclinic
Centering types identify the locations of the lattice points in the unit cell.
Primitive Unit Cell (P) - In this lattice points are found on the cell corners only. It is also sometimes called a simple unit cell. In these constituent particles are found at the corners of the lattice in the unit cell, no particles are located at any other position in the cell. Thus, a primitive cell has only one lattice point.
Non - Primitive Unit Cells - In these unit cells particles are found in other positions of the lattices as well with corners. These can be divided into the following types -
Body-Centered (I) - In this lattice points are found on the cell corners with one additional lattice point at the center of the cell. Thus, it has particles at the corners and center of the body or cell.
Face Centered (F) - In this lattice points are found on the cell corners with one additional lattice point at the center of each face of the cell. Thus, it has particles at the corners and center of each face.
Base Centered (C) - In this lattice points are found on the cell corners with one additional lattice point at the center of each face of one pair of parallel faces of the cell. It is also called end-centered. Thus, it has particles at the corners and one particle at the center of each opposite face.
Not all combinations of lattice systems and centering types give rise to new possible lattices. After combining them, several lattices we get are equivalent to each other.
14 - Types of Bravais Lattice
All 14 Bravais Lattices show few similar characteristics which are listed below-
Each lattice point represents one particle of the crystal.
This constituent particle of the crystal can be an atom, ion, or molecule.
Lattice points of the crystal are joined by straight lines.
By joining the lattice point of the crystal, we get the geometrical shape of the crystal.
Each one of the 14 Bravais lattices possesses unique geometry. Equivalent lattices have been already excluded which we got after combining lattice systems and centering types.
List of 14 - Types of Bravais Lattices -
Cubic - Cubic system shows three types of Bravais lattices - Primitive, base centered and face centered.
a = b = c
\[\alpha = \beta = \lambda = 9{0^0}\]
Tetragonal - Tetragonal system shows two types of Bravais lattices - Primitive, body centered.
a = b \[ \ne \]c
\[\alpha = \beta = \lambda = 9{0^0}\]
Orthorhombic - Orthorhombic system shows four types of Bravais lattices - Primitive, body centered, base centered and face centered.
a \[ \ne \] b \[ \ne \] c
\[\alpha = \beta = \lambda = 9{0^0}\]
Hexagonal - Hexagonal system shows one type of Bravais lattice which is Primitive.
a = b \[ \ne \]c
\[\alpha = 12{0^o} \beta = \lambda = 9{0^o}\]
Rhombohedral - Rhombohedral system shows one type of Bravais lattice which is Primitive.
a = b = c
\[\alpha = \beta = \lambda \ne 9{0^o}\]
Monoclinic - Monoclinic system shows two types of Bravais lattices - Primitive, base centered.
a = b \[ \ne \]c
\[\alpha \ne 9{0^o}\beta = \lambda = 9{0^o}\]
Triclinic - Triclinic system shows one type of Bravais lattice which is Primitive.
a \[ \ne \]b \[ \ne \]c
\[\alpha \ne \beta \ne \lambda \ne {90^o}\]
Thus, from the cubic system - two, from tetragonal - two, from orthorhombic - four, from hexagonal - one, from rhombohedral - one, from monoclinic two and from triclinic one Bravais lattices are found. If you add all these Bravais lattices, you get a total 14 Bravais lattices.
FAQs on Bravais Lattice
1. What is a Bravais lattice in chemistry?
A Bravais lattice is a theoretical infinite arrangement of points in three-dimensional space that represents the geometric structure of a crystal. The key feature is that the lattice looks exactly the same from any point you choose. It's the underlying framework, or 'scaffolding', upon which atoms, ions, or molecules (the basis) are placed to form a real crystal structure. The entire lattice is generated by repeating a single fundamental unit, known as the unit cell.
2. What are the seven crystal systems that form the basis for Bravais lattices?
The seven crystal systems are categories of lattices based on the lengths of their unit cell axes (a, b, c) and the angles between them (α, β, γ). As per the CBSE syllabus, these systems are:
- Cubic (a=b=c, α=β=γ=90°)
- Tetragonal (a=b≠c, α=β=γ=90°)
- Orthorhombic (a≠b≠c, α=β=γ=90°)
- Monoclinic (a≠b≠c, α=γ=90°, β≠90°)
- Hexagonal (a=b≠c, α=β=90°, γ=120°)
- Rhombohedral or Trigonal (a=b=c, α=β=γ≠90°)
- Triclinic (a≠b≠c, α≠β≠γ≠90°)
3. Why are there only 14 possible Bravais lattices in three dimensions?
There are only 14 unique Bravais lattices because not all combinations of the seven crystal systems and the four possible centering types (Primitive, Body-centred, Face-centred, End-centred) are geometrically unique or stable. For example, a face-centred tetragonal lattice can be shown to be equivalent to a simpler body-centred tetragonal unit cell. The 14 lattices represent the only ways to arrange points in 3D space that satisfy the strict requirements of translational symmetry and having an identical environment around every single point.
4. What is the difference between a crystal lattice and a Bravais lattice?
While often used interchangeably, there is a subtle but important difference. A crystal lattice refers to any periodic array of points in space. However, a Bravais lattice is a more specific type of crystal lattice where every single lattice point is equivalent. This means that the arrangement and orientation of all other points around any chosen point are identical. All 14 Bravais lattices are crystal lattices, but not all theoretical crystal lattices meet the strict equivalency condition to be classified as a Bravais lattice.
5. How are the four types of unit cells distributed among the seven crystal systems?
The 14 Bravais lattices are formed by combining the seven crystal systems with four main types of unit cells: Primitive (P), Body-centred (I), Face-centred (F), and End/Side-centred (C). The distribution is as follows:
- Cubic: 3 types (Primitive, Body-centred, Face-centred)
- Tetragonal: 2 types (Primitive, Body-centred)
- Orthorhombic: 4 types (Primitive, Body-centred, Face-centred, End-centred)
- Monoclinic: 2 types (Primitive, End-centred)
- Triclinic: 1 type (Primitive)
- Hexagonal: 1 type (Primitive)
- Rhombohedral: 1 type (Primitive)
6. What is the importance of studying Bravais lattices for understanding the properties of solids?
Studying Bravais lattices is crucial because the geometric arrangement of atoms in a solid dictates its macroscopic properties. This framework helps predict and explain:
- Physical Properties: Such as a material's density, hardness, and how it breaks along specific planes (cleavage).
- Anisotropy: Why properties like electrical conductivity or refractive index can differ when measured along different directions in a crystal.
- X-ray Diffraction: The lattice structure is responsible for creating the unique diffraction patterns used to identify crystal structures.
- Material Behaviour: It provides a basis for understanding how materials will respond to stress, heat, and other external forces.
7. Can you give a real-world example of a substance for each of the main crystal systems?
Yes, many common substances crystallise into these systems:
- Cubic: Sodium chloride (table salt), Copper, and Diamond.
- Tetragonal: Zircon and white tin.
- Orthorhombic: Rhombic sulfur and Epsom salt.
- Monoclinic: Gypsum and monoclinic sulfur.
- Triclinic: Potassium dichromate (K₂Cr₂O₇) and copper(II) sulfate pentahydrate.
- Hexagonal: Graphite and Zinc.
- Rhombohedral: Calcite (CaCO₃) and Quartz (SiO₂).
8. What are the fundamental conditions a lattice must satisfy to be classified as a Bravais lattice?
For any arrangement of points in space to be defined as a Bravais lattice, it must meet two fundamental conditions:
- Point Equivalence: The lattice must be homogeneous. This means the arrangement of points around any one lattice point is identical to the arrangement around any other lattice point.
- Translational Symmetry: The entire lattice must be capable of being generated by repeatedly translating a single point using a set of basis vectors. In 3D, this means you can reach every point in the lattice from an origin point by using integer multiples of three non-coplanar vectors.
