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Bravais Lattice

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Last updated date: 27th Mar 2024
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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 are Bravais lattices in two dimensions, three dimensions?

Bravais lattices are such lattices that fill spaces completely without leaving any gap in between be it two dimensions or three dimensions. Bravais lattice patterns that are possible in two dimensions are as follows:

  • Square

  • Rectangular primitive

  • Rectangular centered

  • Oblique

Bravais lattices possible in three dimensions are as follows:

  • Cubic primitive

  • Cubic body-centered

  • Cubic face centered

  • Tetragonal primitive

  • Tetragonal body centred

  • Orthorhombic primitive

  • Orthorhombic side centered

  • Orthorhombic face-centered

  • Orthorhombic body-centered

  • Monoclinic primitive

  • Monoclinic side centered

  • Hexagonal 

  • Trigonal

  • Triclinic.

2. What is the importance of the topic of Bravais lattice?

The most important building block of solid-state physics and crystallography chemistry is Bravais lattice. The basic translational symmetry present to form a perfect crystal is based on the concept of  Bravais lattice. The concept can be represented mathematically with a translational operation. It is basically the skeletal frame on which the crystal is formed. If the translational symmetry explained by Bravais lattice is known then it becomes quite easier to work in Fourier space than actual real space. This helps to avoid any type of manipulation.

3. How can you say whether a structure is Bravais lattice or not?

The most important conditions which can guarantee a structure to be a Bravais structure are as follows:


  • The surrounding environment of each lattice point should be the same.

  • If a structure is Bravais Lattice only 2 or 3 primitive basis vectors will be sufficient enough to translate to every lattice point. 

  • A lattice can be a periodic set of points in space but to be a Bravais lattice it should fit into the 14 classifications of infinitely possible lattices based on their space group symmetry.

4. What is the importance of the concept of crystallography?

The concept of crystallography is not only important in daily physics but also in daily chemistry. In chemistry, it is important enough to determine the purity of samples. A crystal is the actual skeletal frame of the molecule so many impurities in it will not allow the formation of the crystal. It also helps to determine the catalytic activities of certain materials in chemical reactions. It is quite useful to know the actual pattern structure of a molecule along with the pattern of atoms in it. This helps to determine how the structure behaves in a specific way and reacts accordingly.

5. How is Vedantu useful?

Vedantu is always there to help you in understanding any concept with its resourceful study materials. So is the case for the concept of  Bravais Lattices also. Vedantu provides the solutions to all NCERT problems based on Bravais Lattices. They can be easily downloaded from the Vedantu website or from Vedantu Learning App. Not only NCERT solutions but also revision notes, sample questions with solutions, mock tests on this concept are well designed by subject experts of Vedantu and they are available in free PDF in the Vedantu site and App for easy access of the students. Students can also clear their doubts in this topic from one-to-one doubt clearance classes from subject experts if needed. Live coaching classes are available online for the assistance of the students. Vedantu is the one destination for solutions to all the learning problems of the students.