# Calculation of density of unit cell ( Bravais lattices)

The work of Auguste Bravais in the early 19th century revealed that there are only fourteen different lattice structures (often referred to as Bravais lattices).

These fourteen different structures are derived from seven crystal systems, which indicate the different shapes a unit cell take and four types of lattices, which tells how the atoms are arranged within the unit.

We can unambiguously describe a piece of wallpaper by specifying the size, shape, and contents of the simplest repeating unit in the design.

We can describe a three-dimensional crystal by specifying the size, shape, and contents of the simplest repeating unit and the way these repeating units stack to form the crystal.

The simplest repeating unit in a crystal is called a unit cell. Each unit cell is defined in terms of lattice points the points in space about which the particles are free to vibrate in a crystal.

## Example

Lets take an example and assume that an individual has a unit cell that has an edge ‘a.’ The volume of that unit cell is ‘v,’ and the density of the unit cell is given as the ratio of mass and volume of the unit cell.

As the mass of the unit cell is equal to the product of the number of total atoms in the unit cell and the mass of every atom in the unit cell.

Now one has to learn how to find the density of a one-unit cell to arrive at the final answer. Let us begin the answer by noting down everything that we already know.

Mass of unit cell = number of total atoms in unit cell x mass of every atom = z x m

In this equation for finding out the density of unit cell material science, ‘z’ is the total number of atoms in a unit cell, and ‘m’ is the mass of every atom.

Students must also be familiar with the fact that the mass of an atom can be calculated with the help of Avogadro number and molar mass, that is, M / Na

Here, ‘M’ is the molar mass, and ‘Na’ is the Avogadro’s number. so, the volume of the unit cell or ‘V’ = A3

Hence, the density of the unit cell = Mass of the unit cell / Volume of the unit cell

This means that density of the unit cell is equal to m/V = z x m / A3 = z x M / A3 x Na

It can be concluded that if one knows the total number of atoms in a unit cell, edge length, and molar mass, then one can calculate the density of the unit cell.