What is a Unit Cell and How does Lattice Parameters Relate to them?

The unit cell is regarded as the basic "building block" of a crystal. It is a human construct used to simplify our notion about the size, location, and number of objects contained within the crystal. Pictorially, it is a parallepiped that has lengths and angles, known as the lattice parameters, that are the same as the characteristic angles and repeat distances within the crystal. Theoretically, we should be able to "construct" the entire crystal just by placing a large number of these unit cells next to each other in all directions. A valid unit cell should have a calculated mass density that is very similar to the actual experimentally determined density of the bulk crystal.

The crystal structure of graphite has hexagonal symmetry. The unit cell for graphite can be reduced to a parallelpiped that has two characteristic sides whose length is equal to the "a" lattice parameter. The angle between these two sides measure 120 degrees. The repeat distance along its hexagonal axis is equal to the "c" lattice parameter.

The "a" Lattice Parameter for the Graphite Unit Cell

The "a" lattice parameter for graphite can be obtained by directly imaging the sheets of the graphite crystal using Scanning Tunneling Microscopy. Try your hand at determining the value for the "a" parameter, the periodic basal plane distance that is part of the unit cell, for graphite.

Record the value for "a" using the online activity "Determining basal plane parameter". This information will be needed when you try to calculate the volume for the graphite unit cell.

The "c" Lattice Parameter for the Graphite Unit Cell

The "c" lattice parameter is the repeat distance between the graphite sheets along the unit cell's hexagonal axis. The distance that separates these sheets can be directly imaged by using a Transmission Electron Microscope. Measure this distance and multiply this value by two to determine how big the "c" lattice parameter is.

Record the value of the "c" parameter that you will determine using the online activity "Determining axial parameter". This will be needed for calculating the volume of the graphite unit cell.

The volume of the parallelpiped described for the graphite unit cell can be calculated by using this expression:

where V is the volume of the unit cell,
          a  is the "a" lattice parameter,
and     c  is the "c" lattice parameter.

Record the value for the volume of the graphite unit cell for later use in calculating Avogadro's Number