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Answer 1 · 2016-03-27T12:14:36

The coordination number of an atom in a crystal is the number of its "nearest neighbours".

The atoms in crystals are arranged in various repeating three-dimensional arrays.

www.webelements.com

The atoms have different numbers of nearest neighbours, depending on how they are packed in the crystal.

The coordination number (CN) is a measure of how tightly the atoms are packed together.

Here are some examples.

The atoms in polonium ( $Po$ $"Po"$ ) are arranged at the corners of a cube.

An atom in a polonium crystal has CN = 6.

You can see its six nearest neighbours in the diagram above.

The crystal structure of sodium ( $Na$ $"Na"$ ) has an additional atom in the centre of the cube (a body centred cube)

mrsec.wisc.edu

An atom of $Na$ $"Na"$ has CN = 8.

Its nearest neighbours are the 8 atoms at the corners of the cube.

The atoms in magnesium ( $Mg$ $"Mg"$ ) are packed on top of each other like the apples in a crate (in a hexagonal closest packed structure).

Each atom of magnesium has 12 nearest neighbours, so CN = 12.

The University of Sydney has some great animations that might help you visualise some crystal structures and their coordination numbers.

The video below shows how to find coordination numbers.