Crystalline structures are characterised by a repeating pattern in three dimensions. The periodic nature of the structure can be represented using a lattice .
To generate the lattice from any repeating pattern, we choose an arbitrary reference point and examine its environment. We then simply mark in all the points in the pattern that are identical to the chosen reference point. The set of identical points is the lattice, and each point within it is a lattice point.
A. Putnis, Introduction to Mineral Sciences, Cambridge University Press, 1992
Note that not all atoms within this pattern are sitting on lattice points. The atoms not marked with a spot have different arrangments of atoms around them than those marked with a spot (each atom is surrounded by 3 atoms in a triangle, but the orientation of the triangles is different).
Note: This animation requires Adobe Flash Player 8 and later, which can be downloaded here.
To practice identifying the lattice points within a more complex repeating pattern, try the following game! The brick pattern corresponds to an unusual style of Danish bricklaying where after each normal brick, the next is laid breadthwise,and so on. The original image was taken from the wall of the Centre for Electron Nanoscopy in Copenhagen (thanks to Dr Rafal Dunin-Borkowski).
Note: This animation requires Adobe Flash Player 8 and later, which can be downloaded here.
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