The unit cell

The unit cell is a parallelepiped that is the simplest repeating unit of a crystal (diagram I).

Diagram II shows a crystal that is composed of unit cells where a = b = c and α = β = γ = 90°. Each blue point, known as a lattice point, must have identical surroundings (or environment) in the crystal. An infinite three-dimensional array of lattice points forms a space lattice. The unit cell in II that has eight lattice points at all corners of a cube is called a simple cubic unit cell.

Consider a crystal structure containing two types of atoms (diagram III). As each lattice point must have the same surroundings, it is, in this case, a point consisting of a pair of blue and red atoms (diagram IV). Therefore, each lattice point, in general, may represent an atom, a molecule or a collection of atoms or molecules. Using the pair of atoms as a basis in forming the space lattice, we find that the unit cell for compound III is also a simple cubic unit cell.

Finally, a unit cell must fill all space of the crystal when replicated. As a result, spherical unit cells do not exist.


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