# Space Lattice and Unit Cell

**Space Lattice and Unit Cell**

According to **Hauy **(1784) a crystal is built up by a number of small crystals having the shape of the original crystal as a whole. This led to the concept of space lattice or crystal lattice.

*“A space lattice is an array of points showing how particles (atoms, ions or molecules) are arranged at different sites in three dimensional spaces.”*

A crystal is a three dimensional design in which identical points form a 3-dimensional network of cells each representing the unit and through which whole crystal can be built up. The lattice points can be connected by a regular network of lines in various ways. Thus the lattice is broken up into a number of unit cells. This is done by connecting the points by a regular network of lines as shown in figure on next page.

The unit cell may be defined as, *“the smallest repeating unit in space lattice which, when repeated over again, results in a crystal of the given substance”.*

Therefore space lattice of a crystal has been likened to a wall-paper on which a single pattern is continuously repeated. Each unit cell requires two vectors a and b for its description. A three dimensional space lattice can be similarly divided into unit cells described by three vectors. The exact location of particles in a unit cell can be obtained by X-ray diffraction.

It should be understood that the choice of unit cell is by no means unique. There are various ways in which a cell can be drawn in a unique space lattice. However, it is usually convenient to choose a parallelopipe whose edges are parallel with the crystallographic axes (a, b and c) and with the

shortest possible sides. This is termed as primitive cell. One lattice point is associated with each primitive cell.

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