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

space lattice

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



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