THE CRYSTAL SYSTEMS AND FOURTEEN BRAVAIS LATTICES

The total number of possible crystal forms are On the basis of their symmetry these crystal forms are grouped into 32 classes of symmetry called point groups. The crystallographers have been able to divide 32 point groups and 14 Bravais lattices into seven crystal systems. These systems differ from one another in having different magnitudes of lengths of the various axes and the angles between them for their unit cell In other words, these systems differ from each other in their external shapes due to the arrangement of unit cells in their dimensions: There are seven such unit cells which are necessary to build the external shapes of all known crystals and according to these seven unit cells, all the crystals are classified under seven groups. These groups are called crystallo-graphic systems or simply crystal systems. The individual crystal belonging to the same system are identified from the magnitudes of the lengths of the unit cell only because the corresponding angles have the same values.

it one should know the magnitudes of lengths parallel to the three mutually perpendicular A unit cell, as already mentioned, has a definite geometric shape and to reproduce reference axes as well as the angles between them. It is customary to represent the unit cell length parallel to X-axis with the letter a, parallel to y-axis with & and parallel to Z-axis with c. The angle between a and b is denoted with y, between a and with B and between b and e with a.

 The seven crystal systems are obtained when we use a simple (primitive) unit cell The a unit cell (symbol P). The geometric characteristics of these crystal systems are listed in Table.

Besides these primitive unit cells or lattices we have other types of unit cells or lattices called as (i) Body-centred unit cell (symbol I), having one point at the centre in addition to at the corners, (ii) Face-centred unit cell (symbol F) having lattice points in the centre of each face in addition to at the corners, (iii) End centred unit cell (symbol C) having points at the corners and at the intersections of the diagonals of a pair of opposite faces. The unit cells corresponding to these space lattices are shown in Fig.

the same system are identified from the magnitudes of the lengths of the unit cell only because the corresponding angles have the same values.

it one should know the magnitudes of lengths parallel to the three mutually perpendicular A unit cell, as already mentioned, has a definite geometric shape and to reproduce reference axes as well as the angles between them. It is customary to represent the unit cell length parallel to X-axis with the letter a, parallel to y-axis with & and parallel to Z-axis with c. The angle between a and b is denoted with y, between a and with B and between b and e with a.

The seven crystal systems are obtained when we use a simple (primitive) unit cell The a unit cell (symbol P). The geometric characteristics of these crystal systems are listed in Table 3.1.

Besides these primitive unit cells or lattices we have other types of unit cells or lattices called as (i) Body-centred unit cell (symbol I), having one point at the centre in addition to at the corners, (ii) Face-centred unit cell (symbol F) having lattice points in the centre of each face in addition to at the corners, (iii) End centred unit cell (symbol C) having points at the corners and at the intersections of the diagonals of a pair of opposite faces. The unit cells corresponding to these space lattices are shown in Fig.

 

 

In 1848, Bravais showed that there are fourteen different basic arranger possible for arranging similar points in a regular continuous in three dimensional These arrangements are called Bravais lattices (spaces) and in terms of these the in terms of these are internal structure can be described. The Bravais lattices associated with the seven crystal systema are listed in Table and the unit cells of the fourteen Bravais lattices are shown in Fig.