Solid State
2.0 Types of Lattice
2.0 Types of Lattice
Primitive Unit Cells: In a primitive unit cell, the same type of particles are present at all the corners of the unit cell.
However, it has been observed that the particles may be present not only at the corners but also at some other special positions within the unit cells. Such unit cells are called ‘non-primitive unit cells’. There are three types of non-primitive unit cells as follows:
$1.$ Face Centred: When atoms are present in all $8-$corners and six face centres in a cubic unit cell then this arrangement is known as FCC.
$2.$ End-Centred: When in addition to particles at the corners, there are particles at the centres of the end faces.
$3.$ Body Centred: When atoms are present at $8$ corners as well as in the body centre in a cubic unit cell then this arrangement is known as BCC.
Seven Crystal Systems: The seven crystal systems are given below.
Crystal System | Bravais Lattices | Parameters of Unit Cell | Example | |
Intercepts | Interfacial angle | |||
1. Cubic | Primitive, Face Centered, Body Centered = 3 | $a=b=c$ | $\alpha = \beta = \gamma = {90^ \circ }$ | $Pb$, $Hg$, $Ag$, $Au$ Diamond, $NaCl$, $ZnS$ |
2. Orthorhombic | Primitive, Face Centered, Body Centered, End Centered = 4 | $a \ne b \ne c$ | $\alpha = \beta = \gamma = {90^ \circ }$ | $KNO_2$, $K_2SO_4$ |
3. Tetragonal | Primitive, Body Centered =2 | $a = b \ne c$ | $\alpha = \beta = \gamma = {90^ \circ }$ | $TiO_2$, $SnO_2$ |
4. Monoclinic | Primitive, End Centered = 2 | $a \ne b \ne c$ | $\alpha = \gamma = {90^ \circ },\beta \ne {90^ \circ }$ | $CaSO_4$, $2H_2O$ |
5. Triclinic | Primitive = 1 | $a \ne b \ne c$ | $\alpha \ne \beta \ne \gamma \ne {90^ \circ }$ | $K_2Cr_2O_7$, $CaSO_4.5H_2O$ |
6. Hexagonal | Primitive = 1 | $a = b \ne c$ | $\alpha = \beta = {90^ \circ },\gamma = {120^ \circ }$ | $Mg$, $SiO_2$, $Zn$, $Cd$ |
7. Rhombohedral | Primitive = 1 | $a = b = c$ | $\alpha = \gamma = {90^ \circ },\beta \ne {90^ \circ }$ | $As$, $Sb$, $Bi$, $CaCO_3$ |
Total $= 14$ | ||||
