Question

State the classification of seven crystal system along with axial length and number of bravis lattices in each type (explain in short)

Answer 1

1) Triclinic, $a \neq b \neq c, \alpha \neq \beta \neq \gamma \neq 90^\circ$. Only 1 Bravais lattice - primitive (P).

2) Monoclinic, $a \neq b \neq c, \alpha = \gamma = 90^\circ, \beta \neq 90^\circ$. 2 Bravais lattices - Primitive (P) and Base-centered (C).

3) Orthorhombic, $a \neq b \neq c, \alpha =\beta= \gamma = 90^\circ$. 4 Bravais lattices - Primitive (P), Base-centered (C), Body-centered (I) and Face-centered (F).

4) Tetragonal, $a = b \neq c, \alpha =\beta= \gamma = 90^\circ$. 2 Bravais lattices - Primitive (P) and Body-centered (I).

5) Rhombohedral, $a = b =c, \alpha =\beta= \gamma \neq 90^\circ$. Only 1 Bravais lattice - primitive (P).

6) Hexagonal, $a = b \neq c, \alpha =\beta= 90^\circ, \gamma = 120^\circ$. Only 1 Bravais lattice - primitive (P).

7) Cubic. $a =b = c, \alpha =\beta = \gamma = 90^\circ$ . 3 Bravias lattices - Primitive (P), Body-centered (I) and Face-centered (F).