Bravais lattices

14 bravais lattices and there examples.

1. BRAVAIS LATTICES ragesh nath r st.joseph’s college bangalore (autonomous)

2. 7 CRYSTAL LATTICE We know that a three dimensional space lattice is generated by repeated translation of three non-coplanar vectors a, b, c. Based on the lattice parameters we can have 7 popular crystal systems.

3. C TOM THR Crystal system Unit vector Angles Cubic a= b=c α = β =√=90 Tetragonal a = b≠ c α = β =√=90 Orthorhombic a ≠ b ≠ c α = β =√=90 Monoclinic a ≠ b ≠ c α = β =90 ≠√ Triclinic a ≠ b ≠ c α ≠ β ≠ √ ≠90 Hexagonal a= b ≠ c α = β =90 √=120 Rhombohedral a= b=c α = β =√≠90

4. BRAVAIS LATTICES In 1850, M. A. Bravais showed that identical points can be arranged spatially to produce 14 types of regular pattern. These 14 space lattices are known as ‘ Bravais lattices ’. Each point in a lattice is called lattice point or lattice site. Each point in a crsytal lattice represents one constituent particle which may be an atom, a molecule(group of atoms)or an ion. Lattice points are joined by straight lines to bring out the geometry of the lattice.

5. Unit cell Unit cell is the smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice. it is characterized by; Its dimensions along the three edges a,b and c. these edges may or may not be mutually perpendicular. Angles between the edges α (between b and c) ß (between a and c) and γ (between a and b). Thus a unit cell is characterized by six parameters.

6. Primitive and centred unit cells Unit cells can be broadly divided into two categories , primitive and centred unit cells. When c onstituent particles are present only on the corner positions of a unit cell. It is called as Primitive unit cell . When a unit cell contains one or more constituent particles present at the positions other than corners in addition to those at corners, it is called a centred unit cell.

7. Three types of centred unit cells. Body–centred unit cells. Such a unit cell contains one constituent particle(atom, molecule or ion) at its BODY-CENTRE beside the ones that are at the corners.

8. 2. FACE-CENTRED UNIT CELLS Such a unit cell contains one constituent particle present at the CENTRE of each face, besides the ones that are at its corners.

9. 3.End-centred unit cells. In such a unit cell, one constituent particle is present at the centre of TWO OPPOSITE FACES besides the ones present at its corners.

10. Arrangement of lattice points in the Unit & No . of Lattice points / Cell.

11. fourteen bravais lattices P I F E

12. P I F E White tin , SnO 2 , TiO 2 , CaSO 4

13. P I F E Rhombic sulfur , KNO 3 , BaSO 4

14. P I F E 4 Monoclinic Parallogramic Prism   Monoclinic sulfur , Na 2 SO 4 .10H 2 O

15. P I F E 5 Triclinic Parallelepiped (general)  K 2 Cr 2 O 7 , CuSO 4 .5H 2 O, H 3 BO 3

16. P I F E 6 Hexagonal 120  Rhombic Prism  Graphite , ZnO , CdS

17. P I F E 7 Rhombohedral Parallelepiped (Equilateral, Equiangular)  Calcite (CaCO 3 ), Cinnabar ( HgS )

18. 4 Monoclinic Parallogramic Prism   5 Triclinic Parallelepiped (general)  6 Hexagonal 120  Rhombic Prism  7 Rhombohedral Parallelepiped (Equilateral, Equiangular)  P I F E Crystal System Shape of UC Bravais Lattices

19. Note: The Crystal Systems are defined based on Symmetries (Rotational, Mirror, Inversion etc.  forming the Point Groups ) and NOT on the geometry of the Unit Cell

20. Thank you