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.
7. PRIMITIVE AND CENTRED UNIT CELLS
Unit cells can be broadly divided into two categories , primitive and
centred unit cells.
When constituent 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.
8. THREE TYPES OF CENTRED UNIT CELLS.
1. 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.
9. 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.
10. 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.
13. P I F E
a b c
90
White tin, SnO2, TiO2, CaSO4
14. P I F E
a b c
90
Rhombic sulfur, KNO3, BaSO4
15. P I F E
a b c
90
4 Monoclinic Parallogramic Prism
Monoclinic sulfur, Na2SO4.10H2O
16. P I F E
a b c
5 Triclinic Parallelepiped (general)
K2Cr2O7, CuSO4.5H2O, H3BO3
17. P I F E
a b c
90 , 120
6 Hexagonal 120 Rhombic Prism
Graphite, ZnO, CdS
18. P I F E
7 Rhombohedral Parallelepiped (Equilateral, Equiangular)
a b c
90
Calcite (CaCO3), Cinnabar (HgS)
19. 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
20. 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