Seven primitive unit cells and their possible variations as centered unit cell

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes

Parameters of Unit cell → a, b, c : axial distances or core lengths, α.β.γ : axial angles

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 1

Crystals have seven types of primitive unit cells which are given as follow

→ Cubic : In this type of unit cell, three aixal distances are same and each axial angle is of 90°. Examples: NaCl, Cu, Au, Ag, Hg, KCl, zinc blende (ZnS). KCI, CaF₂, diamond etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 2

→ Tetragonal : In this type of unit cell, three axis are perpendicular to each other in which two axis are same but one axis is different. The axial angle between all faces is 90°
Examples: White tin, TiO₂, SnO₂, CaSO₄, urea etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 3

→ Orthorhombic : In this type of unit cell, three axial distances are different. Here each axial angle is of 90°
Examples: Orthorhombic sulphur, KNO₃, K₂SO₄, BaSO₄, PCO₃, CuSO₃, C – sulphur, I₂ etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 4

→ Monoclinic : In this type of unit cell, three axial distances are different. Two axial angle are equal to 90° and one axial angle is different from 90°.

Examples: Monoclinic sulphur. Na₂ SO₄ 10H₂O₄, PbCrO₄. CaSO₄. 2H₂O, β-sulphur etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 5

→ Hexagonal : In this type of unit cell, two axes are same but third axis is different. Similarly in this, two axial angles are of 90° but one axial angle is of 120°.
Examples: Graphite, ZnO, CdS, Pbl₂, HgS, Agl, SiC, Zn, Cd, Mg etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 6

→ Rhombohedral or Trigonal : In this type of unit cell, three axis are of same length. Axial angles between them are also same but not equal to 90°.
Examples: Calcite (CaCO₃), quartz. NaNO₃, Cinnabar (HgS), Sb etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 7

→ Triclinic : In this type of unit cell, three axis are of different length and three axial angle are also different and also not equal to 90°
Example : K₂Cr₂O₇. CuSO₄ 5H₂O.H₃BO₃ etc.

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 8

Above discussed crystal systems are represented in table 1.3 .

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 9

→ Note : Bravais lattice : French mathematician Bravais (1848) proposed that seven crystal systems have been divided in to 14 different types of crystal lattice on the basis of constituent particles present in unit cell. These 14 different types of crystal lattices are called Bravais lattices. 14 Different Bravais lattices are represented in table 1.4:

Crystal System	Types of Lattices	Number of Lattices
Cubic	Primitive, Body centred, Face-centred	3
Tetragonal	Primitive, Body centred	2
Orthorhombic	Primitive, Body centred, Face-centred, End centred	4
Monoclinic	Primitive, End-centred	2
Hexagonal	Primitive	1
Rhombohedral	Primitive	1
Triclinic	Primitive	1
		Total = 14

The structures of unit cell of 14 types of Bravais lattices ara shown as follows

Seven primitive unit cells and their possible variations as centered unit cell Chemistry Notes 10