12th chemistry solid state - Crystal Lattices and Unit Cells

Crystal Lattices and Unit Cells

Crystal Lattice

• Regular three-dimensional arrangement of points in space

• There are 14 possible three-dimensional lattices, known as Bravais lattices.
• Characteristics of a crystal lattice:

• Each point in a lattice is called lattice point or lattice site.
• Each lattice point represents one constituent particle (atom, molecule or ion).
• Lattice points are joined by straight lines to bring out the geometry of the lattice.

Unit Cell

• Smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice

• Characterised by −

(i) Its dimensions along the three edges a, b and c

(ii) Angles between the edges α, β and γ

• The unit cells can be classified as follows:

Seven Crystal Systems

There are seven types of primitive unit cells, as given in the following table.

The given table lists seven primitive unit cells and their possible variations as centered unit cells.

Crystal Class	Axial Distances	Axial Angles	Possible Types of Unit Cells	Examples
1. Cubic	a = b = c	α = β = γ = 90°	Primitive, body-centred, face-centred	KCl, NaCl
2. Tetragonal	a = b ≠ c	α = β = γ = 90°	Primitive, body-centred	SnO2, TiO2
3. Orthorhombic	a ≠ b ≠ c	α = β = γ = 90°	Primitive, body-centred, face-centred, end-centred	KNO3, BaSO4
4. Hexagonal	a = b ≠ c	α = β = 90°; γ = 120°	Primitive	Mg, ZnO
5. Trigonal orRhombohedral	a = b = c	α = β = γ ≠ 90°	Primitive	(CaCO3) Calcite, HgS (Cinnabar)
6. Monoclinic	a ≠ b ≠ c	α = γ = 90°; β ≠90°	Primitive and end-centred	Monoclinic sulphur, Na2SO4.10H2O
7. Triclinic	a ≠ b ≠ c	α ≠ β ≠γ≠ 90°	Primitive	K2Cr2O7, H3BO3

• Unit cells of 14 types Bravais lattices:

• Cubic lattices: All sides are of the same length, and the angles between the faces are 90° each

• Tetragonal lattices: One side is different in length from the other two, and the angles between the faces are 90° each

• Orthorhombic lattices: Unequal sides; angles between the faces are 90° each

• Monoclinic lattices: Unequal sides; two faces have angles not equal to 90°

• Hexagonal lattice: One side is different in length from the other two, and the marked angles on two faces are 60°
• Rhombohedral lattice: All sides are of equal length, and the marked angles on two faces are less than 90°
• Triclinic lattice: Unequal sides; unequal angles, with none equal to 90°