Structure of Solids

Structure of solids is an expression of variety of ways of arrangement of the atoms and molecules.

Some important definitions:

(i) Space Lattice: Regular 3D-arrangement of particles in a particular fashion is called Space Lattice.

(ii) Lattice Point: Points that represent constituent particles in Space Lattice are called as Lattice points.

(iii) Unit Cell: The building block of space lattice, which cannot be divided further is called a unit cell.

A study of unit cell will be a reflection of entire properties of Space Lattice.

Space lattice and lattice points

In order to uniquely define a unit cell we would require axial properties (cell parameters). Axial properties are (i) length parameter (a, b, c) and (ii) angular parameter (α, β, γ) between two adjacent faces.

Different combinations of a, b, c, α, β, γ can yield seven different crystal systems and a total of 14 Bravais lattices.

Seven Crystal Systems and Fourteen Bravais Lattices

Bravais on the basis of geometrical considerations, suggested that there are 14 possible ways of arrangements of point in regular three dimensional network. These 14 arrangement are known as Bravais lattices.
 

Crystal system	Edge Length	Angles	Example	Bravais Lattices
Cubic	a = b = c	α = β = γ = 90°	NaCl, KCI	Simple, Body centered, Face centred
Tetragonal	a = b ≠ c	α = β = γ = 90°	TiO2, Sn02	Simple, Body centered
Orthorhombic	a ≠ b ≠ c	α = β = γ = 90°	S, BaSO4, PbCO3	Simple, Body centered, Face centered, End centered
Monoclinic	a ≠ b ≠ c	α = β = γ = 90°	Borax, S	Simple, End centered
Triclinic	a ≠ b ≠ c	α = β = γ = 90°	Boric acid, K2Cr2O7	Simple
Hexagonal	a = b ≠ c	α = β = γ = 120°	SiC, ZnO, graphite	Simple
Rhombohedrala	a = b = c	α = β = γ = 90°	Quartz, cinnabar, Simple calcite(CaCO3)	Simple