Module 3 :
Lecture 10 : Material Properties: The Role of Crystal Structure
 



Crystalline Structures

Morphologically, crystalline materials may have 14 different 3-D arrangements of atoms known as lattices.You can see a simple lattice animation below.

 

These 14 lattices are actually derived out of seven different crystal systems. The differences in crystal systems occur due to the fact that a 3d tetrahedral lattice possesses six lattice parameters.

The following table explains the seven basic systems:

Structure
Axes
Axes Angles
Unit Cell Volume
Cubic
a=b=c
α=β=γ=900
a3
Tetragonal
a=b≠c
α=β=γ=900
a2c
Orthorhombic
a≠b≠c
α=β=γ=900
abc
Hexagonal
a=b≠c
α=β= 900; γ=1200
0.866 a2c
Trigonal
a=b=c
α=β=γ≠900
a3(1-3cos2α+2cos3α)1/2
Monoclinic
a≠b≠c
α=β= 900; γ≠900
abc sinβ
Triclinic
a≠b≠c
α≠β≠γ≠900
abc(1-c2α-c2β- c2γ+2cα cβcγ)
cα= Cosα, cβ=Cosβ, cγ=Cosγ