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Crystal systems

The rotational symmetry of a crystal places constraints on the shape of the conventional unit cell we choose to describe the structure. On this basis we divide all structures into one of 7 crystal systems. For example, for crystals with 4 fold symmetry it will always be possible to choose a unit cell that has a square base with a = b and γ = 90°:

4-fold symmetry example

There are 14 unique combinations of the 7 crystal systems with the possible types of primitive and non-primitive lattices. These are referred to as the 14 Bravais lattices.

Crystal systems, lattices and symmetry elements

Crystal System

Defining Symmetry

Unit Cell Geometry

 

Triclinic

Translational Only

a≠b≠c; αβγ

a

Monoclinic

A diad axis
(parallel to [010])

a≠b≠c; α=γ=90°; β>90°

a

Orthorhombic

3 diads
(each should be parallel to each axis)

a≠b≠c; α=β=γ=90°

a

Trigonal

For more information click here

1 triad
(parallel to [001])

a=b≠c; α=β=90°;
γ=120°
( or
a=b=c;
120° > α=β=γ ≠ 90°)

a

Hexagonal

1 hexad (parallel to [001])

a=b≠c; α=β=90°;
γ=120°

a

Tetragonal

One tetrad
(parallel to the [001] vector)

a=b≠c; α=β=γ=90°

a

Cubic

4 triads
(all parallel to <111> directions)

a=b=c; α=β=γ=90°

a

Bravais Lattice Structures

     
     
     
     
 
     

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