The Fascination of Crystals and Symmetry

Unit 3.6

by Frank Hoffmann & Michael Sartor

Classify Crystals into Classes

3rd Example

a

b

c

Classify Crystals into Classes

3rd Example

a

b

c

Introducing viewing directions, here a b c

Classify Crystals into Classes

m

3rd Example

a

b

c

Classify Crystals into Classes

Struvite

MgNH4PO4 · 6 H2O

m

m2 m m 2crystal class

3rd Example

(ortho)rhombic-pyramidal

a

b

c

2 m msymmetry elements

by convention

http://webmineral.com/data/Struvite.shtml

a b c

Classify Crystals into Classes

Zn4Si2O7(OH)2 · H2O

m

m2 mm2crystal class

3rd Example

Hemimorphite

a

b

c

(ortho)rhombic-pyramidal

Classify Crystals into Classes

4th Example

ab

c

120°

viewing directions(hexagonal crystal system)

c a [210]

Lattice directions

a

b (=a)

[210]

[120]

[110]

<210> = [210],

[110],

[120]

2,1

-1,1

-1,-2

[100]

[010]

Classify Crystals into Classes

4th Example

ab

c

120°

6 viewing directions(hexagonal crystal system)

c a

6

[210]

Classify Crystals into Classes

4th Example

ab

c

120°

6

m

viewing directions(hexagonal crystal system)

c a [210]

6m

m

m

Classify Crystals into Classes

4th Example

ab

c

120°

6

m

m

viewing directions(hexagonal crystal system)

c a [210]

6m

m m

Classify Crystals into Classes

4th Example

ab

c

120° (Mg, Graphite, Nickeline)

CuS

Covellite

6/mmmcrystal class

dihexagonal-dipyramidal

Crystal Classes – A collectible

2014 FIFA World Cup Brazil

Collectible

2014 International Year of Crystallography

Collectible

Crystal Classes Poster

Crystal Classes Poster

Crystal Classes Poster

Mapping Crystal Classes to Crystal Systems/Crystal Families

crystal system

triclinic

orthorhombic

trigonal

monoclinic

tetragonal

hexagonal

cubic

crystal classes (point groups)

1, 1

2, m, 2/m

222, mm2, 2/m 2/m 2/m

4, 4, 4/m, 422, 4mm, 42m, 4/m 2/m 2/m

3, 3, 32, 3m, 32/m

6, 6, 6/m, 622, 6mm, 6m2, 6/m 2/m 2/m

23, 2/m3, 432, 43m, 4/m 3 2/m

charact. SE

1 or 1

one 2 and/or m

three 2 and/or m

one 4 or 4

one 6 or 6

one 3 or 3

four 3 or 3

hexagonal crystal family

Picture Credits

If not otherwise stated pictures, images, sketches, clip arts are • self-taken/self-drawn or• public domain

McArthurGlen Designer Outlets | Flickr | CC-BY-SA-2.0

Didier Descouenss | CC-BY-SA-3.0

Walter Kölle | CC-BY-SA-3.0

Rob Lavinsky, iRocks.com – CC-BY-SA-3.0

with kind permission bythe PANINI group

Ulrich Peters| Flickr | CC-BY-SA-2.0