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
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