gs 122 3 crystallographic point groups.pptx
TRANSCRIPT
What are the 32 Point Groups?The interaction of symmetry elements around a common
center, as found in all natural minerals and in their 3-D lattices and external forms
BariteBaSO4
orthorhombic lattice
USC Mineralogy Geol 315 (Anderson)Acknowlegement: some images from John Winter and Joe Smythe
Six Crystal Systems
Name axes angles
Triclinic a b c 90o
Monoclinic a b c = 90o 90o
Orthorhombic a b c = 90o
Tetragonal a1 = a2 c = 90o
Hexagonal
Hexagonal (4 axes) a1 = a2 = a3 c = 90o 120o
Rhombohedral a1 = a2 = a3 90o
Isometric a1 = a2 = a3 = 90o
3-D Lattice Types
a
b
c
PMonoclinic
=a g=90o ¹ ba ¹ b ¹ c
a
b
c
I = Ca
b
PTriclinica ¹ b ¹ g
a ¹ b ¹ c
c
c
aP
Orthorhombic=a b=g=90o a ¹ b ¹ c
C F Ib
a1
c
PTetragonal
=a b=g=90o a1 = a2 ¹ c
Ia2
a1
a3
PIsometric
=a b=g=90o a1 = a2= a3
a2
F I
a1
c
P or C
a2
RHexagonal Rhombohedral
900
a1a2
c90
a1 = a2 = a3
Stereographic Projections
Illustrated above are the stereographic projections for Triclinic point groups 1 and -1
Tetragonal System
Point Groups: 1 or 3 characters1st: symmetry on the c-axis2nd: symmetry on a1 and a23rd: symmetry between a’s
Hexagonal Subsystem
Point Groups: 1 or 3 characters1st: Symmetry along c-axis2nd: Symmetry along a’s3rd: Symmetry between a’s
Isometric System
Point Groups: 2 or 3 characters1st: symmetry along a’s2nd: symmetry on [111]3rd: symmetry between a’s