Geos 306, Lecture 9
Crystallography - Unit Cells

Definition of crystal and mineral

Periodicity

The unit cell
System
a
b
c
bc = α
ac = β
ab = γ
cubic
 a 
 a 
 a 
90
90
90
hexagonal
a
a
c
90
90
120
tetragonal
a
a
c
90
90
90
orthorhombic
a
b
c
90
90
90
monoclinic
a
b
c
90
β
90
triclinic
a
b
c
α
β
γ

Atomic coordinate systems
atom
x
y
z
Si
0.4697
0
0
Si
0
0.4697
2/3
Si
0.5303
0.5303
1/3
O
0.4133
0.2672
0.1188
O
0.2672
0.4133
0.5479
O
0.7328
0.1461
0.7855
O
0.5867
0.8539
0.2145
O
0.8539
0.5867
0.4521
O
0.1461
0.7328
0.8812


Zones

Planes

Reading:
Wenk and Bulakh, Chapter 3
Klein, Chapter 5
Nesse, Chapter 2