A crystal is a three dimensional
periodic discontinuum. It consists
of identical “bricks” called unit
cells, which form a three
dimensional lattice.
The unit cell is defined by the
axes
a
,
b
, and
c
, and the three
angles
α
,
β
,
γ
, which form a right
handed system.
α
a
b
c
γ
β
Volume of the unit cell V:
V =
abc
[1cos
2
α
– cos
2
β
– cos
2
γ
+
2cos
2
α
– cos
2
β
– cos
2
γ
]
½
Going 3D
C
ourtesy of George M. Sheldrick.
Used with permission.
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The Unit Cell
The unit cell is the smallest unit that can generate the entire crystal
structure only by means of translation in three dimensions.
Within each unit cell there may be several symmetry related copies of
the asymmetric unit but in general those are oriented differently.
Even though in the structure of
NaCl there is an atom at every
corner of the unit cell, such an
arrangement is rather rare.
If the structure is centro
symmetric, the unit cell is
chosen so that its origin lies on
an inversion center.
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 Spring '03
 RogerD.Kamm
 Crystallography, Crystal system, George M. Sheldrick

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