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Crystals and Their Structure
Unit Cells in the Cubic Crystal System
Simple Cubic
Body - Centered Cubic
Face - Centered Cubic
Cubic Closest Packing of Frozen Argon
Cubic Closest Packing of Frozen Methane
Coordination Number
Counting Cell Occupancy
Volume of the Unit Cell
r is the radius of an atom in the unit cell
r
The volume of the unit cell is L3
L
But how do you get L?
The Pythagorean Theorem, of course!
Volume of the Unit Cell
L
L 4
22 2r =L +L
16 28
8
3
2cell
3
2 2
r
r = LL= r
V =
rr
r
r
Calculating Packing Efficiency
L
L
Packing efficiency is the ratio of the space occupied in the unit cell to the volume of the unit cell
8 3
2cell
3rV =Cell occupancy = 4
43 0.740
4
8
spheres in cell
3
2cell
3
3=
r
r
V =V
4
34 spheres in cell
3rV =
rr
r
r
Sodium Chloride
Crystalline and Amorphous Silicon Dioxide
Cristobalite, one of the crystallineforms of silicon dioxide, showscubic closest packing.
A glass made from silicondioxide shows the amorphousdisoriented structure.
STM of Silicon
STM of Gold
www.ieap.uni-kiel.de/surface/ag-berndt/ mikro/images/stm.gif 3/27/02
STM Images
www.almaden.ibm.com/vis/stm/atomo.html 3/27/02
Xe atoms on Ni substrate
STM Images
www.almaden.ibm.com/vis/stm/atomo.html 3/27/02
Carbon monoxide on Pt
STM Images
www.almaden.ibm.com/vis/stm/atomo.html 3/27/02
Fe corral on Cu substrate