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