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system.
Also for crystal systems with one atom per basis, the number of atoms bonded to one particular
atom is called the coordination number (CN). These are the nearest neighbor atoms and are Rev 4.1 17 Crystals 1 MatE 25 San Jose State University Lab Notes assumed to be “touching” each other. The coordination number gives information about the
environment around a particular atom (i.e. electron energy states and physical properties).
One property that can be calculated from knowing the arrangements of atoms in the crystal
structure and the radius of the atom is the atomic packing factor (APF). The APF is the number
of atoms in the unit cell multiplied by the volume of the atom and divided by the volume of the
unit cell.
Vatoms
(1)
Vcell
where Vatoms is the volume of the atoms in the unit cell, and Vcell is the volume of the unit cell.
APF = Rev 4.1 18 Crystals 1 MatE 25 San Jose State University Lab Notes Lab Worksheet 1
Coordination Number
Key Member (Encourages all team members to participate, ensures everyone understands the material, and
organizes/divides the tasks amongst the team members):
Other Group Members: 1.0 Using the Solid State Model Kits:
Helpful Hints:
1. READ THE INSTRUCTIONS ON PAGE 4 & 5 OF THE KIT MANUAL.
2. The two plastic bases have marks on them, one is a yellow semicircle and the other is a
green circle. These symbols match the symbols on the lettered templates.
3. If the holes on the template do not match up, turn the template 90o.
4. If you tried hint 3 and they still don’t line up try the other base.
5. Do not force the rods into the base holes. They should slide in easily.
6. Do not force the balls down the rods.
7. The color of the balls used for each model is displayed at the bottom of each page.
8. The numbers for each layer of the model correspond to the balls at the bottom of each
page. Put the balls on in sequential order.
9. At the top of the page there are instructions for building each model and the template you
should use. 2.0 Coordination Number with Crystal Kit Models
1. Build all 5 models in steps 24 below and answer the questions below about coordination
numbers.
2. Build the models for CN 8, 6, and 4 on page 93 of the Model Kit Manual.
3. Build the model for cubic close packed (CCP) CN 12 pg. 99.
4. Build the model for CN 8 pg. 100.
5. Build the model for CN 4 on pg. 103.
a) Which set of structures that you just built represent compounds and which represent
elemental solids?
b) How many nearest neighbors does each model have?
c) Find the plane that has the greatest density (which plane has greatest number of lattice
points per area). Point this out to your instructor, and explain how you figured it out. Rev 4.1 19 Crystals 1 MatE 25 San Jose State University Lab Notes Lab Worksheet 2
Crystal Systems  Elemental Solids
1. Build the models for simple cubic (SC) pg. 9, BodyCentered Cubic pg. 18, and FaceCentered Cubic pg. 27 and fill in the table below as you build each one.
2. Calculate the a/r ratio and APF for each structure. Show your work neatly on the back
page. Label the steps and make sure your instructor can figure out your calculations.
You may check your results to the values in the textbook. You will be asked to do these
calculations for other structures on the tests so make sure everyone in the group
understands the process to calculate them.
Simple Cubic Body Centered
Cubic Face Centered
Cubic # of atoms per basis
# of lattice points
per unit cell
# of atoms per unit
cell
Coordination
Number
a/r Ratio
Atomic Packing
Factor
3. After you calculate the APF in the table above, use the wooden models and sand to measure
the APF for FCC and BCC. (Do this only if you have finished the table on Worksheet 3, and
check with your instructor. When you use the sand be careful not to spill it, and be prepared
to clean up afterwards.)
FCC Measured values: BCC
How do the calculated and measured values compare? Rev 4.1 1  10 Crystals 1 MatE 25 San Jose State University Lab Notes Lab Worksheet 3
Crystal Systems  Compounds
1. Build CsCl (pg. 11), NaCl (pg. 33), DC (pg. 23), and Zincblende (pg. 51) structures and fill
in the table below.
Once you have built each structure, study the structure and identify the lattice type.
Remember there may be more than one atom per basis, so you may need to identify a group
of spheres that belong to one lattice point. CsCl NaCl Diamond
Cubic (Si) Zincblende
(GaAs) Lattice Type
# of atoms per
basis
# of lattice points
per unit cell
# of atoms per
unit cell Rev 4.1 1  11 Crystals 1...
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 Spring '08
 RayChen

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