1. Objective

This project requires model building of the three most common crystal structures: body-centered cubic (BCC), face-centered cubic (FCC) and hexagonal close packed (HCP). The goal for this lab project is to obtain a tangible grasp of the similarities and differences among each of these three crystal structures. To achieve this goal, you will build the models from ping-pong balls using the experimental procedures outlined below. Your assignment lies in composing a succinct memo (one page of text), which clearly describes the most important features of the structures.

To give a somewhat more realistic context to this exercise, assume that you are employed by Crystal Clear Consulting, Inc. A long-standing client has telephoned to discuss his interest in obtaining more insight in the three most common crystal structures and has requested your services. After some deliberation, you deem it necessary to build several models of these structures. You agree to take on the project, and you request that he fax his list of specific questions (see Section 4 of this document). Since this particular client has limited funding and cannot afford your hourly rates, he desires only a one page memo which addresses his queries. You decide to throw in a second page which contains various comparative tables of features for the three structures. You should refer to these tables in your memo to your client.

2. Experimental Procedure

Construction of FCC model (14 balls required)

Method 1

1. Measure the diameters of ping-pong balls and determine the mean value of the diameter of ping-pong balls used in this construction.
2. Construct the close-packed plane using six balls, in a triangle form.
3. Attach a ping-pong ball to this plane at suitable place and use its center as origin, determine x, y, z axes.
4. Attach 3 balls which appear at face centers to the model.
5. Attach the remaining 4 balls which should appear at corners of the model.

Method 2

1. Measure the diameters of ping-pong balls and determine the mean value of the diameter of ping-pong balls used in this construction.
2. Construct 2 close-packed planes using six balls each.
3. Join these 2 planes, rotating them slightly to fit in interstitial positions.
4. Attach remaining 2 ping-pong balls to this structure at suitable positions.

1. Measure the diameters of ping-pong balls and determine the mean value of the diameter of ping-pong balls used in this construction.
2. Use Lucite sheet box provided, drop 4 balls into the box, place them at corners, and drop one ball above them at the center, glue them together.
3. Drop 4 balls above the partially finished BCC model, place them at the corners, glue them to the central ball. Take the model out of the box after the glue hardens.

1. Measure the diameters of ping-pong balls and determine the mean value of the diameter of ping-pong balls used in this construction.
2. Glue seven ping-pong balls in an hexagonal array.
3. Repeat step 2.
4. Glue three ping-pong balls in a triangular array.
5. Sandwich the triangular array between the two hexagonal layers.

(To measure interstitial void sizes build an additional triangular array.)

1. Using modeling clay, find the diameter of a sphere that will fit into the voids (i.e., empty spaces between atoms).
2. Determine what might be the largest diameter sphere that could fill those spaces.

Note that there are two types of interstitial sites: tetrahedral and octahedral.
A tetrahedral void is surrounded by 4 atoms, lying within a tetrahedron. An octahedral void is surrounded by 6 atoms, lying within an 8-sided octahedron.
You might need to use more than one model to make these determinations.

3. Data Collection

1. Measure the diameter of ping-pong balls and determine the mean value of the diameter of ping-pong balls used in these models.
2. Measure and calculate the following interplanar distances for the following:

FCC: (100), (110), and (111),
BCC: (100) and (110),
HCP: lattice parameters a and c.
3. Distinguish the various interstitial sites for each structure.
4. Present this data clearly on a single page in a series of tables.

For example, one of your Tables could include the following information:

Table 3 - Measured Interplanar Spacing (Note that Caption is above the table)
 

Crystal Structure	FCC	BCC	HCP
{100} interplanar spacing	xxx.xx	xxx.xx	xxx.xx
{110} interplanar spacing	xxx.xx	xxx.xx	xxx.xx
{111} interplanar spacing	xxx.xx	xxx.xx	xxx.xx

 

All Tables (presented on the second page of your assignment) must be referred to in the memo text appearing on the first page!

4. Queries from Client

The following list of questions should be addressed in your memo. There is no specific order to this list, so you should determine the best way to organize your remarks.
 

1. Are there any limitations to using these models to experimentally determine the interplanar spacing? (i.e., how do measured values compare with calculated?) HINT: Create a Table of measured and calculated values and discuss three sources of error.
2. Explain which of these three crystal structures are most similar and why.
3. Based on a given atomic radius, which crystal structure has the largest volume?
4. For an HCP structure, is the octahedral or tetrahedral site larger?
5. List a few common materials which occur with each structure.
6. Which crystal lattice structure has the largest interstitial voids? HINT: Extend lattice beyond single unit cell, and use a Table to show your results.

1. William D. Callister, Jr., Materials Science and Engineering, An Introduction,

McGraw Hill, 1997.
2. Craig R. Barrett, William D. Nix, Alan S. Tetelman,

The Principles of Engineering Materials, Prentice-Hall, Inc., 1973.
3. H.P. Myers, Introductory Solid State Physics, 1990.
4. Helen D. Megaw, Crystal Structures, 1973.
5. Martin J. Buerger, Elementary Crystallography, MIT Press, 1978.