Crystallography Experiment
developed by Kenneth Kauffman

Objective:
To understand the concepts of crystal structure, atomic packing, and Miller Indices as well as their applications to materials properties and development. You will not be turning in a report for this lab but your lab notebook will be graded. All items listed in bold below MUST be recorded in your notebook and the TA must inspect it before you leave the lab session.

Procedure:
This experiment will include both individual work and collaborative work with your lab partners. Get to know your lab partners as you will be working with them for the remainder of the semester.

Crystallography kits are available in the laboratory. These kits consist of various Styrofoam balls you will be using. The directions of the experiments are outlined below.

Through the course of this experiment, you will be studying the following atomic structures:

  • Simple Cubic
  • Body Centered Cubic
  • Face Centered Cubic
  • Hexagonal Close-Packed

For each, you should:

  • Identify and draw the repeating pattern of planes identify and draw the unit cell in your lab notebook
  • Identify the number of atoms per unit cell and record this in your notebook
  • Identify and draw distinguishing characteristics of the unit cell in your notebook

But first, let's go through some basics. Each person in the lab group should take a handful of the Styrofoam "atoms." Each person needs 10-15 balls. Arrange those atoms in as many different ways as you can in a single plane. See how many combinations of these planes you can come up with. Identify which crystal structure each of these results in. Which ones have a lot of empty space? Which ones have very little empty space?

For each crystal structure, identify the smallest possible repeating pattern you could use to complete the crystal structure. How many complete atoms are present in this unit cell? How many fractions? How many total atoms are present in this unit cell? For each crystal structure you prepare, assume you have an ideal crystal. Using geometry (you can do this outside of the lab), calculate the fraction of space in the crystal which is taken up by atoms. This is called the atomic packing factor. What fraction of space is empty of matter for the ideal case? How does this relate to the atomic packing factor? Two of the structures you can prepare have a relatively high atomic packing factor (0.74). Which two are these? What property of the repeating arrangement of planes explains this fact? These are called the closest packed planes. Look at each crystal structure and sketch out distinguishing properties. How do these relate back to the properties of the individual planes that you have already sketched?

In the laboratory, you will find a handbook for the crystallography kits titled "Volume 3: Miller Indices." Work through this handbook until you feel comfortable with Miller Indices.

Before leaving the lab, identify the crystal structure of the unknowns at the front of the room. At least one of the unknowns could be more than one type of crystal structure. Explain this. Based on what you have observed, what relationship exists between the shape of the model of the crystal and its overall crystalline structure? There are twelve of these unknown crystal types.

There are also model crystal structures for some common substances. Identify the type of crystal structure in each case. Draw the unit cell for each crystal. Then, using the origin indicated on each model, establish a coordinate system and determine the crystallographic directions for the points indicated. Sketch each figure in your lab. There are six points on two different crystals for you to identify.

Finally, you will be asked to identify the Miller Indices for a plane given to you. You should sketch the plane in your lab notebook (along with the crystal structure of interest) and then determine the Miller Indices. In addition, you will be given a set of Miller Indices and it will be your responsibility to draw a picture that clearly shows these indices for the crystal structure assigned.

The questions listed below were assigned in previous years when a lab report was required for this lab. You DO NOT need to answer these questions or submit a lab report for this lab.

If you were to write a lab report (which you will NOT do - these items are discussed here merely to give you an idea of the kinds of information you would include in a formal report), the background section of the report would include definitions for each of the following terms are included:

unit cell
close packed direction
closest packed planes
family of directions
family of planes
Miller Indices

The background section would also contain answers to the following questions:

  1. What is the significance of crystal structure in materials science?
  2. Give some examples illustrating the application of crystal structure in controlling material properties.
  3. Give examples of crystal properties with cubic, FCC, BCC, and HCP crystal structures.
  4. Make a table comparing the properties of different elements which exhibit polymorphism. Give examples of the properties for each of the crystal structures. Discuss your findings in the conclusions section.

BEFORE LEAVING THE LABORATORY SESSION, your TA must see your lab notebook.

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