This tutorial will introduce students to some of the three-dimensional crystal structures exhibited by ionic and metallic solids. They will examine the simple cubic, body-centered cubic, face-centered cubic, and the hexagonal closest-packed systems. To facilitate visualization of the structures at the atomic level, they will use the Crystal Explorer website at Purdue University.
After completing this tutorial, students will be able to:
- Identify and describe basic crystal structures from their unit cells.
- Describe the relationship between crystal packing and unit cell.
- Determine whether atoms/ions in a crystal structure are closest packed.
- Locate tetrahedral, octahedral, and cubic holes in a unit cell.
- Apply geometric relationships to determine the length of a unit cell edge in terms of the radii of its atoms/ions.
- Determine the coordination number of an atom/ion in a crystal structure.
The Crystal Explorer website is a free resource that contains all of the images needed to complete this tutorial.
When I teach my foundations-level inorganic chemistry class, I have students use Ludwig Mayer’s Solid State Structures JCE Software to complete this tutorial; however, the software is no longer commercially available. It utilizes the PCMolecule application which I am still able to access on newer computers by adjusting the compatibility settings. The images in the software use the same color schemes as the structures in the Solid State Model Kit. See Teacher Notes for further information. I don’t have students use the model kits, though I do assemble one or two structures for them refer to if they need.
Students can complete the tutorial in one lab session or in multiple lecture sessions. I currently use one lecture session to get them started and have them complete it outside of class as a homework assignment.
I grade the Solid State Structures tutorial answer sheet (44pts) in conjunction with the Problem Set to Accompany the Solid State Structures tutorial (26 pts) that incorporates concepts from the tutorial.
The average score (n=32) is 60pts out of 70 (86%). Scores on the Problem Set tend to be about 5 percentage points higher than on the tutorial. Students usually spend some time calculating the length of the unit cell edge, a, in terms of the radius (r) of an ion/atom for each of the basic unit cells. Commonly they substitute diameter for radius or make errors in their trigonometry (see doi.org/10.1021/ed400367x for derivation). They also have difficulty seeing an empty hole which causes their percentage of filled octahedral and tetrahedral holes to be incorrect. I added Figures 6 and 7 for fcc in order to help students in the future know where to look for the holes. Visualizing 3D structures can be a challenge even to visual learners. The average score indicates that manipulating structures on the computer makes them more tangible to students. Wrestling with the questions is often a group effort and an opportunity for students to explain their thinking to others.