Bonding models: Extended systems

14 Mar 2020

Solid State Structures tutorial

Submitted by Terrie Salupo-Bryant, Manchester University
Evaluation Methods: 

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.

Evaluation Results: 

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  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.


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.

Learning Goals: 

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.
Implementation Notes: 

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.

Time Required: 
2.5 hours (longer if using the Solid State Model Kit)
8 Jan 2020
Evaluation Methods: 

I usually grade one student handout per pair and typically have 1 pt per answer on the worksheet, but take the total out of 60 pts (which ends up giving them a couple of free points).  

Evaluation Results: 

Last semester my 17 students had an average of 47 out of 60 on the lab--a bit lower than usual for that lab. The high was a 57 and the low was a 39. There were lots of different individual errors, but errors in identifying which of the first structures were closest packed and errors in % of holes occupied were common. 


This first-year laboratory is designed to give students an introduction to basic solid-state structures using both CrystalMaker files and physical models. I think this would work in a foundations level inorganic course as well. It could be used alternatively as an in-class activity or take-home problem set depending on the instructor. It was adapted by me and later, David Harvey, from an original activity that was posted as an educational resource on the CrystalMaker website in the mid 2000s.  

Learning Goals: 

Students will be able to

  • articulate how the atoms in a simple cubic, face-centered cubic, and body-centered cubic unit cell are arranged
  • determine the coordination number of particular atoms in a unit cell
  • count the atoms or ions in a unit cell and determine the empirical formula based on that
  • determine the length of a side of a unit cell based on the radius of an atom
  • visualize the holes in different kinds of unit cells and see how ionic solids can be built by putting ions in those holes
  • describe the forces holding different solids together
  • calculate the % of filled and empty space in lattices
  • identify closest packed structures
Equipment needs: 
  • Computer lab (approximately two students per computer) with CrystalMaker installed (it can be the student version if necessary)


  • Box of pennies
  • Mineral samples of calcite, fluorite, and NaCl (if you want to do the bonus)
Implementation Notes: 

I usually take one day of class to introduce students to CrystalMaker and all of the basic definitions and ideas of this lab before they start working on the stations. Typically I will work through the first station and then part of NaCl to show them some of the main ideas they will be using, asking them to provide answers (which are typically wrong on the first try!). I am typically circulating around answering questions as the students work through the lab. For a lab section of 24 working in 12 pairs, having one set of physical models seems adequate, but particularly at the beginning of the lab it might be helpful to have two sets of the face-centered cubic and body-centered cubic structures. The 12 computer "stations" are arranged in folders inside a Solid State Lab folder on the desktop of the lab computers, so students can just click on the correct folder and correct files as they work their way through the lab.

Time Required: 
3h lab period
9 Oct 2019

2019 Nobel Prize - Li-ion battery LOs

Submitted by Barbara Reisner, James Madison University

Congratulations to the 2019 recipients of the Nobel Prize - John B. Goodenough, M. Stan Whittingham and Akira Yoshino. It's a well deserved honor!

There are several LOs on VIPEr that talk about lithium ion batteries and related systems. The 2019 Nobel is a great opportunity to include something about these batteries in your class.

I hope to see more LOs in the coming weeks so we can bring this chemistry into our classrooms!



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