Created by Adam R. Johnson, Harvey Mudd College () and posted on VIPEr on May 13, 2016. Copyright Adam R. Johnson, 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs CC BY-NC-ND. To view a copy of this license visit {http://creativecommons.org/licenses/by-nc-nd/4.0/}.
Crystal Field Theory, gemstones and color
Instructor notes
Day 1
I would begin day one with a brief demonstration of orbital overlap at the board. For example, draw a pz orbital on the board next to an s orbital. Show that there is constructive interference with one lobe and destructive interference with the other—no net overlap. Repeat for a px orbital in the plane of the board, clearly constructive overlap. It probably would not be a bad idea to draw an octahedral complex to ensure that students know what they look like.
Depending on whether students have seen spectroscopy before, which seems unlikely, it may be helpful to illustrate a generic absorption of a photon to promote an electron from one generic energy level to another. Point out that for transition metal complexes, the energy of the transition corresponds to visible light, which is why transition metal complexes have color.
A big part of day one is visualization of where the 5 d orbitals point in Oh, D4h and Td crystal field environments. I hope the students can talk their way through it in small groups to get the correct answers.
Day one has a 6 page worksheet that needs to be collected either at the end of class or at the beginning of day 2). Make sure every member of the team writes their name (legibly) on the form.
Day 2
Most of day 2 will be spent using CrystalMaker. I see this exercise as a way to cement in what they learned in the symmetry unit. Hopefully the instructions are clear for the students, but I would make sure that you can do the assignment yourself since I am sure a lot of the buttons are not intuitive and it is possible (likely) that there are Mac/PC differences. Encourage the students to rotate and play with the view dialog to really get a sense of what the structures of Corundum and Beryl are. I found that by putting the exercise together, I really came to a deep understanding of the structures.
You may want to point out that we may see the beryl structure type again in the catalysis unit; it is very close to a zeolite with the long z-axis pores.
The most interesting aspect of this day is that the structure with the shorter Cr-O bonds, which you would expect from a purely ionic standpoint to have a larger ∆o, in fact has a smaller ∆o due to the more covalent network involving the silicate rings and the beryllium atoms. This points to a breakdown in the CFT model when applied to more covalent networks. However, you may want to point out to groups as they reach this point that the symmetry predicted by CFT is exactly correct, just that the magnitude of the ∆o is not correctly predicted without advancing to a higher level of theory (MO theory if they want to know).
The worksheet for day 2 is 3 pages and needs to be filled out and turned in at the start of the next class.
Day 1:
Complete the crystal field theory guided inquiry; complete student worksheet 1 (on Sakai) in class or as homework
Day 2:
turn in the worksheet from day 1
complete the exercise using Crystal maker to examine the solid state structures of ruby and emerald; complete student worksheet 2 (on Sakai) in class or as homework (due at start of next unit)