Bonding models: Extended systems

3 Jun 2017

Literature Discussion of "A stable compound of helium and sodium at high pressure"

Submitted by Katherine Nicole Crowder, University of Mary Washington
Evaluation Methods: 

Students could be evaluated based on their participation in the in-class discussion or on their submitted written answers to assigned questions.

Evaluation Results: 

This LO has not been used in a class at this point. Evaluation results will be uploaded as it is used (by Spring 2018 at the latest).

Description: 

This paper describes the synthesis of a stable compound of sodium and helium at very high pressures. The paper uses computational methods to predict likely compounds with helium, then describe a synthetic protocol to make the thermodynamically favored Na2He compound. The compound has a fluorite structure and is an electride with the delocalization of 2e- into the structure.

This paper would be appropriate after discussion of solid state structures and band theory.

The questions are divided into categories and have a wide range of levels.

Dong, X.; Oganov, A. R.; Goncharov, A. F.; Stavrou, E.; Lobanov, S.; Saleh, G.; Qian, G.-R.; Zhu, Q.; Gatti, C.; Deringer, V. L.; et al. A stable compound of helium and sodium at high pressure. Nature Chemistry 2017, 9 (5), 440–445 DOI: 10.1038/nchem.2716.

Corequisites: 
Learning Goals: 

After reading and discussing this paper, students will be able to

  • Describe the solid state structure of a novel compound using their knowledge of unit cells and ionic crystals
  • Apply band theory to a specific material
  • Describe how XRD is used to determine solid state structure
  • Describe the bonding in an electride structure
  • Apply periodic trends to compare/explain reactivity
Implementation Notes: 

The questions are divided into categories (comprehensive questions, atomic and molecular properties, solid state structure, electronic structure and other topics) that may or may not be appropriate for your class. To cover all of the questions, you will probably need at least two class periods. Adapt the assignment as you see fit.

CrystalMaker software can be used to visualize the compound. ICE model kits can also be used to build the compound using the template for a Heusler alloy.

Time Required: 
2 class periods
10 Apr 2017

Redox Chemistry and Modern Battery Technology

Submitted by Zachary Tonzetich, University of Texas at San Antonio
Evaluation Methods: 

I do not grade this activity, but if I did, I would look for class participation in the discussion or assign several of the questions to be turned in at a later date.

Evaluation Results: 

My impression of this activity is that it really helps students see the value of redox chemistry. In my experience, the aspects of redox chemistry we teach students (balancing equations, calculating cell potentials, etc.) seem both difficult and esoteric. This activity reinforces these concepts while demonstrating their importance to modern life. One of the biggest realizations the students come to is the relationship between cell voltage and the mass of the materials involved in the redox reaction.

Description: 

This In-Class Activity is a series of instructor-guided discussion questions that explore lithium-ion batteries through the lens of simple redox chemistry. I use this exercise as a review activity in my Descriptive Inorganic Chemistry course to help prepare for examinations. However, my primary purpose with this exercise is to impress upon students how basic concepts in redox chemistry and solid-state structure are directly relevant to technologies they use everyday. I do not focus too heavily on the design or operation of the batteries themselves, as other exercises published on VIPEr already do a very good job of that. My intention is to demonstrate how a basic knowledge of redox chemistry is the first step in understanding seemingly complex technologies.

Learning Goals: 

The primary goal of this In-Class Activity is for students to solidify their understanding of redox reactions, cell voltages and the relationship between electrical energy and potential. The exercise is also designed to show students how these considerations are part of the design of modern batteries. A secondary aspect of the activity explores the solid-state structure of metal-oxides and how these materials are important to the operation of the battery. At the conclusion of the activity, the student should be familiar enough with calculaing cell voltages and free energy changes that they can critically evaluate the components of a standard battery.

Equipment needs: 

None.

Course Level: 
Prerequisites: 
Corequisites: 
Implementation Notes: 

I display the pdf file on screen and use the white board to work out simple arithmetic aspects of the exercise, while soliciting responses from the class.

Time Required: 
45 minutes
28 Jun 2016

Close Packing Activity

Submitted by George Lisensky, Beloit College
Evaluation Methods: 

This has been used by the author to illustrate features of class packing in lecture. 

Description: 

Many extended structures can be viewed as close-packed layers of large anions, with the smaller cations fitting in between the anions. Larger holes between close-packed anions can hold cations with octahedral coordination. Smaller holes between close-packed anions can hold cations with tetrahedral coordination. The online jsmol resources show these layers and their holes.

Learning Goals: 

Students will understand octahedral and tetrahedral holes between close packing layers (either hcp or ccp)

Equipment needs: 

A physical model kit such as the ICE Solid State Model Kit (see the related activities) could be used. With the linked web resources for this activity students can display individual layers and the holes between them. Both physical and virtual models are valuable learning tools. Either could be used separately depending on availability but they work together well.

Corequisites: 
Prerequisites: 
Implementation Notes: 

For cubic close packing

Click on item 1 and click on Spacefill. Click on item 2 and item 4. What is the arrangement of atoms around each other in Pa, Pb, and Pc layers?

Click on item 1, then item 3, then item 5 to stack layers. The image can be rotated by dragging. You can add or subtract layers by backing up a step or going forward. You can switch between Ball, Spacefill, and Translucent representations.

To repeat the sequence, where should the next layer go? Click on step 6.

Step 7 shows that these layers contain a face-centered cube, stacked along its body diagonal.

Similarly you can experiment by filling in the spaces between the layers. Where can you fit tetrahedra between the packing spheres? Where can you fit octahedra between the packing spheres?

Try switching the display to Ball and Stick with Translucent Polyhedra.

A similar procedure can be used to examine hexagonal close packing.

A note about color: steps with color names in them change the color. Other steps do not. For example if you want the layers different colors use step 1, 2, 4, 7; if you want the layers the same color use steps 1, 3, 5, 6.

Time Required: 
30 minutes
27 Jun 2016

Online Homework for a Foundations of Inorganic Chemistry Course

Submitted by Sabrina G. Sobel, Hofstra University
Evaluation Methods: 

Students are graded on a sliding scale based on the number of attempts on each question. An overall grade is assigned at the end of the semester, adjusted to the number of points allotted for the homework in the syllabus. 

Evaluation Results: 

Student performance on the overall homework assignments for the semester includes questions assigned on General Chemistry topics that are part of this class syllabus. 

 201420152016
Number404741
Average89%80%83%
S.D.15%19%23%

In addition to gethering data on overall  performance, I and my student assistants, Loren Wolfin and Marissa Strumolo, have completed a statistical study to assess performance on individual questions, and to identify problem questions that need to be edited. We identified two separate issues: incorrect/poorly worded questions, and assignment of level of difficulty. Five problematic questions were identified and edited. The level of difficulty was reassigned for eight questions rated as medium (level 2); six were reassigned as difficult (level 3), and two were reassigned as easy (level 1). I look forward to assessing student performance in Spring 2017 in light of these improvements. Please feel free to implement this Sapling homework in your class, and help in the improvement/evolution of this database.

Description: 

The Committee on Professional Training (CPT) has restructured accreditation of Chemistry-related degrees, removing the old model of one year each of General, Analytical, Organic, and Physical Chemistry plus other relevant advanced classes as designed by the individual department. The new model (2008) requires one semester each in the five Foundation areas: Analytical, Inorganic, Organic, Biochemistry and Physical Chemistry, leaving General Chemistry as an option, with the development of advanced classes up to the individual departments. This has caused an upheaval in the treatment of Inorganic Chemistry, elevating it to be on equal footing with the other, more ‘traditional’ subdisciplines which has meant the decoupling of General Chemistry from introduction to Inorganic Chemistry. No commercial online homework system includes sets for either Foundations or Advanced Inorganic Chemistry topics. Sapling online homework (www.saplinglearning.com) has been open to professor authors of homework problems; they have a limited database of advanced inorganic chemistry problems produced by a generous and industrious faculty person. I have developed a homework set for a semester­-long freshman/sophomore level Inorganic Chemistry course aligned to the textbook Descriptive Inorganic Chemistry by Rayner-Canham and Overton (ISBN 1-4641-2560-0, www.whfreeman.com/descriptive6e ), and have test run it three times. Question development, analysis of student performance and troubleshooting in addition to topic choices, are critical to this process, especially in light of new information about what topics are taught in such a course (Great Expectations: Using an Analysis of Current Practices To Propose a Framework for the Undergraduate Inorganic Curriculum: http://pubs.acs.org/doi/full/10.1021/acs.inorgchem.5b01320 ).This is an ongoing process, and I am working to improve the database all the time.

Prerequisites: 
Corequisites: 
Course Level: 
Learning Goals: 

1.      Increase understanding in these topic areas:

a.      Acid-base chemistry and solvent systems

b.      Bonding models of inorganic molecules and complexes

c.      Bonding models in extended systems (solids)

d.      Descriptive chemistry and Periodic Trends

e.      Electronic structure of inorganic molecules, complexes and solids

f.       Extended structures: unit cells and other solid-state structural features

g.      Molecular structure and shape of inorganic molecules

h.      Inorganic Complexes nomenclature, bonding and shapes

i.       Redox chemistry and application to inorganic systems

j.       Thermodynamics as applied to inorganic solids and inorganic systems

2.      Practice using knowledge in these topic areas:

a.      Acid-base chemistry and solvent systems

b.      Bonding models of inorganic molecules and complexes

c.      Bonding models in extended systems (solids)

d.      Descriptive chemistry and Periodic Trends

e.      Electronic structure of inorganic molecules, complexes and solids

f.       Extended structures: unit cells and other solid-state structural features

g.      Molecular structure and shape of inorganic molecules

h.      Inorganic Complexes nomenclature, bonding and shapes

i.       Redox chemistry and application to inorganic systems

j.       Thermodynamics as applied to inorganic solids and inorganic systems

Implementation Notes: 

The database of homework questions is available through Sapling Learning. They can be implemented as an online homework set for a class. Students need to buy access to the Sapling online homework for the duration of the class, typically $45.

Time Required: 
variable
27 Jun 2016

Solid State Stoichiometry Activity

Submitted by George Lisensky, Beloit College
Evaluation Methods: 

We provide a built solid state 3D physical model that the students had not previously seen as a quiz question where students are asked to show their work in calculating the stoichiometry.

See the evaluation questions and activity answer key in the faculty-only files.

Evaluation Results: 

Most students have been able to explain the empirical formula for any of these structures. They sometimes struggle with the difference between a corner, an edge, a face, and inside the unit cell. Students are generally able to determine the stoichiometry for an extended solid that they have not previously seen.

Description: 

The goal of this activity is to have students calculate the empirical formula of a compound given the contents of a unit cell. 

A repeating building block, or unit cell, is used to represent extended structures since shifting a unit cell along its edges by the length of the edge will exactly replicate the extended structure.

In determining stoichiometry for an extended structure only the fraction of an atom within the unit cell counts. In three-dimensions atoms can be shared between unit cells on corners, on edges and on faces of the unit cell. Atoms on corners are shared by eight unit cells, atoms on edges are shared by four cells and atoms on faces are shared by two cells. Therefore only one-eighth of a corner atom, one-quarter of an edge atom and one-half of an atom on a face is in any one unit cell. The total number of atoms in a unit cell is given by:

Assignment:

For five solid state structures determine the empirical formula. Show your work by indicating how many spheres of each type have their centers located inside the unit cell, on faces, on edges, or on corners. (A given sphere only has one location: inside, face, edge, and corner locations are mutually exclusive.)

Learning Goals: 

Students can determine the empirical formula from an extended solid state structure.

Students will be able to understand that a unit cell represents the contents of an extended solid.

Equipment needs: 

A physical model kit such as the ICE Solid State Model Kit (see the related activities) could be used. With physical models students have to visualize the portion of each atom that is within the unit cell.

With the linked web resources for this activity students can use the "faces" option to shade the faces of the unit cell to help visualize the portion of each atom that is within the unit cell.

Both physical and virtual models are valuable learning tools. Either could be used separately depending on availability but they work together well.

Prerequisites: 
Corequisites: 
Implementation Notes: 

Cubic unit cells are appropriate for an introductory course. The advanced unit cells include all crystal systems and centering options.

We have used a physical model kit to build solid state structures in class for many years. After building a few structures, students often want to try some more structures. These online models were created to allow continued study and practice out of class.

Time Required: 
1 hour
27 Jun 2016

Solid State Stoichiometry Online

Submitted by George Lisensky, Beloit College
Evaluation Methods: 

We provide a built solid state 3D physical model that the students had not previously seen as a quiz question where students are asked to show their work in calculating the stoichiometry

See the evaluation questions file and activity answer key in the companion Solid State Stoichiometry Activity learning object.

Evaluation Results: 

Most students have been able to determine the empirical formula for any of these structures. They sometimes struggle with the difference between a corner, an edge, a face, and inside the unit cell. Students are generally able to determine the stoichiometry for an extended solid that they have not previously seen.

Description: 

The page has JSmol structures for unic cells including cubic, body centered cubic, and face centered cubic unit cells as well as for CsCl, Ni3Al, Cu2O, NaCl, CaF2, ZnS, diamond, Li3Bi, NaTl, NiAl and ReO3The advanced page also has triclinic, monoclinic, hexagonal, orthorhombic, and tetragonal cells with all possible centering.

The purpose of this site is to help students visualize how much of an atom is in the unit cell so that compound stoichiometry can be determined. 

 

 
Corequisites: 
Prerequisites: 
Learning Goals: 

Students can determine the empirical formula from an extended solid state structure.

Students will be able to understand that a unit cell represents the contents of an extended solid.

Implementation Notes: 

We have used a physical model kit to build solid state structures in class for many years. After building a few structures, students often want to try some more structures. These online models were created to allow continued study and practice out of class.

Cubic unit cells are appropriate for an introductory course. The advanced unit cells include all crystal systems and centering options.

The display options "faces" and "perspective" are recommended for counting atoms within the cell. 

Time Required: 
1 hour
16 May 2016

Metal and Ionic Lattices Guided Inquiry Worksheet

Submitted by Adam R. Johnson, Harvey Mudd College
Evaluation Methods: 

I walked through the classroom and guided the students as they worked in pairs or groups of three. All the answers were in prior assigned reading from their text so if they were confused, they had that to look at later.

Evaluation Results: 

Some students had trouble seeing some of the holes in the simple lattices, so it was helpful that I was walking around to show them the holes. It was good to have students work together becasue some students were able to see the holes in the geometries and help their partners.

Description: 

This is a short worksheet that guides students through simple metal lattices (SCP, CCP, HCP) and how filling holes in these lattices results in ionic lattices (NaCl, CsCl, fluorite, etc.).

The worksheet was used as an in-class activity after students had read about the material in the text. This activity is probably suitable for first-year students, though I used it with juniors/seniors.

Learning Goals: 

Students will be able to do the following:

for simple lattices:

draw the lattice

determine how many atoms per cell

determine the coordination number, CN, of an atom

locate common holes and describe their CN

calculate the % of space filled up by the atoms

 

For ionic solids:

draw the lattice and count the number of ions in the cell

relate to a simple lattice by hole-filling

determine the # and CN of both cations and anions

Equipment needs: 

none, though a box of pennies or marbles or ping pong balls might be helpful to visualize closest packing. Having models or computer models would have been helpful to show on a screen at the front of the room. rotatable cif files would be especially good, and next time I do this I will prepare cif files or crystalmaker files and upload them here.

Corequisites: 
Prerequisites: 
Implementation Notes: 

This was a bit too long for a 50-minute class period but students finished it up at home. The students who had spent the time reading the book before class definitely did better on the exercise than those who were clearly doing it for the first time in class. Students struggled a bit with the geometry/trig calculations.

Were I to do this again, I would have 3-d rotatable structures available (cif files or crystalmaker files) to help students with the visualization.

Time Required: 
1-1.5 50 minute class periods
14 May 2016

Crystal Field Theory and Gems--Guided Inquiry

Submitted by Adam R. Johnson, Harvey Mudd College
Evaluation Methods: 

The 2 worksheets were handed in and graded according to the key. I generally used a +, √, - grading scale for the probelms. I gave a single grade for each group. Answer keys are provided as "faculty only" files.

Evaluation Results: 

The day 1 activities were too long and we didn't get to the square planar CFT derivation. For my next offering, I am adding a day to the unit so the students will see all three geometries. Students struggled a bit at first with the software and visualization but were able to figure it out with some assistance. The students in Fall 2015 had already practiced using Crystalmaker in a prior unit; for 2016, this prior unit has been removed so the visualization will probably take more time. I anticipate using 1.5 days for part 1 and 1.5 days for part 2 in Fall 2016.

Description: 

The colors of transition metal compounds are highly variable. Aqueous solutions of nickel are green, of copper are blue, and of vanadium can range from yellow to blue to green to violet. What is the origin of these colors? A simple geometrical model known as crystal field theory can be used to differentiate the 5 d orbitals in energy. When an electron in a low-lying orbital interacts with visible light, the electron can be promoted to a higher-lying orbital with the absorption of a photon. Our brains perceive this as color. Rubies, dark red, and emeralds, brilliant green, are precious gemstones known since antiquity. What causes the color in these beautiful crystals? Using crystal field theory, we can explain the colors in these gemstones.

Learning Goals: 

1.    Derive the crystal field splitting for d orbitals in an octahedral geometry
2.    Predict the magnitude of d orbital splitting
3.    Relate color, energy, wavelength, and crystal field strength
 

Equipment needs: 

Day 1: none

Day 2: access to laptops (one per group or individual) and crystalmaker software (free download avaialbe)

Prerequisites: 
Corequisites: 
Course Level: 
Implementation Notes: 

This LO was used in a first-year chemistry class at Harvey Mudd College in Fall 2015. I started with a brief lecture (see instructor notes) and then turned the class loose in small groups of about 5 students. I walked through the room to answer questions and guide the groups.

The first day’s activities were taken from a J. Chem. Educ. article (J. Chem. Educ., 2015, 92, 1369-1372). This article has a lot of detail that could be adapted for local use. The related activity "metal and Ionic Lattices Guided Inquiry Worksheet" may be appropriate as review/background material, depending on the placement of this activity in your syllabus.

The second day’s activities rely on the use of crystalmaker, a structure visualization program. There is a free demo version available (http://crystalmaker.com/software/index.html)

Fairly detailed instructor notes are included as a "faculty only" file.

The references for the structures I used are here:

Gibbs G V, Breck D W, Meagher E P (1968)  Structural refinement of hydrous and anhydrous synthetic beryl, Al2(Be3Si6)O18 and emerald, Al1.9Cr0.1(Be3Si6)O18 Note: hydrous emerald. Lithos 1:275-285

Wang X, Hubbard C, Alexander K, Becher P (1994)  Neutron diffraction measurements of the residual stresses in Al2O3 - ZrO2 (CeO2) ceramic composites _cod_database_code 1000059. Journal of the American Ceramic Society 77:1569-1575

I relied on a book called "The science of Color" and a website on color theory (linked below) to develop the 2nd days activities.

The Science of Color,” volume 2, edited by Alex Byrne and David R. Hilbert, MIT Press, Cambridge MA, 1997, pp. 10-17.

Time Required: 
2 50 minute class periods

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