Models and Descriptions of Crystal Structures (Worksheet)

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Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

Learning Objectives

• Achieve an understanding and ability to apply and explain the concepts of crystal packing and description of classic crystal structures.
• As a class, complete and understand the systematic table of crystal structures according to the packing model (see table on next page).
• Master the ability to visualize a 2-D picture of a unit cell and from it identify the crystal packing scheme, the types of holes occupied by the smaller ion, the coordination numbers of both ions, and the number of ions in the unit cell.
• Thoroughness and correctness in building a model of your structure and answering the questions below.
• Quality of group interaction and participation of all persons in accomplishing the learning objectives.
• Quality and correctness of group sharing with the class about your assigned structure using a model and a transparency prepared about your structure.

Nanotechnology is the synthesis, study and application of solid structures or assemblies of molecules on the nanometer scale. Nanotechnology is one of the hottest research areas at present with applications of nanotubes or nanoparticles to many interesting problems. For example, see Wang, et al, J. Materials Research 2004 19: 417 – 422 for a paper on the growth and structure of titanium dioxide nanotubes for applications as potential gas sensors for energy conversion devices.

From the structures of compounds (both ionic and molecular) in the solid state, we learn the spatial arrangement of the atoms, the bonds, and the inter- and intra-molecular interactions that are all associated with the structure and function. In this activity, by studying the structures of simple salts, you will learn about the classic crystalline structures in which many more complex substances crystallize. You will see how these structures can be analyzed systematically, and how it can be predicted to a limited extent what structure a given simple compound might adopt.

Resources

• Chapter 7 in Rodgers (Glen E. Rodgers, “Descriptive Inorganic, coordination and Solid-State Chemistry,” Brooks/Cole, Thompson Learning, USA, 2002, ISBN 0-12-592060-1). Read sections 7.2 and 7.3. Tables 7.4 to 7.11 will be important and useful. Do the preliminary assignment to prepare for this activity.
• We will start in class but you will need time in the chem library to work with the models in order to complete the plan and prepare to present to the class about your structure.

Assignments

1. Bring the following completed assignment to class on the day that the activity is scheduled:

Pre-activity assignment: Problems in Rodgers: 7.9 – 7.11

Post-activity assignment: Problems in Rodgers: 7.25, 7.29 and 7.30

Plan

1. Form groups of two.
2. Answer the critical thinking questions listed below. While the group supports each person, you will be individually responsible for presenting the discussion of your assigned structure.
3. The instructor will collect the individual contributions into a class report, filling out the table below. You will be given a copy of the class report.
4. Refer back to the criteria for performance success and assess your group’s work.
5. Prepare your report.
6. Be ready to participate in the class discussion of each structure.

Critical Thinking Questions

1. Mark your assigned structure in the table shown below. Look up the radius of the cation and the anion. What is the radius ratio of smaller ion to larger ion? What type of hole for the smaller ion is predicted from this ratio and the Radius Ratio Rule?

Formula	Type of Packing For X Atoms		Fraction of Holes Occupied by M Atoms		Coordination Number		Number of Ions
	hcp	ccp	Tetrahedral	Octahedral	M	X	M	X
MX	NiAs	NaCl
	ZnS Wurtzite	ZnS Zinc blende
MX2	TiO2 Rutile	TiO2 Anatase
M2X	K2O Antifluorite	F2Ca Fluorite
CsCl
CaTiO3 Perovskite
MgAl2O4 Spinel

2. Build the known structure of your salt using the ICE Solid State Model Kit. Note that the accompanying book in the kit instructs you how to build the structure.
3. Consult your textbook and examine your structure to answer the following questions about your structure:
   1. What is the packing structure type for the larger ion?

   2. How are the smaller ions arranged in the structure in part a.?

   3. What fraction of sites is occupied by the smaller ions?

   4. What is the coordination number of each type of ion?

   5. Explain how many ions of each type are present in the unit cell?

4. Be able to take a transparency of your unit cell (provided) and the model you built and explain how you derived the answers to the questions in part 3. You will present your report to the class.

5. Is the observed structure of your compound consistent with the prediction of the Radius Ratio Rule? See Tables 7.9 or 7.11 for relevant information. Note: Due to incomplete data, we will be able to do this for some but not all of the structures.

Assignments

• CsCl
• NaAs
• NaCl
• Wurtzite
• Zinc blende
• Rutile
• Anatase
• Anti-fluorite
• Fluorite
• Perovskite

Reference

• Susan Jackels, Seattle University