Studying Crystal Structures through the Use of Solid-State Model Kits

Laboratory Experiment pubs.acs.org/jchemeduc

Studying Crystal Structures through the Use of Solid-State Model Kits Deborah Polvani Sunderland* Department of Chemistry, Washington & Jefferson College, Washington, Pennsylvania 15301, United States S Supporting Information *

ABSTRACT: A solid-state crystal structure laboratory exercise for undergraduates in either a general chemistry course or a more advanced inorganic chemistry course is described. Students explore the lattice arrangement of atoms in unit cells by building models supplied by the Institute for Chemical Education. Emphasis is placed on building three-dimensional visual models of various crystal systems to display close packing of atoms, to identify tetrahedral and octahedral holes, to reveal number of atoms per unit cell, and to highlight ion coordination numbers and size differences. The relationship between solid-state bonding and a material’s physical properties is emphasized for elemental carbon.

KEYWORDS: First-Year Undergraduate/General, Second-Year Undergraduate, Laboratory Instruction, Inorganic Chemistry, Hands-On Learning/Manipulatives, Crystals/Crystallography, Solid-State Chemistry, Solids

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tend to enjoy the tactile experience afforded when working with spheres and sticks. Virtual, or computer-based, models are available in several different types such as ball-and-stick, stereo line, or space filling. In addition, operations that include energy minimization or other mathematical functions and unlimited colors and sphere sizes are possible with the virtual models. Significant improvement in student understanding can be attributed to their exposure to physical and virtual models and the active learning that these methods provide. The laboratory exercise presented here utilizes physical crystal-lattice model kits from the Institute for Chemical Education (ICE)18 that are currently sold with a detailed instruction manual.19 The instruction manual is designed to give “layer by layer” directions for building three-dimensional crystal structures by dropping spheres through intentionally placed rods sticking up out of a template base (Figure 1). The instruction manual only provides directions for building the models; it does not prompt the students to answer questions about particular structures based on their observations. We, however, wish to extend the usefulness of this clever kit to the classroom by describing a set of activities in which students can participate as a lab experience. This experiment was designed as a three-hour laboratory session for our Introduction to Inorganic Chemistry course and has been included for the past four years. Students take this one-semester undergraduate course in their second year toward completion of a chemistry degree or to help fulfill their general chemistry requirements en route to a health professional

ost modern general chemistry textbooks will devote a chapter to instruction of solids and crystalline materials. It is interesting to note that, until recently, solid-state and materials chemistry has not had a prominent role in the undergraduate chemistry curriculum, and efforts to provide instructional materials to help modernize introductory courses have been addressed through the Ad Hoc Committee for SolidSate Instructional Materials formed in 19901 and in several of their publications.2−4 Specifically, one way to help illustrate the connection between a crystalline solid’s atomic-level structure and its physical properties is through the use of crystal-lattice models. Considering the recent emphasis on solid-state materials at the undergraduate level, it perhaps is no surprise that there is only a limited collection of published laboratory experiments and classroom demonstrations directly related to construction and manipulation of crystalline models. A search of this Journal5−10 resulted in a few examples from either homebuilt resources or commercially available kits. One online resource11 was found that describes kits from the Institute for Chemical Education (ICE), which are the kits utilized in this laboratory experience, and another presented an activity utilizing virtual models of ionic structures.12 Other references touted the general advantages of teaching chemistry through the use of physical models,13,14 though there were no emphases on any particular model sets. Using a combination of physical and virtual models to supplement instruction in general and organic chemistry courses has distinct advantages.15−17 These results show that students can benefit from using both physical and virtual models alongside each other. The physical (plastic) models provide something tangible for students; they can be touched and manipulated in three dimensions, and students © 2014 American Chemical Society and Division of Chemical Education, Inc.

Published: February 25, 2014 432

dx.doi.org/10.1021/ed400367x | J. Chem. Educ. 2014, 91, 432−436

Journal of Chemical Education

Laboratory Experiment

Figure 1. (Left) Photo of the kit for building models with base plates, a selection of templates, rods, and various sizes of spheres. (Right) Completed solid-state model of sodium chloride.

Figure 2. The number of atoms per unit cell can be illustrated by considering the number of unit cells shared by an atom. Cubic unit cells are shown here. When atoms are present at unit cell corners, they count as one-eigth of an atom per unit cell, body-centered atoms count as one whole atom, and face atoms count as one-half of an atom per cell. The relationship between the edge length (a) and radius (r) of atoms in the simple cubic cell, body-centered cubic (bcc) cell, and face-centered cubic (fcc) cell is additionally shown.

effect this has on physical properties of molecules. Students have started the crystalline solids unit prior to this experiment and are familiar with crystalline lattices, types of unit cells, close-packing, and number of atoms per unit cell. Students should have an understanding of molecular geometry as well as types of intermolecular forces and atomic bonding that includes ionic, covalent, and metallic.

degree. Many students may struggle with visualizing and mentally manipulating three-dimensional objects, and therefore, this experiment was employed to help them conceptualize crystal structures. The model kits are designed so that students are able to build models within minutes of reading through an example in the instruction manual.

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STUDENT BACKGROUND Prior to doing this laboratory experiment, students cover Lewis dot structures and VSEPR theory in the lecture portion of the course. They also have a background in bond polarity and the

LABORATORY WORK Coordinating a multisection laboratory for this experiment is relatively simple. The model kits are available in either a Deluxe 433



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Build NiAs crystal structure Model of silicates (SiO32−, Si4O116−, Si2O52−)

Students deduce oxidation states of the Si and O, the SiO44− tetrahedra can join in a variety of ways and must be charge balanced with cations that can fit into the rings that form through shared O atoms.

Simple, bcc, or fcc unit cells are defined for one kind of atom or ion, provides a 3D visual aid for counting atoms in unit cells.

The cesium ions (or alternatively, the chloride ions) form a simple cubic unit cell. Students count the number of each ion per unit cell. Shows that each carbon atom is tetrahedrally coordinated and the network extends in all three dimensions. Students are then shown that frozen water has the same crystal structure, with each oxygen bonded to four hydrogens. Radius size (As > Ni), As is in a hcp lattice with Ni occupying all octahedral holes, both types of atoms have coordination number of 6. Highlights the unambiguous radius size difference between O and Si (O > Si) and the SiO44− tetrahedron as the basic unit in the structure, provides a 3D visual model of the chains and sheets that form by shared O atoms.

Relate the 3D carbon network to diamond’s inherent hardness. Compare the ice structure to that of diamond and note that two of the hydrogen−oxygen bonds are covalent, and two H atoms are attracted to O via intermolecular hydrogen bonding. Deduce that the extra empty volume in ice is due to the weaker intermolecular bonding. Identify the packing type for As and the hole type for Ni.

Count the number of tetrahedral and octahedral holes, recognize that the ccp arrangement is identical to face-centered cubic (fcc) unit cells. 3D model of ccp crystals, recognition of the ABC layer pattern, tetrahedral holes, octahedral holes, coordination numbers.

Count the number of tetrahedral and octahedral holes, recognize coordination numbers in crystal lattices. 3D model of hcp crystals, recognition of the ABA layer pattern, tetrahedral holes, octahedral holes, coordination numbers.

Learning Objective

DISCUSSION Using physical and virtual models to complement instruction in a general chemistry course can help students comprehend concepts. Having an understanding for the states of matter and knowledge of the spatial arrangement of atoms in matter is vital to understanding the relationship between structure and properties of materials. An overarching goal of this experiment is to provide structural relationships with solids. An ordinary and very familiar substance such as table salt resembles tiny cubes under a microscope, and indeed, the face-centered cubic (fcc) unit cell of NaCl is readily apparent once the unit cell is constructed. This situation is common for crystalline solids; visualization of crystals at the atomic level with physical model kits provides clear parallels to properties such as radius ratios, densities of solids, and packing efficiency. These properties, in turn, can be related to other materials’ characteristics such as hardness or even interesting electrical or magnetic behavior. Building a crystal lattice, layer by layer, with these model kits provides an elegant and direct process for students to visualize and manipulate unit cells so that coordination number, atomic

Students become familiar with the parts of the kit and learn how to build structures using the supplied templates and parts.

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Concept Illustrated

HAZARDS The laboratory session does not involve any chemical reagents, and thus, there are no chemical hazards or waste disposal concerns. The entire lab exercise could be completed in a classroom. Students should treat the solid-state model kits with respect, as there are many small marbles and parts that could be lost. Likewise, students are directed not to share parts of their model kits with other groups, as the small parts might inadvertently migrate among the kits.

Exercise Completed

Table 1. Summary Components and Learning Objectives for the Crystal Structure Model Lab

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Build NaCl crystal structure Model of hexagonal close-packing (hcp) Model of cubic close-packing (ccp) Build CsCl crystal structure Build diamond crystal structure

version or a less expensive Student kit. There are approximately 18 students enrolled per laboratory section of this course. For the purposes of this lab experiment, a Student Version model kit is shared between two students, though it is merely a cost factor that dictates whether students can work individually or if students need to share a kit. Metric rulers and scissors are made available to the students for cutting spacers in order to properly build some of the crystal models. Because no chemicals are involved, a classroom works well for this experiment, so that students can sit at desks while they build their structures. Prior to coming to lab, all students are required to list the seven crystal systems and provide their characteristic lattice parameters (a, b, and c edge lengths and α, β, and γ angles). They are highly encouraged to complete textbook homework problems relevant to crystal structures from the lecture portion of the course. In addition, they are asked to consult their lecture textbook20 so that they understand how to count atoms in cubic unit cells (Figure 2). Lastly, students calculate the density of copper, in grams per centimeter cubed, which crystallizes as a face-centered cubic (fcc) unit cell and has an edge length of 361.49 pm. The relationship between cubic unit cell edge length and atomic radius is also shown in Figure 2. During this laboratory exercise, students need 2−3 h to build their structures, make their observations, and answer questions pertaining to each model. Table 1 summarizes the specific laboratory components correlated with the desired learning objectives. After the laboratory, students provide typed answers to the questions posed for each model and a brief conclusion that summarizes their work. They are encouraged to generalize some of the common features of crystal structures that they observed.

This is the tutorial structure supplied in the kit.





Figure 3. Survey results, represented as a percentage of students that completed the lab and had a positive response to each question. The questions asked of students are given under each graph. Students had to rank their learning for each question (1 = no opinion, 2 = did not help my understanding, 3 = mildly helpful, 4 = definitely helpful, and 5 = extremely helpful.).

concepts are immediately identified. For example, students have particular difficulty visualizing where tetrahedral or octahedral holes exist within certain lattices. The ability for an instructor to directly point out their locations in the plastic models quickly enhances overall recognition and comprehension. This lab is often noted in course evaluations as being interesting, useful, and fun.

size, occupation of tetrahedral or octahedral holes, packing type, and number of ions or atoms in a unit cell are readily apparent. Students responded favorably to specific learning outcomes asked of them in the format of a postlaboratory survey (Figure 3 and in Supporting Information). The survey questions directly correlated with the models that students built to complete the lab. For each question, students had to rank their assessment of how helpful the model-building exercise was to their understanding of particular aspects of solid-state structures (1 = no opinion to 5 = extremely helpful). The survey was divided into two sections: one for “knowledge about crystal structures” and the second for “knowledge about structure− property relationships”. For a majority of the questions, about 80% or more of all students who completed the lab chose that the models were “definitely helpful” (a rank of 4 on the survey) or “extremely helpful” (a rank of 5) for their understanding. It is interesting to note that for question 8 of the survey, which prompted reflection on differences between crystalline and amorphous materials, only 34% of all students chose a ranking of 4 or 5. This low percentage is likely attributed to the fact that models of amorphous materials were not included in this laboratory, and hence, any enhancement to understanding such crystalline−amorphous differences was minimal and incidentally achieved. Anecdotally, students enjoy this laboratory and they see concrete benefits in completing it. Because instructors directly interact with students as they build their models, perplexing

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CONCLUSION

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ASSOCIATED CONTENT

In a single 2−3 h laboratory session, general chemistry students build three-dimensional models of crystalline solids using kits manufactured by the Institute for Chemical Education. Students make observations for each lattice that they build and record them through a series of guided questions supplied by the instructor. This laboratory has a positive influence on students’ understanding of solid-state materials, noted by considerably favorable survey results that aimed to assess student understanding as a direct result of building and manipulating solid-state models.

* Supporting Information S

Complete laboratory experiment directions for students; instructor notes; assessment of this laboratory experiment. This material is available via the Internet at http://pubs.acs.org. 435



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(14) Criswell, B. Do you See What I See? Lessons about the Use of Models in High School Chemistry Classes. J. Chem. Educ. 2011, 88, 415. (15) Dori, Y. J.; Barak, M. Virtual and Physical Molecular Modeling: Fostering Model Perception and Spatial Understanding. Educ. Technol. Soc. 2001, 4 (1), 61. (16) Sinex, S. A.; Gage, B. A. Empowering Student Learning with Molecular Visualization Tools in Discovery-Based General Chemistry. http://www.files.chem.vt.edu/confchem/2004/b/sinex-gage/sinexgage.html (accessed Feb 2014). (17) Hegarty, M. Representation Translation with Concrete and Virtual Models in Chemistry. https://arc.uchicago.edu/reese/ projects/representation-translation-concrete-and-virtual-modelschemistry (accessed Feb 2014). (18) Ludwig, A. M. and George, C. L. Solid-State Model Kits from the Institute for Chemical Education. Institute for Chemical Education, University of Wisconsin: Madison, WI, 2008; http://education.mrsec. wisc.edu/supplies/SSMK/. (19) Lisensky, G. C.; Covert, J. C.; Mayer, L. A. Solid-State Model Kit Instruction Manual, 2nd ed.; Institute for Chemical Education, University of Wisconsin: Madison, WI, 1994. (20) Petrucci, R. H.; Herring, G. F.; Madura, J. D.; Bissonnette, C. General Chemistry Principles and Modern Applications, 10th ed.; Pearson Canada, Inc.: Toronto, Canada, 2011, pp 526−542.

AUTHOR INFORMATION

Corresponding Author

*E-mail: dsunderland@washjeff.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author sincerely thanks the entire Washington & Jefferson College Department of Chemistry for their enduring professional support and advice and for the purchase of the ICE solid-state model kits that made this laboratory possible. Patricia Brletic, Jennifer Logan, and Steven Malinak of the department helped to implement this experiment by teaching laboratory sections. Additionally, the author thanks the CHM 260 students of W&J College for participating in this lab exercise and for providing suggestions.

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REFERENCES

(1) The spirit of the Ad Hoc Committee for Solid-State Instructional Materials is to aid in the incorporation of solid materials in introductory chemistry courses by highlighting metals, semiconductors, superconductors, and polymers. The book in reference 2, Teaching General Chemistry: A Materials Science Companion is one such publication. Members of this committee include: Aaron Bertrand, Abraham Clearfield, Denice Denton, John Droske, Arthur Ellis (Chair), Paul Gaus, Margret Geselbracht, Martha Greenblatt, Roald Hoffman, Allan Jacobson, Brian Johnson, Edward Kostiner, Nathan Leweis, George Lisensky, Thomas Mallouk, Robert McCarley, Ludwig Mayer, Joel Miller, Donald Murphy, Donald Neu, William Robinson, Don Showalter, Duward Shriver, Albert Thompson, Jr., Ray Turner, Stanley Whittingham, Gary Knek, and Aaron Wold. (2) Ellis, A. B.; Geselbracht, M. J.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R. Teaching General Chemistry: A Materials Science Companion; ACS Books: Washington, DC, 1993. (3) Ellis, A. B.; Geselbracht, M. J.; Greenblatt, M.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R.; Whittingham, M. S. Materials Chemistry Companion to General Chemistry: An Update. J. Chem. Educ. 1992, 69, 1015. (4) Ellis, A. B. Elements of Curriculum Reform: Putting Solids in the Foundation. J. Chem. Educ. 1997, 74, 1033. (5) Mattson, B. Cubic Unit Cell Construction Kit. J. Chem. Educ. 2000, 77, 622. (6) Whitfield, M. Demonstrating Void Space in Solids: A Simple Demonstration to Challenge a Powerful Misconception. J. Chem. Educ. 2006, 83, 749. (7) Bindel, T. H. Exploring Solid-State Structure and Physical Properties: A Molecular and Crystal Model Exercise. J. Chem. Educ. 2008, 85, 822. (8) Collins, D. C. A Unit Cell Laboratory Experiment: Marbles, Magnets, and Stacking Arrangements. J. Chem. Educ. 2011, 88, 1318 ; see also references therein.. (9) Donaghy, K. J.; Saxton, K. J. Connecting Geometry and Chemistry: A Three-Step Approach to Three-Dimensional Thinking. J. Chem. Educ. 2012, 89, 917. (10) Birk, J. P.; Yezierski, E. J. Paper-and-Glue Unit Cell Models. J. Chem. Educ. 2003, 80, 157. (11) Crowder, K. N. Solid State Models with ICE Solid State Model Kits. https://www.ionicviper.org/classactivity/solid-state-models-icesolid-state-model-kits (accessed Feb 2014). (12) Bridgeman, A. Solid State Structures. https://www.ionicviper. org/class-activity/solid-state-structures (accessed Feb 2014); this exercise uses animations and Jmol models. (13) Bent, H. A. Uses (and Abuses) of Models in Teaching Chemistry. J. Chem. Educ. 1984, 61, 775. 436


Studying Crystal Structures through the Use of Solid-State Model Kits

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