Making It Clear: Exploring Crystal Structures by Constructing and

Article Cite This: J. Chem. Educ. 2019, 96, 1630−1639

pubs.acs.org/jchemeduc

Making It Clear: Exploring Crystal Structures by Constructing and Comparing See-Through Models Stefanie Lenzer,† Bernd Smarsly,‡ and Nicole Graulich*,† †

Institute of Chemistry Education, Justus-Liebig-University Giessen, Giessen 35392, Germany Institute of Physical Chemistry, Justus-Liebig-University Giessen, Giessen 35392, Germany

‡

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S Supporting Information *

ABSTRACT: Acquiring a basic understanding about the composition of crystal structures and the resulting structure− property relationship is central for chemists and material chemists, enabling the prediction of desired properties and the solution of a wide range of current challenges in sciences, e.g., the development of clean-energy storage. For a deeper understanding of physical and chemical properties of crystals, it is necessary to focus on different global and local structural features that characterize the composition of several atoms or ions as well as the direct environment of single atoms or ions. To improve students’ mental visualization of both global and local features of the three-dimensional order of crystal structures, we developed and implemented a modeling activity with new transparent models. During the activity, students construct and compare models of common crystal structures, like sodium chloride and zinc blend. The usage of clear plastic balls, in particular, allows students to focus on global features such as packing arrangement and lattice structure, as well as on local ones, like coordination number, site occupation, and polyhedral connectivity. The latter features have been difficult to realize so far. We used a design-based research approach to improve the activity and the instructional material, provided herein, through several rounds of evaluation in a course for undergraduate students in materials chemistry. A detailed qualitative analysis of students’ discourse during the activity revealed that students were engaged in various content-related interactions with the models and that it is beneficial to combine a student-centered construction of the models with a subsequent comparison phase. KEYWORDS: Second-Year Undergraduate, Inorganic Chemistry, Hands-On Learning/Manipulatives, Crystals/Crystallography, Solid State Chemistry

U

current challenges in sciences, e.g., the development of cleanenergy storage and harvesting technologies, for instance, solidstate batteries.5 Materials chemists use their submicroscopic understanding to predict how structural features of a crystal can be altered to purposefully design materials with specific types of properties. On the basis of their expertise they understand how properties of a crystal are influenced by their structural features. Some of these structural features characterize the composition of several atoms or ions of a crystal, such as packing arrangement, lattice structure, and unit cell, which we refer to as global features. Other features characterize the direct environment of single atoms or ions in a crystal, e.g., coordination number, site occupation, and polyhedral connectivity. They describe local features of crystal structures. Both the global and local features are important to understand how properties of a crystal emerge. Nevertheless, the local features site occupation and polyhedral connectivity are critical

nderstanding structure−property relationships is an integral part of chemistry. Chemists use these relationships to develop materials with specific properties necessary for their desired use. The relationship between structure and properties of materials can be demonstrated by using an example with graphite and diamond. Due to different structures of carbon modifications, graphite and diamond also have different properties, e.g., the π-bond structure of graphite causes its electronic conductivity, whereas the localized bonds (covalent bonding) in diamond make it an electrical insulator.1 Regarding crystal structures, the comparison of different polymorphs of titanium dioxide provides an interesting example of how structural differences of a crystal influence the properties. In both of the TiO2 polymorphs, anatase and rutile, the titanium cations are octahedrally coordinated by oxygen anions. However, rutile is thermodynamically more stable than anatase due to the different polyhedral connectivity.2−4 Understanding the properties of crystal structures at the submicroscopic level is critical to solving a wide range of © 2019 American Chemical Society and Division of Chemical Education, Inc.

Received: February 8, 2019 Revised: June 7, 2019 Published: July 2, 2019 1630

DOI: 10.1021/acs.jchemed.9b00119 J. Chem. Educ. 2019, 96, 1630−1639

Journal of Chemical Education

Article

Table 1. Comparative Overview of Modeling Activity Features and Materials Educational Focusq

Title of Work

Emphasized Structural Featuresp

Construction Manualr

StudentCentered Constructions

Embedded in Learning Environmentt

Primary Materials Used

A New Type of Crystal Modela

LS

+

−

−

Lattice Entertain You: Paper Modeling of the 14 Bravais Lattices on YouTubeb Crystal Models Made from Clear Plastic Boxes and Their Use in Determining Avogadro’s Numberc

LS

+

+

−

LS; UC

+

−

+

An Inexpensive Kit for Constructing Models of Crystalsd

UC

−

+

−

3D-Printing Crystallographic Unit Cells for Learning Materials Science and Engineeringe Paper-and-Glue Unit Cell Modelsf Use of Pom Pons to to Illustrate Cubic Crystal Structuresg Constructing Cost-Effective Crystal Structures with Table Tennis Balls and Tape That Allow Students To Assemble and Model Multiple Unit Cellsh A Unit Cell Laboratory Experiment: Marbles, Magnets, and Stacking Arrangementsi The Making of Crystal Lattice and Unit Cell Modelsj

UC

+

+

−

UC UC; PA UC; PA

+ − +

+ + +

− − −

UC; PA

+

+

+

Epoxy glue; marbles; spherical magnets

UC; PA

+

−

−

Using Latex Balls and Acrylic Resin Plates To Investigate the Stacking Arrangement and Packing Efficiency of Metal Crystalsk Studying Crystal Structures through the Use of Solid-State Model Kitsl A Simple Method of Building Close-Packed Molecular and Crystal Modelsm Teaching Crystal Structures Using a Transparent Box with Tennis Ballsn Transparent Packing Models of Layer-Lattice Silicates Based on the Observed Structure of Muscoviteo

UC; PA

+

+

+

Cement; low cardboard box; colored glass marbles Knife; acrylic resin plates; latex balls

UC; PA; CN; SO PA

+

+

+

Solid-state model kitv

−

+

−

PA

+

+

−

Balls (made from wood, glass, metal, plastics, cork, etc.); rubber coat Clear plastic boxes; tennis balls

PA

+

−

−

Transparent plastic sheets; cylindrical plastic rods; plywood baseboard; four colored bulbs within single translucent balls Paper; glue; scissors; computer; duplex inkjet printer Knives; watercolors; glue gun; thin-walled transparent plastic cubes; polystyrene snowballs Five trays, one lid; different colored glass marblesu Software VESTA; software Blender; 3D Printer Paper; glue; scissors; computer; printer Different colored pom-pons Dual lock fastening adhesive tape; table tennis balls

Wood with attached paper and nails; glue; transparent plastic balls

a

See ref 11. bSee ref 12. cSee ref 13. dSee ref 15. eSee ref 25. fSee ref 14. gSee ref 16. hSee ref 17. iSee ref 18. jSee ref 19. kSee ref 20. lSee ref 21. See ref 22. nSee ref 23. oSee ref 24. pLS, lattice structure; UC, unit cell; PA, packing arrangement; CN, coordination number; SO, site occupation. q The educational focus was determined for each work; we found no focus on evaluation of students’ interactions with the models, qualitative or quantitative. rConstruction manual included (+) or not included (−). sStudent-centered construction included (+) or not included (−). tModeling activity embedded in a learning environment (+) or not embedded (−). uAvailable as KubiKit. vOnly available by ordering a model kit from the Institute for Chemical Education. m

cognitive load, it can be “off-loaded” by the usage of appropriate external representations6 that support students’ mental models7 of the general composition and characteristic features of a crystal structure. Therefore, teaching crystal structures is often visually supported by a variety of different external representations, e.g., two-dimensional representations in textbooks, three-dimensional ball−stick models, or threedimensional structures animated by computer software.8 The combination of three-dimensional representations and activities requiring students to interact with three-dimensional models benefits the understanding of students’ mental representations of composition and structural features of crystals.6,7,9,10 When considering three-dimensional models of crystals, it is important to recognize structural features, as well as to reflect on these features. This ability forms the basis for creating accurate mental models and further linking structural features to the resulting properties. Helping students in understanding and reasoning with respect to the different features of crystal structures has led to several reports for constructing and manipulating three-dimensional models.11−25 These reports differ in terms of the structural features they emphasize, their educational focus, and the nature of materials used. Table 1 gives an overview of the reports; a more detailed version is

for altering or generating desired properties in a crystal. The polyhedral connectivity, in particular, influences properties like the thermodynamic stability and the electrical conductivity of a crystal. Hence, this feature is of special interest for materials chemists (cf., e.g., Pauling rules4). Without a solid understanding of these structural features of a crystal, however, it is difficult to relate structural features to the resulting properties. To support students’ learning in this field, problem-solving based on structure−property relationships of crystal structures is a key element in applied university chemistry courses, like materials chemistry. To be able to predict how structural features of a crystal can be changed to produce desired properties, students must (1) understand the general composition of a crystal structure and its characteristic global and local structural features and (2) relate structural features of a crystal to the resulting properties. In this report, we present an approach to support the former ability: understanding the general composition and different structural features of a crystal structure. It remains challenging to visualize that the properties of a crystal are shaped by three-dimensional structural features, i.e., differences of site occupation, polyhedral connectivity, or lattice structure. Because mentally representing the threedimensional order of crystal structures often implies a high 1631



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DEVELOPMENT AND IMPLEMENTATION OF THE MODELING ACTIVITY The modeling activity was developed as a joint project between the Institute of Chemistry Education and the Institute of Physical Chemistry. We tested it iteratively, following a designbased research approach.26−28 Through this iterative approach, we piloted a modeling activity with third year undergraduate majors in chemistry and materials chemistry. We revised the instruction and learning materials on the basis of our evaluation of the pilot study.

available in the Supporting Information. It is sorted according to the emphasized structural features and can be used by instructors to find appropriate crystal models for addressing different teaching goals. A comparison of the reports in Table 1 revealed that there are already good approaches for teaching and visualizing crystal structures, but none of the reports focuses on global and local structural features and evaluates the implementation of the models. The former reports only highlight single aspects of structural features and emphasize mainly global features, such as unit cell, overall packing arrangement (e.g., close-packed or not closepacked), or lattice structure (e.g., cubic or hexagonal). Only one model allows recognition of coordination number and site occupation, which are local features of crystal structures.21 None of them mention the polyhedral connectivity, although it is an essential aspect for a deeper understanding of physical and chemical properties of crystal structures. To gain a broader expertise of crystal structures, therefore, it is necessary to support students’ mental visualization and understanding of global and local features. Another difference of the reports is their educational focus. The majority of the reports, unfortunately, do not provide either a construction manual or further instruction material, like worksheets. Only three reports describe a combination of (1) a construction manual, (2) a student-centered construction of the models, and (3) a construction of models as part of a learning environment (cf. Table 1).18,20,21 They describe how to embed the models in a type of active learning environment, e.g., to engage students in calculating packing efficiencies.18,20 However, none of these promising approaches evaluate if and how students are engaged in reflecting about structural features of a crystal while interacting with the models. The reported models also differ in terms of the materials chosen for the construction. The variety of materials available to construct different models is manifold, but most of the materials used are opaque, making it difficult for students to recognize structural features, especially local ones, like site occupation or polyhedral connectivity that are inside the models. To fully address these three issues, we designed and iteratively evaluated a modeling activity that supports students’ understanding and reasoning about global and local features of crystal structures. In particular, the usage of clear plastic balls enables the visualization of all kinds of structural features in one model. Due to the transparency of the model, the students have the possibility to look directly into their crystal model and can easily identify obvious external structural features as well as internal positions of atoms or ions that have been difficult to access previously. The designed modeling activity includes an active learning sequence to engage students in reflecting about inherent characteristics of a crystal structure while constructing a see-through model and in comparing the compositions of different crystal structures in a subsequent discussion. In addition to the evaluation of the learning environment and instructional material, we investigated and qualitatively analyzed students’ discourse and interactions with the models during the activity. On the basis of this detailed analysis, we examined the extent to which students were encouraged in content-related interactions with the models and especially what types of structural features were considered during students’ discussions.

Design of the Modeling Activity

The modeling activity presented is designed as a studentcentered activity that aims at visualizing the general composition of different crystal structures including global and local features with their respective three-dimensional models. Through the construction and manipulation of these models, students are encouraged to reason with respect to important structural features of crystals. The activity is suitable for chemistry or materials chemistry undergraduate majors and can be carried out in a 4 h session divided into four parts: introduction, constructing, comparing, and closing (cf. Figure 1).

Figure 1. Structure of the modeling activity.

During the introduction, the modeling activity is introduced and explained. The students are provided with worksheets for guiding their activity (cf. Supporting Information, worksheets I and II), as well as with material for constructing the models (all materials can easily be ordered online; cf., Supporting Information, material and shopping list and print templates). Building upon former reported models and model kits, we use clear plastic balls for the anions and differently sized and colored cotton or wooden balls for the cations as the basis for the construction. All retailer and instructional material provided for the students and the instructor can be found in the Supporting Information. Inspired by the jigsaw teaching method, the students first work in different expert groups consisting of two or three students (c.f. Figure 1).29,30 Each expert group constructs a three-dimensional model of a common crystal structure, e.g., sodium chloride, zinc blend, wurtzite, nickel arsenide, or Heusler compound. Figure 2 provides a completed model of the sodium chloride structure. Pictures of other models are 1632



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During the comparing part, the students form new groups (mixed groups) with one student from each of the expert groups (c.f. Figure 1). The experts are now in charge of presenting the characteristic features of their crystal structure to the other students in the group. The constructed models are a means to illustrate the packing arrangement, lattice structure, coordination number, site occupation, and polyhedral connectivity to their group members. Through comparing, presenting, and independently verbalizing, students reflect on commonalities and differences to obtain an overview of the structural features of the other crystals. The students complete their worksheets (cf., SI worksheet II) in order to document their results. In the closing part, moderated by the lecturer, the students sum up their results and give feedback about their experiences during the modeling activity. This part is guided, for example, by the following questions: “What are your main takeaways from the modeling activity?” and “If we do a similar activity in the future, should we consider any modifications?” (For more guiding questions, see SI worksheet I.) After the modeling activity, the models can be reused in subsequent lectures to repeat previously learned concepts or illustrate advanced concepts. If single balls have been glued erroneously during construction or if the balls should be reused in another course, the glue can be removed with ethanol. To save time, the first layer pads should be prepared

provided in the Supporting Information (cf., material and shopping list).

Figure 2. Model of the sodium chloride crystal structure (NaCl): (A) side view and (B) top view. Chloride ions are represented by clear plastic balls and sodium ions by yellow wooden balls.

Throughout the constructing part, the students are asked to collect and note information about the structural features of their crystals on their worksheets (cf., SI worksheet II), thereby becoming experts with regard to their model. The stepwise construction process of a sodium chloride model in Figure 3 illustrates the construction process and can be used by instructors to create their own models. These different steps of the process can also be made available as hint cards during the construction process (cf., SI print templates).

Figure 3. Stepwise instruction for the construction process of a sodium chloride model. The important balls in each step are highlighted in green and the auxiliary balls in red. 1633



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Figure 4. Coding scheme. Organization-related codes: organization (ORG), construction (CO). Content-related codes: nonverbal interactions (NVI), content-related interactions (CRI), content-related discussions (CRD). Global structural features: packing arrangement and lattice structure (PL). Local features: site occupation (SO), site occupation + coordination number (SO + CN), coordination number (CN), polyhedral connectivity (PC), and further content-related discussions (FCRD).

by an instructor prior to the activity. Once prepared, the first layer pads are reusable.

to visualize but also to discuss and reflect on prior learned structural features of common crystals. In the following lecture, the students used their self-made models to compare different visualization methods for crystal structures. They were asked to evaluate which method, e.g., the software VESTA or their selfmade models, was appropriate to adequately represent the respective structural features. The students were then introduced in subsequent lectures to diffraction theory, experimental acquisition of powder diffraction data, and data analysis with suitable analysis programs, i.e., X’Pert, Origin, Powdcell, or FullProf. These lectures emphasized how structural characteristics of crystal structures can be measured and changed. During these lectures, some of the students used their self-made models to illustrate and reproduce the recently learned concepts. At the end of the course, students were encouraged to predict how structural features of a crystal can be altered to produce various desired properties. Data Collection. We used videography to collect our data during the constructing and the comparing parts. This data collection method was particularly important to answer the research questions. Since we were interested in students’ content-related interactions with the models, it was important to have both audio recordings and video recordings. It was therefore easier to identify if and when students engaged in such interactions during the modeling activity. We asked the students for their consent before collecting data. Two students from two different expert groups denied consent to publish their data; their respective data were withheld. Data Analysis. To acquire a deeper understanding of how students interacted with the models and what content-related aspects were induced by the activity, we chose a qualitative data analysis. The videos were coded and analyzed via content analysis31 in order to determine if content-related interactions and reasoning about the composition and structural features of crystals were taking place during the described modeling activity.

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EVALUATION OF THE ACTIVITY The activity was developed with the goal of helping students visualize and reflect on different features of crystal structures. Many of the modeling activities or models mentioned in Table 1 also had these goals. However, none of these reports have demonstrated to what extent students are actually engaged in these abilities during a modeling activity. In our case, we were further interested in determining how often students are engaged in reasoning about global and local aspects of crystal structures while interacting with the models. The analysis and evaluation of the activity was therefore guided by the following research questions: • To what extent are the students engaged in contentrelated interactions with the models during constructing and comparing? • What types of global and local features of crystal structures do students consider while constructing and comparing the models? Methods

Setting and Participants. We implemented the revised modeling activity in 2016 in an undergraduate materials chemistry course with 10 undergraduate students (only male students). This fifth semester course focused on the composition of crystal structures and the resulting structure− property relationships. Before performing the activity, the students attended a few lectures on various topics, e.g., crystalline unit cells, lattice structures, close-packing arrangements, coordination numbers, site occupation, and polyhedral connectivity. In a previous activity, the students learned how to visualize different crystal structures by using the computer software VESTA.8 The presented activity was then meant to enable students not only 1634



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Table 2. Examples for the Subcoding Categories Coding Category

Speaker

Packing arrangement and lattice structure (PL)

S

Packing Arrangement: “Wait a minute... this is A, this is B and this is A again. That’s right. Isn’t it?”

S

S1 S2 S1

Lattice Structure: “We have taken the same balls just because we have formed a hexagonal structure consisting of both kinds of atoms... so then both must be the same size, right?” “Which sites are occupied by cations?” “Octahedral sites.” “I think this structure has only octahedral sites... or also tetrahedral sites?” “Of course it has tetrahedral sites! But they aren’t occupied.” “Hmm... How do you determine the coordination? I never got that...” “You have to look at the next neighbors... I can do that for you... for example” [points at the model]. “Look here at this level there are four and here six above it.” “How are the polyhedra connected?” “Hmm. Surface... I would say... the polyhedra are surface-linked.” “Yes, but alloys are not loaded ionically, ah electronically... that’s not balanced then.”

S2

“Yes, an alloy is not ionic anyway.”

Site occupation (SO)

Coordination number (CN)

Polyhedral connectivity (PC) Further content-related discussions (FCRD)

S1 S2 S1 S2 S1 S2

Example Student Statements by Category

students were engaged in content-related interactions with the models. The average distribution of the main coding categories over all groups during the investigated parts is illustrated in Figure 3. As we were interested in how long students spent on each of the organization-related and content-related aspects while constructing and comparing, a value of 100% corresponds to the time of 120 min (constructing) and to the time of 90 min (comparing), respectively. During constructing, students spent 57% of the time organizing their material and arranging the models (ORG, CO, Figure 5), whereas in 31% of this time students were

Derived from our research questions, we developed a coding scheme with five main coding categories and five subcoding categories (cf. Figure 4). All main coding categories were divided either into organization-related codes or contentrelated codes. The former group was further divided into aspects that regarded the organization of the modeling activity (ORG) and the construction of the models (CO). The contentrelated coding categories were divided into nonverbal interactions (NVI), content-related discussions (CRD), as well as the combination of both, content-related interactions (CRI). The category organization (ORG) was coded for all video sequences, in which students selected and organized their material for the modeling activity (e.g., worksheet, first layer pad, sizes of the balls for the anions and cations, etc.). Sequences that showed students gluing and arranging the balls were coded as construction (CO). The coding category nonverbal interactions (NVI) comprises all sequences that showed students (without speaking) interacting with the models to identify or demonstrate structural features of their models. The code content-related interactions (CRI) captures when students were explicitly interacting with the model while reasoning about structural features. All sequences that showed students talking about structural features of their model without an explicit interaction were coded with the category content-related discussion (CRD). The content-related interactions (CRI) were of special importance to evaluate the extent to which the students were engaged with the models. To determine the type of structural features that students were mentioning or showing, we further divided the content-related categories (CRD and CRI) into five subcoded categories in a second round of coding (Figure 4). We defined the five content-related coding categories based on traditional textbooks of solid-state chemistry,3 such as packing arrangement and lattice structure (PL), site occupation (SO), polyhedral connectivity (PC), and coordination number (CN). The coding category f urther content-related discussions (FCRD) comprised all content-related discussions that were not related to the four other topics. Table 2 provides student examples for each of the five subcoding categories.

Figure 5. Average distribution of the main coding categories during constructing and comparing. Organization-related codes: organization (ORG), construction (CO). Content-related codes: nonverbal interactions (NVI), content-related interactions (CRI), content-related discussions (CRD).

occupied with arranging and gluing the balls (CO). These results correspond to our expectations and are satisfying because they indicate that the students worked in a timeefficient manner while constructing the models. However, the time may vary depending on the complexity of a structure; for instance, the Heusler compound is a more complex structure, whereas sodium chloride models are easier to construct. In the

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RESULTS AND DISCUSSION After coding all video sequences of the constructing and comparing parts, we first wanted to know to what extent the 1635



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comparing the models. Figure 6 illustrates the average distribution of the subcoding categories of all groups during

case of heterogeneous groups, the teacher may decide which model to construct based on students’ prior knowledge and experiences. The time to organize the material can be shortened if students are provided beforehand with a set of balls and materials or if parts of the models are preconstructed, e.g., layers. Regarding the content-related coding categories, students spent 43% of the time reasoning about structural features, whereas for 29% of this time the students explicitly used the models when talking about the structural composition. At this point, we expected students to talk more frequently about structural features while constructing their models. For most students, however, the thorough discussion of structural features only took place when comparing the models in the subsequent step. During constructing, the students spent about the same amount of time building the model as they spent engaged in contentrelated interactions with the models. This latter result may not be surprising when looking closely at how students were constructing their models. The video sequences revealed that the students were very focused and often silently constructed the layers. They were only discussing content-related aspects when they either had to make a decision or were unsure about the next step. Surprisingly, the students were rarely distracted or in private conversation while constructing. This might indicate that the difficulty of the task did match the ability of the students. In the subsequent step, when comparing the models, students spent 75% of the time using the models to reason about different features of their crystal structures. The students also spent the remaining time talking about the crystal structures, but without using the models. This result is very satisfying and demonstrates the relevance of this part, since the models are used intensively to compare the differences of the models. The prior engagement with the models during construction might have positively supported this comparing step, as students were familiar with their own model. We were further interested in the extent to which students reasoned about the composition of their crystal structures while interacting with the models. To assess these interactions, the coding category content-related interactions (CRI) was of special importance. When considering the two parts of the modeling activity, the students spent 20% of their time during constructing and 65% of their time during comparing with content-related interactions. Therefore, the extent to which students interacted with the models and spoke about them is much higher when comparing the models. Although students spent much time arranging and gluing the balls during constructing, the intensive work with the models presents an added value for the learning process and forms the basis for later interactions with the models. By arranging and gluing, students build-up the various three-dimensional elements and layers of their crystal structure step by step, e.g., tetrahedral sites, and thus recognize more easily how crystal structures are assembled in the final models. We also noticed a dominant haptic use of the models. To elucidate or exemplify the correct occupation of the sites or to determine the coordination number, the students touched, moved, or modified the arrangement of the balls several times. Hence, the selfconstruction of the model has definitely added value for helping students recognize model compositions and structural features of crystals. Moreover, we wanted to identify what types of global and local features students considered while constructing and

Figure 6. Average distribution of the subcoding categories during constructing and comparing. Global structural features: packing arrangement and lattice structure (PL). Local features: site occupation (SO), site occupation + coordination number (SO + CN), coordination number (CN), polyhedral connectivity (PC), and f urther content-related discussions (FCRD).

the construction and the comparison parts of the modeling activity. The code distributions in this figure refer to the content-related coding categories in Figure 5. For the constructing, the 100% corresponds to the time of approximately 40 min, while comparing corresponds to approximately 81 min. During the two parts of the activity, both the global and local characteristics of the crystal structures were considered. While constructing, students discussed global structural features in 46% of the time and the local ones in 27% of the time. While comparing, students discussed more local (68% of time) than global (31% of time) features. This is because the local features, e.g., the tetrahedral and octahedral sites, only result after the packing arrangement. Regarding the entire modeling activity, students more frequently discussed local features, such as site occupation, coordination number, and polyhedral connectivity, than global features, e.g., packing arrangement and lattice structure. The complexity of the crystal structure also determines how students handle the different features. While building the complex structures, such as nickel arsenide and Heusler compound, students were more concerned with global features. Those who built less complex structures, e.g., sodium chloride and zinc blend, were more often engaged in reasoning about local features. A closer look at the type of local features, however, indicated that students most frequently reasoned about the coordination number and the site occupation in contrast to the polyhedral connectivity. This could be because some students already had problems imagining single polyhedra or recognizing them prior to the activity. In addition, it may be more difficult to imagine and recognize the connection of several polyhedra. Since the polyhedral connectivity significantly influences the properties of crystal structures, but less discussion about polyhedral connectivity took place during the modeling activity, further 1636



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local structural features. These results are not surprising with reference to current literature that demonstrates an increase in students’ learning outcomes through modeling activities.9,10 With regard to the two different parts of the activity, however, it was unexpected that the students were engaged more extensively in content-related interactions during comparing than during constructing. Moreover, these two parts differ not only in terms of the intensity of students’ content-related interactions, but also with respect to the structural features considered in their groups. During constructing, students discussed global features more frequently, for instance, the packing arrangement, whereas during comparing, they focused more frequently on coordination numbers, a local feature. This result demonstrates that embedding both, the construction and the comparison of the models, in an active learning environment is important to actualize the full potential of the models and support students’ understanding of crystal structures.

guidance is necessary to help students recognize and discuss these aspects more frequently. The situations in which the students explored the structure of their crystals by interacting with the models (CRI) were particularly valuable for qualitatively estimating how students connected conceptual understanding with features of the models. A detailed look into the following excerpts illustrates how the students interacted with the models to determine structural features. The first sequence shows two students discussing the coordination number of the nickel arsenide structure (cf., Figure 7). One of the students used the model to count the

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LIMITATIONS The data used in this qualitative analysis were limited to a small group of students. Thus, we can only describe how this particular group of students interacted with the models. We were focusing only on content-related aspects of students’ interactions with the models and did not analyze how students’ discourse while constructing and comparing the models further supported their learning process. Whether students’ understanding and mental models of the three-dimensional composition of crystal structure improved significantly through this type of modeling can be ascertained only by a larger number of students and should be the aim of a future study. Furthermore, we cannot rule out the notion that students would be similarly engaged in reflecting on global and local aspects of crystal structures when provided with preconstructed transparent models. As is common when using models, the constructed models are limited in terms of the structural features they represent. In a final model, for example, it is difficult to recognize the unit cell or a single polyhedron. In addition, the anion−cation relationship is only approximately represented in the models, due to the given ball sizes.

Figure 7. Example for a content-related interaction during the constructing part. The two students (S1 and S2) discussed the coordination number of the nickel arsenide structure.

coordination number of the nickel atoms. He contemplated the model from different perspectives and touched it several times with his hands and a pen. The student then tried to describe how to determine the coordination number with the help of the model. The second sequence shows two students discussing the site occupation of the sodium chloride structure (cf. Figure 8).

Figure 8. Second example for a content-related interaction during the constructing part. Two students (S1 and S2) discussed the site occupation of the sodium chloride structure.

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CONCLUSION AND IMPLICATIONS The modeling activity presented here provides a learning environment to help students visualize, recognize, and reflect on the submicroscopic features of crystal structures. On the basis of the idea of using transparent balls for the construction of the models, we used clear plastic balls to represent the anions, and colored wooden balls to represent smaller cations. The resulting transparency of the models highlights different structural features. Both global structural features that characterize the composition of several atoms or ions of crystal structures (e.g., packing arrangement) as well as local ones that characterize the direct environment of single atoms or ions in a crystal (e.g., site occupation) can be illustrated. Through the use of the jigsaw teaching method, the students not only construct their models but also have the opportunity to compare the models and reflect on differences in composition of the crystal structures. We qualitatively investigated how students in an undergraduate materials chemistry course interacted with their selfconstructed models of different crystal structures. A detailed

They tried to figure out if and how the octahedral sites are occupied. They touched the model several times, disassembled it, changed the size and position of the balls for the cations, and finally determined the right position and occupation of the octahedral sites. Both examples show how the students actively included the models in their considerations regarding the composition of their crystal structure. Instead of sketching or using words, the students used the models as a tool to recognize structural features of the crystals or to explain how to recognize them. In Figure 7, student 2 used the model to first determine the coordination number. He then used the model to explain to his partner how to determine the coordination number. On the basis of our analysis, the entire modeling activity fulfills the desired goals. It encourages students to investigate the three-dimensional structure of different crystals by interacting with self-constructed see-through models and further supports students’ discussion of important global and 1637



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video analysis revealed that the interactions with the models and students’ focus on global and local structural features differ depending on the different parts of the modeling activity. Students mainly focus on global features while constructing the models whereas they are more frequently focusing on local features during comparing. As the examination of local characteristics is particularly important in order to understand advanced structure−property relationships, the comparison provides a valuable supplement to the construction of the models. On the basis of the analysis, the combination of constructing and comparing the models, in particular, is valuable to support students’ understanding and mental representation of different structural features of crystals. Overall, the students in our sample gave positive feedback and reported that they experienced the activity as very valuable for their understanding of crystal structures. Following our design-based research approach, the modeling activity can be further optimized by shortening the construction of the models by providing preconstructed components, e.g., coordination polyhedra or single layers, etc. In order to increase, especially, students’ mental visualization and understanding of the polyhedral connectivity, we developed a complementary modeling activity in which students construct various polyhedra with different connections (corner-, edge-, and surface-linked; Figure 9). This

Figure 10. Model of the perovskite crystal structure (CaTiO3). Oxygen ions are represented by clear plastic balls, barium ions by orange table tennis balls, and titanium ions by red wooden balls.

preconstructed models to carry out the comparing part of the activity.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.9b00119. Extended version of Table 1, materials and shopping list, print templates, and worksheets (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Figure 9. Models of different connected tetrahedra. The connection point of the two tetrahedra is highlighted by the usage of blue tinted balls: (A) corner-linked tetrahedra, (B) edge-linked tetrahedra, (C) surface-linked tetrahedra.

ORCID

Stefanie Lenzer: 0000-0002-4024-6473 Bernd Smarsly: 0000-0001-8452-2663 Nicole Graulich: 0000-0002-0444-8609 Notes

activity should be carried out prior to the modeling activity presented here. The construction of the polyhedra and their connections may help students to better recognize them later during the construction of their models. Since this additional activity was developed on the basis of the data presented here (cf., Figure 6), we have not yet qualitatively evaluated if it actually supports students’ recognition of the polyhedra and their connection in the larger crystal structure models. In a further lecture, students can also construct models of more complex structures, for instance, the perovskite or spinel structure (cf. Figure 10). If enough time is available, we recommend carrying out all three modeling activities: constructing and comparing models of (1) different structural features (e.g., occupied tetrahedra and octahedra as well as their connection), (2) common crystal structures (e.g., sodium chloride and zinc blend), and (3) advanced crystal structures (e.g., perovskite or spinel structure). Furthermore, due to the transparency, the presented models can be reused in subsequent lectures, either to repeat previously learned concepts or to further illustrate advanced structure−property concepts of crystal structures. Another advantage of the transparent models is that, even if there is not enough time for the whole activity, it is possible to use

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication represents a component of the first author’s doctoral (Dr. rer. nat.) thesis in the Department of Chemistry and Biology at the Justus-Liebig-University Giessen, Germany. The project is a cooperation of the Institute of Physical Chemistry (Prof. Smarsly) and the Institute of Chemistry Education (Prof. Graulich). We thank Martin Steinbach, Julian Schaaf, Kevin Reuter, Dr. Pascal Vöpel, and Dr. Christoph Seitz for their support during data collection and analysis, as well as all of the students who participated, and Heiko Barth for capturing our models in photographs.

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REFERENCES

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