Creating and Displaying Virtual Silicate Structures ... - cloudfront.net

Creating and Displaying Virtual Silicate Structures Using Geographic Information Systems Patrick J. Kennelly

Department of Earth and Environmental Science, C.W. Post Campus of Long Island University, 720 Northern Blvd., Brookville, NY 11548, [email protected]

ABSTRACT This paper illustrates the capabilities of geographic information system (GIS) software to create and display silicate structures. These models require no knowledge of editing functionality within the GIS software. Instead, the required input is the coordinates of the individual atoms or tetrahedra constructed in a word processing or spreadsheet program. These coordinates are then imported into the GIS software, and can be used to display chain, ring, sheet, and framework structures. Links to silicate models exported from the GIS software in a virtual reality modeling language (VRML) format are provided. These models can be displayed using a web browser equipped with any freely available VRML plug-in. Creating GIS-based silicate structures is an alternative to other software packages such as CrystalMaker® and Xtaldraw® designed specifically to create and display atomic structures. Although these GIS-based methods do not have all of the functionality of custom applications, GIS is a pervasive and growing technology with numerous applications in earth sciences and many other disciplines. Instructors may consider using this GIS-based method to introduce geospatial concepts, illustrate the breadth of GIS applications, and to establish interactive links between mineralogy and other disciplines.

INTRODUCTION Students in introductory geology and earth science classes are confronted with and often confounded by the challenge of visualizing complex spatial data in three dimensions. One of these first perceptual feats encountered is developing mental pictures of the atomic arrangement of silicate minerals. Such silicate structures are commonly presented as images in most introductory geology and earth science texts (e.g. McGeary and Plummer, 1998; Skinner and Porter, 2003; Press, Siever, Grotzinger, and Jordan, 2004; Tarbuck and Lutgens, 2004; Marshak, 2005). Silicates are important because they are the most abundant mineral group in the earth's crust. In addition to being abundant, silicates are also common rock-forming minerals. Their three dimensional (3D) crystal structures are reflected in their physical properties (e.g. cleavage, no cleavage) and provide links between the atomic arrangement and diagnostic properties used for minerals. The fundamental building block for silicate structures is the silicate tetrahedron. A tetrahedron is a platonic solid with four triangular faces, three of which meet at each vertex. The four tangential oxygen atoms in a silicate tetrahedron can be represented as such a shape, with the silicon atom nestled in the center. A physical model of the silicate tetrahedron assigns effective radii to spheres to represent the distance between adjacent atoms Kennelly - Creating and Displaying Virtual Silicate Structures

or ions (e.g. Nesse, 2000). If multiple tetrahedra can be represented as all sitting on the same plane, the coplanar oxygen atoms are referred to as basal. The apical oxygen atom is offset at a right angle from the plane and above the center of gravity of the first three (Zoltai and Stout, 1984). The silicon atom is confined to the central void, completing the silicate tetrahedron. We can create a tetrahedral representation of the spherical model by using the centers of the four oxygen atoms as vertices. Silicate tetrahedra can link to each other by sharing oxygen ions. Many geometries result, including tetrahedra joined together as single chains, double chains, rings, sheets, and intricate three-dimensional frameworks. These frameworks are especially complex and can be difficult to represent as two dimensional or three dimensional renderings, such as a drawing on a blackboard or a Styrofoam ball model. A number of instructional aids facilitate teaching crystal structures. Activities designed to assist visualization skills are categorized by Libarkin and Brick (2002) into three classes: static materials, animations, and interactive models. Blackboard drawings, projected images, and Styrofoam models would be examples of static materials. Gunter (1993) suggests that balloons may be used to simulate the polymerization of silicate tetrahedra. Other instructional techniques involving the use of ball models using pre-drilled templates and ball and stick models are discussed in Brady et al. (1997). Instructor resource material associated with many modern textbooks includes animated displays of silicate structures (e.g. Tarbuck and Lutgens, 2004). A number of excellent interactive computer applications exist to construct, display and manipulate crystal structures. These include CrystalMaker® (Palmer, 2006) and Xtaldraw® (Bartelmehs, 2002). A comprehensive listing of such programs can be found at the Collaborative Computational Project Number 14 (CCP14) website . An alternative method for creating models displaying 3D visualizations is using geographic information systems (GIS) with input generated by a text editing or a spreadsheet program. The resulting models have the basic functionality of those created with the software packages referenced above. Additionally, creating models within the GIS offers students exposure to software with broad applications within and outside of the geosciences.

METHODOLOGY The Silicate Tetrahedron - The methodology for creating a silicate tetrahedron in GIS uses a list of tab-delimited coordinates for the centers of the silicon and oxygen atoms. To define these coordinates, it is necessary to know the relative location and size of these atoms with respect to each other. A Cartesian coordinate system is used to define the x, y, and z location of the 235

Figure 1. The x,y,z coordinates of the silicate tetrahedron used to create silicate structures in the geographic information system (GIS) software. The three vertices of the triangle represent the basal oxygen atoms. The central circle with the larger z value represents the apical oxygen atom, and the central point with the smaller z value represents the silicon atom.

Figure 2. A silicate tetrahedron created with true 3D point symbols. The radii of the atoms are adjusted to create tangential spheres in accord with Pauling’s rules.

is in accord with applications of Pauling's Rules to silicate tetrahedron, requiring distances between cations and anions to be equal to the sum of their effective ionic 0 0 0 oxygen radii (e.g. Perkins, 2002). In GIS, the "atom" column 10 0 0 oxygen values (know as an attribute) inherited from the 5 8.6603 0 oxygen tab-delimited text file allows the size and color of the 5 2.8868 8.165 oxygen spheres representing silicon and oxygen to be varied independently. GIS users can manipulate and view the 5 2.8868 2.0413 silicon resulting model from various directions. Movie clips can Table 1. Coordinates of oxygen and silicon ions used also be recorded directly from ArcScene during manipulation. to create a silicate tetrahedron. X

Y

Z

Atom

three basal oxygen atoms, the apical oxygen atom, and the silicon atom is shown in Figure 1. Using coordinates from Figure 1, the list of x, y, and z values shown in Table 1 can be created in any word processing or spreadsheet programs. Information regarding individual points can also be included. For example, a column was added to Table 1 to differentiate the silicon from the oxygen atoms. Once the table is complete, it can be imported into many GIS software programs. First, the coordinates should be saved in a tab delimited text (.txt extension) or database files (.dbf extension) format. The data in Table 1 was added to ESRI's ArcMap program as "events". An event is a geographic location stored in tabular rather than spatial format (Wade and Sommer, 2006). Once added to the GIS, the events can be converted into a spatial format and saved as a GIS layer. This layer can then be opened in a separate GIS program designed for viewing GIS data in a 3D environment. Figure 2 shows the GIS layer representing one silicate tetrahedron displayed in ESRI's ArcScene 3D viewer. ArcScene represents points using a true 3D marker symbol, meaning it has properties that allow it to be displayed in three dimensions (Editors of ESRI Press, 2004; Kennedy, 2004; Wade and Sommer, 2006). This allows one to change the size of the spheres in three dimensions until they are tangential. Such an operation 236

Single Chain, Double Chain, Ring, and Sheet Silicate Structures - Silicate tetrahedra share oxygen ions, creating more complex silicate structures. It is possible to build these models by locating individual oxygen and silicon atoms with the procedure outlined above. It is more efficient, however, to use one point to represent one silicate tetrahedron. The point is then displayed as a 3D symbol with a tetrahedron shape (Editors of ESRI Press, 2004; Kennedy, 2004). Knowing distances between atoms from Figure 1 and the general pattern of a single chain silicate, a model is created (Figure 3) based on the coordinates in Table 2 . Because all 5 atoms are now being represented by a single tetrahedron, the "atom" attribute is no longer necessary. A new field entitled "rotate", however, is added. This is necessary as all silicate structures do not use the default orientation of the 3D tetrahedron point symbol in the GIS. Also, moving down a chain, tetrahedra on the left will be rotated 180º from symbols on the right. Knowing the pattern of a double chain silicate, a model is created (Figure 4) based on the the coordinates in Table 3. The construct is the single chain and its mirror image. At this juncture, it is probably easier to work with coordinate values in some sort of spreadsheet, as all x values change by one of two values, all y and z values are the same, and all rotate values change by 180º. Six adjacent tetrahedra in this double chain have the

Journal of Geoscience Education, v. 55, n. 3, May 2007, p. 235-243

Figure 3. A single chain structure of silicate tetrahedra. X

Y

0

0

Rotate 30

5.7736 0

10 20

210 30

5.7736 0

30 40

210 30

5.7736 0

50 60

210 30

5.7736 0

70 80

210 30

5.7736

90

210

Table 2. Coordinates of tetrahedra for a single chain. The table and resulting chain can be extended by continuing to 1) alternate the values in the x column, 2) add 10 to values in the y column, and 3) alternate values in the rotate column.

geometry of a six-membered ring with hexagonal symmetry (e.g. Zoltai and Stout, 1984). The associated points can be copied into a new table, or the six points can be selected in the GIS and exported to create an isolated ring silicate structure (Burke et al., 2004). Various spatial permutations of tetrahedra comprising the ring are possible using capabilities of the GIS to invert or rotate individual tetrahedra. Beginning with the double chain, sheet silicate structures are straightforward to create in the spreadsheet environment (See Figure 5 and Table 4). Adjoining double chains all have the same change in x values, and the same y, z, and rotation values. Once one sheet is completed, the user can create new sheets offset in the z direction by copying the spreadsheet and applying a constant change to the z-value. This step, however, is not necessary with ArcScene. Instead, one sheet can be brought in for display multiple times. Then, each separate display of the same sheet can be offset by a different z-value to a new base height (Editors of ESRI Press, 2004; Kennedy, 2004). The 3D marker symbol for some sheets has been inverted so that tetrahedra point downward instead of upward (Figure 6). This display seems especially useful for demonstrating to students the dominant plane of cleavage associated with sheet silicate minerals. One of the appealing aspects of interactive models is that users can customize the models. This can be as simple as customizing colors to personal preferences, or as complex as adding additional cations or varying silicate structures. For example, the sheet silicate presented in Figure 5 has become an iconic image in numerous textbooks (e.g. McGeary and Plummer, 1998; Nesse, 2000; Skinner and Porter, 2003; Press, Siever, Grotzinger, and Jordan, 2004; Tarbuck and Lutgens, 2004; Marshak, 2005). Many sheet silicate structures are Kennelly - Creating and Displaying Virtual Silicate Structures

Figure 4. A double chain structure of silicate tetrahedra. X

Y

0

0

Rotate 30

5.7736

10

210

0

20

30

5.7736

30

210

0

40

30

5.7736

50

210

0

60

30

5.7736

70

210

0

80

30

5.7736

90

210 30

0

100

17.3206

10

30

23.0942

20

210

17.3206

30

30

23.0942

40

210

17.3206

50

30

23.0942

60

210

17.3206

70

30

23.0942

80

210

17.3206

90

30

23.0942

100

210

Table 3. Coordinates of tetrahedra for a double chain. The table and resulting chain can be extended by continuing to 1) alternate the values in the x column, 2) add 10 to values in the y column (after both values of 100), and 3) alternate values in the rotate column.

composed of interconnected rings that are slightly distorted through rotation, thus lowering their symmetry (e.g. Zoltai and Stout, 1984). The range of these rotations varies from 12° (Figure 7a) to 27° (Figure 7b) (e.g. Zoltai and Stout, 1984). Such models are useful to illustrate the closer packing of the silicate tetrahedra (Zoltai and Stout, 1984). An advantage of true 3D virtual models is that they can be exported so that anyone (with a web browser equipped with a freely available virtual reality modeling language (VRML) plug-in) can display and manipulate the models in 3D. One example of such a plug-in is the Cortona® VRML client available for free download from ParallelGraphics < http://www.parallelgraphics.com/ products/cortona/>. Once installed, a VRML file can be opened in a web browser by double clicking on the file, or pointing the web browser to the file. Exporting VRML models from some interactive crystal modeling software such as CrystalMaker® is trivial. There are, however, some peculiarities of the GIS software that make exporting such models less straightforward. 237

Points exported from GIS do not display well in a VRML viewer, as they have no actual dimension. The spheres and tetrahedra we see in Figures 2 - 7 are 3D marker symbols used simply for display in the GIS. This shortcoming is overcome by using spherical surfaces and triangulate irregular networks (TINs). A spherical surface is explicitly defined by the coordinates of its center and its radius. Once created, its surface is truly three dimensional, but it cannot be resized in the GIS. A TIN begins with points having z values, connects nearby points as edges to create a series of adjacent 3D triangular faces. TINs are used to represent topographic data in GIS because they can store data more efficiently than regular square grid cells (Editors of ESRI Press, 2004; Kennedy, 2004). Using the points representing oxygen atoms, TINs of tetrahedra can be created and exported to VRML (Figure 8). In addition to the VRML model on which Figure 8 is based, models for single chain, double chain, and sheet silicates are also created and exported. Readers are welcome to download these models from for educational use. Silicate Framework Structures - Three dimensional silicate structures, or framework silicates are complex Figure 5. A sheet structure of silicate tetrahedra with and difficult to portray. At least one introductory earth science textbook simply states the structure is "too hexagonal symmetry. complex to be shown by a simple two-dimensional drawing" (Skinner and Porter, 1995). Others default to a X Y Rotate tight arrangement of silicate tetrahedra with any 40.4148 10 210 structure difficult to discern (e.g. Tarbuck and Lutgens, 34.6412 20 30 2004). Although such structures may be illustrative of 40.4148 30 210 minerals without cleavage such as quartz, they do little 34.6412 40 30 to explain how other framework silicates such as feldspars possess two cleavage planes at 90º. 40.4148 50 210 34.6412

60

30

40.4148 34.6412

70 80

210 30

40.4148 34.6412

90 100

210 30

51.9618 57.7354

10 20

30 210

51.9618 57.7354

30 40

30 210

51.9618 57.7354

50 60

30 210

To produce the approximate silicate structure of feldspar (Frye, 1974; Zoltai and Stout, 1984) a more complex model is needed (Figure 9): 1) Tetrahedra are pointing both upward and downward on a single z layer. 2) Sequential z-layers are offset in the x and y direction. 3) Sequential z-layers share oxygen atoms - requiring tetrahedra to touch at points in the z direction.

Another variable called "apex" with possible values of "u" or "d" indicates if a tetrahedron points upward or downward. Tetrahedra are rotated, inverted, and offset 51.9618 70 30 in three dimensions as defined in Table 5 to create the 57.7354 80 210 feldspar framework structure (Figure 9). 51.9618 90 30 True 3D models of silicate structures can also be used to create stereoscopic displays. This offers the advantage 57.7354 100 210 of allowing the user a 3D view from a pair of 2D images. Table 4. Coordinates of tetrahedra for a sheet Figure 10 shows an example of a stereoscopic structure with hexagonal symmetry (add to table 3 to representation of the framework silicate structure create full structure). The table and resulting sheet displayed in Figure 9. can be extended in length by continuing to 1) alternate the values in the x column, 2) add 10 to values in the y column (after all values of 100), and 3) alternate values in the rotate column. The table and resulting sheet can be extended in width by continuing to 1) add ten rows with values of y varying from 10 to 100 by tens, 2) alternate values in the rotate column, and 3) alternatively adding 11.547 ( 17.3206 - 5.7736) and 23.0942 to values of x.

238

DISCUSSION The GIS-based methods presented here are meant to provide instructors with an alternative to traditional crystal structure software such as CrystalMaker® and Xtaldraw®. Ultimately, the instructor interested in virtual interactive silicate structures will base his or her decision on a number of factors, including learning objectives, the availability of resources (software,

Journal of Geoscience Education, v. 55, n. 3, May 2007, p. 235-243

Figure 6. An oblique view of four silica sheet structures looking along the plane of cleavage.

Figure 7. A sheet structure with silicate tetrahedra rotated to represent distortions that naturally occur in phyllosilicate minerals. Tetrahedra a) and b) are rotated 12° and 27° respectively.

Kennelly - Creating and Displaying Virtual Silicate Structures

239

Figure 8. Four views to highlight the relationship between the silicate tetrahedron and the atomic arrangement of the oxygen atoms and the silicon atom. The atoms are represented by spherical surfaces and the tetrahedron is represented by a TIN.

funding to purchase software, technical support, time, etc.), and integration with future coursework. Several advantages and disadvantages of using GIS to create silicate structures are given. These can be used for comparison with specifically designed crystal structure software. Advantages of GIS include: 1) introducing students to basic concepts of GIS, an important and growing technology; 2) utilizing GIS in a number of different exercises in an introductory earth science class to illustrate its broad applications; and 3) linking mineralogical concepts to other fields such as mathematics and information technology. Current trends within and outside of academia indicate GIS is a prevalent and growing technology which students will benefit from learning. In addition, GIS is a skill that is interdisciplinary and portable from one discipline to another. In academia, GIS can be applied across the campus curriculum (Sinton and Lund, 2006). ESRI, makers of ArcGIS software, estimate that 95% of institutions of higher education of over 10,000 students have licensed their GIS software (ESRI, personal communication, 2006). For the future science graduate, GIS skills are cited as being "as important as fieldwork" in natural resource management (Gerwin, 2004). The geospatial workspace is experiencing unprecedented growth (Gaudet et al., 2003). The federal government underscored this trend when "geospatial technology" was included in President George W. Bush's fourteen High Growth Job Training Initiatives in 2003 .

240

X 0

Y 7.8868

Z 0

Rotate 30

Apex d

7.8868 7.8868

0 15.7736

0 0

300 120

u u

15.7736 0

7.8868 35.2074

0 0

210 30

d d

7.8868 7.8868

27.3206 43.0942

0 0

300 120

u u

15.7736 0

35.2074 62.528

0 0

210 30

d d

27.3206 35.2074

-3.6602 -11.547

0 0

30 300

d u

35.2074 43.0942

4.2266 -3.6602

0 0

120 210

u d

27.3206 35.2074

23.6604 15.7736

0 0

30 300

d u

35.2074 43.0942

31.5472 23.6604

0 0

120 210

u d

13.6603 21.5471

15.7736 7.8868

-8.165 -8.165

30 300

d u

21.5471 29.4339

23.6604 15.7736

-8.165 -8.165

120 210

u d

13.6603 21.5471

43.0942 35.2074

-8.165 -8.165

30 300

d u

21.5471 29.4339

50.981 43.0942

-8.165 -8.165

120 210

u d

40.9809 48.8677

4.2266 -3.6602

-8.165 -8.165

30 300

d u

48.8677 56.7545

12.1134 4.2266

-8.165 -8.165

120 210

u d

40.9809 48.8677

31.5472 23.6604

-8.165 -8.165

30 300

d u

48.8677 56.7545

39.434 31.5472

-8.165 -8.165

120 210

u d

13.6603

15.7736

-8.165

30

d

Table 5.Coordinates of tetrahedra for the framework structure approximating feldspar. Additional layers can be included by offsetting all values of z by -16.330.

GIS can have broad applications in a geology department or across a campus. For example, an introductory earth science class could include a number of lessons, exercises, or labs meshing science with geospatial technology. Examples include identifying areas susceptible to landslides with terrain and overlay analysis, documenting temporal changes in coastal landforms, and identifying areas near rivers prone to flooding. Using the GIS-based silicate structures discussed in this paper could also help instructors link concepts of mineralogy to other fields such as geometry and information technology. Dyar et al. (2004) discuss the use of concept maps to establish links between mineralogy and other disciplines. Similarly, having students translate a known geometry into a simple database structure offers an opportunity to interact with technology. Students constructing and displaying silicate structures with GIS must quantify observed spatial

Journal of Geoscience Education, v. 55, n. 3, May 2007, p. 235-243

Figure 9. A framework structure of silicate tetrahedra approximating feldspar.

relationships, which may be less challenging but perhaps also less empowering than using more polished interfaces such as that of CrystalMaker®. Dyar et al. (2004) express caution about having students simply select from listings of symmetry and atomic coordinates in such programs, and suggests "a more engaging student activity is to let the students build or manipulate the input files themselves." Disadvantages of using GIS software compared to custom crystal structure software include: 1) GIS is not specifically designed for creating crystal structures, 2) GIS software does not have as much functionality as crystal software, and 3) the learning curve for GIS is steep. The use of GIS for mapping crystal structures using the Cartesian coordinates of Figure 2 is a straightforward process, but not optimal for all silicate structures. For example, it is appropriate for representing the Si6O18 ring of tourmaline, as it has coplanar basal oxygen atoms. Beryl, a framework silicate composed of interconnected rings, has tetrahedra tilted outward from the center of the ring so that only two oxygen atoms would intersect the x,y plane defined here (Nesse, 2000). Although the x, y, z coordinates of the rings can be calculated, more Kennelly - Creating and Displaying Virtual Silicate Structures

complex trigonometry is required. A polar coordinate system would simplify the assignment of coordinates to vertices. Geographic information systems is a misnomer, as any data with spatial coordinates can be mapped into a spatial reference framework, whether these coordinates are related to locations on the Earth or not. Non-geographic examples range from maps of the universe (Gott et al., 2005) to surface metrology, the numerical characterization of smoothness and defects of objects ranging from machined parts such as automobile-engine cylinders to components for the semiconductor industry (Pike, 2001). GIS is not specifically designed for creating crystal structures, but this methodology is another example of a long list of non-geographic applications of this powerful technology. Crystal structure software has more functionality than the GIS models presented here, such as the ability to switch from a tetrahedral to a ball-and-stick display. Although such features could be added to the GIS models, each enhancement requires additional time and effort. Ultimately, the instructor interested in using virtual interactive silicate models will have to access 241

Figure 10. A stereoscopic representation of a framework silicate structure, viewed from two slightly different orientations (separated by an angle of approximately 2º) from above one of the cleavage planes. The stereoscopic image reveals two different layers that make up this framework structure. The first cleavage plane is parallel to the image. The second cleavage plane is perpendicular to the view and runs from the lower left to upper right of the figure.

what is required to achieve his or her learning objectives and decide which tools are most effective in progressing towards these goals. Libarkin and Brick (2002) point out one of the issues associated with incorporating geospatial technology into curricula: "although GIS can be an effective means of facilitating the use of spatial skills in the classroom, learning is mitigated by the amount of time devoted to the technology itself." The steepness will vary based on a number of factors, but integrating multiple GIS exercises in a course or curriculum will ultimately offer more benefit for the time and effort invested. Crystal structure programs such as CrystalMaker® may require a smaller investment of time for crystallographic or mineralogical exercises, but may not have the breadth of potential applications for students.

SUMMARY GIS offers a technical tool that instructors and students can use to create 3D models of various silicate structures. This paper outlines methods to construct a silicate tetrahedron from x,y,z coordinates representing individual atoms of oxygen and silica. Additionally, it discusses methods to create simple to complex silicate structures by defining the location of silicate tetrahedra and show how to symbolize these within the GIS. Models can be exported from the GIS in a VRML format, which allows anyone with a web browser and free plug-in to examine these models in 3D. Such methods and products are helpful as learning aids designed ot spur interest in one possible use of spatial technology in earth science education.

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ACKNOWLEDGEMENTS The author would like to thank all of the editors and reviewers of the manuscript for helpful guidance and suggestions.

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