A NEW TYPE OF CRYSTAL MODEL
8
1. H. WESTBROOK and R. C. DEVRIES General Electric Research Laboratory, Schenectady, New York
A PERENNIAL problem to the crystallographer or crystal chemist is the adequate representation of various crystal structures, either pictorial or through the use of models. A number of different approaches have been described (1-15). The problsm is particularly acute when demonstrating various relationships between structures. Even building a pair of "Tinker-Toy" models and placing them side by side frequently is inadequate with respect to full and easy visualization of structural relationships. I t occurred to the authors that such visualizations might be considerably facilitated, at least for a simple system, by a model in which the atom positions were represented by lights-the color a t each position to he selected by aswitch. Such a model has been constructed and has proved to be a useful tool both for classroom instruction and for research studies (Fig. 1).
F ~ S U F *I .
General View 09 Lighted Model
Four distinctively colored hulbs were provided within a single translucent, spherical envelope (of the typc described by Hatch et al. (4)) a t each site within the lattice. Appropriate switching circuits permit indcpendent selection of each of the four hulbs at each of the six different types of site-or, any type may be left vacant by leaving all switches controlling that site open. I t is therefore possible to represent even true quaternary compounds, provided only that their s t n ~ r tures he compatible with the basic array of the model. DETAILS OF MODEL CONSTRUCTION
Frameworlc. The framework is made of five transparent plastic sheets (3/s- X 15- X 15-in.) which arc supported by four cylindrical plastic rods (1- X 19-in.) fastened to a plywood baseboard. Three of the plastic sheets (top, middle, and bottom) have atom sites a t the (000), (1/2, 1/2, 0) and (1/2,0, 0) type positions while the sheets interlayered with these have atom sites at (1/4,, 1/4, 1/4) and (3/4, 3/4, 3/4) type positions. The plan of their construction and assembly is shown in Figure 2. I n this model the corner atom sites form a 13- X 13- X 13-in. cube, inset one inch from the edge of the sheets. The atom positions are represented by plastic miniature tube bases inserted into carefully sized holes drilled through the plastic sheet. The four supporting rods are each actually composed of five separate sections, four 2'/s-in. long and one (between baseboard and lower sheet) 5a/4-in.long. All sections were tenoned to fit V8-in. holes in the sheets. The position of the support rods (Fig. 2) is such that interference with atom sites is minimized. Obviously PLAN
ELEVATION
I t was decided that the cubic array to be described would prove most versatile for the common cubic structures. Atom sites were located a t the following positions along the coordinate axes:
1/2, 1/4, 3/4, 3/4, 1/4. . , 3/4, 3/4, 1/4, 'I4,
1/2, 1/4, 3/4, 1/4, 3/4. . . 3/4, 1/4, 3/4, 1/4.
0
cube corners
1/2 1/4
body center
1/41 %
:::/
1/4 a/4
1st tetrahedron 0 ATOM SITES AT 0 0 0 ,
112 lit 0 , 112 0 0 , TYPE POSITIONS IN TYPE
A SHEETS.
2nd tetrahedron
CIATOY SITES AT E* l I16 114 &NO314 314 U4,TYPE POSITIONS I N TYPE B SHEETS.
0 W O ' HOLE FOR SUPPORT RODS Figure 2.
220
Physical Construction of the Model
JOURNAL OF CHEMICAL EDUCATION
Materials and Supplies for Construction of Crvstal Model .Malerial
Size
I'loxiglas sheet Plexiglns rod Plexiglas rod Plastic hemispheres Polystyrene coil forms
X 15 X 15 in. 1 X 19 m. I/, X 2 in. 2 in. (5 prongs) with bases (Amplenol2P5H)
Miniature lamps
G.E. No. 47, E-8v., 0.15 amp., bayonet base 11.5~.input, 6.3". 10 amp.
Filament transformer Toggle switch SPST
a/,
No. of
pieces
5 4 35 35 35 140 1 24
Supplier
Rohm and Haas Rohm and Haas Rohm and Haas Plaxell, Inc. Arrow Electronics, Inc. 65 Cortland Street., New York, N . Y. Radio Shack Radio Shack Radio Shack
Approzimale cost for model
$30.00 8.50 1.20 4.00" 13 0 0 10.00 5.00 8.50
'A minimum order, however, may he somewhat higher than this.
the size of the large cube is determined by the spacing of the separate layers, which in turn is conditioned by the thickness of the plastic sheet and diameter of plastic spheres that are used. Atoms. These are represented by hollow plastic spheres in each of which four differently colored lamps were mounted. Clear miniature lamp bulbs vere sprayed with spar varnish colored with appropriate organic dyes. The hemispheres from which the spheres were made were sandblasted on both inner and outer surfaces to diffuse the light. With this technique, for two of the colors used (red and yellow), the model is effective even in a well lighted room; the appearance of the green and blue bulbs can be enhanced considerFigure 3a. 1nternn1 Conably, however, by reducing the amount of light directly atrustion of en "Atam" ShowFlgvre 3b. insertion oi a n jng Arrangement of Colored ' ' A t o m ' ' into its Sockets nt a incident upon the model. Bulbs Lattice point The internal wiring of each "atom" was accomplished as follows: Using a simple jig, four 6v. lamps were first given a common junction by soldering the tubular 3b. The pins have been shortened to facilitate inserpart of the bases together in a "petal-like" arrangetion and removal (by prying up with a knife edge) of ment. As will be seen, it is important to assemble the "atom" units. A few duplicate units can readily each unit in the same order. Separate wires were then be made as replacements. On the other hand, one or more extra units may be assembled, intentionally wired soldered to the contact button at the base of each lamp with a differentpin arrangement for showing disordered and one to the common junction. This whole assembly ~ositions. was then fastened to a cut down plastic coil form by soldering the wires into the tubular pins of the coil 1st 2nd BODY EDGE CUBE FACE form. The index pin was used TETRAHEDRON TETRAHEDRON CENTER CENTER CORNER CENTER as the common lead and a standardized arrangement of pins with respect to color T\-as employed throughout. The assembly just described was in turn cemented with acetone into a hole cut in the renter of a plastic hemisphere. A plastic rod I/&- X 2-in. cemented a t the center of and perpendicular to the coil form base provided a support for pushing the "atoms" into the socket without crushing the fragile sphere. A photograph of the unit a t this stage of assembly is shown in Figure 3a. The upper and lower hemispheres were then cemented together with acetone. Insertion of the unit into an "atom site" in the model is shown in Fig. Figure 4. Wiring Diawam for the Mods1 VOLUME 34, NO. 5, MAY, 1957
221
Circuitry and Control Panel. The schematic wiring diagram for the model is shown in Figure 4. Each type of s i t e c u b e corner, body center, edge center, face center, and the two tetrahedral arrangements-was wired to allow independent control of both color and position by a set of 24 SPST switches. Care was taken to keep the wiring as unobtrusive as possible by minimizing the amount of wire used, by proper positioning, and by using transparent plastic insulation. The arrangement of switches on the face of the control panel is shown in Figure 5. A standard 110v.-6v. filament transformer serves as a convenient power supply. 1.1. 2nd BODY EDGE CUBE FACE TETRA. TETRA. CENTER CENlERSm(MRSCEHTERS
IdkkH I
YELLOW
I
I
j*j
GREEN
&"E
Fipvrr 5.
Schematic Diagram of Switch Positions on Control Panel
The scheme outlined above obviously has several variations: (1) A more compact arrangement of control panel and model can be effected by mounting six 5-position selector switches in a box-like base upon which the model is mounted. (2) The sheets could be mounted vertically rather than horizontally. (3) The "atoms" could be mounted on vertically placed hollow supports such as pipes (which could conceal the wiring). (4) The atom supports could be movable so as to allow intermediate atom pos:tions to be shown: (5) Less complex models could be made with conventional screw-in sockets holding small bulbs (e.g., spherical 7-watt frosted bulbs). OPERATION OF THE MODEL
A great variety of cubic structures can be represented with this model. Illustration of some of the possible structures will be given with reference to Figure 6. The significance of the 24 switches is shown in Figure 5. The shaded boxes of Figure 6 indicate the closed position of certain switches. Thus, Figure 6a shows schematically that the red switches for the body center and cube corner positions are closed, and i t will be observed that the lighted model will then represent the body centered cubic structure. This structure may be ordered to form the cesium chloride structure simply by opening the red switch for the body center site and closing the corresponding yellow switch as in Figure 6b. The arrangement of switches in Figure 6c yields the face centered cubic structure; this structure may be ordered in an analogous fashion to yield the Cu3Au structure of
Figulr 5.
Schematic Repmsntetion of Switching Configurations for Various Crystel Structurss
Figure 6d. A number of the other common structures possible with the model are indicated schematically in Figure 6, as well as some geometrically possible ones which do not appear to be in the literature. The possibilities have by no means been exhausted, even with respect to binary compounds. It might be noted parenthetically that the schematic notation of Figure 6 may have some merit in its own right as a two dimensional shorthand for certain crystal structures. As an example of the utility of the lighted model in revealing structural relationships, consider the sequence of structuresproduced by the switching arrangements Figure 6e, j, g and h. With the aid of the model it can be strikingly shown that the zinc blende structure is an ordered arrangement of the diamond structure, that the fluorite structure is generated from that of the zinc blende by filling in the other set of tetrahedral sites, and that an ordered ternary compound such as CuSbMg or LaOF evolves from the fluorite structure. A further ordering on cation sites as in Figure 6bl may also be imagined but no such case has yet been reported. The reader may deduce many other similar sequences from a study of the model or from Figure 6. I t will also be observed that in certain instances the same structure may be displayed in more than one may. Consider, for example, the simple body-centered-cubic structure where the number of unit cells shown might be increased from one (Fig. 6a) to eight, simply by closing all of one row of switches. I n other cases, such as the perovskite structure a different representation may be achieved by a change in coordinates, cj., Figures 61c and 61. An appreciation of the utility and versatility of the model can best be achieved by actually working with it. The present model indicates the feasibility of a general idea which could be extended to other lattice types. For example, a hexagonal model is currently under consideration in which sites could be provided a t both tetrahedral and octahedral holes in a close packed hexagonal framework. An effective application of this type of model would be in color movies of the educational type in which structural relationships could be clearly demonstrated. JOURNAL O F CHEMICAL EDUCATION
( I ) BADGELEY, C. D., Plaslies, 3 , 5 6 , 9 0 - 2 (1945). (2) BRonE, W. R., AND C. E. BOARD, J. CEEM.EDUC.,9, 1774 (1932). (3) BUERGER, M. J., A N D R. D. BUTLER, Am. MineralogziI, 21, 150-72 (1936). (4) HATCH,R. A., J. E. COMEFORO, AND N. A. PACE,Am. Minmzlogtit, 37, 58-67 (1952). (5) H~r.scn,R., Z. Physik., 138, 432 (1954).
VOLUME 34, NO. 5, MAY, 1957
NKHOLSON, D. G., Chem. Eng. News,30, 3164 (1952). PERKINS, A. T.,J. CHEM.EUUC., 28, 388 (1951). SEYMOUR, K. M., J. CHEM.EDUC.,15, 192 (1938). STUART, H. A,, Z, physik. Chem.,27, 35&58 (1934). WELCH, A. J. E., Aeta C ~ y s t . 6, , 476 (1953). WOOSTER, N . , J . C. IMCGOWAN, AND W. T. MOORE, J. Sci Instr., 26, 140-41 (1949). R. W. G.. AND C. J. KRANDA. Am. JOW. Sci... 11.. . . WYCKOFF,
377-80 (1926). ' (13) ZINSSER, H. H., J. CHEY.EDUC., 31, 662 (1954).
