FEBRUARY, 1955
75
A JIG FOR MAKING ATOMIC MODELS BEULAH F. DECKER and E. T. ASP General Electric Research Laboratory, Schenectady, New York
TEE visualization of the spatial arrangement of atoms in a molecule or crystal becomes difficult for many structures of high coordination, particularly when several different interatomic distances are involved and the angles are no longer simple. I t is often advisable to make a three-dimensional model to scale in order to see the atomic arrangement in proper perspective. The authors have devised a simple hand-operated instrument for boring holes in cork balls a t positions of interatomic bonds. The balls are then put together with wires of appropriate lengt,h to form the desired structure. Similar machine-operated instruments using wooden balls have been described by B~erger'.~ and Butler, and by T e r p ~ t r a . ~While the same basic principle is used, the instrument described here is simpler, less expensive to construct, and easier to operate. It would serve more readily as a desk instrument for constructing models out of small cork balls. DESCRIPTION OF THE APPARRTUS
The instrument devised, shov-n in Figure 1, is simply a two-circle goniometer, with a cork ball mounted so that its center lies on the horizontal and vertical axes of rotation. The ball remains stationary while a small hand-drill mounted on the vertical semicircular scale is rotated about the vertical axis (through any angle up to a full circle) and the horizontal axis (through any angle up to a half-rircle) to the position desired. A few turns of the drill, and the cork ball "atom" has a hole ready to receive one of its wire "interatomic bonds." Holes are bored at all bond positions on the F,guro 1 upper hemispherical surface of the ball; the ball is then inverted and holes bored a t the remaining bond positiol,s, A cork ball is prepared in this way for each atom. The structure is then completed by putting ' BUERGER, M. J., Rev. Sn'. Instr., 6,412-16 (1935). together the cork ball "at,oms" with pieces of wire cut 1 BUERGER, M. J., A N D R. D. BUTLER, Am. Mimalogist, 21, to the proper lengths for the interatomic distances. 1 5 ~ 7 7 /lo?fi) ,A".,",. remembiring that. ahond length is measured from center T E R P ~ T E AP., , Natuunu. Tijdsehr. (Bdg.). 21,283 (1939).
.-
A-"
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JOURNAL OF CHEMICAL EDUCATION
to center of the atoms, so that radii of the cork balls must be considered in cutting the wire "bonds." The instrument in more detail is shown in the sketches of Figure 2. The base is a brass cylinder 3.5 in. in diameter and 3 in. high; it is hollowed out to a wall and top thickness of in. The height and massiveness are needed for easier manipulation and stability of the instrument. Fastened t o the base by screws is the angular scale (Figure 2A) for rotation abont the vertical axis. Figure 2B shows the angular scale for rotation about the horizontal axis. This scale is fastened to a circular plate which fits over the plate of Figure 2A but is not fastened to it. I t is held in position by the base (Figure 2C) for the ball holder. This base is fastened by screws t o the scale plate of Figure 2A, but is not fastened t o the circular plate of Figure 2B, which leaves this plate free to rotate with respect t o the sample base and the instrument base. The ball holder (Figure 2 0 ) fits into the base 2C and is held stationary by a pin. The cork ball (Figure 2E) fits into the holder and is held in position by a vertical pin and three horizontal pins. Several ball holders may he made to accommodate different sized balls. The drill is shown in Figure 2B, attached so that
it may be moved along the scale. With this arrangement the drill can be rotated about the vertical axis by motion of the entire assembly shown in Figure 2B. Rotation ahout the horizontal axis is achieved by motion of the drill along the scale to which it is attached. During these motions the ball remains stationary with respect to the base of the instrument. Thumb screws we provided for locking both the horizontal and rertical angles. CALCULATION OF ANGLES
Two angles are needed in order tolocate each bond position on the cork balls: an angle a, the rotation about the vertical axis, and 6, the rotation about the horizontal axis, each measured from a chosen zero on the cork balls. These can be determined as follon-s. Let us assume that the positions of all atoms are known with respect t o a rectangular coordinate system, where the unit of distance is the same along the three axes, usually one A. This information will be known or easily calculated for the atomic arrangement studied. Now let the cork ball zero be related to this coordinate system as shown in Figure 3. If xoyozorefer to the atom under consideration, and a bond to, atom xyz is being located, then the angles mill be given by the following equations:
- YO tan a = Y2
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20
aud the bond length I mill he: 1 =
CORK BALL
d(/(3. - zo)=+ (Y - yo)t + ( z - zd2
I t is well t o calculate and list systematically all angles and bond lengths needed for the arrangement before starting the construction. Figure 4 shows models made with this instrument of the four different coordination figures in the alphamanganese structure. ACKNOWLEDGMENT
The authors wish to thank Dr. J. S. Kasper for critical reading of this paper.
