leneth of the edge of the unit cubic cell from the densitv and thetype of cubic structure. Then it determines interplanar s~acinasdhaf,where h, k, and I are the Miller indices. Angles bktween the planes and the diffracted X-ray beams are Ealculated from Bragg's law, nA = 2d,, sin 0 where twicallv the value of X is 154.18 Dm, the weighted average-&avelLngthof the copper Kol radiation doublets. Distances for the lines in the forward and backward reflection parts of the film are obtained by assuming the value of the effective radius of the film in the camera to he 57.23 mm. For the sake of simplicity no attempt was made to make the spectrum more realistic by curving the lines around the collimator hole and beam stop. However, we have used the wavelengths of the doublets Karl = 154.056 pm and Ka2 = 154.439 om to orovide well-resolved doublets in the back reflection region. In a cubic lattice of unit cell dimension a. the interolanar distance is d,, = a/(h2+ k2 + P)ln
(2)
and the angles at which the (hkl) planes diffract are given by
+ +
+
sin28= (X2/402)(h2 + k2 1')
(3)
where h2 k2 12mustbe an integer. Because the sum of the sauares of the Miller indices cannot have the values 7.15.23. . . . 28, 31,. .. , the corresponding lines will be missing in the spectrum of a substance crvstallizing in a cubic lattice. The presence or absence of all other lines is given by the structure factor F, which is obtained by summing the atomic scattering factors fi over all the atoms in a unit cell. Line intensities are given mainly by IFI2 (17).The structure factor can be expressed in terms of the Miller indices and coordinates (xi,
For a simple (primitive) cubic structure the atoms are located a t (O,O, 01, (a, 0, O), ... ,(a, 0, a), . ,(a, a, a); therefore,
..
+
+ ...+ ewchtr)+ . ..+ e2nchtktn)
Fhkl = 1/8f,(l ezSih
(5)
The value of the structure factor can be easily determined by taking into consideration that enri= cos nn i sin n?r.. and. ~~, because h, k, and 1are integers, sines of multiples of n are zero, while the cosines are equal to one. In a face-centered cubic lattice the atoms are located a t (O,O,O), (a, 0, O), . . . , (aI2, a, O), .. . ,(a, a, a!, and it can be shown that diffraction will be observed only if h, k, and 1 are either all even or all odd, making !PI2> 0. A body-centered cubic unit cell has atoms at (O,O, O), (a, 0, a), . . .,(al2, a12, a/2), and absences will be observed whenever the sum of h k 1is odd. In the program, values for the allowed sums of the squares of the Miller indices are contained in DATA statements for each cuhic lattice -.-. ~-~~~ ~ - - ~ Figure 4 shows the original film and a printout of the diffraction pattern of aluminum as obtained with an Olym-
+
+ +
~
oia NP dot-matrix orinter. This ~rinter.as most dot-matrix printers, allows a p;ogrammable n1216-in. forward line feed, which oroduces a minimum separation of 0.12 mm for the diffraction lines. Of course the program is not restricted to real substances, and any combination of formula weight, density, and lattice type providing an interplanar distance greater than 77.03 pm will produce a simulated X-ray powder diffraction pattern of the hypothetical substance. A listing of the program and accompanying instructions are available from the authors. Requests should include a stamped, self-addressed envelope.
Multiple-choice Self-lest James F. Nugent Salve Regina College Newport. Ri02840
Students taking beginning chemistry courses are often unaware of their lack of basic knowledge until it shows up in their first examination. The goal of this computer appication is to help chemistry students tent themselves and also be instructed. Specifically, I wanted to help students in a one-semester course in oreanic chemistrv to test themselves in the areas of reactions and nomenclature. I wrote a file called ALKENE.BAS in Advanced IBM Basic on an IBM PC with a Color Graphics Adapter and color monitor. The student who runs the file sees an alkene reaction question where the starting material and reaction conditions are given, but the product is a question mark. On the same screen the student sees five possible answers labelled "A" through "E". The program congratulates students who choose the correct answer and ins&cts them to go on to the next question. Students who choose an incorrect answer are given a brief explanation of why that specificanswer is incorrect and told to try again. After writine one or two other files on other oreanic functional groups, i realized that there were many pr&ramming steps that were indeoendent of the chemical subiect matter. I t was only necessaiy to delete all specific textual lines to obtain a file called SKELETON.BAS. As new text was added, it became "flesh and blood" on the skeleton and led to the creation of additional files. In this wav, 12 basic files were written on organic reactions and nomenclature. Each file contained from four to 10multiole-choice questions. The files were put together with a menu program so that the student could move between files at will. The SKELETON.BAS file can be used to generate multiple-choice questions in any field. Remark (REM) statements are placed at the Basic line numbers where text should be placed. The instructor can choose wrong answers that illustrate common student misconceptions in the specific subject areas. Then, these misconceptions can be cleared up by the wrong answer explanation screens. I modified SKELETON.RAS to allow a maximum of 25 questions per file and to permit the letters of the correct answers to be scrambled for-each new file. I have also included a blank menu programand adocumenration file saved in ASCII text called SKELWON.DOC to explain fully how to make selftest files from SKELETON.BAS. Copies of all the tiles t'or the IRM PC can be obtained from Project SERAI'H1.M. Literature Clted 1. Bww,
F. Chnin Struecur. ond
Cmfarmotwn of M~eramolsculas;Academic: New
York, 1982.
2. Odian. 0.P~incipleaof Polymorirolion, md ed.; Wiley: New York, 1981:h m p p . P.: Mmrill, E. W . Polymer Synfhe&: HWhigk Wepf: Heidelbeq, 1986.
3. Wehdi, F. W.; WirMin, T Intrrprefolion of Corbon-I3 NMR Spectra: Heyden:
F l g m 4. (A) The X-ray diffractionpowder spechum computer-simulated spsmum.
of aluminum: (6) the
.....
D!.n0.,d"hb ""u.F... ", ,O"R
C. Ed. NMR ond Moemmolecules; ACS Symp. Series 247: American Chemical Soeiaty: Washington, DC,.,l984.
I . Randall. J.
Volume 66 Number 8 August 1989
649
