F. b i s s e
ond P. R. Sundararaian Universit; d e Montr6ol Montreal, Canada
A Practical Method of Simulating X-Ray Diffraction
Two short notes'J have recently appeared in this Journal concerning the visualization of the diffraction phe-
nomenon. This prompted us to report on the diffraction experiments oerformed at the Universitv of Montreal, bv third year &dents in chemistry as part of a course oh X-ray diffraction and structure determination. Durinr two 3-hour laboratorv the basic orinci- ~eriods. . ple of direct and reciprocal lattices, as well as the relation between a crvstal structure and its diffracted nattem. are taught with the aid of an optical diffractometer: In such a setup, the beam of X-rays is simulated by a monochromatic beam of visible light while the crystal is replaced by an optical mask. As such, this is not a new anoroach.3 However. the use of (1) a laser as the monochromatic light souree and (2) photographically prepared masks enable us to ~ r o d u c ea strong diffraction pattern as large as 20 cm. This makes the experiment easily observable by a class of 10-15 students a t the same time. The diffraction pattern can also he photographed on a Polaroid film, so that students can have a permanent record of the phenomenon.
Figure 1. The optical diffractometer setup (distances in m m ) . L, diverging lens. focal distance 50 mm. L, converging lens, focal distance 250 mm. M mask.
Preparation of Masks and the Setup
The optical masks are negatives made by photographic X 11 in. or reduction of molecular patterns drawn on larger sheets of paper to a 2 X 3 mm rectangular domain. The atoms are represented by disks 2-3 mm in diameter and the distances between atoms are of the order of 8-12 mm. The bonds between atoms are not drawn. To ensure more rerularitv in an arrav of identical molecules, it is most coivenieht to make template of the molecule by drilling holes in a piece of Plexirlas at the required atomic positions. The extremely fine grain Kodak High Contrast Film d5069 is used. It is advisable to take two or three pictures of the same pattern with slightly different settings in order to compensate for possible irregularities in the treatment of the film. The quality of the optical masks depends on the care taken in making the original drawing and also on the processing of the photographic film. The best masks are selected by examination under a low-power microscope or a magnifying lens. The area of the negative around the 2 X 3 mm domain is covered with silver tape (Scotch Polyester Film Tape No. 850, silver) in order to block parasite light. The negative is then mounted in a standard 2 X 2 in. slide frame. A set of masks representine a wide varietv of lattices, molecules. and their arrangements is thus &pared and' becomes the "library of masks" accessible to all the students. The optical diffractometer consists of an optical bench supporting a 5 mW He-Ne gas laser wavelength X = 6328 A (Spectra Physics Model 120) (Fig. 1). An advantage in using the laser is that, apart from the intense and clean 'Morrison. J. D.. a n d Driscoll. J . A,. J . CHEM. EDUC.. 49. 558 (1972). ZGam, P.D., J. CHEM. EDUC., 50,294 (1973). 3Lioson. , . H... a n d Tavlar. ~~, . C. A.. "Fourier Transforms and X - r a v r h l t r a r r l m . " Hclls and Suns L t d . , London. 19%. Tmlor. C. A., an4 l.ipr,n. I{.. " O p ~ t c a 'l'mnsfurmi. l The~rI ' r e p n m t i m and Applicatlun to X-Kn, 1)iftrsrum Pmhlems." Hclls ilnd Soni I.td.. ~
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London, 1964. 414 / Journal of Chemical Education
Figure 2. Optical masks (enlarged 10 times) and their respective diffraction patterns. Their relative orentations are conseived, [ a ) oblique lattice l b l the diffraction of an helix 8s shown here: the helix is replaced by its projection as a sine curve ( c ) one molecule of paradimethylbenzene (the hydrogen atoms are omitted) Id) a rectangular array of paradimethylbenzene molecules.
patterns obtained, the radiation is less hazardous, since commercial lasers with power as low as 1 mW are available. A 2 X 2 in. slide holder used to support the masks is placed in front of the laser. The diffracted pattern can be observed on a screen 1-3 m away from the mask. The Experiments
In the first lab period, a standard grating of known spacing is used to determine the wavelength of the laser light, by measurement of the distance between the diffracted spots and the distance of the screen from the grating. At the same time the students observe that the diffraction pattern due to a set of parallel lines (the grating) is a row of points equally spaced with a periodicity in a direction that is parallel to that of the object (the grating periodicity). Conversely, a row of points would diffract into a set of parallel lines. To demonstrate the reciprocal relationship between distances on the object (the mask) and on the diffracted pattern, each pair of students employs a mask of a regular row of points, each with a different periodicitv. With a microscqw they measure the distance k~erw~en nmsrcu. tiw spots on the mask, then place the mask in the opticnl ditiraztometer and measure the distance hetween the dtlfracted lines. When all the groups of students have com-
pleted their observations, they compare results, by plotting the smallest distance of the diffracted pattern versus the measured distance on the mask, in each case. The expected hyperbolic or reciprocal relationship Cv = k l x ) , is observed. It is now easy to introduce the students to the study of the diffraction patterns of different types of lattices. They compare the relative orientations and metric measurements of the direct (mask) and reciprocal (diffracted) lattices (Fig. 2a). In the second lab period, to improve the quality of the
diffracted patterns it is preferable to insert two lenses, as shown in Figure 1. So far the students have understood the diffraction caused by regular arrays of points. From there they proceed to the study of the diffraction pattern due to a single molecule (Fig. 2c) and then, how the periodical distribution of these molecules in the crystal affects the diffraction pattern (Fig. 2d). Later the students observe Friedel's law, the symmetry properties of the planar lattices, and the effect of disorder and of thermal motion on the diffraction pattern.
Volume 52, Number 6. June 1975 / 415
