Symposium on Teaching Crystallogaphy
Teaching Crystallography to Noncrystallographers Jemy P. Glusker The Institute for Cancer Research, The Fox Chase Cancer Center, Philadelphia, PA 19111 Through the ages the study of crystals has been a delight. The lovely colors, well-developed faces, and artistic forms displayed by crystals of many naturally occurring minerals havecaused them to be prized as jewelry and art objects. The early 17th century scientists who were interested in minerals noted a constanm of aneles between the crvstal faces of the same chemiral, r&ardlek of the differing kzes of the crystals (I). This led to the idea of a regularly repeating "building block" that made up, like bricks in a thick wall, a threedimensional array that could form sharp flat faces with orientations dependent on the shape of the unit cell ( 2 ) .This work wasdone at about the time that Dalton, fromstudiesof combining weight8 of compounds, derived his atomic theory of the smallest components in molecules. By analogy crystallographers were trying to find the smallest component in crystals. While the atoms, ions, and electrons that make up the unit cell are really the smallest components of crystals, the concept of a building block was significant in our understandine of the internal reeularitv of a crvstal. The unit cell is an imaginary solid figure drawn around molecules in a crystal to indicate a repeating unit; i t was this important idea that led von Laue to realize in 1912 (3) that a crystal, with its internal regularity of the order of cm (= 1A), could be used to diffract X-rays. The experiment was a success and the concepts were extended by W. L. Bragg who showed that from the X-ray diffraction intensities one could derive the arrangement of atoms in the unit cell (4). Since then the methodhas blossomed and the atomic structures of tens of thousands of compounds have been determined. Examples include diamond (5), sodium chloride (41, the boron hydrides (6).penicillin (7),vitamin BIZ@),lysozyme (9),and the rold virus (101. Diaerams in chemistrv and biochemistrv texts derive mainly from this method of &udure analysis: How can one teach noncrvstallomanhers the methods that X-ray crystallographers use to determine molecular structure? Since i t is quite a task to teach crystallography to would-be crystallographers, it is increasingly hard to keep the attention of noncwstallographers. The important thing is to find out what the majo; interests of the-audience are and to expand from there. My experience has been in teaching biologists and would-be medical students a t the Institute for Cancer Research and the University of Penusylvaniaand talkine to visitors (includine hieh school students and nonscientks) who visit this 1;stikte. Biologists know a lot about the theory and use of the microscope; if the diffraction experiment can be related to microscopy, then they will rapidly follow what is explained to them. In the case of high school students and noncrystallographers I have found that visual descriptions of the method and results work best. I have attempted to address the requirements of each of these groups in the lectures on crystals, diffraction, and structure analysis that I willdescribe. I t is best not to try to teach them too many things a t once, until one is certain that the previously described concepts. are understood. With younger school students one concept is enough for one visit. First, the audience needs to obtain an understanding of what a crystal is, and I have found it useful to have some crystals available to demonstrate and also to show a setup for growing crystals. Many of those present have subse~~~~~
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quently reported that they then went home to try this for themselves. Kits are available.' It is most importani to stress that the regularity of atomicarrangement within the crystal is fundamental to the definition of a crvstal. The analoev of building blocks is helpful. I t is also ill&trative to meiiion that elass eohlets or other obiects. . . commonlv descrihed as "crystal", are not truly crystalline; a description of the random nature of the internal structure of elass can iolt manv a noucrystallographer. Second, one of the-best illukrationsof a crystal is found in a published electron micrograph (11)of crystalline bacteriophage lying in regular ariays, but not completely ordered. Occasionally one phage is packed the wrong way round or out of line; thisis probably how acrystal, composed of molecules or ions in place of bacteriophwe - in these photographs, looks. In stressing the importance of regularity and the development of flat faces as the crvstal is built un. the teacher is provided with an opportunity to talk ab&t isomorphism. One of the most interesting experiments that a high school student can try is togrow a dark purple octahedral crystal of chrome alum. If this n u r ~ l ecrvstal is then suspended in a saturated solution of botash aium (which is coiorless), the crystal will continue to grow forming a transparent exterior with a deep purple center. The recipes for this and many other good high school experiments are contained in the book by Holden and Singer (12). An example of such a crystal can he shown to the audience, who then may be urged to try it after they have grown crystals of rock salt and rock candy (table sugar). Havine exnlaiued about crvstals. one then needs to describe dGfrffraetion. This makes most people gulp because thev think i t is a rather abstract idea that thev mav or mav n o t have encountered in physics textbooks; in f a k it is visually observable phenomenon, encountered in everyday life, and therefore it is important to demonstrate it. 1have used sieves of the type used for separating powders;2 the finest mesh sieves give the best diffraction patterns. A point source of light can be made with an adjustable diaphragm in front of a fiber optic microscope light.3 If the light source is viewed through the sieve, a diffraction pattern is seen. Furthermore it is worth ~ o i u t i n eout to the viewer that the diffracted beams are split intoied andblue; this concept can be expanded to explain wavelength effects since blue light has a shorter wavelength. For young children I use a small piece of fine fabric (pretested to be sure that i t diffracts) and make a small holder for the fabric by stapling it between two pieces of cardboard with a window in them: I write the word 'diffraction" on the cardboard and let them take it away
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' Crystal growing kits are available fromEdmund ScientificCompa-
ny. 101 E. Gloucester Pike. Barrington, NJ 08007. Sieves. I use U S . standard testing sieves. A.S.T.M.E.-11 specifi-
cation. Fine sieve: No. 400, opening 0.0015 in.. Tyler equivalent 400 mesh. Coarse sieve: No. 100, opening 0.0059 in., Tyler equivalent 100 mesh. Available fmm Thomas Scientific. P.O. Box 99. Swedesboro. ~,Nd 08085. Light source. ReicherNung Model 653 microlamp. Available fromThomas Scientific(see footnote 2). ~~
with them. Thev can then look a t all kinds of distant lieht objects and learn one thing that day-what diffraction is: While it is important to stress, after describing the theory of constructive interference that is the basis of diffraction, that regularity is what gives a visible diffraction pattern, i t must also be pointed out that any object can individually scatter radiation and have a diffraction pattern (13.14): the circular "rainbow" seen on low clouds when the sun is diffracted by an airplane provides a good example. The important thing about regularity is that i t reinforces the diffraction effects. Sieves provide a practical example for teaching Dumoses. Two different sieves with different meshes idis&es between wires) will give different diffraction patterns; the finer sieve will give the wider spacing of spots, and the coarser sieve will show anarrower spacing between spots. If the sieve is sufficiently coarse, the diffraction pattern will disappear. If you cannot get a sieve, a piece of fabric will do. A laser is a better light source than the one described above, but I have only rarely used a laser since i t is hard on the audience if not used very carefully! The audience can also be told that they can see diffraction by looking a t a distant street light through a fine gauze drape, such as a hotel curtain, or through an umbrella. The principle to he stressed is that the finer diffracting grid gives a coarser diffraction pattern. These concepts lead up to the idea that if you decrease the scale of the experiment hy many orders of magnitude and go from a sieve to a crystal and from visible light to X-rays with a much shorter wavelength, you still have essentially the same experiment. This is now the X-ray diffraction experiment. The crystal, because of its internal regularity, gives a diffraction pattern that is measurable on photographic film in a matter of minutes; the diffraction pattern of a single molecule would he too weak to be observable under nractical experimental conditions. I t is possible to grind ihe welldeveloped faces of a crvstal so that thev are destroved. but still the remaining ch"nk of crystal diffracts beciusk its internal arrangement is not affected and because the phenomenon that reveals that internal arrangement is diffraction; the faces developed because the internal arrangement was regular and should be considered a result rather than a cause of crystallinity. So far 1 h a v e only explained how you get a diffraction pattern. But, as W. L. Bragg noted in 1913 (4). the diffraction pattern contains information on the detailed structure within the crystal. The optical diffraction pattern should, in theory, tell you what the sieve looks like, and the X-ray diffraction pattern of a crystal should, in theory, tell you what the atomic arrangement is in that crystal. The necessary information is contained in the variation in the intensities of the diffracted beams. There are two features of a good diffraction pattern that are immediatelv obvious. One is the reeular snacine of dif. fraction spots (the nature of this regularky depending on the geometry of the measurement of the ~hotomanh). - . Measurei e n t o f thespacings, together with in?ormationon the wavelength of the radiation used and the geometry of the hot orraphy will give the unit cell dimensions (usu& from two or more photographs to get three-dimensional data). The second feature that isnoticeableis that thesoots havedifferent intensities. The measurement and analysis of these is the major task of the X-ray crystallographer and will give information on the arrangement of atoms in the structure, expressed in coordinates of fractions of unit cell edges. This is the time to show some diffraction patterns, for example, of a simple salt, a larger molecule, and a protein. For an elementary audience you can leave i t at that. The more serious students will want to know how tbis is done. Here goes. I start with DNA because its diffraction pattern-is simple to explain. It is best to have a model on hand, but if this is not possible a diagram can be used. DNA is a helical structure
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(15), and its model looks like that of a spiral staircase. I then show the diffraction pattern of DNA and remark that this is the type of photograph that Rosalind Franklin took (16) and that it can be explained in terms of the regularity of theDNA model. Many have read The Double Helix (17) and know that, when Watson saw Rosalind Franklin's photographs, he knew that DNA was helical. How he knew this will interest the audience. The bases in B-DNA lie perpendicular to the long helical axis of DNA with a spacing of 3.5 A. The large blurs at the top and bottom of the DNA diffraction pattern represent the diffraction from this reeular arraneement of bases viewed end-on. The helices themselves alsopresent a regular arrangement, and tbis is the reason that the "cross" is found in the middle of the diffraction photograph. The spacing between the rows of phosphate groups in the helical folds of DNA (represented by the "cross" in the middle of the diffraction photograph) is larger than that between the bases (represented by the large blurs a t the top and bottom of the photograph); hence the spots in the "cross" of the diffraction pattern are closer (see ref 13). The brilliance of the scientists who had sufficient imagination to be able to interpret this diffraction pattern must be stressed. A comparison of the diffraction patterns of two simple salts will then clarifv some concepts for the audience. The intensities of diffraction of sodium chloride and potassium chloride differ ( 4 ) , although the atomic arraneement is similar. The potassium ion is larger than the s&um ion, and hence the unit cell of potassium chloride is larger but ekes smaller spacings on the diffrartion pattern. ?'Ke diffracting power of an atom depends on its atomic number and, since K' and CI- contain the same number of electrons. for diffracted beams for which their scattering is out of phase there is almost no intensitv; the intensitv is strone when thev scatter in phase. suchweak intensiiies are not seen in t h l sodium chloride diffraction pattern where the difference in atomic numbers is larger. Then a comparison of the diffraction patterns of, for example, sodium chloride and myoglohin (13, 18), a protein like hemoglobin, is helpful. Here the crystallinity is good, and single spots rather than blurs are obtained on the diffraction photographs. However, the spacing in sodium chloride is much, much smaller than that in myoglobin. As a result there are very few spots on the sodium chloride diffraction patternand many on the myoglobindiffraction pattern. Finally it is worth noting that the diffraction pattern is really just a samplinn of the diffraction uattern of a sinele mol&de and that t b i diffraction pattern of crystalline &gonucleotides, which are like ~ o r t i o n sof DNA. contains many of the features of the DNA diffraction pattern when the crystal is mounted in the correct orientation. The measurement of diffraction patterns, that is, the overall set of diffracted beams, is fairly easy to describe if a model is built. A crystal is mounted on a goniometer head, a collimator is stuck into Styrofoam to represent the X-ray source, and a precession photograph is placed on the other side of the crystal; this model has proved very useful for this purpose. I t helps the audience if one explains that the direct beam must be blocked out toavoid fogging the film (as in the problem of trying to photorna~hthe corona round the sun). well-definedspntsappeararound the position of the diredt beam. There are a variety of different cameras that can be used to record the intensities on film. In practice the photographs that are simplest to interpret have complicated mechanical linkages. Nowadays it is more common, since the advent of good computing power, to use computer-driven instruments that move the crystal to the computed orienmtion for diffraction and move the detector to the computed is inifiallv position to interce~tthe diffracted heam. All that ~needed are a few photographs in order for the crystallographer to understand the orientation of the crystal and the spacings of the diffraction spots. The diffraction data are ~
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13. Glwker, J.P.;Truehlood,K.N. C1ystalStructureAnolysis.APrimer,2nded.:Oxlord University: New York. Oxford. 1985. 11. Stout, 0. H.: Jensen. L. H. X-rny Struelure Defermimtion. A Prortkol Guide;
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of D N A by Jama8 D. ~ o f a o nAtheneum: i New ~ o r k1968. ,
ty: ~ r i ~ & n ,1949; ~ ~ 3 1 ~ 6 7 . 8. Hodgkin,D.C.;Pickwmlh, J.; Robertson, J. H.:Truehlmd, K.N..Plosen.R.J.:White, J. G. Nature (London) 1956,176.32M28. 9. Phillipc D.C. Sei. Am. 1964 215.1%90. 10. Amold,E.;Vriend.G.: Luo. M.;Griffith. J.P.:Kamer,G.;Erickson, J.W.: J 0 h m n . J . E.:Rossmann, M. G. AcLo Cryst. 1987.A43.346361. 11. Swyer, J. F.; Khairallah, L. H. J. Mol. R i d 1973: 76.41M11. 12. Halden, A,; Singer, P. Cryat& ond Crystal Orouing; Anchor: Doubleday: Oarden City, NY, 19M).
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18. Kendrew, J.C.;Dickernon,R.E.:Strandbew,B.E.;Hsn,R.G.;Davin,D.R.;Phillips, 0. C.; Shore. V. C. Nofum (London) 1960,185,422427. 19. Wa8er.J. J. Chem. Educ. 1968.45.446451. 20. Clarke, M.Noture (London) I985.317.663. 21. Judson. H. F.The Eighth Day o/Craafion; Simon and Sehuater: New York. 1919. 22. Karle, J.; Hauptman, H.Acto CryrL 1950,3,181-187. l in Chemirlry ondBiology; GlusLsr, J. P., Eds.; Hutehin23. S f r u ~ f v m Crystdogrophy son &Ross: Stmudshun, PA, 1981; pp 2349.
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