Svmtwsium on Teachim Crystallography
Introducing Chemists to X-Ray Structure Determination John H. Enemark University of Arizona, Tucson, AZ 85721 X-ray structure determination plays a major role in modern chemical research. The determination of the structures of new compounds is an important aspect of research in svnthetic chemistrv. ..and a knowledee of molecular structure is the starting point for theoretical modeling of the electronic structures of molecules. For several vears we have offered a one-semester graduate course in "~&ctural Chemistry" to a broad spectrum of students who have had no previous exposure to X-ray crystallography. The ohjective is to provide a first-hand introduction to the use of X-ray structure determination in research. The course combines lectures and problem sets on the theory and practice of X-ray structuredetermination with an ongoing practical laboratory experience in which each student determines the structure of a 1summarizes the various features that real molecule. Fieure " are involved in this introductory course in X-ray structure determination.
dents are aware of all the kinds of symmetry operations for both point groups and space groups, then students can begin to learn how to use and understand the symmetry information tabulated for space groups in the International Tables for Crystall~graphy.~ What is a general position? What is a
Diffraction
Symmetry
The topics covered by lectures and problems are set out in Table 1. The recent text by Ladd and Palmer' provides a good blend of theory and practical examples, which is well suited for this type of course. Symmetry is a key concept in crystallography and a new concept for many of the students in the class. Emphasis is placed on recognizing symmetry in physical objects rather than on deriving mathematical relationships. For point symmetry both the Hermann-Mauguin and Schhflies notations are used. A collection of threedimensionalmodels (Fig. 2) is especially helpful for illustrating point groups and for problem sets. Models of several point groups can be prepared by selectivity coloring the faces of octahedra or tetrahedra (Fig. 2). In addition, each student is asked to make a three-dimensional model of a t least one point aroup. This is a challenaina exercise for the student and is ;useful way of augmen>he collection of point-group models for study bv future classes. Stereoviews also hglP visualize point groips?,z Once the concept of point symmetry is appreciated, translational symmetry and glide planes can be introduced in one dimension using a previous article in the Journal with examples from Hungarian need l e w o ~ kTwo-dimensional .~ plane symmetry is conveniently illustrated by Escher drawings' (Fig. 3) and wallpaper samples with repeating patterns. It is difficult for most people to visualize three-dimensional space group symmetry, even with the aid of models of crystal structures or with stereo packing diagrams. However, the action of a screw axis is readily understood. Once stuPresented at the Symposium on Teaching Crystallography, American Crystallographic Association Meeting. March 17. 1987, Austin, Texas. Ladd, M. F. C.: Palmer, R. A. Structure Determination by X-ray Crystallography. 2nd ed.; Plenum: New York, 1985. Bernal. I.: Hamilton. W. C.;Ricci. J. S. Symmetry.W. H. Freeman: San Francisco, 1972. Hargittai, I.: Gyorgyi, L. J. Chem. Educ. 1984, 61, 1033. Macaillavrv. C. H. Svmmeirv Asoects of M. C. Escher's Perlw'ic ~rawinog:A. disthoek'; ~itaevirsAaatschaooiiNV: Utrecht. 1965. ~ a T., k Ed. 1nternationa;~ables for Crysiaiograph~~eidki:Boston, 1983, Vol. A.
Figure MUW
determination of a structure by a student in this intraductary involves several different activities. 1. T b
Table 1. Lectures and Problems Symmetry Recipmcal space Diffraction,space groups 4. Data reduction 5. Patterson functions 6. Direct Methds 7. Least-squares refinement 8. Distances, angles. errors 1. 2. 3.
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Figure 2. A collection of some of the objects prepared by students to illustrate point group symmetry. Volume 65
Number 6 June 1988
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soecial Dosition? What are systematic absences? What can one say'ahout a molecular structure if only the space group and number of molecules per cell are known? The students are now ready to learn about Miller indices, cell constants, and the fundamentals of X-ray diffraction. Dlffractlon from Real Crystals Most students are familiar with Bragg's law but not with the consequences of extending diffraction to a complex crystal, which may have several thousand observable reflections. This is the time to introduce reciprocal space, that is, each Braez "" reflection is reoresented bv a vector whose length is 1/ A precessionphotodthkl). What sort of array is erauhof adiffraction oattern froma crystal (Fig. 4 ) showsan indistorted view of the reciprocal lattice and ;isually illustrates three very important points. (1) There is a regular spacing of the lattice points; (2) the intensities of the individual points are not identical; and (3) the pattern of the intensikes may he symmetrical relative to the origin. The regular spacing leads to the unit cell parameters; the variation:~-of ~- the ~-~~intensities contain the information needed to determine the positions of individual atoms of the structure; the point symmetry of the intensity array determines the Laue group and lattice type. Regardless of the kind of exnerimental anoaratus used. one of the first tasks of a .. crystalstructure investigation is todetermine the point symmetrv of the intensitv arrav (the Laue . proup) . and the unit cell parameters. At the same time that the concepts of symmetry and reciprocal space are being introduced in lecture, each student is carrying out diffraction experiments on real crystals ~
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Table 2.
Dlllractlon Experiments
Mount crystal Dlffractometerexperiments -optical centering -rotation photo -centering reflections/w scans -reduced cell -oscillation photol~ymmetry -sample datalspace group Ob~ewerle~perimenter method Data Collection (selected ctystalsl
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Figure 3. An example of plane group symmetry from Escher's drawings. Copyright M. C. Escher Heirs c/o Cordon Art-Baarn-Holland.
492
Journal of Chemical Education
in the X-ray laboratory. These experiments are summarized in Table 2. Each student learns how to select a crvstal of appropriate size, how to examine its optical quality using the stereo and polarizing microscopes, and how to mount it appropriatel;on aglasi fiber withglue. Oncea crystal has been successfullv mounted, the student transfers it to the fourcircle diffractometer and begins the preliminary experiments involved in an X-ray structure investigation of any crystal. These include optical centering of the crystal, recording a rotation photograph to obtain a set of sample reflections, centering those reflections, obtaining a preliminary reduced cell, verifying this reduced cell by means of an oscillation photo, and checking the diffraction quality of the crystal by omega scans on several reflections. Finally, a small sample data set is collected over several hours in order to determine the space group from systematic absences. These nreliminarv diffractometer experiments are done by the odserver/experimenter method & which two people are involved in each of the preliminary experiments. One person is the "experimenter" who actually mounts the crystal and does the manipulations on the diffractometer. The "observer" asks questions, takes notes, and reminds the experimenter of precautions. Once the experiment is complete, the two people change roles and proceed through these preliminary experiments again with a different crystal. In this manner two different crystals are examined by the two people. Both learn more, less equipment is broken, and each exneriment takes less time. Tvoicallv two novices can com.. plete the preliminary diffractometer experiments on a crystal in one afternoon with advice and assistance from a teaching assistant. Having done the preliminary X-ray experiments the student knows the cell parameters and probable space group(s) for his or her crystal. An independent measurement of the density will give the molecular weight. Combining this information with that available in the appropriate space group tables may tell something about molecular symmetry. The number of data that will need to be collected to solve the structure can also he calculated. In short. about one dav's effort provides a lot of information about a compound and enables one to decide if a comolete three-dimensional X-ray structure determination shokd be done on this materiai.
Figure 4. Precession photograph of the diffraction panern from a real crystal. the regular spacing between points, which can be used todetermine Note: (I) unit cell parameters: (2) the intensities of the individual reflections are not identical: (3) the panern of the array of intensities is symmetrical. In this instance the pattern shows mm-C2,symmetry.
Euery synthetic chemist should be encouraged to acquire these important skills of preliminary X-ray structure analysis. Structure Determlnation Several of the crystals from the preliminaw experiments are selected for complete data codection and sihsequent solution of the structure. The number of crystals selected depends upon the available diffractometer time, the chemical interest in the structures, and anticipated difficulty in solvine the structures. While data are heine collected the lectur& begin to introduce the factors involvcd in processing diffraction data and the methods for solvine X-rav structures. In the laboratory the practical use of &e x - r i y computing system begins. Students learn about file structures, file manipulation, "help" commands, and sending and receiving electronic mail. Problem sets check their ability to work on the computer. After about six weeks have passed in this 15-week course each student has an X-ray data set deposited in his or her computer file area. Students whose crystal was acceptable for data collection receive their newly collected data. Other students are given raw X-ray data archived from structures that have been previously solved in the laboratory. Each student has a different structure to solve. Students are free to solve the structures hv whatever method is appropriate. Usually this means direct methods or the heaw-atnm Patterson method. During this oeriod the lectures focus on methods of solving struc&res, a i d a problem set is aiven to illustrate the single-heaw-atom Patterson method. Once a o ~ r o a c h e sto solvina the structures are underwav the class bperates like a research group, and frequent interchange of information is encouraged and expected. Students give short presentations in class on the progress they are making oron problems they are havingsohinp, their individual structures. Lecture material moves on todescrihe completing structures by least-squares refinement, errors in bond lengths and angles, thermal motion, disorder, and absolute configuration. The final ohase of structure determination is a written report that includes all tables, an ORTEP drawing and other information required in a short paper describina a crystal structure determination, These reports often f o r k the basis
for published manuscripts and chapters of MS and PhD theses. X-ray structure determination is hecomine increasinelv automited and most compound* encounteredcan be sol;ed within the one-semester time oeriod allowed for this course. However, occasionally mo1ec;les defy structure determination for one reason or another. These cases are not reearded asdisasters but aschallenges to the particularstuden
