tronzetry Group Bull., S o . 9, 207
(1956). Lundquist, R., Markle, G. E., Boltz, D. F., A s . 4 ~ . CHE?d. 27, 1731 (1955). McKeehan, C. JV., Graham, I. C., J . Opt. SOC.Ani. 46, 141 (1956). RIacNevin, W. AI., Kriege, 0. H., ASAL. CHEM.28, 16 (1956). Rfalmstadt, H. ST., Roberts, C. B., Zbid., 28, 1408 (1956). Matsen, F. A,, in “Chemical Applications of Spectroscopy,” Vol. 1 X of “Technique of Organic Chemistry,” Chap. 5, Part 2, pp. 629706, W. West, ed., Interscience, New Tork, 1056. Maurice, &I. J., RIulder, J. L., Afikrochim. Acta 1957, 661. Meloche, V. W.,Martin, R. L., ANAL.CHEX.28, 1671 (1956). blichelsen, 0. B., Zbid., 29, 60 (1957). Miles. J. IT7.. Enelis. D. T.. Zbid.. 27,‘1996 (1955): ‘ Miller, D. J., J . Assoc. Ojic. Agr. Chemists 39, 892 (1956). Miller, J. W.,DeFord, D. D., AXAL. CHCM.29, 475 (1957). RIitchell, J., Jr., Zbid., 28, KO.1, 33A (1056). hlitchell, J., Jr., Kolthoff, I. M., Proskauer, E. S., Weissberger, A., eds., “Organic Analysis,” Vol. 111, Interscience, Nen- Tork, 1956. Rlohler, E. F., Jacob, L. K.,ANAL. CHE~I. 29. 1369 (1957).
AsAL. CHEX.‘29, 756 (1957). O’Connor, R. T., J . Am. Oil Chentists SOC.32, 616 (1955). O’Hara, F. J., Keely, W.&I.,Fleming, H. W.,AKAL.CHEAI.28, 466 (1956). Oster, G., Pollister, A. W.,eds., “Optical Techniques,” 1701. I of “Physical Techniques in Biological Research,” Chaps. 3 & 4, Academic Press, New Tork, 1955.
REVIEW OF FUNDAMENTAL DEVELOPMENTS IN ANALYSIS
(92) Page, J. E., Analyst 81, 185 (1956). (93) Paige, B. E., Elliott, &I. C., Rein, J. E., ANAL.CHEM. 29, 1029 (1957). (94) Pefnslet J. P., Rev. Sei. Znstr. 28, 274 (1957). (95) Pflaum, R. T., Howick, L. C., AN\.~L. CHEX.28, 1542 (1956). (96) Phillips, PIT. A., Hinkel, R. D., J . Agr. Food Chem. 5 , 379 (1957). 197) Podall. H. E., AXAL.CHEM.29,1423 (1957). ‘ Polgar, A., Jungnickel, J. L., “Organic Analysis,” Vol. 111, Chap. 4, pp. 203-386, J. hlitchell, Jr., others, eds., Interscience, New York, 1956. Prem, D., Duke J., Rubber World 113, 353 (1955). Prescott, B. E., Jaycox, E. K., A p p l . Spectroscopy 9, 147, 187 (1055); 10, 48, 110, 177, No. 4-15A (1956); 11, KO. 1-!24A, KO,211A, NO. 3-11.4 (1957). Price, W.C., Beaven, G. H., British Bull. Spectroscopy, No. 23, 99 (1957). (102) Reketti, K. A., ANAL.CHEW29, 869 (1957). (103) Robin, M., J . Chem. Educ. 33, 526 (1956). (104) Rosenbaum, E. J., ANAL.CHEU.29, No. 1, 44A (1957). (105) Sager, E. E., Byers, F. C., J . Research Aratl. Bur. Standards 58. 33 (1957). Schramm, &I., ASAL.CHEII. 28, 963 (1956). Scott, J. F., in “Optical Techniques,” Vol. I of “Physical Techniques in Biological Research,” Chap. 4, pp. 131-203, G. Oster and A. W.Pollister, eds., Academic Press, New York, 1955. Scott, W7. G., Taylor, R. J., Analyst 81, 117 (1956). Seeber, R. E., White, R. C., Ferber, K. H., A p p l . Spectroscopy 11, 113 (1957). Shore, T.i C., Katz, M., ASAL. CHEM. 28. 1399 . ~ - 11956). -- - ~ -,Shreve, 0. D., “Organic Analysis,” 1701. 111, Chap. 6, pp. 443-508, J. Mitchell, Jr., others, eds., Interscience, New York, 1956. ~~~~~
- I
\
(112) Silvermm, I,., Houk, W.,AKAL. CHE~V. 27, 1956 (1955). (113) Sniullin C. F., 1l7etheran, F. P., Ibid., 27, 1836 (1955). (114) Stansfield, J. R., Hilger J . 3, 3 f 19.56’1.
St&: ,f. B., Teranishi, R., Bailey, G. F., ANAL.CHEM.29,861 (1957). Strouts, C. R. N., Gilfallan, J. H. Wilscn, H. N., eds., “Analyticai Chentistry, The Working Tools,” Vol. 11, Chap. 20, pp. 620-36 Chap. 22, pp. 660-748, Osford Univ Press, London, 1955. Sundheim, B. R., Greenberg, J., Reu. Sci. Instr. 27, 703 (1956). Swann, Rf. H., Adams, M. L., Weil, D. J., ANAL.CHEM.28, 72 (195tl). Taylor, L. W.,Jones, L. C., Jr., Zbid., 28, 1706 (1956). Thompeon, H. W., J . Chenz. SOC. (London) 1955, 4501. Thornburg, W., Rev. Sci. Znstr. 27, 99 (1956). Timell, T. E., Glaudemans, C. P., Curs e, A. L., ANAL.CITE&l.28, 1916 (1956). Toren, P. E., Heinrich, B. J., Ibid., 27, 1986 (1955). Tunnicliff, D. D., Zbid., 28, 1657 (1956). Turner, D. W.,Nature 179, 1022 (1951).
Uzumasa, Y., Washizuka, S., Bull. C h e w Sac. J a p a n 29, 403 (1956). Vodar. B.. Romand. J.. Mikrochim. Act; 1955. 429. Wadelin, C.‘ W.,ANAL.CHEM.28, 1530 (1956). Watson, C. C., J . A g r . Food Che7;i. 5 , 679 (1957). West, P. T.V., Coll, H., AKAL.CHEM. 28, 1834 (1956). West, W.,ed., “Chemical Application!! of Spectroscopy,” Vol. IX of “Technique of Organic Chemistrv .’, Interscience. New Pork. 1953: (132) White. C. E., Hoffman, D. E., Mae,ee,J. S., Spectrochinz. Acta 9, 105 (1957). (133) ~\7ilkir!son,P. G., J . Opt. SOC.Ani. 45, 1044 (1955). (134) Zbid., 47, 182 (1957).
I
I.
I X-Ray Diffraction I I
’
I
I
F
ISIDOR FANKUCHEN Polytechnic Institute of Brooklyn, Brooklyn
earlier reviews (16-19, 34) on x-ray diffraction have appeared in this journal since 1949. I n these reviews, H. S. Kaufman, Benjamin Post, and the author have tried t o sumniarize briefly the advances in the field of x-ray diffraction which they considered of interest to chemists. Before starting the present review the author reread its predecessors and emerged from this experience with the IVE
I , N. Y.
feeling that n-e have lost sight of the forest because of the trees. I n 1949, x-ray diffraction mas already a very active field of research. The eight years since then have only substantially increased the research output in this field. An attempt t o list in three or four pages a substantial part of the work done in the last year or two would be thoroughly futile and confusing. Hence, a n attempt is rather made
here to appraise the situation-to discuss the various uses of x-ray diffraction of interest to chemists and t o evaluate their poteniial. The Novelco Reporter has recently reviewed the broad field of x-ray crystallography in two special issues (26). Specialized reviews like that of Kendrem and Perut6 ($0) on “Compounds of Biological 1nterest” provide a thorough, detailed coverage of isolated sections of VOL. 30, NO. 4, APRIL 1958
593
the field. A brief review by Lieberman (21) suniniarizes concisely the activities of recent meetings held in July 1957 at the Massachusetts Institute of Technology and in Montreal. By far the widest use of x-ray diffraction methods is as a tool in identification. I n addition, crystal structures can be worked out and the information obtained is often useful to chemists. A third application might properly be labeled “textural studies” and include studies of orientation, percentage of crystallinity in materials like synthetic high polymers, and textural characteristics of sheets, wire, and similar materials. Substantial developments have also continued to appear in the field of instrumentation. These are particularly concerned with extension of temperature range over which systematic x-ray studies can be made and with methods for detection of the scattered radiation. IDENTIFICATION
The powder method was historically the first used for identification of materials by x-ray diffraction in any kind of systematic way. While undoubtedly the earliest uses go back almost to the announcement of the powder method, it became a practical technique only with a now classic publication in 1938 by Hanawalt, Rinn, and Frevel (f0). I n this paper, x-ray data (spacings and relative intensities) were listed for 1000 compounds-data which had been collected in the laboratories of the Dow Chemical Co. It was quickly realized, particularly by Wheeler P. Davey, that this collection of data could form the nucleus of a systematic index system which would be of great value to industry. Largely as a result of his initiative, the data were made available in card index form under the auspices of the American Society of Testing Materials. For approximately 15 years, Davey, almost single-handedly, supervised the preparation and editing of data for subsequent sets of cards, a service for which chemistry must be forever in his debt. However, the steadily increasing amount of data becoming available made i t necessary to espand the editorial staff. NOWa group of four senior scientistsan editor-in-chief and three associate editors-is responsible for the continued expansion of this ASTM Card Index System. At the present time, this editorial board is confronted nrith a large number of serious problems and must soon make an equally large number of major decisions. These problems arise principally from the diversity of apparatus used throughout the world to collect x-ray data. For example, powder diffraction is obtained with cameras in
594 *
ANALYTICAL CHEMISTRY
which the x-ray h a i n is defined by a double pinhole sysi,em, a combination of one slit and one pinhole, or by two slits. Also, there are nom diffractometers for collecting data. It is true that the relative intensities of the various diffraction lines are affected by the experimertal setup. I n fact, it is possible to hitve reversals so that two lines can be put in different order, depending on the experimental technique. Another factor affecting the relative intensities is the wave length of the radiation used. This, too, can introduce serious :hanges. How then shall the data be li rted? There are several schools of thought. It is probably true that the most uniform and consistent results could be obtained with direct-reading diffractometers, if proper experimental procedures were observed. Howewr, these instruments are expensive and r o t everywhere available. It seems cerlain that t h t chemical pubIic would not be adequately served if data obt,iined on diffractometers were used wclusively. A subcommittee of the ASTM Committee on X-Ray Diffraction Powder Data is supervising the preliaration of a manual for recommended PI ocedures, which, it is hoped, will permit those interested in x-ray diffraction from the identification point of view to prepare data which will work well with the card index system. I n addition, it will soon be necessary to decide whether the card file should list patterns of all crystalline solids as available, or shoulc be limited to substances considered most useful for identification purposes. For example, approximately 1,000,000 organic compounds have been synthesized and characterized. Inclusion of patterns of even a fraction of these in the card index file would make th. file unwieldy and probably less useful A solution to this problem may be tlic inclusion of the most useful patterns in the card file, which is to be distributed to users in the field, and the simultaneous establishment of a central sll-inclusive library of x-ray patterns E t some convenient place. There are occasio 1s in which powder x-ray diffraction data cannot be used for identification. ‘I’lius, only a fern very small single crystals of a rare material may be available-crystals which cannot be sacrificed by crushing. In certain systems powder data simply are not detailed enough to permit unique identification. I n the field of steroid chemistry th?re are hundreds of steroid molecules of about the same size and shape crystallizing in unit cells of very much the same volume. Single crystal data-cell irize, space group, etc.-would be adcmquate to identify such materials, but the powder diagrams would, for the most part, resemble one
another so that identification by this method would be risky. A start has been made in compiling x-ray data from single crystals. Donnay and Nonwki (7) in 1954 issued a volume of single crystal data so arranged that identification can be based on unit cell dimensions and crystal system. The first edition of this monumental work collates single crystal data which have been published up to approximately 1950 and lists almost 4000 different compounds. In the years since then, many additional compounds have been studied and other data have come to light. It is this reviewer’s understanding that a thoraugh revision of this book is in preparation. It should prove very usefulif chemists will trouble to learn how to collect x-ray data from single crystals! STRUCTURE WORK AND ITS MEANING FOR
CHEMISTS
Almost immediately after the discovery of x-ray diffraction, the structures of some simple crystals-e.g., sodium chloride and diamond-were worked out. These were followed by more difficult but still simple structures, such as calcite and iron pyrites. Very quickly, the solving of structures resulted in a revision of our thinking of the arrangement of many kinds of materials. The outlook in certain fields, such as silicate chemistry, was completely metamorphosed as a result of the findings of structure work; our understanding of alloys was widened. Even the realm of organic chemistry eventually felt the impact of x-ray studies. It is obvious that if one can work out the structure of a crystali.e., find out where every atom is located in the unit cell-then, if the crystal contains individual molecules, this is equivalent to saying that one knows the stereochemistry of the molecule. I n the earlier days of x-ray diffraction, only crystals of materials of which the chemistry was completely certain were investigated. But, as long as 20 years ago, a fern daring workers used x-ray methods to determine the stereochemistry of molecules where the situation was still obscure to chemists. A striking demonstration of this was the work of Bernal ( I ) in the steroid field. Much later, Crowfoot and coworkers (6) showed how the stereochemistry of penicillin could be established by x-ray methods. Alargegroup led by Hodgkin has now completed a study of vitamin B-12 (16). In this country, Pepinsky has been very active in studying complex organic molecules of biological interest (31). The determination of the crystal structures of such complex molecules is not an easy or straightforward task; crystal structure work is to some extent an art. At the present time, clear-cut
methods are not available from x-ray rvork which would enable the structure worker to go directly from the data to the structure. Bragg showed a long time ago that a crystal structure from the point of view of an x-ray beam is a continuous, varying electron density distribution with the periodicity of the unit cell. He showed that such a continuous electron density distribution could be represented by a three-dimensional Fourier series whose coefficients are related to the x-ray intensities observed. There is, however, an indeterminateness in the situation. I n general, the coefficients of the Fourier series are complex numbers (real numbers when a center of symmetry is present and it is used as the origin of coordinates). While the amplitude of the coefficient can be obtained directly from the x-ray observations, the phase angle cannot. It is these unknown phase angles which cause all the difficulty in crystal structure determination. Of course, in many cases these can be determined. The proof of this is that thousands of crystal structures have been worked out by now. Perhaps the most powerful method for working out structures was developed by Patterson (29) in 1934. He showed that a Fourier series whose coefficients could be uniquely determined from the x-ray data-namely, with coefficients that were the square of the amplitudes of the scattered waves -gave a summation in which the peaks represented st distribution of interatomic vectors. This distribution could, in many cases, be interpreted in such a way as to locate a t least some of the atoms in the crystal. The proper use of Fourier methods, as a method of successive approximation, led to the desired structure. Various modifications were quickly made by Harker (12), Robertson (Sj), and others. The widespread use of Patterson’s methods and their modifications led to a tremendous increase in the amount of structure work being done. For a long time, however, no further major improvements were made until, in 1947, Harker and Icasper suggested a method of determining phases by means of inequality relations. The first paper ( I S ) mas followed by a veritable torrent of n-ork by Hauptman and Karle (14), Sayre (SO), Zachariasen (@), Wilson (SS), Cochran (4), and many others-work which resulted in a large number of new inequalities, equalities, and probability relations which i t was hoped would lead unequivocally to the solution of the problem of phase determination. These methods work-sometimes-but i t is this reviewer’s opinion that up to now they represent no substantial advance over the Patterson approach, when the latter
is applied in a sophisticated way by an experienced worker, Some better method must be found if the structure determination of complex crystals is to be undertaken by more than a handful of experienced and imaginative scientific artists. The answer, when it is found, may in part reside in improved physical experimentation. Two possibilities now assert themselves: one, used successfully by Bijvoet (2) and more recently by Pepinsky (SB), involves the use of anomalous dispersion. If a noncentrosymmetrical crystal is studied with radiation of a n’ave length shorter than the characteristic absorption edge of some of its constituent atoms, then, because of anomalous dispersion, the rule ordinarily obeyed that It,kl = I= does not hold. Peerdeman, van Bommel, and Bijvoet used this fact to determine the handedness of an organic molecule, a tartrate (SO), while Okaya and Pepinsky (27) recently showed that it can be used directly to determine not only the handedness but the structure itself. Ironically, this method does not work when the crystal structure possesses a center of symmetry. The second possibility was suggested about 10 years ago by Eckstein and this reviewer (8), and then independently by Lipscomb (2Z)-namely, the use of simultaneous reflections. This is a method related, in a sense, to phase contrast microscopy. All attempts with x-rays to demonstrate the usefulness of this approach have so far been negative, but in the case of electron diffraction, hIiyake (23) has indicated that information concerning phases is derivable when simultaneous reflections occur. Vork is continuing in these directions (37)* The various methods for crystal structure determination have led to the need for very lengthy computations; the advent of high-speed computers has made it possible t o do these computations. The IBM 650 has been programmed extensively for almost every kind of crystallographic computation and higher-speed computers have also been so used. This means that approaches involving massive computations can nom be considered, if such high-speed computers are available. Instrumental developments continue to be important. Thus, many papers have appeared which are associated with the extension of x-ray diffraction methods to higher (39) and lower (33) temperatures. These methods enable one to study solid phase changes and, perhaps what is more important from the chemist’s point of view, to study materials which are liquids or gases a t room temperature. I n recent years, a major trend towards the use of Geiger and scintillation
counters tts detectors, in plgce of film has devel3ped among powder diffractionists. The application of pulse height d scrimination techniques in conjuncticn with the appropriate filters and deteci,ors results in greatly reduced backgrourd on the x-ray patterns (28). In many European laboratories the use of monochromatized radiation in x-ray powder photography is increasing rapidly. To reduce exposure times, bent crystal monochromators are generally utilizttd to focus the incident beam. It is hoped that this trend will spread tc. American laboratories. The quality of x-ray patlerns obtained in this way is generally much better than that obtained with the techniques usually used in the United States. I n the past few years a number of im= portant bcoks have appeared. Cullity’s. textbook (6) has proved useful to mc%) chemists and particularly to metallurgists. Buerger’s “Elementary Crystallography” (3) is perhaps a misnomer. It is, however, an excellent book devoted essentially to the theory of space groups. “Small-Angle Scattering of X-Rays” by Guinier and Fournet (9) is a thorough treatment of this increasingly important field of x-ray study. The 32nd volume of “Handbuch der Physik” (11) devoted to structuial research, is destined to be very usef 11 to both beginners and advanced workers in the field. Finally, Wooster’s “Pperimental Crystal Physics” 140) is an entry in a new field as far as books are concerned. I n the field of polymer chemistry, a revix%d interest in structure has resulted from the production of the new isotactic polymers. These materials in general crystallize very much better than the earlier polymers and their structures are currently being intensively stuc’ied by x-ray methods (24, 26). TRAINING
I n this brief survey of the state of crystal1ogr:tphy as it involves chemistry one subject has been neglected-namely, the relatior of chemists t o x-ray crystallography. Here a sad state exists. Journals li
