V O L U M E 28, NO. 4, A P R I L 1 9 5 6
591
Laning, S. H., Division of Analytical Chemistry, 128th Meeting, ACS, Minneapolis, hlinn., September 1955. Land, L. H., Skaggs, L. S., Pingel, J. H., Rose, J. E., Rea. Sci. Instr. 24,394 (1953). Lapp, R. E., Andrews, H. L., “Nuclear Radiation Physics,” Prentice-Hall, New York, 1948. Leboeuf, 31. B., Miller, D. G., Connally, R. E., Nucleonics 12. No. 8.18 (1954). Liebhafsky, H. A., A ~ A LCHEM. . 21, 17 (1949). Ibid., 22,15 (1950). Ibid., 23,14 (1951). Ibid., 24,16 (1952). Ibid., 25,689 (1953). Ibid.. 26.26 (1954). Liebhafsky, ‘H. +4., Pfeiffer, H. G., Zemany, P. D., Ibid., 27, 1257 (1955). LiebhaGky, H. A., Smith, H. ll.,Tanis, H. E., Winslow, E. H., Ibid., 19,861 (1947). Liebhafsky, H. A., Zemany, P. D., Ibid., 23, 970 (1951). Lindstrijm. B., Acta Radwl. Supp2. 125 (1955). Lindstrom, B., hloberger, G., Ezitl. Cell Research 9, 68 (1955). Macdonald, G. L., Harwood, -M. G., Brit. J . A p p l . Phys. 6, 168 (1955). LIaeder, D., Rev.s e i . Instr. 26,805 (1955). hIariC?e,Ll., Chim. I n d . 72, KO.3 bis, 156 (1954). Mihalisin, J. R.. Iron Age 174, No. 3, 108 (1954). Miller, D. C., il’orelco Reporter 2 [l], 3 (1955). >lorlet, J., Bull. classe sci., Acad. roy. Belg. 39, 205 (1953). Xorrison. G. H.. Coserove. J. F.. Pittsburgh Conference on ilnalytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 1955. ;\lortimore, D. >I., Romans, P. A., Tews, J. L., Sorelco Reporter 1, [7], 107 (1954). lloteff, J., Nucleonics 13, KO.7 , 24 (1955). llottlau, -1.Y., Driesens, C. E., Jr., ASAL. CHEX 24, 1852 (1952). Aloxnes, N. H., 2. physik. Chem. A144, 134 (1929). Ibid., A 152,380 (1931). O’Kelley, G. D., U. S. Atomic Energy Commission, Tech. Inform. Service, Oak Ridge, Tenn., MTA-31, 5-17 (1952). Peirson, D. H., Franklin, E., Brit. J . A p p l . Phys. 2, 281 (1951). Pfeiffer, H. G., Zemany, P. D., Nature 174, 397 (1954). Pollard, E. C., Davidson, W. L., “Applied Xuclear Physics,” 2nd ed., Wiley. New York, 1951. Pringle, R. TV.. Roulston, K. I., Brownell, G. W.,Lundberg, H. T. F., Trans. Am. Inst. Mining M e t . Engrs. 196, Tech. Pub. 3642-L; Mining Eng. 5 , No. 12, 1255 (1953).
REVIEW OF FUNDAMENTAL
(116) (117) (118) (119) (120) (121) (122) (123) (124) (125) (126) (127) (128) (129) (130) (131) (132) (133) (134) (135)
(136) (137) (138) (139) (140) (141) (142) (143) (144)
Rev.Sci.Instr. 26,94 (1955). Ibid., p. 630. Rowland, R. E., J . A p p l . Phys. 24, 811 (1953). Russell, W.L., Econ. Geol. 46,427 (1951). Salmon, A I . L., Blacklodge. J. P., 16th Midwest Regional Meeting, ACS, Omaha, -Neb., November 1954. Segr6, E., “Experimental Nuclear Physics,” Vol. 1, p. 304 (H. A. Bethe and J. Ashkin), Wiley, New York, 1953. Sherman, J., Am. SOC.Testing Materials, Spec. Tech. Pub. 157,27 (1954). Shurkus, A. A., I n d . Labs. 4, No. 2, 8 (1953). Simon, H.. Ann Physik 12,45 (1953). Spencer, L. V., Fano, U., Phys. Rev. 81, 464 (1951). Steinhardt, R. G., Jr., Serfass, E. J., AKAL.CHELI.23, 1586 (1951). Ibid., 25,697 (1953). Steljes, J. F., Brit. J . A p p l . Phys. 3, 203 (1952). Sterk, A. A., Pittsburgh Conference on rlnalytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 1955. Stevenson, J. S., Am. Mineralogist 39, 436 (1954). Taylor, J., Parrish, W., Rev.Sei. Instr. 26, 367 (1955). Terrell, H. D., Davidson, J. C., Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 1955. Thomas, B. W.,I n d . Eng. Chern. 46, S o . 3, 93.4 (1954). Titus, A. C., Power Apparatus and Systems, No. 14, 1160 (October 1954). Titus, A. C., Winslow, E. H., “Review of Control and Evaluation of Carbon Brush Impregnation Treatments Using X-Rav” (Photometer) iibsorution 3Iethod.” General Electric \ Co., Schenectady, ’ N. I !., Tech. Information Series R 53MG301. Tournay, AI., BUZZ. SOC. franc. mineral et crist. 76, S o . 10-12, LXIII (1953). Ibid., 77,725 (1954). Tournay, M., Compt. rend. 234,2527 (1952). Traill, R. J., Can. Mining J . 76, 55 (March 1955). Untermyer, S., ivucleonics 12, KO.5, 35 (1954). T’ollmar, R. C., Petterson, E. E., Petruzeelli, P. .4.,ANAL. CHEY.21, 1491 (1949). Kuhns, P. TV., Ifatl. Advisory Conim. BeroWeltmann, R. N., naut., Tech. Tote 3098 (1954). Wilkinson, D. H., “Ionization Chambers and Counters,” Cambridge hlonographs on Physics, Cambridge University Press, Cambridge, 1950. Zemany, P. D., Winslow, E. H., Poellmitz, G. S., Liebhafsky, H. d.,ANAL.CHEM.21,493 (1949).
i Diffraction
I I I
I
BENJAMIN POST and ISIDOR FANKUCHEN Polytechnic Institute o f Brooklyn, Brooklyn 1, N. Y.
N THE present review no effort has been made t o comment on, or even to list, all papers dealing with x-ray diffraction which have appeared during the past year. Rather, an effort has been made to limit the discussion to items which are believed t o be of general interest t o chemists; emphasis has been placed on analytical methods and crystallographic studies of organic and inorganic compounds. Several books dealing with various aspects of x-ray crystallography have appeared during the past year; two are especially noteworthy. Both deal with “powder” methods of x-ray difhaction-i.e., the x-ray studies of polycrystalline materials. ‘‘XRay Diffraction Procedures” b y Klug and Alexander (44)is an excellent manual of techniques ; “X-Ray Diffraction b y Polycrystalline Materials” by Peiser, Rooksby, and Wilson (59) is a
collection of essays which deals extensively 11ith a n-ide variety of topics in x-ray diffraction. Both volumes present large amounts of material not readily available n-ithout a thorough search of the literature. Two journals are now devoted exclusiveiy t o publication of crystallographic papers: Acta Crystalloyraphica and Zeitschrifl f u r Kristallographie. T h e latter resumed publication in October 1954, after discontinuing publication during the war. APPARATUS AND TECHNIQUES
A goniometer has been described which is designed t o facilitate the investigation of diffraction intensities from single crystal8 using Geiger counters (30). T h e crystal may be rotated about each of t h e Eulerian axes; each reciprocal lattice point may be
592 brought into reflecting position in the equatorial plane where all measurements are made. A careful comparison has been made of Geiger counter and photographic techniques in single crystal x-ray studies (78). The Geiger counter method is found to be somewhat more reliable than the photographic, but is more time-consuming. The usefulness of the improved accuracy is being tested i n various crystal structure determinations now in progress. A careful study has been made of the available x-ray diffraction detectors (7f). These include the conventional end-window Geiger counter tubes as well as more recently developed sidewindoff proportional counters and scintillation counters. Rfethods have also been described for x-ray diffraction studies of radioactive materials using diffractometric techniques (46). Usually, thick layers of lead are placed strategically to cut down unwanted background; the authors show how scintillation counters or proportional counters, with pulse height discrimination, may be used to cut background to very small values without using lead shields. h device for computing two-dimensional Fourier series by optical methods has been described (88). The instrument appears to be superior, for this purpose, to the well-known "Huggins masks" which were designed for the same purpose. Examples are given of the use of the newer device in the determination of the crystal structure of p-toluidine hydrochloride; it has also been found useful in the computation of "difference" Fourier series. Interest in the use of high-speed digital computers for crystal structure calculations continues Robertson (64) has described a fast digital computer for Fourier operations which is the mechanical analog of the widely used Beever Lipson strips. Cochran (18) has discussed the possible utilization of high-speed computers for the direct determination of crystal structures. He describes a method whereby the computer can be used to select a set of signs for the coefficients of the Fourier series such that the Fourier series satisfies given conditions. Examples are given of the successful application of the method to the determination of the structures of some crystals of moderate complexity and of its unsuccessful application to the structures of somewhat more complex crystals (nitroguanidine and asparagine). Brown, Moneypenny, and Waltelin (15) have discussed procedures for measurement of intensities of diffraction lines on film photographs of powdered specimens. They describe a servocontrolled microdensitometer for automatic scanning of film photographs which is accurate to 0004 part in three density units. The precision attainable in the determination of lattice constants using the Geiger counter diffractometer has been discussed in detail (69). Precise lattice constants have been determined for a number of elements and simple cubic compounds. I t \!as found that the limiting factor in the accuracy attainable by this method was the inaccuracy in the knowledge of the wave length of the x-radiation used. The lattice constants could be measured with an accuracy of one part in 250,000, but our knowledge of the absolute values of s-ray wive lengths is only half as accurate. -4theoretical investigation of the thermal motion of atoms in niolecular crystals by Higgs ( 3 9 ) indicates that there exists a linear relation between the root mean square amplitude of atomic motion and the square of the distance of the atom from the center of mass of the molecule. I t is felt that this type of thermal libration may account in large part for the variations in the electron density of carbon peaks which have been reported for anthracene and naphthalene. Improved precision of crystal structure determinations in recent years hac made possible the location of hydrogen atoms in the electron density maps of many molecules. McConnell ( 1 9 ) has compared optical methods of testing possible H-atom positions with the more objective difference synthesis. The latter is found to be more definite, hut the former is more useful in non-
ANALYTICAL CHEMISTRY centrosymmetric projections where difference methods cannot be used. IDENTIFICATION O F CRYSTALLINE SUBSTANCES
The use of x-ray diffraction data for the identification of crystalline substances is continuing its rapid growth. With few exceptions this technique utilizes "powdered" specimens; it iq nondestructive and may be used effectively with milligram, or even microgram, quantities. During the past year emphasic has been placed particularly on the application of the method to the identification of organic compounds. A group of Canadian workers has been particularly active in this connection. Barnes, Donaldson, and Phillips (6) have published patterns of various alkaloids for identification purposes. Barnes and others have also published large numbers of patterns of narcotics (7-9). X-ray powder patterns of 52 aliphatic and aromatic amine hydrochlorides (14,45),of many tetrazole derivatives, and of large numbers of steroids (57, 58) have been published recently in h . 4 L Y T I C A L CHE\f ISTRY.
A section devoted to crystallographic data is also a regular monthly feature of this journal. Rose (66, 66) has published patterns of alkaloids and other compounds of pharmaceutical interest. The Xational Bureau of Standards is continuing the publication of carefully collected standard powder diffraction patterns of inorganic compounds and elements. During 1955, two volumes devoted to these x-ray patterns have been published (65). All the patterns in these volumes, together with hundreds of others, including the organic patterns mentioned above, ore included in the newest set (6th) of the ASTbl card file of powder diffraction patterns which has just been published. ALLOYS AND ELEMENTS
I n solid solutions random displacements of both the solvent and solute atoms from their mean positions occur as a result of the elastic strains associated with the different effective sizes ot the two types of atoms in the crystal. .4 careful study of the integrated intensities of reflections from 15% solutions of gold iii copper has enabled CoyIe and Gaie (20) to determine the root mean square atomic displacement due to distortion. I n thi. calculation it was first necessary to allow for displacements due to thermal vibrations, which affect the x-ray intensities in :I manner similar to the distortion being investigated. It wa. found that the root mean square "distortion" displacement was 0.11 A,, compared with a value of 0.13 A. computed from elasticity theory. Heaton and Gingrich (38) have re-examined the structure of RInoSb. Atomic parameters were refined and these new value> were used in a careful investigation of the integrated intensities of selected reflections over the temperature range from 100" to 500" K. From the variation of these intensities with temperature it was possible to compute Debye characteristic temperatures; for reflections from the (001) planes it is 300" K. and for (hOO) reflections it is 280" K. Evidence of changes in the Debye temperatures a t elevated temperatures was reported. A careful investigation has been made of the lattice expansion of iron from 20' to 1502" C., using high temperature x-ray diffraction techniques ( 5 ) . I n combination with earlier low temperature work, the new data yield complete experimental information regarding the thermal expansion of iron from 0" K. to the melting point (1534" (2.). A study of a rhombohedral modification of natural graphite has been carried out by Boehm and Hofmann (IS). The rhombohedral modification is fairly common in selected specimens of natural graphite, but only one specimen of artificial graphite revealed the presence of this form, and then only in small amounts
V O L U M E 28, NO. 4, A P R I L 1 9 5 6 Single crystals of graphite were invariably found to be of the usual hexagonal type. On heating t o 2000' to 3000" C. the I hombohedral form is converted to the hexagonal type, which is considered to be the stable modification for all temperatures below 3000" C. INORGANIC COMPOUNDS
Efforts to determine the exact electron distribution in simple ~ r y s t a l shave been described by Wagner, Witte, and Wulfel (76). Details of the experimental setup for accurate intensity measurements are given. I n the sodium chloride crystal slight deviations from spherical symmetry of the charge distribution of the two ions were detected. The calculation indicated that 10 05 electrons Tyere associated R-ith the sodium ion and 17.70 with chlorine-Le., ionization is essentially complete. Thewlis (72) has made precise measurements of the lattice rlimensions of Li6F and Li7F; the cubic unit cells were found to have lattice constants of 4.0271 and 4.0263 A., respectively. The difference, 2 parts in 10,000, is well beyond the limits of experimental error and is attributed by the author to differences in zero point energy between the two lithium isotopes. A difrerence of about 3.3 parts in 10,000 between the unit cell dimen\ions of the two types of lithium fluoride has been predicted theoI etically. The effect of nuclear radiation on the structure of zirconium +ilicate has been investigated (40). It was found that during the course of the irradiation the density of the zircon dropped by 16%; it became isotropic and so disordered that it failed even t o give recognizable x-ray diffraction peaks. The observed effects .,re attributed to the displacement of atoms by recoil nuclei and hy the high temperatures generated in the irradiation process. The mechanism of the structural breakdown is discussed. .4mmonium dihydrogen phosphate (SH4H2P04) undergoes a phase transition a t 140" K . Pepinsky and Keeling (43) have examined the structure of this compound at 5' below and 5" above the temperature of the transition. They found that on passing through the transition the low temperature orthorhombic unit cell changes to one of tetragonal symmetry. It is shown that charge displacements take place in the transition which lead to antiferroelectricity below the transition temperature. Little r a s known until recently concerning the stereochemistry and bond lengths of cyclic siloxane compounds. Peyronel ( 6 1 ) has found that the six-membered (Si-0-Si-0-Si-0) ring of hexaniethyl cyclotrisiloxane is planar within the limits of experimental error; the Si-0 bond length is 1.61 A., Si-C is 1.93 A.; the 0-Si-0 angle is 136". The crystal structure of the analogous eight-membered ring iionipound (octamethyl cyclotetrasiloxane) has been determined -45' C. (70). The siloxane ring is puckered; bond lengths are Si-0, 1.65 -4.;and Si-C, 1.92 A. The Si-0-Si angle IS 142.5" and the 0-Si-0 angle is 109'. A solid phase transtormation occurs a t - 17" C.; above that temperature-Le., between - 17" and the melting point, 16' C.-individual molerules may assume randomly any one of four alternative orientations. The onset of disorder is inarked by an increase in crystal symmetry above the transition temperature. Kasai and Kakudo have computed two-dimensional electron llensity maps of diallylsilanediol(42). They found that the molecules are linked in the crystals in the form of infinite 0-H-0 honded chains; the 0-H-0 bonds are 2.53 A. long; the Si-0 bond IS 1 63 rl , and the Si-C bond is 1.90 -4., in good agreement with measures of the same bonds in the cyclic siloxanes. The 0-Si-0 and the C-Si-C angles were reported as both 110' within experimental error. .4 study of the crystal structure of alpha-KOp ( 1 ) has revealed two types of anion-cation closest contacts in the crystal: one of 2.71 A , , the other 2.92 A.. Similar results had previously been found for Ba02 by the same authors-i.e, 2.68 and 2.79 .4.
593 The 0-0 bond is 1.28 A4.long: its order is estimat,ed to be close t o 0.5. A somewhat surprising molecular arrangement has been found in crystalline BrCN (33). Molecules of BrCY are arranged i n the solid in the form of straight chains with the bromine atom of one molecule weakly linked to the nitrogen atom of the next molecule in the chain. The crystal structure of trichloromercury oxonium chloride has been determined (67). The structural units were found to consist of (C1Hg)aO cations and C1 anions. The conventional way of miting the formula of this compound-Le., 2HgC12,HgO/Hg-Cl is therefore incorrect. The C1-Hg-0 ion 'Hg-C1 is planar, with oxygen, mercury, and chlorine atoms very nearly in a straight line. The crystal structure of SnIa, originally determined by Dickinson in 1922, has been reinvestigated (53). It was found that Dickinson's structure is essentially correct but that the observed diffraction pattern can be adequately explained without invoking all deviations from the "ideal" structure used by Dickinson. The structure of TiOF2has been determined from x-ray powder photographs (73). Titanium atoms are octahedrally coordinated by randomly distributed oxygen and fluorine atoms. The octahedra share all six corners with neighboring octahedra. The authors feel t'hat powder diffraction data, previously attributed to TiF,, are probably due to TiOFp. The crystal structure of -41s was originally determined in 1929; it was then assigned the ideal wurtzite structure. Jeffrey and Parry ( 4 1 ) have reinvestigated the structure and find two types of deviations from the ideal wurtzite structure: the axial ratio of the hexagonal cell is 1.600 instead of 1.633, and the bond length is 0.385 parameter which determines the A1--N instead of 0.375. Two types of N-.41--N angles, 107.7" and 110.5", are present; Al--T\' spacings are 1.885 and 1.917 A. Hamilton has completed a detailed study of the crystal structure of the dimethyl phosphinoborine trimer (37). The determinat,ion was based on the use of full data in three dimensions; results were refined by least square and difference Fourier techniques. The structure consists of cyclohexane types of rings of alternating phosphorus and boron atoms; two methyl groups are bonded to each phosphorus atom and, two hydrogen atoms are bonded to each boron atom. Vos and Wiebenga have determined the crystal structure of P& and P& (74). I n the former they found S-P-S and angles P-S-P angles of 109.5'. I n P,S7 some of the S-P-S deviated significantly from 109.?io. I n both structures two types of P-S bonds may be distinguished with bond lengths of 2.08 and 1.95 A. The structures are made up of discrete molecules of P&o and PdS;,respectively. An interesting structure has been proposed by Edstrand and Blomquist for NH4C1.As2O8.1/zH20 (26). The atoms appear to be arranged in sheets perpendicular to the c axis of the hexagonal unit cell. The structure contains uncharged layers of arsenic trioxide with all arsenic atoms arranged in pairs on one side of the oxygen sheet. Water molecules are probably located in holes in the layers. B e h e e n layers of arsenic trioxide are layers of ammonium chloride molecules. .-ln investigation of the crystal structure of calcium monochloride, CaCl, has been completed by Ehrlich and Gentsch (26). The substance crystallizes in the form of a layer structure; double layers of Ca-Ca alternate with Cl-Cl double layers. All layers are parallel to one another. The shortest Ca-Ca distance is 3.38 A,, twice the calculated Ca+l radius. I n the C1 layer, the bonding appears to be of the van der Waals type. Geller and coworkers have continued their crystallographic investigation of the phases formed in various binary systems. The crystal structure of C02Siwas redetermined and found to be a distorted S i p I n structure (3,$). The structure of RhSel was
[
]
+
ANALYTICAL CHEMISTRY
594
determined from powder data (32). I n the Rh-Ge system, the crystal structures of the Rh2Ge, Rh,Ge,, and PhGe phases, all previously unreported, have been determined (31). A low temperature study of the crystal structure of H S C O has been completed (23). Below about 100' C., two phases appear to be stable; the structure determined was that of the form stable from -100' to the melting point. Molecular dimensions are similar to those in the vapor phase. Surprisingly, no N-H-0 bonds were found; the molecules are held together by N-H--S bonds, about 3.07 A. in length. A low temperature (-60" C.) study has been made of the crystal structure of hydroxylamine (54). The N-0 bond is 1.476 A., in good agreement with other values determined for bonds were found: single N-0 bonds. Two types of N-H-0 one approximately 2.74 A. long, the other about 3.10 A. long. The third hydrogen atom in each molecule does not appear to participate in hydrogen bonding. A cagelike (clathrate) structure has been found in crystals of H P F e .6H20 (12). The water molecules form cubo-octahedral cages of twenty-four oxygen atoms about each PFs group. In the center of each cage is a phosphorus atom.
-
ORGANIC COMPOUNDS
A recent redetermination of the crystal structure of benzene has been refined further by Cox, Cruickshank, and Smith (19). Cox had reported surprisingly short C-C bond lengths of 1.378 A. in 1954. I n the present work, a careful re-examination of the data, taking into account the anisotropy of thermal motion of the carbon atoms-Le., movements perpendicular to the plane of the ring as well as radially and tangentially within the plane of the ring-indicated that the C-C distance is 1.39 A., in better agreement with values determined by other methods. Work is continuing on the crystal structure of 9,lO-dihydroanthracene (29). iilthough some remarkable similarities have been observed between the structure factors of this compound and those of anthracene, 9,l0-dihydroanthracene1 unlike anthracene, is not planar. The molecule is bent a t an angle of about 145" along a line, joining the two central carbon atoms. The crystal structure of fluorene (17) has been determined; its carbon skeleton is planar to within experimental error. Bond lengths are discussed in detail in the paper. A precise determination of the structure of s-triazine using full data in three dimensions has been carried out by Wheatley (77). The molecule is planar, but not a regular hexagon; the C-S distance is 1.319 0.005 A.; the iT-C-N angle is 126.8', compared with a C-IS-C angle of 113.2'. A plot of C--N bond length us. bond order indicates that the 1.319 A. C-S bond distance corresponds to approximately 50% double bond character. Marsh has completed a determination of the crystal structure of 1,4dithiane (65'). Precise values of atomic parameters were obtained by a least squares refinement of full three-dimensional data. Like l,Pdiselenane, the 1,4dithiane molecule has the centrosymmetrical chair configuration. Unlike l,bdiselenane, in which the Se-C bond is appreciably longer than the sum of the covalent radii of selenium and carbon the S-C bonds in in 1,Pdithiane (1.80 and 1.821) are "normal"; the sum of the covalent sulfur and carbon radii is 1.81 A. A determination has been made of the crystal structure of benzene seleninic acid (50). The molecules are found to be linked bonds only 2.52 A. long. together in infinite chains by 0-H-0 Selenium to oxygen bond lengths of 1.707 and 1.765 were reported; other bonds were normal. Benzoic acid has been found (68) to crystallize in the form of centrosymmetric dimers; the dimers are almost planar and are held together by hydrogen bonds 2.64 A. long between carboxylic oxygen atoms. The two carbon to oxygen bonds in one carboxylic group were reported as 1.29 and 1.24 A. long.
*
Electron density difference maps computed for p-aminosalicylic acid show peaks which have been attributed to hydrogen atoms (10); two-dimensional data were used. Inter- and intramolecular hydrogen bonding between oxygen atoms are found in the crystal, as well as indications of weak 0-IY and N-K hydrogen bonds. The crystal structure of creatinine consists of strings of molecules linked by hydrogen bonds (24). The molecule is esentially planar; intramolecular bond lengths indicate a nearly complete system of resonance with the exception of one N-C bond. Gupta (36) has continued work on the structure of CIHIOB. 2H20; previously ( 3 5 ) he had established that the configuration is trans-i.e., that the compound is dihydroxyfumaric acid. In the more recent work he has confirmed the trans configuration by means of electron density maps. ?\To hydrogen bonding between COOH groups of adjacent molecules was observed; the structure is held together by molecules of water. -4 precise determination of the crystal structure of parabanic acid (22) has been carried out by Davies and Blum. Threedimensional data were used in the determination; a least squares refinement of the structure was carried out, folloa-ed by the computation of three-dimensional difference maps of electron density. The latter revealed the location of peaks %-ithan electron density of approximately 0.7 electron per A.3, 1 A. from each of the nitrogen atoms. These were evidently hydrogen atom peaks. Use of all the available diffraction data together with the extremely careful refinement process reduced the average standard deviations of atomic locations to &0.003 A. and those of bond lengths t o 1 0 . 0 0 4 A. The C-C bond is 1.541 A. long, in good agreement with previously determined C-C single bond lengths; the carbon to oxygen bonds range from 1.208 to 1.212 A . and are somewhat shorter than expected. The CIS2 and ClNl bonds are 1.380 and 1.382 A., and the NsCs and S I C Sbonds are 1.360 A. long. All appear to possess a high degree of double bond character. Nowacki and Burki (56) have determined the structure of xanthazol monohydrate by two independent methods: one was based on parameters computed from a three-dimensional Patterson analysis; the other was based on signs of Fourier coefficients determined by the use of Harker-Kaspar and Zachariasen inequalities. There are two, almost coplanar molecules, per unit cell; they are held together by hydrogen bonds; the hydrogen atoms in the bonds show up clearly in the electron density maps. Eiland and Pepinsky ( g 7 ) have described the crystal structure of cyclotetramethylene tetranitramine. Full data in three dimensions were used in the investigation, The nitramine group is planar; N-N bonds are 1.38 and 1.40 A. long. Intermolecular C-0 bonds of 3.01 and 3.12 A. were found. Blackmore and Abrahams have determined the structures of the isomorphous di-p-tolyl telluride, selenide, and sulfide compounds (11). Bond lengths and intermolecular di-Qtances were of the expected magnitudes; the normals to the two aromatic rings were inclined a t the angle of 62" to one another in the case of the telluride, 53' for the selenide, and 56" for the sulfide. .4n interesting example of the "sandwich" type of metalloorganic compound, dicyclopentadienyl manganese, has been investigated by Weiss and Fischer ( 7 6 ) . The structure resembles that of a double cone with a manganese atom a t the center and with the CsH5 groups serving as the basal planes of the two cones. LARGE MOLECULES AND HIGH POLYBIERS
I n determining the crystal structure of codeine hydrobromide dihydrate, Lindsey and Barnes ( 4 7 ) obtained the signs of phases of reflections, in three zones, by direct comparison of intensities with those of codeine hydroiodide dihydrate. The structure was deduced from electron density projections onto (hOO), (000,
V O L U M E 28, NO. 4, A P R I L 1 9 5 6 and (OrZO). The stereochemical configuration wsumed for codeine by organic chemists was fully confirmed; although the bond lengths and angles found by Lindsey and Barnes differed in some instances from those usually assumed, it was not possible to establish whether these differences were statistically significant. The crystal structure of morphine hydroiodide dihydrate has been determined ( 5 1 ) . Analysis of electron density projections made possible the location of all the atoms (except for hydrogen) in the unit cell. The spatial configuration of the molecule has been unequivocally established; the structure generally assumed by chemists is correct. Bunn and deP. Danberry ( 1 6 ) have determined the crystal structure of polyethylene terephthalate (Terylene) from the x-ray diagrams given by drawn fibers. The positions of atoms in the crystal were found by the usual Fourier methods. The molecules are nearly planar; bond lengths and van der Waals distances are “normal.” From comparisons of the density of crystals of polyethylene terephthalate (1.455 grams per cc.) with that of amorphous material (1.335 grams per cc.) it was possible to establish the proportion of crystalline material in ordinary drawn yarn (48%). Aggarwal and Tilley (3) have described methods of determining the crystallinity of polyethylene by x-ray diffraction methods using a Geiger-counter diffraetometer. Alternative procedures for determination of per cent crystallinity in oriented and unoriented specimens are discussed. I t is \Tell known that small angle x-ray scattering yields useful informntion concerning the size and shape of protein molecules in solution. Beeman and coworkers ( 4 ) have carried out a detailed analysis of small-angle x-ray scattering from solutions of bovine serum albumin, human mercaptalbumin, and mercaptalbuminmercury dimer over a wide range of experimental conditions. Radii of gyration of 29.8 A. for bovine serum albumin, 31.0 A. for human mercaptalbumin and 37.2 A. for the human mercaptalbumin dimer are obtained. Molecular models reasonably consistent with both the small angle scattering and single crystal work have been computed. Liquori has studied the molecular configuration of stretched polyisobutylene (48). The configuration is helical, with */& monomer per turn. The C-C-C angle within a chain is 114”. Three-polymeric forms of crystalline reduced human hemoglobin have been found (60); all appear to belong to the same space group. The analysis of the Patterson projection of the simplest of the three indicates that the two molecules in the unit cell are almost parallel to one another. Ramachandran and Kartha have proposed (61) a coiled-coil structure for collagen; three polypeptide chains, each with a threefold screw axis, are assumed to wind slowly about one another t o yield a coiled coil. Rich and Crick ( 6 3 ) agree with the coiled-coil aspect of the structure but criticize the proposed arrangement of polypeptide chains. The crystal structure analysis of vitamin B-12 (22) has established the molecular configuration of this compound. Full details of the analysis have not yet been published; the determination is a landmark in crystal structure analysis, as this is the largest molecule yet to be attacked successfully by the methods of x-ray diffraction. BIBLIOGRAPHY
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