CRYSTALLOGRAPHY.1. INTRODUCTION.AGAIN this report is far from an annual report in scope-it now has tocover papers published over a period of four years. In its arrangement, wehave followed somewhat the plan we adopted last year. The first sectiondeals with one aspect of crystallographic technique, that of neutron crystal-lography, while the second section describes the crystal structures of organiccompounds studied in the four years, 1947-50.We have again found it impossible to deal with many interesting researcheswhich have by common consent fallen in past years within the scope ofcrystallographic reports-particularly X-ray scattering in liquids and parti-ally ordered systems, such as many high polymers. There are also interestingdevelopments of technique, such as the use of polarised infra-red and ultra-violet radiation in crystal analysis, to which a whole section of the reportmight well be devoted another year.In connection with crystal optics, theappearance of the new edition of “ Crystals and the Polarising Microscope,’’by Hartshorne and Stuart, is particularly welcome.2. NEUTRON CRYSTALLOGRAPHY.Introduction.-A new development has arisen in crystallography withthe advent of nuclear piles, namely the application of neutron diffraction toproblems of crystal structure. This was briefly mentioned in last year’sreport on crystallography but otherwise the topic has not been referred toin these pages. It is therefore proposed to survey the subject as a whole.As long ago as1936, Elsasser pointed out the tbeoretical possibility of the diffraction ofslow neutrons by crystalline materials, and in the same year the existence ofthe phenomenon was shown experimentally by Halban and Preiswerk,2and by Mitchell and power^.^ Monochromatic neutrons were, of course, notavailable and the experimental results were not such as to permit of anyuseful practical application, but nevertheless about a dozen papers on thesubject appeared up to 1940, mostly in Physical Review.With the building of nuclear piles the possibility arose of obtainingmonochromatic neutron beams of sufficient intensity to put neutron diffrac-tion on an entirely new basis, and since 1946 a steady stream of papers hasappeared.Reference will be made at this stage only to some of the moregeneral papers on the s u b j e ~ t .~ - ~The idea of neutron diffraction is, of course, not new.Elsassor, Compt. rend., 1936, 202, 1029.Halban and Preiswerk, ibid., 1936, 203, 73.Mitchell and Powers, Phys. Review, 1936, 50, 486.* Wollan and Shull, Nucleonics, 1948, 3, 8 , 17.Shull and Wollan, Science, 1948,108, 69.Wollan and Shull, Phys. Review, 1948, 73, 830.Bacon and Thewlis, PTOC. Roy. SOC., 1949, A , 196, 50.* Lonsdale, Nature, 1949,164, 205THEWLIS : NEUTRON CRYSTALLOGRAPHY. 421The first neutron spectrometer to be built was erected at the ArgonneNational Laboratory in 1945, and was used principally for nuclear-physicalexperiments requiring a monochromatic beam of neutrons. Serious attentionwas nevertheless also given at the outset to neutron scattering by crystals,and Zinn,g Fermi and Marshall,lo and Goldberger and Seitz l1 publishedimportant papers on this question.The main body of work on neutroncrystallography has, however, come from Oak Ridge where Shull and Wollanand their co-workers have published a series of' papers which will be referredto in more detail later in the report. Work of this type is also being carriedout at Chalk River in Canada, and at Harwell in this country.With this brief introduction a more detailed account of neutron diffractionwill now be attempted and a comparison with X-ray diffraction given.Some idea of the experimental techniques involved will be presented andapplications to crystallography described. A final section will be devoted tofuture developments.The Wave-length of Neutrons.-In a conventional nuclear pile the fastneutrons produced by fission are slowed down by repeated collisions withina " moderator " of heavy water or graphite until they are slow enough toprovide further fission.The favourable energy for the occurrence of suchfission is obtained when the neutrons are in thermal equilibrium with theirsurroundings a t or about room temperature. These thermal neutrons giverise to further thermal neutrons by the successive processes of fission andslowing-down, and if a collimator is inserted in the pile some of these neutronswill emerge from it in the form of a beam which may be used in neutron-diffraction experiments.The equivalent wave-length h of a beam of neutrons of energy E is givenby the expressionA = 2/(0.081/E) x lod8 cm.where E is expressed in electron-volts ; and the equilibrium temperature in apile, which is normally in the range 0" to loo", corresponds to a peak energyof several hundredths of an electron-volt ; so that the wave-lengths concernedare of the order of l ~ ., i.e. they are very like the X-ray wave-lengths usedfor crystal analysis and are, of course, similar to the inter-atomic distancesin crystals. For example, the peak wave-lengths corresponding to 0" and100" are 1.9 and 1 - 6 3 ~ . , re~pectively.~It is therefore to be expected that thermal neutrons will be diffracted bycrystals; but, since the distribution of energy among the neutrons in thebeam follows approximately the Maxwellian curve appropriate to theequilibrium temperature, there is nothing to correspond to characteristicradiation, and the beam is, in effect, "white." Fig.1, due to Bacon,12gives, for example, the variation of neutron counting rate with wave-lengthfor a typical equilibrium temperature of 50". It refers to the thermalcolumn of the Harwell pile, in which a mass of graphite ensures that theenergies of the neutrons present are, for the most part, in the thermal region.Zinn, Phye. Review, 1947,71, 752.I1 Goldberger and Seitz, ibid., p. 294.lo Fermi and Marshall, ibid., p. 666.l2 Bacon, unpublished data422 CRYSTALLOORAPHY .In view of this energy spread it is customary to monochromatise theneutron beam for use in neutron crystallography, usually by reflection at aflat crystal surface, although a bent-crystal monochromator has been usedfor neutron cross-section measurements.13 Fig.1 shows the band of wave--Bud sejectedat 8 = 175"6g monochromatorWave-length, A.FIG. 1.Spectrum of thermal neutrons as diflracted by calcium fluoride.lengths selected by a fluorite monochromator in use at Harwell. It isdeliberately chosen to be on the short wave-length side of the peak to avoid thecomplications that would arise from the presence of an appreciable second-order component in the monochromatised beam.X-Ray and Neutron Dieaction.-It has been seen that a neutron beam, asit emerges from a pile, is analogous to a beam of '' white " X-rays and that itis usually monochromatised for use in neutron crystallography.Only aboutone thousandth of the neutrons in a collimated pile beam are reflected from themonochromator. Photographic detection of neutrons presents considerabledifficulties for neutron crystallography is not generally applicable. In orderto achieve a sufficiently high counting rate in the boron trifluoride detectorsusually employed, neutron beams of 106-107 neutrons per second arecommonly used. To obtain neutrons in these numbers from the nuclearpiles at present available, very wide beams must be utilised, the cross sectionsof which are measured in square. inches, whereas those of X-ray beams are,of course, measured in square millimetres. As a result, neutron spectro-meters have had to be constructed on a massive sca1e.6v9*14*16 Theyresemble gargantuan X-ray spectrometers, may weigh several tons and arecorrespondingly expensive. Recent developments at Harwell suggest thatthis massive equipment may not always be necessary, but more will be saidlater about techniques in general. At this stage it is sufficient to point outthat neutron diffraction demands different techniques from X-ray diffraction.Sawyer, Wollan, Bernstein, and Peterson, Phys.Review, 1947, 72, 109.Hurst, Pressesky, and Tunnicliffe, Rev. Sci. Instr., 1950, 21, 705.l5 Bacon, Smith, and Whitehead, J . Sci. I'nstr., 1950,27, 330THEWLIS : NEUTRON CRYSTALLOGRAPHY. 423Not only, however, does neutron diffraction differ from X-ray diffractionin the techniques employed, it differs fundamentally in certain underlyingphenomena.Perhaps the most obvious difference is in the extremely lowabsorption of most elements for thermal neutrons. Table I gives the massabsorption coefficients Bf a number of common elements for thermal neutronsand for X-rays (Fe K J , together with those for lithium, boron, cadmium, andgadolinium which are among the most highly absorbent elements for thermalneutrons. It will be seen that even these elements have mass absorptioncoefficients which are of only the same order as that of most elements for acomparable X-ray wave-length. For other elements, the neutron absorptionis very much less indeed.TABLE I.X-Ray and Neutron Absorption Coeficients.Mass absorption coefficient.X-Rays NeutronsElement. At.NO. (A = 1.934.). (A = 1-84.).Lithium ............... 3 1.5 5.8Boron .................. 5 5.8 38.4Carbon ............... 6 10.7Aluminium ............ 13 92.8 0.005Iron ..................... 26 72.8 0.026Bromine ............... 35 169 0.057Silver ............... 47 402 0.32Cadmium ............ 48 417 13.0Gadolinium ......... 64 199 183.0Gold .................. 79 390 0.29Lead .................. 82 429 0.00060-00023Copper ............... 29 98.8 0.032Another difference in absorption is that, whereas for X-rays the massabsorption coefficient varies in a regular fashion with atomic number, forneutrons there is no such regularity. The latter fact has no particularbearing on problems of neutron crystallography, but the extremely low valueof neutron absorption that occurs in general means that multiple scatteringis possible, with a consequent increase in background intensity; and that,for imperfect crystals, extinction plays a much more important part thanabsorption, with striking effects on the integrated intensity.The latter wasfirst pointed out by Bacon and Thewlis,’ and the theory was developed indetail by Bacon and Lowde.16 It will be recalled that, for XLrays and perfectcrystals, the integrated reflection is proportional to the structure factor F,“ true ” absorption playing no part : this is also true for neutrons. I npractice, however, crystals are usually ‘‘ imperfect,” and the integratedX-ray reflection is then proportional, apart from small extinction effects,to F2.In the case of neutron diffraction, on the other hand, the integratedreflection may be controlled almost entirely by secondary extinction.Indeed, for a thick mosaic crystal it is, in general, independent ofstructure factor, increasing with the degree of mosaic spread. The theorypredicts however that, for very thin crystals, the integrated reflection willbe proportional to F2, and also suggests that there will be a range ofl6 Acta C y s t . , 1948, 1, 303424 CRYSTALLOGRAPHY.somewhat greater thicknesses where it will be proportional to F. As pointedout by Bacon and Lowde,ls the latter result explains the observations madeby Fermi and Mar~hall,~ who found in a number of cases that their measuredintensities were proportional to P rather than F2. Recent quantitativeresults obtained by Bacon l2 confirm the theory, and it seems fair to concludethat, if single crystals are to be used successfully in neutron crystallography,they will have to be much thinner than those used by Fermi and Marshall.So far, use has been made of transmission through blocks of powdered crystal,where the situation is not complicated by extinction, and where diffractedbeams of adequate power may be obtained by using large specimens andneutron beams of large cross-section.The reflecting power of such a blockis proportional to F2 just as for X-rays.There are other differences between X-ray and neutron diffraction thatmust be taken into account to complete the picture. For example, neutronscattering is in general spherically isotropic, since such scattering is a nuclearphenomenon.In other words the f-curve takes the form of a horizontalstraight line. Lonsdale has suggested * that this means that only " trialand error " methods of structure analysis are possible. In the Reporter'sopinion, however, it should be possible in principle to use the usual Fouriermethods in neutron crystallography, for example by using the device of anartificial temperature factor. Even so it would appear to be foolish toexamine an unknown crystal by neutron diffraction until all possible inform-ation had been obtained by X-ray difhaction.Another difference is concerned with the intensity of scattering per atom.For X-rays, of course, this increases with atomic number and is proportional,other things being equal, to the square of the atomic-form factor; but forneutrons, where the scattering is by the nucleus, it appears to be quiteunpredictable. Not only does the scattering power per atom vary a t randomfrom atom to atom, but also from isotope to isotope of the same atom;moreover the sign of the scattering amplitude may also vary in the sameway.For X-rays the scattered wave from an atom is 180" out of phasewith the incident wave; and whereas for neutrons this is also true in mostcases, the scattered and incident waves are in phase for certain isotopes, andhence for certain elements. By convention the scattering amplitude isregarded as negative in the latter cases, and it is so shown in Table 11, inwhich X-ray- and neutron-scattering amplitudes are given for a number ofelements and individual isotopes.It will be noticed that different isotopesof the same element (e.g. lithium and nickel) can have scattering amplitudesof different signs.In neutron diffraction there is the possibility of much more " background "scatter than in X-ray diffraction. In the latter case some background scatteralways results from the temperature effect and from the Compton effect;the excitation of fluorescent radiation and the presence of a disordered ordeformed structure in the material under investigation will also contributeappreciably in appropriate cases. Of these possible causes, only three canoperate in neutron diffraction, namely the temperature effect and the disordeTFIEWLIS : NEUTRON CRYSTALLOGRAPHY. 425and deformation effects, but the absence of the others may be more thancompensated for by new effects which have no parallel in X-ray diffraction.One of these, multiple scattering, has already been noted ; but the main effectarises from the fact that almost all structures are disordered from the point ofview of neutron scattering.A disordered structure is essentially a structurein which the atomic scattering power varies randomly from site to site in thestructure. In X-ray diffraction, this arises in a disordered alloy, for example,TABLE 11.Ordered scattering amplitudes * *for X-rays and thermal neutrons.Scattering amplitude.1' Scattering amplitude."Element.HDLiBeCN0FNa 3 8c1KCaTiVCrMnFeAt.NO.11346789111213161719202223242526X-Rays (forsin ep=o.s)x 10-12 cm.0.020.020.28 { 6Li'Li0.390.480.540.620.751-141.351-551.932.042-232-37 { 40Ca44Ca2.682.852.993-13rThermalneutronsx lo-" cm.- 0.40-0.18- 0.250.640.70.780-640.850.580.550.350.440.350.3 10.990.350.490-490.18- 0.38(0.09 -f0.370.960.421.000.23- 0.33Element.coNicuZnGeAsseBrRbSrZrNbMoPd4 3SnSbI csTaWPtAuT1PbBiAt.No.2728293032333435373840414246475051535573747879818283X-Ra s(forx lo-" cm.3.42sin e:K=o.b>r3.58 {::;:62Ni3.753-924.234.404.544.7 15-055.195.565-705-87 :::: { l07Ag7-227.427.758.0911.2511.4212.1712.3712.7012-9013-10lo9AgThermalneutronsx 10-1* cm.0.281.031.480.280-760.590-840.630.890.670.550.570.620.690.640.630.610.830.430-610.540.520.490.700.5 10.950.770.75 l80.960.89- 0.85* For meaning of ordered amplitude see preceding paragraph.t Sign of amplitude in doubt owing to small magnitude.from the random occurrence at the various atomic sites of different kinds G fatom. In neutron diffraction it can actually arise for a single element, sincethe nuclear scattering power may vary in a random fashion from site to siteon account of the random distribution of isotopes and sometimes of nuclearspins. It has already been seen that different isotopes of the same elementhave, in general, different scattering powers, and the existence of isotope-disorder should be a t once apparent.The existence of spin-disorder also[Added in proof:These figures have now been published-Shull and Wollan, Phys. Review, 1951,81,527.]1' Figures except those for T1, kindly supplied by Dr. C. G. Shull.I* Winsberg, Meneghetti, and Sidhu, ibid., 1949,76, 975426 CRYSTAILOGRAPHY.follows when it is realised that the scattering amplitude of a nucleus will bedifferent according as its spin is parallel or antiparallel to that of the neutron,and that spins, like isotopes, are randomly distributed. Where the nucleushas no spin, as in the case of isotopes of even atomic mass above 14N,there will, of course, be no spin-disorder.In some cases, e.g. hydrogen,the disordered scattering is so great that the " Bragg " or ordered scatteringamplitude (Le. the amplitude scattered into the Bragg peaks) is very muchless than the total scattering amplitude, but in many others10 there isevidence that the dependence of scattering amplitude on spin orientation andisotopic constitution is not so marked. With hydrogen the total scatteringamplitude is 2.5 x cm. whereas the ordered scattering amplitude isonly 0.4 x 10-l2 cm., a difference that arises largely from spin-disorder. Indeuterium on the other hand, although the ordered amplitude is not muchgreater, namely 0.63 x cm., the spin-disorder is relatively low, and it isoften advisable, therefore, to carry out neutron-structure determinations ondeuterated compounds if possible.This has been done for sodium hydridc 19and ice 2o with results to be described below.There are four other ways in which neutron diffraction differs fromX-ray diffraction. The first is concerned with the binding of the nuclei,and the second with inelastic scattering of the neutrons. In addition, furtherscattering (both elastic and inelastic) occurs for ferromagnetic * and stronglyparamagnetic substances on account of an interaction between the magneticmoment of the neutrons and the orbital magnetic moments of' the atomicelectrons. Finally there is the fact that neutrons are not, in general,polarised on scattering, except in a few cases where polarisation arises fromthe effect of magnetic fields.Theneutron-scattering amplitude for an element is different according as theatoms are free (as in a gas) or bound (as in a liquid or solid).The ratio ofthese two amplitudes is A / ( A + 1) where A is the mass number of the isotopeconcerned, and it will be seen that this ratio is effectively unity for all butlight atoms.The possibility of appreciable inelastic scattering arises from the fact thatthe frequency of vibration of the thermal neutrons is of the same order as thatof the atomic vibrations (about 1013 per second). In consequence a neutronwill lose an appreciable fraction of its energy in exciting a quantum ofvibrational energy ; in other words appreciable inelast.ic scattering (i.e.scattering with a change of ware-length) will occur, which will again manifestitself as an increase in background scattering.Weinstock 21 has calculated,for a " free " atom of polycrystalline iron, that 0.6% of the scattering will beinelastic at absolute zero and that this will rise to 19% at 1000"~. Cassels 22We will now revert to binding and inelastic scattering effects.19 Shull, Wollan, Morton, and Davidson, Phys. Review, 1948, 73, 842.2o Wollan, Davidson, and Shull, ibid., 1949, 75, 1348.2 1 Weinstock, ibid., 1944, 65, 1.22 Cassels, " Progress in Nuclear Physics," (Frisch) , Butterworth-Springer, London,* Antiferromagnetic substances are referred to later.19.50, Ch.8THEWLIS : NEUTRON CRYSTALLOGRAPHY. 427has more recently treated the problem in some detail. I n the correspondingX-ray case the loss of energy is too small to be noticed, since the frequency ofvibration of X-rays is about 1018 per sec. and the quantum energy is thereforeof an entirely different order of magnitude.To summarise, then, the main differences between X-ray and neutrondiffraction may be stated as follows :Phenomenon. X-Rays.Absorption Regular variation with in-creasing atomic number.Extinction Subordinate to absorption.Bragg scattering Electronic atomic-form factorexists. Scattering power peratom increases regularlywith atomic number.Scattered wave 180' out ofphase with incident wave.Effect of thermal Intensity reduction accordingvibrations to Debye-Waller formula.Diffuse scattering.Nomeasurable change in wave-length.Polarisation Scattered wave is polarised.All isotopes of same elementhave same scattering power.Isotope effectSpin effectNeutrons.Irregular variation. Absorptionnearly always small. Back-ground increased by multiplescattering.Generally outweighs absorption sothat large single crystals im-practicable for much structurework. Powders must be usedin these cases.Nuclear scattering sphericallyisotropic. Scattering powervaries at random.Scattered wave usually 180' out ofphase, but eometimes in phase.Similar phenomena to be expected,but also appreciable amount ofinelastic scattering with largechange in wave-length and in-creased background intensity.Scattered wave is not polarisedexcept for magnetic effects'Isotopes may have different scat-tering powers, resulting in iso-tope-disorder and increase inbackground intensity .Scattering power is different, forfinite spin, according as this isparallel or anti-parallel.Re-sults in spin-disorder, withincrease in background scatter - - ing.Experimental Techniques.-As already indicated, measurements inneutron crystallography are usually made with the aid of wide neutron beamsand large spectrometers in which provision is made for monochromating thebeam, and the neutrons are detected by means of a boron trifluoride counter.Laue photographs have been taken by Wollan, Shull, and Marney23 by amethod involving the use of an " intensifying screen " of indium foil, whichemits (3-rays when bombarded by neutrons; but, apart from this one type ofapplication, photographic methods have not been used in neutron-diffractionwork up to the present.The reason for this is obvious when one considersthat the exposure time for even a Laue photograph is about 10 hours.The boron trifluoride counter depends on the reactionliB + in --+ iLi + :He.ms Wollan, Shull, and Marney, Phys. Review, 1948,73,627428 CRYSTALLOGRAPHY.It is arranged to record the a-particles emitted in this reaction, but is insensi-tive to y-rays. Ordinary boron contains only about one part in five of thel0B isotope, so that whenever possible separated loB is used to make theboron trifluoride gas with which the counter is filled; the efficiency of thecounter may then be as high as 80 or 90%.Great care is necessary to shield the counter from unwanted radiation,and it is also necessary to keep a watch on variations in the intensity of theincident neutron beam by some form of a monitor, for example a fissionchamber may be inserted in some convenient place in the pile.The mono-chromating crystal may take the form of the usual flat plate or the crystalmay be cut obliquely, as first recommended by Stephen and Barnes z4 andlater used by Fankuchen 25 for X-ray work, so as to " foreshorten '' thereflected beam with consequent increase of intensity. The type of equipmentin use a t Oak Ridge is a restricted double-crystal instrument, using sodiumchloride or a metal single crystal as the monochromating crystal, capable ofemploying a single wave-length only.* A true double-crystal instrument is inuse a t Harwel1,l53n which both monochromating crystal and specimen maybe rotated a t will.This spectrometer is also mobile. As in most of theneutron spectrometers so far used the counter arm is arranged to turn a ttwice the angular speed of the specimen table, so as to enable the counter toreceive the reflected beam for single crystal work and to maintain the sym-metrical transmission position for powder work.A rather different type of technique is also being developed a t Harwell 26in which an attempt is being made to reduce the dimensions of the neutronspectrometer to the X-ray scale, and to use small single crystals, again as inX-ray techniques.The use of such crystals should, of course, overcome theextinction problems already referred to, and the lack of neutrons is beingovercome by not monochromatising the beam (thus gaining a very largefactor), setting up the specimen in the reflecting position for a given plane andwave-length, and placing a miniature counter (made of multiple boron-coatedfoils) 27 in the correct position to receive the reflected beam. In this way, asingle measurement of counting rate gives the required integrated reflection.Difficulties will undoubtedly arise from the presence of unwanted high-ordercomponents in the beam, and, of course, reflections must not overlap; butpreliminary results have been very encouraging, and the ratio of peak count-ing rate to background appears to be such that hydrogenous crystals may beexamined directly without the need for deuteration.The possibility ofusing orthodox methods is being examined, and the first results suggest that,given an increase in neutron flux of only ten or twenty over that availablein the Harwell pile,? monochromatic beams might be used which wouldpermit rotating-crystal techniques exactly analogous to those used ineveryday X-ray analysis.24 Stephen and Barnes, Nature, 1935,136,793.26 Lowde, ibid., 1951, 167, 243.* [Added in proof.]t Such as the flux provided by the heavy-water pile at Chalk River.2s Fankuchen, ibid., 1937, 139, 193.e7 Idem, Rev. Sci. Instr., 1950,21,835.A true double-crystal instrument is now in operation atOak RidgeT H E W S : NEUTRON CRYSTALLOGRAPHY.429Applications of Neutron Diffraction to CrystaUography.-The firstpossibility that suggests itself, when the phenomenon of neutron diffractionby crystals is considered, is that of the determination of the positions oflight atoms in a structure. It is well known that it is very difficult, andoften impossible, to determine by X-ray analysis the positions of light atomsin a structure in which heavy atoms are also present, since the contributionsof the latter swamp those of the former. I n the case of neutron diffraction,however, since the scattering powers of all atoms are roughly of the sameorder, it should clearly be possible to determine the positions of light atomsin the circumstances considered.In particular it should be possible to deter-mine the positions of hydrogen atoms, although, as already explained, therelatively high background scattering from hydrogen makes i t advisable tosubstitute deuterium if possible. The first work of this kind was done byShull, Wollan, Morton and Davidson l9 on sodium hydride and sodiumdeuteride. They showed that the structure is the sodium chloride structureand found, as expected, a much greater amount of background scatter withsodium hydride than with the deuteride. Also, owing to the fact thatsodium and deuterium scatter neutrons with a positive scattering amplitudeand hydrogen scatters with a negative scattering amplitude, a marked reversalof the relative intensities of the 111 and 200 reflections was observed insodium hydride and sodium deuteride.Further work on the structural positions of hydrogen atoms, this time byWollan, Davidson, and ShuIl,20 has been carried out on ice.Ice made fromheavy water (D,O) was used and maintained at -90" during the experi-ments; from the results i t was possible to decide between the various struc-tures that had been proposed, although the resolution was not sufficient toenable all the lines to be separated. Intensity measurements were made onan absolute scale, and supported the model proposed by Pauling on thegrounds of the existence of residual entropy a t low temperatures, in whichthe hydrogen molecules possess some randomness, one hydrogen atom andone only lying on each of the lines joining neighbouring oxygen atoms.Since the oxygen atoms are arranged tetrahedrally this means, in effect, thatthere are, on the average, four half-atoms of hydrogen arranged tetrahedrallyaround each oxygen atom, as shown in Fig.2.Such a random type of structure should give rise to disordered scatteringof its own, and such disordered scattering was indeed observed, the measuredand calculated values agreeing quite well.A second type of application, which also utilises the difference betweenthe relative scattering powers of different elements for X-rays and neutrons,is the demonstration by Shull and Siegel 28 of the existence of superlatticelines in ordered samples of FeCo and Ni,Mn. In these two alloys the X-ray-scattering powers of the elements involved are practically identical, whereasthe neutron-scattering powers, as can be seen from Table 11, are sensiblydifferent, indeed manganese has a negative scattering amplitude.I nconsequence Shull and Siegel were able to reveal the existence of superlattice28 Shull and Siegel, Phys. Review, 1949,75, 1008430 CRYYTAIJAOORAPHY.lines which could not be obtained by X-ray methods. Conversely, as mightbe expected, they were unable to show the existence of such lines in Cu3Auby neutron diffraction, although X-rays show them up quite clearly.Shull and Siegel, in this connection, make sn interesting suggestion, basedon the fact that the neutron scattering amplitudes of various isotopes mayvary not only in magnitude but in sign.They take the case of nickel, forwhich the scattering amplitude is +0.3 for and + l o 4 1 for 58Ni, andcompare it with manganese, for which the elemental scattering amplitude is-0-32; and suggest making up an alloy Mn60 Ni, for which the intensitiesof the usual diffraction lines should be vanishingly small, while the super-lattice lines should be quite strong.Other applications of a metallographic nature have been carried out bySidhu,2Q who showed, by transmitting monochromatic neutrons throughsolid solutions and mixtures of titanium carbide and tungsten carbide, thatthe scattering power was related in a definite way to the degree of solid 8Fra. 2.solution obtaining; and by Arnold and Weber,30 who showed that theeffects of the preferential orientation of aluminium on the observed intensitiesof neutron reflection agreed, for various orientations, with those expected.Naturally a considerable amount of work has been devoted to measure-ments of scattering amplitude, since these are essential before neutroncrystallography can be developed. As will be seen from Table I1 values formany elements and some separated isotopes are now known.Work has been carried out on liquids by Chamberlain:' and on gases byAlcock and Hurst 32 and Spiers.= Chamberlain's results on sulphur, lead,and bismuth agree well with those obtained by X-ray examination.Alcockand Hurst, and Spiers, working on oxygen, carbon dioxide, and deuteriummade the interesting discovery that the correct but complex and laboriousquantum-mechanical method of calculating the neutron scattering by a gasgives a result not very different from a semi-classical calculation in whichSidhu, J.Appl. Phys., 1948, 19, 639.Arnoldand Weber,Phys. Review, 1948,73,1385. s1 Chamberlain,ibid., 1950,77,305.s2 Alcock and Hurst, &bid., 1949,76, 1609. aa Spiers, W., 1949, 75, 1766T H E W S : NEUTRON CRYSTALLOGRAPHY. 431the neutron is represented by a wave and the molecule by a rigid system ofpoint scatterers, the normal procedure for X-ray scattering being used.An application of a somewhat different kind has recently been reportedby Bacon,= who has studied the electron distribution in graphite by acomparison of X-ray and neutron intensities. The X-ray intensity of the1010 line relative to that of the 1120 is found to be about 85% too high, andthat of the 1011 relative to the 1122 to be about 80% too high, and Franklin 35has suggested that this can be explained if the L-electrons are not distributedspherically about the carbon nucleus but are concentrated about the centresof the C-C bonds.If the explanation is indeed concerned with electrondistribution and not with atomic positions the corresponding intensitiesobtained by neutron diffraction should show no anomalies since the scatteringcentres are the nuclei and the electrons play no part. In fact Bacon finds noanomalies, although he restricts his comparison to the ratios of the theoreticaland measured intensities of the pairs of lines 1010 and 1011, and 1120 and 1122,owing to lack of resolution.Another novel application of neutron diffraction is t o the detection ofantiferromagnetism.36 An antiferromagnetic material is one in which belowa certain temperature, the Curie temperature, the magnetisation directionsof neighbouring pairs of atoms are opposed, so that no net spontaneousmagnetisation exists.Above the Curie temperature the thermal energy issufficient to overcome the tendency of the atoms to set themselves in anti-parallel pairs and the behaviour is that of a normal paramagnetic substance.Since, as already mentioned, there is magnetic scattering of neutrons in thecase of certain magnetic atoms, the possiblity arises of the existence ofsuperlattice lines in the antiferromagnetic state, owing to the differentscattering amplitudes of the parallel and antiparallel atoms.In manganousoxide, which has the sodium chloride structure, Shull and Smart have shownvery beautifully the presence of magnetic superlattice lines below theCurie point (122°K.) of this material. At these temperatures the chemical(and X-ray) unit cell has a side of 4.43 A. whereas the magnetic unit cell sideis 8.85 A. Similar effects have also been found for a-ferric oxide. Neutrondiffraction has thus provided a direct way of detecting the orientation ofmagnetic moments.Future Developments.-Future developments in such a new subject asneutron crystallography are difficult to forecast, but it seems reasonable toassume that work will continue on the determination of the positions ofhydrogen and other light atoms in simple substances; and that this will beextended to more complex structures as suitabJe methods are developed andsingle-crystal techniques are perfected, as they must be if adequate progressis to be maintained.This stage of the development will call for the closestco-operation between X-ray and neutron diffraction to make full use of thefact that, in effect, we can alter the relative scattering powers of the atoms ina structure, and sometimes the scathering phases, although the atoms them-34 Bacon, Nature, 1950, 166, 794.a6 Shull and Smart, Phy8. Review, 1949, 76, 1256.a6 Franklin, ibid., 1950,165, 71432 CRYSTAIXOGRAPHY.selves remain in exactly the same configuration. Work on metallic order-disorder will also no doubt proceed where the scattering powers of the metalsconcerned warrant it, as, for example, in the brasses, and there is undoubtedlyscope for the determination of structures containing atoms which are closeneighbours in the Periodic Table, and for which the neutron-scattering ampli-tudes may differ more than the X-ray-scattering amplitudes.New types ofapplication, such as to antiferromagnetism and to problems of electronicstructure, will presumably continue to arise. One such application, suggestedby C a s ~ e l s , ~ ~ is to the study of atomic vibrations by the investigation of thechanges of wave-length that occur when inelastic scattering takes place.Problems concerned with the determination of the nature or degree ofpreferential orientation may well present a wide scope for neutron crystal-lography, since the whole body of a specimen may be examined, and not onlyits surface.Indeed this possibility of examination in depth may well turnout to be of great importance for many types of problem. It should bepossible to make measurements on large pieces of material and average theresults over a considerable volume, which would be quite impossible by X-rayexamination owing to the large absorption involved. It should, for example,be possible to determine the orientation of large single crystals which couldnot otherwise be examined.Another possible type of application is to phenomena which are difficultto deal with by X-rays on account of the falling off in scattering power withincreasing angle.For example problems could be attacked which areconcerned with the effects of temperature or other disturbing influences onthe stability or nature of the atomic arrangement. I n much of this work,as already indicated, it will be advantageous if not essential to combine theresults of X-ray and neutron diffraction ; partly because they will in so manyrespects turn out to be complementary, and partly because the pressure ofwork on any one neutron spectrometer is likely to be heavy. It seemsdesirable indeed to restrict the use of neutron dift'raction to critical experi-ments as much as possible, so as to prevent the overloading of the facilitiesavailable, and it is clearly undesirable to carry out experiments by neutrondiffraction that can be done just as well by X-rays.One should obtain allthe information possible by X-ray examination and turn to neutron diffrac-tion only when necessary. In this way it should be possible to make thebest use of this powerful new crystallographic tool.J. T.3. ORGANIC COMPOUNDS.I n early Reports on crystallography, the organic compounds on which adetailed X-ray analysis was carried out were rather few, and these wereoften grouped with similar-sized inorganic molecules as a combined group-molecular crystals. Any measurements that led fo a set of proposed atomicpositions within the crystal of an organic compound appeared a notableachievement. Now we recognise that an approximate structure analysis,Caeseb, private communicationHODGKIN AND PITT : ORQBMC COMPOUNDS.433giving atomic positions based even on calculated electron densities can becarried out relatively easily by present methods for most types of organiccompound, crystalline at ordinary temperatures, and with molecularweights of less than about 200. We have about 120 such analyses to reportthis year; these provide a variety of interesting evidence on the way in.\ ' .J2 3I J A. 0 1SaleFIG. 3.A section through the plane of the athracene molecule. Electron-densitycontours are at intervals of + 8. A.-~, the Erst one dotted.[Reproduced, by permission, from Acta Cryst., 1950, 3, 254.1which molecules pack in crystals and on the factors determining the dis-position in space of non-bonded atoms, while as many as twenty of thetotal number lead to the direct deduction of the correct chemical or stereo-chemical formulation of molecules of imperfectly known structure.But itis clear that the conditions under which the exact measurement of bondlengths and electron densities can be achieved through X-ray analysis haveto be carefully considered in relation to each individual structure. Inonly a handful of the structure analyses described can %he bond lengths b434 CRYSTALLOGRAPHY.considered to be accurate to within rt0.02 A., limitations being imposed inmost cases either by the nature of the available experimental data or byincomplete refinement of the electron-density series.I n the most careful structure analyses reported, such as those oft h r e ~ n i n e , ~ ~ na~hthalene,~~ and anthra~ene,~~ the electron-density dis-tribution can be calculated sufficiently accurately to provide evidence ofthe positions of hydrogen atoms (compare Fig.3), but only very tentativeconclusions can yet be drawn, even in cases such as these, on the characteror shape of the chemical bonds. Brill*l has re-examined the structure ofdiamond from this point of view, and has shown that the differences betweenobserved and calculated structure factors for diamond, summed as a Fourierseries, do give an electron distribution which is most marked along the linejoining the two atoms-the covalent bond; here it corresponds to a densityof about &-+ electron per bond. In graphite, too, as mentioned above,deviations between calculated and observed structure factors can becorrelated with an asymmetric electron-density distribution.I n both ofthese structures there have been interesting new measurements of latticeconstants. Lonsdale finds that the carbon-carbon distance varies a littlein different diamonds from 1.54465 to 1.54444 A . , ~ ~ figures which agree wellwith the mean value given by Riley, 1.54453 A j 3 I n graphite the c dimen-sion varies with crystallite size-it appears to be an almost linear functionof the reciprocal of the number of carbon layers.44 In certain carbons,produced by pyrolysis of polydichloroethylene, highly perfect graphiticlayers about 16 A. across have been shown to be present, usually arrangedin pairs a t a mean distance of about 3.7 A.45 Such graphitic layers are notmuch larger than the largest aromatic molecules of which detailed X-rayanalyses exist.Some of the general principles determining the ways in which moleculespack in organic crystals have been the subject of a number of recentreviews,46 and were also discussed in an earlier Report.47 As more crystalstructures are analysed, we can examine the situation in greater detail.It is possible to collect groups of compounds that fall into well-definedcrystal-structure types and then to examine the deviations that occur inindividual cases on account of the actual peculiarities of molecular shapeor inter-atomic attractive forces.A number of such structure types havebeen recognised for a long time.For example, small roughly sphericalmolecules such as tetranitromethane 48 or quinuclidine 49 pack in crystal38 Shoemaker, Donohue, Schomaker, and Corey, J . Amer. Chem. Soc., 1950,72,2328.40 Mathieson, Robertson, and Sinclair, ibid., 1950, 3, 245, 251.41 Ibid., p. 137.43 Nature, 1944, 153, 587.44 Bacon, Acta Cryet., 1950, 3, 137.d6 Macgillavry, Chem. Weekbkzd, 1948, 44, 169; Kitaigorodski, Uepekhi Fiz. Nauk.4 7 Powell, Ann. Reports, 1946, 45, 88.4i1 Nowacki, Helv. Chim. Acta, 1946, 29, 1798.Abrahems, Robertson, and White, Acla Cryst., 1949, 2, 233, 238.42 Phil. Trans., 1947, 240, A , 219.4 6 Franklin, ibid., p. 107.1948, 34, 122; Uspekhi Khim., 1948,17, 287.Oda and Matsuba, X-Rays, 1950,6, 27HODCfKIN AJ5iD PIT" : ORGANIC COMPOUNDS.435structures based on body-centred or face-centred cubic close packing. Itis characteristic that at ordinary temperatures these crystals have toohigh a symmetry corresponding to molecular disorder or rotation. Recentstructure-factor calculations, however, indicate that disorder is not complete-there are usually certain preferred orientations of the molecular axes inthe crystals. In hexamethylenetetramine one can see the situation atthe other end of the order-disorder scale. Calculations by Schaffer M,show that the best agreement with the observed structure factors can beobtained by assuming that the molecule is performing anisotropic oscillations-the calculated root mean square amplitude normal to the radius joiningan atom to the molecular centre is 0.26 A.With short-chain molecules,somewhat similar conditions are found. The chain axes may take uproughly criss-cross positions in relation to one another, and rotation oroscillation is usual a t high temperatures. As the chain length increases,parallel chain packing in at least one layer is the rule, though in succeedinglayers various crossed arrangements are being discovered in the structuresstudied. With small aromatic molecules two varieties of packing arecommon-either parallel disc packing, with an interval between layersof about 3.5 A,, similar to graphite, or a criss-cross arrangement with thedisc centres in nearly hexagonal close packing. The first is shown byhexaniethylbenzene, several pyrimidines, 61 and coronene with one celldimension 3 .5 4 4 A., the second by durene, aniline hydrochloride,62dibenzyl, and many others, with the shortest cell dimension between 5.3and 6.5 A.The condition of close packing may be disturbed by the existence ofparticular active groups in the molecule, each of which favours certaintypes of arrangement of neighbouring atoms. Regular co-ordinationpolyhedra about ions can seldom be established in organic crystals, butthere is a marked tendency for the co-ordination numbers and interionicdistances found among inorganic crystals to be preserved. Thus sodiumhas six oxygen neighbours in sodium ben~ylpenicillin,~~ potassium six inpotassium decanoate (capr~ate),~* seven in potassium benzylpenicillin,53calcium eight 5s and strontium eleven 66 in calcium and strontium formates, theform of the co-ordination polyhedra being in all cases quite irregular.Inthe case of negative ions, such as the halogens, the co-ordination polyhedraare smaller-usually only three or four atoms are involved s2-and theposition of these often suggests hydrogen bonding. When halogens occurin the un-ionised state, the molecules are frequently so arranged that thehalogen atoms of neighbouring molecules are in contact-presumably owingto the greater contribution they make to van der Waals interaction. Aparticularly striking example is provided by the three varieties of p-iodo-bo J . Arner. Chem. SOC., 1947, 60, 1557.sa Crowfoot, Bunn, Rogem-Low, and Tumer- Jones, " The Chemistry of Penicillin,"64 Vand, Lomer, and Lang, Actcr Cryst., 1949, 2, 214.ss Nitte and Osaka, X-Rays, 1948, 5, 37.Clewsand Cochran, Acta Cryst., 1948,1,4.b* Brown, dbid., 1949, 2, 228.Princeton Univ. Press, 1949, p. 310.Nitta and Sailo, ibdd., 1949, 5, 89436 CRYSTALLOGRAPHY.N-picrylaniline, in all of which the iodine atoms of neighbouring moleculesare within the van der Waals distance of one another.67 Again, whereverhydroxyl or amino-groups are present hydrogen- bonding systems can betraced. Some of these form particularly stable types which are repeatedwith variations, e.g., substitution of nitrogen or chlorine for oxygen, in anumber of crystal structures. One might expect, for example, a closerelation to exist between the system found in phloroglucitol dihydrate mand diammoniate where the water or ammonia molecules link threeneighbouring phloroglucitol molecules together and are themselves linkedthrough a fourth bond.It is more surprising that a similar system is foundin 2-hydroxy-4 : 6-dimethylpyrimidine dihydrate 6o where a planar moleculeis substituted for the puckered cyclohexane ring.Distances described by different authors as hydrogen bonds range fromall lengths between 2.51 A. in oxalic acid dihydrate to 3.2 or 3.3 A. incompounds involving nitrogen (the term has even been used for theN . . . . HC distances in hexamethylenetetramine which are 3.88 A. long !).It is clear that very varying degrees and probably also types of interactionare involved in different structures.Within the range of " hydrogen-bonded " distances there are also now observed a number of short distancesinvolving carbon to which the term is not usually applied. Some of these,as for example, the short contact CH . . . 0, 3.28 A., in threonine, seem tobe forced on the molecule by packing considerations. Others, such as thedistance, 2.66 A. in p-nitroaniline,61 between one oxygen and the benzenering carbon atom, appear to have a more specific character. A particularlyinteresting example is provided by the silver perchlorate-benzene complex .62Here each silver ion is a t a distance of about 2.6 A. from two carbon atomsof each of two benzene rings, an arrangement which suggests x-bonding.The perchlorate ion is pushed away from one side of the silver to makeroom for the benzene rings.Once normal stereochemical standards of molecular shape have beenestablished, it becomes interesting to examine the conditions under whichdistortions from these occur.The necessity for a special packing, or theformation of a particularly stable hydrogen-bond system, appears sufficientto deflect the bond direction between an atom and attached benzene ringfrom the normal position directed to the ring centre. In tetraphenylcyclo-butane,63 for example, the deflection of one such bond is 7' from the planeof the ring. The distortion of an aliphatic chain from the planar zig-zagform would be expected to be much easier; so far, one or two examplesonly have been observed. A distortion from the planar form of the benzenering itself must, on the other hand, be much more difficult.In the only6 7 Grison, Actu Cryst., 1949, 2, 410.1.9 Anderson and Hassel, Acta Chem. Scad., 1948, 2, 527.Idem, Nature, 1949, 163, 721.6 1 Abrahams and Robertson, ibid., p. 252.62 Rundle and Goring, J . Amer. Chem. SOC., 1950, 72, 6337.6s Dunitz, Actu Cryst., 1949, 2, 1.6o Pitt, Actu Cryst., 1948, 1, 168HODGKIN AND PITT : ORGANIC COMPOUNDS. 437example, di-p-xylylene,a the distortion is forced by covalent bonds withinthe molecule.Another aspect of the X-ray crystallographic investigation of organiccompounds is the use of crystallographic data as a means of identification.This subject has been reviewed recently by Franzen 6s and by Bannister 66who have described both morphological and X-ray methods.The forth-coming publication of the first volume of the Barker index should encouragesome return to the first method. The body of data in the powder indexon organic compounds is not so far very great, and the problem of decidingwhich compounds should be included in it is one of considerable interestand importance. I n many cases an identification of an organic compoundis undertaken with reference to one particular investigation, e.g., to dis-tinguish different penicillins or to identify their degradation products withsynthetic specimens 53*67 or to show that gramicidin yields on hydrolysisa mixture of D-valyl-L-valine and L-vaIyl-D-valine.6s Data on many ofthese compounds would be doubtfully useful in a general index, while otherdata collected, e.g., on a series of constituents of explosive^,^^ ought to beincorporated.There are also certain special warnings that have to beattached to the use of crystallographic data in general. More complicatedmolecules may often crystallise in polymorphic modifications which showvery little tendency to be converted one into the other, for example, thethree forms of glycylglycine. Often also the crystal structure may beeasily deformed or affected by the exact conditions of crystallisation andthis, in turn, affects the appearance of the powder photographs. Stosick 70has pointed out that a number of the ‘ polymorphic ’ modifications of soapscan be explained in terms of crystals with varying degrees of disorderedstructure and not in terms of phase change.One interesting point is the occasional possibility of effecting theidentification, by crystallographic means, of a natural, optically activeisomer with molecules in a synthetic DL-preparation.The vast majorityof DL-preparations crystallise as racemic crystals containing both D- andL-molecules and often having crystal structures very different from thoseof the separated D- and L-isomers. Direct identification of the molecularspecies present by crystallographic means is then, of course, impossible,Not infrequently, however, the crystal structures of the racemic crystalsbear a marked resemblance, allowing for the presence of different symmetryoperations, to those of the optically active crystais-some examples are D- andDL-alanine, D- and DL-leucine, D- and DL-penillamine hydrochlorides. Itis relatively seldom that the D- and the L-crystals separate, as in Pasteur’soriginal experiments, but it happens occasionally, and has recently beenBrown and Farthing, Nature, 1949, 164, 9156 5 Chem.Weekblad, 1948, 44, 217.6 7 Clark, Kaye, Pipenberg, and Schisltz, “ The Chemistry of Penicillin,” Princeton66 Ibid., p. 220.Univ. Press, 1949, p. 367.Hinman, Caron, Louis, and Christenson, J . Amr. Chem. SOC., 1950, 72, 1620.Bg Soldate and Noyes, Anulyt. Chem., 1947, 19, 442.70 J . Chem. Phyeic8, 1950, 18, 757, 1035438 CRYSTALLOGRAPHY.observed in the case of one form of p-phenylglyceric acid, tetrachlorocycb-hexane, m. p. 174", and threonine. Crystals of natural L-threonine are,for example, indistinguishable by X-ray methods from those in preparationsof synthetic DL-threonine.The number of organic compounds which we have to consider this yeartempts us to draft this Report in the form of an outline text-book of organicchemistry, although sections of our text are still absent or very incomplete.Few measurements on organic compounds have yet been made a t lowtemperatures, and the first members of most of the aliphatic homologousseries are, therefore, still missing.These have, for the most part, beenalready examined by electron diffraction, and the series here described maybe completed, so far as molecular structure is concerned, by reference tothe very useful summary of electron-diffraction data given by Allen andSutton in, significantly enough, Acta Crysdallographica.72D. C. H.Aliphatic Compounds.-Although they raise a number of other problemsas well, the crystal structures in the first six classification groups below areconcerned principally with the character and influence of long hydrocarbonchains. The way in which long-chain molecules fit into crystals has beenapproximately known for some time. But the accurate knowledge nowobtained introduces detail that could not have been guessed, both in thearrangement and in the structure of the chains. The interest of thecrystal structures in the lat,er classification groups is rather different, partly~t~ereochemical and partly concerned with the effect of active groups oncrystal and molecular structure.Hydrocarbons. The smallest hydrocarbon we have to mention isdimethyltriacetylene (octa-2 : 4 : 6 - t r i ~ n e ) , ~ ~ which has a very simplecrystal structure based on rod close packing, with one molecule in therhombohedra1 unit cell.The bond lengths have been measured with goodaccuracy and are given in Fig. 4. They agree well with those in otheracetylenes that have been recorded.The zig-zag paraffin chain introduces crystallographic complications ;the hydrocarbon C,,H3, for example, of which preliminary measurementlsare This is the low-temperature form. The higher-temperature modification, which is ortho-rhombic, has been re-examined for several hydrocarbons by Mazee 76 whofinds that the a and b axes do not begin to change appreciably when thecrystals are heated until a certain definite temperature is reached and thattheir ratio never quite reaches the hexagonal value that might be expectedfor fully rotating chains.The mean atomic positions in very long hydrocarbons have beeninvestigated in a new and most interesting way by Pinsker and others using71 Furberg and Hassd, Acta Chem.Scund., 1950,4, 1020.75 Jeffrey and Rollett, Nature, 1950, 166, 476.74 Muller and Lonsdale, Acta Cryst., 1948,1,129.crystallises in a one-molecule triclinic cell.Bid., 1950,8, 46.70 Rec. Trav. chim., 1948,67,197HODGKIN AND PITT : ORGANIC COMPOUNDS. 439electron diffraction of the crystal^.'^ A Fourier series formed, using theelectron-structure amplitudes, gives a density function in which the maximashow the nuclear positions.Small peaks due to hydrogen atoms appearclearly visible and the mean bond dimensions are given as C-C 1.52, C-H1.17 A., L C-C-C 110", L H-C-H 105".The very remarkable complexes formed by shaking straight-chaincompounds with urea in the presence of a little solvent have been investigatedby Smith who has proved that the complexes are of the clathrate type."I 1-19, I 1-45CH31.44C1.13N164 hFFFFFIU. 4.Interatomic distances i n (a) dimethyltriacetylene (octa-2 : 4 : 6-triyne), (b)diucetylenedicurboxylic (butadienediuarboxylic) acid, ( c ) methyl cyanide-boron trifluoride, and (d) methylamine-boron triJuoride.The urea molecules are arranged in a hexagonal unit cell on a spiral frame-work held together by hydrogen bonds.In the centre of the spiral lie thehydrocarbon chains, the plane of the zig-zag having a random distributionabout three directions at 120" to one another. The parameters of thecarbon atoms in the chain-length direction are not fixed unless it happensthat this length is a near multiple of the urea repeating unit. Similarstructures are formed with thiourea-the channels are wider hereand branched-chain hydrocarbons or cyclohexane derivatives can beaccommodated.X-Ray diffraction effects observed for liquid ethylalcohol suggest a gradual change as the temperature is lowered betweenassociation of the molecules in pairs at -75" and in chains in the super-7 6 Vainshtein and Pinsker, Dokl. Akad. Nauk., S.S.S.R., 1950, 72, 53; cf.Weinsteinand Pinsker, ibid., 1949, 64, 49.Alcohols und Ei&rs.7 7 J . Chem. Physics, 1960, 18, 150cooled liquid at -150".78 No detailed structure anal$& of a simple alcoholhas, however, been reportsd and only preliminary measurements are givenon higher-chain alcohols, such as the cetyl alcohols 79 and 9 : 10-epoxy-octadecanols.sOAn important ester structure described is that of pentaerythritoltetranitrate.*l The bond lengths found are recorded in Fig. 5a and arenot as expected, particularly the short CH,-0 bond of 1.37 A. Dipolemeasurements suggest that this bond has little double-bond character, asfar as effect on restriction of rotation is concerned.82 It is possible that theX-ray data are not yet sufficiently refined for the inter-atomic distancesto be completely established, but it is at least suggestive that CH,-0 shows0AFIG. 6 .and (c) chain form i n di-(2-iodoethyZ) trisulphide.a progressive change from 1-46 A.in pentaerythritol 83 to 1.41 A . in thetetra-acetate 84 and 1.37 A. here; the explosive character of the compounda h suggests that some abnormality might be present.From among the huge volume of preliminary data recorded on long-chain esters and particularly glycerides, one may select for mention the factthat X-ray data have been used to show the identity of (-)-cc-(dipalmitoy1)-lecithin and the natural (dipalmitoyl)lecithin.86The most interesting feature ofsulphur-containing chains appears to be their tendency-shown in plasticInterdomic distance8 in (a) pentaerythritol tetranitrate, (b) bisnitraminoethne,Alkyl Sulphides and Polysulphides.Jagodzinaki, 2.Natzsrforsch., 1947, 2u, 465.Sano and Ktakiuchi, J . Phys. SOC., Japan, 1949,4, 178.Witnauer and Swern, J . Amr. Chem. SOC., 1950,72, 3365.Booth and Llewellyn, J . , 1947,837.Springall and Spedding, Research. 1949, 29.5.Llewellyn, Cox, and Hardy, J., 1937, 887.Goodwin and Hardy, Proc. Roy. SOC., 1938, A , 164,369.B a r and Rates, J . Amer. Chem. Soc., 1950,72,942HODQKIN AND PITT : ORGANIC COMPOUNDS. 441sulphur and S, itself-mt to conform to the planar zig-zag hydrocarbontype. Dawson and Robertson 86 were able to show that in di-(2-iodo-ethyl) trisulphide the sulphur atoms form an unbranched chain.Theirarrangement of the carbon atoms has, however, been revised by Donohuewho has given reasonably convincing evidence that the molecule as a wholehas a twisted structure (Fig. 5c) with the dihedral angles S-S-S-C andS-S-C-C both close to 90" (cf. dimethyl trisulphide and the groupS-C-C-I coplanar and trans.88A mines, A1 kyhmmonium Sa Its, and Nit roarnines .-Meth ylamine itselfmay be taken as represented by the compound methylamine-boron tri-fluoride,8a although the main interest here lies in the comparison of thiscompound with methyl cyanide-boron trifluoride and the characteristicsof the boron-nitrogen link. The bond distances in the methylamine andmethyl cyanide parts of the molecules appear to be quite normal. Butthe B-N bond, the co-ordinate link, is long in both compounds, and theadditional lengthening in the methyl cyanide compound is correlated bothwith a shortening of the B-F distance and increase in the angle F-B-F,and also with the decreased stability of the substance (Fig.4c and d). Thegeneral arrangement of the atoms conforms to staggered packing, and thehydrogen atons can be placed in the crystal.With the next amine on the list, n-propylamine as hydrochloride, wehave a crystal structure which caused some controversy many years agountil the possibility of chain rotation was rec~gnised.~~ I n the room-temperature structure of n-propylammonium chloride, the cations have adisordered arrangement in relation to the tetragonal axis. They are takingpart either in rotation, or in hindered rotation, about the chain axis as awhole and there seems also rotation about the central carbon-carbon bondwith production of some of the " gauche" or twisted form of chain.At-80" to -90" there is an arrest of the cooling curve of the salt suggesting asecond-order transition, disorder-order, in the solid. The diffraction spotsbecome doubled, indicating break up of the crystal into domains of lowersymmetry. Here the cations are fixed in the planar zig-zag form and liein the (1 TO) planes of the room-temperature structure, with consequent,small changes in lattice constants and symmetry.we reachstable room-temperature structures with an intricately fitted together criss-cross arrangement of the chains. The molecules have a planar zig-zagform with the exception of the terminal C-NH bonds which lie 7-10"from the plane of the other atoms.This is almost certainly caused bythe necessities of packing round the C1 ions, and hydrogen-bond formationwith them, since in the very beautiful structure of hexamethylenediamineWith hexamethylenediamine dihydrochloride 92 and86 J . , 1948, 1256.89 Geller and Hoard, Acta C y s t . , 1950, 3, 121.90 Hoard, Owen, Buzzell, and Salmon, ibid., p. 130.S1 King and Lipscomb, ibid., pp. 222, 227.*a Binnie and Robertson, ibid., 1949, 2, 180.Donohue and Schomaker, J . Chem. Physics, 1948,16, 92.J . Amer. Chem SOC., 1950, 72, 2701.OS Idem, ibid., p. 116442 CRYSTALLOGRAPHY.itself the atoms are coplanar throughout.M In both structures there appearsto be an alternation in the bond lengths along the chain (Fig.6). suggestinghyperconjugation, and the angles within the chain are generally slightlygreater than the tetrahedral. Again hydrogen atoms appear in the electron-density projection.With amine salts having much longer chains, such as the stearyl- andpalmityl-choline salts, of which very approximate electron-density pro-jections have been cal~ulated,~5 the molecular arrangement conforms moreclosely to the ionic double layer-parallel chain type.The two nitramines studied have little relation to the other compoundsin this group. The molecular structures are dominated by the nitro-group.In dimethylnitramine, all the atoms lie in one plane; g6 in s-bisnitramino-114' & 4150 122FIG.6.Interatomic distance8 in (a) hezamethylenediamine, (b) adipic acid, and( c ) glutaric acid.ethane,Q7 the half molecule CH,*NH*NO, is nearly planar. In both, theN-N bond is considerably shorter than the normal single bond distance(Fig. 5b).I n view of the enormous volume of workpublished on long-chain acids and their salts, one is particularly grateful forthe first detailed analyses of some of these compounds, potassium hexanoate(caproate) 51 and strontium l a ~ r a t e . ~ s In both compounds the aliphaticchains have the planar zig-zag structure and the slightly long carbon-carbon repeat interval 2-59,-2.60, A. along the chain agrees well with thatin other structures where the L C-C-C is about 115" and C-C about 1.54 A.I n potassium decanoate, the potassium ions are arranged in a double layer,each surrounded by six carboxyl oxygens, four from two chains on one side,Monobasic Acids and their Salts.94 Binnie and Robertson, Acta Cryst., 1949,2, 424.06 Stora, Compt.rend., 1949, 228, 324; 229, 874; 1950,230, 1675.Costain and Cox, Nature, 1947,160, 826.97 Llewellyn and Whitmore, J . , 1948, 1316.98 Morley and Vand, Nature, 1949, 163, 284HODGKIN AND PITT : ORGANIC COMPOUNDS. 443two from one chain on the other. But within a single decanoate layer,bounded by the ions, the molecules form further layers in which the chaindirections are crossed to one another at angles of about 60". In such astructure, it is not surprising that frequent faults occur in the regulararrangement of the molecules.Measurements of unit cell dimensions have been reported for a numberof other fatty acid salts and acids 99 and it is to be hoped that some of theother structure types reported will soon be known in detail.One interestingpossibility has been proposed for aluminium monolaurate 100-tliat thereare oxygen octahedra present similar to those in alumina, joined by sharingof two corners, the carboxyl oxygen atoms occupying the remaining fourcorners of each octahedron.The appearance, in natural products, of a number of long-chain com-pounds with small branched chains, such as tuberculostearic acid, (-)-lo-methyloctadecanoic acid lol and phthiocerane, which is mainly ( -J-)-4-methyltristriacontane,102 has led to a good many X-ray measurements oftheir different crystalline forms.Usually the compounds show markedsimilarities with the normal straight-chain derivatives; in the case of oneseries of amides, Velick lo3 noticed marked deviations, which he suggestedmight be correlated with the appearance of a spiral-chain configuration.However, later observations indicate the occurrence of different crystallinemodifications here.10P While therefore a spiral carbon-chain structureremains still to be found, definite distortions from the planar zig-zag-chainform do occur in the next group of compounds, the dibasic acids.As a result, principally, of two independent series ofresearches carried out in Holland and at Glasgow, we can now considerdetails of the crystal structures of six different straight-chain dibasic acidsin the interval oxalic to sebacic acid.These are particularly interestingin relation to the marked alternation in physical properties which occursbetween acids of the odd and the even series.As might be expected, the early members of both series, oxalic, malonic,and succinic acids, show deviations from the types of crystal structurecharacteristics of the higher members. Oxalic acid itself crystallises inthree different modifications, a- and p-oxalic acid which are both anhydrous,l06and the dihydrate. Of these, the a-form is unique in that the moleculesare linked in sheets by hydrogen bonds between the oxygen atoms of onecarboxyl group and two other carboxyl groups. Malonic acid has not yetDibasic Acids.Iball, Nature, 1947, 159, 95; Vand, Acta Cryst., 1948, 1, 109; Vand, Aitken, andCampbell, a i d ., 1949, 1, 398; Lingafelter and Jensen, ibid., 1950, 3, 257; Minor andLingefelter, J . Amer. Chem. Soc., 1949, 71, 1145; Witnauer, Lee, and Senti, ibid., 1950,72, 283 ; Kohlhaas, Ber., 1949, 82, 487.loo McGee, J . Amer. Chem. SOC., 1949, 71, 278.Iol S. Stallberg-Stenhagen, Arkiv Kemi, Min., Geol., 1948, 26, A , No. 12.lo2 S . Stallberg-Stenhagen and E. Stenhagen, J . Biol. Chem., 1948, 173, 383; 1950,Io4 Arosenius, Stallberg, E. Stenhagen, and B. Tagstrom-Eketorp, Arkiv Kemi, Min.,183, 223.Geol., 1948, 26, A , No. 19.lo3 J . Amer. Chem. SOC., 1947, 69, 2317.lo6 Hendricke, 2. Krist., 1936, 91, 48444 CRYSTALLOGRAPHY.been studied in detail; only cell dimensions are recorded for the differentvarieties. In all the other crystal structures found, the molecules arelinked in chains with the carboxyl groups of succeeding molecules joinedend to end through hydrogen bonds.I n the dihydrates, the water mole-cules are inserted into the hydrogen-bond system; in all the others, theform of the group -C C- is remarkably constant, whateverthe rest of the crystal structure may be like, with O * * * . O contacts of2.64-2-69 A.The even acids, adipic lo6 and sebacic acid,lo7 are characterised by asimple monoclinic crystal structure in which the molecules are centro-symmetrical. The atoms have a nearly planar zig-zag arrangementthroughout the length of the molecule: in adipic acid the atoms of thecarboxyl group lie in a plane tilted about 6" from the plane of the otheratoms; in sebacic acid this tilt is only 3", in p-succinic acid 9O.108 Thea- and the p-form of succinic acid differ from the higher members chieflyin the relative arrangement of the molecules normal to the chain, thetriclinic or-form approximating most closely to the packing shown by thehigher numbers.lo9The most obvious difference in the crystal structures of the acids of theodd series, glutaric no* 111 and pimelic acid ll1 is that the molecules are nolonger nearly planar, but have a twisted form; even the carbon atoms donot lie strictly in one plane, and the terminal carboxyl groups lie in twoplanes a t about 60" to one another and 30" to the plane of the centre threecarbon atoms.As a whole, the molecules have a, two-fold axis of symmetry,a centre of symmetry being, of course, impossible. It seems very probable,from calculations carried out by MacGillavry et al., that the twisted formof the molecule is responsible for the extra energy content of crystals inthe odd series. The potential barrier to rotation in acetone, m. 1 kcal.,suggests that the extra energy in the odd series molecules would be of theorder of 2 kcals., a difference which corresponds in magnitude to observeddifferences in the heats of combustion. Morrison and Robertson make twoobservations : first, that there is a tendency to alternation in the carbon-carbon bond lengths along the hydrocarbon chains in the even series andno such effect in glutaric acid (Fig.6 ) ; this may be correlated with themolecular twisting; and, secondly, that one very short contact, 3.29 A.,occurs between an oxygen and a carbon atom of neighbouring moleculesin adipic and sebacic acids and not in glutaric acid; this may also affectthe melting point and hardness of the crystals. We have the impressionthat the hydrogen-bond system is the dominating factor in determiningthe crystal structures, molecular compression or distortion occurring asnecessary to fit this with particular conditions of molecular shape.106 MacGillavry,Rec. Trav.chim., 1941,60,605 ; Morrison andRoberteon,J., 1949,987.10' Idem, ibid., p. 993. 108 Idem, ibid., p, 980.109 Riech,Rec. Trav. chim., 1944,63,170. 110 MorrisonandRobertson,J., 1949,1001.111 MacGillavry, Hoogachagen, and Sixma.Rec. Trav. chim., 1948,67, 869./ / O * * * * H O\\O H . . . . O / HODGKIN AND PITT : ORGANIC COMPOUNDS. 445Another series of acids is the series formed by oxalic acid dihydrate 112 andacetylene- 113 and butadiyne (&acetylene) -dicarboxylic acid dihydrates.l14The system by which two succeeding carboxyl groups are linked in a chainthrough the water molecules is the same in all three crystals; all show thevery short hydrogen bond, 2051-2.56 A., between one carboxyl-oxygenatom and the water molecule, here probably an oxonium ion. The systemholds in spite of the fact that oxalic and acetylenedicarboxylic acid areessentially planar and centrosymmetrical molecules, while butadiyne-dicarboxylic acid has, like the odd acid series above, a two-fold axis ofsymmetry and carboxyl groups turned in two planes a t an angle of 57"to one another.The evidence on the bond distances within the oxalicacid molecule itself has been reviewed by Dunitz and Robertson ; 112 theirpreferred values may still have to be modified further after three-dimensionalanalysis. The figures for bond lengths in the acetylenic chains ought to beless liable to change; the most remarkable bond length here is the centralbond length in the diacetylenic acid, the shortest formal single carbon-carbon link so far recorded, 1-33 & 0-02 A. In this molecule, however, thecontraction of the bond lengths does not appear to be correlated withdecreased freedom of rotation, if the relative arrangement is taken asevidence-compare the situation in pentaerythritol tetranitrate discussedabove.Hydroxy-acids : the Tartrates.To tho crystal structure of Rochellesalt,l15 sodium potassium tartrate tetrahydrate, we can now add those ofsodium potassium DL-tartrate tetrahydrate,ll6 D,-tartaric acid,l17 andracemic acid,li8 a group of crystals interesting on account both of Pasteur'soriginal work on molecular asymmetry and also of the electrical propertiesof Rochelle salt.In all four crystal structures the asymmetric tartaric acid moleculemaintains essentially the same relative arrangement of the atoms present :the two groups HO'C-CRo are both closely planar and are arrangedwith their planes a t an angle of approximately 60" to one another. Thereis a certain similarity between the packing of the molecules in the two salts,which is partly controlled by the requirements of the ions.The differencesintroduced by the centre of symmetry and the changed hydroxyl-grouprelations in the crystal of the racemate are however enough to destroy theunidirectional series of hydrogen bonds found in Rochelle salt, and hencethe development of abnormal electric properties. The relation between theexact atomic positions and these properties in the Rochelle salt crystal isin any case very sensitive, as illustrated by the correlation found byUbbelohde and Woodward between the thermal expansion and the dielectric\OH112 Dunitz and Robertson, J., 1947, 142.113 Idem, ibid., p.148.115 Beevers and Hughes, Proc. Roy. SOC., 1941, A , 177, 251.116 Sadanaga, Acta Cryst., 1950, 3, 416.11' Stern and Beevers, ibid., p. 341.11* Idem, ibid., p. 1145.11* Parry, Nature, 1949,164, 885446 CRYSTALLOGRAPHY.constant of the crystal,llg and also by the effect of altering the proportionsof the ions in the crystals.120 The view that the crystal between the twoCurie points consists of domains of lower symmetry has received someadditional confirmation from measurements on the integrated intensityof X-ray reflections.121 These are higher between the Curie points thanabove them, as might be expected from the imperfect kind of crystalformed. Changes in the size and nature of the domains might account forthe marked effect that certain impurities such as cupric ion and boric acidalso have on the electric properties of crystals grown in their presence.The differences between the crystal structures of D-tartariC and racemicacid are pronounced.In the racemic acid crystal unit there are only twomolecules related by a crystallographic centre of symmetry. But, as ex-pected, there is no definite pair association of D- and L-units, no racemic acidmolecule present, but an over-all hydrogen- bond system holding the moleculesin the crystal. Parallel to the a axis, columns of D- and L-molecules are con-nected by a square system of hydrogen bonds between the hydroxyl groups.End to end, D- and L-molecules are also linked through one pair of carboxylgroups as in the other dibasic acids described.The second carboxyl groupin each case makes contacts with both carboxyl- and hydroxyl-oxygenatoms of neighbouring molecules. In D-tartaric acid, the system of hydrogenbonding is necessarily different from that in racemic acid. The two moleculesin the unit are related by a screw axis of symmetry and in this crystalstructure there is no pairing of carboxyl groups of neighbouring moleculesof the dibasic acid type. Instead a more complex linking of carboxyl groupswith hydroxyl groups is present.One particularly interesting point about the D-tartaric acid crystalstructure is that correlation of the molecular arrangement found with theface development of the crystals would permit a determination of the absoluteconfiguration of the molecule.This has been attempted by Waser,122but it is doubtful whether our knowledge of the factors affecting crystalgrowth is sufficient to feel complete confidence in his assignment 123-~hi~his the exact opposite of Fischer’s assumed arrangement.Amino-acids and Peptides. The X-ray analysis of the amino-acidL,-threonine 38 establishes unambiguously the stereochemical relationbetween the sugar-lactic acid and the amino-acid series.124 The relationis the one derived as most probable by the original observations of Meyer andRose,126 following the first isolation of threonine, and recently independentlyestablished through kinetically-controlled chemical reactions.12s It is shown inFig. 7 by a perspective drawing of the threonine molecule, which illustratesboth the arrangement of the atoms and the bond lengths within the molecule.119 proc.ROY. soc., 1946, A , 185,448.110 Thorp and Buckley, Acta Cryst., 1949, 2, 333.121 Mujake, ibid., p. 192.123 Turner and Lonsdale, J. Chem. Physics, 1950,18, 166.12* Cf. Neuberger, Adv. Protein Chem., 1948, 4, 297.126 J . Biol. Chem., 1936, 115, 721.126 Brewster, Hughes, Ingold, and Rm, Nature, 1950, 166, 178.laa J. Chm. P h y e h , 1949, 17, 498HODGKIN AND PITT : ORGANIC COMPOUNDS. 447The crystallographic investigation of threonine constitutes the mostcomprehensive and thorough study yet undertaken of an asymmetricmolecule and provides a fund of useful information on the technique ofcrystal analysis. The full, three-dimensional electron-density distributionhas been calculated six times in the course of refinement-until recentlya single such calculation would have been considered to involve an impossibleamount of labour.The electron-density distribution shows the positionsof hydrogen atoms as separate, but not very precise, maxima, and enablesthe positions of all the remaining atoms to be fixed with a high degree of?0 0I L.540 0NH1.48o--- - 0 q 2 1.29 C 1-31 1.510 <:2 C 1.27(di O(c) ?&-56FIG. 7 .Interatomic distances in (a) threonine, (b) alanine,( c ) acetylglycine, and (d) 8-glycylglycine.precision. The C-N distance, 1.49 A., is close to that expected from thesum of the covalent radii, and it is clear that the short values reportedearlier for glycine and alanine 12’ were based on insufficient refinement ofthe data.Both have been found to be normal from recent three-dimensionalanalyses.Within the threonine molecule it is noticeable that the staggered arrange-ment of the atoms is very precisely observed, so that the contacts betweennon-bonded atoms are of the most favourable form-even to placing thehydrogen of C(3) in the gap between NH3+ and C0,- rather than the largerOH and CH, groups. At the same time, a high density of packing of themolecules in the crystal is achieved with all the hydrogen atoms of the1-2’ Donohue, J. Amer. Chent. SOC., 1950, 72, 949448 CRYSTALLOGRAPHY.NH3+ and OH groups involved in hydrogen bonding. It is clear from thedistribution found for the hydrogen atoms that the molecule has thezwitter-ion structure.There is one comparatively short distance, 3.28 A . ,between one carbon atom and the hydroxyl group.The analyses of other amino-acids reported as begun during these years-glycylglycine hydrobromide,12* DL- and ~-leucine,l~~ and L-proline 130-have not yet reached the stage at which interatomic distances can be given.But two analyses, those of acetylglycine 131 and of @-gIycylgly~ine,~~~provide a useful basis for the theoretical construction of extended peptidechains.133 Both molecules are planar or very nearly so; in glycylglycinethe terminal nitrogen atom only is out of the plane of the other atoms. Itis noticeable that the C-0 distances in the acetylglycine carboxyl group,which has no zwitter-ion character, are markedly asymmetric, correspondingto not greatly modified C=O and C-OH distances.Apart from this:the crystal structures have considerable similarity ; in both, the moleculesare linked in sheets by hydrogen bonds between carboxyl, keto-, amino-,or imino-groups. In both, one can see a formal relationship to the extended@-form of peptide-chain structure, though the sideways linking in one caseinvolves C0,H and NH groups, in the other case C=O and NH,, and inneither case the postulated C=O * * NH bonds of the @-keratin structure.NH linking occurs are, however,well established by the work of Bunn and Garner and others on certainpo1yamides.la These are fibres and give only limited X-ray diffractiondata; 135 consequently the position of the atoms cannot be very preciselyfixed.But they are sufficiently clear to prove that here too the moleculesare held in sheets, the oxygen-nitrogen separation of neighbouring moleculeswithin the sheets being 2-8 A. The sheet thickness, 4.4 A., compares verywell with the backbone spacing of the @-keratin type of fibrous protein.Alicyclic Ring Systems. With the alicyclic ring compounds stereo-chemical problems are again dominant. Few of the X-ray analyses in thisseries are sufficiently accurate for the interatomic distances found to beworth reporting, but there are one or two interesting exceptions.No cycbpropane derivative has yet been analysed in detail by X-raymethods. For completeness, we may quote Skinner's conclusion 136 thatthe ring-carbon atoms are arranged in a regular equilateral triangle of siderather smaller than 1.54 A., in accordance with certain quantum-mechanicalcalculations.In all the cyclobutane derivatives studied on the other hand, the carbon-carbon distance has proved, unexpectedly, greater than normal.The mostcareful analysis is that of the centrosymmetrical isomer of 1 : 2 : 3 : 4-Structures in which the C=O * - -128 Barney, Amer. Min,, 1947, 685.130 Wright and Cole, Acta Cryst., 1949, 2, 129.131 Carpenter and Donohue, J . Amer. Chem. SOC., 1950,72, 2315.132 Hughes and Moore, ibid., 1949, 71, 2618.133 Corey and Donohue, ibid., 1950,72, 2899.135 Beauvalet, Champetier, and Tertian, Compt. rend., 1949, 228, 2028.136 Nature, 1947,160, 902.ltO Moller, Acta Chem.Scand., 1949, 3, 1326.13' Proc. Roy. SOC., 1947, A , 189, 39HODGKIN AND PIl'T: ORGANIO COMPOUNDS. 449tetraphenylcycZobutane,m which is formed by the photochemical dimerisationof stilbene. The analysis of this compound was undertaken, in the firstinstance, to establish the nature of the toxic irradiation-product of the drug" Stilbrtmidine," from which it had been obtained. The crystal structureshowed both that the four-membered ring was present, and that the phenylgroups were disposed centrosymmetrically round it. As a result, this arrange-ment is different in relation to the two adjacent bonds in the four-memberedring alternately, cis and trans, which may account for the fact that thesebonds appear to be of unequal length, 1.585 and 1-555 A.respectively.The other X-ray analysis of a four-membered ring derivative, that ofthe centrosymmetrical dimer of acenaphthylene,l3' is not complete, but ittoo shows bonds in the ring which are longer than 1.54 A . Bond iengtheningalso appears very markedly from the electron-diffraction data on octafluoro-cyclob~tane,l~~ for which the carbon-carbon distance in the ring is given&s 1.57-1-62 A. and the ring appears to be non-planar. The lengtheningof the bond is probably correlated with a greater proportion of p-bondcharacter, the angle between the C-C valencies in the ring being nearly90". Repulsion between non-bonded atoms must also have an efrect.Certainly with five- and six-membered rings, it is clear that the packingof non-bonded atoms plays a dominant part in determining their overallarrangement.The five-membered carbon rings so far observed are allnon-planar, usually with one atom out of a plane formed by the other four.They include the five-membered rings in bromo-, chloro-, and cyano-camphor 139 and ring D of cholesteryl iodide 140 and calciferol 4-iodo-5-nitr0ben~oate.l~~ In almost all cyclohexane derivatives so far studied,including the cis-decalins, the ring has the staggered or chair form. Onlyin the camphor derivatives mentioned does the boat form appear, imposedby the fusion with five-membered rings. In 1 : 2-epoxycy~Zohexane,~~~ring fusion again imposes a constraint but the atomic arrangement foundby electron diffraction is still approximately staggered.The simpler derivatives of cyclohexane, the hydrocarbon itself,143 cyclo-hexanol,lqq and dodecafluoracy~lohexane,~~~ crystallise in cubic cells inwhich the molecular arrangement is considerably disordered. The mole-cules appear not to be freely rotating, but to have certain preferred orient-ations in relation to their neighb0~rs.l~~ With additional hydroxyl groupsattached, the cyclohexane molecule can be readily held in a fixed position.Particularly good examples are provided by a-phloroglucitol dihydmte 58and diarnm~niate.~~ The molecules have trigonal symmetry, which13' Dunitz and Weissman, Acta Cryst., 1949,2, 62.13* Lemaire and Livingston, J.Chem. Physics, 1950,18, 569.13D Wiebenga and Krom, Rec. Trav. chim., 1946,65, 663.140 Carlisle and Crowfoot, Proc.Roy. SOC., 1945, A , 184, 64.141 Crowfoot and Dunitz, Nature, 1948,162, 608.I r a Otter, Acta Chem. Scand., 1947, 1, 283.143 Oda, X-Rays, 1948, 5, 26.145 Christoffers, Lingafelter, and Cady, J. Amer. Chem. SOC., 1947, 89, 2502.14* King and Lipscomb, Acta Cryst., 1950,3, 155.144 Oda, ibid., 1949, 5, 95.REP.-VOL. XLVII. 450 CRYSTGOGRAPHY .establishes their stereochemical form (Fig. 8), and are linked in threes roundwater or ammonia molecules which form a fourth bond between one another.It is dficult to summarise adequately the crystal analyses of the veryinteresting group of different halogenated cyclohexanes-all of which involvethe determination of the nature of the stereochemical isomer present, andin two cases, those of the hexachlorocyclohexane, m.p. 145",14' and tetra-chlorocyclohexane, m. p. 174", the carbon atoms to which the chlorineatoms were attached. " Gammexane," 148 as an insecticide, is the mostimportant of these compounds. The molecule proves to have the structureshown in Fig. 8, which was unexpected since it had been supposed thatsteric hindrance might prevent altogether the formation of the isomer withchlorine atoms a t 1 and 3 both in the erect position. There is a slightdistortion of the molecule as a result-the bonds C,l,-Cl and C,3,-CI are notquite parallel, but the distortion is small. The same problem does not arise inthe case of the other isomers studied, vix., 6- lg9 and ~-hexachlorocycZohexane,150though all show small deviations from the quite regular form of the moleculesindicated in Fig.8, which all should have planes of symmetry. 1 : 2: 4: 5-Tetrachlorocyclohexane, m. p. 174", and 1 : 2 : 3 : 4-tetrabromocycZohexane,m. p. 142", both have two-fold axes of syrnmetry;l5l in the first case i tshould be possible to separate the crystals by hand into (+)- and(-)-forms. Actually one polymorphic modification of 1 : 2 : 4 : 5-tetra-bromocyclohexane, m. p. 218", was picked out by hand from a mixture ofcrystals and the molecule proved by X-ray analysis to have the structuregiven in Fig.Rings in which methylene groups have been replaced by oxygen atomsor imino-groups have not been so fully investigated but appear from thefew known examples to have similar stereochemical characteristics.Theseexamples include di-iodomethyloxacycZobutane,153 the furanose and pyranoserings of the sugars discussed in the next section, and 1 : 4-dichloropipera~ine.~~It should be possible to get really good measurements from di-1 : 3-dioxa-~yclopentyl,~~~ the chemical structure of which was found by the calculationof a Fourier projection from data on crystals which had been supposedpreviously to be a cis-decalin type of isomer of naphthodioxan.The crystal structures of three sugars have recentlybeen analysed or partly analysed : r~-D-ghCOSe,l~~ difructose strontiumCarbohydrates.Ellefsen, Hassel, and Wang Lund, Acta Chem. Scand., 1950, 4, 1145.148 van Vloten, Kruissink, Strijk, and Bijvoet, Acta Cryet., 1950, 3, 139; Nature,149 van Bommel, Strijk, and Bijvoet, ?roc.K . Akud. Wetensch., 1950, 53, 50.l50 Norman, Acta Chem. Scand., 1950,4, 251.151 Hassel and Wang Lund, ibid., 1949, 3, 203; Acta Cryst., 1949, 2, 309 ; Mrang152 Haak, Thesis " De berciding en structure van cyclohexadieen-1, 4 en van enige153 Toussaint, Bull. SOC. roy. Sci. Likge, 1948,1, 18.154 Anderson and Hasel, Acta Chem. Scand., 1949, 3, 1180.155 Dano, Furberg, and Hasel, ibid., 1950, 4, 965.156 McDonald and Beevers, Actu Cryst., 1950, 3, 394.1948,162, 771 ; Rec. Truv. chim., 1948,67, 777.Lund, Acta Chem. Scand., 1950, 4, 1109.derivaten," P. Harte, Bergen op Zoom, 1948HODGKIN AND PITT : ORUANIC COMPOUNDS. 451chloride trihydrate,l57 and sucrose sodium bromide dihydrate.lS8 Thedetermination of the structure of a-D-ribofuranose is also involved in theanalysis of ~ y t i d i n e .l ~ ~ I n all cases the stereochemical arrangement ofthe hydroxyl groups, predicted on chemical grounds, is confirmed. Thisincludes the cis-arrangement of the 1- and the 2-hydroxyl group in the twoor-glucose units.Tetrachloroc yclohexane,m. p. 174".(a)a-Phloroglucitol.(b)&Tetrabromoc yclohexane,m. p. 218'.(4'' Qammexane." 8-Hexachloroc yclohexane.(4c-Hexachloroc yclohexane. Hexachloroc yclohexane,FIG. 8.Stereochemical form of some substituted cyclohexane derivatives.m. p. 145".Both the glucose ring and also the fructose ring in the strontium chloridecomplex are six-membered in the Sachse trans-configuration. In sucrosethe fructose ring is five-membered as expected, and non-planar, one carbonatom being removed from the plane of the other four.Bond lengths arenot accurately determined in any of these compounds, but the ct-D-g1uCOSecrystal structure is being further refined and should provide a good set ofmeasurements. All the hydroxyl groups in both this and the sucrosestructure are involved in hydrogen-bond formation. I n ct-D-ghCOSe, as1 5 7 Eiland and Pepinsky, Acta Cryst., 1950, 3, 160.1 5 8 Beevers and Cochran, Proc. Roy. SOC., 1947, A, 190. 257.150 Furberg, Acta Cryst., 1950, 3, 325.REP.-VOL. XLVIL P 452 CRYSTALLOGRAPHY.in cytidine, the ring-oxygen atom itself appears to be bonded to the hydroxylgroup of a neighbouring molecule.A consideration of the stereochemical conditions obtaining in pyranoseand in cyclohexane rings has led Hassel and Otter to suggest a new way oflinking P-glucose units in a chain with an 8-5-A.period 160 that may corre-spond to the arrangement in many natural polymers, such as alginic acid,which show periods of this kind. This arrangement seems more probablethan that put forward originally by Astbury.lG1 For cellulose itself, inspite of much controversy, the structure proposed by Meyer and Mischstill seems the most likely.162 A three-fold spiral arrangement is suggestedby the cell dimensions found for cyanoethyl cellulose. 163More complicated unit cells are found among starches, and varioustentative structures involving helical arrangements of the molecules havebeen proposed for different forms.16* The variety known as V-amylose,starch, or amylose precipitated from alcohol forms a lattice which suggeststhat the glucose residues are arranged in a six-fold helix of external diameterroughly 17 A.and height 7.9 A., and this idea receives some confirmationfrom an exceedingly rough Fourier projection derived by comparison withthe iodine ~omp1ex.l~~ The iodine fits into the column surrounded by thehelix, and observations by West suggest that the iodine molecules dis-sociate ; l 6 6 characteristic diffuse layer lines appear indicating a layerinterval of 3.1 A. in the direction of the iodine column.The very interesting Schardinger dextrins form true crystalline latticesfrom which the molecular weights of the units present may be calculatedin the usual way.They correspond to six, seven, and eight glucose residuesrespectively for a-, p-, and y-Schardinger dextrins; 16' more than onepolymorphic modification appears to exist for the a- and the p-dextrins.D. C. H.Aromatic Compounds.-The structures of aromatic compounds have forsome time been studied very largely because they provide a wide variety ofexamples of bonds the characters of which are intermediate between singleand double. This applies not only within the ring systems, but also in thebonds from the rings to substituting atoms or groups, and in the latterinstance in particular has a bearing on the chemical reactivity of the sub-stituents. While earlier work was of interest in indicating qualitatively thesevariations of bond length, it is only in the past few years that advances incrystallographic computing methods, and in the theoretical methods of calcu-160 Acta Chem.Scand., 1947, 1, 929.162 van der Wyk and Meyer, J . Polymer Sci., 1947, 2, 583.1e3 Happey and MacGregor, Nature, 1947, 160, 907.164 Kreger, ibid., p. 369; Rundle, ibid., 1948, 162, 107; Senti and Witnauer,166 J . Chem. Physics, 1947,15, 689; cf. Rundle, ibid., p. 880.1 6 7 Borchert, 2. Naturforsch., 1948, 3b, 464; cf. Gruenhut, Cushing, and Caesar,161 Nature, 1945, 155, 667.J . Amer. Chem. SOC., 1948, 70, 1438. 165 Rundle, ibid., 1947, 69, 1769.J . Amer. Chern. Soc., 1948, 70, 424HODGKIN AND PITT : ORGANIC COMPOUNDS. 453lating bond characters and bond lengths, have made possible a detailedcomparison of experiment and theory. The calculations on both sides areeven now very long and arduous, so that a full correlation can be expectedonly for a relatively small number of compounds. This correlation has beenachieved for a few of the compounds discussed below, but in many of the othercases there are fresh indications of the occurrence of bonds of intermediatecharacter.Naphthalene and anthra-cene were among the first organic crystals to be analysed by X-ray methods,and the recent full three-dimensional analyses (Fig.3) by Robertson and hisco-workers ~ 4 0 are of particular interest in confirming and extending theprevious findings. The bond lengths found are shown in Fig. 9, and thecorrelation between the chemical reactivity of the a-p-bonds and theirrelative shortness is immediately apparent.The authors claim that errors inthese bond lengths should not exceed 0.01 A., and they observe that bondsCurbocyclic Compounds.-(a) Hydrocarbons.1.359 1.420 1364 1.419 1.391(1.395) (1.450)FIG. 9.Aromatic hydrocarbons : (a) naphthalene ; (b) anthracene. Observedand calculated (parentheses) bond lengths are shown.which are crystallographically different but chemically identical have lengthswhich differ by about 0.01 A. This however raises the difficult question ofthe distortions caused by the packing of molecules in a crystal lattice, whichappear to be noticeable in certain cases where observations of both the crystaland the vapour have been made. It may be pointed out that no correctionhas as yet been applied for series-termination errors.Superposition of the simple Kekul6-type structures is insufficient in thecases of naphthalene and anthracene to explain the observed bond lengths,but it is now recognised that the contributions of the excited states mustbe included if a quantitative estimate is to be made.The bond lengths fromsome recent wave-mechanical calculations 16** 169 are shown in parentheses inFig. 9.Further investigations by two-dimensional Fourier methods have beenreported on pyrene (1),170 1 : 2-5 : 6-dibenzanthracene (11),171 1 : 12-benzperylene ovalene (octabenzonaphthalene) (IV),173 and triphenyl-16* Vroelant and Daudel, Compt. rend., 1949, 228, 399.lag Daudel and Daudel, J .Chem. Physics, 1948,16, 639.170 Robertson and White, J., 1947, 358.171 Idem, ibid., p. 1001.173 Donaldson and Robertson, Nature, 1949, 164, 1002.172 White, J . , 1948, 1398454 CRYSTALLOGRAPHY.ene (V),174 and in all cases bond lengths of intermediate character have beenfound. It would be unreasonable to expect very close correlation between(111.)these experimental measurements and the results of calculations based onthe simple non-excited Kekul6 structures, but in fact in a number of in-stances there is quite good qualitative agreement. This sometimes improvesslightly if the contributions of the various Kekul6 structures are weightedaccording to their benzenoid character, lending support to the Fries rule thatstructures with benzenoid rings are more important than those with quinoinoidrings.175Another modification of hexamethylbenzene has been reported, stablebetween 110" and the melting point (165°).176 It is more symmetrical thanthe form stable a t ordinary temperatures but very closely related to it.Thelattice energy and thermal expansion have been discussed by Seki andChihara.177( b ) Benzene derivatives : halogen compounds. The sequence of compounds,pdichloro-, p-bromochloro-, p-dibromo-benzene, was first shown by Hen-dricks to be isomorphous. More recent work 178 has verified that the bromo-chloro-compound has a statistical structure, the chlorine and bromine atomsoccupying two sets of crystallographically different positions a t random.The bonds from the benzene ring appear equal, 1.77 A., a value intermediatebetween that for C-C1 (1.69) found in the dichloro-compound and that forC-Br (1.84, 1-88) in the dibromo-compound. In p-chloroiodoxybenzene 179the 10, plane is almost a t right angles to the benzene ring, the 0-1-0 anglebeing 103".The 1-0 distances are shorter than usual (1.60, 1.65 A.) and theiodoxy-groups of neighbouring molecules approach one another very closely.The chlorine atom is displaced from the plane of the benzene ring, and theI-C bond does not make equal angles with the adjacent sides of the ring.17* Klug, Acta Cryst., 1950,3, 165.1 7 6 Watanctb6, Ssito, and Chihara, Sci. Papers Osaka Univ., 1949, No. 1, p. 9.177 Ibid., p. 1.1 7 ~ Archer, Acta Cryst., 1948, 1, 64.175 Robertson, ibid., 1948,1, 101.178 Klug, Nature, 1947, 160, 570HODGKIN AND PITT : ORGANIC COMPOUNDS. 455(c) Nitrogen compounds.The crystal structure of p-dinitrobenzene cannotyet be considered t o be entirely satisfactorily elucidated. The early work,based on Fourier projections, led James, King, and Horrocks to the conclusionthat the molecule was centrosymmetrical but distorted so that the benzenering was not regular, the nitro-groups not coplanar with it, and the N-0distances unequal. Criticism of these distortions by Pauling led to a repeti-tion of the analysis by Llewellyn lSo utilising three-dimensional methods forgreater accuracy. He obtained a set of atomic co-ordinates which gave a,disagreement factor of 0.24, and he stated that they corresponded to a planarmolecule, a regular benzene ring and equal N-0 distances, whereas in factthey require angles of l l + O between the planes of the NO, groups and the ben-zene ring.An independent investigation by Abrahams lS1 seems to indicatethat there is a small angle between these planes, but it is clear that morecareful three-dimensional analysis is required if the finer details of thestructure are to be elucidated. As reported in 1946, the structure of m-dinitrobenzene was reconsidered by Archer 18, and the reputed space-groupshown to be incorrect. A new trial structure was proposed and the principalFourier projection of the unit cell calculated; this showed the moleculealmost completely resolved, but gave no reliable evidence of any smalldeviations of the nitro-groups from the plane of the benzene ring; this hasbeen independently confirmed by Gregory and Lassettre.ls3 The bondlengths quoted in these two accounts are not identical but, since the structureis one in which there is adequate resolution in only one projection, it isunjustifiable to attach any quantitative significance to the deviations found.I n p-nitroaniline the evidence is in favour of a symmetrical nitro-groupcoplanar with the benzene ring, the N-0 distances being slightly greaterthan those found in the dinitrobenzenes, while the C-N distances appearto be somewhat short.Considerable interest centres on the remarkablyclose approach of one oxygen atom to the carbon atoms of the adjoiningmolecule : distances of 2-66, 2-99, and 3-03 A.are found, all much shorterthan the normal van der Waals value of 3-4 A. It is suggested that a powerfulattraction, possibly of an electrostatic nature, exists between the atomsconcerned, a self-complex being formed by the nitro-group of one moleculeacting as ‘‘ acceptor ” while the benzene ring of another molecule acts as“ donor.’’ Independent evidence of complex formation in p-nitroanilinecomes from the ultra-violet absorption spectrum and the entropy of vaporis-ation, and the authors incline to the view that this attraction may be thecause of some molecular complexes formed between aromatic nitro-compoundsand polycyclic aromatic hydrocarbons although no evidence of short inter-molecular distances has as yet been found.By analogy with the propertiesof structures involving short hydrogen bonds between molecules, it would beexpected that the thermal expansion parallel to the short intermolecularC-0 linkage would be anomalous. This has been confirmed by McKeown,lSo J., 1947, 884.lB2 PTOC. Roy. SOC., 1947, A , 188, 61.lS1 Acta Cryst., 1950,3, 194.lS3 J. Arner. Chem. SOC., 1947,69, 102456 CRYSTALLOGRAPHY.Ubbelohde, and Woodwardl84 who find for the total contraction from288" K. to 90" K. the coefficients :(at 55" to c axis, i.e., within 11" of direction of short" bond "),(parallel to 71)all : 2.95 xa22 : 0-24 xam : 0.45 xThe molecular complexes of 4 : 4'-dinitrodiphenyl with diphenyl, 4-bromo-and 4-iodo-diphenyl, benzidine, etc., have been shown to be all of the sametype as that previously described with 4-hydroxydiphenyl, the proportionsof the two components being determined by geometric factors.The com-plexes with 4-bromo- and 4-iodo-diphenyl show diffuse X-ray scatteringexplained in terms of random displacements of the latter component alongthe holes in the lattice of dinitrodiphenyl molecules. No close intermolecularapproaches appear to occur in these complexes.185* 186* 18'The mode of dimerisation of nitrosobenzene has previously been uncertain,but two independent investigations (of dimeric p-bromonitrosobenzene 188and dimeric tribromonitrosobenzene 189) have shown conclusively that themolecular formula is (VI) and not e.g. (VII), the positions of the formalR'charges not being definitely known owing to the approximate nature of thebond lengths so far determined.I n the p-bromo-compound the molecule iscentrosymmetrical, the planes of the benzene rings being parallel butstaggered (cf. dibenzyl), whereas the tribromo-molecule has a two-fold axisof symmetry, the benzene rings being twisted in opposite directions by about72" from the plane of the nitroso-groups. The difference is probably due tothe effect of the extra bromine atoms which have to be packed in.Aniline hydrochloride and hydrobromide form ionic structures of differingtypes. I n the former,s2 all the cations point in the same direction in thelattice and each nitrogen atom has three contacts with chlorine ions at3.17 A. ; the chlorine ions are more than 5 A.apart, and the determining factorin the packing is the size of the cation, In the hydrobromide lgo howeverthere are cations facing in opposite directions, lying on the two-fold axesin the space-group P2,22,. Each nitrogen atom makes contact with fourbromine ions at about 3-5 A., and the arrangement is somewhat similar tothat in some alkylammonium halide structures.la* Nature, 1950, 166, 69.18* James and Saunder, ibid., p. 518.la' van Niekerk and Saunder, Acta Cryst., 1948,1, 44.la8 Darwin and Hodgkin, Nature, 1950,166, 827.lBg Fenimore, J . Amer. Chem. SOC., 1950, 72, 3226.loo Nitta, Watanabe, and Taguchi, X-Rays, 1948,5, No. 1, p. 31.186 Saunder, Proc. Roy. Soc., 1947, A , 190, 508HODGKIN AND PITT : ORGANIU COMPOUNDS. 457The polymorphism of p-iodo-N-picrylaniline has been studied byGrison with some very interesting results.57 Three crystalline varieties(red, orange, and yellow) all appear together on recrystallisation of any one.The orange is the stable variety a t ordinary temperatures; the red form isstable at temperatures near the melting point ; and the yellow form is meta-stable.X-Ray analyses demonstrate that the molecule preserves itsstereochemical form almost unchanged in all three forms; only in the redform is there a slight reduction of the valency angle at the amino-nitrogenatom, the molecule becoming a little more compact. This together withother minor differences can be interpreted as the outcome of rotations aboutthe single C-N bonds according to the exigencies of packing; for example,steric interactions appear to be the governing factor in the inclination of thenitro-groups to the plane of the benzene ring. The polymorphism is thuscaused by the same molecules being packed in three different stable ways,The energies of the three forms must be nearly equal since they all appearNFIG.10.s p- p- Chlorobenzaldoxine molecule, with hydrogen bonds (broken).simultaneously from solution. A further form, obtained when a melt iscooled, and described as vitreous, clearly represents the result of moleculesbeing unable to take up one of the stable packing arrangements. The pres-ence of a hydrogen bond between the amino-nitrogen atom and one of theoxygen atoms of an o-nitro-group is thought to explain the absence of basicproperties in the picrylanilines.Some fairly short intermolecular distances(about 3 A.) occur in all three structures.with polarised infra-red radiation led topredictions of the directions of the C,H,-N, N-H, C=O, and C-CH, bondsin the structure of acetanilide which facilitated the early stages of determin-ation of the atomic co-ordinates. A short note by Brown and Corbridge 192gives the arrangement of the molecules in the unit cell, linked in chains byN-H-0 bonds, but does not claim sufficient accuracy to warrant discussionof the bond lengths.The structure of syn-p-chlorobenzaldoxime confirms the configurationwith the hydrogen atom attached to carbon and the oxygen atom attached tonitrogen on the same side of the C-N double bond.lg3 As shown in Fig.10,lD3 Jerslev, ibid., 1950,166, 741.Observations, by191 Nature, 1947,160, 17. lea Ibid., 1948,162, 72458 CRYSTALLOGRAPHY.the nitrogen and the oxygen atoms of adjacent molecules are engaged inhydrogen bond formation in a manner which makes it possible that thehydrogen atoms are at XX or YY. If it is accepted that the rules of stereo-chemistry apply with smaller force to the atom on the side of the hydrogenbond remote from the hydrogen atom (Pauling),lS4 then the hydrogen atomswould be placed at XX, and thus the molecular formula would be (VIII).While this is of interest in connection with N-ether formation by oximes, itis in conflict with generally accepted views that, if tautomerism occurs, theequilibrium is strongly on the side of (IX).A detailed investigation of thecrystal structure might settle this question in the way that the lactam-lactim controversy in isatin was settled (see below).(d) Salts and esters ; ethers. Zinc and magnesium benzenesulphonatesare isomorphous, crystallising with six water molecules per X(C,H5*S03),.195Both structures may be described as consisting of sheets of metal atomssurrounded by regular octahedra of water molecules and separated by sheetsof benzene rings; the oxygen atoms of the sulphonate groups are hydrogen-bonded to the water molecules at distances ranging from 2-72 to 2.86 A.The S-C and S-0 distances appear to be normal, the valency angle of thesulphur atom being tetrahedral. The isomorphous zinc and magnesiumtoluenesulphonates have closely similar structures,1s6 the a axis of the unit cellbeing lengthened to accommodate the extra methyl groups.I n potassium hydrogen bisphenylacetate 197 there are again planes ofmetal atoms separated by the aromatic rings, but in this case the oxygenatoms of the carboxyl groups make up the octahedral co-ordination about themetal atoms.The potassium and hydrogen atoms must occupy specialpositions in the unit cell, and it is found that the potanssium atoms lie on two-fold axes; the hydrogen atoms must therefore lie a t centres of symmetry,halfway between oxygen atoms 2.55 A. apart. This situation is similar tothat reported for trona (Na,C03,NaHC03,2H,0) .lS8Aromatic esters have not until recently been studied in detail by X-rayor electron-diffraction methods.Although the structure assigned todiethyl terephthalate lS9 is not claimed to have the highest accuracy itshows that the molecule is planar except for a tilt of the ethyl groups of about9", and that the C-0 bond to the ethyl group is unusually long (1.510.05 A.). The structure is built up of layers between which the ethyl groupsand ketonic oxygen atoms make contact at about 3.5 A.The structure of quinol dimethyl ether provides evidence that theralency angle of oxygen is here about 120", in general agreement with the" The Nature of the Chemical Bond," Cornell, 1939.ls5 Broomhead and Nicol, Acta Cryst., 1948, 1, 88.lS6 Hargreaves, Nature, 1946, 158, 620.lug Ann. Reports, 1949, 46, 82.lS7 Speakman, J., 1949, 3357.Bailey, Acta Cvyst., 1949, 2, 120HODGKIN AND PITT : ORGANIC COMPOUNDS.459expectation of Sutton and Hampson.200 In the crystal the molecules assumea planar tram-configuration, and there is no indication of rotation of themethoxy-groups. Although the molecule is centrospmetrical in the crystalit cannot be so in solution, where a dipole moment has been observed. TheC-O-C angle appears to have the same magnitude in di-p-iodophenyl ether.201There is considerableinterest in the question of the planarity or otherwise of diphenyl derivatives.Diphenyl itself is known to be planar in the crystalline state because thespace-group demands a centre of symmetry in the molecule; 202 electron-diffraction studies of its vapour 203 however indicate that the two benzenerings must be inclined to each other a t an angle of about 45".Ultra-violetabsorption measurements confirm that the molecule is planar in the crystal,and non-planar in the vapour, and also show it to be non-planar in solution,as confirmed by measurement of a dipole moment.204 The steric repulsionbetween the 2 : 2'-hydrogen atoms tends to make the free molecule take up anon-planar form in opposition to the tendency towards coplanarity due toconjugation ; in the crystal lattice the additional effect of intermolecularforces may be sufficient to make the planar configuration the more stable.(In 2 : 2'-dipyridyl 205 the effect of steric forces between the hydrogen atomsis eliminated if the nitrogen atoms are trans to the 1 : 1'-bond, and in thecrystal structure this configuration has in fact been proved, the moleculebeing again strictly planar. The fact that the ultra-violet absorption spec-trum of 2 : 2'-dipyridyl in solution is similar to that reported for diphenylhowever seems to indicate non-planarity in the free molecule.) 3 : 3'-Dichlorobenzidine, 3 : 3'-dibromodiphenyl, and 3 : 5 : 3' : 5'-tetrabromo-diphenyl deviate from the cis-planar form by about the same angle asdiphenyl in the vapour state,206 whereas in solid 3 : 3'-dichlorobenzidine thechlorine atoms are tram and the molecule is planar, or approximately ~0.207In gaseous 2 : 2'-dichloro-, 2 : 2'-dibromo-, and 2 : 2'-di-iodo-diphenyl thephenyl rings are rotated from the cis-planar position so that the anglebetween them is about 75°.206 A similar configuration is found in crystalline2 : 2'-dichlorobenzidine (72") 208 and m-tolidine dihydrochloride (71") ; 209 inthese structures the bond joining the phenyl rings is equal in length, withinexperimental error, to a single C-C bond, but the lengths of some of the bondsin the phenyl rings may be abnormally short.When the two benzene rings are linked not by a single bond but throughone or more atoms, the valency angles at the latter influence the molecularconfiguration. In diphenylmercury the valency angle at the mercury atomis 180", and the molecule is again planar and centrosymmetrical in the(e) Compounds containing unfwed benzene rings.Goodwin, Przybylska, and Robertson, Acta Cryst., 1950,3, 279.201 Pleith, 2.Naturforsch., 1947, 2a, 409.202 Dhar, Proc. Nat. Inst. Sci. India, 1949,15, 11.=03 Bastiensen, Acta Chem. Scand., 1949, 3, 408.204 Merkel and Wiegand, 2. Naturforsch., 1948, 3b, 93.205 Cagle, Acta Cryst., 1948,1,158.307 Toussaint, Acta Cryst., 1948, 1, 43.208 Smare, ibid., p. 150.206 Bastiensen, Acta Chem. Scand., 1950, 4, 926.209 Fowweather and Hargreaves, ibid., p. 81460 URYSTALLOGRAPHY .erystal.210 The angle between the two phenyl links a t the ketonic carbonatom in 4 : 4'-dichlorobenzophenone is 127", and the molecule now has two-fold symmetry about the C=O bond, the benzene rings being twisted by 30'about the line joining the chlorine atom to the keto-group.211 A correlationbetween the approximate bond-lengths, the dipole moment, and the possibleresonant structures has been drawn.Di-p-bromophenyl sulphide, disulphide,and sulphone also all have molecules possessing an exact two-fold axis ofsymmetry.212 In the sulphide Toussaint claims to have found the S-C bondto have 12% double-bond character, and he deduces that the C-S-C angle iaincreased from the theoretical value of 90" to l09$" owing to this partialdouble-bond character ; van der Waals repulsion between the o-hydrogenatoms prevents the adoption of a planar configuration, the benzene ringseach making an angle of 36" with the BrS-Br plane. In the disulphide theS-C and S-S bonds are thought to be single, and the inclination of thebenzene rings at 43" to the BrS*S-Br plane arises from steric repulsion ofthe hydrogen atoms, unaffected by resonance in the S-C bonds; the S-S-Cangle is 107", apparently owing to steric repulsion between the 1-carbon atomand the 1'-sulphur atom.The benzene rings are inclined at 90" to theBrS-Br plane in the sulphone, where the S-C bond is again single. Owingto the increased tilt of the molecule, the C-S-C angle falls to 100" withoutsteric hindrance. The isomorphous dichloride and dibromide of di-p-tolyl-selenium 213 have molecular structures essentially identical with thosepreviously found for the diphenylselenium d i h a l i d e ~ . ~ ~ ~ The C-Se-C angle(107") resembles the sulphur valency angle in the sulphide discussed above,while the halogen-Se-halogen angle is 177", representing a slight deviationfrom linearity so that the halogen atoms are bent away from the p-tolylgroups. Theselenium-halogen bond distances are approximately 0.23 A.longer thanthe sum of the accepted single-bond covalent radii.The tetraphenylmethane molecule has h symmetry, and has been studiedas a two-parameter problem : 216 the angle (0) of rotation of a phenyl groupabout the bond joining it to the central carbon atom (measured from a planeparallel to c), and the angle (+) of rotation of the whole molecule about thec axis (measured from the a plane). The best fit was obtained with 8 = 55", + = 7.5". The structure is an open one owing to the awkward shape of themolecules.Therelated compounds meso-ap-divinyldibenzyl-(3 : 4-diphenylhexa-1 : 5-diene)and meso-ap-diethyldibenzyL(3 : 4-diphenylhexane) (X ; R = CHXH, orC2H,) have been shown to exist in the staggered configuration of dibenzyl inwhich the plane of the central bonds is approximately perpendicular to theThe benzene rings are inclined a t 40" to the C-Se-C plane.The fully-refined structure of dibenzyl was reported last year.210 Kitaigorodski and Grdenic, Izv.Akad. Nauk. S.S.S.R., 1948, NO. 2, 262.811 Toussaint, Bull. SOC. roy. Sci. Lidge, 1948, No. 1, 10.212 Idem, Bull. SOC. chim. Belg., 1945, 54, 319.213 McCullough and Marsh, Acta Cryst., 1950, 3, 41.214 McCullough and Hamburger, J . Amer. Chem. SOC., 1942, 64, 508.216 Sumsion and McLachlan, Acta Cryst., 1950, 3, 217BODGKIN AND PITT : ORUANIC COMPOUNDS. 461benzene rings.21s a@-Diethylidenedibenzyl (3 : 4-diphenylhexa-2 : 4-diene)(XI) is concluded to have the bTcans-trcans-configuration from considerations.R'Meof space-group symmetry and steric interaction. None of these structureshas however been analysed in detail.Two other compounds may be mentioned here, in which the demands ofnormal bond lengths and valency angles conflict with the van der Waalsseparation of atoms in the molecule.The first of these is di-p-xylylene (XII),a compound so far obtainable only as a result of drastic low-pressurepyrolysis.6* The formula shown has been established by X-ray methods, andthe bond lengths have normal values, while the valency angle a t the CH,group is 114.3;". If the benzene rings remained planar under these conditions,the distance between them would be 2-83 A.instead of the usual van der Waals(Benzenerings aromatic.)value of about 3.5 A. While the substituted carbon atoms of the benzene ringsare in fact separated by this short distance, the benzene rings are distortedso that the remaining atoms have a separation of 3-09 A. The second com-pound,217 bisdiphenylene-ethylene (9 : 9'-difluorenylidene) (XIII), is anorn-alous from several points of view : it is chemically more reactive and absorbslight of wave-lengths further towards the red end of the spectrum than mightbe expected by comparison with other members of the homologous series.Steric interaction between the carbon atoms marked * may be expected ifthe molecule is completely planar since on the basis of customary bondlengths the separation of these carbon atoms will be only 2.5 A.Unfortun-ately the crystal structure is rather complex and will not readily yield accurateatomic co-ordinates, but evidence has been deduced that the molecule is infact centrosymmetrical and approximately planar and that the separationof the carbon atoms marked * is about 2.5 A. ; it is not however possible tosay whether there is any tendency to form a doubled radical with oppositecharges on adjacent carbon atoms marked *.216 Jeffrey, Koch, and Nyburg, J., 1948, 1118.217 Fenimore, Acto Cryst., 1948,1, 295.REP.-VOL. XLVII. 462 CRY STAUOGRAPHY .( f ) Naphthalene and anthracene derivatives. A number of naphthalenederivatives have been studied by Kitaigorodski and others, but detailedresults are in general not yet available.21s The methods of analysis seem notto present any novel features beyond a rather detailed consideration ofpacking efficiency where the molecules can be approximated in shape bytriaxial ellipsoids.Among other structures reported as under consideration,those of a- and @-naphthol are perhaps of greatest interest.219 In theformer the molecules form close-packed layers with six-fold co-ordination,and the hydroxyl groups are linked in chains by hydrogen bonds (2.54 A,).The @-naphthol structure is very similar to that of the parent naphthalene,the unit cell being doubled in the c direction. The molecules are linked inpairs by hydrogen bonds (2.60 A.) perpendicular to the c axis, and the separ-ation parallel to the c axis corresponds to van der Waals interaction.Considerations of packing have been used to solve the structure of theawkwardly shaped di-n-octylnaphthalene.220 Approximate results havealso been published for 1 : 5-dinitro-,,,l 2 : 6-diphenyl-, and 2 : 6-dicyclo-hexyl-naphthalene,21s all of which have centrosymmetrical molecules ; in the2 : 6-diphenyl compound, the angle between the phenyl ring and thenaphthalene plane is .23".Acenaphthene has been resurveyed, and foundto have a flat molecule, the bond joining the CH, groups being at least1.8 A . , ~ ~ ~ a surprising result requiring confirmation.The molecule of anthraquinone is also centrosymmetrical, and shows ageneral similarity to benzoquinone. As in the latter compound, the C=Obond is short (1.15 A.) while the adjoining C-C bonds are relatively long(1 6 0 A.) .223The stereochemistry of this interesting compound isstill unsettled : it remains questionable wheth& it should be classified asaromatic (if it is regular and highly resonant) or aliphatic (if an alternationof double and single bonds exists in the ring).The former view is supportedby electron-diffraction study of the vapour : according to the interpretationby Bastiensen and Hassel the crown form with angles 1213" fits the databest, the mean C-C distance being 1.425 A. with small alternations p0ssible.22~X-Ray crystallographic evidence (of a somewhat limited nature as yet) leadsKaufman, Fankuchen, and Mark to support the latter view : the tub formwith angles 125" and alternate single (1-54 A.) and double (1.33 A.) bondsis Infra-red absorption measurements also agree with a crownform .226Heterocyclic Compounds.-(a) Six-membered ring jused to jice-memberedring.The most important structural investigation in this group is that,cyclooctatetraene.218 Izv. Akad. Nauk. S.S.S.R., 1947, No. 6, 561.219 Kitaigorodski, Dokl. Akad. Nauk. S.S.S.R., 1945, 50, 319.220 Idem, Acta Phys. Chem. U.R.S.S., 1947, 22, 309.221 Sevastyanov, Zhdonov, and Umansky, J . Phys. Chem. Russia, 1948,22, 1153.2a2 Kitaigorodski, ibid., 1947,21, 1085.224 Acta Chem. Scand., 1949, 8, 209.226 Lippincott, Lord, and McDonald, ibid., 1950,166. 227.Sen, Indian J . Physics, 1948,22, 347.225 Nature, 1948,161, 165HODGEIN AND PITT : ORGANIC COMPOUNDS.463of isatin 227 which has been carried out with considerable accuracy in orderto distinguish between the lactam (XIV) and the lactim (XV) structure.H(XIV.)The bestassuming0 0agreement with the observed bond lengths can be obtained bythat the lactam and the lactim form contribute in a ratio of aboutsix to one. The molecule therefore exists in a state close to pure lactam.Molecules are related in pairs by a centre of symmetry and linked by N-H-0bonds of length 2.93 A. which do not lie exactly in the planes of the molecules.Considerable use was made of electron-density maps on the plane z = 22which show the outline of the whole molecule since the latter makes an angleof not more than 10" with (109); the authors claim that the apparentdecrease of the electron-density maxima with increasing distance from t4heorigin is probably due to the greater thermal motion at the benzenoid endof the molecule (a somewhat similar effect was found in geranylamine hydro-chloride).In the present case, however, it must be borne in mind that thetilt of the molecule out of the section plane x = 22 means that for atoms remotefrom the origin the electron density is being sampled on a section of the atomwhich does not pass through its centre ; a decrease of the maxima is thereforeonly to be expected.In piazthiole and piaselenole (XVI; X = S or Se) there is again aheterocyclic ring fused to a benzene ring, but owing to theabsence of hydrogen bonds the packing arrangement is x quite different.22* The isomorphous structures have been\\ NN/ solved in projections by the heavy-atom technique, and agenerous estimate of the probable errors in bond lengths hasbeen given.The N-S distances are 1.57 A., and the N-Sedistances 1.85 (-+ 0.08) A.(b) Two five-membered rings fused together. The accurate analysis ofthiophthen by three-dimensional Fourier methods 229 was mentioned brieflyin last year's Reports. This compound was examined in order to discoverwhether theoretical calculations gave better agreement with the deductionsfrom experimental than that in the case of thiophen (experimental data byelectron diffraction). The theoretical calculations for thiophthen are anextension by Evans and de Heer 230 of the molecular-orbital treatment ofthiophen by Longuet-Higgins in which it is assumed that the sulphur 3 p and3d atomic orbitals are hybridised and compounded with the carbon 2porbitals in the formation of molecular x orbitals (vide Schomaker and(xvI.) i"j""'227 Goldechmidt and Llewellyn, Acta Cyst., 1950, 3, 2?4.228 Luzzati, Compt.rend., 226, 738; 227, 210.22s Cox, Gillot, and Jeffrey, Ada. 1949, 2, 350. Ibid., p. 363464 CRYSTALLOGRAPHY.Pauling 231). I n the comparison of the bond lengths experimentallydetermined with those calculated in the above manner it is necessary toestablish a relation between bond order and bond length for C-S bonds, inaddition to that well established for C-C bonds. The available estimatesof the lengths of pure single and double C-S bonds seemed to the authors some-what unreliable, and they conclude that there is a possibility that thedifferences between the observed and calculated C-S bond lengths may bedue to incorrect standard bond lengths and not to inadequacy in themolecular-orbital calculations.The agreement in the case of the C-Cbond lengths was found to be very satisfactory except for the bond commonto the two rings which is found experimentally to be 0.05 A. shorter than thetheoretical value. Longuet-Higgins 232 has subsequently pointed out thatEvans and de Heer's calculations assume that the a-bond system is free fromstrain, whereas the results of the X-ray analysis indicate that the exteriorangles a t the tertiary carbon atoms are about 135", and hence the a-skeletoncannot be strain-free.When the effect of this strain is allowed for, the centralbond is shortened by 0.06 A., bringing the calculated length into excellentagreement with that determined experimentally.The stereochemistry of the amino-and hydroxy-pyrimidines has been established in some detail by Clews andCochran and Pitt. A reliable basis is thus available from which may beundertaken the investigation of some of the many interesting and importantcompounds containing these groupings which occur in biological systems.The isomorphous 2 -amino-4 : 6 -dichloro- and 2 -amino-6-chloro -4-methyl-pyrimidines first studied by Clews and Cochran s1 are related to each other ina manner similar to that in p-dibromo- and p-lpomochloro-benzene mentionedabove, the methyl groups and chlorine atoms in the second compoundoccupying at random the 4- and 6-positions which are both occupied bychlorine atoms in the first compound.Weak N-H-N bonds (3.21, 3-37 A.)link the molecules in sheets, all three nitrogen atoms in the molecule partici-pating; the amino-nitrogen atom forms two such bonds almost coplanarwith the molecule, while the nitrogen atoms in the ring each form one non-coplanar hydrogen bond. The chlorine atoms pack together in columns, onehaving contact with six near neighbours and the other with seven, some ofthe CI-C1 distances being unusually short. The C-Cl distances resemblethose found in aliphatic compounds more closely than those found in chloro-benzenes, and this is in accordance with the high chemical reactivity.Avery careful analysis of 4-amino-2 : 6-dichloropyrimidine shows it to existin the amino- rather than the dihydroimino-pyrimidine form.233 Thenitrogen atoms are again engaged in hydrogen-bond formation, and theauthors claim that there are low maxima in the electron density near thenitrogen atoms which could be explained as due to (i) hydrogen atoms nearthe amino-nitrogen atoms, and (ii) unshared electron pairs of the ring-nitrogen atoms, interacting with (i), on the basis of Pauling's theory of(c) Pyrimidine and purine derivatives.233 J. Amer. Chem. SOC., 1939,61, 1779.232 Acta Cryst., 1950.3, 76. *38 Clews and Cochran, ibid., 1949, 2, 46HODGKIN AND PITT : ORGANIC COMPOUNDS.465hydrogen-bond formation. The heights of the latter peaks are not muchabove the background undulation, and the interpretation seems notaltogether convincing to the Reporter who, having encountered similarsmall regions in electron-density measurements of another structure, recentlycalculated the corresponding " Fc-synthesis " baaed on the calculated struc-ture factors (without hydrogen-atom contributions) and found that theregions persisted and were thus due to termination-of-series errors. Althoughthis may not be the explanation in the previous case, some such confirmationwould carry more weight than the series-termination corrections actuallyapplied.In 2-hydroxy-4 : 6-dimethylpyrimidine the hydrogen-bond system iscomplicated by the presence of water of crystallisation.60 The structure ismade up of interlinked corrugated sheets of molecules united by hydrogenbonds of three types : (i) from 2-hydroxy- to water molecule(2.8,2-9 A.) (not coplanar with the ring) ; (ii) from 1- or 3-nitrogento water molecule (2.8, 2.9 A.) (coplanar with the ring) ; (iii) fromwater molecule to water molecule (2.8 A.).More recent workshows that there is a definite tendency towards a quinonoidtype of molecule, with the C=O bond short ; this may imply thatstructures of the type inset make an appreciable contribution tothe description of the molecule. If this is so, the negative charge on the5-position can be correlated with the chemical reactivity at this point.Adenine hydrochloride has been found by Broomhead234 to have aplanar molecule and bond lengths comparable to those in the amino-pyrimidines except for the C-C bond common to the two rings which is long(1.44 A.).The hydrogen bonding again forms a major factor in determiningthe arrangement of purine molecules, chlorine ions, and water molecules inthe lattice, and it is understood that the hydrogen atoms have all been locatedin more recent work involving the (F,-FJ-synthesis.The nucleic acids have molecules too large for detailed study by X-raymethods as yet developed, but chemical evidence shows that they arebuilt up from a relatively small number of nucleotides (composed of apyrimidine or purine with ribose or deoxyribose and a phosphate group),and X-ray methods will no doubt be very valuable in the determination ofthe steric relations in these compounds of rather unpredictable shape.As aprelude to the examination of one of the nucleotides, cytidilic acid, Furberghas investigated the nucleosides ~ytidine,~~5 and (in outline) uridine, adeno-sine, and g ~ a n o s i n e . ~ ~ ~ Direct confirmation is obtained that cytidine iscytosine-3 p-D-ribofuranoside. The pyrimidine ring has dimensions com-parable to those found in the structures mentioned above ; the C=O distanceis very similar to that in the hydroxypyrimidine, while the C,6,-N distanceresembles that in the aminopyrimidines. The C-N bond between the ringsis effectively a pure single bond. The D-ribose ring is approximately planarexcept for one carbon atom which is displaced by 0-5 A.; the hydroxyl group7' N/\N I] 11-234 Acta Cryst., 1950, 3, 324.,236 Acta Chem,. Bcnnd., 1950, 4, 751.a35 Ibid., p. 325466 CRYSTALLOGRAPHY.attached to this atom then falls in the plane of the ring, as was found byBeevers and Cochran in the case of fructofuranoside. The bond joining thetwo rings lies in the plane of the pyrimidine ring but makes approximatelytetrahedral angles with the adjacent sides of the ribose ring, so that the tworings are nearly perpendicular, contrary to Astbury’s prediction. All theactive groups are engaged in hydrogen-bond formation and, in addition, thedistance from C(4, of the pyrimidine ring to the 0(5) atom of the ribose ringis short (3.24 A , ) and may represent a weak linkage, possibly to be correlatedwith the chemical stability.G. J. P.Natural Products of Moderate Complexity.-The three compounds wehave to consider in this group, strychnine, penicillin, and calciferol, arechemically very different and are linked here by the crystallographic problemsinvolved in the determination of their structures. In all three cases, theX-ray analysis has been achieved largely through the use of heavy atomderivatives to assist in the process of phase determination.The structure of strychnine has been found independently by two groups,Bokhoven, Schoone, and Bijvoet in Utrecht 237 and Robertson and Beevers inThe analysis in both cases proceeded remarkably smoothly.The Dutch workers used the isomorphous series, strychnine sulphate andselenate, and calculated electron-density projections.Prom the first ofthese, a centrosymmetrical projection, they found it possible to select thecorrect formula and to confirm this by calculation of a second projection.Robertson and Beevers proceeded directly to the determination of theelectron density in three dimensions via the calculation of a three-dimensionalPatterson series for strychnine hydrobromide and the correct selection of theBr-light atom vectors. Curiously enough, although the crystal structuresstudied differ in symmetry and ionic content, the arrangement of themolecules is very similar in relation to the crystal axes and their appearancein the electron-density contours in the main projections, viewed down 7.58and 7.64 A.respectively, is almost identical. The large roughly boat-shapedmolecules are fitted together as closely as possible, the spaces between thembeing filled by the ions and a few odd water molecules. By a happycoincidence, the same structure was deduced on purely chemical groundsalmost simultaneously with the first X-ray analysis.239The structure analysis of penicillin was also based on the examination ofthree salts having two types of crystal structure-sodium, potassium, andrubidium benzylpenicillin-and these were investigated, to a large extentindependently, by two groups of research workers.53 Here, owing partly tothe low atomic weight of sodium and to the special positions occupied bypotassium and rubidium in the crystal, the direct phase determination wasvery incomplete. Extensive trial-and-error analysis by the use of opticaldiffraction and the direct comparison of rough electron-density patternsobtained in the two investigations played a part in the solution of the237 Proc.K . Ned. Alcad. Wet., 1947, 50, 8 2 5 ; 1948,51, 990; 1949, 52, 120.238 Nature, 1950,165, 690. 239 Robinson, ibid., 1947, 160, 18HODGKTN AND PITT : ORGANIC COMPOUNDS. 467structure. At the time that the atomic arrangement shown in Fig. 11 wasreached by calculation of the electron density in three dimensions, there wasstill considerable weight of chemical opinion against the formula found. Itis somewhat amusing now, five years later, to find the C-N and K-0 distancesin penicillin quoted as reasonable standards with which to compare distancesfound in such molecules as alanine and potassium hydrogen bisphenylacetate.Actually the accuracy of bond-length measurement in the penicillin structureas published is not high, though fully sufficient to establish the general arrange-ment of bonds within the molecule.A later refinement of the three-dimensional electron-density distribution in potassium benzylpenicillin hasprovided a series of more accurate bond lengths; 240 the greatest deviationof these from generally accepted values is now 0.06 A. instead of 0.13 A. inthe earlier refinement. The new bond lengths agree very well with those0 9CCH(a) (b )FIG. 11.(a) Bensylpenicillin. (b) Strychnine.to be expected from the straightforward p-lactam formula ; within theamide side chain the inter-atomic distances are, for example, similar to thosein acetamide within the limits of experimental error.I n the benzylpenicillin molecule, neither the thiazolidine five-memberednor the p-lactam four-membered ring is planar, in agreement with conclusionson other similar rings. The two are fused together in the cis-position andthe phenylacetamide group is attached to the p-lactam ring on the same sideas the thiazolidine-sulphur atom. This arrangement fixes the stereochemicalconfiguration at the two centres and C,,,, as opposite to one another;chemical degradation has established them as D and L respectively. I n bothcrystal structures the molecule has a compact semicircular form, with thethiazolidine and benzene rings not far from parallel to one another. This mustlargely be due to packing considerations ; it enables all the oxygen atoms, bothof the p-lactam and the amide groups, as well as the carboxyl groups, to bearranged around the ions to form an ionic layer in the structure, and, as inmany inorganic crystals, the change in crystal structure when passing from240 Pitt, p arsonal communication468 CRYSTALLOGRAPHY.the potassium to the sodium salt enables seven oxygen atoms to makecontacts with the potassium ion, while only six make contact with each sodiumion. Owing to the complex geometry of the molecule, however, the packingsituation is also very complicated-for example, the oxygen atoms of sixdifferent penicillin ions have to make contact with each potassium ion inthe potassium salt.The third crystal structure in this group, that of calciferol 4-iodo-5-nitrobenzoate, is not completely solved. But the single electron-densityprojection obtained is sufficient to show both the intricate way in which themolecules fit into the crystal and the general form of the molecule i t ~ e 1 f . l ~ ~Earlier preliminary crystallographic measurements on calciferol had suggestedthat the molecule should be not very unlike cholesterol and had thrown somedoubt on the chemical evidence for the breaking of ring B.241 However, thepresent more exact data show that, in this crystal, ring B is not only openbut wide open. The molecule is fully extended and the projected atomicpositions agree very well with those expected from chemical evidence.Certain stereochemical details can be added-for example, the arrangementa t the 22 : 23 double bond is clearly trans.The use of heavy atoms in all these structures to achieve a t least partialphase determination raises the question of how long the process can becontinued-what is the maximum size of molecule for which this processmight work. Calciferol 5-iodo-4-nitrobenzoate has 41 atoms * and is thelargest organic molecule for which an electron-density projection showingindividual atoms has yet been published. But there are a number of othersimilar-sized molecules under investigation, including chloromycetin anda u r e o m y ~ i n , ~ ~ ~ and a t least one larger, of which the crystal structure hasbeen essentially The possibility of structur? analysis, with orwithout a heavy atom, certainly does not end a t this order of complexity.I n a rough way this can be shown by the comparison of the average scatteringpower of a single heavy atom in the crystal unit to that of a number ofcarbon atoms, assuming as correct the deduction by Wilson 244 and others ofthe statistical distribution of the intensities of X-ray reflections in complexcrystals. It seems most probable that, in practice, the limit will be set bythe intensities of the observable reflections. As the molecules become morecomplex, reflections from planes of small spacing no longer appear on X-rayphotographs. For a molecule of the order of magnitude of vitamin BI2, forexample, for which the crystal asymmetric unit has a weight of about 1600,no reflections are visible from planes with spacings smaller than about1.1 A.245 At this limit, it should still be possible, at least theoretically, tocalculate an electron-density distribution showing resolved atoms. Butwhen we come to molecules of much greater weight, such as proteins, this is241 Bernal, Crowfoot, and Fankuchen, Phil. TTans., 1940, 239, A , 135.242 Dunitz and Leonard, J. Arne?-. Chem. Soc., 1950, 72, 4276.s13 Vend, Personal communication.mi Hodgkin, Porter, and Spiller, Proc. Roy. Soc., 1950, B, 136, 609.* Not counting hydrogen.244 Wilson, Acta Cryst., 1949,2, 318HODGKIN AND PITT : ORGANIC COMPOUNDS. 469no longer true, beautifully crystalline though many proteins may be. Theinterpretation of their crystal structures raises problems of an altogetherdifferent dimension from those discussed here and must be left for yetanother Report.D. C. H.We were very greatly assisted in covering the field of this Report by theuse of the classified bibliography issued by the American Society for X-Rayand Electron Diffraction and the American Crystallographic Society, and alsoof the abstracts prepared for forthcoming Structure Reports through theInternational Union for Crystallography. We are much indebted for theloan of these to Professor Lonsdale and Dr. A. J. C. Wilson. We alsoacknowledge the help we received in preparing the report from Dr. ClaraBrink and Dr. June Broomhead.DOROTHY CROWFOOT HODGKIN.G. J. PITT.J. THEWLIS