CRYSTALLOGRAPHY.1. CRYSTAL GROWTH.THE remarkable outburst of interest in the mechanism of crystal growthappears to have been stimulated by the recognition that all crystals areimperfect and that dislocations can be self-perpetuating. In addition, therecent development of multiple-beam interferometry as a tool 1y 2y shouldbe mentioned. Since the Faraday Discussion in 1949 something like100 papers have appeared reporting observations relevant to the dislocationmechanism, or developing the mathematical theory of imperfect crystalgrowth. So striking are the results found, in certain cases at least, thatthere cannot now be any doubt of the important part played by screwdislocations in crystal growth, in these instances even if not more generally.Theoretical physicists have developed the theory of the perfect crystaland, in particular, of the nucleation of new phases4f5 This led to thepredictions, (1) that, given nucleation, growth rate should be proportionalto supersaturation, a relation which was found to hold rather wellexperimentally, and (2) that growth-rate, as determined by the rate offormation of fresh 2-dimensional nuclei on existing crystal faces, should beexcessively small for the principle faces of a perfect crystal, unless super-saturation were as high as, say, 50%. At 1% supersaturation, the rate ofgrowth should be about 10100* times less than at 50%.Burton hasremarked that this must be one of the largest known discrepancies betweentheory and experiment! It was recognised very early that the observedrate of growth of real crystals must be connected with their lattice im-perfections but as late as 1949 there was no clear conception of how thetheory should be modified.Crystal imperfections were by no means thecentral concern for the Faraday Discussion. that thecredit is due for pointing out that a screw-dislocation can be self-perpetuating, and that the classical conceptions of the critical nuclear size,etc., when applied to a growth step of this kind, predict a spiral-shapedgrowing edge, in agreement with certain well-known features of some crystalsurfaces. The self-perpetuating step allows growth of the crystal to proceedwithout fresh nucleation, as the continual winding upon itself of an infinitesingle layer of unit elements, thus avoiding altogether the need for freshnucleation of successive layers, and explaining the observed rate of growthof crystals in a most elegant fashion. Burton, Cabrera, Frank,', 8 y 9 7 lo andothers have been developing the theory of dislocations very considerably.The dislocation translation (Burgers' vector 11) may be either the unit cellIt is to FrankS.Tolansky and M. Omar, Nature, 1952, 170, 81.I. N. Stransky and R. Kaischew, Physikul. Z., 1935, 36, 393.R. Becker and W. Doering, Ann. Physik, 1935, 24, 719; W. K. Burton andW. K. Burton, N. Cabrera, and F. C. Frank, Nature, 1949, 163, 398. * Idenz, Phil. Trans., 1951, 243, A , 299; F. K. N. Nabarro, Adv. Physics, 1952, 1, 271.F. C. Frank, Phil. Mug., 1951, 42, 809; Adu. Physics, 1952, 1, 91.a S.Tolansky, 2. Elektvochem., 1952, 56, 263. Idem, Nature, 1952, 169, 445.N. Cabrera, Discuss, Fumduy Soc., 1949, 5, 33, 40. 13 F. C. Frank, ibid., p. 48.lo Idem, Actu Cryst., 1951, 4, 497 ; 2. Elektvochern., 1952, 56, 429.l1 J. M. Burgers, Proc. K . Ned. Akud. Wet., 1939, 42, 293344 CRYSTALLOGRAPHY.translation or some simple multiple thereof; screw dislocation may beright- or left-handed and, if several are present on one face (densities upto lo4 dislocations per mm.2 have been observed) , they will give characteristicand easily recognisable patterns on the surface. The new concepts havebeen applied to explain polytypism l2 and twin-formation.13What makes the Frank mechanism so convincing is the striking confirm-ation it has received from the study of crystal surfaces.The range ofcrystals on which markings consistent with Frank's theory have beenobserved includes graphite,14 corundum,15 haematite,16 pyrites,17 bery1,lsquartz,lg apatite,20 mica,21 and cadmium iodide ; 2* also, amongst the metals,A u , ~ ~ Mg,24 Cd,24 and Ti.25 AlBzZ6 gives evidence of screw dislocations inthe centre of the crystals, since the action of acid is to create a hole at thispoint; most elegadt of all, and incidentally the only organic compoundsrepresented in this list, the hydrocarbons C,,H,, 27 and C100H202,28 examinedin the electron microscope by Dawson and Vand, show well-marked spiralsof unimolecular step height.It is certainly too early to form any proper assessment of the generalityof the screw-dislocation mechanism in crystal growth.From the observ-ations so far available, it would seem to be more important in minerals,simple inorganic salts, and elements. The spreading of layers outwards overthe surface of a growing crystal has, of course, been observed in manyinstances, inorganic and organic, particularly by B ~ n n , ~ ~ but, as a generalrule, spiral patterns are not seen. Electron micrographs confirm theexistence of layers on protein crystal faces (e.g., the Rothamsted necrosisprotein 30) but show neither spirals nor the hole at the site of the dislocationitself, which in the case of protein crystals was predicted to be of the orderof 100 m ~ . ~ 1 The necessity for some form of %dimensional nucleation isclear ; but that it is always a screw dislocation cannot be said to have beenproved.Dawson and Vand have shown (for C,,H,,) 28 that twinning cangive rise to an indestructible step resulting in unimpeded growth in onedirection. Perhaps many other such mechanisms remain to be found.Possibly, too, the role of impurities may have to be taken more into account.l2 F. C. Frank, Phil. Mag., 1951, 42, 1014; V. Vand, Nature, 1951, 168, 783; Phil.Mag., 1951, 42, 1384; G. Honjo, S. Miyake, and T. Tomita, Acta Cryst., 1950, 3, 396;see also L. S. Ramsdell and J. Kohn, ibid., 1951, 4, 75, 111.13 A. H. Cottrell, and B. A. Bilby, Phil. Mag., 1951, 42, 573.l4 F. H. Horn, Nature, 1952, 170, 581.15 A. R. Verma, ibid., 1951, 167, 939; 168, 430, 783; 2. Elektrochem., 1952, 56, 268;Phil.Mag., 1951, 42, 1005; 1952, 43, 441; S. Amelinckx, Nature, 1951, 168, 431;H. E. Buckley, 2. Elecktrochem., 1952, 56, 275.16 A. R. Verma, Nature, 1952, 169, 540.l8 L. J. Griffin, Phil. Mag., 1951, 42, 775, 1337; 43, 827.19 C. S. Brown, R. C. Kell, L. A. Thomas, N. Wooster, and W. A. Wooster, Nature,1951, 167, 940; G. van Praagh and B. T. M. Willis, ibid., 1952, 169, 623; B. T. M. Willis,ibid., 170, 115. 2o S. Amelinckx, ibid., 169, 841; 170, 760.21 Idem, ibid., 169,580 22 A. J . Forty, Phil. Mag., 1951,42,670; 1952,43,72,377.23 S. Amelinckx, ibid.. p. 562; S . Amelinckx, C. C. Grosjean, and W. Dekeyser,Compt. rend., 1952, 234, 113. 24 A. J. Forty, Phil. Mag., 1952, 43, 481, 949.26 M. A. Steinberg, Nature, 1952, 170, 1119.z6 F.H. Horn, E. F. Fullam, and J. S. Kasper, ibid., 169, 927.27 I. M. Dawson and V. Vand, ibid., 1951, 167, 476; Proc. Roy. SOC., 1951, A , 206, 555.28 I. M. Dawson, ibid., 1952, A , 214, 72.20 C . W. Bunn, Discuss. Faraday SOC., 1949, 5, 119.30 R. W. G. Wyckoff, Acta Cryst., 1948, 1, 292 (Fig. 7).31 F. C. Frank, ibid., 1951, 4, 497.l7 A. F. Seager, ibid., 170, 425DUNITZ : THE TECHNIQUE OF STRUCTURE ANALYSIS. 345The case of CdI, is instructive. Initial crystallisation proceeds at first withgreat rapidity, excessively thin platelets being formed ; growth then slowsdown, the plates begin to thicken, and it is only then that terraced steps, etc.,begin to appear on the (0001) faces. CdI, affords some of the most beautifulexamples of spiral growth patterns.But if screw dislocations account onlyfor the second phase of its growth, what shall we postulate for the first?Buckley in particular has expressed scepticism in this c~nnection.~,Another line of evidence which must in due course be brought to bear onthe subject is the mosaic-block theory of crystal texture, strongly supportedby the intensities of X-ray reflection^.^^ Light scattering indicates anaverage grain diameter of about 2000 It is clear that beforemore can be said about the growth of crystals in general, very much moreexperimental work will have to be done.There is more work on related aspects of crystal growth much harder tosummarise. In this report only the briefest indication can be given of themain directions of such endeavours-the alterations of crystal form by thepresence of impurites, dyes,35 etc.; oriented overgrowths ; 36 and the studyby interferometry of cleavage surface^.^'for NaC1.34J. H. R.2. THE TECHNIQUE OF STRUCTURE ANALYSIS.Since 1949 when this subject was last reviewed considerable attentionhas been given to the development of methods for the determination ofcrystal structures directly from diffraction data. Trial and error methodshave been used for many years with great success and there is no doubt thatin the hands of a capable investigator, and especially when used in con-junction with molecular transforms, they can be very powerful. They haverecently been strongly implemented (at least in 2-dimensional cases) by thefurther development of optical methods utilising the correspondence betweenthe diffraction of X-rays and the diffraction of light.Lipson and hiscollaborators have pointed out that the original fly's eye procedure may begreatly simplified by the use of masks containing only a few, instead ofseveral hundred, unit cek38 The revised procedure is not only faster andmore convenient but also, in some respects, more useful, since the patterncan conveniently be compared with the molecular transform also obtainedoptically on the same scale. Positive and negative regions of the transformsmay be distinguished by inserting a " pseudoatom " at a centre of symmetry.It is evident that some otherwise laborious aspects of trial analysis may begreatly eased by use of optical methods, and applications to the solution of32 H.E. Buckley, Proc. Ph-vs. Soc., 1952, B, 65, 578; 2. Elektrochem., 1952, 56, 275.33 See, however, A. J. C . Wilson, Acta Cryst., 1952, 5, 318.34 R. Furth and S. P. F. Humphreys-Owen, Nature, 1951, 167, 715.35 J. Whetstone, ibid., 168, 663; H. E. Buckley, Mem. Manchester Lit. Phil. Soc.,1950-1951, 92, 77; H. Seifert 2. Elektrochem., 1952, 56, 331.3s L. G. Schulz, Acta Cryst., 1951, 4, 483; 1952, 5, 130, 264; D. W. Pashley, ibid.,p. 850; Proc. Phys. Soc., 1952, A , 65, 33; J. Willems, 2. Elektrochem., 1952, 56,345 ; A. Neuhaus, ibid., p. 453 ; E. Stanley, Research, 1951, 4, 293 ; A. A. Fuller, Nature,1951, 168, 471 ; D. M. Evans and H. Wilman, Acta Cryst., 1952, 5, 731.37 S. Amelinckx, Phil.Mag., 1951, 42, 342.38 H. Lipson and C. A. Taylor, Acta Cryst., 1951, 4, 485; A. W. Hanson and H.Lipson, ibid., 1952, 5, 145346 CRYSTALLOGRAPHY.several structural problems have been described.39 Optical methods havealso been applied to the summation of Fourier seriesM It is clear, how-ever, that, for complex crystals where the steric arrangement of the atoms isnot even approximately known, trial methods may become impossible, andit is evidently desirable to have more direct routes to the solution of suchstructures.Buerger 41 has described certain formal re€ations between the idealisedelectron density and the corresponding Patterson function. Regardingboth maps as being composed of sets of points, the fundamental set and thevector set, he has given systematic methods of obtaining the former fromthe latter.Since the Patterson map can always be obtained directly fromdiffraction data this is equivalent to a proof that, in principle at least, thecrystal structure may be solved directly from such data. The difficulty isthat in practical cases the density of peaks in the Patterson map may be sogreat and the degree of resolution so small (for X-ray wave-lengths incommon use) that the individual elements of the vector set are not separatelyrecognisable. The function may, of course, be sharpened by the use ofsuitable modification functions but only a t the cost of introducing spuriousdetail. Nevertheless, some degree of sharpening is certainly useful and anumber of fairly complex crystal structures have been solved by thesystematic interpretation of the sharpened 3-dimensional Patterson function ; adetailed description of such an analysis has been given for hydroxy-~-proline.~~Provided that some of the atoms in the structure can be located, severalmethods of determining the positions of the other atoms are available.Oneof these (the “ heavy atom ” method) based on Fourier synthesis withcoefficients F, and phase angles uc, is well known and has been of greatimportance in solving some very complex structures. Luzzati 43 has givena useful critical examination of the method and has shown that its power isgreatly increased by the presence of a centre of symmetry. Other methodsbased on the systematic analysis of the Patterson function have now beenproposed for such cases.Beevers and Robertson have described the“ vector convergence diagram ” and have applied it with success to thestrychnine hydrobromide structure.45 The method involves a summationof superimposed Patterson functions, appropriately weighted if necessary,with their origin displaced to the known atomic positions; it is usuallyapplied graphically but it may easily be shown that this process is equivalentto calculating the Fourier series with coefficients FO2Fc and with phaseangles ac. Buerger 46 has made use of a Product function and a minzimumfunction in place of the previous summation over Pattersons’ and it isclaimed that the minimum function provides the best convergence to theelectron density. Other forms of Fourier coefficients have been proposed 4739 A.W. Hanson, C. A. Taylor, and H. Lipson, Nature, 1952, 169, 1086; C. A. Taylor,ibid., p. 1087.40 A. W. Hanson, C. A. Taylor, and H. Lipson, ibid., 1951, 168, 160; A. W. Hansonand H. Lipson, Acta Cryst., 1952, 5, 362.42 J. Donohue and K. N. Trueblood, ibid., 1952, 5, 414.43 V. Luzzati, ibid., in the press.44 C . A. Beevers and J. H. Robertson, ibid., 1950, 3, 164.4 5 J. H. Robertson and C. A. Beevers, ibid., 1951, 4, 270.4 6 M. J . Buerger, ibid., p. 531.4 7 D. McLauchlan, Proc. Nat. Acad. Sci., 1951, 37, 115; I. D. Thomas and41 M. J. Buerger, ibid., 1950, 3, 87.D. McLauchlan, Acta Cryst., 1952, 5, 301 ; D. Rogers, Research, 1951, 4, 295DUNITZ : THE TECHNIQUE OF STRUCTURE ANALYSIS.347but, in the Reporters’ view, it remains to be shown that any of the methodsdiscussed above are superior to the original heavy-atom method.A great deal of interest has centred on direct methods in which theproblem is handled in transform space rather than in crystal space. Theapproximate structure can be recognised from a Fourier series containingcomparatively few strong terms, provided that the correct phase angles(or signs) can be assigned to these, and the problem becomes one of devisingmeans of fixing or of limiting the possible phase relations amongst thestrongest terms. The Harker-Kasper (H-K) inequalitie~,~~ derived byapplication of Schwartz’s inequality to the structure factor expression, havenot only been of some practical importance, but have also provided thestimulus for further theoretical development.have shown that inequality relations result from the conditions that theelectron density be everywhere positive and have given a general formula forderiving all such relations.No symmetry properties are required but theymay readily be introduced to give the H-K inequalities as special cases.It is shown 50, 51 that if the U’s (unitary structure factors) rather than theF’s are considered, then some of the inequalities reduce to equalities, specialcases of which have been reported p r e v i ~ u s l y . ~ ~ A method of deriving theH-K inequalities for any space group has been described.53 Additionalphase limitations are imposed if the electron density is known over a portionof the unit cell 54 or if it is restricted to a maximum possible value; 55 nosuch limitations are imposed, however, by the condition that atoms must beseparated by a certain minimum distance.54 Some linear inequalties havebeen derived for centrosymmetric crystals; 56 these are not quite sorestrictive 57 as the H-K inequalities (which involve quadratic relations) butthey are easier to apply and may prove very useful.Methods for thesystematic application of inequalities have been described 58 and they havebeen used to solve the crystal structures of oxalic acid d i h ~ d r a t e , ~ ~decaborane,60 a- and P-seleniumG13 62 p-di-tert.-b~tylbenzene,~~ ethylene-diamine ~ u l p h a t e , ~ ~ and realgar.64For the H-K inequality relation to produce definite restrictions on thesigns, the F values involved must be greater than some minimum value.Their usefulness thus decreases as the unit of structure becomes larger until,a t a certain stage, no limitations whatsoever are imposed.65 In principle,high-order determinantal inequalities 51 could be used in such circum-stances, but their practical application is likely to be rather difficult.Karle and Hauptmann 4934 8 D.Harker and J. S. Kasper, Acta Cryst., 1948, 1, 70.49 J. Karle and H. Hauptman, ibid., 1950, 3, 181.50 H. Hauptman and J. Karle, Phys. Review, 1950, 80, 244.51 J. A. Goedkoop, Acta Cryst., 1950, 3, 374.52 I<. Banerjee, Proc. Roy. Soc., 1933, A, 141, 188; M. J. Buerger, Proc. Nut. Acad.54 J. A. Goedkoop, C. H. MacGjllavry, and R.Pepinsky, ibid., 1951, 4, 491.5 5 R. Pepinsky and C. H. RlacGiUavry, ibid., p. 284.5 6 Y. Okaya and I. Nitta, ibid., 1952, 5, 564. 5 7 K. Sakurai, ibid., p. 697.58 I d e m , ibid., p. 546; J. Gillis, ibid., 1948, 1, 174; E. Grison, ibid., 1951, 4, 489.59 J . Gillis, ref. 58.6o J . S. Kasper, C. M. Lucht, and D. Harker, Acta Cryst., 1950, 3, 436.61 R. D. Burbank, ibid., 1951, 4, 140.63 €3. S. Magdoff, ibid., 1951, 4, 176, 268.64 T. Ito, N. Morimoto, and R. Sadanaga, ibid., 1952, 5, 775.6 5 E. W. Hughes, ibid., 1949, 2, 34.Sci., 1948, 34, 277. 53 C. H. MacGillavry, Acta Cryst., 1950, 3, 214.Idem, ibid., 1952, 5, 236348 CRYSTALLOGRAPHY.For a crystal composed of atoms whose atomic numbers do not differtoo greatly, the electron density p(x) and its square p2(x) have approximatelythe same form.Sayre has shown that, as a consequence, F(h) must equalits self-convolution C,F(p)F(h - p); the phase angles (or signs) must besuch as to satisfy this set of equations. The equations hold in twodimensions provided that the atoms are well resolved and they have beenapplied to the [loo] projection of hydroxy-L-proline. The equations implya tendency for the sign of F(h + p) to be the same as that of F(h)F(p).This result has also been derived by considering the extent to which aFourier series containing only a few large terms can represent p(x),G7 andalso by a statistical argument.68 The relation (1) S(h -/- p) = S(h).S(p)which can be proved from inequalities to be true when the correspondingstructure factors are sufficiently large, is thus Probably true in other circum-stances, as indeed is suggested by a simple trigonometric manipulation ofthe structure factor expression.When some signs can be obtained frominequalities, the probable validity of (1), especially when appliedstatistically,68 provides a useful extension by which more signs may bediscovered. The structures of glutamine 69 and of metaboric acid 68 havebeen solved by this method. I t has been suggested that the statisticalapplication of (1) may be valid even for structures containing up to 200 atomsin the unit cell but, from the Reporters’ experience, this would appear tobe a highly optimistic estimate.A new approach to direct structure analysis has been introduced byHauptman and Karle.’O Each structure factor is regarded as a closedvector polygon; the magnitudes of the vectors ( t i ) are known, but theirorientations (+i) are to be found.For each observation of F(h), theapplication of the random-walk analysis leads to a distribution functionfor the +i’s, and hence for the atomic co-ordinates. The strict couplingbetween the polygons is ignored and the individual distribution functionsare multiplied together to yield a resultant probability distribution functionfor the co-ordinates. I t remains to be seen whether this method, in itspresent form, will be of practical importance ; the calculations are excessivelylengthy and it is shown too that the final probability function is closelyrelated to a “ super-sharpened ” Patterson, exp [ P ( x ) ] .The introductionof coupling between the vector polygons must necessarily strengthen therelations and we understand that this extension is being developed.None of the methods so far described seems generally applicable tomolecules of very high molecular weight. For these, rather specialisedmethods of restricted application are likely to be required. Vand 71 hasdescribed one such method for compounds containing structural periodicities,where the crystal unit cell may contain sub-cells. The structure may, infavourable cases, .be inferred from the relations between the structure factorsof the main cell and those of the sub-cell, as in the analysis of t r i l a ~ r i n . ~ ~13ragg and Perutz 73 have applied knowledge of the general shape of thehzmoglobin molecule to the absolute F values a t various shrinkage stagesand are well on the way to a direct projection of the electron density.6 6 D.Sayre, ActaCryst., 1952,5,60.W. H. Zachariasen, ibid., p. 68.70 H . Hauptman and J . Karle, ibid., p. 48.7 1 V. Vand, ibid., 1951, 4, 104.73 Sir W. I,. I3ragg and M. F. Perutz, Yvoc. Roy. SOC., 1952, A , 213, 425.6 7 W. Cochran, ibid., p. 65.72 V. Vand and 1 . 1’. Bell, ibzd., p. 465.\V. Cochran and B. R. Penfold, ibid., p. 644DlTKITZ THE TECHNIQUE OF STRUCTURE ANr\LYSIS. 349The statistical treatment of X-ray intensities is capable of yielding muchinformation concerning crystal structures. One of the earliest applicationsgave an easy method of placing relative intensity measurements on anabsolute scale.74 A very important new development has been to providean X-ray method of distinguishing between centrosymmetric and non-centrosymmetric crystals.75 The method is quite simple and dependsessentially on the different characteristics of the one- and two-dimensionalGaussian functions which describe the distribution of real and complexstructure factors respectively. Centrosymmetric molecules arranged centro-symmetrically give a “ hypercentric ’’ distribution 76 distinguishable fromthe ordinary centric one. Other symmetry elements may also bere~ognised.~’ I t is noteworthy that all of the 219 distinguishable space-groups may now be recognised from X-rayWe come now to the questions of determining the degree of reliabilityto be associated with a structure analysis a t any given stage.Luzzati 79has extended some earlier arguments of Wilson and others and has derivedrelations between the reliability index R and the mean value of cos 2 x ( A r . s)where Ar is the error in an atomic co-ordinate and s = 2 sin O/h. For thesame degree of precision of the atomic co-ordinates, K is lower in non-centrosymmetric than in centrosymmetric structures, I t is shown that ifthe Ar’s are normally distributed about zero, then R plotted against sin 8must lie on a family of curves corresponding to different values of I r I .This thus provides a much more delicate test for the approximate correct-ness of a structure than the value of K itself, for, if the errors are notdistributed normally, the proposed structure is incorrect, but it may never-theless yield K values as low as approximately correct, though unrefined,structures.Examples of structures which gave reasonably low R values,but which had to be radically modified because they were found incapableof further refinement, are “ cis-naphthodioxan ” 80 (where an incorrect ringstructure was first tested) and purpurogallin 81 (where one translationalparameter of the molecule was wrongly estimated). I t is possible thatother examples are to be found in the literature.The accuracy of the final co-ordinates obtainable by the Fourier and theleast squares method has been discussed by 1300th and by Cruickshank.82The relation between the two methods has been examined by the latter,83who finds an exact similarity between the equations for co-ordinate refinement.The convergence of the Fourier method has been discussed by Luzzati,84 whoconfirms some of Cruickshank’s conclusions.The principal results are asfollows : (1) The same corrections (provided they are sufficiently small) aregiven by both methods. (2) Under identical conditions the final errors inatomic positions are twice as great for the non-centrosymmetric as for the74 A. J . C. LVilson, Nature, 1942, 150, 152.7 5 I d e m , A d a Cvyst., 1949, 2, 318; E. R. Howells, 11. C. Phillips, and D. Rogers,7 7 D. Rogers, ibid., 1950, 3, 455.79 V. Luzzati, ibid., 1952, 5, 802.*O S. Furberg and 0. Hassel, Acla Chem. Scand., 1950, 4, 1584.J .11. Dunitz, Nature, 1952, 169, 1087.n2 -4. D. Booth, Proc. R o y . Soc., 1947, A , 188, 77; A , 190, 482, 490; A , 193, 305;D. W. J. Cruickshank, Acla Cryst., 1948, 1, 92 ; 1949, 2, 65.O3 D. \V. J . C,ruickshank, ibid., 1950, 3, 10; 1952, 5, 511.84 V. Luzzati, ihid., 1051, 4 ,367.78ibzd., 1950, 3, 210. 7 6 H. Lipson and M. M. Woolfson, ibid., 1952, 5, 680.M. J . Buerger, ibid., p. 465350 CRYSTALLOGRAPHY.centrosymmetric cas?. Cochran 85 has given a detailed discussion of the(F, - F,) synthesis. In the early stages, this type of synthesis may bevaluable in indicating the need for structural revisions of a drastic character ;Cochran has shown that it possesses a number of properties which make ituseful for accurate structure analysis.One advantage of the method is thattermination of series errors are largely eliminated; another is thattemperature-factor parameters as well as atomic co-ordinates are refined.The method seems particularly useful for the unequivocal placing ofhydrogen atoms, and for investigation of the fine detail of the electrondistribution (e.g., in bonds).For very accurate results it is of course necessary to have data of thehighest accuracy. With photographic recording and visual estimates it isdifficult to obtain intensities more accurately than to within about 10%.Considerable advances have taken place in the techniques of using Geiger 86and proportional 87 counters for the measurement of intensities. Absorptionconstitutes another serious source of error and methods of applyingcorrections have been described 88 although perhaps the best procedure is toeliminate such errors as far as possible by using either uniformly shaped orvery small crystals where practicable. Indeed, experimental measurementsof the electron distribution can only be regarded as meaningful providedthat they include all the above precautions for ensuring the accuracy of thedata, and have been carried out at sufficiently low temperatures.J.D. D.3. STRUCTURAL CHEMISTRY.1ntroduction.-In this report, we have tried to cover three years ofinorganic and two years of organic structure analyses by X-raycrystallographic methods. Metal and alloy structures have been omitted-it seemed preferable to leave them for a subsequent report than to deal withthem inadequately in the space available this year.But limited space is aproblem which future Reporters will have to face more and more in futureyears. Acta Crystallographtica alone in 1948 contained 348 pages, whichincluded 61 papers and 15 short communications; in 1952 the figures were860, 150, and 67 respectively. Several factors seem to have contributed tothis remarkable expansion.The more widespread adoption of modern computing techniques hasbrought with it a corresponding increase in the use of three-dimensionalmethods. This is important for high-precision work but it also means thatstructures of very great complexity are now being attacked by X-raymethods. One molecule, whose structure is slowly being elucidated,contains about 100 atoms, and already more than ten three-dimensionalPatterson and Fourier series have been computed in the course of thisanalysis alone; a few years ago the labour involved would have beenconsidered pro hi bi t ive.Structural problems concerning substances which are gaseous or liquid85 W.Cochran, Ada. Cryst., 1951, 4, 408.8 7 A. R. Lang, Nature, 1951, 168, 907; PYOG. Phys. SOG., 1952, A , 65, 372; U. W.Arndt and D. P. Riley, ibid., p. 74.8 8 R. G. Howells, Acta Cryst., 1950, 3, 366; D. GrdeniC, ibid., 1952, 5, 283;H. T. Evans and M. G. Ekstein, ibid., p. 540.8 6 I d e m , ibid., 1950, 3, 268DUNITZ AND ROBERTSON STRUCTURAL CHEMISTRY. 351under ordinary conditions have also now been brought within the rangeof crystallographic analysis by recent advances in low-temperaturetechniques.89 Phase transitions, residual entropy, and dielectric anomalieshave already been extensively studied ; hydrogen cyanide,g0 carbonylchloride,s1 1 : Z-dichlor~ethane,~~ methanol,93, 94 n-propylammonium halides,95cycl~pentane,~~ n e ~ h e x a n e , ~ ~ ne~pentane,~' and thiophen 98 are among thecompounds examined and others will be discussed later in connection withaspects of molecular structure. Some points from the analysis of methanolillustrate the problems involved. The two independent investigations ofthe high-temperature modification, carried out within approximately thesame temperature range, lead to different results. One,93 based on single-crystal data, gives an orthorhombic cell in which the molecules are linked byinfinite zig-zag chains of hydrogen bonds; the other,s4 based on powderdata and therefore perhaps not completely reliable, leads to a hexagonal cellof a somewhat related structure.The situation is evidently more complexthan had been thought and may be clarified by further X-ray work,especially as another transition point (at 156.3" K) has now been detected s9in addition to the well-marked one a t 159.2" K. Tauer and Lipscomb havealso succeeded in interpreting the data for the low-temperature modification.The infinite zigzags of hydrogen bonds are preserved, but they becomesomewhat more puckered. It is concluded that the residual entropy iszero, and that the dielectric anomaly is associated with puckering of thehydrogen-bond chains.Carbonyl chloride, at -160" c, is found to have acompletely ordered structure, so that the residual entropy of 1-63 e.u.remains unexplained and presents an apparently very serious problem.Structuralproblems concerning the location of light, in the presence of heavy, atomsmay now be attacked. The most extreme example of this kind, thestructure of uranium hydride, UH,, has already been solved.loO Thehydrogen atoms lie in distorted tetrahedra equidistant (at 2.32 A) from foururanium atoms and not, as previously thought, between the pairs whoseseparation is 3.71 A. Thorium and zirconium hydrides lol have deformedfluorite structures with similarly large M-H distances, 2.41 A. Earlierviews on thorium carbide must be completely revised; lo2 the cell is nottetragonal but monoclinic, the C-C distance is 1.5 A, and the Th-C bondsseem to have considerable covalent character.In ammonium chloride(room temperature phase) the N-H bonds (1-03 A) are directed towardsS. C . Abrahams, R. L. Collin, W. N. Lipscomb, and T. B. Reed, Rev. Sci. Inslr.,1950, 21, 396; H. S . Kaufman and I. Fankuchen, ibid., p. 733; B. Post, R. S. Schwartz,and I. Fankuchen, ibid., 1951, 22, 218.W. J. Dulmage and W. N. Lipscomb, Acta Cryst., 1951, 4, 330.Neutron diffraction extends the range in other directions.g1 B. Zaslow, M. Atoji, and W. N. Lipscomb, ibid., 1952, 5, 833.92 M. E. Milberg and W. N. Lipscomb, ibid., 1951, 4, 369.93 K. J. Tauer and W. N. Lipscomb, ibid., 1952, 5 , 606.0p B.Dreyfus-Alain and J.-M. Dunoyer, Compt. rend., 1952, 234, 320; B. Dreyfus-n5 M. V. King and W. N. Lipscomb, Acta Cryst., 1950, 3, 222, 227.96 B. Post, R. S. Schwartz, and I . Fankuchen, J . Amer. Chem. SOC., 1951, 73, 5113.9 7 A. H. Mones and B. Post, J. Chem. Phys., 1952, 20, 755.98 S. C . Abrahams and W. N. Lipscomb, A d a Cryst., 1952, 5, 93.9B L. A. K. Staveley and M. A. P. Hogg, personal communication.loo R. E. Rundle, J . Amer. Chem. SOC., 1951, 73, 4172.lol R. E. Rundle, C . G. Shull, and E. 0. Wollan, Acta Cryst., 1952, 5, 22.lo2 E. B. Hunt and R. E. Rundle, J . Amer. Chem. SOC., 1951, 73, 4777.Alain and R. Viallard, ibid., p. 536352 CRYSTALLOGRAPHY.four of the surrounding chlorine ions, the two possible orientations beingoccupied at random.103 In potassium hydrogen fluoride] the hydrogen atomis at the centre of the F-H-F bond.lo4 Another type of result beyond thepower of X-ray diffraction is the establishment of the relative positions ofMg2+ and A13+ spinel as the normal rather than the inverse arrangement.lo5Fairly accurate location of hydrogen atoms can also be given by X-rayanalysis, if the data are sufficiently accurate and the other atoms presentare not too heavy.Cochran106 has provided an elegant demonstrationthat in the hydrogen bonds of salicylic acid the hydrogen atom is a t nearlythe normal covalent distance from one oxygen atom and that O-H-*.OFIG. 1. (Fo - Fc) synthesis for saliczlic acid projected on (001). The carbon and oxygenHydrogen atoms and bonding electron density may atoms have been " subtracted out.be recognised in the residuai function.is approximately collinear (Fig.1). The whole question of hydrogenbonding in organic crystals has been discussed by Donohue lo' who hasshown that strong hydrogen bonds are only formed when the H atom isapproximately collinear with the bonded atomx ; he estimates that symmetricO*.*O hydrogen bonds will occur only when the O - - - O distance is about2-3 A. In the several recent cases where a symmetric 0 * * H * * 0 bond appearsto be demanded by the crystal symmetry] e.g., in sodium sesquicarbonatedihydrate,loS in potassium hydrogen bisphenylacetate, log and in potassiumGoldschmidt and D. G. Hurst, ibid., p. 797.la3 H. A. Levy and S.W. Peterson, Phys. Rev., 1952, 86, 766.lo4 S. W. Peterson and H. A. Levy, J . Chem. Phys., 1952, 20, 704.lo5 G. E. Bacon, Acta Cryst., 1952, 5, 684.lo7 J. Donohue, J . Phys. Chem., 1952, 56, 602.lo8 C . J. Brown, H. S. Peiser, and A. Turner-Jones, Ada C v ~ s t . , 1949, 2, 167.loo J . C . Speakman, J . , 1949, 3357.See also G. H.lo6 W. Cochran, ibid., in the pressDUNITZ AND ROBERTSON STRUCTURAL CHEMISTRY. 353hydrogen bis-P-hydroxybenzoate hydrate,llo the O-H * * * 0 distance is greaterthan 2.5 A and Davies and Thomas have shown,lll for the second exampleat least, that the spectroscopic data are in marked disagreement with thesymmetric hypothesis. I t seems likely that these bonds are not reallysymmetric, but rather, that the crystal symmetry arises as a result ofrandomness in the structure.Entropy measurements would be of con-siderable interest. In two cases, however, the possibility of a O-..H---Obond cannot be excluded. In nickel dimethylglyoxime an 0 - - 0 approachof 2-42 A occurs and no absorption maxima corresponding to free 0-H ornormally bonded O-H*..O are detected in the infra-red spectrum.l12 Inmaleic acid, an intramolecular 0 * * - 0 distance of 2.46 A is observed ; 113 herethe bond distances in the carboxyl groups (Fig. 2) show fairly conclusively(a) (b)FIG. 2. Interatomic distances (in A) in (a) nickel dimethylglyoxime and(b) maleic acid.that the hydrogen atom is more firmly associated with one oxygen atom thanthe other. In the singly ionised maleate ion the negative charge should tendto be equally distributed between the two carboxyl groups and the protonshould therefore adopt a more symmetric position.The infra-red absorptionspectrum of potassium hydrogen maleate has been examined and nocharacteristic O-H - * - 0 bands seem to occur.114Together with the widening of the range of crystal analysis comes asignificant increase in depth. It is only within the last few years that allthe diffraction data available from a given crystal have been exploited to thefull in the course of analysis. Urea, one of the first organic compounds tohave been studied by X-ray methods, has been the subject of a recentreinvestigation ; 115 the final molecular parameters and probable errorsreported are : C-0, 1.262 & 0.011 A ; C-N, 1.335 & 0:009 A ; N-C-N,118" 0.9"; N-C-0, 121" 3 0.45".While probable errors close to theabove have been claimed for many years, it may be useful to call attentionto the length of the refinement process considered necessary for this simplestructure in which only four parameters define the atomic positions. Of120 reflections accessible with Cu-K, radiation, the intensities of 11 1 could110 J. M. Skinnerand J. C. Speakman, J., 1951, 185.111 M. Davies and W. J. 0. Thomas, ibid., p. 2858.l1* L. E. Godycki, R. E. Rundle, R. C. Voter, and C. V. Banks, J . Chem. Phys., 1951,113 M. Shahat, A d a Cryst., 1952, 5, 763.11* H. M. E. Cardwell, J. D. Dunitz, and L. E. Orgel, unpublished.l15 P. Vaughan and J. Donohue, Acta Cryst., 1952, 5, 530.19, 1205.REP.-VOL.XLIX. 354 CRYSTALLOGRAPHY.be estimated, the remaining 9 being negligibly small. The final parameterswere obtained after 12 Fourier sections and 2 least-square analyses in whichhydrogen atom contributions and variation of the atomic form factors wereboth taken into account. In this report we shall mention about a dozenother analyses, many of them much more complex than this, for which similarcalculations have been carried out.Meanwhile theoretical chemists have been calculating bond lengths onthe basis of various quantum-mechanical approximations, particularly forconjugated and aromatic molecules, and it is claimed 116 that, in favourablecases, they may be estimated to within 0.015 A. We shall be discussingsome of the results in later pages, noting here only that while in some cases(e.g., anthracene) the agreement between observation and theory is good,in others (e.g., naphthalene, dimethyltriacetylene) quite serious discrepanciesappear to occur.One tends to question whether comparison between bond lengths andangles derived from crystal measurements and from theoretical calculationsis really valid when applied a t this order of refinement.In crystals,molecules are packed in fairly close contact with one another and it seemsquite likely that the attainment of the most favourable packing arrange-ment may, in some cases, be associated with small displacements from theequilibrium state of the molecule considered in isolation. In the fatty acidsand soaps, the mean carbon-carbon repeat distance appears to vary fromcompound to compound-in strontium laurate it is 2-610 A, but in lauricacid 117 2.521 & 0.007 A.Decreases of about 2% in bond length fromthe gas to the crystal have been noted for hexamethylenetetramine 118 andfor pentab0rane.1~~9 I2O Such changes may well depend on the compressionforces within the crystal. As yet, the nature and magnitudes of the inter-molecular forces involved are not well understood but Lowdin's recentcalculations 121 on lattice energies may point the way for future development.Elements.-The analysis of solid chlorine provides a good example ofthe increased power of modern low-temperature techniques. The structurehad been reported to contain a Cl-C1 bond of length only 1.82 A, considerablyshorter than the distance (2.01 A) found in the gas by electron diffraction,122and also an unusually short intermolecular approach of 2.52 A.With newsingle crystal data obtained at -160" c, Collin 123 has shown that the earlierresults were incorrect ; the structure is similar to that of bromine and iodine,with Cl-C12-02 A and Cl.*.C13-34 A.The morestable a-form is shown 61 to contain %membered puckered rings of symmetryDdd as in the rhombic sulphur S, molecule. The Se-Se distance is 2-34 A,considerably longer than the 2-19 A found in the gaseous Se, molecule [thecorresponding distances for sulphur are 2.07 A (S,) and 1.89 A (S2)], andLSe-Se-Se is 105". For the second, less stable, p-modification, Burbank 62The two monoclinic varieties of selenium have been studied.116 C.A. Coulson, J . Phys. Chem., 1952, 56, 311.11' V. Vand, W. M. Morley, and T. R. Lomer, Acta Cryst., 1951, 4, 324.11* P. A. Shaffer, J . Amer. Chem. SOC., 1947, 69, 1557.llg W. J. Dulmage and W. N. Lipscomb, Acta Cryst., 1952, 5, 260.leo K. Hedberg, M. E. Jones, andV. Schomaker, J . Amer. Chem. Soc., 1951, 73, 3538.121 P. 0. Lowdin, J . Chem. Phys., 1951, 19, 1570, 1579.122 For a compilation of electron-diffraction results see P. W. Allen and L. E. Sutton,Acta Cryst., 1950, 3, 46. Iz3 R. L. Collin, Acta Cryst., 1952, 5, 431DUNITZ AND ROBERTSON STRUCTURAL CHEMISTRY. 355proposed a molecule which may be described as an &membered ring inwhich one bond has been broken; we understand, however, that his datamay be re-interpreted in terms of a normal &membered ring.lM Whitephosphorus has a cubic cell containing 56 P, molecules but the completestructure has not yet been e~tab1ished.l~~Very carefulmeasurements of the unit-cell size appeared to show a systematic decreaseof c with increasing quality of crystallinity (size of crystallites, measuredby line broadening).226 It has now been established fairly definitely thatthe variation is only apparent, the observed spacing being the mean valueof two inter-layer spacings, 3.35 k for graphitic carbons and 3.44for " non-graphitic carbons ".I279 128 The a-axis remains ~ 0 n s t a n t .l ~ ~Various modifications of the graphite lattice have been put forward,lZ9 toexplain extra reflections that appear, e g ., indicative of a cell twice as largein the basal plane, or of orthorhombic symmetry. I t has been suggested,however, that these effects arise from impurities; at least, the effects cancertainly be reproduced by the addition of bromine.130 The nature ofgraphites in general has been studied, particularly by Franklin,lz83 131 whohas been able to estimate the proportions of the material in the crystallineand the non-crystalline state, and to postulate grouping of the crystallites,as well as to determine their average dimensions. The crystalline perfectionof graphite can be reduced by grinding : the crystallite size is reduced fromabout 400 x 1200 to about 100 x 400 A (thickness and diameter).132Graphite flakes in cast iron can be shown to be more perfect near their corethan near their e ~ t e r i 0 r .l ~ ~Of particular interest in the case of graphite is the evidence concerningthe distortion of the outer electron shell of the carbon atom owing to bonding.Neutron diffraction intensities agree so well with calculated values that theBernal structure is certainly correct, though deformation from strictlyhexagonal symmetry is still a p6s~ibility.l~~ X-Ray intensities do not agreeso well. But therecan be no doubt as to the agreement of the observed data with McWeeny'snew scattering f ~ n c t i o n , l ~ ~ derived from Duncanson and Coulson's wavefunctions.136 Strong support for the McWeeny curve is also given byBrill's results on diamond.237 The graphite results point to the existence ofabout 0.08 electron in the region of each C-C bond.134 Brill had earlierestimated 0.5-0-75 electron/bond for diamond.But the latest results ofCochran's very accurate work appear to confirm the lower value.106For boron nitride, Hassel's long accepted structure,138 thoughlZ4 L. Pauling, personal communication.lZ5 D. E. C. Corbridge and E. J. Lowe, Nature, 1952, 170, 629.126 G. E. Bacon, Acta Cryst., 1950, 3, 137.127 Idem, ibid., 1951, 4, 558, 561.12g G. E. Bacon, ibid., 1950, 3, 320; J. Hoerni and J. Weigle, Nature, 1949, 164, 1088;J. S. Lukesh, Phys. Reviews, 1950, 80,226; 1951, 84,1068; J . Chem. Phys., 1951,19,383.130 J. S. Lukesh, J . Chem. Phys., 1951, 19, 1203.131 R. E. Franklin, Acta Cryst., 1950, 3, 107.132 G.E. Bacon, ibid., 1952, 5, 392. 133 E. Matuyama, Natuve, 1952, 170, 1123.134 G. E. Bacon, Acta Cryst., 1952, 5, 492.136 R. McWeeny, ibid., 1951, 4, 513; 1952, 5, 463.136 W. E. Duncanson and C. A. Coulson, Proc. Roy. SOL. Edinburgh, 1944, 63, 37.137 R. Brill, Acta Cryst., 1950, 3, 333.138 0. Hassel, Norsk. geol. Tidsskr., 1926, 9, 266.A good deal of attention has been given to graphite.This is now clearly due to the f-curves used hitherto.lz8 R. E. Franklin, ibid., p. 253356 CRYSTALLOGRAPHY.correct in outline, must be modified in favour of a pseudo-graphitic 0 n e . 1 ~ ~Hexagonal networks of B3N3 rings (B-N, 1-45A) are stacked in directregister (B above N), not shifted laterally as in graphite. This stackingsequence is undoubtedly due to the polarity of the B-N bonds.An analysisof BBB-trichloroborazole,140 B,N3H3C13, furnishes a fairly accurate valueof the B-N distance, 1.41 A, somewhat shorter than the value (1-44 A)reported earlier for borazole itself. 122 Some striking similarities existbetween these boron-nitrogen compounds ;and the isoelectronic carboncompounds (e.g., the chemical behaviour of borazole and benzene) but onthe other hand, B3N3 and graphite differ markedly both in electric propertiesand in colour. The electronic band structures of both graphite and boronnitride have been discussed.141FIG. 3. Arrangement of atoms in (a) elementary boron, (b) boron carbide,( c ) decaborane, (d) calcium b o d e , and (e) pentaborane.A structure has at last been presented for elementary boron.142 In thetetragonal unit cell 48 B atoms occur a t the vertices of four nearly regularicosahedra which pack so that every atom forms 6 bonds in a pentagonalpyramid arrangement.Two extra atoms in special positions form tetra-hedral bonds. The B-B distances are 1.75-1.80 A, which agree well withdistances found in boron hydrides and in the diborides of Al, Cr, Ti, Zr, Nb,Ta, and V, where the boron atoms form graphite-like nets.143 The eicoso-hedral arrangement of boron atoms occurs also in boron carbide and (lesstwo atoms) in decaborane. Some quite striking relations may now berecognised in several structures containing boron (Fig. 3). The structure oflSg R. S . Pease, Acta Cryst., 1952, 5, 356.l40 D.L. Coursen and J . L. Hoard, J . Anzer. Chem. SOC., 1952, 74, 1742.C. A. Coulson and K. Taylor, Proc. Phys. SOC., 1952, 64, A , 815, 834.1'8 J. L. Hoard, S. Gellar, and R. E. Hughes, J . Amer. Chem. SOC., 1951, 73, 1892.143 J. T. Norton, H. Blumenthal, and S. J. Sindeband, J . Metals, 1949, 1, Trans. Sect.,749; R. Kiessling, Acta Chem. Scand., 1949, 3, 595DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY. 357stable pentaborane, which can now be regarded as firmly established,llg9is clearly related to that of calcium boride. Boron and its compounds arecontinuing to supply theoretical chemistry with problems of a uniquecharacter ; Longuet-Higgins has discussed some of the electron-deficientcompounds in terms of non-localised molecular orbitals and Hedberg 145has given a detailed discussion of the bond lengths in the boron hydrides andrelated molecules.It is tetragonal with twoparallel but dissimilar planar sheets between which lie other atoms, bound,not to one another, but only to the sheets on either side.It is suggested thatthis relatively complex arrangement is stabilised by the presence of a nearlyfull Brillouin zone. Essentially the same structure is found in the 0-phaseof the Fe-Cr,14’ C O - C ~ , , ~ ~ and V-Ni 149 systems.Simple Inorganic Molecules.-Low-temperature studies are reported forhydrazine 150 and for hydrogen peroxide,151 two molecules important in anyscheme of standard covalent radii. The X-ray results are 1.49 A for 0-0and 1.46 for N-N, in pleasing agreement with earlier values from spectro-scopic and electron-diff raction evidence.lZ2 In hydrogen peroxide thearrangement of the hydrogen atoms, inferred from the intermolecularhydrogen bonding, is that predicted from theoreticdl ~onsiderations.1~~ Thehydrogen bonds form infinite helices round the 4, screw axes of the crystal togive a rather compact structure (the density is 1.70 g.~ m . - ~ ) . In any onehelix there are only two possible arrangements of hydrogen atoms and,since a given helix must retain the same arrangement throughout the crystal,no measurable residual entropy is to be expected at absolute zero. Forhydrazine the possibility of residual entropy due to randomness of orientationin the solid has been suggested in view of the small discrepancy (0.44 e.u.)between the entropies calculated from calorimetric data and from structuralparameters and spectroscopic assignments,153 but here again the structuredoes not appear to permit the retention of any measurable entropy a t lowtemperatures.Hydrogen bonds occur in infinite zig-zag chains in such away as to suggest that the molecules must have either the CZv eclipsed or theC, semi-eclipsed configuration, instead of the staggered as usually assumed,and the same configuration must be retained throughout the length of thechains. Spectroscopic evidence, while not in serious disagreement with theeclipsed forms, has been interpreted as favouring the C, staggeredconfiguration ; a trans(C2h)-configuration has also been suggested, on thebasis of infra-red and Raman spectra, for the solid at -190°.155 It is likelythat there is only a small difference in stability between the various formsThe p-uranium structure has been s01ved.l~~144 H. C.Longuet-Higgins, J., in the press.145 K. Hedberg, J . Amer. Chem. SOC., 1952, 74, 3486.146 C. W. Tucker, Acta Cryst., 1951, 4, 425; 1952, 5, 389, 395.147 B. G. Bergman and D. P. Shoemaker, J . Chem. Phys., 1951, 19, 515.148 D. J. Dickens, A. M. B. Douglas, and W. H. Taylor, J . Iron Steel Inst., 1951, 167,149 J. B. Pearson and J . W. Christian, Acta Cryst., 1952, 5, 157.lSo R. L. Collin and W. N. Lipskomb, ibid., 1951, 4, 10.lS1 S. C. Abrahams, R. L. Collin, and W. N. Lipscomb, ibid., p. 15.162 W. G. Penney and G. M. B. Sutherland, Trans. Faraday SOC., 1934, 30, 898.153 D.W. Scott, G. D. Oliver, M. E. Gross, W. N. Hubbard, and H. M. Huffman,lg4 P. A. Giguere and E. A. Jones, J . Chem. Phys., 1952, 80, 136.155 E. L. Wagner and E. L. Bulgozdy, ibid., 1951, 19, 1210.27; J . S. Kasper, B. F. Decker, and J. R. Belanger, J . AppZ. Phys., 1951, 22, 361.J . Amer. Chem. SOC., 1949,- 71, 2293358 CRYSTALLOGRAPHY.and that the eclipsed molecules are stabilised in the crystal by hydrogenbonds.In hydrazine dihydrogen sulphate (N,H,,+) (SO,,-) 15G the hydrogenatoms have the staggered arrangement, as in the dihydrofluoride 15’ anddihydroch10ride.l~~ In all three salts the N2He2+ ion shows a shortening ofthe N-N distance, from 1.47 to 1.40-1-42 A. has beenreported for this distance in the N,H,+ ion.159that the shortening is caused by increased coulombic attraction between theextra formal charge on the nitrogen atoms and the charge of the surroundingelectronic cloud, but this mechanism has been criticised 15* on the groundsthat the expected degree of shortening would be much smaller than thatactually observed.I t is difficult to make a quantitative estimate of theeffect; the coulomb attraction is increased but so is the internuclearrepulsion, and it is certain that the latter will predominate for very largecharges. Theoretical calculations do indicate that, in a hydrogen-likemolecule, the internuclear distance is decreased as the positive charge on thenuclei increases from unity,160 and ample spectroscopic evidence is availableto show that the internuclear distance invariably decreases (and often by aconsiderable amount) in passing from a diatomic molecule to the corre-sponding isoelectronic positive ion, where the latter exists.IG1 Thesecomparisons are not strictly analogous to that between N,H, and N,H6++,but they appear to suggest that the formal charge effect may well be largeenough to account for the observed shortening. lG2The value 1.45It has been suggested(a) (b) (c)FIG. 4. Arrangement of atoms in (a) diamond, (b) “-cage ” molecule, e.g., As,S6, and( c ) “ cradle ” molecule, e.g., As&. Sulphur occupies the square positions in As$,but the tetrahedral positions in N,S,.Two very interesting molecular crystals, sulphur nitride 163 and realgar(arsenic sulphide),a whose structures have long defied analysis, have nowbeen solved and found to be closely related.Both contain tetrameric“ cradle ”-shaped molecules (Fig. 4) as found by Lu and Donohue 16* for166 I. Nitta, K. Sakurai, and Y . Tomiie, Acta Cryst., 1951, 4, 289.157 M. L. Kronberg and D. Harker, J . Chem. Phys., 1942,10,309.158 J. Donohue and W. N. Lipscomb, ibid., 1947, 15, 115.15B K. Sakurai and Y . Tomiie, Acta Cryst., 1952, 5, 289, 293.160 T. L. Cottrell and L. E. Sutton, Proc. Roy. SOC., 1951, A , 207, 49.161 Compare, for example, internuclear distances for ground states of : LiH 1.595 Awith (BeH)+ 1.312 A ; NaH 1.887 A with (MgH)+ 1.649 A ; BeH 1-343 A with (BH)+1.215 A ; N, 1.094 %I with (NO)+ 1.066 A ; NO 1.151 A with (0,)f 1.123 A : extractedfrom the compilation of.G. Herzberg, “ Spectra of Diatomic Molecules,” Van Nostrand,1950, pp. 501 et seq.16P See also L. Pauling, “ Nature of the Chemical Bond,” Cornell Univ. Press, 1940,p. 169.164 C. S. Lu and J. Donohue, J . Amer. Chem. Sot., 1944, 66, 818.D. Clark, J., 1952, 1615DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY. 359the vapour state. The bond distances, S-N 1-60, S-S 2.58 (in N,S,), and S-As2-24, As-As 2.59 A (in As,S,) agree fairly well with the electron diffractionresults. The vapour of another arsenic sulphide, orpiment, contains “ cage ”-shaped As,& m01ecules.l~~ It is worth remarking that the “cradle”molecule is derived from the “ cage ” by removal of two atoms at oppositevertices of an octahedron. The “ cage” molecule is itself derived byisolating a portion of the diamond lattice, with distortion if necessary, andoccurs in a wide variety of substances, adamantane (CloH16), hexamethylene-tetramine (CloH12N4), P,O,, As40,, As,S,, and also in the A1,0, moleculeswhich have been shown to constitute the film on the surface of aluminiummetal.lG5a The orpiment crystal does not contain discrete rnole~ules.~~Instead, we have superimposed layers of S-shaped chains in which each As issurrounded by three S atoms, each shared by two As atoms.The structureis nevertheless related geometrically to that of realgar, and also to that ofClaude tite, As,O,. 16%A single-crystal analysis of nickel carbonyl, Ni(C0),,166 confirms thatthe molecule is tetrahedral with linear Ni-C-0; the bond distances, Ni-C1.84 and Ni-0 2.99 A, agree well with the electron-diffraction results.122Oxides and Oxy-acids of the Non-metals and Related Compounds.-Oxides and oxy-acids of nitrogen have received much attention.Nitricoxide crystals contain dimeric molecules N,02, with N-0 1-10 and N-m.02.38 A, rectangular in shape.167 The electron densities are interpreted assupporting a random distribution of the two possible arrangements inN...o o . . . N agreement with the observed residual entropy of nearlyI I 1 I QR In 2 per mole. A statistically arranged dimer with theo ’ * ‘ N N’’’o short N-0 groups parallel would also satisfy the data butone would hardly expect this arrangement to give even approximatelyrectangular molecules.It seems difficult to reconcile these results withthe infra-red and Raman results which indicate the absence of a centre ofsymmetry. 168Nitrogen pentoxide has been examined a t -60” and a t +20° c ; apartfrom an expansion of the lattice the structure does not change within thistemperature range; 169 it is of an ionic type and may be represented as[NO,J+[NO,]-. apart,and the nitronium ions are placed perpendicular to the sheets with theirnitrogen atom in the plane of the sheet. The low-temperature analysis hasbeen carried out with a high degree of accuracy, and the N-0 distances aregiven as 1.154 and 1-243 A in the positive and the negative ion respectively.The nitronium ion occurs also in nitronium perchlorate and in the crystallinesolids isolated from nitric-sulphuric acid mixtures.170Two independent refinements of Ziegler’s early work 171 lead to widelydiffering results for the dimensions of the nitrite ion. Truter 17, has reportedThe planar nitrate ions are arranged in sheets, 3-28165e H.G. F. Wilsdorf, Nature, 1951, 168, 600.l e S b K. A. Becker, K. Plieth, and I. N. Stransky, 2. anorg. Chem., 1951, 266, 293.167 W. J . Dulmage, E. A. Meyers, and W. N. Lipscomb, J . Chem. Phys., 1951, 19,1432.16* A. L. Smith, W. E. Keller, and H. L. Jonston, ibid., p. 189.170 K. Eriks, Thesis, Amsterdam, 1952.171 G. E. Ziegler, Phys. Review, 1931, 38, 1040.172 M. R. Truter, Nature, 1951, 168, 344.J. Ladell, B. Post, and I. Fankuchen, A d a Cryst., 1952, 5, 795.E. Grison, K. Eriks, and J.L. de Vries, Acta Cryst., 1950, 3, 290360 CRYSTALLOGRAPHY.1-14 A for N-0 and 132" for LO-N-0, while Carpenter,173 on the basis ofa least-squares refinement, finds 1-23 A and 116". A high degree of accuracyis claimed for both analyses and it seems very difficult to reconcile theresults. Carpenter's result is more likely on theoretical grounds since it givesa sensible sequence for the three molecules NO,' (1.15 A, 180"),169NO, (1-20& 132"),17* and NO,- (1-23 A, 116"). The nitronium ion with16 valency electrons is expected to be h e a r and the bond angle shoulddecrease from 180" as each extra electron is added,175 with diminishingdegree of N-0 bonding.In the gas phase, one bond in nitric acid is markedIy longer than theothers (N-OH, 1.41 A ; N-0, 1.22 A) 122 but in condensed phases, wherehydrogen bonding is possible, the proton becomes less firmly associated withany one oxygen atom and the distances tend to become more nearly equal.A very good example of this is found in the structure of ammonium tri-nitrate, NH,N0,,2HN03.176 The two protons from the acid molecules areinvolved in hydrogen bonds to form a trimer diagramatically representedin Fig. 5.The bond distances are sufficiently accurate to indicate significantshortening of the N-OH distance in the acid molecules. It is also to benoted that the 3-fold symmetry of the nitrate ion is destroyed by theFIG. 5. Trimer formed by two nitric acid molecules and one nitrate ion inNH,N0,,2HN03.perturbation produced by the close approach of protons to two oxygen atomsbut not to the third.Other interesting examples of the way in which nitricacid molecules may be linked are found in anhydrous nitric acid 17' (a verycomplex structure), in nitric acid r n o n ~ h y d r a t e , ~ ~ ~ and in nitric acidtrihydrate. 179Borates and Silicates.-A structure for boron trioxide, B203, has beenderived from powder photographs.180 The rather open 3-dimensionalframework is built of distorted BO, tetrahedra with one B-0 distance muchlonger (about 2-1 A) than the other three (about 1.5 A), an apparentcompromise between trigonal and tetrahedral co-ordination. Cobalt 181and magnesium 182 pyroborate, M2B205, contain discrete (B,O,)*- ions,formed by two BO, triangles with one oxygen in common.B,O,.groupsoccur together with BO, tetrahedra in endless chains in metaborlc acid,HB02.68 Boron is triangularly co-ordinated also in the mineralswarkwickite, ludwigite, and pinakiolite,'= where the structural type is173 G. B. Carpenter, ActaCryst., 1952, 5, 132.174 S. Claesson, J . Donohue, and V. Schomaker, J. Chem. Phys., 1948, 16, 207.1 7 5 A. D. Walsh, Nature, 1952, 170, 974.1 7 6 J. R. C. Duke and F. J. LIewelIyn, Acla Cryst., 1950, 3, 305.1 7 7 V. Luzzati, ibid., 1951, 4, 120.1 7 0 Idem, Compt. rend., 1951, 232, 1428.181 Idem,Acta Chem. Scand., 1950,4,1054.178 Idem, ibid., p. 239.lab S. V. Berger.ActaCryst., 1952,5,389.182 Y.TakCuchi,AcSaCrysl., 1952,5,574.Y. Takkuchi, T. WatanabC, and T. Ito, ibid., 1950, 3, 98DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY.361determined mainly by the packing of oxygen atoms in bands, boroncementing these bands together. One may compare the boroferrites.lsqBoron is tetrahedrally surrounded by four OH’S, however, in teepleite,2NaC1,Na2B,0,,H,0,185 and in bandylite, CuC1,,CuBq04,4H,0 1859 lS6 [wherethe Cu atoms are in planar 4-fold co-ordination, as in malachiteCu,(OH),CO, l 8 7 and basic copper nitrate, CU,(OH),(NO,),~.~~~ In boracite,CIMg,B,Ol,,lsg high, and low-temperature forms, boron is found in tetra-hedra and in BO,-O pyramids, the latter built on a nearly planar BO,triangle. The tetrahedra and pyramids share all their corners, so forming arigid unbroken boron-oxygen network in which relatively large spaces areleft for Mg and C1 ions.Isolated SiO, groups exist in chloritoid, (Fe,Mg),Al(OH) 4A120,(Si0,),,190where the arrangement is in layers similar to those in muscovitebut without fusion of the SiO, groups into sheets.Like moscovite,this mineral contains an OH group; it was identified (by balancing theelectrostatic valencies) but the position of the hydrogen atom was notinferred. Infinite chains of tetrahedra are found in sodium silicate,Na2Si0,,lg1 where the structure is essentially similar to that of diopside. Inthe mineral axinite, Ca,A1,(Fe,Mn)B0,SiO120H,192 the SiO, tetrahedraassociate into rings of Si,012, similar to the P40,, rings of the tetrameta-phosphate ion.lg3 This is the first time that independent Si, rings havebeen observed (in beryl, for example, they are fused with Si,Ol, rings).The BO, g.roups are planar and symmetrical.The OH group identified byelectrostatic considerations is situated almost equidistantly between theFez+ and one Al3+ ion. Its distances from four oxygen neighbours includeone of 2.5 A, while the others exceed 2-9 A, from which the position of thehydrogen bond might well be deduced. But unfortunately the accuracy ofatomic parameters is not sufficient to allow certainty in this : at least fourother 0-0 distances are apparently below 2-5 A. The Si6Ol8 ring isexemplified by tourmaline. The original note by Buerger and Hamburger,mentioned in 1949, has been followed by a full account of their analysis ofthis complex and beautiful stru~ture.1~4 In the meantime Japanese workershave given a detailed report of an independent analysis,lg5 the first announce-ment of which was as early as 1947.There are no essential differences inthe results obtained, although some atomic parameters differ by asmuch as 0-5 A. Another very beautiful structure is that of milarite,~,~a,~e,~~,~~,,~,o,~2~,196 where double rings, Si,,O,o, have been found,formed by the fusion of six additional SiO, tetrahedra, by edges, to theSi,018 ring. These rings are linked into three-dimensional framework by(Be,Si) atoms, with K+ and H20 in the centres of the double rings, and Ca2+ions in the spaces between the rings. The peculiar optical properties oflS4 E. F. Bertaut, Acta Cryst., 1950,3,473.lS6 R. L. Collin, Acta Cryst., 1951, 4, 204.lS8 W.Nowacki and R. Scheidegger, Helv. Chim. Acta, 1952, 36, 375.lS9 T. Ito, N. Morimoto, and R. Sadanaga, Acta Cryst., 1951, 4, 310.lg0 G. W. Brindley and F. W. Harrison, ibid., 1952, 5, 698.lol A. Grund and M. M. Pizy, ibid., p. 837.lQ2 T. Ito and Y . Takkuchi, ibid., p. 202.lv3 C. Romers, J. A. A. Ketelaar, and C . H. MacGillavry, ibid., 1961, 4, 114.lg4 G. Donnay and M. J. Buerger, ibid., 1950, 3, 379.lQ5 T. Ito and R. Sadanaga, ibid., 1951, 4, 385.lg6 T. Ito, N. Morimoto, and R. Sadanaga, ibid., 1952, 5, 209.lS5 M. Fornaseri, Ric. sci., 1951,21, 1192.A. F. Wells, ibid., p. 200362 CRYSTALLOGRAPHY.this mineral were attributed to “ incipient ” twinning; but it is probablethat this requires further investigation. A continuous layer structure isfound in the mineral amesite, long thought to be a chlorite, but now clearly akaolin-type crystal.lg7Several calcium silicate minerals occurring in cement have been studiedrecently, with interesting results. Isolated SiO, tetrahedra are found ineach case. The dicalcium Ca,SiO, has a, a’, p, and y forms,in order of temperature stability. The second, stable a t moderatetemperatures, has a P-K2S04 structure; the @-form is only slightly distortedfrom this. The y-form, into which the p-crystal changes slowly, has anolivine structure. Tricalcium silicate lg9 also has .a number of distinctforms, but with more marked pseudo-hexagonal symmetry, rather moretendency to disorder and, relatively to the dicalcium salt, a somewhat moreopen structure which is thought to explain its much more rapid rate ofhydration by water.The structures of two hydrates are reported. InCa2Si0, cc-hydrate,m the 50, groups are arranged so as to accommodateone water molecule per formula unit. From consideration of thetemperature required to dehydrate the crystal, the water is thought to bepresent as hydroxyl ion, with loss of a proton to an SiO, group.Unfortunately, owing to the limited data available, it is not possible todiscuss the hydrogen bonding. Hydrogen bonding has been studied withgreat care, however, in the afwillite crystal, Ca,(Si0,0H)22H20,201 occurringin cement. The combined evidence of the electrostatic balance and inter-atomic distances establishes the presence of 6 hydrogen bonds, which fallstrikingly into two groups, of mean length 2.52 and 2.72 A.They are allsituated near the plane across which cleavage is thought to occur.Before leaving the silicates, mention should be made of the observationrecently made, that, at a controlled temperature, acid will remove the A1atoms from tetrahedral and octahedral sites at quite different rates202Also there is the important study of the Iaminated structure of certainsilicate minerals, m i c r o c l a ~ e , ~ ~ ~ anorthocla~e,~~ and chrysotile,m where twodifferent crystal structures have been found associated on a sub-microscopicscale. Stacking disorder, where successive layers suffer rotational andtranslational displacements, is very frequent among the silicates. The caseof the chlorites has been given detailed attention.205Phosphates and Sulphates, etc.-An interesting phosphate structure isthat of tervalent cerium (and the rare earths La, Pr, Nd).206 The hexagonalcrystal has oxygen-lined channels containing zeolitic water.The opencharacter of the structure is emphasised by the startling increase in density-25y0-on passing to the monoclinic modification monazite. The hydratediron phosphate minerals, vivianite 207 (and the isomorphous arsenate) andludlamite,2O* have related structures in which FeO, octahedra, some sharingedges and corners, are linked by PO, groups into bands. These are held197 G. W. Brindley, B. M. Oughton, and R. F. Youell, Acla Cryst., 1951, 4, 552.198 C. M. Midgley, ibid., 1952, 5, 307.200 L. Heller, ibid., p.724.202 G. W. Brindley and R. F. Youell, ibid., 1951, 4, 495.203 T, Ito and R. Sadanaga, ibid., 1952, 5, 441.204 E. J. W. Whittaker, ibid., 1951, 4, 187.206 G. W. Brindley, B. M. Oughton, and K. Robinson, ibid., 1950, 3, 408.206 R. C . L. Mooney, ibid., p. 337.207 H. Mori and T. Ito, ibid., p. 1 .J . W. Jeffery, ibid., p. 26.201 H. D. Megaw, ibid., p. 477.208 Idem, ibid., 1951, 4, 412DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY. 363together in vivianite only by hydrogen bonds between the water molecules, inludlamite by the sharing of water molecules. A synthetic mineral, ironlazulite, Fe,(PO,),(OH) ,,m9 has a similar, though closer packed, arrange-ment. Potassium, ammonium, and czsium hexafluorophosphates have anNaC1-type structure formed of K+ and (PF,)- ions.210An interesting thiosulphate structure is that of sodium thiosulphateNa,S,0,,5H20; sodium is surrounded by a distorted octahedron of watermolecules and oxygen atoms, and columns of linked octahedra are heldtogether laterally by the thiosulphate groups (which are approximatelytetrahedral, S-S 1.97 A).,ll It is instructive to compare the Na co-ordination in this salt and in Na3SbS,,9H,0.212Inpotassium sulphamate the S-N distance, 1.60 A, indicates considerablex-bonding corresponding to H,NzSO,--.In potassium and ammoniumdinitrososulphite S-N is 1.79 A, exceptionally long even for a single bond(Tables of covalent radii give 1-74 A). Within the planar N,O, groups thebonds lengths are shortened, in fair agreement with results of molecular-orbital calculations. For sulphamic acid itself,214 S-N is 1.73 and S-01.48 A.Here, as expected from the high melting point, 206" c (cf. sulphuricacid loo), the molecule is a zwitterion, H,N=S03-. The S-0 distance isratherJonger than is usual in molecules of this type. This distance remainsremarkably constant in systems involving d orbitals on the central sulphuratom (see ref. 213), a point which is emphasised by a recent low-temperaturestudy of sulphur dioxide where the value 1-430A is in perfectagreement with micro-wave and electron-diffraction results.The C1-0 distance in systems involving d orbitals on the central atomlikewise seems constant, 1-49 A in C10, and 1.48 A in LiC10,,217 the onlycases for which accurate results are available.With selenium as central atomthe corresponding distance varies much more. and inSeO, vapour it is 1.61 but in selenious acid 219 and in crystallineSeO, 220 the bonds are much longer, between 1-72 and 1.78 A.Metallic Oxides and Related CompQunds.-In discussing these com-pounds, it is convenient to note the transition from low to high co-ordinationnumber ; in particular, from tetrahedral to octahedral environment of themetal atom.Tetrahedral CrO, groups are found in chromium trioxide,,,l linked inchains by sharing of corners. The complex oxide, Th(OH),CrO,,H,O 222contains discrete CrO, tetrahedra situated between infinite zig-zag chainsDetailed analyses are reported for three sulphuric acid derivatives.++In selenic acid20g L.Katz and W. N. Lipscomb, Acla Cryst., 1951, 4, 345.H. Bode and H. Clausen, 2. anorg. Chem., 1951, 265, 229.211 P. G. Taylor and C. A. Beevers, Acta Cryst., 1952, 5, 341.A. Grund and U. Preisinger, ibid., 1950, 3, 363.213 G. A. Jeffrey and H. P. Stadler, J., 1951, 1467.214 F. A. Kanda and A. J . King, J . Amer. Chem. SOC., 1951, 73, 2315.215 B. Post, R. S. Schwartz, and I. Fankuchen, Acta Cryst., 1952, 5, 372.217 R. E. Gluyas, 10th Ann. Pittsburgh Diffraction Conference, 1952.218 M. Bailey and A. F. Wells, J., 1951, 968.220 J. D. McCullough. J. Amer. Ckem. SOC., 1937, 59, 789.2z1 A. Bystrom and K. A. Wilhelmi, Acta Chem. Scznd., 1950, 4, 1131.a22 G. Lundgren and L. G. Sillen, Arkiv Kemi, 1949, 1, 277.J . D. Dunitz and K.Hedberg, J. Amer. Chem. SOC., 1950, 73, 3108.Idem, ibid., 1949, 1282364 CRYSTALLOGRAPHY.of Th(OH),. [Similar chains occur in Th(OH)2S0,.223] The ferrate ion,FeOg2-, as found in BaFeO, etc.,224 has almost the same dimensions as theCrO, grpup. The Cr0,Cl- ion is very similar too; 225 the Cr-C1 distance,2.16 A, incidentally, agrees with that in chromyl chloride.122 In carnotite,KU02VOg(H20) i.5, and the synthetic compound, KU02V0,,226 2-dimensionalsheets are formed by linear U02+ groups and tetrahedral V042- groups, withthe K+ ions and water of crystallisation between the layers.Nickel complexes are commonly square coplanar ; the BaNiO, structureprovides a further example. In NiO,BaO, planar 4-fold co-ordinationoccurs, although the magnetic moment shows two unpaired electrons.A quite unusual planar %fold arrangement is shown by NiO,SBaO,however.22An unusual formation with 5-fold co-ordination exists apparently invanadium pentoxide, V,05, where the octahedron of oxygen atoms around thevanadium is so much distorted (longest bond 2-81, others between 1.54 and2.02 A) that the group is virtually a trigonal bipyramid.228 Tetrahedraoccur, however, in heavy metal orthovanadates, M3V04, such as the rare-earth salts (all of which are isomorphous) which have the zircon structure,with M in 8-fold co-~rdination.~~~As regards octahedral complexes, much attention has again been givento such structures as those built up by the oxides of Mo and W.A numberof these, notably the near-trioxides Mo,02, and were described inthe previous Report.(The structure of the trioxide itself, known since1931, has been confirmed and refined.230) A still more complex oxide,W02.g0, has been e~amined,~,l as well as a mixed oxide (MO,.,~W~.,~)O,.,.~~All these near-trioxides may be written as Mn03n-1. In this type of structure,octahedra are linked by corners infinitely in three dimensions (whichwould give the composition MOO,) except that, in one direction, after everyn octahedra, edges are shared instead of corners, thus giving riseto the ratio of metal to oxygen, n : 3n - 1. The pdramolybdate ion[ M O ( M O ~ O ~ ~ ) ] ~ - , as it exists in the salt (NH,),Mo?0,,,4H20, has beenfound 233 to be slightly different from the corresponding ion Te(M0602p)6-whose structure, a regular hexagon of MOO, octahedra round the telluriumatom, was obtained by Evans.234 In the homopolyacid anion, the 7 octa-hedra do not lie in a single plane; instead, three lie in a plane a littleseparated from that of the remaining four; this distortion gives the ion agreater compactness.The paratungstate ion, however, in the compound5Na20,12W0,,28H20,235 consists, not of 6, but of 12 tungsten atomsassociated with 46 oxygen's rather than the 41 needed to give the ion acharge equal and opposite to 10Na+. The tungsten atoms themselves appear223 G. Lundgren, Arkiv Kemi, 1951, 2, 635.Z z 4 H. Krebs, 2. anorg. Chem., 1950, 263, 175.226 L. Helmholz and W. R. Foster, J . Amer. Chem. Soc., 1950, 72, 4971.226 P. Sundberg and L.G. Sillen, Arkiv Kemi, 1950, 1, 337.227 J. J . Lander, A d a Cryst., 1951, 4, 148.z28 A. Bystrom, K. A. Wilhelmi, and 0. Brotzen, Acta Chem. Scand., 1950, 4, 1119.220 W. 0. Milligan and L. W. Vernon, J . Phys. Colloid Chem., 1952, 56, 145.230 G. Anderson and A. MagnCli, Acta Chem. Scand., 1950, 4, 793.231 A. Magnkli, Nature, 1950, 165, 356.s33 I. Lindquist, Acta Cryst., 1950, 3, 159; Arkiv Kemi, 1950, 2, 325.234 H. T. Evans, J . Amer. Chem. Soc., 1948, 70, 1291.236 I. Lindquist, Acta Cryst., 1952, 5, 667.232 Idem, Research, 1952, 5, 394DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY. 365to be grouped as a hollow cage ; but the oxygen atoms of their octahedra areactually all in contact, in hexagonal close packing. Incidentally thedisposition and function of the water molecules in these structures is still anopen question.Another ion, Mo,O,~- (and the corresponding W207") , hasbeen found to be an infinite chain made up of MOO, tetrahedra andMOO, octahedra.,36 MOO, (or WO,) tetrahedra are not common, but dooccur in such compounds as M,MoO, where M = Ag, Na, gCa, etc. A six-membered ring of WO, octahedra, is formed in the tungsten bronzes,M,WO,.237 Continuous sheets of octahedra are found in yellow molybdicacid, Mo0,,2H20, the octahedra sharing corners in two directions to give thelayers the composition (Moo,),. The remaining oxygen atom must liebetween the layers and the very interesting speculation has been advancedthat, by analogy with BaUO,, a doubly charged ion H,02+ is present.238In lithioph~rite,~~~ MnO, octahedra form sheets stacked alternately withsheets of (Al,Li)(oH)G octahedra. The layers are bound to one another byhydrogen bonds very much as in hydrargillite. A three-dimensional frame-work of continuous tubes is built up by MnO, octahedra in psilomelane,(BaH,O),Mn,O,,.The arrangement is reminiscent of the zeolites and,indeed, dehydration properties are closely similar.240The co-ordination of titanium with oxygen, as illustrated by bariumtitanate, can vary enormously-from a perfect octahedron with all oxygenatoms shared, to a trigonal pyramid with no sharing of oxygen. Bariumtitanate has received much attention, owing to its very importantferroelectric properties. The structures of the cubic 241 and the tetragonal 242forms have been examined-as also have the structures of the ferroelectricniobates and tantalate~.~,~ Twinning and polymorphism in these andother ferroelectrics has been discussed.2u A comprehensive study of theorigin of ferroelectricity in BaTiO, in particular, and covering PbZnO,,NaNbO,, KNhO,, NaTaO,, KTaO,, RbTaO,, and WO,, has been made by-mega^.^^ There are also more complex titanates and niobate~.~~,Another structure determination from powder photography is that ofNa,Pt,O, ( x < l).247 Pt atoms, in continuous rods, surrounded by oxygenin square array, form an infinite cubic stage structure, with the Na ions atthe centre of each cubic hole, between 8 oxygen atoms.As to oxides ofvery low oxygen content, it has been found that those of the formulaM,Ti,O, where the metal is Mn, Fe, Co, Ni, or Cu (but not V, Cr, or Zn) , havethe high-speed steel carbide structure, Fe3W3C, and show metallicproperties.%*Halide Structures.-The fluorides present cases of very varyingcomplexity.The simple hydrate, KF,2H20, consists of distorted octahedraabout both K+ and F- ions, and distorted tetrahedra of two positive and236 Idem, Acta Cheun. Scand., 1950, 4, 1066. 237 A. Magndli, Nature, 1952, 169, 791.23E I. Lindquist, Acta Chena. Scund., 1951, 5, 670.258 A. D. Wadsley, Acta Cryst., 1952, 5, 676. 240 Idem, Nature, 1952, 170, 973.e41 J. W. Edwards, R. Speiser, andH. L. Johnston, J. Amer. Chem. SOC., 1951, '43,2934.*42 H. T. Evans, A d a Cryst., 1951, 4, 377.243 P.Vousden, ibid., p. 68, 373, 545; 1952, 5, 690; R. Pepinsky, ibid., p. 288.244 E. A. Wood, ibid., 1951, 4, 353; R. G. Rhodes, ibid., p. 105.245 H. D. Megaw, ibid., 1952, 5, 739.*46 B. Aurivillius, Arkiv Kemi, 1950, 1, 499; 1951, 2, 519; 1951, 3, 153.247 J . Waser and E. D. McClanahan, J. Chem. Phys., 1951, 19, 413; 1952, 20, 199.249 N. Karlsson, Nature, 1951, 168, 558366 CRYSTALLOGRAPHY.two negative ions about the H20 molecules.2P9 In K2TiF6, titanium isoctahedrally surrounded by fluorine (Ti-F 1-91 A) while the potassium has12 fluorine neignbours.250 Quite simple structures are also found forMnF2,251 MoF,, and TaF,.252 In VF3253 the structure may be regarded asbuilt up of alternate planes of fluorine and vanadium atoms. In C S S ~ , F , , ~ ~however, the antimony is approximately tetrahedrally surrounded byfluorine (Sb-F 2.2 A); two tetrahedra sharing corners form the anionSb2F,-.A more complex situation appears to exist in the salts MSb,F,,(M = K, Rb, Cs, NH,, or Tl).255 The Sb is linked to three F’s by threeshort bonds (pyramidal, Sb-F, 2.0 A) and then through three more fluorineatoms at about 3-0 A to three other SbF, tetrahedra forming in this way afinite complex Sb,F13-. Some double fluoride structures have been brieflysurveyed and the relationships between them and oxide structuresdiscussed.256 The oxyfluoride of actinium has the fluorite structure ;LaOF, YOF, and PuOF are closely related.257Like potassium cuprochloride, the compounds (NH,),CuCl,, (NH,),CuBr,,and K2AgI, have been found to be based on MX, tetrahedra sharing cornersto form long chains of composition MX,, with the positive ions situatedbetween them.258 Copper is tetrahedral also in CSCUC~,.~~~ Indiummonobromide, InBr, has a rather unusual double-layer structure with oneIn-Br distance 2-80, and four others 3.29 A, indicating considerablecovalency.260 InBr is isostructural with orthorhombic TlI, which isinteresting, in view of the similar electronic configuration of indium andthallium.However, TI1 can also crystallise with a CsC1- or NaC1-typestructure.261 Another markedly covalent halide is ThBr,, with two Th-Brdistances of 2.57 A.262 NaAlCl, forms an ionic lattice of Na+ and AlC1,-ions (Al-Cl 2.13 A),263 in marked contrast to the octahedral arrangementin aluminium chloride ; presumably the strongly electro-positive sodiumis responsible.The bridged structure for fused aluminium chloride, Al,CI,,has been confirmed. For fused indium(Ir1) iodide the X-ray analysis doesnot distinguish clearly between the monomeric and the dimeric form;fused tin(1v) iodide, as expected, contains monomeric tetrahedral molecules.264In K,Ru2Cl1,O,H2O, the anion is a double octahedron composed of twoRu atoms joined by 0 and surrounded each by five C1 atoms (Ru-O-Ruis linear).265 The compounds Co(NH3),,T1C1, and Co(NH,),,TlBr, havea simple NaC1-type lattice, with Co and T1 surrounded by octahedra249 T. H. Anderson and E. C. Lingafelter, Acta Cryst., 1951, 4, 181.260 S. Siegel, ibid., 1952, 5, 683.251 M. Griffel and J. W.Stout, J . Amer. Chem. Soc., 1950, 72, 4351.258 V. Gutmann and K. H. Jack, Acta Cryst., 1951, 4, 244.253 Idem, ibid., p. 246.254 A. nystrom and K. A. Wilhelmi, Arkiv Kemi, 1951, 3, 373.255 Idem, ibid., p. 17.2s6 W. L. W. Ludekens and A. J. E. Welch, Acta Cryst., 1952, 5, 841.257 W. H. Zachariasen, ibid., 1951, 4, 231.258 C. Brink and H. A. S. Kroese, ibid., 1952, 5, 433 ; C. Brink and A. E. van Arkel,260 N. C. Stephenson and D. P. Mellor, Austral. J . Sci. Res., 1950, 3, A , 581.261 L. G. Schulz, Acta Cryst., 1951, 4, 487.263 N. C. Baenziger, Acta Cryst., 1951, 4, 216.264 R. L. Harris, R. E. Wood, and H. L. Ritter, J . Amer. Chem. Soc., 1951, 73, 3161 ;266 A. McL. Mathieson, D. P. Mellor, and N. C. Stephenson, Acta Cryst., 1952, 5, 185.i b i d ., p. 506. 259 L. Helmholz and R. F. Kruh, J . Amer. Chem. SOC., 1952, 74, 1176.262 R. W. M. D’Eye, J . , 1950, 2764.R. E. Wood and H. L. Ritter, ibid., 1952, 74, 1760, 1763DUNITZ AND ROBE~TSON : STRUCTURAL CHEMISTRY. 367(Bond lengths in A.)of ammonia and halogen respectively ; 266 the bismuth compound,Co(NH,) ,,BiCl6, is i s o m o r p h o ~ s . ~ ~ ~ In the lead which isdiamagnetic, the lead appears to exist in two valency states; PbCl, octa-hedra of differing dimensions are indicated by extra lines in the powderphotographs. The structure of K,ReBr, is of the K,PtCl, type, asexpected.268 Other halide anions which have been studied by X-raydiffraction of their solutions include PtC16, PtBr,, Ta6Br,,, and Ta6C1,,.269Another bromide recently studied is FeBr,.270, The mixed halide PCl,I has been shown to be tetrachlorophosphoniumdichloroiodide, where the cation [PCl,] + is tetrahedral and the anion[Cl-I-ClI- is linea1-.~~1 A series of polyiodide anions, I,-, 15, 17-, and evenIg-, may be obtained by dissolving iodine in aqueous potassium iodide. TheI,- ion has been found to be linear with 1-1 distances 2-82 and 3-10 272(cf. 2.67 A in 12).In NMeJ, 273 we have two sets of almost squarenets of iodine atoms (represented diagramatically below) separated by43A. The cations are situated in the large empty spaces between the1 1I II 3-14 I----I-I-I 1-I !I 3.55 I 2-93 I I__-. I-I--I 1-i 3.11 2.93 3.55 fnets (see inset). The distances vary sufficiently so that discrete V-shapedI,- ions may be recognised.I t seems very probable that these complex ionsarise from the polarisation of I, molecules by I- ions to give 1-1 - * - I-,1-1. - I- - . - 1-1, etc. The high members are formed only with very largecations and it would be very interesting to know their structures.Mercury Compounds.-Several interesting compounds of mercuryremain -to be described. Aminomercuric chloride and bromide containzig-zag chains -Hg-NH,+-Hg-, linear about Hg, tetrahedral about N, withthe halide ions between the chains.274 The structure of Millon's base,Hg2N*OH,2H,O, must be rather similar, although here the -Hg-N-Hg net-work is of the cristobalite type.275 Cinnabar, HgS, has infinite spiralchains, -Hg-S-Hg- with an angle of 105" a t S, and the bonds nearly collinearat Hg (172°).276Chelate Compounds.-Chromium has provided some rather interestingexamples of chelate co-ordination in the oxalato-complexes.InK3[Cr(C,0,),)],3H,O, the chromium is surrounded octahedrally by the sixoxygen atoms (Cr-0 1.90 A) of the three oxalate groups, and the complex so2 6 6 T. WatanabC, M. Atoji, and C. Okazaki, Acta Cryst., 1950, 3, 405.2 6 7 M. Atoji and T. WatanabC, J . Chern. Phys., 1952, 20, 1045.268 D. H. Templeton and C. H. Dauben, J . Amer. Chenz. SOC., 1951, 73, 4492.269 P. Vaughan, J. H. Sturdivant, and L. Pauling, ibid., 1950, 72, 5477.270 N. W. Gregory, ibid., 1951, 73, 472.271 W. F. Zelezny and N. C. Baenziger, ibid., 1952, 74, 6151.272 R. C. L. Mooney, 2. Krist., 1935, 90, 143.27s R.J. Hach and R. E. Rundle, J . Amer. Chem. SOC., 1951, 73, 4321.274 W. h'. Lipscomb, A d a Cryst., 1951, 4, 266; L. Nijssen and W. N. Lipscomb, ibid.,276 K. L. Aurivillius, A d a Chem. Scand., 1950, 4, 1413.1932, 5, 604. 276 W. N. Lipscomb, ibid., 1951, 4, 156368 CRYSTALLOGRAPHY.formed is packed by ionic and hydrogen bonding with the K 1 ions and theH20 molecules. The rubidium salt is isomorphous but not the ammoniumsalt, owing, probably, to the ability of NH,+ to form tetrahedrally directedhydrogen bonds resulting in a more open structure. In the red dioxalato-complex, trauts-K2[Cr(C204)2(H20)2],3H20, the two oxalate groups lie in asingle plane and the two co-ordinated water molecules are above and belowat slightly greater distances (Cr-0 1.92 for carboxyl oxygen, 2.02 A forwater).277Copper is in roughly planar co-ordination with two molecules of ethylene-diamine in the compound Cu{en),,Hg(SCN),; here the sulphur atoms aretetrahedrally arranged round the mercury but the LS-C-N reported differsfrom 180" by as much as 24°.278 In copper 279 and nickel dimethyl-glyoxime 112 the entire molecule is planar with nitrogen in a square aboutthe metal atom (Ni-N 1.87; Cu-N 1.92 A).The nickel compound containsan unusually short 0 - 0 0 approach of 2-42 A, and the possibility that thehydrogen bond might be symmetric has been discussed.In the copper-DL-proline complex, Cu(C,H80202N),,2H20, copper againforms square coplanar bonds.280 The amino-acid molecules are attachedby N (Cu-N 1-99 A) and by 0 (Cu-0 2.03 A).Two longer bonds, 2.52 A,to water molecules complete the distorted octahedron so frequent in copperco-ordination. In cupric acetate [Cu(CH3*C02),,H20],, the two Cu atomsform a pair, bridged by the four carboxyl ions (Cu-0 1.97 A), which arearranged symmetrically about the Cu-Cu axis. The octahedron is com-pleted by two water molecules (at 2-20 A), one on either side of the copperatom.2s1 Particularly striking is the Cu-Cu distance, 2-64 A, very close tothat found in metallic copper (2-56 A).An organic base is involved in co-ordination, though not in chelation,in MnC12,2(CH2)6N,,2H20.282 The Mn, at a centre of symmetry on thecommon three-fold axis of the two hexamethylenetetramine molecules, issurrounded by two chlorine atoms (at 2.47 A), two water molecules (at2.00A) and two nitrogen atoms (at 2-40 A).The bonding is sp3d2 andmagnetic susceptibility measurements indicate five unpaired electrons.Hexamethylenetetramine forms complexes with a variety of simple salts ;in CaBr2,2(CH,),N4, 10H,O, however, the organic molecule is not involvedin co-ordination round the calcium atom.283Molecular Compounds.-A series of complete structure determinationsof molecular compounds of boron trifluoride with ammonia, methylamine,trimethylamine, and methyl cyanide has been made and the results havebeen discussed in relation to the relative stabilities of the complexes.2MThe methyl cyanide compound is much less stable than the others, and in it2 7 7 J.H. van Niekerk and I;. R. L. Schoening, Acta Cryst., 1951, 4, 35; 1'352, 5, 196,278 H. Scouloudi and C. H. Carlisle, Nature, 1950, 166, 357.279 E. Bua and G. Schiavinato, Gazzetta, 1951, 81, 212, 847; S. Bezzi, E. Bua, and280 A. McL. Mathieson and H. K. Welsh, Acta Cryst., 1952, 5, 599.2 8 1 J . N. van Niekerk and F. R. L. Schoening, Nature, 1953, 171, 36.282 Y . C. Tang and J . H. Sturdivant, Acta Cryst., 1952, 5, 74.283 A. Addamiano and G. Giacomello, Ric. sci., 1951, 21, 2121.284 J. L. Hoard, S. Geller, and W. M. Cashin, A d a Cy-yst., 1951, 4, 396; S. Geller andJ . L. Hoard, ibid., p. 399 ; J. L. Hoard, S. Geller, and T. B. Owen, ibid., p. 405 ; S. Gellerand J . L. Hoard, ibid., 1950, 3, 121; J - L. Hoard, T. B. Owen, A. Buzzell, and 0. N.Salmon, ibid., p.130.475, 499.G. Schiavinato, ibid., p. 856DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY. 369(1) the B-N distance, 1.635 A, is significantly longer than in the others (1.67-1.60 A) and (2) the BF, molecule undergoes much less alteration in shape(compared with free BF,). Preliminary data are also reported for methylcyanide-BCl,, methyl cyanide-BBr,, trimethylamine-BH,, and dimethyl-amine-BF,. 285Clathrate compounds (complexes in which molecules of one kind form aframework within which molecules of a second kind are trapped) havecontinued to provide interesting results. The magnetic susceptibility ofthe oxygen-quinol complex has been measured and it is found that practicallyno magnetic interaction occurs between the oxygen Thedielectric properties of some quinol clathrates have been st~died.~87 Theexistence of= optically active clathrate-type frameworks 2880 has been utilkedfor the resolution of racemic mixtures of asymmetric molecules capable ofentering the enclosures.sec.-Butyl bromide has been resolved by formationof its complex with trithymotide 2886 (here the exact nature of the enclosureis not yet known), and optically active derivatives of long-chain hydro-carbons have been resolved2S9 by formation of complexes with urea andthiourea (here the void spaces are channels rather than completelyenclosed cages as in the quinol and ammonia-nickel cyanide 291 compounds).Resolutions have also been achieved by formation of addition compoundswith c y c l o d e ~ t r i n s .~ ~ ~It now appears that the crystalline hydrates formed by many gases(Kr, Cl,, SO,, H,S, CH,Cl, etc.) constitute a further example of clathratecompounds in which the " inert gas " molecules are enclosed within polyhedraformed by the oxygen atoms of interlinked water molecules. Severalalternative structures have been proposed 293 but we shall mention only onedue to Pauling and Marsh who have obtained X-ray evidence for it in thecase of chlorine hydrate. In the cubic cell 46 water molecules are arrangedto form two pentagonal dodecahedra and six tetrakaidecahedra ; formolecules as large as chlorine only the latter are occupied, to give theformula 6C12,46H,0 or very nearly Cl,,8H20.Organometallic Compounds.-Dimethylberyllium has been examined bySnow and R ~ n d l e .~ ~ ~ Linear chains >Be(CH,),*Be(CH,),*Be < in whichthe CH, groups are tetrahedrally arranged about the Be atoms are found,showing the tendency of the metal atoms to use all their low-energy orbitalsfor bond formation even though combined with elements or groups containingno unshared pairs. A similar structure is found for beryllium d i ~ h l o r i d e . ~ ~ ~The very unusual " sandwich " structure (I), first suggested by Woodwardz 8 5 S. Geller and 0. N. Salmon, Acta C~yst., 1951, 4, 379; S. Geller, R. E. Hughes,z86 D. F. Evans and R. E. Richards, Nature, 1952, 170, 246.287 J. S. Dryden and R. J. Meakins, ibid., 1952, 169, 324.288a A. C. D. Newman and H. M. Powell, J., 1952, 3747.2886 €3. M. Powell, Nature, 1952, 170, 155.289 W. Schlenk, Internat.Congr. Analyt. Chem., Oxford, 1952.zg0 Idem, Annalen, 1949, 565, 204; A. E. Smith, Acta Cryst,, 1952, 5, 224.291 J. H. Rayner and H. M. Powell, J., 1952, 319.292 I;. Cramer, Ajigew. Chewz., 1952, 64, 136.2s3 L. Pauling and R. E. Marsh, Proc. Nut. Acad. Sci., 1952, 20, 112; M. vonStackleberg and H. R. Miiller, Natuvwiss., 1951, 38, 456; J . Chem. Phys., 1951, 19,1319; W. I;. Claussen, ibid., pp. 259, 1425.294 A. I. Snow and R. E. Rundle, Acta Cryst., 1851, 4, 348.2*5 R. E. Rundle and P. H. Lewis, J . Chem. Phys., 1952, 20, 132.and J. L. Hoard, ibid., p. 380; S . Geller and M. E. Milberg, ibid., p. 381370 CRYSTALLOGRAPHY.et aZ.296 for the remarkable new aromatic molecule dicyclopentadienyliron(ferrocene) has been confirmed by X-ray analysis.297 Accurate bondlengths are not yet available but the indications are C-C 1.4 and Fe-C2-0 A.Non-localised molecular orbitals give perhaps the best description ofthese molecules. It is not possible to write a simple 10-bonded structurefor (I), but Dunitz and Orgel have shown that its stability can be attributedto bonding between an atomic d orbital of the iron atom and a molecularorbital associated with the pair of cyclopentadienyl radicals.(1) (11)Hydrocarbons.-Among the hydrocarbons we have three analyses ofoutstanding accuracy to report but, before proceeding to these, it isconvenient to mention some other analyses which have been carried out withrather less attempt at precision. The structure of P-di-tert.-butylbenzenehas been investigated in connection with a study of hyperconjugation; nomarked shortening of the bonds connecting the phenyl with theattached groups is observed.63 In 3 : 4-5 : 6-dibenzophenanthrene (11)steric cwsiderations prevent the molecule from adopting a planar configur-ation ; In octamethyl-naphthalene, mutual interference of the methyl groups, which lie alternatelyabove and below the mean molecular plane, occurs; 'the ring system itselfappears to be slightly distorted but the bond lengths are normal.2mthe individual rings are but little distorted.298FIG.6. Interatomic distances (in A) observed (and calculated) in naphthalene andanthracene.The 3-dimensional X-ray data for naphthalene and anthracene have nowbeen corrected for termination-of-series The resultant changes inthe bond lengths are not large, the maximum being 0.018 and the mean0.0068.The new averaged lengths are given in Fig. 6 together with (inparentheses) results of the most recent calculations based on molecular2*6 G. Wilkinson, M. Rosenblum, M. C. Whiting, and R. B. Woodward, J . Anzev.Chem. SOC., 1952, 74, 2125.297 E. 0. Fischer and W. Pfab, 2. Naturforsch., 1952, 7, B, 377; P. F. Eiland andR. Pepinsky, [. Amev. Chem. Soc., 1952, 74, 4971 ; J. D. Dunitz and L. E. Orgel, Nature,1953, 171, 121.298 A. 0. McIntosh, J. M. Robertson, and V. Vand, Nature, 1952, 169, 322.*09 J. M. Robertson, personal communication.300 F. R. Ahmed and D. W. J. Cruickshank, Acta Cryst., 1952, 5, 852DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTKY.371orbital theory ; 301 for anthracene the agreement is good, but for naphthalenethere are still significant discrepancies.Jeffrey and Rollett 302 have taken full advantage of an opportunity forunusually accurate structure analyses in the case of dimethyltriacetylene(Fig. 7). The rod-shaped molecules lie on %fold axes, and the atomicFIG. 7. Interatomic distances (in A) in dimethyltriacetylene.positions are defined by only four parameters. In the calculations allowancehas been made for tennination-of-series corrections, free rotation of themethyl groups, thermal anisotropy, and for bonding-electron density. Thefinal R factor is 0.08 and the estimated standard deviation of the bond lengthsis less than 0.01 A.But here again marked discrepancies seem to existbetween theory and the observed bond distances. One difficulty concernsthe length of the triple bonds, which in conjugation should be greater thanthat of an isolated triple bond. In dimethyltriacetylene (and in other similarmolecules) they are rather shorter than the acetylene value, 1.204 A. I t ispossible, of course, that a smaller value than this should be adopted asstandard triple bond because of the stretching effect of H C=C H ; Jeffreyand Rollett suggest 1.185 A, but it can be estimated that, for stretching of0.02 A, the improbably large charge of about 0-4 electron per carbon atomwould be required.The results of structure analysesof small alicyclic rings are in some respects rather puzzling.Owen andHoard 303 have determined the structure of octachlorocyclobutane and haveshown that the ring is non-planar with markedly long C-C bonds. Non-planar ring systems are also found by electron diffraction in octafluorocyclo-butane 304 and in cyclobutane it~elf,~05 although in the latter a planarequilibrium configuration with large amplitude of out-of-plane bending isalso compatible with the evidence. Planar, centrosymmetric, four-membered rings are found in tetraphenylcyclob~tane,~~~ in dinaphthylene-~yclobutane,~O7 and in dimethylketen dimer.308, 299 In all these cyczobutanederivatives the ring C-C distances are 1-56-1-60 A, i.e., markedly longer thannormal. The obvious interpretation of this elongation as being due toweaker bonding as a result of Baeyer strain is, however, quite unacceptablesince, in 3-membered rings where the strain is much more severe, the ring-C-C distances are consistently shorter than normal.Coulson and Moffitt 309have suggested that, since the bonding orbitals do not point in the bonddirections, some degree of X--x bonding must exist in addition to the usual301 C. ,4. Coulson, R. Daudel, and J . M. Robertson, Proc. Roy. Soc., 1951, A , 307, 306.302 G. A. Jeffrey and J . S. Rollett, ibid., 1952, A, 213, 86.303 T. B. Owen and J . L. Hoard, Acta Cryst., 1951, 4, 172.304 H. P. Lemaire and R. L. Livingston, J . Amer. Chem. Soc., 1952, 74, 5732.305 J . D. Dunitz and V. Schomaker, J . Chem. Phys., 1952, 20, 1703.306 J . D. Dunitz, Acta Cryst., 1949, 2, 1 .307 J .D. Dunitz and L. Weissman, ibid., p. 62.308 W. N. Lipscomb and V. Schomaker, J . Chem. Phys., 1946,14, 475.30e C. A. Coulson and W. E. Moffitt, Phil. Mug., 1949, 40, 1.+ - - +Carbocyclic Compounds.-Small YZngs372 CRYSTALLOGRAPHY.0-0 bonding, and that this might lead to bond shortening. Dunitz andSchomaker305 have drawn attention to the fact that cyclobutane is thermo-chemically much more unstable than would be expected, and have tentativelyascribed this to repulsion of the non-bonded atoms (separated by only 2.2A), which may also result in elongation of the bonds. A combination ofthe two effects, one leading to shortening, the other to lengthening, mightseem to offer one interpretation of the bond-distance evidence, but it cannotbe said that the situation has been satisfactorily explained.cycloHexane rings.The halogen derivative, 1 : 2-dibromo-4 : 5-di-chlorocyclohexane, has the configuration KKEE 310 and is isomorphous with the1 : 2 : 4 : 5-tetrachloro- and -tetrabromo-compounds.3~~ Of particularchemical interest is the fact that elimination of hydrogen chloride from6-hexachlorocyclohexane by alkali removes that chlorine atom whichprotrudes most directly from the ring, as shown by X-ray analysis of theresulting pentachlorocy~Zohexene.~~~ a-Phloroglucitol, a 1 : 3 : 5-hydroxy-cyczohexane with the configuration KICK, gives a dihydrate and a diammoniatewhich are i~omorphous.~1~ The dihydrate of 1 : 3 : 5-triaminocyclohexanehas, it seems, the same structure also, so that, curiously enough, replacementof the O-H.-*O bonds, which hold the structure together, by bonds of thetype N-H * - 0 or O-H * * N leaves the arrangement of the moleculesunaffected.Naphthalene tetrachloride (a preliminary examination of whichwas made by W. H. Bragg as long ago as 1927) can be regarded as 1 : 2 : 3 : 4-tetrachloro-5 : 6-benzocyclohexene, in which the chlorine atoms have theconfiguration l c , Z K , 3 K , 4 ~ . ~ ~ ~ Analyses of a- and p-l-chloromercuri-2-methoxycyclohexane have shown that, contrary to earlier opinions based onchemical evidence, the a-form has the trans-configuration, while the p-formis c Z S . ~ ~ ~A well-resolved projection of the cupric tropolonestructure provides confirmation 316 of the planar 7-membered ring system(111) which is supported also by electron-diffraction e~idence.~l' Thechemical structure of purpurogallin (IV) has also been ~onfirmed.~l*Several papers pertaining to the structure ofcyclooctatetraene have appeared.The D2d or " tub " model withunequal bond lengths is supported by two electron-diffraction studies ofcyclooctatetraene itself ,319 by an X-ray analysis of the monocarboxylica~id,3~0 and also by theoretical consideration^,^^^ in addition to the earlierSeven-membered rings.Eight-membered rings.310 The notation used is due to 0. Hassel (Tidsskr. Kjemi, 1943, 5, 32); E and Kcorrespond to the p (polar) and e (equatorial) of K. S. Pitzer and C. W. Beckett ( J .Amer. Chem. Soc., 1947, 69, 977). The co-existence of these two nomenclatures oftenleads to confusion.311 0.Bastiansen and 0. Hassel, Acta Chem. Scand., 1951, 5, 1404; 0. Hassel andE. W, Lnnd, ibid., 1952, 6, 238.812 R. A. Pasternak, Acta Cryst., 1951, 4, 316.313 P. Anderson and 0. Hassel, Acta Chenz. Scund., 1951, 5, 1349.314 M. A. Lasheen, Acta Cryst., 1952, 5, 593.315 A. G. Brook and G. F. Wright, ibid., 1951, 4, 50.316 J. M. Robertson, J . , 1951, 1222.3 1 7 E. Heilbronner and K. Hedberg, J . Amer. Chem. SOC., 1951, 73, 1386.318 J. D. Dunitz, Nature, 1952, 169, 1087.319 I. L. Karle, J . Chem. Phys., 1952, 20, 65; K. Hedberg and V. Schomaker, 115thAmer. Chem. SOC. Meeting, San Francisco, 1949.320 D. P. Shoemaker, personal communication.321 W. B. Person, G. C. Pimentel, and K.S. Pitzer, J . Amer. Chem. SOC., 1952,74,3437DUNITZ AND ROBERTSON STRUCTURAL CHEMISTRY. 373X-ray evidence.322 The D, (crown) model and the D,d (tub with equalbonds) model have also been proposed323 but the balance of the evidenceseems to favour D,d.HO 0Heterocyclic Compounds.-Compounds containing oxygen. A chemicalproblem has now been settled by a low-temperature X-ray analysis ofdiketen.324 The arrangement of carbon and oxygen atoms corresponds toa p-lactone structure ; the but-3-eno-p-lactone formula (V) is supported bythe distribution of the bond lengths.Structures assigned to two other molecules on chemical grounds must bealtered in the light of X-ray evidence. The compound previously-known asI' cis-naphthodioxan " (VI) has been shown by Furberg and Hassel 325 to bedi-1 : 3-dioxacycEopent-2-y1 (VII).The molecule is centrosymmetric, the ringsare non-planar (ascribed to mutual interference of neighbouring methylenegroups), and the bond distances are quite normal (C-C 1.52; C-0 1.41 A).GrdeniC 326 has shown that the compound supposed to be l-oxa-4-mercura-cyclohexane (VIII) has actually a structure corresponding to the 12-memberedring formula (IX). The angle C-Hg-C is close to 180".CH,*HgCH,*CH,OCH, I OCH, II I CH,*CH,*Hg*CH, (IX)Compounds containing nitrogen. A very careful refinement of theadenine hydrochloride structure has been undertaken by C ~ c h r a n , ~ ~ ' usingthe (F, - F,) synthesis, and taking into account anisotropic temperaturevibration for every atom.Geiger-counter intensity data were employed.The result, showing individual peaks for all the hydrogen atoms, allowsunequivocal decision as to the particular tautomer present in the crystal (X),a conclusion reached independently by Donohue lo' by consideration of thehydrogen bonding. The structure of the hydrochloride of guanine, theother purine base occurring in nucleic acid, is closely related to that of theadenine salt, despite the different symmetry of the crystals.328 A322 H. Kaufman, I. Fankuchen, and H. Mark, Nature, 1948, 161, 165.323 0. Bastiansen and 0. Hassel, Acta Chem. Scund., 1949, 3, 209; B. D. Saksena andH. Narain, Nature, 1950, 166, 723 ; E. R. Lippincott, R. C. Lord, and R. S. McDonald,J. Amer. Chem. Soc., 1951, 73, 3370.s24 L.Katz and W. N. Lipscomb, A d a Cryst., 1952, 5, 313.835 S. Furberg and 0. Hassel, Acta Chem. Scund., 1950, 4, 1584.S t 6 D. Grdenid, Acta Cryst., 1952, 5, 367.sa7 W. Cochran, ibid., 1951, 4, 81. 328 f . M. Broomhead, ibid., p. 92374 CRYSTALLOGRAPHY.substituted pyrimidine, 5-bromo-2-metanilamidopyrimidine, an active anti-malarial, has been studied, and the crystal structure reported.329A 3-dimensional analysis for tetramethylpyrazine (XI) shows that theN\ H c(H/ I MeHN NHH > q M e (XIV)molecule is planar and centrosymmetric. Within the ring C-C is reportedto be 1-44 and C-N 1.31 A, and the external C-C bonds are 1.50Presumably the x-electrons are concentrated more in the C-N bonds than inC-C because of the greater electronegativity of the nitrogen atoms.Forphenazine (XII), a 2-dimensional study does not reveal such large differencesin the bond lengths; C-N is given as 1.32-1.34 and C-C as 1.38-1.39 A.331A preliminary announcement of a refinement of the cyanuric acidstructure (XIII) has appeared.332 In the earlier analysis one C - 0 bondlength had been reported to be different from the other two but the newmeasurements show that the approximation to %fold molecular symmetrymust be very close indeed. The C-0 distances are virtually identical ; thosefor C-N are also very nearly equal. The mean values are 1-21 and 1.355 A,respectively, indicating some contribution of resonance structures in whichNH is positively charged. In “ aldehyde ammonia,” according to L ~ n d , ~ a reduced triazine ring (XIV) has the chair form, with the methyl groups inmK-configuration.The water, hydrogen-bonded to the nitrogen atoms,forms what are effectively puckered six-membered rings of H,O molecules(0.. 00 2.71 A)-a striking and unusual arrangement.The material previously thought to be quinocol (XV) has been shown byDavies and Powell 334 to be quinaldil (XVI). The arrangement in the crystalis very curious, since the cis-configuration is adopted, and the moleculesall point in the same direction to give a highly polar structure. The quinolinering is coplanar with its neighbouring carbonyl group, and the moleculetwists about the central C-C bond to achieve steric clearance.szs J. Singer and I. Fankuchen, Acta Cryst., 1952, 5, 99.330 D.T. Cromer, A. J. Ihde, and H. L. Ritter, J . Amer. Chem. SOC., 1951, 73, 5587.331 F. H. Herbstein and G. M. J. Schmidt, Nature, 1952, 168 323.332 E. H. Wiebenga, J . Amer. Chem. Soc., 1952, 74, 6156.833 E. W. Lund, Acta Chem. Scand., 1951, 5, 678.asp D. R. Davies and H. M. Powell, Nature, 1951, 168, 386DUNITZ AND ROBERTSON STRUCTURAL CHEMISTRY. 375Compounds containing sulphur or selenium. The structures of piazselenole,piazthiole, and benzofurazan (XVII; X = Se, S, and 0 respectively) havebeen determined.335 The molecules are planar and appear to possess theexpected symmetry. The distance N-X is given as 1.83, 1.60, and 1.20 Arespectively and N-C is close to 1.34 A in all three compounds. The mostinteresting feature of the bond lengths, however, is the very short distancequoted for C(1)-C(2) 1-30A and 1-29A in the selenium and the sulphurcompound respectively.The other C-C distances are all greater than 1.4 A.If these results are significant, they indicate almost complete double-bondfixation in the 1 : 2-position. It is noteworthy, though, that in a recentrefinement of the structure of p-isoprene sulphone, termination-of-serieserrors alone were found to cause changes in the atomic co-ordinates of asmuch as 0-06 A.336In the crystal the ring adopts the chairform; the angle C-Se-C is 99” and C-Se is found to be 2-01 A, rather longerthan the value (1.94A) based on Pauling’s covalent radii. The expectedvalue is found in diphenyl diselenide, where the planes of the phenyl groupsare almost normal to one another.338Benzene Derivatives.-9-Dichlorobenzene is isostructural with thedibromo-analogue; the crystal packing is of the parallel disc t ~ p e .3 ~ ~ In+-aminophenol,340 a polar structure, the rings are packed in layers, and theplane of the rings is almost normal to the layer plane ; three hydrogen bondsper molecule are formed. A three-dimensional analysis shows that theC-N bond distance is about 1.39 A, shorter than normal; C-0 is 1.47 A,longer than in other phenols. In m-tolidine,=l no hydrogen bonds areformed and the structure is very open. As in m-tolidine hydrochlorideand 2 : 2’-dichlorobenzidine, the phenyl groups are nearly normal to oneanother; such molecules must be rather awkward for packing purposes.Like diphenyl itself, 4 : 4‘-dihydroxydiphenyl must be planar, at least in thecrystal where a molecular centre of symmetry is imposed.342Carboxylic Acids.-The most common form of association in crystals ofthe monocarboxylic acids, dimerisation of type ( A ) , is now found to occur inp-chlorobenzoic a ~ i d , ~ ~ 3 salicylic acid,3& lauric acid, 117 “ isopalmitic acid,” 345and trans-p-ionylidenecrotonic acid (related to vitamin A) ,346 in addition toearlier examples. It is found also in potassium hydrogen carbonate, wherepairs of bicarbonate ions are linked as in (A).347 Formic acid, although itforms dimers in the gas phase,122 is associated in the solid, to form infinitechains of type (B).”* End-to-end bonding of type ( A ) , is also usual fordicarboxylic acids, though here, by association at both ends, infinite chainsDiselenan has been studied.33733s V.Luzzati, Acta Cryst., 1951, 4, 193.337 R. E. Marsh and J. D. McCullough, J . Amer. Chem. Soc., 1951, 73, 1106.338 R. E. Marsh, Acta Cryst., 1952, 5, 458.339 U. Croatto, S. Bezzi, and E. Bua, ibid., p. 825.3p0 C. J. Brown, ibid., 1951, 4, 100.341 F. Fowweather, ibid., 1952, 5, 820.342 S. C. Wallwork and H. M. Powell, Nature, 1951, 167, 1072.343 J. Toussaint, Acta Cryst., 1951, 4, 71.344 W. Cochran, ibid., p. 376.345 E. Stenhagen, V. Vand, and A. Sim, ibid., 1952, 5, 695.346 C. H. MacGillavry, A. Kreuger, and E. L. Eichhorn, Proc. K . Ned. Akad. We#.,347 I. Nitta, Y. Tomiie, and C. H. Koo, Acta Cryst., 1952, 5, 292.348 F.Holtzberg, B. Post, and I. Fankuchen, J. Chem. Phys., 1952, 20, 198.336 G. A. Jeffrey, ibid., p. 58.1951, 54, 449376 CRYSTALLOGRAPHY.rather than dimcrs are formed. Type (B) occurs too, in a-oxalic acid, forexample. Maleic acid 113 is an interesting case. One hydrogen atom formsa strong internal bond, so that, for intermolecular hydrogen bonding, wehave two carboxyl groups but only one hydrogen atom per molecule. Onceagain we find infinite chains, but of type (C}.Careful re-investigations have been made of the structures of a-oxalicacid,349 oxalic acid d i h ~ d r a t e , ~ ~ and ammonium oxalate m0nohydrate.~51The oxalic acid molecule is planar in both structures but the oxalate ion isnon-planar, the angle between planes of opposite carboxyl ions being 28".In none of these structures is the central C-C bond distance significantlydifferent from 1.54& so that the earlier interpretation of the evidence asfavouring a somewhat contracted central bond in the dihydrate must now bediscarded.As Jeffrey and Parry have indicated,352 the absence ofappreciable shortening is presumably due to removal of x-electrons from thecentral bond towards the more electronegative oxygen atoms. The relativestabilities of planar and non-planar forms of the molecules will thereforedepend only to a minor degree on the x-conjugation; the formal chargedistribution may be of greater importance.Amino-acids and Peptides.-There is no doubt that the amount ofprecise structural information available for amino-acids and peptides isgreater than for any other comparable class of molecules.The Pasadenagroup alone, in addition to providing several standard analyses, havecontributed no less than 7 determinations (for urea,115 ~-threonine,~5~ DL-alanine,3" N-a~etylglycine,~~~ hydroxy-~-proline,3~~ ~ ~ - s e r i n e , ~ ~ ? glycyl-L-asparagine 358) in which the full force of structure analysis has been broughtto bear on three-dimensional data. Other structure studies, for DL-methionine,359 g l ~ t a m i n e , ~ ~ and ~ysteinylglycine,~~~ have also added to theevidence. The results are, of course, of particular importance in connectionwith the recent Pauling-Corey protein models, and we shall mention one ortwo points which seem especially interesting.(1) theinvariable occurrence of zwit terions (acetylated glycine being an obviousexception) and (2) the tendency towards planar configurations.In the freeTwo main features seem to emerge from these structures :Sd0 E. G. Cox, M. W. Dougill, and G. A. Jeffrey, J., 1952,4854.360 F. R. Ahmed and D. W. J. Cruickshank, Acta Cryst., in the press.351 G.A Jeffrey and G. S. Parry, J . , 1952, 4864.363 D. P. Shoemaker, J . Donohue, V. Schomaker, and R. B. Corey, J . Amer. Chem.366 G. B. Carpenter and J . Donohue, ibid., p. 2315.JC* J. Donohue and K. N. Trueblood, Acla Cryst., 1952, 5, 419.557 D. P. Shoemaker, R. E. Barieau, J . Donohue, and C. S. Lu, 2nd Internat. Congr.'68 L. Katz, R. A. Pasternak, and R. B. Corey, Nature, 1952, 170, 1066.359 A.McL. Mathieson, Acta Cryst., 1952, 5, 332.360 W. Cochran and B. R. Penfold, ibid., p. 644.S6l H. B. Dyer, ibid., 1951, 4, 42.Idem, Nature, 1952, 169, 1105.SOC., 1950, 72, 2328. 554 J. Donohue, ibid., p. 949.Cryst., Stockholm, 1951DUNITZ AND ROBERTSON : STRUCTUR-41, CHEMISTRY. 377amino-acids one may distinguish two possible planar groupings. Thecarboxylgroups may lie coplanar with either the amino-group as in (a) (Fig. S),or the P-carbon atom (b). Type (a), shown by hydroxy-L-prolone, acetyl-glycine , serine, glycylglycine, and nearly so by threonine, alanine, andglutamine, is clearly favoured by the opposite charges of the NH,+ and the0FIG. 8. Planar groupings possible in amino-acids ( a and b) and peptides ( c ) .carboxyl-oxygen atom.It does not occur, however, in a- or p-methionineor the peptide glycyl-L-asparagine, which show instead planarity of type ( b ) .Both of these molecules contain carbon side chains and it seems possible thatthe preference for arrangement (b) may be associated with the tendency ofcarbon chains to adopt the planar zig-zag configuration, as, for example, inRFIG. 9. Some interatomic distances (in k ) and bond angles for glycyl-L-asparagine,with Corey-Donohue dimensions (in parentheses).the long-chain hydrocarbons and de~amethylenediamine.~~~ In peptides,planarity is found for the five atoms of the peptide group, of the type (c).This planar configuration, expected theoretically and already found inN-acetylglycine and in p-glycylglycine, has been confirmed again by theanalysis of glycyl-L-asparagine.Indeed, this molecule , lying almostexactly in two planes, simultaneously illustrated cases ( b ) and (c). Thecombination of planarity ( b ) and (c), if general in polypeptide structure,would impose a certain limitation on the mutual disposition of adjoiningpeptide groups, but more peptides must be studied before the importanceof this can be properly assessed.Turning to finer details, it is gratifying that the evidence of the last twoyears leaves the Corey-Donohue model 363 substantially unchanged. InFig. 9 it is compared with the results for glycyl-L-asparagine.The variation of the C-0 distances in the carboxyl ions is interesting.362 A. 0. McIntosh and J. M. Robertson, ibid., 1952, 5, 149.363 R.B. Corey and J. Donohue, J . Amer. Chem. SOC., 1950, 72, 2899378 CRYSTALLOGRAPHY.The isolated ion should be symmetrical ; in different crystal environments,double-bond fixation in one or other C-0 link is often present, to a greateror less degree, according to the symmetry of the hydrogenbonding with respect to the two oxygen atoms. Generallywe find that the oxygen with the longer link forms two,'O-.--. and that with the shorter only one, hydrogen bond (XVIII).Glutamine is exceptional here, as in this case it is the oxygen(XVIII) with the shorter link which has two hydrogen bonds, and theother only one, all being of roughly equal strength.The dimensions of the amide group as found in asparagine (C-0 1-22,C-N 1-38A) are similar to those in acetamide; but in glutamine the C-0and C-N distances are almost identical (1.28 A) , indicating considerabledouble-bond character in the C-N linkage. This is thought to be connectedwith the susceptibility of glutamine to hydrolysis or attack by nitrous acid.For asparagine, hydrolysis is slower and the amide group is not affected bynitrous acid.Incidentally, the petide analysis shows the asparagine residueto be an extended chain, and not cyclic as proposed recently,364 notwith-standing the fact that the amide and carboxyl groups are still free tointeract.0ximes.-Pitt 365 has drawn attention to the fact that, while thehydrogen atoms could not be located with certainty, application of stereo-chemical rules to the hydrogen-bonding arrangement in syn-@-chloro-benzaldoxime leads to the conclusion that the bonds are N-H*--O, whichwould imply that oximes are to be represented as RR'C:iH6, rather than,as usually written, RR'CN-OH.Although two new structure determinations are now available, it is stillnot possible to settle this point with certainty. In a ~ e t o x i m e , ~ ~ ~ themolecules are linked into trimers; the angle O-N-.-O is 129" andN-0-a.N is 111" so that the arrangement is compatible with eitherdisposition of hydrogen atoms.In dimethylgly~xime,~~~ each oxime groupis linked by hydrogen bonds to another related by a centre of symmetry.An obvious error occurs in the published paper where theangles N-0. - * N' and O-N - * * 0' are both given as 75.9".I 1.38A The centre of symmetry, however, requires that their sumbe 180".It would appear that N-O.*.N' is indeed about75", so we assume for the present that the published value75.9" refers to that angle and not to O-N-.*O', which is therefore 104.1".The arrangement is thus probably N-H * - * 0', in agreement with Pitt's sug-gestion and contrary to the usually accepted view. The dimethylglyoximeanalysis has been carried out in considerable detail with the use of full 3-di-mensional data. The refinement process was, however, effected by least-squares analysis only and it is to be regretted perhaps that the more orthodoxFourier method was not employed in this case since an (F, - F,) synthesismight have provided a quite unambiguous determination of the positionsof the hydrogen atoms.In dimethylglyoxime (and acetoxime), C-N is given as 1-27 A (1.29 A),0 ....--c/2-83 AN .. . . . 0'I 0.. . . . N'364 F. C. Steward and J . F. Thompson, Nature, 1952, 169, 739.365 G. J . Pitt, Ann. Reports, 1950, 47, 458.366 T. K. Bierlien and E. C. Lingafelter, A d a Cryst., 1951, 4, 450.367 L. L. Memitt and E. Lanterman, zbzd., 1952, 4, 811DUNITZ AND ROBERTSON : STRUCTURAL CHEMISTRY. 379N-0 as 1-38 A (1.36 A), quite consistent with double and single bondsrespectively. In dimethylglyoxime the central C-C bond is 1.44 A, slightlyshorter than the corresponding distance in buta-1 : 3-diene,122 and about0.1 A shorter than in oxalic acid.349Carbohydrates.-The crystal structure of a-D-glucose was reviewed in1950 but a fuller publication 368 allows us to mention several finer pointsrelating to the structure.Of the five hydrogen atoms available for hydrogenbonding, all are utilised in intermolecular bonds, four in inter-hydroxyllinkages, 2-70-2-78 A, and one in a hydroxyl-ring-oxygen link, 2-86 A. Itmay be noted that in the long bond the donor hydroxyl group does notitself accept hydrogen bonds from another atom, as in the other bonds.Another point of interest is the shortening, by about 0-1 A, of the C-0distance in the primary alcohol group-a feature shown also in cytidine andconnected possibly with the somewhat different chemical behaviour of theterminal CH2*OH. The a-OH in the reducing group position exhibits asimilar contraction. Unfortunately, the results for sucrose are notsufficiently accurate for a study of the details of bond distances, but thestereochemical configuration is given.369 The general shape of the sucrosemolecule in the sodium bromide compound is similar to that in sucroseitself, except that the molecule is rather more tightly curled, and oneterminal hydroxyl group is differently oriented.More accurate analysesof the sugars, comparable with those now available for several amino-acidsand peptides, would be of the greatest value.Steroids.-Following on the analyses of cholesterol and calciferol, twomore analyses, also by the " heavy atom " technique, have furthered ourknowledge of the steroid field, providing a detailed stereochemical picture oflanostenol 370 and l u m i ~ t e r o l .~ ~ ~ (Lumisterol is one of the compoundsformed during the photochemical transformation of ergosterol intocalciferol.) The inversion of the methyl group at C(lo) has been confirmed.In addition, the chair form of rings A and c has been found, together withthe &-configuration of the hydroxyl group. This is in agreement withrecent infra-red In the case of lanostenol (dihydrolanosterol)chemical evidence was considerably confused as to the D-ring system andthe point of attachment of the side chain. The X-ray evidence now showsring D to be &membered, and the c8 chain to be attached in such a waythat the molecule does not fit the isoprene rule. The latter result wouldsuggest that this and related triterpenes should really be considered astrimethylated steroids-a possibility emphasised by the co-existence oflanostenol and sterols such as ergosterol and cholesterol in Nature.Alkaloids.-The simultaneous confirmation of the strychnine structureby the chemical work and by two independent groups of crystallographerswas described in the 1950 report; fuller details of the analyses have nowappeared.373 A 2-dimensional analysis 374 of a colchicine adduct withCH,X, (X = Br or I) yields a projection which appears to confirm Dewar's3b8 T.R. R. McDonald and C. A. Beevers, Acta Cryst., 1952, 4, 654.369 C. A. Beevers, T. R. R. McDonald, J. H. Robertson, and F. Stern, ibid., p. 689.370 R. G. Curtis, J. Fridrichsons, and A. McL. Mathieson, Nature, 1952, 170, 321.371 D.C. Hodgkin and D. Sayre, J., 1952, 4561. 372 A. R. H. Cole, ibid., p. 4969.s7s J. H. Robertson and C. A. Beevers, Acta Cryst., 1951, 4, 270; C. Bokhoven,sT4 M. V. King, J. L. de Vries, and R. Pepinsky, ibid., 1952, 5, 437.J. C. Schoone, and J. M. Bijvoet, ibid., p. 275380 CRYSTALLOGRAPHY.ring structure 375 with the substituents placed according to Cech andS a n t a ~ y . ~ ~ ~ The structure of ergine is confirmed, also by %dimensionalanalysis, but with much better resolution of the individual at0ms.3~~ Thesolution of the structure was obtained from a difference Patterson mapprepared from the isomorphous hydrochloride and hydrobromide.Antibiotics.--A 3-dimensional analysis of chloramphenicol (and ofbromamphenicol) 378 confirmed the chemical structure of this well-knownantibiotic. The molecules adopt a curled configuration in the crystal,owing to a fairly strong intramolecular hydrogen bond between the twohydroxy-oxygen atoms. Attention is being given to terramycin and aureo-mycin, the close relation between this pair having been noted.379 Thecrystal structure of potassium benzylpenicillin has been refined by a second3-dimensional synthesis based on improved intensity data.380 Koj ic acid,a substance of mild bacteriostatic activity, has been studied, and itsconstitution confirmed.381Protein Structures.-As a comprehensive and far-reaching review of thisfield was given last year, we propose to mention in only the briefest termssuch developments as were not already covered in that report. X-Rayanalysis is being applied to a variety of proteins : a " carbonmonoxy-haemoglobin " ; 382 silk fibroin ; 383 p-lactoglobulin 384 and actinomycin 385(for the molecular weight); and others. Knowledge of the external formof the haemoglobin molecule 386 is being applied to sign determination; 73interpretation of the Patterson function is being contin~ed.~S~ Informationof a general kind as to the arrangement of polypeptide chains in the crystalhas been sought from 3-dimensional Patterson syntheses, notably forlysozyme hydrochloride 388 (using nearly 200 reflections) and for acid insulinsulphate 389 (where about 100 reflections were available).Of very great interest is the continuing discussion concerned with thenow well-known " 3-7 helix," the non-integral spiral structure proposed byPauling and Corey for the polypeptide chain. Cochran, Crick, and Vand 390have shown that the intensities of X-ray reflections given by poly-y-methyl-L-glutamate are in remarkably close agreement with the intensity distribu-tion predicted from the helix. The best agreements is obtained when thep-carbon atom is assumed to be in position 2.391 This is true also of bovine375 M. J . S. Dewar, Nature, 1945, 155, 141.376 J. tech and F. Santavy, Coll. Trav. Chim. Tchecosl., 1949, 14, 532.3 7 7 J. L. de Vries and R. Pepinsky, Nature, 1951, 168, 432.378 J. D. Dunitz, J. Amev. Chem. SOC., 1952, 74, 995.379 J . D. Dunitz and J. H. Robertson, ibid., p. 1108; R. Pepinsky and T. Watanabe,380 G. J. Pitt, Acta Cryst., 1952, 5, 770.381 H. A. McKinstry, P. F. Eiland, and R. Pepinsky, ibid., p. 285.383 Y. C. Tang, ibid., 1951, 4, 564.383 F. Happey and A. J. Hyde, Nature, 1952, 169, 921.s8p I . M. Dawson and D. P. Riley, ibid., 1951, 168, 241.s86 H. Sarlet, J. Toussaint, and H. Brasseur, ibid., p. 469.386 Sir W. L. Bragg and M. F. Perutz, Acta Cryst., 1952, 5, 277, 323.387 Sir W. L. Bragg, E. R. Howells, and M. F. Perutz, ibid., p. 136; F. H. C. Crick,388 R. B. Corey, J . Donohue, K. N. Trueblood, and K. J . Palmer, ibid., p. 701.388 B. W. Low, Nature, 1952, 169, 955.390 W. Cochran and F. H. C. Crick, ibid., p. 234; W. Cochran, F. H. C. Crick, andaD1 H. L. Yakel, L. Pauling, and R. B. Corey, N u t w e , 1952, 169, 920.Science, 1952, 115, 541.ibid., p. 381.V. Vand, ActaCryst., 1952, 5, 581DUNITZ .4ND IiOBERTSON STRUCTURAL CHEMISTRY. 381serum albumin, where the method of radial distribution curves was applied.392One rather important objection to the 3.7 spiral in poly-y-methyl-L-glutamate, the density discrepancy,393 seems to have been overcome by anew measurement of the unit-cell parameters.391 Another apparentdiffic~lty,~g~ that the dichroism of the C=O absorption band is not as markedas that of N-H, may have been removed by calculations which show that thedirection of the transition moment of the 1650-cm.-l band should be inclinedby about 20" to the C-0 direction, leading to a dichroic ratio comparablewith that experimentally observed.394 I t has been suggested that a coiledcoil is perhaps a general feature of polypeptide and protein structure, sincehelices inclined a t about 18" should pack together more effectively; themeridian reflection at 5.2 A given by a-keratin would be explained by thishypothesis.395 A symposium on the structure of proteins was held at theRoyal Society on May lst, 1952,396 and a Faraday Discussion on the bio-chemistry of proteins in August of the same year. Despite the bafflingcomplexity of this field, substantial progress is undoubtedly being made.We gratefully acknowledge assistance from Dr. B. Oughton, Mr. E. Wait,and Mrs. D. Crowfoot Hodgkin in the preparation of this report.J. D. DUNITZ.J. H. ROBERTSON.392 D. P. Riley and U. W. Arndt, Nature, 1952,169, 138.393 C. H. Bamford, L. Brown, A. Elliott, W. E. Hanby, and I. 1;. Trotter, ibid.,394 R. D. B. Fraser and W. C. Price, ibid., 170, 400.395 F. H. C. Crick, ibid., p. 882; L. Pauling and R. B. Corey, ibid., 1953, 171, 59.396 J . T. Edsall, ibid., 1952, 170, 53.p. 357