CRYSTALLOGRAPHY, 1947, 1948, AND 1949.1. INTRODUCTION.THE most important event in the last three years for crystallography hasbeen the formation of the International Union of Crystallography and thedecision by this Union to publish a new journal for crystallographic papers,Acta Crystahgruphica. The International Union of Crystallography itselfwas established after the informal meeting of crystallographers from manycountries which took place in London in 1946, and the first general assemblyof the Union followed a t Harvard in 1948. The proposal that a newcrystallographic journal should be published, to replace the older Zeitschrgtfur Krista$bgruphie, was made a t the London meeting and the first numberappeared in March 1948 shortly before the Harvard Assembly.The newjournal is the property of the International Scientific Union and is, from itsfoundation, international in character ; papers may be published in itspages in English, French, German, and Russian.It must be admitted that the appearance of yet another scientific journalis not necessarily a blessing, and particular misgivings about the publicationof a journal for crystallography were felt by many who were interested inthe application of crystallographic methods in chemistry. We feared thatthe average chemical reader might lose touch with crystallographic develop-ments if these were less frequently published in the existing chemicaljournals. In fact, something rather different appears to be happening.Such a high concentration of crystallographic papers of the greatest im-portance for chemical theory has already been published in the Actu that noone interested in structural problems can afford to neglect its existence.Already there are signs that other papers, not strictly crystallographic incharacter, but bearing on chemical problems raised by crystallographicresearch, are being attracted to its pages.And certainly the concentrationof such a large proportion of crystallographic papers in one place is anenormous boon to your Reporters.The preparation of this particular report on crystallography presentsgreat problems. Owing to a variety of circumstances, no formal report oncrystallography has appeared since 1946 and there is an abnormally longinterval of three years to be covered. This interval is one in which therehas been a very great deal of new and interesting work in all branches ofthe subject, further swollen in volume by papers which describe resekhescarried out during the war.In the circumstances we have had to limitseverely our field for discussion. We have decided to attempt to combinea short account of technical developments in X-ray analysis with a surveyof structureanalyses in the inorganic field alone, leaving a survey of the organicfield as a whole to next year. We have also decided to omit this year alldescriptions of problems allied to X-ray analysis, such as crystal texture58 CRYSTALLOGRAPHY.diffuse X-ray reflections, and crystal growth. Some of these topics arepartly covered by recent reviews, e.g., of organic compounds of biochemicalinterest and of protein crystals,2 and by the Faraday Society Discussionon crystal g r o ~ t h .~ The subject of neutron diffraction is in a rather differentcategory but has also been recently re~iewed.~Mostimportant is probably R. W. James’s long awaited Vol. I1 of “ The CrystallineState,” “ The optical principles of the diffraction of X-rays,” which islikely to remain for many years to come the authoritative text on the subject.5A. J. C. Wilson has also written a short monograph on some aspects of X-rayoptics,s and A. D. Booth has given a useful summary of Fourier techniquein X-ray organic structure analy~is.~ The English translation of the text-book “ X-Ray analysis of crystals ’’ by J.M. Bijvoet, N. H. Kolkmeijer,and C. H. Macgillavry provides a very useful student’s hand-book to practicalX-ray analysis.8 R. W. G. Wyckoff has begun the labour of once againcollecting together all crystal-structure analyses. In “ Crystal Structures ”he has published the first section of the whole collection in a form to whichadditions can easily be made as new &tructures are s ~ l v e d . ~ Useful shorterreviews of crystal structures have been given by A. Tovborg Jensen onsalt hydrates,1° A. F. Wells on oxides,11 H. Bassett on basic salts,l2 and A.Bystrom on the stereochemistry of lead.13Several useful books have appeared during these three years.D. C. H.2. THE TECHNIQUE OF STRUCTURE ANALYSIS.In general terms, investigations of crystal structures can be divided intothose undertaken primarily to elucidate the chemical nature of the substance,and those in which the emphasis is on accurate atomic co-ordinates andelectron densities.Recent developments in technique have been concernedwith problems raised in both of these groups, pahicularly where the crystalstructures involve the determination of a considerable number of parameters.In the first category many structures have been published, such as thoseof penicillin,l4 strychnine,15 substituted cycZohexanes,169 l7 decaborane,181 D. Crowfoot, Ann. Reviews Biochem., 1948, 115.2 M. F. Perutz, Research, 1949, 2, 52.4 K. Lonsdale, Nature, 1949, 163, 205.6 “ The diffraction of X-rays by finite and imperfect crystals,” Methuen, 1949.7 Cambridge Univ.Press, 1948.8 Interscience Publ., Inc., New Pork, 1949.9 Interscience Publ., Inc., New York, 1948.10 “ Kristallinske Salthydrater,” Arnold Busck, Copenhagen, 1948.11 Quart. Reviews, 1948, 2, 185.12 Ibid., 1947,1, 247. .18 Arkiv .Kern&, Min., Geol., 1948,2!5, A , No. 13.14 “ The Chemistry of Penicillin,” Princeton Univ. Press, 1949, p. 310.15 C. Bokhoven, J. C. Schoone, and J. M. Bijvoet, Proc. K. Ned. Akad. Wetensch.,1 6 0. Hassel and E. W. Lund, Acta Cryst., 1949, 2, 309.17 J. M. Bijvoet, Rec. Trav. chim., 1948, 67, 777.18 D. Harker, J. S. Kasper. and C. M. Lucht, J. Amer. Chem. Soc., 1948,70,881.Trans. Faraday Soc., 1949, No. 5.Bell, 1948.1948,51,990; 1949,52,120PITT: THE TECHNIQUE OF STRUCTURE ANALYSIS.59and tourmaline,lB where the likely arrangement of chemical bonds was a tleast partly unknown beforehand. In these structures so many atoms areinvolved that trial methods of analysis seem hopeless and direct means ofderiving electron-density syntheses are needed. Attention is thus focusedon the problem of finding the phases or signs to be allotted to the measuredF values.Very large molecules are excluded from the second category becausethe experimental data are too limited to permit the accurate location ofindividual atoms, and systems containing a heavy atom are unsuitableowing to the relative insensitivity of the data to the positions of the lighteratoms. Purely organic compounds therefore form the largest group ofsuitable subjects, and in the simpler molecules both the bond-lengths andthe electron densities are of particular interest for comparison with theresults of wave-mechanical calculations.The accuracy of the experimentalresults is here of the first importance.In a great many of the published structures the Patterson synthesishas provided sufficient evidence of the positions of the molecules to deter-mine the phases approximately, from which stage the structure could berefined by Fourier methods. The complexity of the Patterson synthesis,however, increases rapidly with increasing number of atoms in the cell,and the interpretation becomes difficult unless there is a predominantlyheavy atom present. In the case of a moderately large molecule such aspenicillin, even with the help of a heavy atom, the deductions from thePatterson synthesis may not be sufficient to permit the refinement of thestructure, and it is necessary to resort to some form of trial and error, whichis often a protracted and uncertain procedure.The systematic explorationof the Patterson and Harker syntheses has been discussed by M. J. Buerger,mwho shows that Harker section syntheses perpendicular to symmetry axescan be transformed into " implication diagrams " which contain peaks a tpositions corresponding to atoms in the Fourier synthesis, plus satellitepeaks in geometrically simple relation to them, plus ambiguity peaks dueto the systematic absence of some of the coefficients needed. The methoddepends on the resolution of the Harker diagram, and the recognition andremoval of the satellite and ambiguity peaks; it becomes more and moredifficult as the complexity of the structure increases.Many machines have been developed for the approximate calculationof structure factors and Fourier syntheses in order to make possible a morerapid survey of different arrangements of the molecule.One valuablemethod of determining the structure factors corresponding to a givenprojection of the unit cell is the " Fly's Eye " which uses optical diffractionby a two-dimensional grating as an analogue of X-ray diffraction by thecrystal.21 This method was used extensively by C. W. Bunn in the workon sodium penicillin, and the structure factors for a trial projection of thelD M. J. Buerger and G.Hamburger, Arne?'. Min., 1948, 33, 532.81 See Ann. Reports, 1946, 43, 90.2o J . Appl. Phy&CS, 1946, 17, 579; A ~ t a Cryst., 1948, 1, 25960 CRYSTALLOGRAPHY.molecule could be estimated in about an hour compared with several daysto Gztlculate them on desk machines. As a result of a paper by P. J. G. deVos *2 the optical diffraction amplitude can be made to simulate more closelythe atomic scattering function, and atoms of differing atomic number canbe represented accurately in relation to one another.Available methods of calculating Fourier syntheses have up till nowbeen too slow to render the examination of extensive permutations of signsfeasible. If the effect of sign changes could be observed at once it would bepossible to approach the deduction of electron-density series (or at leasttheir refinement) by some form of systematic consideration of sign changes.This possibility has now been realised in the large-scale electronic Fouriersynthesiser described by R.Pepinsky 23 which produces a contoured electron-density map on the cathode-ray screen, the Fourier coefficients being seton potentiometers. The sign of any term may be changed by means ofa switch, the resulting change in the electron density being seen almostat once.Attempts to discover additional means of circumventing trial and errorin phase determination have achieved a measure of success, although noneof the methods described has been widely used in the solution of unknownstructures. A new approach by D. Harker and J.S. Kasper 24 has shownthat the application of the purely mathematical Schwartz and Cauchyinequalities to the observed values can yield limitations on some of thephases, due to the crystal symmetry. Defining f;'(hkZ) as ~(hkZ)~f(hkZ)where f(hLZ) is a suitable mean atomic scattering factor fiormalised to makeF(000) = 1, it is shown that in a crystal with a centre of symmetry forexample :F2(hkZ) < 9 + f 2 ( 2 h , 2k, 21)Hence if i;l^z(hkZ) >&, F(2h, 2k, 21) must be positive ;or if $(hkZ)>f, and IF(2h, 2k, 2Z)l = 9, then F(2h, 2k, 2Z) is again positive.This technique has been extended by J. Gilli~,2~ so that the signs of the40 most important terms in the P(h0Z) data for oxalic acid dihydrate couldbe deduced from the magnitudes observed.It has been of use wherePatterson and Harker methods proved insufficient in the solution of thestructure of decaborane,ls but no details are available: Owing to theassumption of a mean atomic scattering factor,' the method is probablymost reliable where all the atoms are of much the same atomic number,and it may supplement the Patterson technique which is least helpful insuch cases. E. W. Hughes 26 has pointed out that the success of this elegantmethod depends on the occurrence of a t least a few reflexions to whichmost of the atoms contribute nearly a maximum amount, i.e., _F(hkZ)>i.On an empirical basis justified by a more extensive statistical treatment byAAA22 Acta Cryst., 1948, 1, 118.23 J . Appl. Physics, 1947, 18, 601; Nature, 1948, 162, 2 2 .24 Acta Cryst.? 1948, 1, 70.25 Ibid., pp. 76, 174. 2 s Ibid., 1949, 2, 34, 37PITT : THE TECHNIQUE OF STRUCTURE ANALYSIS. 61A. J. C . WilsonF7 Hughes shows that the structure factors for tb centro-symmetric crystal composed of atoms of similar scattering powers have anapproximately normal distribution about zero if the number of atoms (N)in the unit cell is greater than ten. The R.M.S. value of 121 is l/l/x, andhence the proportion of reflexions strong enough to be of use in the equalitiesfalls as the number of atoms in the asymmetric unit increases, and forstructures of more than moderate complexity i t is unlikely that any signrelationships will be obtained. It is just for such complex structures thatsome assistance from new techniques is most needed.Another possible way of eliminating trial determination of phases arisesfrom the use of the method of steepest descents proposed by A.D. Booth.28In this is a procedure for minimising systematically a function of the observedand calculated structure factors [e.g., R =21 1 IFobs,[ - lFcalc.I 1 or R, =C (El&,. - F",lc.)2 or R, = C (log - log Icalc.)2].29 R can be representedas a set of surfaces (R = constant) in 3N-dimensional space, N being thenumber of crystallographically different atoms present. The methodminimises R, by proceeding in the direction of the normal to the initialsurface until the function no longer decreases. Having thus arrived at anew R-surface the procedure is repeated until the minimum is reached.It has been suggested (though not yet satisfactorily demonstrated) that itmay be possible to start with a random set of atomic positions and stillconverge to a solution of the structure.The general method is capable ofadaptation to take account of any partial information available about themolecule, and in particular will deal with cases where (a) the atomic positionsare approximately known, (b) the configuration of the molecule is knownbut not its position or orientation in the cell, and ( c ) the molecular shape isonly vaguely known as an approximate electron-density distribution (asmight be the case in megamolecular structures). Tentative applicationsof the method have been reported in the refinement of co-ordinates fromFourier projections in two structure^,^^,^^ and in the case of the partly-ordered C-phase of Ag-Zn, M.M. Qurashi has refined the atomic co-ordinatesand an order parameter simultane~usly.~~ Intended for use with anelectronic c o m p ~ t o r , ~ ~ the method is not very suitable for calculations ondesk machines.The concept of structure analysis as a minimisation process mentionedabove has recurred in a number of papers dealing with accurate structuredeterminations. W. Cochran 34 has shown that Fourier refinement minimises22 7; (Fobs. - FcalcJ2 and is therefore a special case of the least-squares methodhkl hkl1J27 Acta Cryst., 1948, J, 318.28 Nature, 1947, 160, 196; Proc. Roy. SOC., 1949, A, 197, 326.2% V. Vand, Nature, 1948,161, 600; 1949,163, 129.3* Idem, Ada Cryst., 1949, 2, 214.s2 Ibid., 1949, 2, 404.33 A.D. Booth, Proc. Roy. Soc., 1948, A, 195, 286.s1 G. J . Pitt, ibid., 1948, 1, 168.Acta Cryst., 1948, 4 13862 CRYSTALLOGRAPHY.of Hughes 35 which minimises 2h.uto an observation.- Fcalc.)2 where w is the weight givenThe possibility therefore arises of modifying the FourierW method by weighting the observations and minimising C 7 (Fobs. - FCalc.J2 inorder to reduce the effect of the less reliable terms. While this may beadvantageous where atomic co-ordinates are sought the Fourier seriesremains the only one for finding the electron density. It is concluded thatthe co-ordinates derived from an appropriately weighted series are some-what more accurate than those from the unweighted one, but that in reducingthe uncertainty in the atomic positions it is more important to obtain moreaccurate observed and calculated structure fact0rs.3~The atomic co-ordinates derived from Fourier syntheses are liable toerror due to : (1) experimental errors in the observed structure factors;(2) termination of the Fourier series a t a finite 8 value while the coefficientsare still appreciable; and (3) rounding-off errors in computation.A. D.Booth37 estimated the errors liable to arise from these causes, and morerecently D. W. J. Cruickshank 38 has extended his treatment and developedprocedures for correcting the systematic errors and estimating the standarddeviations of the random errors. He recommends the application ofstatistical-significance tests to the differences in bond-lengths deduced.The probability is calculated that the difference in lengths of two bondsbetween atoms whose co-ordinates have errors of known standard deviationscould be due to the random errors alone; if this probability is greater than5% the difference is not significant; if less than 1% it is significant; andbetween these limits it is possibly significant.The adoption of this proposalwould render comparisons between results in different structures much morereliable.The relative effects of the first and the third source of error on the electrondensity have been discussed by Cochran.39 . The Beevers-Lipson methodof summation (rounding-off F and F cos 2xhx to the nearest integer) is shownto be sufficiently accurate unless the structure factors are measured to anaccuracy such that their standard deviation of error is less than 2.Round-ing-off to the nearest 0.1, which is possible with the new Fourieris adequate in all cases.The effect of terminating the Fourier series while the coefficients arestill appreciable, and the effect of applying an artificial temperature factorto the coefficients to ensure the convergence of the terminated series, havebeen studied by Booth,37 Cruickshank,38 and J. M. Robertson and J. G.VVhite.41 The use of an artificial temperature factor is shown to lead toa smearing-out of detail, and the atomic positions are subject to error owingto overlapping from adjacent peaks. The omission of all terms beyond8s J .Amer. Chem. Soc., 1941, 63, 1737.86 D. W. J. Cruickshank, Acta CryskrtZ., 1949, 2, 154.38 Acta Cryst., 1948, 1, 92 ; 1949, 2, 65.$0 Ibid., 1949, 8, 131.€'roc. Roy. Soe., 1947, A , 188, 77; A , 190,482, 490; A , 193, 305,Ibid., 1948, 1, 54.4l PTOC. Roy. Soe., 1947, A, 190,329PITT : THE TECHNIQUE OF STRUCTURE ANALYSIS. 63a certain 8 value causes the superposition of a set of ripples on the electron-density diagram, tending to displace the maxima. The errors are small ifobservations are included up to the limit obtainable with copper radiation,and can be corrected satisfactorily from a dummy Fourier synthesis basedon the calculated structure factors.As yet few structures have been determined with the full accuracypossible on these considerations, but it is already clear that much newinformation will be brought to light, with respect not only to the atomicpositions and consequently their mutual configurations, but also to the electrondensity throughout the lattice.It is now certain that, with careful measure-ment of the intensities of the reflexions, the influence of the hydrogenatoms on the structure factors of an organic compound can often be demon-strated, and peaks can result in electron-density maps in positions consistentwith known lengths of bonds to hydrogen,q2 The effect is particularlywell marked in three-dimensional electron- density series such as thosecalculated for naphthalene 43 and decaborane,l* Theawell-known statementthat “ the positions of hydrogen atoms cannot be found by X-ray analysis ”must therefore be modified.Moreover, it is claimed that electron-densitymaps can be obtained with sufficient accuracy to warrant deductions beingdrawn from regions where the density is less than 9 electronl~.~; directevidence may thus be provided for various features of modern valencytheory. An example is provided by the investigation of the aminopyri-midines, where C. J. B. Clews and W. Cochran *4 find small electron-densitypeaks near the nitrogen atoms which they claim could be explained if tihydrogen atom were attached to one nitrogen atom and were interactingwith an unshared electron pair on the other, lending support to this con-ception of the hydrogen bond.The accuracy of the structure of dibenzyl has been discussed in detailby Cruick~hank,~~ and G.A. Jeffrey’s conclusions 45 about the shorteningof the central bonds are placed on a firmer basis. It is understood thatthe bond-lengths and the angles are now in good agreement with thosecalculated by the molecular-orbital method. It is perhaps instructive tonote the length reported for this central bond a t the various stages of theanalysis :(1) From two-dimensional Fourier projections . . . . -1.58 A.(2) From three-dimensional Fourier section and line syntheses 1.48 A.(3) From three-dimensional differential Fourier syntheses . 1.501 A.(4) After correction for finite-series error . . . . . . 1-510 A.The estimated standard deviation of the last result is 0.015 A.It will be seen that bond-lengths in crystal structures of this complexitycannot be considered to be of the highest accuracy unless the analyses fromO2 W.P. Binnie, J. D. Morrison, and J. M. Robertson, Nature, 1948, 162, 889.Oa S. C. Abrahaxns, J. M. Robertson, and J. G. White, Acta Cryst., 1949, 2, 233,O4 Ibid., p. 46.238.Proc. Roy. Soc., 1947, A, 188,22264 CRYSTALLOGRAPHY.which they are deduced conform to the following conditions : (1) theintensities of all reflexions a t least to 8 = 90" for copper radiation havebeen measured and corrected accurately ; (2) three-dimensional methodshave been applied to the refinement of co-ordinates ; and (3) corrections forsystematic errors have been applied, and an estimate of the random errorsis made. Of structures so far published, those of dibenzyl, thiophthen,46and 2 : 6-dichloro-4-aminopyimidine 44 alone satisfy these conditions fully.G.J. P.3. CRYSTAL CHEMISTRY.In March 1947 a very sad event occurred, the death of V. M. Goldschmidt.The framework of crystal chemistry which he established is still the frame-work within which we can describe all inorganic crystal structures. It isimpossible to survey this field, as we propose now to do, without realisingagain and again how deep and wide is Goldschmidt's infl~ence.*~Inorganic Crystal Structures.-The field, this year, is dominated by thevery remarkable series of papers published by W. H. Zachariasen. Thesecontinue, in more than one sense, Goldschmidt's own researches, his use ofsurveys to establish chemical relations and his particular interest in theuranium metals.Zachariasen's papers are concerned with the crystalchemistry of all the elements of the 5f series, from actinium to americiumand curium, and the investigations were first described in Manhattan Pro-ject Reports. The fact that the elements and $heir compounds were, inmany cases, first obtained in microgram quantities, unweighable and un-analysable by ordinary chemical methods, made it necessary to use X-raymethods not only to deduce the relative positions of the atoms in the crystalsbut also the relative numbers of different atoms present-even, in somecases, which atoms were present. Many of the identifications could bemade by finding that the crystals present belonged to known structuretypes.Others were effected through a study of compounds of relatedelements, particularly of the rare earths. But, in many cases, new individualstructures were involved, and here Zachariasen made use of certain particularcharacteristics of the phases he studied-the fact that they consisted usuallyof a heavy element of high scattering power combined with light elementsof known volume. The number of heavy atoms in a unit cell could thereforebe determined from the intensities of X-ray lines, the number of light atomsfrom the volume, and the formuh deduced could be checked against thepossible ~ a l e n c i e s . ~ ~One or two examples may perhaps best illustrate the kind of processesinvolved in Zachariasen's researches. In one experiment E.F. Westrumattempted it calcium reduction of plutonium trifluoride in a barium sulphidecrucible. The product gave powder lines characteristic of the sodiumchloride lattice, and from the relative intensities might have been either* 8 E. G. Cox, G. A. Jeffrey, and R. J. Gillot, Acta Cryst., 1949, 2, 356.*' Cf. The Goldschmidt Memorial Lecture, J. D. Bernal, 1948 (J., 1949, 2108).W. H. Zachariasen, J . Arner. Chem. Soc., 1948, 70, 2147HODGKIN : CRYSTAL CHEMISTRY. 65barium oxide or plutonium sulphide; it was shown to be the latter byfurther oxidation to plutonium dioxide, the X-ray spectrum of which wasknown. Both the existence and structure of plutonium monosulphidewere hence establi~hed.~~ In another experiment a micro-sample knownto contain chlorides of uranium was prepared by sublimation into a thin-walled glass capillary.Three zones appeared, green, reddish-brown, andblack, far enough apart for powder photographs to be taken of themseparately. The patterns showed that the green zone consisted of UCl, andthe red one of UCl,, which had been previously examined. The black zonegave a new pattern which could be indexed on the basis of a hexagonal cell,just large enough to accommodate 18 chlorine atoms, while the reflectionsmissing required the presence of three uranium atoms. Hence the blackphase was UCl,; and further details of the intensity distribution could beused to fix the arrangement of the chlorine atoms and to show that in thecrystals separate UCl, molecules were present with U-cl 2.42 A.50Apart from the great experimental ingenuity involved in Zachariasen'sstudies, the most striking feature about them is the number of compoundsinvolved.His first paper in Acta Crystallographica describes 17 new struc-ture types and lists 60 compounds belonging to them, one of his latest, thetwelfth, lists 58 compounds belonging to known structure types, and manyof the intervening papers deal with structures in neither of these lists. Itis characteristic that he has examined compounds of the elements studiedin a large number of valency states. We have, as a consequence, extremelyinteresting examples of the change of structure type with valency, whichinvolves changes in the character of the bonds present. Examples are theseries of chlorides of uranium from predominantly ionic UCl, to covalentUCI,, or the uranium silicides with silicon present as isolated atoms, chains,networks, or three-dimensional structures.A far more complete pictureof the crystal chemistry of the elements of the uranium period can be giventhan of almost any other. And the results suggest that much more intensivestudy of other systems is necessary before we can understand many of thecomplexities that appear in structure types and bond distances.TABLE I.Radii in 5f series.510 Th4+ ............ 0.95 Ac3+ ............ 1.11 La3+ ............ 1.041 Pa4+ ............ 0.91 Th3+ ............ 1.08 Ce3+ ............ 1.022 U4+ ............... 0.89 Pa3+ ............ 1.06 Pr3+ ............ 1.003 Xp*+ ............0-88 U3+ ............... 1.04 NdS+ ............ 0.995 Am4+ ............ 0.85 Pu3+ ............ 1-01 Sm3+ ............ 0.976 Am3+ ............ 1.00 Eu3+ ............ 0-974 Pu4+ ............ 0.86 Np3+ ............ 1.02 Pm3+ ............ (0.98)From the crystal structures of the dioxides and trifluorides of theelements 89-95 Zachariasen has derived the ionic radii listed in Table I49 Acta Cryst., 1949, 2, 291.5 1 Zachariasen, Physical Rev., 1948, 73, 1104.Ibid., 1948, 1, 285.REP.-VOL. XLVI. 66 CRYSTALLOGRAPHT.which may be compared with the corresponding values for elements of thelanthanide series deduced from Goldschmidt’s early researches. Thedioxides are all of the fluorite type, fluorides of the tysonite type.It is notable that in the 5f series there are two prominent valency states-he two ionic series may be described as thoron and actinon respectively-whereas the 4f elements show only one.The decrease in ionic size isparalleled in the size of the ions (X0,)+2 in uranyl, neptunyl, and plutonylcompounds. But in other valency states there are many variations incrystal radii among these elements which are difficult to explain.In his investigation Zachariasen used almost entirely powder data.I n many of the structures examined the heavy atoms so dominated theintensities of the reflections that the light atoms had to be placed largelyby packing considerations. In some cases, therefore, the interatomicdistances are not determined with high accuracy. The last three yearshave, however, seen much extended use of single-crystal measurements andFourier series to assist in placing atoms accurately in inorganic crystals.More and more complex systems have been examined-one silicon carbideis now recorded with a unit cell dimension of 219.65 A.52 At the same timedetailed studies of the electron density have been made in compounds asdifferent as magnesium oxide,53 the alloys NiA154 and Co2A1,,55 and the boronhydride, B,,H,4.18 As a consequence, the body of interatomic distancesin complex structures determined with good accuracy is growing rapidly.The details of the interpretation of interatomic distances in manyinorganic compounds are however, a t present, still a matter for considerablediscus~ion.~~ Until it comprehensive theoretical treatment of the electrondistribution in these systems can be undertaken, it it3 usual to consider,in each case, the possible operation of a variety of factors.Some of these,ionic size, co-ordination, and the number of available electrons in covalentsystems, wsre recognised by Goldschmidt. Others, such as the characterof the orbitals used in single and multiple covalent binding, have beenintroduced later. But the fact that many bonds are clearly intermediatein character makes it often necessarily difficult to account in such terms forparticular interatomic distances without an appearance of special pleading.The most important recent development in this field has been the deductionby Pauling of new series of standard covalent radii for different valencystates and the extension of their use to fractional as well as t o multiplebonds.57 This development followed from Pauling’s theory of metals andis fully treated by Dr.Hume-Rothery elsewhere (see p. 42). Here one ortwo points only will be made.5i L. S. Ramsdell, Amer. Min., 1947, 32, 64.5p N. V. Ageev and L. N. Guseva, Isvest. Akad. S.S.S.R., Otdel. Khimisch, 1949, 3.i35 A. M. B. Douglas, Nature, 1948, 162, 565.56 A. F. Wells, J., 1949, 55; T. L. Cottrell and L. E. Sutton, Chem. Reviews, 1948,5 7 J . Amer. Chem. Soc., 1947, 69, 542; Proc. Roy. SOC., 1949, A , 196, 343.R. Brill, C. Hermann, and C. C. Peters, 2. anorg. Chem., 1948, 257, 151.2, 260HODQEIN : CRYSTAL CHBMISTRY. 67Pauling’s treatment throughout is largely experimental ; it is basedon the extension of relations found in one series of compounds or elementswhere the bond type is known to predict covalent radii for other elementsor bond types.The observed change of interatomic distance with multi-plicity in benzene and graphite, where there is resonance of single and doublecarbon-carbon bonds, leads, for example, to the derivation of an empiricalequation appropriate to resonating bonds in metallic systems,where n, the bond number, is the number of electron pairs involved in abond of radius R. Thus for bonds with one electron pair resonating betweentwo bond positions, bond number n = Q, the interatomic distance is increasedby 0.18 A. from that to be expected for a single bond of the same hybridtype.Furthersuggested relations are (2) that there is a linear decrease in radius withatomic number in one period for bonds of one hybrid type and (3) a lineardecrease with d character for bonds derived from hybrid dsp orbitals. Thefirst of the three relations has already been widely applied in electron-deficient systems ; it does appear to provide an explanation, interestingeven if very approximate, of many of the interatomic distances observed.The field most affected by this treatment, that of metal chemistry,merges with that of the semi-metallic “ interstitial ” compounds, whichprovides the first group of crystal structures to be considered here. Alloysystems formed by uranium and mercury 58 or indium and gallium 59 withthe transition elements form a natural link between the two.Here wemay mention only one point concerning metallic structures, that the crystalstructure o f technetium, element 43, artificially prepared from fissionproducts, has been determined by R. C. L. Mooney.60 The lattice is hexa-gonal close-packed, similar to that of rhenium, and falls in lattice constantsinto the expected sequence with ruthenium.Compounds between the Transition Metals and the Lighter Non-Metals-Interstitial ’’ Compounds.---The hard metal-like phases formed by thetransition metals between non-metals (such as boron, carbon, nitrogen,and to some extent oxygen and silicon) have long been classified as interstitialin character, formed essentially by fitting small atoms into holes in themetallic lattice.As more of them have come to be studied it is clear thatmany of their characteristics are not consistent with this picture alone butsuggest the operation of covalent forces between the metaI and non-metallicatoms, and as the concentration of the latter increases, between neighbouringnon-metallic atoms.Uranium hydride, UH,, is a good example of the phenomena involved.It is a metal-like hydride of definite composition, very hard, and havinga crystal structure quite unrelated to that of any of the forms of uranium58 R. E. Rundle and A. S. Wilson, Acta Cryst., 1949, 2, 148.58 E. Hellner and F. Laves, 2. Naturforsch., 1947, 2a, 177.6o Ackt Cryst., 1948, 1, 161.For bond number 4, the increase is 0.36 A. and so on68 CRYSTALLOGRAPHY.metal.61 There are two types of uranium atom in the structure.Onlytwo uranium atoms are at a distance apart, 3.316 A., at which a metallicbond can be formed between them. The remaining U-U distances arelonger, 3-707 A. ; the half of this value, 1-85 A,, is nearly equal to the value1.87 A. that might be expected for a half-bond between uranium andhydrogen.62 The hydrogen atoms may thus be described as linking theuranium atoms together by fractional bonds. U, forms 12 such half-bondsto hydrogen and would have a valency of 6. UII forms four half-bonds tohydrogen and two of fractional order -0.15 to uranium atoms. Its calculatedvalency is therefore about 2.3, corresponding to resonance between bivalentand tervalent states. A similar valency is suggested for one type of uraniumatom in U,Si.63Bonds of half or two-thirds order between the metal and non-metalwould account for the observed interatomic distances in a large number oftransition metal monocarbides, mononitrides, and monoxides.Thesecharacteristically adopt the sodium chloride lattice although the arrange-ment of the atoms in the pure metals is seldom face-centred cubic. Thestructure may be determined by the tendency of the non-metal to formoctahedrally-directed bonds by the use of two hybrid sp orbitals and tworemaining p orbitals. Similar bonding can be used t o explain the morecomplex structures of cementite Fe,C or iron silicide FeSi.65The behaviour of these systems as the proportion of non-metallic atomsincreases is illustrated by two very interesting series of researches, that byR.Kiessling on borides of chromium,66 zirconium,G7 tsntalumyGs molybdenum,and tungsten,6g and that by Zachariasen on uranium ~ilicides.~~ With metalatoms in excess, the non-metal atoms are usually isolated from each otherin the structures, at the 50% composition, MB, they are arrayed in zig-zagchains and a t the ratio MB, in layers which are graphitic in form (Table 11).TABLE 11.Arrangement of non-metallic atoms in borides, carbides, and silicides.Singleatoms.M0,BTa,BW2B--U,SiFeSicf. Fe,CPairs. Chains.- FeB- CrBI MOB - WB- TaBU,Si, USi - -Cr,C* -Double Flat Puckeredchains. layers. sheets. Networks- CrB2 - CaB - Mo2B 5 Mo2B5- W2B5 W*B,-R. E.Rundle, J . Amer. Chem. Soc., 1947, 69, 1719.L. Pauling and F. J. Ewing, ibid., 1948, 'PO, 1660.W. H. Zachariasen, Acta Cryst., 1949, 2, 94.and R. A. Mcdonald, J . Amer. Chem. SOC., 1948, 70, 99.84 R. E. Rundle, ibid., 1948, 1, 180; R. E. Rundle, N. C. Baenziger, A. S. Wilson,6 5 L. Pauling and A. M. Soldate, Acta Cryst., 1948, 1, 212.66 Acta Chem. Scand., 1949, 3, 595. 6 7 Ibid., p. 90.68 Ibid., p. 603. Be Ibid., 1947, 1, 893HODGKIN : CRYSTAL CHEMISTRY. 69There are several intermediate stages represented by individual structures.The silicon atoms are in pairs in U,Si,. In Ta,B, a very interesting double-chain arrangement appears as in Fig. 1. The limits of accuracy are notsufficient to determine whether the sides of the hexagon are irregular asshown, or regular of edge 1-72 A.In the molybdenum and the tungstenE boride phases, the structure, if all possible holes are filled with boron atoms,has one set of boron atoms arranged in a flat graphitic layer and another ina puckered close-packed hexagonal sheet in which each boron atom wouldhave six neighbours, at 1.76 and 1-92 A. Actually the ideal compositionMe,B, is not reached in this phase and some of the holes must usually beempty. The final stage is a three-dimensional network of non-metal atomswith the metal atoms in the interstices. This is shown by a-USi, whichhas the structure early found for ThSi,. (Zachariasen points out thatthere might be a form of carbon having the same arrangement as the siliconatoms here.) An old example among borides is CaB,.fi97- i 8 1.72- 1-79(a) (b) (4 ( d )(a) Chain ; (b) double chain ; (c) sheet ; (d) puckered sheet.FIG.1.Types of arrangement of boron atoms found in borides.In the silicide structures the distances between silicon atoms correspondroughly to single bonds, except in p-USi, (graphitic layers) where it is shorter.In all the borides, the boron-boron distance is greater than Pauling’s latestsingle-bond length, -1.60 A., derived largely from CaB,. In CaB, each boronis surrounded by five others at 1-72 A. and Pauling assumes the bond numberis 0.6 (giving the valency 3 for boron). In the present structures the boron-boron distance varies between 1.72 and 1.91 A. in different chains and layersand seems to depend on the radii of the metallic atoms.Similar phenomena have been observed in different carbide structures,e.g., single atoms, cementite ; chains, chromium carbide Cr&, ; and layers,potassium graphite.In chromium carbide also the distance given toC-C, 1.64 A., is greater than the normal single bond distance.Metallic Sulphides, Oxydphides, and Se1enides.-Sulphide structuresshow several relations to the semi-metallic group just discussed. Again anumber of systems has been studied, illustrating the gradual change instructure type with change in the proportion of the constituent^.^^70 E.g., nickel sulphides, D. Lundqvist, Ariciv Remi, &fin., @sol., 1947, 24, no. 2170 CRYSTALLOGRAPHY.We may list first some of the sulphides of metals of the fanthanon andactinon series examined by Za~hariasen.~~ A survey of phases formedbetween cerium, thorium, uranium, and sulphur was made, and individualsulphides of many other elements were studied (cf.Table 111). Many of thephases belonged to known structure types ; others, particularly Ce2S3,Th7S12, and Ce,O,S, represent new structure determinations.TABLE 111.Structure type ... NaCl Sb2S3 Th,P, Th,SI2 PbCIa PbFCl Ce202S- Ce,S,-Ce,S, - ._. - Ce,O,S Ce .................. CeSTh .................. ThS ThzS3 - Th,Sia ThS, ThOS -- - - - - u ..................... us u2s,Np .................. - Np2S3 - - - NpOS -Pu .................. PUS - p'Zs3 - - I PU2O2SThe phase Ce,S, has the structure type found earlier for Th,P4, witheach metallic atom surrounded by eight non-metallic atcms.In the unitcell a t the composition Ce,S, there are the correct number (16) of sulphuratoms, but too few cerium atoms (log), for the available positions. Nophase change occurs as the composition is changed to Ce,S,, but a contractionof the lattice takes place and the substance becomes more metallic in ap-pearan~e.~, Th7S1, also has metallic character and a disordered crystalstructure. The thorium atoms may occupy the alternative positions, andcertain sulphur parameters must vary according to the actual thoriumpositions occupied.73There are some puzzling relations in the interatomic distances observedand also in such facts as that Am2& and Pu,S, are isostructural with Ac,S3and Ce,S,, while neptunium, thorium, and uranium sesquisulphides have adifferent structure.Zachariasen considers that all the monosulphides (cf.monoxides in the preceding group) are metallic in character, and also thesesquisulphides of the uranium group and Th,S,,. The sulphides of thecerium group seem intermediate. Whereas the radius of plutonium isonly 0.01 A. smaller than that of cerium in the ionic trifluorides it appearsto be 0.12 A. smaller in the metallic monosulphide and disilicide and 0.06 A.smaller in Ce2S3.Cerium oxysulphide, Ce,02S,74 was first identified as such by the structureanalysis of one constituent of a mixed cerium oxide-sulphide preparation.In the crystal structure, which is also shown by La,O,S and Pu20,S, eachmetal is bonded to four oxygen and three sulphur atoms; the metal-to-sulphur distances are somewhat longer, and the metal-to-oxygen distancessomewhat smaller, than the sum of the ionic radii.The arrangement ofseven groups about the metal atom is shown in Fig. 2 , where it is comparedwith the very similar plan found in zirconium oxysulphide. In the lattercompound the seven-membered group is composed of four sulphur and threeoxygen atoms, and the interatomic distances agree well with those found71 Acta Cryst., 1949, 2, 291.73 Idem, ibid., p. 288.72 W. H. Zachariasen, Acta Cryst., 1949, 2, 57.?4 Idem, ibid., p. 61HODGKM : CRYSTAL CHEMISTRY. 71in ZrO, and ZrS,.V5found in K,ZrF,-derived from a distorted octahedron.In both cases the arrangement is essentially that9FIG.2 .Seven co-ordination groups in zirconium and cerium oxysulphides.The other sulphide and selenide structures examined conform approxi-mately to one of two recognised types, with either tetrahedral or octahedralarrangements of the non-metal around the metallic atom. The structuresof the gallium sesquisulphides, selenides, and tellurides, for example, arebased on the zinc-blende lattice, but the structure is a defect structurewith the gallium atoms distributed among tthe available tetrahedral holes. 76In the ferromagnetic mineral, cubanite, CUF~,S,,~~ the arrangement is alsoone with the metal atoms surrounded tetrahedrally by sulphur atoms, butin one plane the iron-sulphur tetrahedra share edges which brings the ironatoms within 260 A.of one another. The arrangement suggests covalentbonding as in KFeS, 78 where chains of FeS,- teetrahedra sharing edgesexist (Fig. 4). The iron-to-iron distance, 2.50 A., is shorter in cubanitethan in KFeS,, 2.70 A., and may be connected with the magnetic propertiesof the material. Buerger is investigating the related iron sulphide pyrrhotiteto test this view.79Among the octahedral co-ordination group further examples, TiSe-TiSe,, and TiTe-TiTe,, have been found of the phenomenon first observedwith cobalt tellurides, of gradual change of structure type without changeof phase.80 As more metal atoms are introduced, octahedral holes in thecadmium iodide lattice are filled, to give the nickel arsenide structure. Inthe alkali thiochromites and selenochromites, the chromium and non-metalatoms form complex ionic layers of the cadmium iodide type.81 As thesizes of the alkali metals or non-metals increase the chromium atoms areforced further apart and this affects the magnetic properties of the material.The interatomic distances fit reasonably well with ionic radii but the crystalsthemselves are deep bluish-black and show metallic lustre.7 5 J.D. McCullough, L. Brewer, and L. A. Bromley, Acta Cryst., 1948, 1, 287.7 6 H. Hahn and W. Klingler, 2. anorg. Chem., 1949, 259, 135.77 M. J. Buerger, Amer. Min., 1947, 32, 415.7 8 J. U'. Boon and C. H. Macgillavry, Bee. Trav. chim., 1942,61, 910.7g Amer. Min., 1947, 32, 411. 80 P. Erlieh, 2. anorg. Chem., 1949, 260, 1.W. Rudorff, W. R.Ruston, and A. Scherhaufer, Acts Cryst., 1948,1, 19672 CRYSTALLOGRAPHY.Oxides and Metal Oxide Complexes.-Most of the oxides recently studiedinvolve octahedral co-ordination of the oxygen atoms around the metalatoms. But there are so many complexities in the distortion and methodof linking of the oxygen octahedra that it is often difficult to see the chemicalimplications of the atomic arrangements found. Even a simple oxide likenickel oxide has recently been shown to have, a t ordinary temperatures,lattice constants corresponding to a very slightly deformed sodium chloridelattice-rhombohedra1 and not cubic. The deformation vanishes aboveabout 200" and increases at low temperatures ; possibly here it is connectedwith the nickel-oxygen size ratio.82One of the most remarkable series of oxide structures is that found byA.Magneli working on molybdenum and tungsten oxides, particularlyMOO,, Mo,O,,, Mo,O,,, and Mo,O,. The dioxides, MOO, and W0,,83 havedistorted rutile structures. The metal-oxygen octahedra, MeO,, are coupledby edges to form strings, running through the crystal. Within the stringstEe molybdenum atoms are alternately 2.48 and 3-72 A. apart. The shortFIG. 3.The arrangement of linked octahedra in Mo,O,, .distance implies a covalent bond between the molybdenum or tungstenatoms; it is even shorter than the single-bond distance, 2-58 A., calculatedon Pauling's radii for the hybrid state found in metallic molybdenum.Between the strings, on the other hand, the distance between metal atomsis 3.72 A.The crystal structures of Mo,O,, and Mo,O,, 84 are built on ratherdifferent principles.In each of these, two-dimensional " boards " areformed of MO, octahedra sharing corners. These boards extend throughoutthe crystal parallel to one axis, but normal to this they extend for eightoctahedra in Mo,O, and for nine octahedra in Mo,O,,. The two octahedraa t each end of a board share edges with corresponding octahedra of otherboards, the remaining octahedra being linked by corners. Hence gaps arisein the structure (Fig. 3). A somewhat similar arrangement is shown in thevanadium oxide, V1202,, where again overlapping strings of octahedra arepresent.85 The maintenance of order in these complex systems presentsa very interesting problem.82 H.P. Rooksby, dcta Cryst., 1948, 1, 226.88 A. Magneli, Arkiv Kemi, Min., Geol., 1946, no. 24 A.84 A. Magneli, Acta Chem. Scand., 1948, 2, 501.F. Aebi, Helv. Chins. Acki;, 1948, 31, 8HODGKIN : CRYSTAL CHEMISTRY. 73The deficiency of oxygen relative to MOO, is made up in these structuresby linking octahedron edges, Another method is shown in Mo401, 86where one-quarter of the molybdenum atoms is surrounded only by a tetra-hedron of oxygen. The structure is much looser than those already men-tioned-the cell volume corresponds to 20 A.3 per oxygen as against 16.4in MOO, and nearly 19 ~ . 3 in the other oxides. In y-tungsten oxide,w18049," the arrangement of tungsten atoms is even more irregular. Andhere a short W-W distance, 2-60 A., similar to those in WO, and MOO, againappears.The oxygen atoms can be placed in an intricate way to formoctahedra linking corners and edges.With the tetragonal tungsten bronzes the ratio W : 3 0 is reached andthe tungsten oxide framework is formed of octahedra linking corners only.But according to Magneli's structure, these octahedra are joined in a verycomplex way to form strings or polygons of three, four, or five octahedra.The potassium or sodium atoms are then situated in interstices of adjacenttetragons or pentagons surrounded by twelve or fifteen oxygen atoms.ssA group, Ti,O,, exists in the recently studied non-ferro-electric bariumtitanate structure. Here the group is formed by two distorted TiO, octa-hedra sharing a face. And again the Ti-Ti distance, 2.67 A., is of the orderof magnitude of a single covalent bond length.89 It is clear that thecharacter of the ferro-electric modification depends closely on the actualsize relations and ion distribution in this form,9o In the magnetic ferriteswhich have a spinel type of structure, there are also very interesting relationsbetween cation sizes, distribution, and magnetic proper tie^.^^Several new X-ray analyses involving manganese have been carriedout.The mineral hollandite consists of a framework of linked octahedraof approximate formula MnO, enclosing barium ions in cuboid spacs~.~2y-MnO, (ram~dellite)~~ and HMnO, (groutite) 94 both crystallise in the sameform as AIHO, (diaspore), with the exception that the distortion of theoxygen octahedra due to hydrogen bonds in diaspore and groutite is absentin ramsdellite.R. L. Collins and W. Lipscomb 94 point out that there isyet another distortion present in manganite which may be found, on moredetailed study, to be present in the other structures. Four oxygen atomssurround the manganese atom in a square a t 1435-1-95 A., while two othersare further away a t 2-30 A. The arrangement is more easily understoodif the bonding is partly of the covalent dsp, type.Still stronger evidence of the existence of directed covalent bonds occurs8 e A. Magneli, Acta Chem. Scand., 1948, 2, 861.87 Idem, Arkiv Kemi, 1949, 1, 223.88 R. D. Burbank and H. T. Evans, Acta Cryst., 1948, 1, 330.88 fbid., pp. 213, 269.R. G. Rhodes, Acta Cryst., 1949, 2, 416.E.J. W. Verwey, P. W. Haayman, and E. L. Heilmann, PhiZipa Tech. Rev.,1947, 9, 185; E. J. W. Verwey, F. de Boer, and J. H, van Santen, J . Chem. Physics,1948,16, 1091.O2 A. Bystrom and A. M, Bystrom, Nature, 1949, 164, 1128.Og A. M. Bystrom, Acta Chem. Scand., 1949, 3, 163.g4 R. L. Collins and W. Lipscomb, Acta Cryst., 1949, 2, 10474 CRYSTALLOGCRAPHX.in certain uranium oxides and mixed UO,, U30,,96 uranyl fluoride(UO,F,), and lithium, sodium, potassium, strontium, and calcium uranyloxides. In all these, hexagonal or pseudo-hexagonal layers occur in whichuranium atoms are surrounded by six oxygen atoms at about 2.29 A. inflat octahedra and by two oxygen atoms forming a linear group normal tothe layer. In UO, these linear groups are linked to form continuous chains-U-0-U-0-. In all the other compounds a definite group UO, is formedwith U-0 about 1.91 A.This distance is nearly that required for a doublebond on Pauling’s radii, suggesting the group is O=U=O ; the larger distance,2.29 A., might correspond to a one-third bond, but presumably here thevalency is partly ionic. In the mixed oxides the metal ions pack betweenthe layers, binding them together. In uranyl fluoride, fluorine replacesalternate oxygen atoms in the octahedra, and the layers are loosely stackedwith some disorder. A uranyl group with the same dimensions is alsofound in barium uranyl oxide, Ba(U0,)02, but here the layer has tetragonalsymmetry and the uranium atom has four neighbours, a t 2-12 and 2.22 A,,other than those of the uranylHades.--Some of the clearest examples of transition from ionic- tocovalent-structure types are provided by new halide structures.To begin with, aluminium trichloride has, after all, an ionic crystalstructure.98 The chlorine atoms are arranged in slightly deformed cubicclose packing as originally proposed, but the aluminium atoms are singlyin one set of octahedral holes, not in the tetrahedral holes, as required forthe structure, A12C1,.All the crystal structures of copper halides and mixed halides, cupricand cuprous, have structures characteristic of covailent binding.In bothCuC1,gQ and CuBr2lo0 flat chains appear, as in Fig. 4 (i) below, of the PdCI, type.I n CsCuC13,10L the co-ordination of the chlorine atoms round the copper isalso planar but the chain is spiral in form.Formally it could be representedas in Fig. 4 (iia). A. F. Wells compares the chain (i) to its tetrahedralanalogue in SiS,-FeS,- is another example-and (ii) to the silicate SiO,chain in diopside. A closer tetrahedral analogy is with the CuCf, chain inthe cuprous compound K2CuCI, where the bonds at the chlorine atoms arebent, not nearly linear as in the silicates.lo2In all the cupric halides, including also the hydroxy-chloride and-bromide, Cu,Cl(OH), lo3 and Cu2Br(OH),,1M it is noticeable that, in addition95 W. H. Zachariasen, Acta Cryst., 1948, 1, 281.96 Cf. F. Grenwald, Nature, 1948, 162, 70.97 S. Samson and L. G. Sillen, Arkiv Kemi, &fin., Geol., 1948, 25, no.21.s* J. A. A. Ketelaar, C. H. Macgillavry, and P. A. Renes, Bee. Truv. chim., 1947,88, 501.A. F. Wells, J., 1947, 1670.loo L. Helmholz, J . Amer. Chem. Soc., 1947, 09, 886.lol A. F. Wells, J., 1947, 1662.lo2 C. Brink and C. H. Macgillavry, Actu Cryst., 1949, $3, 158.lo8 A. F. Wells, ibid., p. 175.lo4 F. Aebi, Helv. Chim. Ada, 1948, 31, 369IXODGKIN : CRYSTAL CHEMISTRY. 75to the four strong bonds of the square dsp, type, the copper atom is a tintermediate distances, corresponding to bonds of very low order, awayfrom two other atoms, halogen or hydroxyl, which complete a distortedoctahedron. Wells suggests that this arrangement may be connected withthe presence of an odd electron, with some bonding power, in one of thep orbitals in the cupric valency state.The situation may be comparedwith that of manganese in mangsnite, but here the difference between thebond lengths is rather greater ; in CuCl,, for exsmple, Cu-4C12.3 A., Cu-2Cl2.95 A.An interesting example of the distinction between planar and octahedraltypes comes from the study of Pt(NH,),Br,,Pt(NH,)2Br4.105 Here planarand octahedral groups succeed one another in a chain in the crystal. Inthe double salt 2NH,C1,FeCl3,H2O an octahedral ion [FeC1,,H,0]2- isformed.lo6'' (ia)(ila) (iib)FIG. 4.Diagram of chain arra.ngements i i ~ : (ia) cu.pric chloride, (ib) potassium thioferrite,(iia) cmsium cuprichloride, and (iib) potassium cuprochloride.With the halides of the uranium metals we can trace the effects ofboth change of halogen and change of valency.The number of compoundsexamined is too great to permit their individual mention; we can give onlythe types of structure found in each valency state.Here it is noticeable that the co-ordination number of theheavy metal changes from 11 in UF, to 9 in UCl, and UBr,, and to 8 in uI,.107 The crystal structures of the first three are of ionic types; UF,and thirteen others have the LaF, structure, while eighteen compoundsare listed with the UC1, structure.108 UI,, like PuBr, and many otherbromides and iodides, has a layer structure.(a) AX,.lo5 C . Brosset, Arkiv Kemi, Min., GeoE., 1948, 25, no. 19.lo6 I. Lindqvist, ibid., 1947, 24, A , no. 1.lo' W. H. Zachariasen, Ada Cryst., 1949, 2, 388.lo8 Idem, J .Cliem. Phgsics, 1948, 16, 254; Acta Cryst., 1948,1, 26576 CRYSTALLOGRAPHY.(b) AX,. The fluorides belong to a complex monoclinic structure typerepresented by ZrF,, not fully worked out. UCl, and ThC1, have interestingstructures; log each metal atom is surrounded by four near neighbours ina flat tetrahedron, with U-4Cl 2.46 A., and four other neighbours, withU-4C1 3.09 A. The compounds are at least partly covalent and sublimea t high temperatures.Each uranium atom is here bondedto nine fluorine atoms a t a mean distance 2.31 A. The uranium atoms areequivalent in the structure and presumably there is resonance between thevalency states 4 and 5. Correlated with this is the black colour of thecrystals. The same arrangement is shown by NaTh,Fg, where the sodiumatoms fit into four or the six possible holes in the U2F9 structure.l1°Uranium pentafluoride crystallises in two different structures,cr-UF, and p-UF,.lll In the first, each uranium atom is surrounded by sixfluorine atoms in an octahedron, and the octahedra are linked by oppositecorners in chains (cf.T12AIF5). Zachariasen considers that the U-F bondshere are predominantly ionic, but the forces between adjacent chains mustbe largely of van der Waals character. In P-UF, each uranium atom isbonded to seven fluorine atoms, four of the seven corners being shared withadjacent polyhedra. The U-F distances are very similar in the two struc-tures, those in p-UF5 being very slightly longer.At the stage AX,, a definite molecule uc1, is formed.50Each uranium atom is surrounded by six chlorine atoms in a regular octa-hedron a t a distance U-C1 2.42 A.From this the single covalent radius ofsexivalent uranium may be calculated as 1.43 A., in good agreement (toogood for the limits of error involved !) with Pauling’s value of 1-42 A.Among mixed halides some ordered structures exist such as Cs2PuC1,,ll2where the czesium ions are in 12-co-ordination positions and the plutoniumin 6-co-ordination. However, there is a very large number of disorderedphases in which, for example, alkali or alkaline-earth ions occupy at randomthe same positions in the crystal as the heavy-metal ions. Examples arecr-K,ThF, or cr-KLaF, which both have the fluorite structure, or a seriesMThF, with the lanthanum trifluoride arrangement, where M is any alkalineearth.Phenomena of this kind we have become most accustomed to in thenext group, the silicates.Silicates and Silicones.-The silicates have continued to provide us withgood problems both in chemical organisation and in structure analysis.We may begin with the type of silicates usually treated last, frameworkstructures, which happen to adopt some of the less complex crystal structures.Three of these, eukryptite, LiA1Si0,,l13 nepheline, (NaK)MSiO,, 114 and(c) AX,., is represented by U2F9.(d) AX,.( e ) AX,.log R. C. L. Mooney, Acta Cryst., 1949, 2, 189.110 W. H. Zachariasen, J. Chem. Physics, 1948,16, 425; Acta Crystall., 1949, 2, 390.ll1 Idem, ibid., p. 296.l13 H. G. F. Winkler, ibid., p.27.11* M. J. Buerger, G. E. Klein, and G. Hamburger, Amer. Min,., 1947, 32, 197.Idem, ibid., 1948, 1, 268HODGKIN : CRYSTAL CHEMISTRY. 77kalsilite, KAlSiOq,l15 have been studied and their close relation to oneanother established. All three are based essentially on silicon dioxidelattices suitably distorted to permit the entry of extra atoms. That ofLiAlSiO, is the @(high temperature)-quartz lattice with aluminium andsilicon alternately at the positions of silicon in @-quartz, and the lithiumions in channels in the structure. As H. G. F. Winkler points out, largerholes can be formed more easily in a tridymite lattice which is 15.5% lessdense than in @-quartz, and this has now been established in both nephelineand kalsilite, which accommodate sodium and potassium ions.In all theselattices the Si-0-A1 bonds are bent at some, a t least, of the oxygen atoms.The angle is 145.5” in LiAlSiO,, nearly tetrahedral in parts of kalsilite, andstraight in others. In nepheline the distortion produces two sizes of holesand this suggested to the investigators that potassium as well as sodiumwas present-a fact verified subsequently by chemical analysis.The structure of tourmaline, one of the outstanding problems in thisfield, has been put forward by M. J. Buerger and G. Hamburger.llG Herethe formula may be given as approximately g iB313Jsi6027(0H)*; inorder to assist the X-ray analysis use was made of tourmalines of ratherdifferent composition from this with Mg replaced by Fe, and implicationfunctions derived from Patterson syntheses were employed. The silicon-oxygen tetrahedra were found to be linked in rings, Si,O,,, with one set ofoxygen atoms pointed down from the plane of the ring.These form part ofa system of linked oxygen octahedra surrounding magnesium ions as inbrucite. The units formed are similar to the “Mg kaolin’’ in Aruja’sstructure for chrysotile ; they are cemented together by aluminium, boron,and sodium ions, the boron in a plane triangular co-ordination.A solution for another major silicate problem, the structure of epidote,has been given by T. Ito.l17 The most interesting feature here is theproposed linking of the silicon-oxygen tetrahedra into bands of formulaSi,O,, or rather AlSi,O,. Somewhat similar bands occur in eudidymite,HNaBeSi308,11s and in a slightly different version in epididymite.Herethe main Si,O, bands are linked together with a sodium ion between themin octahedral co-ordination, forming sheets, NaSi,O,. The beryllium andhydroxyl ions in eudidymite are linked into the sheets so that the mainforces between them are of van der Waals character and the crystals easilycleave.In these three analyses the data are too limited for the atomic positionsin such complex crystals to be precisely fixed, though Fourier methods havepartly assisted in finding them. However, one of the most interestingdevelopments in this field is the further application of electron-densitycalculations to structures previously solved. A full three-dimensionalanalysis of sanidinised orthoclase has now been carried out, for example,to test the postulate that heat treatment of orthoclase resulted in the random115 G.F. Claringbull and F. A. Bannister, Acta Cryst., 1948, 1, 42.116 Amer. Min., 1948, 33, 532. 117 Ibid., 1947, 32, 532. 118 Ibid., p. 44278 ORYSTALLOGIRAPHY.distribution of silicon and aluminium in the framework. The new analysis 119established that the " Si "-0 distances in different tetrahedra were thesame, mean 1.642 A., and that the aluminium was accordingly randomlydistributed. However, it became clear in the analysis that the accuracyof the earlier work, which suggested differences in the tetrahedra in un-treated orthoclase, was insufficient to prove the point.Very interesting differences in silicon-oxygen bond distances and anglesappear in the Fourier projection calculated for Bolivian crocidolite, a fibrousasbestos-like variety of amphibole.f2* Here most of the individual atomswere observed resolved in projection by a process of subtracting, one afteranother, the contribution of atoms whose position could be fixed.TheFIG. 8.(a) ' ' Octumethylspirof 5 : 5]pentasiloxune. "crocidolite.(b) Silicate chain in Bolivianover-a11 accuracy of the analysis is not high but good enough to establishthe main character and distortion of the structure. The interatomicdistances within the double silicon-oxygen chain, much altered from the idealform, are shown in Fig. 5b. The metal ions lie in bands between the chains,and from the different heights of the electron-density peaks it is possibleto work out a scheme of distribution between them of the different metal ionspresent, K, Na, Ca, Mg, Al, and Pe.This distribution is a compromisebetween entropy considerations leading to random distribution and energyconsiderations which require unequal distribution in holes of differingco-ordination number.A silicate structure containing small finite groups is afwillite,121 in whichthe arrangement of the oxygen atoms strongly indicates the presence of119 W. F. Cole, H. Sorum, and 0. Kennard, Acta Cryst., 1949, 2, 280.120 E. J. W. Whittaker, ibid., p. 312.lel H. D. Megaw, ibid., p. 419HODGKM : URYSTAL CHEMISTRY. 79hydroxyl groups linked to the silicon atoms. Accordingly, one might writethe formula Ca(OH),,Ca*Si(OH),O,.In lawsonite, CaAI,(Si,O,)( 0H)2,€€20,according to F. E. Wickman, the more usual arrangement with hydroxylattached to aluminium appears, the silicon atoms being present in Si,O,groups.122It is very interesting to be able to compare these silicate structures withthat of ‘‘ octamethylspiro[5 : Eilpentasiloxane ” (I), measured by W. L./SiMe2*O\ / O*SiMe2\0, ,Six .O\SiMe2*O/ \O*SiMe2/ (1.1Roth and D. Harker.123 Here the silicon-oxygen rings are similar to thosefound in the mineral benitoite, though the physical properties of the spiro-siloxane are very different; it is volatile and crystallises from toluene.Calculations of the electron density in three dimensions established thegeneral shape of the molecule shown in Fig. 5a.Within the limits of experi-mental error the Si-0 bond, 1.64 A. long, is of the same order as that foundin the silicates, a distance much shorter than the sum of the covalent radii,1-83 A. Pauling considers this bond to be 50% ionic and 60% covalent;certainly the Si-0-Si bond angle, 130°, as in many silicate structures seemsintermediate in character. On the other hand, the methyl groups areattached to silicon a t the tetrahedral angle, and the Si-C distance, 1.88 A,,is only slightly smaller than the covalent-bond length 1.94 A. From theelectron density found, the whole SiMe, group appears free to oscillate, as ina ball and socket joint, movement to which the ionic undirected character ofthe Si-0 bond might contribute.Phosphates, Arsenates, and Mo1ybdates.-Phosphate and arsenate crystalstructures have an obvious relation to silicate structures except that a greaternumber of orthophosphate structures have been studied.New analysesare those of phosphates of the rare earths,12, barium, and strontium; 125bismuth arsenate has also been investigated.126 The hydrated ferricphosphates and arsenat es , Fe, (PO,), , 8H20 and Fe,( A s O ~ ) ~ ,8H20 , havecrystal structures in which there appears a group of four water moleculesarranged in a tetrahedron.12, These form part of the oxygen-atom octa-hedra surrounding the iron atoms, which are partly linked through phosphorusor arsenic and partly through water.The most interesting phosphate structure determined is probablyammonium tetrametaphosphat e , NH,PO, or rat her (NH ,) ,P,O 16.l2 Here,as in calcium metaphosphate, four PO, tetrahedra are linked in a ratherflat ring. (These arethe only inorganic metaphosphates so far analysed in detail; nothing com-Within the ring, P-0 is 1-62 A . ; outside it, 1.46 A.122 Arkiv Remi, Min., Ceol., 1948, 25, A , no. 2.lea Acta Cryst., 1948, 1, 34.lZ* R. C. L. Mooney, J . Chem. Physics, 1948, 16, 1003.125 W. H. Zachariasen, Acta Cryst., 1948, 1, 263.126 R. C. L. Mooney, ibid., p. 163.128 C. Romers, J. A. A. Ketelaar, and C. H. Macgillavry, ibid., p. 960.lZ7 T. Ito, Nature, 1949, 164, 44980 aRYSTALL00RAPHY.parable with the biochemically important trimetaphosphates has yet beenso examined.) The structure may be compared with that of the third formof phosphoric oxide where six PO, tetrahedra form a ring and these arefurther linked in sheets.129One of the most complex condensed acid structures is shown in theammonium and potassium molybdotell~rates,1~0 where the molybdenumatoms are arranged in a hexagon around the tellurium atoms, as in thestructure suggested by J.S. Anderson. The oxygen atoms in layersabove and below the hexagon form octahedra about both tellurium andmolybdenum. For the Mo-0 bond length, the best value is probably1.83 A. from the re-examined crystal structure, Ag2M004. Here the Ag-0distance, 2.42 A., is not as short as was expected from the bright yellowcolour of the compound.f31Oxy-acids and Acid Salts.-The crystal structures of the commoninorganic acids have so far not been fully examined, owing to experimentaldi6culties.A. F. Wells and M. Bailey have pointed out that they shouldprovide examples of hydrogen-bond systems which differ geometricallyaccording to the relative number of hydrogen and oxygen atoms present. 132Four main groups can be distinguished on their hydrogen : oxygen ratio :(a) <1 : 2, HNO,, HIO,, HCO,' ion; ( b ) 1 : 2, H2S0,, H,P04' ion; (c) from1 : 2 to 1 : 1, H,SeO,; and (d) 1 : 1, H,BO,, H,TeO,. The last group iswell known ; the arrangement found, with each oxygen atom distant -2.75 A.from two others, is one which is characteristic of the presence of OH groupsin many organic structures. In each of the other three groups, shorterinter-oxygen distances have now been found, one of the oxygen atoms atleast making only one such contact.SeIenious acid (group c) necessarily has an intermediate character ; theSeO, groups are arranged in double layers, and the oxygen atoms, linked a tshort distances, 2.60 and 2.56 A.as shown in Fig. 6, must differ from oneanother. It is tempting to write hydrogen at the end of the two longSe-0 bonds, 1.76 and 1.75 A., and to see these as OH groups each makingcontact with a third essentially Sex0 group, which is at the receiving endof two hydrogen bonds.In the type structure for group (a), the HCO,' ion chain system, found insodium hydrogen carbonate, the X-ray analysis suggests that the hydrogenatom is mid-way between two oxygen atoms. Wells 133 points out that itis possible to see also in the linking of HIO, groups in iodic acid a singlehydrogen-bonded chain system, provided that it is recognised that othershort oxygen-oxygen contacts in the crystal are due to the weak additionalattractive forces between iodine and oxygen.Similar chains appear in thecrystal structure of nitric acid.ls4 However, in both these last structures,12* C. H. Macgillavry, H. C. J. de Decker, and C. M. Nijland, Nature, 1949,164,448.130 H. T. Evans, J . Amer. Chem. Soc., 1948, 'SO, 1291.J. Donohue and W. Shand, ibid., 1947, 69, 222.13* J., 1949, 1282.134 M. V. Luzatti, Compt. rend., 1949, 229, 1349.133 Acta Cryst., 1949, 2, 129HODGKIN : CRYSTAL CHEMISTRY. 81the oxygen atoms in the chain are not symmetrically arranged.In thepyramidal 10, group, one 1-0 bond is longer than the others,135 and oneN-0 bond is longer in the planar NO, group, suggesting definite I-OH0FIG. 6.Diagram to illustrate arrangement of hydrogen bonds in (a) carbonate-bicarbonateion, (b) nitric acid, ( c ) iodic acid. and (d) selen,ious acid.and N-OH bonds respectively. More detailed information about boththese structures is needed to be sure of these points. The nitric acid crystalstructure particularly is very complex and affected by disorder in thecrystals. The outline presented by M. V. Luzatti is clearly reasonable;the flat molecules are packed in layers, and within each layer held in parallellS5 M. T. Rogers and L. Helmholtz, J . Amer. Chem. Xoc., 1941, 63, 28282 CRYSTALLOGRAPHY.chains by the hydrogen-bond system; but there are details of the solutionwhich call for further discussion.By far the most accurate X-ray analysis in this field is that of trona,Na2C0,,NaHC0,,2H,0 where three-dimensional electron-density serieshave been calculated and the bond lengths may be accurate to -j=O.Ol--0.02 A .~ ~ ~ Here again a similar system appears. Two planar CO,” groupsare linked by a short hydrogen bridge (2.53 A . ) ; and here crystallo-graphically the hydrogen atom should be placed midway between them at acentre of symmetry, a situation also found in potassium hydrogen phenyl-acetate and p-hydroxybenzoate, 137 However, the true relation of thehydrogen atom to the centre of symmetry may be either time average orstatistical. It is noticeable that a ridge of electron density above the l eper A . ~ runs along the line of the hydrogen bond in projection.Also thelongest of the three C-0 links is directed towards the hydrogen bond.0 0(&@+$? (6)N0 0 >- yo (e)C”3 0FIU. 7.Interatomic distances in (a) nitroniunz ion, (b) nitrogen dioxide, ( c ) dinitrogentetroxide, (d) dinitrososulphite ion, and (e) dimethylnitramine.It may be noted that the bond lengths in the CO, group in trona are agood deal shorter than in calcite (1.31 A.). No accurate figure for thisdistance can be gained from the other carbonate structure lately studied,basic bismuth carbonate, where the carbonate groups have a disorderedarrangement packed between BiO layers. 138Some Structures containing Nitrogen.-Several long-standing problemsof nitrogen chemistry have been solved by recent X-ray analysis, only toraise new questions of the interpretation of interatomic distances withinthe systems studied.These interatomic distances are shown, with othersrecently found, in Fig. 7.The new single-bond distances for N-N, 1-42 A., and N-0, 1.45 A.,13@ C. J. Brown, H. S. Peiser, and A. Turner-Jones, d c t a Cryst., 1949, 2, 167.13’ J. Speakman, Nature, 1948, 162, 698.13* A. Lagercranz and L. G. Sillen, Arkiv K e m i , Mim., CeoE., 1948, %, no. 20H0I)GB;IN : CRYSTAL CHEMISTRY. 83observed in hydrazinium dichloride 139 and hydroxylammonium chlorideand bromide,140 are shorter than might be expected from measurementson gaseous hydrazine and hydrogen peroxide.While the N-0 distancemay be modified by the difference in the electronegativity of the twoelements, this would not account for the shortening of the N-N distance.The two crystal structures are closely related. In each, four chlorine atomslie at distances about 3.1-3.2 A. from the nitrogen atom, one along theline joining N-N or N-0, the others at positions making angles of about100” with this line. These positions suggest an orientation of the hydrogenatoms attached to nitrogen which is trans or staggered in the hydrazinium ion.Intermediate bond lengths for N-0, 1-35 A., corresponding to a calculatedbond order about 1.2, are found in potassium dinitros~sulphite.~~~ Theseare similar in length to the length N-0 found in trimethylamine oxide,1.36 A., from electron diffraction,142 and suggest the ion could be formulatedhN-0-approximately O~S--N+’’ .The S-X link is 1.63 A. long, close to\O-single bond in character ; it is markedly longer than that (1.57 A.) in sulphamicacid. Probably the S-0 distances in these compounds, 1-43-1.44 A., might betaken as a standard S=O distance in syst3ms involving d orbitals. TheN-N distance is also double bond in character. It may be compared withthe distances found in dimeth~1nitrarnine.l~~ The planar character of bothmolecules supports the view that the wave function in each case involvessp, hybridisation.In nitronium perchlorate, the linear character of the ion is establishedand indicates a formulation O=-U=0.144 The N-0 distance is not accuratelydetermined yet but seems clearly shorter than that found in gaseous nitrogend i 0 ~ i d e .l ~ ~ The most interesting structure in this group is that of di-nitrogen tetroxide. m The crystal structure has been re-investigated bysingle crystal and Fourier methods and, while the atomic arrangement isclosely similar to that given originally by Hendricks, the interatomicdistances are quite unexpected. The long distance, N-N, 1-64 A,, wouldcorrespond to something of the order of a half-bond in length. It suggeststhat the nitrogen dioxide molecules remain virtually unchanged in the solidcompared with the gas, with only a weak force of attraction between them.Two azides have been investigated, cuprous azide 14’ and strontiuma ~ i d e , ~ ~ ~ the latter by three-dimensional Fourier methods.In both, thei-J. Donohue and W. M. Lipscomb, J . Chem. Physics, 1947,15, 115.14* B. Jerslev, Acta Cryst., 1948, 1, 21.141 E. G. COX, G. A. Jeffrey, and H. P. Stadler, Nature, 1948,162, 770; J., 1949, 1783.Ire M. W. Lister and L. E. Sutton, Trans. Faraclay Xoc., 1939, 35, 495.144 E. G. Cox, G. A. Jeffrey, and M. R. Truter, ibid., 1948, 162, 259.145 S. Claesson, J. Donohue, and V. Schomaker, J. Chem. Physics, 1948, 16, 207.lr6 J. S. Broadley and J. M. Robertson, Nature, 1949, 164, 915.lr7 H. Wilsdorf, Acta Cryst., 1948, 1, 115.14* F. J. Llewellyn and F. E. Whitmore, J., 1947, 881.W. Costain and E. G. Cox, Nature, 1947, 160, 82684 CRYSTALLOGRAPHY.azide group is symmetrical and linear; the N-N distance in strontiumazide, 1.12 A,, agrees with that in similar structures.These come close tothe distance in nitrogen itself and complete the range of N-N bondsexamined from 1.64 A. downwards. It is clear that N-0 bonds tend to beshorter than N-N for comparable bond number, particularly in the systemsinvolving resonance.Boron Hydrides.-Wi th the boron hydrides and particularly decaboranewe return, as in the first section of this Report, to an electron-deficientsystem. But the system here is one which, in its molecular character, formsa natural link with many organic structures.The first, a simple one,is that of sodium borohydride, which is shown by A. M. Soldate to consistof Na” and BH,- i0ns.14~ The powder data employed were insufficientto place the hydrogen atoms; the crystal symmetry suggests a tetrahedralarfangement, and the space is sufficient to allow oscillation or even possiblyrotation of the tetrahedra.Two crystal structures have been determined.FIG.8.Proposed arrangement of atoms in (a) decaborane, (b) diborane.Decaborane, on the other hand, proves to have an utterfy unexpectedatomic arrangement, found largely through a new method of phase deter-mination, combined with the rigours of three-dimensional electron-densitysynthesis.ls Some confirmation that the atomic positions proposed are,at any rate, one solution of the diffraction problem, is provided by the factthat they also fit the electron-diffraction data. The molecular structure,shown in Fig. Sa, is a slightly modified version of that already published,from which it differs principally in the position of certain of the hydrogenatoms.* For comparison, the latest inter-atomic distances suggested fordiborane are given in Fig. Sb.150The interatomic distances found in decaborane show relations both withthose m diborane and with those in metallic borides. With the exception of14* J . Amer. Chem. Xoc,, 1947, 69, 987.150 B. V. Nekrasov and V. V. Shtutser, J . Gen. Chem., Russia, 1948, 18, 832.* I am greatly indebted to the authors for this information from a. paper now inthe pressHODGEM : CRYSTAL CHEMISTRY. 85the long B-B distance of 2-01 A., all the B-I3 distances are equal, within thelimits of experimental error, to 1 . 7 6 ~ . (cf. W2B5 and CaB,). The B-Hdistances are less precisely fixed ; ten of the hydrogen atoms are attached toonly one boron atom; four lie in bridge positions attached to two boronatoms, as in the structure shown for diborane. Bond numbers may beassigned to keep the boron atoms tervalent and hydrogen atoms univalent,the preferred arrangement being one in which the majority of the boronatoms form five bonds each of number -0-4 to boron and hydrogen andone to hydrogen of number 1.0. As in the metallic borides and otherelectron-deficient systems, the bonds have no longer the directional characterascribed to normal covalent bonds. However, it must be admitted that, inspite of these relations, the theoretical interpretation of the decaboranestructure is quite obscure, and further details of its analysis are awaited withgreat interest.Clathrate Compounds.-There is one group of compounds, clathratecompounds, which cannot happily be grouped as either organic or inorganicsince both kinds of molecule occur together in one crystal in the examplesrecently s t ~ d i e d . 1 ~ ~ The first type, found by H, M. Powell and D. E. Palin,152was discussed shortly in 1946. Here quinol molecules form a hydrogen-bonded framework in the crystal inside which different molecules may betrapped. New experiments show that the framework may be somewhat dis-torted to admit longer molecules than the sulphur dioxide first observed ; thelimit is reached at methyl cyanide.153 The latest trapped molecules includethe rare gases argon and krypton, the presence of which can be establishedfrom electron-density projections. Since the cavities in which they lie are7.5 A. across, only van der Waals forces occur between these atoms and theenclosing framework.In a second type of clathrate compound, the framework is inorganic,Ni(CN),NH,, and the trapped molecules organic, e.g., benzene or thiophen.154The nickel atoms and cyanogen groups form sheets similar to a single layerof the Prussian-blue structure. From these, ammonia groups project,giving the nickel atoms alternately planar and octahedral co-ordination.Between the layers and their projecting groups, there is too much space,and crystallisation cannot proceed unless suitably sized solvent moleculesare present and can be trapped and fitted into the interval. There must bemany other compounds of this kind to be found in purely organic systems.D. C. H.In conclusion we thank Miss J. Broomhead, A. Addamiano, and D.Sayre for help in the preparation of this Report.DOROTHY CROWFOOT HODCIKM,G. J. PITT.1 5 1 I€. M. Powell, J., 1948, 61.154 H. M. Powell and J. H. Raper, Nature, 1949, 188, 566.153 Ibid., p. 571. lS3 Ibid., p. 815