CRYSTALLOGRAPHY.1. INTRODUCTION.IT becomes increasingly difficult to define the scope of a modernarticle on crystallography. The old historical isolation of thesubject has, of course, long disappeared. Most of the recentinvestigations have as their immediate object the determinationof the precise spatial positions of atoms in a molecule or crystal,and if this can be carried out completely then the results form astarting point for. an accurate discussion of the structure in termsof modern theory. The same kind of information regarding positionsof atoms can frequently be obtained from gases and liquids byanalogous experimental methods, and it would obviously be amistake to relegate the discussion of such results to a separatearticle. Finally, in discussing the structure obtained by thesemethods a large variety of other data and experiments may have tobe mentioned.Considered in this wider aspect, the most outstanding contributionto the subject during the past year has undoubtedly been thepublication of “ The Nature of the Chemical Bond and the Structureof Molecules and Crystals ” by Linus Pau1ing.l The fundamentalpast played by crystallography and diffraction methods in generalin developing the ideas of modern structural chemistry is immediatelyapparent in this work. The theory of the chemical bond is developedin a lucid and straightforward manner, and questions relating tointeratomic distance and ionic sizes, and the factors which governthem, are dealt with very fully.The examples quoted to illustratethe various arguments cover an enormous range of experimentalwork. Another book dealing with crystal chemistry from anentirely different and more restricted aspect has also been publishedduring the year.2We have found it convenient to divide the present Report intothree sections, which follow roughly the classification adopted inprevious Reports.The first section deals with the more physicalaspects of crystallography. During the last few years a great dealof attention has been devoted to the difficult subject of vibrationalenergies in crystals and lattice energies generally, and, as little ofthis work has been previously reviewed in these Reports, a specialtreatment is now given from the therinodynamic point of view.1 Cornell University Press and Oxford University Press, 1939.2 K.C. Evans, “ Crystal Chemistry,” Cambridge University Press, 1939ROBERTSON : INTRODUCTION. 149The onset of molecular rotation and the structural changes whichaccompany thermal transitions in crystals are other aspects whichhave not been fully elucidated, and a review of this work is alsogiven.The remainder of the Report is devoted to a discussion of currentwork in structural chemistry and crystallography. In the past ithas been customary to describe the work in two sections under“ crystal chemistry ” and “ molecular structures.” Although thedistinction is a significant one, we feel it is not fundamental. Themolecules of closely related substances may combine to formindefinitely large polymers or remain as discrete units in the crystal,the distinction depending upon the relative sizes of atoms andstoicheiometric relations rather than upon abrupt changes in bondtype.Accordingly, we have preferred to adopt the convenientchemical classification into inorganic and organic structures. Thelatter are, of course, predominantly “ molecular ” structures.New determinations of simple inorganic structures are naturallynot so numerous as in the past, and most of the work concernsrelatively complex substances such as iron enneacarbonyl, Fe,(CO),,which has now been worked out with interesting results. Unusualco-ordination numbers have long been a matter of interest, andseveral new examples, such as in the ZrF,’ and TaF7z ions and inneodymium bromate enneahydrate, Nd(BrO,),,SH,O, have recentlybeen discovered, and the configurations of the resulting polyhedradetermined.So far no quanturn-mechanical treatment of suchcases has been made, although the 8-co-ordinated complex hasreceived some a t t e n t i ~ n . ~The application of X-ray and electron-diffraction methods to thestudy of organic compounds yields information about interatomicdistances and valency angles which is of fundamental importanceto any discussion of their structure. As the application of theresonance concept becomes more quantitative, the importance ofmore accurate data increases. The accuracy attainable even in thebest investigations, usually about &0-03 A., is insufficient for manypurposes, but if the distances can really be trusted to within theselimits a great deal of information regarding the electronic structureof the molecules can safely be deduced.Unfortunately, the accuracyof some of the earlier investigations now appears to have been over-estimated, and much revision has recently been in progress. Suchrefinement of known structures will undoubtedly become one of themore important, if less exciting, tasks for the future, particularlyas neither the electron-diffraction nor the X-ray method of analysishas yet been pushed to its limit of accuracy. For example,3 MT. G. Penney and J. S. Anderson, 7’ran.r. Faruduy SOC., 1937, 33, 1363160 CRYSTALLOGRAPHY.quantitative intensity measurements are still rare in X-ray work,and seldom, if ever, have all the measurable reflections beenutilised in deducing the details of a structure.During the year, and largely as the result of such revision, someoutstanding problems have been cleared up in connection withinteratomic distance and resonance in conjugated systems.Anomalous results obtained from acetylenic compounds have beendiscussed from different points of view, and more accurate data arenow available for a number of these compounds.New structure determinations of a detailed character have beencarried out for glycine, the cis- and the tram-form of azobenzene,and certain hydrocarbons.In simple compounds like trimethyl-amine oxide interatomic distances have been measured, and someconflicting values for the G-N distance await explanation.In-complete determinations and preliminary‘ accounts of a number ofother interesting structures are available, which must, however, bedeferred to a later Report. J. M. R.2. CRYSTAL PIIYSICS : THERMODYNAMICS AND STRUCTURE.The equilibrium locations of atoms and molecules in a crystalresult from an interplay between forces of attraction and repulsion,and various kinds of heat motion in the lattice. A discussion ofthese heat motions is thus an essential part of theories of crystalstructure. The increasing attention being paid to this subjectmakes it desirable to collect rather scattered information into aspecial section of these Reports.Peculiarities in the rate of attainment of equilibrium may restrictthe application of standard thermodynamic principles tocrystals,ll 2y 3 but when these restrictions can be neglected, theequilibrium structure is that which makes its free energy G4 aminimum.Since G = H - TS, at the absolute zero the equilibriumstructure is that with the minimum heat content Ho. When thegaseous state of the substance is chosen as reference state, fromwhich to measure changes in heat content, Ho is numerically thesame as the heat of sublimation at absolute zero, or lattice energy;the sign of Ho is, however, negative when the acquisitive conventionis followed, according to which heat absorbed by the substance isreckoned positive. At temperatures above the absolute zero, thecrystal structure may undergo continuous or discontinuous changes,so as to increase its heat content.These changes are accompaniedA. R. Ubbelohde, Proc. Roy. SOC., 1937, A, 159, 300.Idem, Tram. Paraday SOC., 1937, 33, 1198.A. Eucken, 2. Elektrochem., 1939, 45, 138, 145.,i “ Symbols for Thermodynamical Quantities,” J., 1938, 2193UBBELOHDE : CRYSTAL PHYSICS. 161by increases of the entropy 8, and the crystal must wait till aSufEciently high transition temperature T, has been reached to keepthe free-energy change AG = AH - T,AS zero. T , may refer toenantiotropic change, melting, or one of the processes discussedbelow. A systematic account of the thermodynamic properties ofcrystals would have to discuss the determination of lattice energies andof heat contents a t higher temperatures, and would have to include adescription of the various ways in which a crystal can increase itsentropy.In order to make this report fairly representative ofrecent work, only part of this programme will be dealt with.Lattice Energies.-In the absence of previous Reports, a recentarticle5 can be taken as datum line for measuring progress. Noentirely new method for the experimental determination of heatsof sublimation has been suggested, though an interesting correlationbetween the electron levels and lattice energy of metallic zincdeserves further theoretical and experimental investigation. Recentdeterminations based on vapour-pressure measurements include anumber of metals,’ polymethylene lattices 8 and alkali halide^.^When experimental difficulties prevent measurements over a,sufficient range of temperatures to give a reliable vapour-pressureequation, from which to calculate heats of sublimation, theoreticalcalculations of the entropy change on vaporisation can make even asingle measurement of some value.10 The lattice energy of alkaline-earth sulphides has been calculated from heat data and newmeasurements on the absorption spectra of the vapours.llA renewed discussion of measurements on the velocity ofvaporisation of carbon filaments l2 has been presented on the basisof spectroscopic determinations of the heat of dissociation of carbonmonoxide.By assuming that carbon atoms break three bonds andtwo bonds alternately on volatilising from graphite, the heat ofactivation determining the velocity of vaporisation (about 177 kg.-cals./mol.) has been shown to be in fair agreement with the spectro-scopic value for the sublimation process 139 l4Thermodynamic measurements show the lattice energy of theR.H. Fowler, “ Statistical Mechanics,” Cambridge, 1936.M. Sato, Sci. Rep. T6hoku Imp. Univ., 1937, 26, 341.F. Coleman and A. Egerton, Phil. Trans., 1935, 234, 177.A. R. Ubbelohde, Trans. Paraday SOC., 1938, 34, 282.W. Kangro and H. Wieking, 2. physikal. Chem., 1938, A, 183, 199.lo J. Mayer and I. Wintner, J . Chem. Physics, 1938, 6, 301.l1 L. S. Mathur, Proc. Roy. SOC., 1937, A, 162, 83.l2 A. L. Marshall and F. Norton, J . Amer. Chem. SOC., 1933, 55,431.l3 G. Herzberg, K. F. Herzfeld, and E. Teller,J. Physical Chem., 1937,41,325.l4 P. Goldfinger and W.Jeunehomme, Truns. FarMEay SOC., 1936, 32, 1591152 CRYSTALLOGRAPHY.ordinary form of diamond to be practically the same as that ofgraphite, though IIO spontaneous transition graphite -+ diamond isto be expected below about 20,000 atm.15~ 16 The lattice energy ofthe second form of diamond l7 has not yet been determined. I nview of the importance of the heat of atomisation of solid carbonin the calculation of bond energies from thermochemical data,l*further confirmation of the value 124 kg.-cals./g.-atom seemsdesirable.In theoretical calculat!ions of the lattice energy in terms of thecrystal structure, the various structures may be classified accordingto the predominant force of attraction; in decreasing order ofmagnitude, the attractions which lead to the ordering of moleculesin a crystal lattice are due to covalency, ionic and dipole effects,and to various types of molecular polarisation, of which the effectdue to the zero-point motion of the electrons (the so-called dispersioneffect) is the most widespread.lg, 2O Metals form ionic lattices inwhich special quantum-mechanical forces are operative, owing tothe small mass of the electron.21 Dipole effects in crystals contain-ing hydrogen may become unusually large owing to the formationof hydrogen bonds.22For ionic crystals, recent calculations of lattice energy in terms ofstructure have shown refinements in points of Fairlysuccessful calculations have been made for carbon di0xide,~4 andfor polymethylene lattices,25 in which dispersion forces predominate.Owing to the close approach of dipoles in crystals, these are besttreated as pairs of point charges in making the calculation.22p24Zero-point energy of crystal lattices.Although the lattice energy ismeasured at O"K., thermal vibrations and other heat motions,discussed below, affect the value of H , by their contribution ofzero-point energy. The average thermal energy of a quantisedoscillator of frequency v is 2 = hv/(ehv/kT - 1) + i h v , and thelarger tho zero-point energy contribution X i h v , the smaller theheat required for sublimation. For crystal lattices of the heavierl 5 F. D. Rossini and R. S. Jessup, J . Res. Nut. Bur. Stand., 1938,21,491.1 6 J. Basset, J . Phys. Radium, 1939, 10, 217.17 (Sir) R.Robertson, J. J. Fox, and A. E. Martin, Proc. Roy. SOC., 1936,A , 157, 579.Ann. Reports, 1931, 28, 375.19 F. London, Trans. Paraday SOC., 1937, 33, 8.20 H. Margenau, Rev. Mod. Physics, 1939, 11, 1.21 N. F. Mott and H. Jones, " Properties of Metals & Alloys," Oxford, 1936.22 E. Bauer and M. Magat, J. Phys. Radium, 1938, 9, 319; see, however,23 A. May, Physical Rev., 1938, 54, 629.24 H. Sponer and M. Bruch-Willstiitter, J . Chem. Physics, 1937, 5, 745.2 5 -4. Muller, Proc. Roy. Xoc., 1936, A , 154, 624.refs. (56) and (62)UBBELOHDE : CRYSTAL PHYSICS. 153inert gases,26 allowance for the zero-point energy only leads to acorrection term of a few units per cent. in the calculation of variousproperties of the lattice in terms of structure.For crystal latticesof less massive atoms, the zero-point energy may become comparablewith the total potential energy due to molecular attractions, as inthe case of solid H,, HD, and D,. The thermodynamic propertiesof such crystal lattices are quite abnormal.27, 28 In the case ofhelium, the forces of molecular attraction are about ten timessmaller than for hydrogen, and the zero-point energy of motionmakes any rigid crystal lattice impossible at ordinary pressures,even at 0" K. Only semi-empirical calculations of the remarkablethermodynamic properties of helium have been prop0sed.~~3 30Differences in the zero-point energy of hydrides and deuterideslead to differences in the heats of formation, which can be calculatedfrom dissociation-pressure curves, e.g., for alkali-metal hydride~.~~For NaD the heat of dissociation has been given as 15.8 kg.-cals.,for NaH 14-4 kg.-cals., for KD 14.5 kg.-cals., and for KH 14.2 kg.-cals.32 These differences are, however, subject to a large specific-heat c~rrection,~~ and until the specific heats have been determined,the results cannot be used for calculating the zero-point energy ofthe crystalline hydrides and deuterides in question.As the temperature of a crystalrises above O'K., it may acquire various forms of thermal energy,each of which is best considered separately.Thermal energy ofvibration is present in all crystals, and the vibrations of atoms andmolecules in a lattice can be studied from such phenomena as thespecific heat, the effect of temperature on the reflection of X-raysfrom crystals, thermal expansion, and infra-red and Ramanspectra.When the crystal can be treated as a set of harmonic oscillatorsof various frequencies vl, v2 .. ., in all 3N per g.-atom, the totalthermal energy of vibration isVibrational energy in crystals.where the summations extend over all the frequencies. In practiceit would be impossible to evaluate all the 3N natural frequencies2 6 J . Corner, Trans. Paraday Soc., 1939, 35, 711.27 H. D. Megew, Phil. Mag., 1939, [vii], 28, 129.28 M. E. Hobbs, J . Chem. Physics, 1939, 7, 318.29 F . London, Proc. Roy. Soc., 1936, A, 153, 576.so Idem, J . Physical Chem., 1939, 43, 49.31 E. Sollers and J. Crenshaw, J . Amer. Chem. Soc., 1937, 59, 2015, 3724.32 L.Heckspill end A. Borocco, Bull. SOC. chim., 1939, 6, 91.33 A. R. Ubbelohde, Trans. Faraday SOC., 1936, 32, 526154 CRYSTALLOGRAPHY,separately, and some assumption has to be made as to theirdistribution in a vibrational spectrum, in order to calculate E,,.A well-known method, proposed by Debye, is to replace thevibrational spectrum of actual crystal lattices by that of a continuum,for which the distribution of frequencies in the spectrum is known;the thermal energy of vibration is calculated to bewhere 0 = hvH/k, and the vibrational spectrum of the continuumis broken off at the maximum frequency vu, to correspond with thefact that crystal lattices have a maximum frequency of thermalvibration, whose wave-length is twice the lattice spacing.Thespecific heat corresponding to the thermal vibrations is simplyC, = dEv/dT.Debye's expression has the striking property of representing thevibrational energy of crystals in terms of a single parameter8 determined by the crystal structure. The assumption that thelattice vibrations of a real crystal may be replaced by those of acontinuum has been criticised 6, on the grounds that the velocityof sound waves in a crystal lattice is not constant, as assumed for acontinuum, but falls off with rising frequency. Furthermore, theactual distribution of vibrational frequencies favours certain regionsof the spectrum, instead of being smooth, so that formulae for thevibrational energy should contain more than one 8 parameter.These parameters have not yet been calculated in terms of thecrystal structure.The Debye expression for the vibrational energy gives a specificheat at constant volume which tends to the constant Dulong andPetit value 3R when 5" > 0.35 The anharmonicity of latticevibrations in crystals should, however, lead to a falling off in C,below the Dulong and Petit value, at still higher temperatures.Thisbehaviour is observed for ionic lattices such as sodium chloride andpotassium chloride and bromide, but not for metals such as copperand lead, for which C, increases above 3R.36 A still more strikingincrease in C, has been observed in the case of solid potas~ium,~7and appears to be due either to the free electrons in the metal,which may make an appreciable contribution to the specific heat at84 M.Blackman, Proc. Roy. SOC., 1935, A, 148, 365, 384; A, 149, 117;96 Landolt-Bornstein, " Physikal. Chem. Tabellen," 6th Edn., 1927,36 G. Damkohler, Ann. Phyaik, 1935, [v], 24, 1.87 L. G. Carpenter and C. J. Steward, Phil. Mag., 1939, [vii], 27, 561.1938, A, 164,62.Erg. I, 705UBBELOHDE : CRYSTAL PHYSICS. 155high temperatures, or to the break UP of the lattice as the meltingpoint is approached.Some progress has been made in calculating the specific heat ofcomplex crystals such as sulphur, carbon dioxide, and ammoniumchloride, in terms of experimentally observed Raman frequencies.38 39Molecular models have been constructed to represent latticevibrations in simple cases.4oIntensity of X-Ray ReJlections.-The chief disadvantage of specific-heat measurements in throwing light on the lattice vibrations is thevery fact that they can be expressed as a function of one or at themost a few 8 parameters.In principle, much more direct informationis obtainable from the intensity of X-ray reflections. Subject tocertain restrictions, the intensity of reflection I T from any crystalplane is related to the intensity I , at 0" K. by the equation IT ='lo e-2Jf where 211 = 2n22/a2 and 2 is the mean square displace-ment of the atoms normal to the reflecting plane whose spacingis u.In simple crystal lattices the amplitudes of the heat motions,measured by the values of (c2)4, can be correlated with a Debyevibrational spectrum, and from the values obtained for M acharacteristic temperature 0 can be calculated for the lattice, usingthe Debye-Waller formulawhere x = B/T, #(x) is the Debye function, and rn is the mass of theatoms.Recent determinations include the characteristic temper-ature of magnesium oxide41,42 and of magnesium, zinc, and45 The Debye-Waller formula does not alwaysgive satisfactory results,46y 4 7 3 48 however, and a major advantage ofthe X-ray measurements is that they give a direct measurement ofthe amplitude of atomic vibrations, independent of assumptions38 S. Sirkar and J. Gupta, Indian J . Physics, 1938, 12, 145.38 S. Bhagavantam and T. Venkatarayuda, Proc. Indian Acctd. Sci., 1938,40 V. Deitz and D. H. Andrews, J . Franklin Inst., 1935, 219, 459, 565,dl G.W. Brindley and P. Ridley, Proc. Physical SOC., 1939, 51, 69.42 H. S. Ribner and E. 0. Wollan, Physical Rev., 1938, 53, 972.43 G. W. Brindley and P. Ridley, Proc. Physical SOC., 1938, 50, 757.44 Idem, ibid., 1939, 51, 73.45 E. 0. Wollan and G. Harvey, Physical Rev., 1937, 51, 1054.4e E. A. Owen and R. Williams, Nature, 1938, 142, 915.4 7 A. H. Compton and S. Allison, " X-Rays in Theory and Experiment,"48 M. Blackman, Proc. Carnb. Phil. SOC., 1937, 33, 380.A , 8, 115.703.Macmillan, 1935, p. 435256 CRYSTALLOURAPHY .about the vibrational spectrum. cf. 49 The amplitudes of typicalatomic vibrations may be illustrated by the results for cadmium :Temp., I(. c Axis. Basal plane.86' 0.100 0.067293 0.182 0.118Amplitude of atomic vibrations, in A.The thermal vibrations of crystal lattices also affect the intensityof diffuse scattering of X-rays,5o and the reflection of cathode rays.61A formal analogy between the amplitudes of heat motions, and thedisplacement of atoms from equilibrium positions in the lattice,due to various forms of cold working, has been used in correlatingthe excess lattice energy of pyrophoric and " active " preparationsof certain crystals with observed X-ray intensity changes.52Thermal Expansion.-The normal thermal expansion of crystalsis due to the fact that the characteristic frequency v y changeswhen the volume of the crystal changes. If one writes y =- d log vM/d log V , the coefficient of thermal expansion a is given bya = y xo CVlVOwhere xo is the compressibility and Vo the volume at 0" K.Asimple derivation of this expression has been given by Mott andJones (op. cit., p. 15). A more general derivation has been givenby H. Jones,53 who points out that an expression formally similar tothe above is obtained for the thermal expansion, whenever theentropy of the solid can be expressed as a function of the temperature,and a single crystal parameter such as vM. The original should beconsulted for details, which are important in explaining anomalousthermal expansions such as those of nickel 54 and the invar alloys,55and also negative values of thermal expansion, such as are observedfor helium-I1 53 and a-silver Measurements of thermalexpansion are important in the knowledge of crystal structures, ingiving information about the anharmonicity of lattice vibrationsin various directions in the lattice.56 A number of recently devisedX-ray cameras for use at high temperatures may be mentioned in4Q C.Mauguin and J. Laval, Compt. rend., 1939, 208, 1446, 1512.50 G. E. M. Jsuncey and E. McNatt, Physical Rev., 1939, 55,498.51 D. Coster and P. Van Zanten, Physica, 1939, 6, 17.52 R. Fricke and E. Gwinner, 2. physikal. Chem., 1938, A , 183, 165, 177.53 Proc. Camb. Phil. Soc., 1938, 34, 253.54 E. A. Owen and E. Yates, Phil. Mag., 1936, [vii], 21, 809.5 5 Idem, Proc. Physical SOC., 1937, 49, 17, 178, 307 et seq.55a E. Cohen'and H. L. BredBe, Proc. K . Akad. Wetensch. Amsterdam,5 6 J. Monteath Robertson and A. R. Ubbelohde, Proc. Roy. SOC., 1939, A,1936, 39, 358.170, 222UBBELOHDE CRYSTAL PHYSICS.157this c~nnection.~’ Some of the recent experimental work relatingexpansion to structure has been summarised by H. D. mega^.^*Isotope EfSects.-In the case of crystals containing hydrogen, theeffect of lattice vibrations and other thermal motions of the moleculeson crystal structure can be investigated by a comparison with thecorresponding deuterium compounds.33 When the hydrogen isbound by metallic or ionic forces, a contraction of the lattice isnormally expected on substituting deuterium, since the zero-pointenergy is smaller for deuterium compounds, and has an effect similarto that of the thermal energy in leading to lattice expansion. Whenthe hydrogen is bound by covalency to specific atoms, the effectivemolecular radius should also be lessened.This can lead to largerheats of absorption of deuterium oxide than of water in salthydrates. 59 The smaller molecular radius in deuterium compoundsalso h a a marked effect on the transition temperature in variouslattice transformations,6l the change being usually in the samesense as that due to an increase in pressure on the crystal. Finally,when the hydrogen forms “hydrogen bonds” in the crystal, thesubstitution of deuterium leads to a lattice expan~ion.~~, 62 Thishas been interpreted as indicating the importance of special resonanceforces in hydrogen bonds.Other Sources of Thermal Energy in Crystals.-Many crystals haveother sources of thermal energy, in addition to the lattice vibrations.Uncertainties in the calculation of C, from the experimentallyobserved Cp and in using the Debye expression for the vibrationalspecific heat, make it difficult to detect other sources of energywhen their contribution to the specific heat is small.Small non-vibrational specific-heat contributions can, however, be observedat very low temperatures in certain metals, and are probably dueto the thermal energy of the free electrons.63 : and see 36, 37Many crystals are known, however, in which certain changes ofstructure are accompanied by considerable increases in heat contentand entropy. In enantiotropic transformations, or in melting, thechange in structure may take place isothermally, and the heatabsorbed at the transition temperature is called a latent heat.s 7 W.Hume-Rothery and P. Reynolds, Proc. Roy. SOC., 1938, A , 167, 25;F. Schossbarger, 2. Krist., 1938, 98, 259; A. R. Ubbelohde, J. Sci. Instr.,1939, 16, 155.5e 2. Krist., 1938, 100, 68.5B J. Bell, J., 1937, 459; but see ref. (60).6o F. Miles and A. Menzies, J . Amer. Chem. SOC., 1938, 60, 87.61 K. Clusius, 2. Elektrochem., 1938, 44, 30.62 A. R. Ubbelohde and (Miss) I. Woodward, Nature, 1939, 144, 632.s3 W. H. Keesom, Physikal. Z., 1934, 35,939; W. H. Keesom and C. Clark,Physica, 1935, 2, 513158 CRYSTALLOGRAPHY.When the transformation takes place over a range of temperatures,the heat intake is added to the normal increase in vibrational energywith rise in temperature, so that the observed specifh heat isanomalously large.In nearly all cases the specific heat " anomaly "rises sharply to a maximum, and then decreases again even moresteeply till normal values are reached. A typical example isprovided by the specific heat of crystalline methane,74 for which thecurve over a short range of temperature is given in Fig. 1.Recent work relating structural changes in crystals with latentheats and specific-heat anomalies has been too intensive to permita report covering all the various kinds of transformation in any oneyear. The order-disorder effect was the subject of a recent report,64Absohte temperature.FIG. 1.Thermal transformation in crystalline methane.and the present account will be limited to the phenomena whicharise from the onset of molecular rotation in crystals.The possibility that moleculesrotate in crystals was first suggested from a comparison of thethermodynamic properties of ortho- and para-hydrogen.sh Ortho-hydrogen rotates even in the lowest quantum state, and since it haspractically the same latent heat of fusion and evaporation as para-hydrogen, it must continue to rotate in the crystal lattice in order topreserve this equality.It was suggested by Pauling that in anumber of other crystals the molecules might oscillate aboutequilibrium orientations at low temperatures, and rotate freely athigher temperature^.^^ The following table indicates how commonMolecular rotation in crystals.Ann. Reports, 1936, 32, 185.6b K. Clusius and K. Hiller, 2. physikal.Chem., 1929, B, 4, 166.e6 L. Pauling, Physical Rev., 1930, 36, 430UBBELOHDE : CRYSTAL PHYSICS. 159this phenomenon may be even in lattices of comparatively simplemolecules.Sfhermnl Transformations in Simple Molecular Crystals.I11 _3 11. I1 --+ I. I + Liquid.P -- Molecule. T,. Range. AS. T,. Range. AS. T,,,. AS.0 2 66 ......... 23.7" s 0.9 43.7' 2.0 4.0 54.3" 2.0N, 8 7 ......... - - - 35.4 s 1.5 63.1 2.7 co 6 8 ......... - - - 61-5 s 2-5 68.1 2.9HCl 69 ......... - - - 98.4 s 2.9 158.9 3.0HBr 70 ...... 89.0 3.0 0.7 {ti: 2'5 1.5 ::;} 186.2 3.1HI 71 ......... 70.0 5-0 0.3 125 5.0 1.5 222.3 3.1H2S 72 ......... 103.6 0.8 3.5 126-2 3 0.9 187.6 3.0D2S 73 ......... 107.8 0.5 3.7 132.8 s 0.9 187.1 3.0CH, 74 ......... - - - 20.5 3.0 0.8 90.6 2.5CH3D 75 ...... 15.5 2.0 0.9 22.6 3.0 1.7 90.6 2.4CD4 76 .........21.4 1.5 0.9 26.3 4.0 2.2 89.2 2.4SiH, 7 7 ...... - I - 63.5 2.0 2.3 88.5 1.8CF, 78 ......... - - - 76.3 8 4.6 84.5 2.0CCl, 7s ...... - - - 222.5 s 4.8 250.3 2.3CBr, 80 ...... I - - 320 8 3.6 365.5 -From this table it will be observed that many molecular crystalshave one or even two thermal transformations below the meltingpoint. The range of temperatures over which the change takes placeis indicated in each case. The letter s indicates that the transform-ation is isothermal, and is accompanied by the intake of latent6 6 K. Clusius, Z.physika1. Chem., 1929, B, 3,41.6 7 W. F. Giauque and J. Claydon, J . Amer. Chem. SOC., 1933, 55, 4879;68 W. F. Giauque and R. Wiebe, J .Arner. Chem. SOC., 1928,50, 101, 2193;8g G. Hettner, E. Hettner, andR. Pohlmann, ibid., 1938,108,45.70 Cf. ref. (68) ; also G. Damkohler, Ann. Physik, 1938, [v], 31,76 ; J. Zunino,2. Physik, 1936, 100, 335.W. F. Giauque and R. Wiebe, J . Amer. Chem. SOC., 1929, 51, 1441;C. P. Smyth and C. Hitchcock, ibid., 1933, 55, 1830.72 K. Clusius and A. Franck, 2. physikal. Chem., 1936, B, 34,420; A. Kruisand K. Clusius, ibid., 1937, B, 38, 156; C. P. Hitchcock and C. P. Smyth, J .Amer. Chem. SOC., 1934, 56, 1084; E. JustiandH. Nitka, Physikal. Z., 1937,38, 514.M. Ruhernann, 2. Physik, 1932, 76, 368.F. Simon and C1. v. Simson, 2. Physik, 1924, 21, 168.73 A. Kruis and K. Clusius, 2. physikal. Chem., 1937, B, 38, 156.'* K. Clusius and A. Perliak, ibid., 1934, B, 24, 313; A.Schallamach,Proc. Roy. SOC., 1939, A, 171, 669; W. Heuse, Z . physikal. Chem., 1930, A ,147, 282.7 5 K. Clusius, Physica, 1937, 4, 1105.7 6 E. Bartolomh, G. Drikos, and A. Eucken, 2. physikal. Chem., 1938,7 7 K. Clusius, ibid., 1933, B, 23, 213.7 8 A. Eucken and E. Schroder, ibid., 1938, B, 41,307.79 R. C. Lord and E. Blanchard, J. Chem. Physics, 1936,4, 707.8o C. Finbak and 0. Hassel, 2. physikal. Chem., 1931, B, 30,301.B, 39,371160 CRYSTALLOGRAPHY.heat, where= a finite temperature range indicates a specific-heatanomaly. The entropy change corresponding with each transform-ation is of the same order of magnitude as the entropy change onmelting, which is given on the right of the table in cals./mol./degree.In the case of specific-heat anomalies the figures for the entropychanges are only approximate, and the value of T, indicates thetemperature a t which the additional specific heat reaches amaximum.Similar anomalies associated with rotational transitions havebeen reported for H2Se and D,Se, PH,, ASH,, CH,*OH, CH,*NH,,BF,, SF,, a number of paraffins, cyclohexane and its derivatives,hexamethylbenzene, NH4F, NH4Cl, ND4C1, NH,(C,H,,)Cl, NH,Br,RbNO,, AgN0,,81 NaCN,82 perchlorates and flu~borates,~, KH,PO,,KH,As04, Rochelle pentaerythrit~l,~~ camphene derivatives,s6pentade~ane,~' hexachloroethane, 88 and have been looked for inother crystals without success.89 The above list is not necessarilyexhaustive.The factors which determine whether a thermal transformationwill be associated with a latent heat, or with a specific-heat anomaly,have not yet been fully elucidated. For example, the case ofhydrogen bromide, which has three successive transformations withspecific-heat anomalies, below its melting point, may be contrastedwith hydrogen chloride, which has only one transformation takingplace sharply at 98.4" K.The justification for Pauhg's suggestionthat these entropy increases in the crystal are associated with theonset of molecular rotation in the lattice is based on the followingargument : The onset of rotation in quantised rotators is a gradualprocess when these are in the gaseous state, but in the crystal theclose packing leads to preferred orientations of the molecules, and aresultant potential barrier preventing free rotation of the moleculesat low temperatures.The thermal energy required for the f i s tfew molecules to rotate freely may be quite large, but in rotating theylessen the restraining field on their neighbours, with the result thatthe number of molecules rotating increases " autocatalytically " asND4Br7 m41, (NH4)zSO4, (ND4)2SO4, (NH4)3PO4, NaNO3, m O 3 ,*l A. Eucken, 2. Elektrochem., 1939, 45, 126.83 H. J. Verweel and J. Bijvoet, 2. Krist., 1938, 100, 201.83 C. Finbak and 0. Hassel, 2. physikal. Chem., 1936, B, 32, 130, 433.84 P. Schemer, 2. Elektrochm., 1939, 45, 171 ; W. Bantle and P. Scherrer,86 I. Nitta and K. WatanabB, Bull. Chem. SOC. Japan, 1938,13,28.8 6 W . A. Yager and S . 0. Morgan, J .Amer. Chem. SOC., 1935,67,2071.13' A. R. Ubbelohde, Trans. Faraday SOC., 1938, 34, 289.s 8 C. Finbak, Chern. Abs., 1938, 32, 1996.69 C. P. Smyth, Chem. Reviews, 1936, 19, 329.Nature, 1939, 143, 980UBBELOHDE : CRYSTAL PHYSICS. 161the temperature rises. Quantitative expression has been given tothis idea, without yet reaching very detailed agreement withe~periment.~~ An experimental test has also been carried out bydiluting the lattice of methane with argon or krypton atoms.g1As the number of inert-gas atoms in solid solution increases, themutual restraints between neighbouring molecules of methane rapidlydiminish, and for quite small percentages of krypton the specific-heat curve of solid methane no longer shows a sharp anomaly. AfterO l I 1 I75 O 20 25"Abso/ute temperature.FIG.2.Thermal transformation in mixed crystals of methane f krypton.certain adjustments, the intake of rotational heat in the methane-krypton crystals corresponds with that calculated for gaseousmethane.The specific-heat curves for crystals with increasing amounts ofkrypton (Fig. 2) should be compared with the curve for pure methane(Fig. l), which is plotted on a smaller scale. Addition of kryptonextends the range of the anomaly, decreases its maximum contribu-R. H. Fowler, Proc. Roy. SOC., 1935, A , 149, 1 ; A , 151, 1 ; T. S. Chang,Proc. Camb. Phil. SOC., 1937, 33, 524.91 A. Eucken and H. Veith, 2. physikal. Chem., 1938, B, 38, 393.REP.-VOL. XXXVI. 162 CRYSTALLOGRAPHY.tion to the specific heat, and shifts the maximum to lowertemperatures.In addition to specific-heat determinations, other physical measure-ments have been made on the crystals, in order to elucidate thenature of the structural change accompanying the entropy increaseduring a transformation.When the molecules in the crystal carrypermanent dipoles, important information is obtained fiom meamre-ments of the dielectric constant, and the dielectric loss, by usingelectric oscillations of Merent frequencies, and maintaining thecrystals at different temperatures [cf. refs.66-88 and especially 89].Permanent dipoles cannot contribute appreciably to the dielectricconstant so long as the molecules are constrained to perform harmonicoscillations about equilibrium positions, but aa soon as themolecules are free to rotate, a large increase in dielectric constant isobserved.This increase could, however, also be interpreted byassuming two or more equilibrium orientations for the dipoles inthe lattice, with different energies.The assumption that the molecules are not rotating freely, buthave increased possibilities for alternative orientation above thetransition temperature, has certain advantages in explaining theimportant phenominon of dielectric loss, i.e., the fact that energyis dissipated in the solid when acted on by an alternating electricfield.92 It may also help to explain the striking fact that the meresubstitution of deuterium for hydrogen in methane gives rise totwo thermal transitions in place of one, though here an alternativeexplanation assumes separate rotation about the different molecularaxes a t different temperatures.*l Methane only gives indicationsof the I11 +- I1 transition a t higher pressures.Other investigations on the structural changes accompanyingthermal transitions have used X-rays (e.g.,66-80, 821 839 93).Whenthe change in structure is small, a more sensitive method is to usethe polarising microscope (e.g., for the hydrogen halides).94 In thecase of ammonium chloride a change of structure below the transitiontemperature is only indicated by the fact that the crystals becomepiezoelectric .95Th&rrwdynumic CEassiJication of Rotational Transformations inCrystah-When the structural change and heat intake whichaccompany a thermal transformation in a crystal take place sharplyat one temperature, the equilibrium between the two crystal formsS2 A.H. White, J . Chem. Physics, 1939,7,58; R. W. Sillars, Proc. Roy. SOC.,1938, A , 169, 661; R. Guillien, Compt. rend., 1939, 208, 980, 1561; J. H.Bruce, Trans. Faraday SOC., 1939, 35, 706.e3 C. Finbak, Physihl. Z., 1939, 40, 26.94 A. Kruis and R. Kaischew, 8. physikal. Chem., 1938, B, 41,427.s5 S. Bahrs end J. Engl, 2. PhysS, 1937, 105,470UBBELOHDE : URYSTAL PHYSICS. 163follows the ordinary thermodynamic rules, with respect to changesof temperature and pressure. When the structural change and heatintake take place over a range of temperatures, the latent heat isreplaced by a specific-heat anomaly, and the discontinuous volumechange by abnormal coefficients of thermal expansion along thevarious crystal axes.The adaptation of formal thermodynamics tosuch transformations of the second and third order, as these gradualchanges are called, has given rise to much interesting discus~ion.~~This has not yet thrown much fresh light on crystal structure, andreference should be made to the originals for details.A thermodynamic problem of more immediate importance fortheories of crystal structure is the origin of hysteresis. Whenhysteresis is present, the state of apparent equilibrium of thecrystal is different according as the temperature is raised or loweredthrough the transition range. The existence of hysteresis has beenvariously ascribed to mechanical strain,l and to the existence ofdomains or a mosaic structure subdividing the crystalbut some of the difficulties attending a solution are indicated bythe fact that the substitution of deuterium for hydrogen lessens oreven suppresses hysteresis in transformations such as those ofresorcinol97 and ammonium chloride.9*Rotation and Melting.-The reason why a crystal melts, in spiteof the increase in heat content, is that melting is accompanied by alarge increase in entropy, due to the increase in freedom of motionin the liquid.A quantitative measure of this increase of freedomis the ratio W,l W, in the expression O9 Ah', = R log, Wl/WJ. Thisentropy increase has various contributing factors, the discussion ofwhich must be deferred to a later Report owing to the large volumeof work on the subject.It can be stated here, however, that inlattices with a rotational transformation below the melting point,the entropy increase on melting will be smaller than in comparablelattices without such a transformation. It has been suggested 100that this fact may help to explain some of the relations betweenmelting and the structure of molecular lattices. A. R. U.96 E. Justi and M. v. Laue, PhysiEaZ. Z., 1934, 35, 945; A. J. Rutgers andS. Wouthuysen, Physica, 1937, 4, 235, 515; N. F. Woerman and G. Muller,Physikal. Z., 1937, 38, 298; F. C. Frank and K. Wirtz, Naturwiss., 1938, 26,688, 697.9 7 J. Monteath Robertson and A. R. Ubbelohde, Proc. Roy. SOC., 1938, A,167, 136.9s A. Smits, G. Muller, and F.Kroger, 2. physikal. Chem., 1937, By 38,177.99 J. W. H. Oldham and A. R. Ubbelohde, Trans. F a r a d a y Soc., 1939, 35,332.1 W. 0. Baker and C. Smyth, J. Amer. Chem. Soc., 1939, 61, 1695164 CRYSTALLOGRAPHY.3. ~NOXGANIC STRUCTURES.Most of the structure determinations during the year have beenconcerned with complex compounds involving, in certain cases,unusual co-ordination, although a number of interesting investig-ations have also been made on some relatively simple compounds.Of the elements, scandium is one of the last of the metals to bennalysed; it exists in two allotropic modifications with cubicclosest -packed and hexagonal closest-packed arrangements. In theformer the twelve nearest neighbours are a t a distance of 3.205 A .,in the latter six are a t a distance of 3.30 A. and six at 3.23 A.Scandium thus fits in satisfactorily with its neighbours in thePeriodic Table. X-Ray diffraction patterns of liquid yellowphosphorus indicate that there are three permanent nearestneighbours at a distance of 2.25 A. from a given atom, this arrange-ment being in accord with the assignment of P, molecules. Thisdistance of 2.25 A. does not change with temperature, as is observedin the case of some other liquid elements where there is no suchrigid molecular aggregation. The symmetrical shape of the peakat 2.25 A. in the atomic distribution curve suggests that all thephosphorus atoms are equivalent, this equivalence giving the P,molecule in liquid yellow phosphorus the same tetrahedral sym-metry as was found for P, vapour by electron diffra~tion.~ TheP-P distance reported in the latter case was 2.21 A.The second" co-ordination sphere " corresponding to the nearest averageapproach of phosphorus atoms not in the same molecules occursa t about 3.9 A. in liquid yellow phosphorus. The atomic dis-tribution curves for amorphous red and amorphous black phosphorusalso indicate three nearest neighbours due to the covalent bondingof P atoms, the P-P distances being respectively 2.29 A. and 2.27 A.The high melting points of these substances, however, would suggestthat here there are no simple P, molecules, as in liquid yellowphosphorus, and it is possible that in these cases there is a puckerednetwork somewhat similar to that found in crystalline blackphosphorus .4there From the scattering of X-rays by liquid sulphur a t 128"1 K.Meisel, Naturwiss., 1939, 2'4, 230.C. D. Thomas and N. S . Gingrich, J . Chem. Physics, 1938, 6, 659. Forreport on the structure of liquids and amorphous solids, see J. J. Randall,Ann. Reports, 1937, 34, 169.L. R. Maxwell, S. B. Hendricks, and V. M. Moseley, J. Chem. Physics,1935, 3, 699.* R. Hultgren, N. S. Gingrich, and B. E. Warren, ibid., p. 351; Ann.Reports, 1935, 32, 157.N. S . Gingrich, Bull. Amer. Physical Soc., 1938, 13, 9HAMPSON : INORGANIC STRUCTURES. 166appear to be two nearest neighbours at a distance of 2.05 A. (cf.S-S = 2.12 A. in crystalline rhombic sulphur 6).X-Ray powder photographs of solid (HF),, at 91" cry show thatthe crystal is built up of infinite zigzag chains of FH-FH-FHmolecules, the F-H-F distance being approximately 2 .7 ~ . and theFH-FH-FH angle approximately 134". The same type of structurehas been observed in the gas phase from electron-diffraction measure-ments, the gas consisting of zig-zag polymers of comparativelylow molecular weight (trimers, tetramers, and pentamers) withlinear 3'-H-F = 2.55 A. and the F angle = 140" -J= 5". The photo-graphs rule out the suggested hexagonal polymer of compositionCyanogen iodide9 forms a lattice of separate molecules and notan ionic lattice; an exact determination of t,he positions of thecarbon and nitrogen atoms could not be made owing to the largescattering power of the iodine atom, but a linear structure with thedistances., I-C = 2.03 A.and C=N = 1.18 a. is compatible withthe observed intensities. The linear trihalide IC1,- ion is confirmedin tetramethylammonium dichloroiodide,1° the I-C1 distance(2.34 A.) being equal to the sum of the covalent radii.Of the oxides, Rb,O has the anti-fluorite structure, the distancebetween the Rb + and the four surrounding 0- - ions being 2.92 A.,whereas Cs,O has an anti-CdC1, layer structure with a Cs' to 0- -separation of 2.91 A . ~ ~ The so-called tetroxides RbO, and CsO,have been shown to contain the superoxide 0,- ion as inK0,.12A number of nitrides which have been investigated during theyear indicate once asgain the tendency in these compounds for themetal atoms to take up a closest-packed arrangement with thesmall nitrogen atoms occupying the interstices of the lattice.(HF)S.*B.E. Warren and J. J. Burwell, J . Chem. Physics, 1935, 3, 6.P. Gunther, K. Holm, and H. Strunz, 8. physikal. Chem., 1939, B, 43,S. H. Bauer, J. Y . Beech, and J. H. Simons, J . Amer. Chem. Soc., 1939.J. A. A. Ketelaar and J. W. Zmartsenberg, Rec. Trao. chim., 1939, 58,lo (Miss) R. C. I;. Mooney, 8. Krist., 1939, 100, 519; cf. ibid., 1938, 98, 324.l1 A. Helms and W. Klemm, 8. anorg. Chem., 1939, 242, 33.l a Idem, ibid., 1939, 241, 97; cf. Ann. Reports, 1936, 33, 194, 210;L. Pauling, " The Nature of the Chemical Bond," p. 252.* A careful redetermination of the F-H-F distance in crystalline KHF, hasgiven the value 2.26 f 0.01 A. (L. Helmholz and M.T. Rogers, J . Amer. Chem.SOC., 1939, 61, 2590). This is 0.29 A. shorter than the value reported forgaseous (HF), and suggests that in ths latter case the F-H-F bond is weakenedby the formation of additional hydrogen bonds.229.61, 19.448166 CRYSTAILOQRAPHY.Cu,N l3 has the three copper atoms along the edges of a cube withnitrogen atoms (1.90 A. from six copper atoms) at the cube corners.TiN l4 has the rock-salt cubic closest-packed arrangement, the Ti-Ndistance being 2.11 A., but GaN and InN l3 have the wurtzitestructure (Ga-N = 1-96 A., In-N = 2.12 A.), the axial ratios beingalmost exactly those required for hexagonal closest-packing.Ge3N4,l5 on the other hand, has a phenacite (Be,SiO,) structure,each germanium being surrounded tetrahedrally by four nitrogenatoms, three tetrahedra having one nitrogen atom in common.In the body-ceotred cubic thorium phosphide, Th3P4,16 there is asimilar sharing of tetrahedra, these being so disposed that eachthorium atom is surrounded by eight phosphorus atoms at a distanceof 2.98 A., the nearest P-P distance being 3.20 A.Some evidencehas also been obtained of a sub-phosphide ThP having the sodiumchloride structure .Of the more complex structures which have been determinedduring the past year, both by electron and X-ray diffraction, asurprisingly large number have been found to involve odd co-ordination numbers such as 5, 7, and 9, and also an increasinglylarge number of compounds have been shown to exhibit some'' randomness " in their crystal structure.17 MoC15,18 PF5,19Ip5,I9 and Fe(CO),20 have been investigated in the vapour phaseby the method of electron diffraction and all have a trigonal bi-pyramidal configuration ; the same arrangement also occurs incrystalline trimethylstibine dihalides Me,SbX2.21 This thereforewould appear to be the natural configuration for covalent com-pounds of the type AB, irrespective of the number of unsharedelectrons on the central atom (cf.the case where the valency groupdoes not exceed an octet and where the unshared electrons them-selves then appear to have definite stereochemical requirements).Chromium hexachloride,18 and chromium, molybdenum, andtungsten hexacarbonyls 22 have the expected regular octahedralstructure, but iron and cobalt carbonyl hydrides 23 are tetrahedral1s R.Juza and H. Hahn, 2. anorg. Chem., 1938,239,282.l4 A. Brager, Acta Phwicochim. U.R.S.S.. 1939, 10, 593.15 R. Juza and H. Hahn, Naturwiss., 1939, 27, 32.16 K. Meisel, 2. anorg. Chern., 1939, 240, 300.1 7 Cf. Ann. Reports, 1938, 35, 174.R. V. G. Ewens and W. M. Lister, Trans. Paraday Soc., 1938,34, 1358.19 H. Braune and P. Pinnow, 2. physikal. Chem., 1937, B, 35, 239.20 R. V. G. Ewens and W. M. Lister, Trans. Faraohy Soc., 1939, 35, 681.31 A. F. Wells, 2. Krist., 1938, 99, 367.32 L. 0. Brockway, R. V. G. Ewens, and W. M. Lister, Trans. Faraduy Xoc.,98 R. V. G. Ewens and W. M. Lister, ibid., 1939, 36, 681.1938, 34, 1350EAMPSON : MORGANIC STRUCTURES. 167and so should be formulated as Fe(CO),(COH), and Co(CO),(COH),and not as Fe(CO),H, or Co(CO),H with hydrogen atoms linkeddirectly to the metal at0m.~4 On this view the relationship betweenthe carbonyls, the nitrosyl carbonyls, and the carbonyl hydridesbecomes quite clear.In all these compounds the bonds to thecentral metal atom are shorter than the sums of the single-bondcovalent radii and this has been interpreted in terms of single-bond-double-bond resonance, though it now seems probable thatother factors besides the multiplicity of the bond are involved indetermining bond lengths.25Ill0(1.)0.>FIG. 3.The crystal structure of iron enneacarbonyl, Fe,(CO),, has beendetermined by H. M. Powell and R. V. G. Ewens26 with a veryinteresting and unexpected result.In order to give each ironatom the effective atomic number (E.A.N.) of the next inert gas,krypton, N. V. Sidgwick and R. W. Bailey2' suggested the con-stitution (I) (Fig. 3) for this compound with a co-ordination numberof five about the iron atoms as in Fe(CO),. Powell and Ewens,however, find that the iron atoms are not joined together in thisway, the molecule having a horizontal plane of symmetry. Threecarbonyl groups are co-ordinated to each iron atom in the usual24 Cf. W. Hieber and H. Schulten, 2. anwg. Chem., 1937, 232, 29.25 W. M. Lister and L. E. Sutton, Trans. Faraday Soc., 1939, 35, 495;G. C. Hampson and A. J. Stosick, J . Awr. Chem. SOC., 1938, 60, 1814.a* J., 1939, 286.27 Proc. Roy. Soc., 1934, A, 144, 521168 CRYSTALLOGRAPHY.way Fe+CzO, but the remaining three carbonyl groups arenot co-ordinated CZO groups but are bonded (through the carbon)to both of the iron atoms by ordinary single bonds, and so have astructure similar to that in ketones.The difference between thetwo sets of these groups is shown by the carbon-oxygen distances;in the C Z O groups this is 1.15 A., and in the >C=O groups itis 1.3 A. The structure is represented diagramatically in (11)(Fig. 3). If the only bonds to each iron atom are the six Fe-Cbonds, the iron atoms will have an E.A.N. of 35 with an odd elec-tron on each. It seems extremely improbable that such an arrange-ment should hold when, by the pairing of these odd electrons, theiron atoms could attain the E.A.N. of 36, the same as that ofkrypton.The observed diamagnetism of the substance shows thatthe spins of the odd electrons are opposed, and this, together withthe extremely short Fe-Fe distance of 2-46 A. (roughly twice thecovalent radius of iron), strongly suggests that the two iron atomsare linked by a covalent bond. Each iron atom therefore probablyforms seven bonds, six with carbon atoms and one with the otheriron atom. Exactly the same kind of co-ordination polyhedronhas been found for the A-modification of lanthana and other rare-earth sesquioxides 28 in which each rare-earth ion is surrounded byseven oxygen ions, and also for the ZrF7= ion in ammonium andpotassium heptafl~ozirconate.~~ 0. Hassel and H. Mark's sug-gestion 30 that (NH,),ZrF, is built up of NH,+ ions, [ZrFJ ions, andF- ions, has been shown to be incorrect, both the ammonium andthe potassium compound containing the complex ion ZrF,= in whichzirconium has the co-ordination number seven.The structure ofthe crystals is similar to that of the. face-centred cubic (NH,),A1F6,but with the AIF6= octahedra replaced by ZrF,-. The seventhfluorine atom is introduced along one of the cubic three-fold axes,the configuration of the resulting complex being that of an octa-hedron distorted by spreading one face and inserting the seventhatom at its centre, as shown in Figs. 4 and 5 . Each of the sevenZr-F distances is equal to 2.1 A., the most regular distributionof fluorine atoms about the zirconium atom giving a minimumF-F separation of 2.64 A.(only slightly less than twice the ionicradius of fluorine, 2.72 A.) and an F-Zr-F angle of 77" 50'. Theorientation of these ZrF,= complexes is not uniquely determined,however, but shows some randomness, permitting the crystals toassume higher point -group and space-group symmetry than wouldbe possible otherwise. A similar phenomenon occurs with some2 8 L. Pauling, 2. Krist., 1929, 69, 415.29 G. C. Hampson and L. Pauling, J . Amer. Chem. SOC., 1938, 60, 2702.2. Physik, 1924, 27, 89HAMPSON : INORGANIC STRUCTURES. 169ferricyanides of the type M,[Fe(CN),],, (M = Cd, Mn, Zn, Co, Cu,or Ni).31 Here again the crystals have a Laue holohedral face-centred cubic unit of structure, and as with the heptafluozirconatesthis symmetry is incompatible with the number of atoms whichhave to be arranged in the cell.The only solution is to have twoof the metallic cations distributed randomly over more than twopositions, these being the 32 positions on the octant diagonalsFIa. 4.Fra. 5.The ZrF,z complex viewed along its three-fold axis.tetrahedrally arranged about the octant centres. This rathercurious fact that a small number of atoms are distributed statistic-ally over a large number of positions has been observed before,e.g., in silver iodide.32 These salts have the anion-cation skeletontypical of perovskites and the complex cyanides of the Prussian-blue series,33 the Fe+++, M++, and (CN)- ions forming a skeleton3 1 A. K. van Bever, Rec. Trav. chirn., 1938, 57, 1259.32 L. W.Strock, 2. physikal. Chem., 1934, B, 25, 441; L. Helmholz, J .Chem. Physics, 1935, 3, 742; see also Ann. Reports, 1935, 32, 188; 1938,35, 174. 33 Ibid., 1934, 31, 213170 CRYSTALLOGRAPHY.of cubes (which are octants of the unit cell) with the (CN) groupsalong the edges of the cubes and the metal ions a t the corners. Avarying number of water molecules appear to occupy the holes inthe octant centres randomly.A different type of AB, polyhedron occurs in potassium hepta-fluoniobate, K2NbF7, and potassium heptafluotantalate, K,TaF, .34These crystals have monoclinic (pseudo-orthorhombic) symmetry,unlike the heptafluozirconates which are cubic. The NbF,= andTaF,’ groups, which are clearly shown to exist as discretecomplexes within the structure, have the configuration as shownin Fig.6. This can be visualised as being derived from an MP,group in the form of a trigonal prism by the addition of a seventhfluorine atom through the centre of one square face, followed by theappropriate distortion. The Nb-P (or Ta-F) distances lie betweenFIU. 6.1.94 A. and 2-01 A., and the thirteen shortest F-F distances withinthe anion lie between 2.41 A. and 2.98 A., with an average of 263 A.The adjacent fluorine atoms therefore approach closer within thesecomplexes than they do within the ZrF7= complex, the values in-dicating a considerable degree of interpenetration of the closedvalency shells.Fig. 6 possesses the symmetry C,, - mm, vix., a two-fold axisin which two mutually perpendicular mirror planes intersect, andso is quite different from ZrF7- which has the symmetry C3, - 3m.Considering the complexes as being built up of metal ions andfluorine ions, there seems to be little to choose between the twomodels, since for a given M-F separation the repulsions betweenthe fluorines should be about the same; similarly, if the complexesare considered as covalently bound, it is impossible to make aJ.L. Hoard, J. Amer. Chem. Soc., 1939, 61, 1252HAMPSON : INORGANIC STRUCTURES. 171choice in the absence of any quantum-mechanical treatment of7-co-ordinated covalent complexes. In view of the differencewhich has been observed, however, it would be interesting to knowwhether the configuration of the TaF,- complex was that of anoctahedron or a trigonal prism.It is surprising that no workappears to have been published on the structure of compoundscontaining the group AB,, such as TaP,= or the very stable ions[MO(CN),] --- and [Mo(CN),] ----.* Again, no theoretical pre-diction has been made regarding the disposition of eight covalentbonds from a central atom, though if the bonds are ionic the moststable co-ordination polyhedron should be a twisted cube ” orArchimedean a n t i p r i ~ m . ~ ~Other compounds which have been reported to exhibit randomnessin their structure are potassium and caesium fluorochromate 36 andneodymium bromate enneah~drate.~’ The first two are isomorphousand of the scheelite (CaWO,) type, an oxygen atom being replacedby a fluorine atom which is almost equal in size (cf.potassium osmi-amate K,OSO,N).~~ In the caesium compound the parameters ofthe oxygen and fluorine atoms could not be determined accuratelyowing to the large scattering power of the cmium atom, but inKCr0,F the [CrO,P]- group is almost a regular tetrahedron aboutthe chromium atom with a Cr-0 (or Cr-F) distance of 1-58 A. Asto the way in which a fluorine atom replaces an oxygen atom, i.e.,whether it is a completely random orientation of Cr0,F groups ora macrostructure of regions of lower individual symmetry, remainshere, as in most other cases of random structures, very uncertain.When the replacement involves such a small change in shape andsize as in [CrO,F]- the randomness is probably complete; in thecase of [ZrF,]=, on the other hand, the crystal is probably builtup of different orientations of small regions of lower symmetry,these regions being of smaller dimensions than those giving coherentX-ray scattering.36 L.Pauling, J . Amer. Chem. SOC., 1939, 61, 361.38 J. A. A. Ketelaar and (Frl.) E. Wegerif, Rec. Traw. chim., 1938, 57,37 L. Helmholz, J . Amer. Chem. Soc., 1939, 61, 1544.38 F. M. Jaeger and J. E. Zanstra, Rec. Traw. chim., 1932, 51, 1013.* Since going to press a paper has appeared in which the structure ofK4Mo(CN),,2H,O has been described (J. L. Hoard and H. H. Nordsieck,J . Amer. Chem. SOC., 1939, 61, 2853). The codguration of the MO(CN), - - - -group is shown to be that neither of a cube nor of an Archimedean antiprismbut of a duodecahedron with triangular faces and eight vertices, havingapproximately the symmetry Da.For a given Mo-CfN distance, therepulsion between adjacent CN groups in this polyhedron is very nearlythe same as that in the antiprism and coneiderably less than that in thecube.1269; 1939, 58, 948172 CRYSTALLOGRAPHY.In neodymium bromate enneahydrate Nd(BrO,),,SH,O, theneodymium ions are surrounded by nine water molecules, six atthe corners of a trigonal prism a t a distance 2.47 0.05 A. andthree out from the prism faces a t a distance 2.51 & 0.05 A. (Fig. 7).These distances are somewhat larger than the sum of the ionic radii(approximately 2.35 A.) obtained from the structure of Nd,0,,39the increase being ascribed partly to an increase in the co-ordinationnumber and partly to a difference in the character of the bond.These hydrated ions are packed on top of one another to formx --P-FIG. 8.vertical strings of Nd(H,O), groups in relatively close contact,columns of Br0,- ions fitting into the holes enclosed by six suchstrings.The arrangement is revealed in the Fourier projectionshown in Fig. 8. The water molecules of the [Nd(H,O),]+++ groupare probably linked to the oxygen atoms of the bromate ions byhydrogen bonds, the 0-H-0 separation being 2-77 0.10 A.There is some choice in the way in which the bromate ions canorient themselves, and though a pyroelectric experiment shows thec-axis to be polar, indicating that they are all oriented in onedirection, this does not agree with the observed intensities, whichcan only be explained by assuming a certain amount of random-ness.The dimensions of the Br0,- ion could not be determinedvery accurately, although the reported Br-0 distance, 1.74 & 0.07 A.,agrees with the value 1-78 A. found in sodium b r ~ r n a t e . ~ ~39 L. Pauling, 2. Krist., 1930, 75, 128.(Miss) J. E. Hamilton, ibid., 1938, 100, 104HAMPSON : INORGANIC STRUCTURES. 173An interesting new type of ABX, structure has been found inthe case of ammonium cadmium chloride NH,CdCl, 417 42 andrubidium cadmium chloride RbCdC1,.42 Cadmium is known t oexhibit octahedral co-ordination in cadmium chloride (CdCl, octa-hedra, each corner being common to three octahedra), and tetra-hedral co-ordination in the compounds K,Cd(CN),, CdS, CdSe,and CdTe, hence [CdCl,], might be expected to be built up ofCdC1, octahedra, with shared corners as in perovsbite, or of CdC1,tetrahedra with two shared corners as in the metasilicates.Actually,FIG. 9.the structures are found to be built up of CdCl, octahedra, butinstead of sharing corners they share edges to form infinite double" rutile " strings as shown in Fig. 9. Each octahedron shares twoopposite edges AB and CD to form strings of octahedra parallelto the c-axis as in rutile, and these rutile strings are then furthercondensed in pairs, each octahedron sharing two edges AE and CEwith octahedra of the adjacent string. Hence of the six chlorineatoms in each CdCI, octahedron, three of them (A, C , and E) arecommon to three octahedra, two of them (B and D) are common*l H.BrasseurctndL. Pauling, J. Amer. Chem. SOC., 1938, 60, 2886.4 2 C. H. MacGillavry, H. Nijveld, S. Dierdorp, and J. Karsten, Rec. Trav.chim., 1939, 58, 193174 CRYSTaLLOGRaPHY.to two octahedra, and P belongs to only one ootahedron. Theoctahedra themselves are very nearly regular, the average Cd-Cldistance (2.65 A.) being the same (2.66 A.) as that found in CdCl,.Each ammonium or rubidium ion is surrounded by nine chlorineatoms, the co-ordination polyhedron being of the form shown inPig. 7; the average NH,-Cl distance, 3.31 A., is very nearly thesame as that found in ammonium chloride. The structure of thesecompounds is therefore intermediate in type between that ofperovskite, in which the cation is 12-co-ordinated, and thatof ilmenite, in which the cation is 6-co-ordinated, this being inaccordance with the radius ratios.Similar columns of " rutile octahedra " occur in K,HgCl,,H,O *3and in K,SnC1,,H,0,44 but in these cases the columns are notcondensed together in pairs.In the latter compound E. G. Cox,A. J. Shorter, and W. Wardlaw45 proposed a planar configurationfor the SnCl,= ion, from the presence of a centre of symmetry, thoughit now appears probable that the SnC1, groups are derived fromSnC1, octahedra sharing two opposite edges.The planar configuration ( d q 2 hybridisation) of 4-covalentauric compounds is now well established, but an interesting andunexpected result has recently been obtained for 4-covalent aurouscorn pound^.^^ The compounds investigated were potassium 2 : 2'-dipyridyl aurous cyanide K[Au(CN) zdipy], and potassium 4 : 5(0)-phenanthroline aurous cyanide K[Au( CN) ,phenan]. That thesecompounds really involve 4-covalent gold and not 2-covalent gold,as [Kdipy][Au(CN),], is shown by the fact that an ammoniumderivative NH,[Au(CN),phenan] can readily be prepared in whichthe co-ordinating group must be associated withthe gold atom, the nitrogen of the NH, group alreadyhaving its maximum covalency.One of the unitand this must mean that the complex is either planarCN The gold atom in these corn-plexes has an E.A.N. 86, the same as that of radon,and a planar rather than a tetrahedral distribution of valenciesseems very surprising.A planar oonfiguration for the hydrated ion [Mn,4H20]++ inK2Mn(S0,),,4Hz0 has also been reported,,' with a Mn-0 separationof 2.40 A.loo, 212.cell dimensions in each case is very small (3.74a.)>A!.< cn or very nearly so.G.C. H.4s C. H. MWGillavry, J. H. D e Wilde, and J. M. Bijvoet, 2. KriSt., 1938,44 H. Brassem and A. de Rassenfosse, Nature, 1939, 143, 332.46 Ibid., 1937, 139, 71 ; Ann. Reports, 1938, 35, 162, 185.46 H. J. Dothie, F. J. Llewellyn, W. Wardlaw, and A. J. E. Welch, J.,4' H. Anspach, 2. Krbt., 1939,101, 39. 1939, 426ROBERTSON : ORGANIC STRUCTURES. 1754. ORGANIC STRUCTURES.Interatomic Distance and Resonance in Conjugated Systerns.-Thefundamental assumption in this work is that the internucleardistance between two atoms depends only upon the type of bondbetween them, and not, for example, on some invariant radiusapplying to all the bonds formed by the atom.A pure single G-Cbond should then have a constant length of about 1-54 A. irrespectiveof its surroundings, and deviations below this value will indicateresonance with multiple-bonded structures.That the situation is not really as simple as this may be inferredfrom results previously noted in these Rep0rts.l The methyl-group bond length is an important reference value in this con-nection, because it might be expected to remain a typical singlebond in all circumstances. Yet deviations from the 1-54 valuehad been noted in a number of compounds, and some of these caseshave now been revised and clarified. The present situation may besummarised : in hexamethylbenzene an accurate redeterminationof the structure by X-ray methods2 gives a methyl-group bondlength of 1-53 5 0.02 A.in agreement with electron-difFractionmeas~ements.~ In addition, the planar molecule is found to betilted out of tho (001) plane by lo, the packing of the molecules inthe crystal is rediscussed and shown to be governed by the hydrogen-hydrogen repulsions, but apart from these modifications, Lonsdale'sprevious structure 4 is fully confirmed. An attempted revisionof the durene structure 6 v 2 still leaves the methyl-group bondlength at 1.49 A., although this value may not be so accurate as inhexamethylbenzene. But electron-diffraction studies of isobutene,tetramethylethylene, and mesitylene 3 give single-bond values of1.54 & 0.02 A.On the whole, there is no evidence of any seriousdeparture from the single-bond value when the methyl group isadjacent to a double bond or a benzene ring; but when the methylgroup adjoins a triple bond definite contractions of about 0.08 A.are now established. The spectroscopic value of 1.462 & 0.005 A.for the CH3-C distance in methylacetylene has now been verifiedby electron-diffraction studies,' and in dimethylacetylene anddimethyldiacetylene similar values of 1-47 & 0.02 A. are reported,whereas in methyl cyanide the CH3-C distance is 1.49 & 0.03 A.These results have been interpreted in two different ways, byL. 0. Brockway, Ann. Reports, 1937, 34, 196.L. 0. Brockway and J.M. Robertson, J., 1939, 1324.L. Pauling and L. 0. Brockway, J . Amer. Chem. SOL, 1937, 59,(Mrs.) K. Lonsdale, Proc. Roy. SOC., 1929, A, 123, 494.J. M. Robertson, ibid., 1933, A , 142, 659.G. Herzberg, F. Patat, and H. Verleger, J. Physical Chem.,123; R. M. Badger and S. H. Bauer, J . Chem. Physics, 1937,5,599.J . Arner. Chem. SOC., 1939, 61, 927.1223.937, 41176 CRYSTALLOGRAPHY.L. Pauling, H. D. Springall, and K. J. Palmer,' and by J. B. Conn,G. B. Kistiakowski, and E. A. Smith.8 According to the formerauthors they may be due to two causes. First, the CH,-C bondmay remain a single bond, but, contrary to the usual assumption,the single-bond covalent radius of the triple-bonded carbon atommay change, owing to an increase in the s character of the hybrid8-p bond orbital, due to the formation of the triple bond.Secondly,the CH,-C bond may acquire some double-bond character owingto resonance with certain unconventional electronic structures.That the first of these causes must be significant is probable becausethe G-H bond distance is appreciably less in acetylene (1.057 A.)than in methane (1.093 A,). The hydrogen atom can only formone covalent bond, so this contraction must be due to a change inthe single-bond radius.The contraction of the methyl group bond-length in the acetyleniccompounds, however, is greater than can be explained by this causealone, and so we must infer a certain double-bond character as well.In a full discussion, Pauling, Springall, and Palmer attribute onlyabout 0.02 A.of the shortening to change in the single-bond radius,and the remainder to resonance among the structures (1)-(IV).H H I H* Y=C=&-H (11.)I(I.) H--S;r-EC-HI I H HH H + I -H C=C=C-H (IV.) II I (111.) H: C=C=&-HH HIt may be noted that the structures (11)-(IV) contain onecovalent link less than the conventional structure (I), and so wemight expect their contribution to be small. The unique featureof the postulated resonance in methylacetylene, however, is the factthat it involves the rupture of a C-H link. Apart from this it isclosely similar to the ordinary resonance in conjugated systems,e.g., in butadiene, where the contributing structures may be writtenas in (V)-(VIII).(v.) CH2=CH-CH=CH2 - 6'H2-CH=CH-6H2 - (vI.)(VII.) CH,-CH=CH-6H2 6H2-CH=CH-CH2 (VIII.)When a double bond is adjacent to a methyl group a similar butsmaller conjugation may be expected, only the C-H bonds in theC - h c plane now being involved. Any covalent radius change8 J.Amer. Chem. SOC., 1939, 61, 1868ROBERTSON : ORGANIC STRUCTURES. 177will also be small (the C-H distance in ethylene, 1.087 A . , ~ is onlyslightly less than in methane, 1-093 From these considerations,the estimated methyl-group bond-length in methylethylene and themethylbenzenes is about 1.51 A. The best observed values areabout 1.53 A. as in hexamethylbenzene, but slightly smaller valuesare not excluded by the experiments, and in fact may be expectedin the case of the less fully substituted benzenes where fewer methylgroups compete for the available conjugating power of the ring(compare the experimental result for durene 5).approach the problem in quitea different way, vix., from an extensive study of heats of hydro-genation, including those of the acetylenic compounds.11 Theirwork reveals the large magnitude of the steric hindrances exercisedby non-bonded atoms in organic molecules, and they attributethe C-H bond shortening in acetylene as compared with methanewholly to reduced steric hindrance by adjacent atoms.For theC-C bond in the methylacetylenes they consider that the shorteningmay be largely due to the same cause.Although these interpretations may differ, there is now a con-siderable amount of new data, and the six possible types of con-jugated systems involving double bonds, triple bonds, and benzenerings have been reviewed by Pauling, Springall, and Palmer withthe following results :Conn, Kistiakowski, and SmithAmount ofType of conjug- Observed C-C double bondated system.Substance. distance, A. character, yo.Butadiene la 1-46 f 0.03 18 f 10cycZoPentacliene l2 1.46 5 0.03 18 & 10Stilbene l3 1.44 & 0.02 25 & 7{ -\=p-Diphenylbenzene l4 1.46 f 0.04 18 & 12 WJ { Diphenyl 1.48 & 0.04 13 & 12<>-\Vinylacetylene -=-\Tolan l6 1.40 4 0.02 33 f 8Diacetylene 1.36 0.03 44 5 13Cyanogen 1-37 4 0-02 33 & 10(Dirnethyldiacetylene 1.38 0.03 34 f 13E. H. Eyster, J . Chem. Physics, 1938, 6, 580.lo N. Ginsburg and E.F. Barker, ibid., 1935, 3, 668.l1 T. W. J. Taylor, Ann. Reports, 1937, 34, 220.la V. Schomaker and L. Pauling, J . Amer. Chem. SOC., 1939, 61, 1769.la J. M. Robertson and (Miss) I. Woodward, Proc. Roy. Soc., 1937, A , 162,565.l4 (Miss) L. W. Pickett, ibid., 1933, A , 142, 333.l5 J. Dhar, Indian J . Physics, 1932, 7, 43.l6 J. &I. Robertson and (Miss) I. Woodward. Proc. Roy. SOC., 1938, A ,164,436178 CRYSTALLOGRAPHY.It is pointed out that roughly the same conjugating power isexpected for the first five systems, as only the pz orbitals of thetriple bond are effective in conjugation with a double bond orbenzene ring. Thus the tolan result agrees with stilbene if a single-bond covalent radius change of 0.04 A. is allowed (the observedC-H contraction in acetylene compared with methane).Pauling,Springall, and Palmer, bowever, estimate the radius change at only0.02 A. when triple bonds are formed, and this correction is appliedin calculating the double-bond character given in the last column.They suggest that the low tolan distance may rather be due tothe fact that rotational oscillation must be effective in reducingresonance to some extent in the first three systems, by bringingthe molecules into non-coplanar configurations, but not, of course,in the triple-bonded structures.The lower C-C distance and higher double-bond character of theconjugated triple-bond systems are in accordance with expectation,interaction through the pz or pDy orbitals now being possible. Itwill be interesting to compare these new electron-diffraction measure-ments for conjugated triple bonds with detailed X-ray results fordiphenyldiacetylene, about which a preliminary note has beenpub1ished.l'In conclusion, it may be noted that detailed calculations of theC-C bond length in butadiene l8 have predicted a value of 1.43 A.rather than the 1.46 A.recorded above, whereas in phenylethylene l9similar calculations give a value of 1.45 A. in agreement with thestilbene result.Other Hydrocarbon Structures.-An interesting study of certainhigh molecular-weight parafks with chains exceeding 130 and upto several thousand carbon atoms in length has been carried outby C. W. Bunn20 The great length of the chain is really a simplify-ing feature because end effects can be neglected, and the c translationof the orthorhombic cell is simply the length of the C-C\c zig-zag(2.534 A.).The C-C distance is given as 1.53 A., and the zig-zagangle as 112". Detailed electron-density maps are derived froma triple Fourier analysis, and it is concluded that the electroncloud of the CH, group is distended in the plane of the nuclei, due inpart, but not wholly, to anisotropic thermal motions. It may benoted, however, that the number of terms in the triple Fourierseries is extremely small (27) and in such cases one must beware offalse detail. A single-crystal analysis of n-triacontane, C90H62, has17 E. H. Wiebenga, Nature, 1939, 143, 980.l 8 J. E. Lennard-Jones, Proc. Roy. Xoc., 1937, A , 158, 280.'O Trans.Faraday SOC., 1939, 35, 482.W. G. Penney, ibid., p. 306ROBERTSON : ORGANIC STRUCTURES. 179also been published,21 leading to a C-C distance of 1.57 & 0.05 A.and a zig-zag angle of 106' &- 4".The study of complex condensed ring compounds has beenextended by J. Iball to 3 : 4-benzphenanthrene, CI8Hl2, and someof its derivatives, and cell dimensions, optical and magnetic dataare recorded.22A very extensive single-crystal study of anthracene by electron-diffraction methods has recently been made,23 and the results arein agreement with the structure as determined by X-rays.24 Thesignificance of this study, however, lies in the detailed interpretationof certain new features in the diffraction patterns, which are shownto be equivalent to gas diffraction patterns of oriented moleculesmoving past the electron beam.The results may be explained bysupposing the molecules to vibrate thermally as rigid units abouttheir mean positions in the lattice. The method would seem tohave considerable application to complex molecules.GZycine.-A very complete account of the crystal structure ofglycine has now been published,25 which supersedes a number ofprevious tentative structures.26* 27 The monoclinic cell containsfour asymmetric molecules, and the approach to the structure byPatterson and Harker methods of analysis is described in consider-able detail and forms an interesting contribution to the techniqueof structure analysis. The final results reveal nearly flat moleculeswith the dimensions shown in Fig.10. I n the crystal the atomsare coplanar, with the exception of the nitrogen which lies 0.27 A.above the plane of the others. The interatomic distances, which theauthors estimate to be accurate to within & 0;02 A., call for littlecomment except for the carbon-nitrogen value of 1 . 3 9 ~ . which iscertainly abnormal but agrees closely with the N-C (methylene) value(1.41 A.) in diketopiperazine reported by R. B. Corey last year.28Both these distances are well below the G-N single-bond value of1.47 A., and it is difficult to see how any form of bond-multiplicitycan account for the discrepancy. I n the crystal the moleculeprobably has the " zwitter-ion " structure, H,N+*CH,*COO-, andso the formal charge effect, recently discussed by N.Elliot,29 should21 R. Kohlhaas and K. Soremba, 2. Krist., 1938,100,47.22 Ibid., p. 234.2s A. Charlesby, G. I. Finch, and H. Wilman, Proc. Physical SOC., 1939,24 J. M. Robertson, Proc. Roy. SOC., 1933, A, 140, 79.25 G. Albrecht and R. B. Corey, J . Amer. Chem. SOC., 1939, 61, 1087.26 J. D. Bernal, 2. Krist., 1931, 78, 363.2 7 A. Kitaygorodsky, Acta Physicochim. U.R.S.S., 1936, 5, 749.28 J. Amer. Chem. SOC., 1938, 60, 1598.29 Ibid., 1937, 69, 1380.51, 479180 CRYSTALLOGRAPHY.be operative. The decrease in the C-N distance to be expectedfrom this cause would amount to only about 0.03 or 0.04 A . , ~ O butthe effect is in the right direction.The situation is made more confusing, however, by the resultsof an interesting electron-diffraction investigation on trimethyl-a'niine oxide and dimethylsulphone recently carried out by M.W.Lister and L. E. Sutton31 They find that the nitrogen atom ap-pears to have a greater radius when 4-covalent than when 3-covalent,the C-N bond length in (CH,)3&-0 being given as 1.54 & 0.03 A.,corresponding to a 4-covalent radius of 0.77 A., whereas from the;formal charge rule we might have expected a decrease in this caseas well as in glycine.@FIG. 10.I 7FIG. 11.These conflicting results call for a careful examination of theestimated limits of accuracy in the experiments, and for the studyof further cases if possible. Owing to the number of parametersinvolved, the estimated accuracy appears to the Reporter to beslightly optimistic.In the case of glycine it should be noted thatthe intensities are obtained by visual estimates, and the final co-ordinates by direct adjustment of parameters and not by E'ourierseries methods. It may be recalled that when oxalic acid dihydratewas investigated by similar methods a C-C distance of 1-58 A. wasobtained,32 whereas a later study by means of quantitative absoluteintensity measurements and Fourier series methods gave a revisedvalue for the same bond length of 1.43 A.%L. Pauling, " The Nature of the Chemical Bond," p. 159.31 Trans. Paraday SOC., 1939, 35, 495.32 W. H. Zachariasen, 2. Krist., 1934, 89, 442.33 J. M. Robertson and (Miss) I. Woodward, J., 1936, 1817ROBERTSON : ORGANIC STRTJCTURES. 181The complete determination of the glycine structure is an im-portant initial step towards an exact knowledge of the linkagespresent in protein structures, and one most interesting aspectconcerns the intermolecular connections of the glycine molecules.The crystal is composed of double layers of nearly flat moleculesheld together by hydrogen bonds and electrostatic forces operativebetween the nitrogen and oxygen atoms of adjacent molecules.Asingle layer of molecules lying nearly in the (010) plane is shown inFig. 11. Fairly strong hydrogen bonds of 2-88 and 2.76 A. holdthis layer together, and the fact that these bonds are disposed a tnearly the tetrahedral angle to themselves and to the N-C linksuggests that a third hydrogen atom may occupy the fourth tetra-hedral position, and be capable of engaging with oxygen atoms ofthe next layer.This next layer of molecules is related by a centreof symmetry to the one shown, and is found to be closely bound toit, the minimum distances being 2.93 and 3-05 A. These unusualdistances may, therefore, represent very weak hydrogen bonds, dueto the third hydrogen sharing its bond-forming capacity with thetwo nearest oxygen atoms of the adjacent layer. Between suc-cessive double layers only van der Waals forces are operative, theclosest approaches being about 3.4 A.Preliminary data have been reported for p-azotoluene 34 anddi~henylamine,~~ and a somewhat more complete study of oxamideis recorded.36 The unusual C-C distance given as 1-65 A. requiresfurther study .The Isomeric Axoben2enes.--A fully quantitative analysis of thetrans-azobenzene structure has now been completed.37 It belongsto the dibenzyl series of structures,13~ 38 and like stilbene and tolan,is complicated by the fact that two crystallographically independentmolecules contribute to the asymmetric unit.It is an interestingfact that these two molecules, which exist side by side in the crystal,do not appear to be identical. The two kinds of molecules can beclearly distinguished in the contour map reproduced in Fig. 12,where it may be noted that the resolution of the central pair ofnitrogen atoms is rather poor ; but by various methods the positionsof all the atoms can be determined with considerable accuracy.It is then found that much of the apparent difference between themolecules is due to a difference in orientation which reveals itself34 M.Prasad and M. R. Kapedia, J . Univ. Bombay, 1938, 7, 94.35 J. Dhar, Indian J . Physics, 1939, 13, 27.36 L. Misch and A. J. A. van der Wyk, Arch. Sci. ph.ys. nat., 1938, V, 20,37 J. J. de Lange, J. M. Robertson, and (Miss) I. Woodward, Proc. Roy.38 J. M. Robertson, ibid., 1935, A, 150, 348.Suppl., 96.Soc., 1939, A , 171, 398182 CRYSTALLOGRAPHY.in the projection, but when full allowance is made for this thereremains a small difference in the dimensions of the two molecules.Such differences have previously been attributed to an accumulationof experimental errors (e.g., in stilbene), but in the case of azobenzeneit seems almost certain that a real molecular difference exists...._ ....,, __.. . '. .6 j.Whereas one molecule is almost exactly flat, in the other the benzenerings appear to be rotated by ca. 15" about the C-N link, out ofthe plane containing the central atoms, and the dimensional changesare in the direction to be expected from the decrease in resonancewhich must accompany this distortion. The altered dimensionsare thus not a, permanent feature, such as would lead to a neROBERTSON : ORGANIC STRUCTURES. 183molecular species, but appear rather to be imposed by the immediatesurroundings. A full discussion of these relations has not yet beengiven.If we disregard these small-scale variations, the mean dimensionsof the trans-azobenzene molecule are as shown in Fig.13. Thesefigures are in accord with the accepted covalent radii of the atomsconcerned when allowance is made for the resonance expected forthis type of system. It may be noted, however, that, whereasFIG. 13.LFIG. 14.in stilbene the Car.-Cal. distance of 1-44 A. is just half-way betweenthe single-bond (1-54) and the double-bond (1.34) value, in azobenzenethe corresponding distance is distinctly nearer to the C-N single-bond value of 1-47 A. than to the C-N double-bond value of 1.28 A.This result is probably due to a greater tendency for the multiplebond to remain between the nitrogen atoms in azobenzene.The recently isolated cis-form of azobenzene 39 has also been sub-jected to a detailed X-ray analysis,40 but the results have not yet39 G.S. Hartley, J., 1938, 633. 40 J. M. Robertson, J., 1939, 232184 CRYSTALLOGRAPHY.been refined to the same extent as in the trans-isomer. As might beexpected, t,he crystal structure is quite different, and the cis-molecule is found to possess a two-fold axis of symmetry insteadof the centre of symmetry which exists in the trans-molecule. Thedimensions are shown in Fig. 14, and it may be noted that any chanceof a planar molecule is completely ruled out by the steric repulsionswhich would occur between the atoms of the benzene rings. Theserings are actually found to be rotated by 50" from the plane ofFig. 14, giving a clearance between the non-bonded atoms of about3.1 A. Such a result must inhibit resonance to a considerableextent, and this effect is indicated, but not proved, by the dimensionsobtained. The uncertainty in the figures is rather large a t present,but a more detailed study would be of considerable interest.Other ,Structures.-Preliminary reports are available for severalimportant structures which have not yet been published in detail.A notable advance in the difficult carbohydrate structures appearsto have been made by E. G. Cox and G. A. Jeffrey 41 in their analysisof a-chitosamine hydrobromide and hydrochloride. The iso-morphism of these compounds enables direct synthetic methods tobe employed, without any stereochemical assumptions, and theatomic positions (with one exception) can be determined to withinabout 0.08 A. The results show that chitosamine is a derivativeof glucose and not of mannose. The existence of the pyranosering in a crystalline sugar is established, and it is confirmed thatin the a-form of a d-glucose derivative the oxygen atoms on thefirst and the second carbon atom are in the cis-position.H. M. Powell and G. Huse42 have examined the 1 : 1 molecularcompound of picryl chloride and hexamethylbenzene and find thatthe two molecules lie in parallel planes with apparently no valencylinkings between them. Some degree of disorder is indicated inthe structure, which appears to be of a complex type.X-Ray analysis and dipole-moment measurements have beencombined in a study of benzi143 (reported to show a skew con-figuration) and of 1 : 2 : 4 : 5-tetrabromocycZohe~ane.~ An X-raystudy of 4 : 4'-dihydroxydiphenyl sulphide decamethylene ether 45is claimed to give a C,,.-S distance of 1-71 & 0.04 A. and an anglebetween the sulphur valencies of 112.4" & 1.5".InsuZin.-An extremely interesting account of X-ray measure-ments on wet insulin crystals has just been announced by (Miss)Nature, 1939, 143, 894. 42 Ibid., 144, 77.43 (Miss) I. E. Knaggs and (Mrs.) K. Lonsdale, ibid., 143, 1023; C. C.4c E. Halmoy and 0. Hassel, J. Amer. Chem. SOC., 1939, 61, 1601.45 R. Kohlhaas and A. Luttringhaus, Ber., 1939, 72, $97.Caldwell and R. J. W. Le FBvre, ibid., p. 803ROBERTSON : ORGANIC STRUCTURES. 185D. Crowfoot and H. Riley.46 Zinc insulin crystals in several im-mersion media are studied, and the wet unit cell is shown to be amoderately expanded version of that present in the air-driedcrystal^.^' X-Ray reflections are more numerous and there arestriking intensity changes. The results, expressed by means ofa Patterson vector diagram on the basal (0001) plane, show that themain interatomic vectors are similar in magnitude to those obtainedfrom the air-dried crystals, but are shifted through a small angle.This indicates that a reorientation of the molecules relative to thecrystal axes takes place on drying.The interpretation of the vector maps obtained from the originalair-dried crystals has been the subject of much contr~versy,~~ andwith the more extensive data now available from the wet crystalswe may perhaps expect some more fruitful discussions. J. M. €3,.G. C. HAMPSON.J. 11. ROBERTSON.A. R. UBBELOHDE.4 G Nuture, 1939, 144, 1011.4i (Miss) D. Crowfoot, Proc. Roy. SOC., 1938, A , 164, 580.4 8 (Mrs.) D. M. Wrinch and I. Langmuir, J . Arner. Chem. SOC., 1938, 60,2005, 2247; Nature, 1938, 142, 581; W. L. Bragg, J. D. Bernal, and J. M.Robertson, ibid., 1939, 143, 73; D. P. Riley and I. Fankuchen, ibid., p. 648;L. Pauling, J. Anter. Chem. SOC., 1939, 61, 1860