CRYSTALLOGRAPHY.1. LATTICE DEFECTS IN POLAR CRYSTALS.(a) Electrolytic Conduction in Polur Crystals.THE first theoretical treatment of electrolytic conduction in polarsalts is due to J. Frenke1,l whose ideas have recently been extendedand made more precise in a number of papers by W. Jost,2 W.Schottky,3 and C . Wagner.4 A discussion of these developmentsoccupies the greater part of a recent book by J ~ s t . ~ It is thepurpose of this article to give a brief account of this work.On the experimental side we may refer to summaries by A. vonHevesy6 and A. Smekal.7 The observations on rock salt aretypical of the alkali halides and are illustrated in Fig. 1.It will be seen that below about 600" ( 103/T >1.14) the conductivityis " structure-sensitive," i.e., it depends on the purity and pasthistory of the crystal, but that above 600" it is not structure-sensitive.Similar results follow from the investigations ofW. Lehfeldt 8 on alkali and silver halides.According to Smekal's report,g in the low-temperature region theconductivity is almost entirely due to cations, while in the high-temperature region in rock salt both ions become mobile; he statesthat the observed conductivity may be made up of the sum ofthree terms : (1) A structure-sensitive term representing conductiondue to cations, having the form Ae-B'T, with A of the order 0.8ohm-em., and B - 10,300". (2) A structure-insensitive term,1.4 x lo6 x e-23*G00!T, representing conduction due to cations.(3) A structure-insensitive term, 3.6 x lo6 x e-259700'T, repre-senting conduction due to anions.The theoretical work reported here deals only with the structure-insensitive (high-temperature) conduction.Two mechanisms havebeen proposed :(1) The mechanism of Jost.-According t o Jost, in a crystal in1 2. Physik, 1926, 35, 652.J . Chem. Physics, 1933, 1, 466; 2. physikal. Chem., 1934, A, 169, 129;W. Jost and G. Nehlep, ibid., 1936, B, 32, 1.W. Schottky, ibid., 1936, By 29, 335.C. Wagner and W. Schottky, ibid., 1930, B, 11, 1163." Diffusion und Chemische Reaktion in Festen Stoffen," Dresden, 1937," Handbuch der Physik," 1928, 10. Ibid., 1933, 23, [ii].8. Physik, 1933,85, 717, op. cit., p. 883MOTT : LATTICE DEFECTS IN POLAR CRYSTALS. 155equilibrium at temperature T, a certain number of ions will leavetheir normal lattice positions and migrate to an “ interlatticeFIU. 1.Dependence om temperature of the electrolytic conductivity 04 rock-salt crystals.A@ X Single crystals.o Polycrystalline material.position,” as shown in Pig.2. If E is the work necessary to removean ion from its normal position to an interlattice position, then thefraction of the total number of ions in interlattice positions is shownto be e-*Elkg’. Both cations and anions can move into inter-lattice positions; where, however, the ions are of very differentsizes (e.g., in sodium chloride), only for the smaller ion will E besmall enough to give an appreciable number. In an applied fiel156 CRY RTALLOGRAPHY.the ions which are in interlattice positions will be able to movethrough the lattice; their mobility will be proportional to a factore-vikT, where W is the activation energy necessary to move anion from the centre of the cube in Fig.2 to the centre of a face,which is t'he position of highest potential energy that the ion has toFIG. 2. nIon in interlattice position in sodium chloride structure.pass.will be given by a formula of the typeThus the dependence of conductivity CT on temperature T= Ae-(*E++V)lk* . . . . . . (1)where A is a constant. The vacant lattice points will also bemobile (with a different activation energy), since an ion may moveinto the vacant place from an adjacent lattice point. Eitherprocess may be the more important for the conductivity, dependingon the relative values of the activation energies.(2) The mechanism of Schottky.-According to Schottky, if thetemperature of a crystal be raised, vacant lattice points of eithersign will be formed a t the surface, or at cracks, and travel inwards.Vacant lattice points may thus exist without any ions forcingthemselves into interlattice positions.If Ef, E- are the energiesrequired to remove respectively a positive and a negative ion out ofthe crystal, and Eo the lattice energy per ion pair (and thus theenergy gained if the ions adhere to the surface), then the proportionof vacant lattice points is shown to beexp[- &(Ef f- E- - E,,)/kT] . . . - (2)For a crystal in thermal equilibrium this is, of course, independentof the number of cracks and surface, but the rate a t whichequilibrium is attained will depend on the area of surface fromwhich holes can start.Vacant lattice points of either sign will be mobile, with onlyslightly different activation energies.We thus expect motion oMOTT: LATTICE DEFECTS IN POLAR CRYSTALS. 157ions of both signs in salts where the Schottky mechanism is themore important. At sufficiently high temperatures we also expectan increase in the specific volume, unaccompanied by any increasein the lattice constant.Only rough theoretical calculations of the energies E, W , etc.,have been made a t present.1° Consider, for instance, the quantity+(E+ + E- - * . . (3)which determines the number of vacant lattice points. If only theelectrostatic forces between the ions considered as point chargeswere important, we should haveE+ = E- = E, = 1.74 e2/awhere a is the interionic distance, which gives for (3) an energy ofthe order 4 e.v.for sodium chloride. By taking into account thehigh dielectric constant of these salts, however, Jost has been ableto show that the true value is very much smaller, of the order 1 e.v.In general, a high dielectric constant will lead to a low value of thedissociation and activation energies occurring in these theories.Estimates of the energies involved suggest that conduction inthe alkali halides is mainly due to the Schottky mechanism, thatin the silver halides to the Jost mechanism. This is confirmed bythe fact that conduction by cations and anions is found in thealkali halides.Moreover, measurements by C. Wagner and J.Beyer l1 on the density and lattice constant of silver bromide a t410" show that vacant places in the anion lattice cannot be presentto any extent.The absolute magnitude of the conductivity, and thus theconstant A in (l), has been considered by Jost.12Phenomena, in which vacant lattice points present in a crystal int'hermal equilibrium play a part, are classed by these authors as" Fehlordnungserscheinungen." It may be remarked that if acrystal is cooled rapidly to a temperature at which these latticeholes are no longer mobile, a number will be " frozen in." Arock-salt crystal a t room temperature will normally have a muchlarger number of holes than the equilibrium value a t thattemperature.(b) Colour Centres in Alkali Halides.Transparent crystals may be coloured either by the presence ofcolloidal specks of some foreign substance-as, for instance, silverbromide, which after exposure to light contains colloidal silver-orby the presence of impurities dispersed in atomic form.Anlo Cf. Jost, op. cit., p. 68.l2 Ibid., 1934, A, 169, 129.11 2. physikal. Chem., 1936, B, 32, 113158 CRYSTALLOGRAPHY.example of a crystal coloured by a mechanism of the latter type isyellow rock salt. Coloured alkali halides have been investigated ingreat detail by R. W. Pohl and his co-workers, and also by Smekal.Recently, an hypothesis as to the nature of the colour centres hasbeen advanced by J. H. de Boer l3 which seems to be in agreementwith the observed facts.It is the purpose of this article to presentthe facts which can be explained by this hypothesis. Space doesnot allow any complete summary of the properties of colouredalkali halides; for this, the reader is referred to recent arti~1es.l~The absorption coefficient of coloured alkali halides plottedagainst wave-length shows a characteristic bell-like form. Theabsorbing centres are called in the literature F-centres (Farbzentren).The concentration of P-centres can be obtained from the absorptioncoefficient, values from 1015 to 1019 per cm.3 being obtained.The hypothesis of de Boer is that an P-centre is an electronreplacing a negative ion in the crystal lattice. A point where anegative ion is inissing will behave in a crystal as a positive charge,and therefore be capable of capturing a free electron.The colouris assumed to be due to the absorption spectrum of these trappedelectrons.Colour centres may be formed in the following ways :(i) By illuminating the crystal with X-rays or with certainwave-lengths of the ultra-violet light. Now, we have seen thatan alkali halide crystal at room temperature will normally have anumber of vacant lattice points. On illumination with X-rays, anumber of electrons will be raised from the inner levels of the ionsinto excited levels, where they are free to move about through thecrystal; some of these electrons will be trapped a t points wherenegative ions are missing. Crystals coloured in this way fade withincreasing time, especially a t high temperatures.Electronseventually return to their original positions.(ii) By heating the crystal in the vapour of the alkali metal.The crystal then acquires a stoicheiometric excess of a,lkali metal.The number of colour centres formed is proportional to (at hightemperatures practically equal to) the number of alkali atoms inan equal volume of the vapour.The explanation advanced is that a vacant negative lattice pointis formed a t the surface and traps an electron from an alkali atom.The positive and negative ions so formed adhere to the surface ofthe crystal, thus increasing its volume; the P-centre is mobile a thigh temperatures and travels into the body of the crystal.lS Rec. trav. chim., 1937, 56, 301.l4 R.W. Pohl, Proc. Physical SOC., 1937, 49 (extra part), 3 ; J. H. dc Boer," Electron Emission and Absorption Phenomena," Cambridge, 1936COX : CRYSTAL CHEMISTRY. 169(iii) Alkali halide crystals containing small amounts of alkalihydride show a new absorption band in the ultra-violet, on the longwave-length side of the characteristic band of the halide. Themost simple explanation of this is that H- ions replace the halogenions in the lattice; since the electron affinity of hydrogen is lessthan tha.t of the halogens, less energy will be required to excite anelectron, and the absorption will be shifted to the red.If a crystal is illuminated in this band, F-centres are formed;but the quantum efficiency, ca. lOOyo a t 4Q0°, is only 20% at 0"and falls to zero below - 100".The explanation suggested is asfollows : when a quantum of light is absorbed, an electron is movedfrom the H- ion on to a neighbouring cation. At high temperaturesthe hydrogen atom will then have time to diffuse away, leavingbehind a vacant lattice point and an electron, i.e., an P-centre. Atlow temperatures, however, the diffusion process will not havetime to take place before the electron drops back to its originalposition.N. F. M.2. CRYSTdL CHEMISTRY.A notable addition to the literature of crystal chemistry is'' Atomic Structure of Minerals " by W. L. Bragg,l which containslucid and admirably illustrated descriptions of all the principalmineral structures determined up to 1936. A perusal of this book,whilc showing very clearly the enormous advances which have beenmade in our knowledge of oxides, sulphides, silicates, and othergroups, indicates also the large regions of the mineral kingdom stillunexplored.Very little information has accumulated in the pastupon phosphates, for example, and it is satisfactory to observerecent progress in this direction. In other fields, the number ofexact structure determinations of complex co-ordination compoundsremains disappointingly small, in spite of the importance of thistype of substance both practically for determining the structure oforganic molecules and from the point of view of valency theory.From its unit cell dimensions,2 it seems probable that poloniumhas a structure analogous t o those of selenium and tellurium, but oflower symmetry.The nitrides and phosphides of lanthanum,cerium, and praseodymium 3 have rock-salt lattices, and galliumnitride 4 has the wurtzite configuration.1 Oxford University Press, 1937.2 M. A. Rollier, Gaxzetta, 1936, 66, 797.3 A. Landelli and E. Botti, Atti R. Accad. Lincei, 1936, [vi], 24, 459; 1937,4 J. V. Lirmann and H. S. Schdanov, Acta Physicochim. U.R.S.S., 1937,[vi], 25, 129.5, 306160 CRYSTALLOGRAPHY.Oxides.-Valentinite, the high-temperature form of antimQnousoxide, has been found 5 to have a structure, in marked contrast withthe molecular lattice of senarmontite containing infinite covalentdouble chains of the form (I). The Sb-0 distance in the chain is(1.12.00 A. and there is an inter-chain Sb-0 distance of 2-51 A., which isconsidered to represent a weak secondary bond holding thestructure together.The oxygen valency angles are 116" and 132",and those between the antimony bonds are 81", 89", and 93".Another interesting structure is that of selenium dioxide,6 in whichsingle chains (11) occur, with Se-0 distances of 1.73 and 1.78 A. and0 0(11.) -o-8~-o-se-o-8e-o-c,bond angles of 90" and 98" for selenium and 125" for oxygen. Thelinking between the chains is here not as strong as in Sb,O,, theSe . . . 0 distance being 2-63 A. ; on the other hand, the 0 . . . 0distance is the same in both substances, z l i x . , 2 . 5 4 ~ . The Se-0distances in the chain are about 5% less than the sum of thecovalent bond radii, and this is possibly due to resonance betweentwo structures such as (111) and (IV), the former predominating.-0-Se-O-(111.) .c.0The dioxides of selenium and tellurium are among the raresubstances which are transparent in the solid state and havecoloured liquid and vapour phases.Tellurium dioxide is recordedas having the rutile structure, but it is noteworthy that its c-axis isappreciably longer than that of any other rutile-like substance, andin the form of the mineral tellurite it is not tetragonal; are-examination of its structure would be of interest in view of thepossibility of the existence of covalent chains in this substancealso.M. J. Buerger, Amey. Min., 1936, 21, 206; M. J. Buerger and S. B.Hendricks, J. Chem. Physics, 1937, 5, 600; 2.Krist., 1937, 98, 1 ; see alsoM. C. Bloom and M. J. Buerger, ibid., 1937, 96, 365.J. D. McCulIough, J. Amer. Chem. Soc., 1937, 59, 789COX : CRYSTAL CHEMISTRY. 161I n the C 9 structure assigned by It. W. G. Wyckoff 7 toP-cristobalite, the silicon atoms occupy the same positions as thecarbon atoms in diamond, and the oxygen atoms lie midwaybetween them, thus having a valency angle of 180". From newintensity data, W. Nieuwenkamp * concludes that the oxygenatoms revolve in circles about the posit'ions assigned by Wyckoff,so that their valency angle is about 150" and the distance Si-0 is1.59 A. The fact that the transition from high to low cristobalite isnot sharp is in agreement with this suggestion, although the X-rayresults would be equally well explained by a statistical distributionof oxygen atoms over circles of the same radius.New measure-ments have also been made on or-quartz; in this case the oxygenangle is given as 142" and the Si-0 distances as 1-58 and 1.64 A.Pyrolusite, MnO,,1° is reported to have a rutile structure, andtitanium monoxide l1 probably has the sodium chloride lattice withTi-0 = 2.08 A. I n lead titanate, PbTi03,12 where the titanium isalso six-co-ordinated, the Ti-0 distances are given as 2.10, 2.00,and 1.94 A.8uZphides.-A new study of arsenopyrite, PeAsS, by M. J.Buerger 13 shows that it is monoclinic and not orthorhombic asformerly supposed, its structure being a superstructure based uponthat of marcasite. Each iron atom is surrounded by a distortedAs3S, octahedron, one face of which is a triangle of sulphur atomsand the opposite one a triangle of arsenic atoms, so that thearrangement is the same as that in cobaltite, CoAsS, which, however,has much higher (cubic) symmetry, probably because the cobalticis more symmetrical than the ferric ion.The distances areFe-S = 2.19 and 2.28 A,, Fe-As = 2.36 and 2.37 A., and S-As =2.30 A., and Buerger considers that these and other figures indicatethe presence of ferric ion not only in arsenopyrite (a conceptionwhich is not so novel as he suggests) but also in lollingite, FeAs,,and marcasite, FeS,. His conclusions are open to criticism,however; in the case of marcasite, for example, its electricalconductivity is only a small fraction of that of pyrites, whereas thepresence of ferric ions would be expected to increase the conduc-tivity.Nevertheless, a re-examination of marcasite 15 confirmsthat the distances are not the same as in pyrites ; the Pe-S distances7 " Strukturbericht," I, 169.9 F. Machabchki, Foortschr. Min., 1936, 20, 45.10 G. Vaux, Min. Mag., 1937, 24, 521.11 W. Dawihl and K. Schroter, 8. anorg. Chcm., 1937, 233, 178.12 S. S. Cole and H. Espenschied, J. Physical Chern., 1937, 41, 445.13 2. Krist., 1936, 95, 83; Amer. Min., 1937, 22, 48.14 M. L. Huggins, 2. Krist., 1937, 96, 384.15 M. J. Buerger, ibid., 97, 504.REP.-VOL. XXXIv. F* 8. Krist., 1937, 96, 454162 CRYSTALLOGRAPHY.are 2.25 and 2-23 A. (2.26 in pyrites) and the S-S distance is 2.21 A.(2.10 in pyrites).The reason for this increased S-S distance is notclear.The structure of palladous sulphide16 proves to be morecomplicated than that of ~ooperite,~' the platinous analogue, butshows the same essentjial feature, viz., a tetrahedral environmentof sulphur atoms by metal atoms each of which is surrounded byfour sulphur atoms in a plane. As in cooperite, the planar andtetrahedral systems are both distorted to accommodate each other,but to a greater extent; whereas the S-Pt-S angles are 824" and972~"~ the angles between Pd-S bonds vary from 77" to 100".Three types of PdS, co-ordination occur in the structure, slightlypuckered squares, plane rectangles, and plane trapeziums, andfrom the smaller extent of the distortion in the first case it seemsprobable that there is greater resistatnee to deflection of the bondsout of the plane than in it.In any case the resistance of the planeconfiguration to distortion is at least as great as that of thetetrahedral, since some of the Pd-S-Pd angles differ from 109*" byas much as 14". The Pd-S distances range from 2.26 to 2.43 A.,and this variation of nearly 0.2 A. is perhaps further evidence ofthe stability of the planar and the tetrahedral configurations.Apart from its bearing on the above stereochemical points, thestructure of palladous sulphide is of special interest on account ofits isomorphism with braggite (Pt,Pd,Ni)S,18 the first mineral tobe isolated and determined by X-ray methods.Among other sulphides studied,lg the stmcture of cubanite,CuSFe,S3,20 is notable for the occurrence of the iron atoms inpairs.The strong tendency of boronto form chains or nets with oxygen (as in calcium borate and boricoxide glasses) is further exemplified by the structure of potassiumrnetaboratey2l which has the structure IC,(B,O,).In this case theBO, ion has polymerised to form a six-membered flat ring of threeBO, triangles which may be looked upon as a resonance structurebetween (V) and (VI), with the former predominating, since theB-0 dista'nces are 1-38 A. in the ring and 1.33 A. outside it. TheXaZts of Oxygen Acids.-Micates.16 T. F. Gaskell, 2. Krist., 1937, 96, 203.17 F. A. Bannister, Min. Mag., 1932, 23, 188.18 Idem, {bid., p. 626; 2. Krist., 1937, 96, 201.G. A. Harcourt, Amer.Min., 1937, 22, 517; D. Lundqvist and A.Westgren, Arkiv Kemi, Min. Ceol., 1937, 12, B, No. 23; W. Biltz, J. Laar,P. Ehrlich, and K. Meisel, 2. anorg. Chem., 1937, 233, 257; W. S. Miller andA. J. King, 2. Krist., 1936, 94, 439.20 M . J. Buerger, Amer. Min., 1936, 21, 205.2 1 W. H. Zachariasen, J . Chem. Physics, 1937, 5, 919163 COX : CRYSTAL CHEMTSTRY.angle 0-B-0 in the ring is 1134". This resonating system bears amarked resemblance to certain organic structures such its the C3N3- 8 ?oHB\O/B\o -o/B\o~B\o-o/B\o OHB 0 + 0- I 1 + II -(*-(V.) VI.1 (VII.)ring in cyanuric chloride and should have high diamagneticanisotropy.22 Since NaBO, is isomorphous 23 with the potassiumsalt, its structure is presumably the same, and it seems doubtfulwhether the Raman spectrum of its solution, which is said24 toshow the presence of BO,- ions, has been correctly interpreted.N.ElliottZ5 has remeasured the G O and the N-0 distance incalcite and sodium nitrate and obtained the values 1 . 3 1 3 ~ . and1.210 A. respectively. Whereas the former is in good agreementwith the expected value, the predicted26 N-0 distance is 1 . 2 6 ~ .This discrepancy is attributed to a hitherto unrecognised effect,that of the resultant charge carried by an ittom on its covalentradim. It is pointed out that the progressive diminution in theradii of the neutral atoms carbon, nitrogen, oxygen, and fluorinemay be regarded as due to the inereatsing effective nuclear charge,and that in the nitrate ion (VII) the covalent radius of N+ shouldtherefore be smaller than that of N, and that of 0- larger than thatof the neutral atom.These two effects cancel approximately inthe case of the N+-0- bond, but the N+=O distance is estimatedt o be about 0.05 A. less than NZO (1.18 A.), with the result that thepredicted N-O distance for the actual structure of the nitrate ion[produced by resonance between the three possible forms of (VII)]is now in good accord with experiment.J. Beinterna 2' finds that although some per-rhenates andperiodates have the scheelite (CaWO,) structure, others (e.g.,CsReO,) have a very similar orthorhombic structure which it isproposed to call pseudo-scheelite. The scheme on p. 164 is suggestedto represent the effect of ionic size on the structure of RXO,compounds; tvit>h very small R and X ions, e.g., boron and22 Seep.185.23 S. Fang, J. Amer. Ceramic SOC., 1937, 20, 214; cf. S. 8. Cole, S. R.Scholes, and C. R. Amberg, ibid., p. 215.24 J. R. Nielsen and N. E. Ward, J . Chem. Physics, 1937, 5, 201.2 5 J . Amer. Chem. SOC., 1037, 59, 1380.26 L. 0. Brockway, J. Y . Beach, and L. Pauling, ibid., 1935, 57, 2693.27 8. Krist., 1937, 97, 300164 CRYSTALLOGRAPHY.aluminium phosphates, the structure approximates to that ofp-cristobalite. i Cssium osmiamatePseudo-scheeliteScheeliteMonazite Barytes ' Zircon Anh ydrit eAluminium phosphateWolframite ' Boron phosphateDiminishingradius of cationIt------+Diminishing radius of XThe significance for mineral chemistry generally of the tetrahedralco-ordination of silicon and aluminium is now fully recognised andthe classification of mineral structures on the basis of differentaggregations of SiO, and A10, tetrahedra has been one of theoutstanding achievements of modern crystallography. It is clear,however, that in principle any cation of small radius and largecharge may be able to co-ordinate oxygen tetrahedrally and thatin the most general classification of mineral types, ions such asP5*, Ass+, Ge4+, Ti4+, and Fe3+ should be regarded as capable ofplaying the same r81e as silicon, while Be, Mg, and Zn may takethe place of aluminium.An outstanding example of the co-ordinating power of a small highly charged cation is afforded bysilicon pyrophosphate,28 Si[P,07], in which (as in other cubicpyrophosphates) the phosphorus occupies a tetrahedral position,forcing the silicon into octahedral co-ordination, so that thestructure contains [P207] groups similar to the [Si,O,] groups inhemimorphite, thortveitite, Sc,Si,07, and gehlenite. It is interestingto note also that the close analogy between gehlenite, Ca,A1,Si07,and hardystonite, Ca,ZnSi,O,, is not due primarily to a commonsilicon-oxygen structure but to the possibility of zinc replacingaluminium in tetrahedral co-ordination.To take account of such cases as these, H.Strunz 29 has developeda system which constitutes a simplification of the more completeclassification of P. Niggli.30 The general formula of a mineral iswritten[RK* :Owl ( O,OH,F),]R~~VIA,,xH,Owhere RKom and RKpV1 are cations with co-ordination numbers 4and 6 respectively, and A is a cation with co-ordination number38 G.R. Levi and G. Peyronel, 2. Krist., 1936, 92, 190 ; G. Peyronol, ibid.,94, 311.29 Ibid., 1937, 98, 60; cf. H. Berman, Amer. Miiz., 1937, 23, 342.30 See Anm. Reports, 1933, 30, 387COX : CRYSTAL CHEMISTRY. 165greater than 6 (usually alkali or alkaline-earth ions). The squarebrackets enclose the whole of the complex electronegative part ofthe structure, the 0 before the vertical bar representing oxygenengaged in tetrahedral co-ordination and the (O,OH,F) followingit representing the anions not so engaged (" eingelagert " or" embedded " anions). Cations with co-ordination number 3 mustbe put inside the square bracketas.Six classes of minerals are thendistinguished :I. Framework structures. Examples : orthoclase, [Si,AlO,]K,and phenacite, [Be,SiO,]. Note that the latter does not contain acontinuous silicon-oxygen framework and would not be put in thiscategory in a classification based on SiO, and AIO, tetrahedraalone.[Si,AIO1,l (OH),]Al,K, and hemimorphite, [Zn,Si,O, (OH),]Ii,O.11. Layer structures. Examples : muscovite,111. Chain structures. Example : amphibole,IV. Group structures (RX, tetrahedra linked together to formfinite groups). Examples : barysilite, [Si,O,]Pb,, and wollastonite,[Si,O,]Ca, .V. Island structures (containing isolated RX, tetrahedra).Examples : olivine, [SiO,](Mg,Fe), ; titanite, [SiO,(O]TiCa ; andmany phosphates, arsenates, sulphates, etc.[Si,O,,l( OH)4]Al,(Mg,Fe),Cal,, which contains both [SiO,] and[Si,O,] groups.rsi*o,, I (OH),13%5Ca,.VI. Mixed structures.Example : vesuvianite,This primary classification is subdivided according as embeddedanions are present or not, etc.No great novelty appears to be associated with this scheme forthe systematisation of mineral structures when stated briefly asabove, and indeed, it does not bring about any change of outlookon the majority of silicate structures already investigated. At thepresent time, however, minerals of continually increasing complexityare the object of detailed study, and a classification such as that ofStrunz, in which the importance of cations other than silicon andaluminium in tetrahedral co-ordination is emphasised, should bevery helpful.Numerous phosphates and arsenates in particularhave been studied recently, and their relationships to correspondingsilicates demonstrated. The aluminium phosphate structure 31 isderived from that of cristobalite by replacement of silicon byaluminium and phosphorus, and in addition to the pyrophosphates31 F. Machetschki, Fortachr. Min., 1936, 20, 47166 CRYSTALLOGRAPHY.mentioned above, that of magnesium32 has been shown t o haveessentially the same structure as thortveitite, Sc,Si,O,. Aninteresting stereochemical point is that in these substances and inhemimorphite the Si-0-Si and P-0-P angles are 180", whereas inthe Si,O, groups in melilite the Si-0-Si angle is about 130°, whichis of the same order as the oxygen valency angle in per- andpyro-sulphates.The pyrophosphates furnished thefirst examples of shared PO4 tetrahedra ; another interesting caseis that of aluminium metaphosphate, Al(PO,),, the main structuralfeatures of which have been determined by L.Pauling and J.The lattice containsP4OI2 groups (Fig. 3) consisting of aring of four PO4 tetrahedra eachsharing two corners; the other twocorners of each PO4 tetrahedron areshared with AlO, octahedra.The relationships between silicates,phosphates, and arsenates is wellshown34 by the series andalusite,A1(A10)Si04 ; libethenite,Cu( CuOH)P04 ;olivenite, Cu(CuOH)As04 ; andadamine, Zn(ZnOH)As04. The struc-ture of the last mineral has now beenworked out in detail 35 and proves to be very similar indeed to thatof andalusite, containing the unusual five-co-ordinated trigonalbipyramid [Zn040H] corresponding with the AlO, group inandalusite.The shortest As-0 distance is 1 * 5 9 ~ . , and the maindifference from andalusite is the presence of hydroxyl bonds oflength 2-68 A. A point of some interest is that sdamine is probablyclosely related to higginsite Ca( CuOH)As04, descloisite(Pb,Zn)(PbOH)VO,, and particularly tilasite Ca[Mg(OH,F)]AsO,,which in turn appears 36 to have the structure of sphene Ca(TiO)SiO,.Since in this last mineral titanium has the usual octahedralco-ordination, a detailed study of the whole series would be usefulin elucidating the conditions which determine the change from5- to 6 - co-ordination .Although hydroxyl bonds undoubtedly pIay an important partas far as the energetics of crystals are concerned, their influencein the geometry of acid radical structures is frequently quite34 H.Strum, ibid., 1936, 94, 60.36 H. Strum, ibid., p. 7.Phosphates, arsenates, etc.FIG. 3.32 V. Caglioti, Atti V Congr. Naz. Chim., 1936, 1, 310.33 2. Krist., 1937, 96, 481.35 P. Kokkoros, ibid., 1937, 96, 417COX : CRYSTAL CEEMISTRY. 167small, since the length of the hydroxyl bond is very little differ-ent from the ordinary ionic 0-0 distance. Thus pharmacolite,C~[ASO,OH]~H,O,~~ and brushite, CU[PO,OH]~H,O,~~ have unitcells and presumably atomic arrangements very close to that ofgypsum, and similarly hamlinite, [P,O,OH] (A102H2)Sr, is nearlyrelated to alunite, [S,08](A10,H2)Sr.37* 39Studies of substituted apatites *O have shown that nearly all thephosphorus can be replaced by silicon and sulphur without anyessential change in structure, and have also led to the suggestionthat the carbon present in some apatites partly replaces phosphorusin tetrahedral co-ordination and partly occupies calcium positions ;in the latter case slight adjustment of the oxygen positions issupposed to take place so that CO, groups are formed.The generalformula for apatites should thus be written :Complex Ions and Co-ordination Compounds.-Of complex saltscontaining AX, groups (X = F, C1, CN, OH, H,O, NH,, NO,, etc.)over a hundred are known to possess cubic structures with abetween 10 and 11 A., in which the complex ions lie on a face-centred (Le., close-packed) lattice.Apart from the case of nickelphthalocyanine,4l one of these, [Zn(H,0)6]( Br0,),,42 is the onlycomplex compound to be analysed completely by Fourier methodsduring the period under review. The Zn(H,O)6 octahedron is verynearly regular, with Zn-H,O = 2.12 A., and the pyramidal bromateion is considerably smaller than previous measurements suggested,the distances being Br-0 = 1.54 A. and 0-0 = 2.43 A. In additionto the link to the zinc atom, each water molecule has two hydroxylbonds of 2.72 and 2.74 A. to oxygen atoms, the angle between thembeing 121". The general environment of the water molecules isthus very similar to that in various other salt hydrates (e.g.,CuS04,5H20).M.van Driel and H. J. Ver~eel,*~ assuming the dimensions ofthe nitrite group from sodium nitrite, have shown that in triplenitrites of the type A,[M(NO,),] and A,B[M(NO,),] the X-ray datarequire the NO, groups to be attached to the metal atom bynitrogen and not by the oxygen atoms as had been suggested37 B. Gossner, Portschr. Min., 1937, 21, 34; 2. Rrist., 1937, 96, 488.38 P. Terpstra, ibid., 9'7, 229.39 S. B. Hendricks, Arner. Min., 1937, 22, 773.40 D. McConnell, ibid., p. 977; J. W. Gruner and D. McConnell, 2. Krist.,41 See p. 187.43 S. H. Yu and C. A. Beevers, 2. Krist., 1936, 95, 426.43 Ibid., p. 308.1937, 97, 208168 CRYSTALLOGRAPHY.earlier. The Co-N distance in the cobaltinitrites is given as2 .0 3 ~ . Other compounds which prove to have the same generaltype of structure are several ferr~cyanides,~~ chloro- a-nd bromo-antim~niates,~~ ferrihexaflu~rides,~~ hypophosphite hexahydrates,[M(H,O),] (H2P0,)2,47 and magnesium chlorite hexahydrate,[Mg(H20)6](C102),.48 The lower symmetry of the anions in the lasttwo cases reduces the crystal symmetry from cubic to tetragonal,but without any essential change in structure type. All theantimony atoms in the lattice of A2[SbX6] (A = alkali metal,X = halogen) appear to be equivalent, so that the possibility ofalternate ter- and quinque-valent antimony in the structure is ruledout. The magnesium atoms in Mg(N0,),,4CO(NH2),,2H20 49 lie onsymmetry centres, so that if, as seems probable, the octahedralcomplex [Mg4(urea)2H20] is present, the water molecules in itoccupy trans-positions.Various quadricovalent derivatives of bivalent lead and tin,50cobalt and manganese 51 have been shown from considerations ofcell dimensions and symmetry to have planar configurations.Thestructure of the alkali pentabromodiplumbates, A P ~ , B I = , , ~ ~ is builtup of alkali and bromine ions together with PbBr, molecules, inwhich Pb-Br = 2.89 A. and the lead valencyEt \ /Br, /Et angle is 854'. I n dimeric diethylmonobromo-Et/ kBr/ gold (VIII), the planar distribution of auriccovalencies is confirmed; 53 the Br-Au-Brangle is approximately loo", and the Au-Brdistance 2.65 A. The relations between various double cyanideshave been further studied,54 but the suggested 55 planar configur-ation of [CdBr,] in Ba[CdRr4]4H,0 is rendered still more unlikelyby the results of an optical examination 56 of'the substance.Au Au(VIII.)44 R.Rigamonti, Guzzettu, 1937, 67, 137, 146; S. Fordham and J. J.45 K. A. Jensen, 2. anorg. Chem., 1937, 232, 193.4 0 W. Minder, 2. Krist., 1937, 98, 15.4 7 A. Ferrari and C. Colla, Gaxzetta, 1937, 67, 294. 48 Idem, ibid., p. 424.49 J. Y. Yee, R. 0. E. Davis, and S. E. Hendricks, J . Amer. Chem. Soc.,50 E. G. Cox, A. J. Shorter, and W. Wardlaw, Nature, 1937, 139, 71.5 1 E. G. Cox, A. J. Shorter, W. Wardlaw, and MT. J. R. Way, J., 1937,52 H. M. Powell and H. S. Tasker, ibid., p. 119.53 A. Burawoy, C. S. Gibson, G. C. Hampson, and H. M. Powell, ibid.,54 M. Brasseur and A.de Rassenfosse, Mkm. Acad. roy. Belg., 1937, 16, 1 ;55 Idem, ibid., p. 22.513 F. M. Quodling and D. P. Mellor, 2. Krist., 1937, 97, 522.Tyson, J . , 1937, 483.1937, 59, 570.1556.p. 1690.Bull. SOC. TOY. Sci. Libge, 1937, No. 1, 20RANDALL : THE STRUCTURE OF LIQUIDS AND AMORPHOUS SOLIDS. 169Other investigations 57 of complex compounds include severalof the heteropoly-acids 58 and a further study of phosphine andarsine derivatives of argentous and cuprous halides, 59 the mainfeatures of which were described last year .60E. G. C.3. TXE STRUCTURE OF LIQUIDS AND AMORPHOUS SOLIDS.During the last few years there has been a remarkable interestin liquids and amorphous solids, and it is significant of the changeof outlook that the tern1 " structure '' is now used without question.Not so very long ago it was usual to compare the liquid with thegas rather than the solid, but elementary considerations of density,the entirely different dependence of viscosity on temperature inthe two cases, and the evidence of X-ray diffraction experiments,have contributed to the fundamental change of outlook.It is the object of t'his section to consider the evidence of X-raydiffraction, and t o indicate how this method has helped in thegeneral development of facts and ideas concerning liquids andamorphous solids.A detailed account of this aspect of the subjecthas been given comparatively recently in book form; moregeneral discussion of the liquid state is to be found in a recentvolume of Faraday Society Discussions,2 and in another section ofthese report^.^The comparatively fixed positions of atoms or molecules incrystalline solids give rise to the familiar sharp diffraction spectra.In a gas, however, in which the atoms or molecules are far apartcompared with the wave-length of X-rays, the intensity of thescattered coherent beam a t any given angle depends only on thescattering unit and the number of atoms; the question of the' arrangement ' of the atoms with respect to one another does notarise.The intensity of scattering by a monatomic gas such asargon is given by the expression kP . N .fe2, where P is equal to(1 + ~0~228)/2, 28 being the scattering angle, and f e is the ratio ofthe amplitude of the wave scattered by a single atom to thatscattered by a single electron; fe is in fact the well-known structure5 7 H.A. Klasens and P. Terpstra, Rec. traw. chim., 1937, 56, 673; J. A. A.Kctelaar, Physica, 1937, 4, 619; A. F. Wells, 2. Krist., 1937, 96, 433.5 8 0. Kraus, Nutumuiss., 1937, 25, 250; 2. K r i s t . , 1936, 94, 256; J. H.Sturdivant, J . Amer. Chem. SOC., 1937, 59, 630; J. S. Anderson, Nature,1937, 140, 850.513 F. G. Mann, A. F. Wells, and D. Purdie, J., 1937, 1828.Go Arm. Reports, 1936, 33, 167; A. F. Wells, 2. Krist., 1936, 94, 447.1 J. T. Randall, " The Diffraction of X-Rays and Electrons by AmorphousSolids, Liquids, and Gases," London, Chapman and Hall, 1934.2 Trans. Paraday SOL, 1937, 33, 1. 3 seep. 75170 CRYSTALLOGRAPHY.amplitude of X-ray crystallography, which arises because of thefinite size of the atom and consequent interference effects withinit; k involves fundamental physical constants and those of theapparatus. In a liquid, even a monatomic liquid such as an alkalimetal, the density is such that the atoms are only, on the average,a little farther apart than in the solid.X-Rays scattered by oneatom will interfere with those scattered by its nearest neighbours.The neighbours are constant neither in number nor distance, andany effects observed when X-rays are scattered by liquids are aresult of the average distribution of atoms around any other. Theliquid is to be regarded as homogeneous in that the averagedistribution is independent of any atom we may choose. It is theobject of X-ray analysis to try to give more precise informationconcerning this distribution.The form of the expression for the scattering of X-rays by aliquid can most easily be seen by consideration of the scattering bya more and more complicated single molecule.The expressions inthe simpler cases are precisely those for gaseous molecules. If thesingle molecule is increased enormously in size, the scattering is thatof any piece of matter in which distances from atom to atom areknown. P. Debye was the first to develop the expression in thisway.4 He showed that if there were two kinds of atom p and q,the scattering intensity for X-rays of wave-length A would be givenI - PCZfpfq sinsrpq/wpq . . . . (1)byP 4where fp and fs are the structure amplitudes for the two types ofatom, rpq is the distance between atoms p and q, s = 41~0/1, and Phas the same meaning as before.Those familiar with this type ofexpression will realise that it reduces in simple cases to the fornmlzfor single molecules. For molecules containing one kind of atomI - Pnf2X sinsrn/srn . . . . . ( 2 ) O d YnWhere the interatomic distances are unknown, it is necessary tointroduce the idea of the average distribution of scattering matteraround any given atom ; 4xr2g(r)dr represents the number of atomslying between spheres of radii r, r + dr, surrounding any atom, andg ( r ) is called the distribution function. If we consider the case ofa monatoniic liquid, expression (2) can be transformed intoI - Pnf2Z sin synlsrn .g(r)dr . . . . (3)nAnn. Physik, 1915, 46, 809RANDALL : THE STRUCTURE OF LIQUIDS AND AMOSPHOUS SOLIDS. 171The more familiar form of this equation isI = kPnf2(l + 4m2[g(r) - p] . sin srjsr . dr ] . (4) idawhere p now represents the average density of the liquid in atomsper C.C. F. Zernike and J. A. Prins were the first to develop thisform of the expression, apparently without realising that it wasimplicit in Debye’s much earlier equation (2). As Debye did notapply this equation to the structure of single molecules for someyears,6 it seems probable that he did not realise its great importance.By the use of Fourier’s integral theorem,’ it is possible to putexpression (4) into a much more useful form, in which the distributionfunction is removed from under the integral sign, and replaced byan expression depending on the observed intensity of scattering.By puttingit can be shown that( V P -f2)/f2 == +(s)4nr2g(r) = 4nr2p + 2r/7t.lorn s$(s) . sin rs . ds . (5)The development of (4) and ( 5 ) has been set out in some detai1,sas it is on these that all quantitative estimates of the atomic ormolecular distributions within liquids and amorphous solids havebeen made.The practical importance of ( 5 ) over (4) is obvious, for it allowsus to deduce g(r) from observed intensities. To apply (4) to apractical case requires the insertion of inspired guesses at probableforms of g(r), and the working out of a laborious integral before i tis known whether g(r) is of the correct form.These equations asthey stand may be applied only to monatomic liquids, or to liquidsin which there are two equivalent scattering units, as in potassiumchloride; or where one unit scatters negligibly compared with theother, e.g., the hydrogen of water or hydrogen peroxide. There isno reason, however, why the equation cannot be used for molecularliquids in a limited way. For example, the application of theequation to sulphuric acid implies that the g(r) now refers to thedistribution of molecules, and the f 2 of equation (4) musk now bereplaced by the scattering function for the single molecule-in thiscase effectivelyfS2 + 4fO2 + 12jO2 sin sr/sr + 8fsf0 sin sl/sZ2. Physik, 1927, 41, 184.6 P. Debyo, L. Bewilogua, and F. Ehrhardt, Ber. Verhandl.Sachs. Akad.7 H . Bateman, “ Partial Differential Equations of Mathematical Physics,”* See ref. (10); also J. T. Randall, Proc. Rag. SOC., 1937, A , 159, 83.Wiss., 1929, 81, 29.p. 206, Cambridge University Press, 1932.Idem, Nature, 1936, 138, 842172 CRYSTALLOGRAPHY.where thef’s have obvious meaning, and r is the distance betweenoxygens, and I the distance from oxygen to sulphur. I n otherwords, it is necessary that the structure of the single moleculeshould be known before the general case of a complex liquid canbe solved from X-ray measurements. Knowledge of this kindfrequently exists from investigations of the solid or the vapour.Accurate results can only be obtained from (5) if greah care is takento obtain reliable values of the scattering a t large angles, and forthis either a hydrogen camera or a vacuum camera together withstrictly monochromatic radiation is advisable.Equations (4) and( 5 ) may also be applied to amorphous solids, such as glasses; thereis of course no restriction with regard to crystalline solids. B. E.Warren and N. S. Gingrich lo have, in fact, applied these equationsto the analysis of complicated powder photographs ; although theprocess is extremely laborious, it is obviously a possible methodwhere single crystals cannot be obtained. With regard toamorphous solids, it is clear that g(r) will give a space average ofthe distribution of atoms around a given one, whereas, in the caseof liquids, the g( r ) derived from the experimental intensity curvesis a time as well as a space average.Much of the earlier inspiration concerning both liquids andamorphous solids was derived from the work of G.W. Stewart,llwho was the first to show the general similarity between the X-raypatterns for liquids and the corresponding solids. Although suchsimilarity by no means always exists, the idea gradually grew upthat there was a tendency for the liquid to imitate the solid ingeneral atomic or molecular arrangement. I n a long series ofpapers, Stewart had developed the idea of cybotaxis, or theexistence of groups of molecules in the liquid. Stewart confinedhis attention to organic molecules, where the anisotropy predisposesthe molecules to some sort of arrangement over small elements ofvolume. This anisotropy on an exaggerated scale is responsible forthe unusual stages apparent between true solid and liquid which isobserved with liquid crystals.l2. l3 It is easy to see such tendencyto arrangement of molecules by the use of two-dimensional modelsof, e.g., grass seeds or small rods.Such two-dimensional modelsare in fact highly instructive, and not nearly so trivial as mightappear. They were first introduced by J. A. Prins,l4 who madethe important observation that the g(r) function was of a very10 PhysicaZ Rev., 1934, [ii], 46, 368.l1 Rev. Mod. Physics, 1930, 2, 116; Physical Rev., 1931, [ii], 37, 9.l2 See op. cit., ref. (l), pp. 251-261.13 J. T. Randall, Trans. Faraday SOC., 1933, 29; Discussion on Liquidl4 Naturwiss., 1931, 19, 435.CrystalsRANDALL : THE STRUCTURE OF LIQUIDS AND AMORPHOUS SOLIDS.173similar type for two-dimensional models and for actual liquids.W. E. Morrell and J. H. Hildebrand l5 have extended this work tothe study of three-dimensional models. By the use of gelatin ballssuspended in a gelatin sol of the same density, they have shown,from thousands of photographs taken simultaneously in pairs a tright angles, that the distribution function for such balls is verymuch the same as t'hat proposed by Prins for liquid mercury.16The use of two-dimensional models has also enabled J. D. Bernal 17to work out a very suggestive theory, which will be referred to below.Meanwhile reference must be made to a number of otherimportant investigations. The work of J.D. Bernal and R. H.Fowler l8 on the structure of water, and its applications to certainfeatures of ions in solution, is now well known; it is only necessaryto add that equation (4) was used to obtain the approximatetetrahedral distribution of water molecules around a given one.The liquid alkali metals were shown l9 to give a remarkably sharpmaximum in the intensity curve, and this was interpreted as asimilarity between the co-ordination grouping of liquid and solid.Further examination of liquid sodium 2* in greater detail confirmsthis view. Liquid lead and bismuth appear to give identicaldiffraction patterns, and the quantum theory of metals suggeststhat this should be so.21 K. Lark-Horovitz and E. P. Miller 22 havestudied liquid potassium and lithium chlorides by the method ofFourier analysis.They conclude that the number of nearestneighbours in the former liquid is less than in the solid, but it mayreasonably be questioned whether the method yet allows of suchclose distinctions. It is very important from many points of viewthat the method of Fourier analysis outlined in this summary shouldbe used in the investigation of some simple close-packed liquid atdifferent temperatures. Practically no liquid other than water 23has yet been studied in this way.In the field of amorphous solids, the carbonaceous materials suchas soot and cokes, coal, and graphitic acid complexes have receivedsome attention.24 In particular, amorphous carbon has beenexamined by B. E. Warren by the method of Fourier analysis.251 5 J .Chem. Physics, 1936, 4, 224.1 7 Trans. Paraduy SOC., 1937, 33, 27.1 8 J . Chem. Physics, 1933, 1, 515.l9 J. T. Randall and H. P. Rooksby, Nature, 1932, 130, 473.20 L. P. Tarasov and B. E. Warren, J . Chem. Physics, 1936, 4, 236.21 J. T. Randall and H. P. Rooksby, Trans. Paraduy Soc., 1937, 33, 109.22 Physical Rev., 1936, [GI, 49, 418.2 3 H. H. Meyer, Ann. Physik, 1930, [v], 5, 701.24 Op. cit., ref. (l), pp. 188-197.25 13. E. Warren, J . Chem. Physics, 1934, 2, 551.l6 2. Physik, 1929, 56, 617174 CEY STALLOGRAPHY.The apparent differences between some of the forms of phosphorushave been shown to arise from differences in size of crystallites.26Perhaps the more interesting work, however, has been confined toglasses.All true glasses give broad diffraction bands in theirX-ray patterns, and are entirely similar to liquids in this respect.Superposed lines, such as had been observed by R. W. G. Wyckoffand G. W. Mcrey27 are due to devitrification products. It wasfirst shown by J. T. Randall, H. P. Rooksby, and B. S. Cooper 28that the X-ray patterns of simple vitreous oxides and silicates boreobvious similarities to the patterns of the crystalline forms, andthis work was later extended to other vitreous compounds.29 Theconclusion reached at the time, wix., that the glass was composed ofminute crystallites, possibly of slightly differing lattice constants,would in the light of later work receive rather a different inter-pretation. It is unlikely that the regularity of arrangement arounda8ny given atom extends beyond the first and second co-ordinationspheres. Moreover, a glass is not usually in equilibrium, and itappears probable that the positions and the numbers of neighbourswill vary slightly from point to point.The X-rays can only measurethe average effect, and it appears from later Fourier analysis workthat the average effect is usually the same as that in thecorresponding crystal. B. E. Warren and his collaborators 30 haveexamined a number of glasses in this way, in particular, vitreoussilica and germania, boric oxide, and a series of soda glasses. W. H.Zachariasen3l was the first to postulate the extended networkidea, in which the arrangement is never completely regular, andthe unit cell has infinite dimensions.That considerable groups ofatoms must exist as such is suggested by the high viscosity of theglass, but the irregularity of these groups is borne out by the longmelting range of most glasses.The striking feature about liquids and amorphous solids at thepresent time is not so much any new experimental work as thegeneral tendency towards clarification of ideas and development ofnew ones. This is most clearly shown in Bernal's work,17 togetherwith his recent contribution to a Royal Society discussion.32 He26 See op. cit., ref. ( l ) , p. 198.27 J . SOC. Glass Tech., 1925, 9, 256.2* Nature, 1930, 125, 458; J . SOC. Glass Tech., 1930, 14, 219; 2. Krist.,1930, 75, 196.20 J. T. Randall and H. P. Rooksby, Glass, 1931, 8, 234; J .SOC. GlassTech., 1933, 17, 287.30 2. Krist., 1933, 86, 349; B. E. Warren and A. D. Loring, J . Arner.Ceramic SOC., 1935, 18, 269; B. E. Warren, H. Krutter, and 0. Morningstar,ibid., 1936, 19, 202.31 J . Arner. Chem. SOC., 1932, 54, 3841 ; Physical Rev., 1932, 39, 185.32 Proc. Roy. SOC., 1937, A, 163, 320RANDALL : THE STRUCTURE OF LIQUIDS AND AMORPHOUS SOLIDS. 175has shown that a much deeper physical meaning may be attachedto a closer study of distribution functions. This function, eitherfor a two-dimensional model or for a liquid, takes the form of anumber of peaks when plotted againstl r, and the first peak occursa t some small value of r representing the nearest avera.ge approachof surrounding atoms or molecules.The first peak is of outstandingintensity, the subsequent ones gradually diminishing until theyultimately coincide with the mean density line. Each peak ineffect corresponds to a co-ordination sphere, and Bernal hasamplified and extended Prins's notion s3 of artificially splitting upg(r) into a number of functions so thatg(r> = g1+ g2 + g3 + gk + - *each gk corresponding to the kth co-ordination sphere for thecorresponding solid. The approximation to a liquid was finallyobtained by blurring out these sharp peaks by means of an errorfunction. Bernal goes more deeply into the matter by showingthat we may represent the distribution function as one dependingon three variables, the mean distance of closest approach, rl, ofneighbours to a given atom, the number N of close neighbours ofany given molecule, and the irregularity h of their distribution.Thus the greater the irregularity h, the further does the value of Ndepart from the ideal, which is the co-ordination number for thesolid, The development of these ideas leads to the expression forgl(r) of the forme-(T- ~ I W I A ' gdr) = 4 3 - F- *, *where r is the actual distance of the points from the central one.This case may be extended to the more general one of the sum ofthe individual distribution funct!ions, purely from geometricalconsiderations.More precise physical meaning is then obtained bya consideration of the free energy based on the relationF = U - XT + 3kcTlog (hv/IcT)and the €act that U is of the form am/rm + unlrn.The furtherassumption that the entropy is bound, from fundamental con-siderations, to depend on the irregularity h leads to extremelyinteresting conclusions concerning the specific heat of a liquid. Itis apparent from the analysis that Cp consists of three parts andmay be writtenwhere C N and C;, correspond to any changes in energy broughtabout by changes in co-ordination and irregularity, and Cc is the33 J. A. Prins and H. Petersen, Physica, 1936, 3, 147.cp = C N + CA + c176 CRYSTALLOGRAPHY.specific heat of the crystal. For the first time we have the idea ofa configurational specific heat; energy may be absorbed, not forproducing further degrees of freedom, but in changing potentialenergy. In this way it is possible to explain qualitatively thedeviations of the specific heats of liquids from the Dulong andPetit value.The sharpness of transition from crystal to liquid receivedinteresting confirmation from a study of the distribution of circlesaround a given one.In liquid metals, where the interatomic forcesvary comparatively slowly with distance, the co-ordination N willbe high and approximately the same as in the solid; in the liquidrare gases, on the other hand, co-ordination will be low andirregularity 1 will be high. Where low values of co-ordinationnumber exist and the forces vary rapidly with distance, there is notlikely to be such a sharp distinction between liquid and solid, andthe question of the precise nature of liquid helium-I1 is of someinterest.W. H. Keesom and K. W. Taconis 3* have shown thatboth liquid helium-I and liquid helium-I1 give rise to diffuse X-raypatterns. The band for helium-I1 is, however, more diffuse thanthat of I , which may mean a lower co-ordination.35 The viscosityof a liquid on Bernal’s ideas is related to the rate of change ofmutual configuration of the molecules .32 The variation of viscositywith pressure a t a given temperature is empirically represented insome cases by Batchinsky’s relation q = C/(v - vo); if q, is putequal to the volume of the solid, w - vo is then the extra volumetaken up by the molecules in the liquid.The idea of a free volume common to all the molecules in theliquid in virtue of their motion, together with the ideas of “ holes ”in liquids of the order of size of molecular dimensions has beenreintroduced with much effect by Eyring and ~ollaborators.3~ Bymeans of arguments based on statistical mechanics, features of theviscosity relations for liquids, the law of rectilinear diametersrelating to the densities of the liquid and vapour phases, and otherproperties have received interesting interpretations which have beensummarised elsewhere in this v01ume.~J.T. R.4. MOLECULAR CRYSTALS.Progress in the study of crystal structures of molecular substancesmarches parallel with, and is to a large extent responsible for,increasing precision of ideas on the various questions arising out ofthe nature of both intra- and inter-molecular forces. As regards34 Physica, 1937, 4, 28.36 See this vol., p. 81.35 See also P.Kapitza, Nature, 1938,141, 74COX : MOLECULAR CRYSTALS. 177the former, valuable work has been done during the past year inobtaining a more satisfactory theoretical basis for dealing withthose molecules in which ‘‘ resonance ” occurs.has established a convention whereby it is possible to calculate byquantum-mechanical methods a quantity known as the “ order ”of a bond, replacing the empirical “double bond character” ofL. 0. Brockway, J. Y. Beach, and L. Pauling.2 The bond energiesand bond lengths can be obtained by interpolation when the orderis known, and the predicted bond lengths in naphthalene and @herhydrocarbons are in good agreement with the experimental work ofJ. M. Robertson and with calculations by J.E. Lennard-Jones3using a different method. L. Pauling and L. 0. Brockway,4 as aresult of an extended study of many hydrocarbons, have revisedthe value of the C-C distance to 1.34 A., so the percentage reductionson the single-bond radius for double and triple bonds now become13% and 22% respectively. These figures differ only very slightlyfrom those previously adopted by N. V. Sidgwi~k.~ Quantum-mechanical treatment has also been applied in a satisfactory mannerto the diamagnetic anisotropy of organic molecules.6With regard to intermolecular forces, preliminary results 7suggest that in the substitution of deuterium for hydrogen lies apowerful method for studying hydrogen bonds in more detail.While the hydroxyl bond (as in ice or resorcinol 9, has been shownto be practically unchanged by this substitution, it is found thatthe lattice of oxalic acid dihydrate expands markedly along thedirection of the hydrogen bonds when the latter become deuteriumbonds.The increase in length may be as much as 0.04 A. Apartfrom the purely theoretical aspects (which a t present appear to besomewhat involved) of this effect, its existence provides a means ofdetecting the occurrence of hydrogen bonds in a structure withoutthe necessity of detailed analysis, and, in favourable cases, ofdetermining their orientation. It may be added that the differencebetween hydrogen and hydroxyl bonds in this matter affordsfurther justification for maintaining a fairly sharp distinctionbetween the two, contrary to the views of various Americanwriters.W. G.PenneyProc. Roy. SOC., 1937, A , 158, 306.J . Amer. Chem. SOC., 1935, 57, 2693.Proc. Roy. SOC., 1937, A , 158, 280; J. E. Lennard-Jones and J.Turkevich, ibid., p. 297.4 J . Amer. Chem. SOC., 1937, 59, 1223.7 J. M. Robertson and A. R. Ubbelohde, Nature, 1937, 139, 504.8 (Miss) H. D. Megaw, ibid., 1934, 134, 900.9 A. R. Ubbelohde and J. M. Robertson, ibid., 1937, 140, 239.“ The Covalent Link in Chemistry,” 1933, p. 82. 6 See p. 185178 CRYSTALLOGRAPHY.Last year the Erst absolutely direct analysis of an organicmolecule was reported,lO that of phthalocyanine by J. M. Robertson.Similarly a very much simpler molecule, pentaerythritol, has duringOhe current year been analysed completely l1 without making useof chemical evidence. There is no doubt; that cases of this sort willmultiply within the next year or so, and although in general theresults of organic chemistry are sufficiently well established as notto need such independent confirmation, these tendencies are ofgreat importance in indicat,ing that the time is near whencrystallographic technique will successfully be applied to thedetailed analysis of substances whose structures have so far notproved amenable to treatment by the older methods.Excellent accounts of the more technical aspects of thedetermination of molecular structures by X-rays are given byJ.M. Robertson l2 and by H. Mark and F. Schossberger.13SirnpZe Molecular Compounds.-Although the bromine moleculeapproximates in size more nearly to that of chlorine than of iodine,yet it proves to be isomorphous with iodine at - 15Oo.l4 Owingto experimental dSculties, the Br-Br distance, 2.27 A., is subjectto a probable error of about & 0.1 A., but is in excellent agreementwith other data.The Br . . . Br distance between molecules is 3.3 A.Monoclinic (p-) sulphur has been examined by J. T. Burwell; 15there are 48 atoms in the unit cell, and if the existence of S,molecules is assumed, two of them at least must be centro-symmetrical. As this is inconsistent with the accepted structurefor the s8 molecule,16 it is supposed that the central symmetry isattained by oscillation of the molecules in the lattice. Asmonoclinic sulphur is stable only over a few degrees below themelting point, this is a plausible hypothesis; nevertheless, it isremarkable that increasing temperature should destroy the two-foldaxis which exists in the molecule of rhombic sulphur and replace itby a time-averaged centre of symmetry.Further light may bethrown on the sulphur problem by the study of the compoundsRI3,3f& (R = CH, P, As, Sb), preliminary data for which arerecorded by C. D. West.17The rhombohedra1 (C,i or C,) symmetry of the p-form of icereported last year l8 is now confirmed; l9 it is found to have cell10 Ann. Reports, 1936, 33, 214.la Physical SOC. Reports, 1937, 4, 332; see also Science Progress, 1937,18 Ergebn. exalct. Naturwiss., 1937, 16, 183.14 B. Vonnegut and B. E. Warren, J . Amer.Chem. SOC., 1936, 58, 2459.l5 2. Krist., 1937, 9 7 , 123.1' 2. Krist., 1937, 96, 459.l1 Seep. 181.32, 346.l6 Ann. Reports, 1935, 32, 225.Ann. Reports, 1936, 33, 217.N. J. Seljakov, Compt. rend. Acacl. Sci. U.R.S.S., 1937, 14, 183COX : MOLECULAR CRYSTALS. 179dimensions practically the same as those of ordinary (a-) ice, intowhich it is converted by pressure or grinding. I n agreement withearlier work,18 solid hydrogen sulphide is reported 20 to undergotwo transitions due to molecular rotation, at - 147" and - 170".The departure from cubic symmetry in the lower forms can onlybe very slight.21 S. C. Sirkar and J. Gupta22 have proposed astructure similar to that of fluorite; this involves a S-H distanceof 2.5 A. and a H-S-H angle of log", which is much larger than thevalue (92") deduced from infra-red spectra.23 Although a similarchange of valency angle occurs in ice, there can scarcely be anyanalogy between the two cases, as the tendency of sulphur to formhydrogen bridges must be exceedingly small.It has long been known that sulphur trioxide exists in at leasttwo crystalline phases, an ice-like form melting at about 17"(considered by A.Smits to be the stable modification and designated7 by him) and an asbestos-like p-form melting a t about 31". Fromstudies of dielectric constants 24 and Raman spectra 25 it is nowsuggested that the y-form contains trimeric molecules, possiblyhaving the form (I), whereas the p-form consists of endless chains(11) forming a structure resembling that of chromic anhydride.Itis to be hoped that in spite of experimental difficulties (one ofwhich is the effect of X-rays in bringing about the metastable --+stable transformation) more definite evidence on the structures ofthe various forms of crystalline sulphur trioxide will be forthcoming ;-0-80, --o--so,--o- .(11.)on the one hand, some analogies might be expected wit8h thestructure of solid oxygen, whose molecules, known to be 0,, havepresumably the same configuration as the monomeric trioxide,while on the other hand, in view of the resemblance 2G between thepolymerisation of the trioxide and that of aldehydes, it is of interestthat the proposed ring structure (I) is essentially the same as thoseof trioxymethylene and trithioformaldehyde .2720 A.Kruis and K. Clausius, Physikal. Z., 1937, 38, 510.2l E. Justi and H. Nitka, ibid., p. 514.22 Indian J . Physics, 1937, 11, 119.23 €3. L. Cramford and P. C. Cross, J . Chem. Physics, 1937, 5, 371.24 A, Smits and N. F. Moerman, Rec. trav. chim., 1937, 56, 169.25 H. Gerding and N. F. Moerman, 2. physikal. Chem., 1937, B, 35, 216.2 6 S00, e.g., G. Odd0 and A. Sconza, Gazzetta, 1927, 57, 83. 27 See p. 183180 CRYSTALLOGRAFHY.It is remarkable that the crystalline structures of the carbontetrahalides are still somewhat uncertain. C. Finbak and 0.Hassel28 now find that a t room temperature the tetraiodide is notcubic, as was formerly supposed, but is probably isomorphous withthe monoclinic low-temperature modification of the tetrabromide,for which revised cell dimensions are given.The reason for thelow symmetry of these simple compounds is not clear. Thiophos-phoryl bromide, PSBr,, is reported29 to have a cubic structuresimilar to that of stannic iodide; exact parameters were notdetermined.Electron-diffraction studies 30 show that the molecular structuresof arsenious and phosphorous oxides are essentially the same as thatdeduced for the former from early X-ray measurements; 31 theoxygen valency angle in arsenious oxide, however, appears to beconsiderably larger (probably about 140") than that previouslyassigned, and a redetermination of the atomic parameters in thecubic variety (and in senarmontite, Sb,O,) would be valuable.These results confirm that the phosphorus valency angle is about100"; in phosphorous oxide the 0-P-0 angle is 98" (cf.102" inblack phosph~rus,~~ 101" in phosphorus trichloride 33 and 104" inphosphoryl The P-0 dist'ance is 1-67 A. which is lessthan the sum of' the bond radii (1.76 A.) ; a similar contraction hasbeen found for the phosphorus halides. Phosphoric oxide, P,O1,,is less symmetrical, but appears to have approximately the structureshown in Fig. 4; this is derived from that of t'he lower oxide bythe attachment of an additional oxygen to each phosphorus, whichis thus surrounded by four oxygen atoms in a distorted tetrahedron.It is noteworthy that discrete molecules no longer exist in thestructure of the high-temperature form of antimonous oxide(valentinite) .34Aliphatic Compounds.-Very few complete structure determin-ations have been made during the past year.The earlier atomicparameters 35 given for glycine were almost certainly incorrect, and28 2. physikal. Chem., 1937, B, 36, 301; see also H. A. Levy and L. 0.Brockway, J . Amer. Chem. Soc., 1937, 59, 1662.29 I. Nitta and K. Suenaga, Sci. Papers Inst. Phys. Chem. Res, Tokyo,1937, 31, 121; A. E. van Arkel and F. J. Lebbink, Rec. trav. chim., 1937,56, 208.30 I,. R. Maxwell, S. B. Hendricks, and (Miss) L. S. Deming, J . Chew$.Physics, 1937, 5, 626.31 R. M. Bozorth, J . Amer. Chem. Xoc., 1923, 45, 1621.32 Ann. Reports, 1935, 32, 226.33 L. 0. Brockway, Rev. Mod. Physi~s, 1936, 8, 231; H. Braune and p.34 Seep. 160.35 J. Hengstenberg and F. V.Lenel, 2. Krist., 1931, 77, 424.Pinnow, 2. physikal. Chem., 1937, B, 35, 239COX : MOLECULAR CRYSTALS. 181revised values, said to be in better accord with X-ray intensities,have now been proposed ; 36 these lead to bond lengths C-C = 1-47,G N = 1-40, and G O = 1-39 A., all of which are less than the sumof the single-bond radii. It is possible to visualise 37 a system ofhydroxyl (or “ amino ”) bond chains throughout the structure ofcrystalline glycine which would increase its stability and reduceinteratomic distances, somewhat as in the case of oxalicalthough not in so marked a manner ; the above bond distances, iffully confirmed, are thus of very great importance in the develop-ment of the study of hydrogen bridge problems.FIG. 4.Another structure in which hydroxyl bonds play an importantp a t is that of pentaerythritol, C(CH,*OH),, the structure of whichhas been completely determined from Harker and ordinary Fouriersyntheses by F.J. Llewellyn, E. G . Cox, and T. H. Goodwin.39This substance was the cent,re of acute controversy40 some yearsago on account of the supposed possibility of a pyramidaldisposition of the valency bonds around the central carbon atom;although this controversy has long since been decided, on generalgrounds, in favour of the usual tetrahedral configuration, it is ofinterest that the carbon valency angles all prove to be exactlytetrahedral within the limits of experimental error (2” or less),The principal bond distances are C-C = 1-50 and G O = 1-46 A.,both h0.03 A,, so the former distance is definitely less than the36 A.Kitaigorodski, Acta Physicochim. U.R.X.X., 1936, 5, 749.37 M. L. Huggins, J . Org. Chem., 1936, 1, 407; Nature, 1937, 139, 550.38 Ann. Reports, 1936, 33, 218.40 See, e.g., ” Strukturbericht,” 1, 643; Ann. Reports, 1929, 26, 74, 304.39 J . , 1937, 883182 CRYSTALLOGRAPHY.accepted value (1.54~.), while the latter is in accordance withexpectation. It is not clear why the C-C distance should be short,since there can scarcely be any question of double-bond characterin such a substance; on the other hand, very few accuratemeasurements on aliphatic compounds are available for comparisonof a direct kind, while a similarly low value (1.52 A.) is reported forpentaerythritol tetra-a~etate.~~ The molecules of pentaerythritolare held together by a system of hydroxyl bonds remarkablysimilar to that in resorcinol,42 the chief difference being that in thelatter case the bonds form fom-sided spirals, whereas in the formerFIG.5.they extend in two dimensions only, forming closed squares, so thatthe crystals have a layered structure (Fig. 5). The length of thebonds is 2.69 A. This close similarity between the hydroxyl bondsin a phenol and a primary alcohol justifies the assumption that thehydroxyl bond is essentially the same whether in alcohols, sugars,or phenols, so it becomes possible in investigating a substance ofany of these types to eliminate from consideration all moleculararrangements except those in which each hydroxyl group is linkedto two others at a distance of 2.7 A. ; this restriction is of particularvalue in alcohols and sugars where no assistance can be derived41 T.H. Goodwin and R. Hardy, Proc. Roy. Xoc., 1938, A , 164, 369.42 Ann. Reports, 1936, 33, 221183 COX : MOLECULAR CRYSTALS.from optical or magnetic data. Naturally there will be a fewexceptional cases where steric considerations make the applicationof this criterion impossible.A preliminary report 43 has been made of an investigationleading to a structure for pentaerythritol in which the moleculesare differently oriented and have bond distances G-C = 1.57 A.and G O = 1.46 A. Further details will be awaited with interest,but the hydroxyl bond length (2.55 A.) which is involved is almostcertainly too short.A third independent analysis by E. W.Hughes44 is substantially in agreement with that of Llewellyn,Cox, and Goodwin.The molecules of trio~ymethylene,4~ (CH,O),, and trithioform-aldehydeP6 ( CH2S)3, are very similar, both containing Sachsetrans-rings consisting of three carbon atoms alternating with threeoxygen (or sulphur) atoms, but whereas the former has trigonalsymmetry, the latter has only a plane of symmetry, buildingorthorhombic crystals. The bond distances are G O = 1.42&0.03 A.and C-S = l.Sl&O*OS A,, and the valency angles are tetrahedralwithin the (rather wide) limits of error. The intermoleculardistances in trithioformaldehyde me all about 3-6 A., and intrioxymethylene the CH, . . . 0 distance is 3.04 A.More detailedanalysis of these interesting substances is highly desirable, sinceexact knowledge of valency angles would be valuable from severalpoints of view.F. Francis, F. J. E. Collins, and S. H. Piper47 have madeavailable more precise X-ray spacings and other data for manyn-fatty acids and their derivatives which are of considerable valuefor identification purposes in view of the frequent occurrence ofsuch substances in Nature. In addition, since the members of thisseries are more numerous and more readily obtained in a purecondition than those of any other type of long-chain compound,they are particularly suitable for studying the relations betweenchain length and physical properties. The glycerides furnishanother example of substances where accurate X-ray and thermaldata48 are not only essential for determinative purposes, but arelikely to lead to interesting views on the structure of branched-chainmolecules ; structural changes shown by the polymorphic trans-formations of di- and tri-glycerides, for example, may well prove toinvolve changes in molecular configuration as well as in the43 I.Nitta and T. Watanab6, Nature, 1937, 140, 365.44 Private communication.45 N. F. Moerman, Rec. trau. chim., 1937, 56, 661.46 N. F. Moerman and E. H. Wiebenga, 2. Krist., 1937,9'7, 323.47 Proc. Roy. SOC., 1937, A , 158, 691.48 T. M a w , M. R. el Shurbagy, and M. L. Meam, J., 1937, 1409184 CRYSTALLOGRAPHY.distribution of intermolecular forces, in contrast with simplerunbranched chains where the molecules retain a constant formthroughout the range of polymorphic transformati~n.~~ Thechanges which occur in the X-ray spectra of long-chain compoundsnear the melting point have been attributed to partial or completerotation of the molecules about their long axes, and further supportfor this view has been obtained from dielectric-constant measure-ments; 5o the results of A.Muller 51 for two symmetrical ketonesare particularly unambiguous, and show that rapid diminution ofthe directional forces between molecules sets in a t about 15" belowthe melting point so that from that temperature upwards themolecular dipoles are able to orient themselves in the electric field,Ketones are particularly suitable for this work, since the carbonylgroup provides the necessary polarity to show up the molecularrotation in the electric field, and a t the same time it is sufficientlysmall not to make the structure appreciably different from that ofa simple hydrocarbon, for which therefore the results are also valid.With regard to the forces between the terminal groups in fattyacids, which are generally held to be responsible for the inclinationof the molecules to the basal plane, it has been suggested 52 thatoxonium bonds are operative, but it is difficult to see whatadvantages this hypothesis possesses over the accepted ideas ofassociation between carboxyl groups.Among miscellaneous compounds studied, W.H. Taylor 53 hasdetermined the space-groilp and approximate molecular orientationin @-carotene.The molecules are centro-symmetrical, but detailedanalysis has so far not been possible.Aromatic Compounds.-The marked diamagnetic anisotropy ofaromatic compounds has been explained qualitatively by variousauthors 54 on the hypothesis that the diamagnetic currents in suchsubstances are not limited, as is normally the case, to individualatoms, but circulate from one atom to another in orbits of the orderof magnitude of, e.g., a benzene ring. This idea, indeed, is implicitin the theory of molecular orbitals as applied by Huckel and others49 F. D. la Tour, J. Phys. Radium, 1937, [vii], 8, 125; 1,. H. Storks and50 C. P. Smyth and W. 0. Baker, ibid., p. 666; see also A. H. White and51 Proc. Roy. SOC., 1937, A , 158, 403.52 V.V. Tschelincev, Cornpt. rend. Acad. Sci., U.R.R.S., 1937, 16,63 2. Krist., 1937, 96, 150.54 (Sir) C. V. Raman and K. S. Krishnan, Proc. Roy. SOC., 1927, A , 113,511; C. V. Raman, Nature, 1929,123, 945; 124, 412; E. Huckel, 2. Physik,1931, 70, 204, and later papers.L. H. Germer, J. Chem. Physics, 1937, 5, 131.S. 0. Morgan, ibid., p. 655.95COX MOLECULAR CRYSTALS. I85to aromatic molecules. L. Pauling 56 has calculated the diamagneticanisotropy of benzene and similar molecules on the assumption thatthe p , (i.e., the ‘‘ aromatic ”) electrons are free to move under theinfluence of a magnetic field from one carbon atom to an adjacentone. In order to obtain reasonable agreement with experiment hefound it necessary to introduce empirical corrections attributed tovariations in electronic density and bond lengths.F. London 56has now developed a more general theory, of the molecular orbitaltype, which represents aromatic molecules as behaving likesupra-conductors in a magnetic field, and which, withoutassumptions regarding “ aromatic ” electrons, shows that inter-atomic electronic circulation will occur in benzenoid substances andnot in saturated molecules. The theory has the merit of givingcalculated magnetic anisotropies in very good agreement withexperiment without the necessity of introducing correcting factors.On the other hand, combining the older theoretical ideas withexperimental data, (Mrs.) K. Lonsdale 57 has shown that, if it beassumed that the diamagnetic anisotropy of aromatic compounds isdue to the p , electrons occupying molecular orbits which arerestricted to the plane of the atomic nuclei, then the radii of theseorbits, calculated by the classical Larmor-Langevin formula, arerather greater than that of a benzene ring (1.39 A.), increasingsomewhat with the size of the molecule.Moreover, when allowanceis made in this way for the anisotropy, the radii of the orbits of thevalency electrons are found to be in excellent agreement with theaccepted value for the radius of the aromatic carbon atom (0.70 A.).Similar considerations apply to cyanuric triazide and metal-freephthalocyanine ; in the latter case, Mrs. Lonsdale’s calculationsshow that molecular orbitals, encompassing the whole of the16-membered inner ring of the molecule, probably exist.Thesediscussions emphasise the importance of the precise work which isbeing done on the crystal structures and magnetic properties ofaromatic compounds, since only from such work can data beobtained of sufficient accuracy to test the finer details of the varioustheories. The desirability of experimental work on conjugatedheterocyclic compounds is suggested by London’s statement of thesufficient conditions for the occurrence of diamagnetic molecularcurrents; these are, the existence of cyclic chains of equivalentpairs of atoms, and an odd number of electrons per link in the ring.It is not clear whether these conditions are also necessary, and5 5 J . Chem. Physics, 1936, 4, 673.5 6 Compt.rend., 1937, 205, 28; J . Chem. Ph,ysics, 1937, 5, 837; J . Phys.57 Proc. Roy. SOC., 1937, A , 159, 149.Radium, 1937, 8, 397186 CRYSTALLOGRAPHY.whether heterocyclic substances of the type of, e.g., thiophen should,according to the theory, show marked diamagnetic anisotropy.A detailed account of the diamagnetic and paramagneticnnisotropy of crystals has recently been given by Mrs. L~nsclale.~*Complete structure determinations of stilbene 59 and nickelphthalocyanine 6o have been recorded ; preliminary mention hasbeen made of the structures of tolan 61 and anthraquinone,G2 butdetails are not yet available. The structure of stilbene has unusualinterest from the point of view of crystallographic theory. Thespace-group is P2&(Cgh) and its symmetry elements consist ofglide-planes perpendicular to two-fold screw-axes, together witheight symmetry centres; this symmetry can be achieved by theappropriate arrangement of four asymmetric units or two centro-symmetrical units.The structures of very many substances areknown to be based upon this space-group, some having fourmolecules to the unit cell and others two. I n the former case it isassumed that the molecules are crystallographically asymmetric,while if the unit cell contains only two molecules (of finite molecularweight) each must contain a centre of symmetry coinciding with oneof the eight in the crystal lattice. One of the numerous examplesof this is diphenyl. Kow, in the case of the unit cell containingfour molecules, the conditions are more elastic, and it is possiblefor all four to be centro-symmetrical and to Be situated on four ofthe eight symmetry centres in the unit cell, but this is very unlikelybecause two such molecuIes are sufficient for the space-grouprequirements, and double the number would normally produce astructure of higher symmetry.Nevertheless, this exceptionalsituation actually arises with stilbene, the molecules of which aretruly centro-symmetrical although four of them are contained inthe unit cell. The larger number of molecules has made theanalysis more difficult than that of dibenzyl, but the full structurehas been determined with considerable accuracy. Within thelimits of error the molecules, which have a trans-configuration, arecompletely flat, in marked contrast with d i b e n ~ y l .~ ~ This flatnessis due to the conjugation of the central double bond with thebenzene rings; its implications and its influence Qn interatomicdistances are discussed el~ewhere.~* The principal bond lengthsare C-C (in the benzene rings) = 1-39 A., C-C (outside the rings) =1 . 4 4 ~ . , and C-C = 1.33 A. The angle C-GC is 130" and the58 Physical SOC. Reports, 1937, 4, 368.59 J. M. Robertson and (Miss) I. Woodward, Proc. Roy. SOC., 1937, A , 162,6" Idem, J . , 1937, 219. 61 J. M. Robertson, J., 1938, 130.62 B. C. Guha, Mature, 1937, 139, 969.63 Ann. Reports, 1935, 32, 230. 64 Seep. 203.568COX : MOLECTJLAR CRYSTALS. 187shortest intermolecular CH . . . CH distance is 3 .5 8 ~ . In tolan,conjugation maintains a flat molecule, but in addition the triplebond causes the whole molecule to be linear ; the progressive changein molecular form as the central single bond in dibenzyl is replacedby a double bond and then by a triple bond is beautifully shownby the electron-density maps 65 in Fig. 6. (It should be borne inFIG. 6.Dibenxyl. Stilbene. Tolan.. .Scale0- J 'Amind that these two-dimensional projections are not necessarily inplanes parallel to those of the benzene rings, and that dibenzyl is athree-dimensional molecule.)The analysis of nickel phthalocyanine shows that the moleculehas a more nearly tetragonal configuration than has the metal-freecompound. This is probably due to the replacement of the internalhydrogen bridges by the four nickel covalencies.The four Ni-Nlinks are each 1.83 A. in length and almost exactly at right angles;this bond length is nearly equal to the sum of the atomic radii ofneutral nickel and doubly-bonded nitrogen, but it is not yet quiteclear as to what are the exact valency relations around the centralmetal atom, and possibly further investigations of co-ordinationcompounds may show how far a metal atom participates in theresonance phenomena of an organic molecule to which it isco-ordinated. A notable feature of the nickel phthalocyaninestructure is that the increase in two C-N links caused by the covalent65 Reproduced by the courtesy of Dr. J. M. Robertson188 OBYSTALLOGRAPHY.binding of the nitrogens to the nickel atom is accompanied by asimilar expansion of the C-N links in the molecules, so that allremain equal as in the metal-free conipound, although about 0.04 A.longer.Commenting on the fact that the signs of nearly all thestructure factors are determined by that of the nickel contribution,the authors emphasise the advantages, previously noted in theseReports,66 of introducing a metal atom a t a known point in anorganic structure, and suggest that a method of direct analysis ispossible by choosing the metal atom of sufficient scattering powerto " swamp " all the reflections. This attractive procedure maynot prove to be withdut difficulties, however ; it is recognised thatin trial and error analysis the advantage of the presence of a heavyatom is discounted by the fact that the structure factors becomerelatively insensitive to the adjustments of lighter atoms, andsimilarly in direct Fourier analysis the spurious subsidiary maximaand minima associated with the heavy atom would tend to falsifydetail in its neighbourhood.It has been recognised €or some years that, in organic molecularstructures, atoms not maintained in juxtaposition by covalentbonds do not normally approach each other nearer than about3.6..More recently it has been realised that many polynucleararomatic molecules such as diphenyl, the parts of which, from thestandpoint of the older stereochemistry, could rotate aboutconnecting single bonds, are actually maintained in a planar formby the conjugation between rings, which confers some double-bondcharacter on the single bonds.It is thus a matter of some interest 67to study molecules in which there must be a conflict between thetendency to coplanarity and the tendency of groups to repel eachother a t distances less than 3.5 A. Such a molecule is that ofo-diphenylbenzene ; 68 detailed analysis has not yet been made,but it has been shown from magnetic data that the planes of thetwo ortho-phenyl groups are probably inclined a t about 50" to theplane of the parent ring, thus allowing a CH . . . CH distance ofabout 3 A. between them. There is evidence also that even in themeta-position phenyl groups repel each other slightly, since in thecrystals of s-triphenylbenzene the three phenyl groups appear tobe rotated approximately 16" out of the plane of the nucleus.Itshould be clearly understood that there is no evidence from these(or any other) compounds to suggest that the single bonds areotherwise than collinear with the centres of the rings which theylink.6 6 Aim. Reports, 1936, 33, 213.6 7 (Mrs.) K. Lonsdsle, 2. Krist., 1937, 97, 91.6 8 C. J. B. Clews and (Mrs.) K. Lonsdale, Proc. Roy. Xoc., 1937, A , 161, 493COX : MOLECULAR CRYSTALS. 189The unit cells and space-groups of several aromatic compoundshave been determined,6g and in some cases the molecularorientation has been found. Superficially the structures ofhydrazobenzene 70 and p-azotoluene 71 do not appear to resemblethat of azobenzene, but the data for the former are not self-consistent, and further study may show that it falls in thedibenzyl-azobenzene series.The atomic parameters given foracenaphthene 72 are almost certainly incorrect, and according tomeasurements made by the Reporter, the lattice dimensionsassigned to t?hianthren 73 are not primitive; the true unit cellcontains only four molecules, so that speculations regardingpolymerisation are unnecessary. Preliminary data have beenrecorded 74 for a series of quinhydrones ; the suggested interpretationof them is not entirely free from objection, but at least it is clearthat the earlier picture of infinite polymerisation chains by meansof hydrogen bonds 75 is too and it is greatly to be hopedthat the full‘ elucidation of the structure of these interestingcompounds will shortly be possible.Chlorophyll-a itself is amorphous, but by the substitution ofethyl for the phytol group a crystallisable compound can beobtained.This does not appear to have a particularly simplestructure, however,77 and its investigation has not been carriedbeyond the space-group determination.Cellulose.-The results of earlier work on the structure of cellulose,as summarised by K. H. Meyer and H. Mark,78 have been acceptedwithout serious question for some years; it is to be expected,however, that in the near future advances both in technique and inour general knowledge of organic structures will require the olderviews to be modified. Proposals for such modification have in factbeen made during the past year, and although finality has by nomeans been reached, the present time seems appropriate for areview of the situation.69 M.Milone, A t t i R. Accad. Sci. Torino, 1937, 72, 425; I. Nitta and T.Watanab6, Sci. Papers Inst. Phys. Chem. Rm. Tokyo, 1937, 31, 225; M.Prasad and J. Shanker, J . Indian Chem. SOC., 1936, 13, 663; is. Banerjeeand A. C. Guha, 2. Krist., 1937, 96, 107.70 J. Shanker and M. Prasad, Current Sci., 1937, 5, 387.7 1 M. R. Kapadia and M. Prasad, ibid., p. 423.‘i2 K. Banerjee and K. L. Sinha, Indian J . Physics, 1937, 11, 21.7 3 M. Prasad, J. Shanker, and B. H. Peermohamed, J . Indian Chern. SOC.,74 J. S. Anderson, Nature, 1937,140, 583. 75 Ann. Reports, 1933,30,420.7 6 J. Palacios and 0. R. Foz, Anal. Pis. Quim., 1936, 34, 779.7 7 J.A. A. Ketelaar and E. A. Hanson, Nature, 1937, 140, 196; cf. E. A.78 “ Der Aufbau der Hochpolymeren Organischen Naturstoffe,” 1930.1937, 14, 177.Hanson, Proc. K. Rkad. Wetensch. Amsterdam, 1937, 40, 281190 CRYSTALLOGRAPHY.All results agree in showing that the unit cell dimension parallelto the fibre-axis (" fibre-period ") is 10.3-10.4 A., correspondingvery well with the calculated length of one anhydrocellobiose unitin the cellulose chain. This axis has been assumed to be thesymmetry axis b of a monoclinic unit cell, the other dimensions (atright angles to the fibre axis) being a = 8.3 and c = 7.9 A., inclinedto each other at an angle (p) of 84". This cell contains twoanhydrocellobiose units, one of which can be regarded as part of achain running along the b-edge of the unit cell while the other isparallel to it but differently oriented in the centre of the cell.0. L.Sponsler 79 had indeed suggested an orthorhombic cell witha' = 10.7 and c' = 12.2 A., containing four C1, units, but it wasFIG. 7.pointed out 80 that (with small numerical adjustments) this mightvery well be merely an alternative and less fundamental descriptionof the monoclinic cell, which would thus remain the true unit, asshown in Fig. 7.Recently E. Sauter,B1 applying his improved experimentalmethods,B2 has obtained cellulose photographs, showing many newreflections, and has concluded that the unit cell of Meyer and Markhas only half the volume of the true cell, the dimensions of whichshould be a = 10.8, b = 10-4, c = 11-8 A., with p = 85", closelyresembling Sponsler's figures.Apart from the minor question ofexact numerical values (Sauter's results give a slightly higher7s Nature, 1930, 125, 633. (Sir) W. H. Bragg, ibid., p. 634.81 2. physikal. Chem., 1937, B, 35, 83.az 2. Krist., 1936, 93, 93; cf. Ann. Reports, 1936, 33, 224COX : MOLECULAR CRYSTALS. 191density than Meyer and Nark's), the main issue is thus whether ornot the two cellobiose units represent,ed by each of the points A(Fig. 7) are oriented identically as those represented by B ; if theyare, the true cell is as given by Meyer and Mark, and if not, theSponsler-Sauter lattice is more nearly correct. Since in thediscussion 83 of this point the same experimental results have beengiven diametrically opposite interpretations, it may be useful todescribe in detail the facts involved, with a view to clarifying thematter.An X-ray photograph of cellulose taken with the beam parallelt o the fibre shows inter ulia three prominent lines due to planesparallel to the fibre axis (Le., (h01) planes), usually called A,, A,,and A,, with spacings of approximately 6-0, 5.4, and 4 .0 ~ .respectively (Fig. 8, u). If as a result of natural growth, stretching,FIG. S.(a -1 ( h.)or otherwise, tlhe cellulose crystallites are oriented parallel to eachother, the reflections are concentrated into certain arcs of theDebye-Schemer circles and it becomes immediately obvious thatthe planes A, and A, are nearly at right angles. Referred to theMeyer-Mark lattice, these planes have indices (101) and (101).The A, reflection also breaks up into arcs, which according to theolder investigations are nearly at 45" to A, and A , (Fig.8, b) so thatA , is taken to be (002); Sauter on the other hand claims that theyare parallel to A, (Fig. 8, c), in which case, as the spacings of A,and A, are in the ratio of 3 to 2, the former cannot be a first-orderreflection. The indices assigned by Sauter are therefore A, (002),A , (200), and A , (003), necessitating the larger cell dimensionsalready given.It is exceedingly difficult to arrive at a clear-cut decision inmatters of this kind, particularly as the estimation of the positionsof intensity maxima in diffuse rings is liable to considerablesubj ect,ive errors.Nevertheless, an examination of the available83 H. Mark and K. H. Meyer, 2. physikal. Chem., 1937, B, 36, 232; €2.Sauter, &id., pp. 405, 427; 37, 161192 CRYSTALLOGRAPHY.photographs suggests very strongly that the reflection A, is due totwo sets of planes, one approximately parallel to A, and the othera t about 45" to it. There are undoubtedly reflections a t 45"(Fig. 8, b), but in all the photographs they appear to overlapconsiderably more at X than a t Y , giving the effect of 8, b + 8, c.Now in actual fact the A, reflections should not be exactly at 45"but should be a few degrees nearer A,, so that any tendency tooverlapping (on account of imperfect orientation) would be showna t Y rather than X, and the only explanation of the observedcontrary result would seem to be that there is another reflection a tX .Sauter's main conclusion that the unit cell has twice thevolume of Meyer and Mark's thus appears to be correct, but thereflection A, is probably due not only to (003) as supposed by him,but also to (202) and/or (202).A further point established by Sauter is that the b-axis is not ascrew-axis, since the (030) and (050) reflections definitely occur(although not very intensely). His suggested rotation of successiveglucose units to account for this is not acceptable in its presentform, however, either on crystallographic or on stereochemicalgrounds; the arrangement he depicts would certainly remove thescrew-axis but would still result in halving of (OlO), whereas presentinformation regarding valency angles suggests that any largerotation of the glucose rings with respect to each other is unlikely.Nevertheless, the presence of the odd orders of (010) must be takeninto account in any detailed study of cellulose, and is interestingfrom a chemical point of view in that it shows that successiveglucose units in the chain are not crystallographically identical andthat the unit of structure therefore consists of two anhydroglucoseunits.Detailed measurements of the new photographs are not yetavailable, but it is by no means clear what real evidence there isfor a monoclinic unit cell for cellulose, as opposed to an orthorhombicone.It is exceedingly difficult to believe, as Sauter suggests, thatit can be inferred from equatorial photographs that the angle p is85".His photographs were made upon oriented B-cellulose, whichis produced from a sheet of unoriented crystallites by drying undertension; thus, in the oriented specimen there will be approximatelyequal numbers of crystallites with their b-axes pointing in oppositedirections (their unit cells appearing as in Fig. 9 when viewed alongthe fibre axis), so that the photograph should show orthorhombicsymmetry. All previously reported reflections can certainly beaccounted for by an orthorhombic cell of approximately the sameaxial lengths as Sauter's monoclinic cell.I n earlier investigations it was assumed that the cellulose chainCOX : MOLECULAR CRYSTALS. 193in a crystallite were all arranged in the same sense, but as K.H.Meyer 84 has pointed out, the supposition that equal numbers ofchains run in opposite directions is equally plausible, and indeedstatistically this must be so in hydrate cellulose prepared artificially.From the fact that this regenerated hydrate cellulose has the same(or nearly the same?) lattice as hydrate cellulose prepared directlyfrom ramie, Meyer infers that in the native fibre also the chains runalternately in opposite directions. Although this may quite wellbe so, it seems to the Reporter that the above-mentionedresemblance can be explained without recourse to any hypothesisof reversed chains. It is now generally recognised that bondsFIG. 9.between hydroxyl groups are responsible for holding carbohydratemolecules together in the crystalline state, and that other forcesinvolved (as e.g., between CH groups) are relatively unimportant.Now the configuration of cellobiose is such that the six hydroxylgroups have very nearly two-fold axial symmetry; reference toFig, 10 will show that rotation through 180" about an axis through0, perpendicular t o the plane of the paper brings 0, into theposition of 0'3, 0, into that of 0'2, and 0, nearly into the position ofO',.Consequently, as far as hydroxyl-bond formation (whichconditions the molecular arrangement) is concerned, it is largely amatter of indifference if the molecule goes into the latticeupside-down, and a resemblance between regenerated hydratecellulose and that derived from ramie would be expected whetherthe latter contained reversed chains or not.It is of some interest to note that, in order to obtain as close anapproximation to the above-mentioned axial symmetry as possible,it is necessary to arrange 0, and O', slightly differently relative to84 Ber., 1937, 70, 266.ItEP.-VOL. XXXIV. 194 CRYSTALLOGRAPHY.their respective glucose rings, thus destroying the two-fold axialsymmetry parallel to the fibre axis. It is tempting to suggest thatin cellulose there is a statistical distribution of reversed chains andthat the consequent adjustment of primary alcohol groups to formhydroxyl bonds destroys the two-fold axial symmetry along thefibre-axis and gives rise to the “forbidden” (030) and (050)reflections. It should be understood that Meyer’s suggestion is foran ordered distribution of reversed chains, each chain in the latticebeing surrounded by four others running in the opposite direction.It is perhaps hardly necessary to say that at a time when there isstill controversy over the cell-dimensions, a specific suggestion ofFIG. 10.this kind, and still more the development of it to obtain exactatomic positions,85 is entirely speculative. Unless it proves possibleto obtain cellulose preparations of a considerably higher degree ofcrystallinity and orientation than those now available, it is verydoubtful whether it will ever be possible to determine the preciseat’omic arrangement by measurements on cellulose itself. Progresswill more probably be made by utilising exact data regarding theconformation of anhydrocellobiose derived from the study ofcrystalline oligosaccharides in conjunction with the best availableevidence from cellulose.Two further points in connection with the idea of reversed chainsmay be mentioned. The suggestion that cellulose chains mightform closed loops is not a new one; it is evident that if they existin the cellulose lattice then reversed chains (distributed at random)85 K. H. Meyer and L. Misch, Helv. Chim. Actcc, 1937, 20, 232COX : MOLECULaR CRYSTALS. 195must occur, but closed loops do not appear to fit in very well withpresent views on micellar and inter-micellar structure. The otherpoint is that the presence of equal numbers of chains running inopposite directions in the fibre would destroy the polar nature ofthe b-axis and would be more likely to give a structure withorthorhombic rather than monoclinic symmetry ; indeed, onaccount of the symmetrical nature of the cellobiose unit, this istrue for fibres built of unidirectional chains.To sum up, it seems probable that the cellulose unit cell isorthorhombic as suggested by Sponsler, with axial lengths as givenapproximately by him and more accurately by Sauter; in viscoseand similar artificial preparations half the chains are reversed anddist.ributed statistically, but whether this is true of celluloseproduced biologically is a matter for further investigation. In anycase, there is very little evidence at present to show exactly howthe atoms are arranged in the unit cell.In the limited space available it is impossible to discuss numerousother recent investigations 86 of cellulose, but special mentionshould be made of several papers 87 discussing its inter-micellarstructure. E. G. C.E. G . Cox.N. P. MOTT.J. T. RANDALL.86 H. Dostal and H. Mark, Trans. Paraday SOC., 1937, 33, 350; W. K.Ferr, J . Appl. Physics, 1937, 8, 228; G. L. Clark and E. A. Parker, Science,1937, 85, 203; G. L. Clark and A. F. Smith, Rev. Sci. Instr., 1937, 8, 199;0. R. Howell and A. Jackson, J., 1937, 979; J. Gundermann, 2. physikd.Chem., 1937, B, 37, 387; R. Hosemann, ibid., 1937, A, 179, 356; H.Staudinger, Naturwiss., 1937, 25, 673; K. Hess and J. Gundermann, Ber.,1937, 70, 1788, 1800; P. Nilakantan, Proc. Indian Acad. Sci., 1937, 5, A ,166 ; W. A. Sisson, Contr. Boyce Thompson Inst., 1937, 8, 389.8 7 0. Kratky and H. Mark, 2. physikal. Chem., 1937, B, 36, 129; P. H.Hermans and A. J. de Leeuw, Naturwiss., 1937, 25, 524; E. Sauter, 2;.physikal. Chem., 1937, B, 35, 117