ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1. PHYSICAL ASPECTS OF THE HYDROGEN BOND.THE term “hydrogen bond” was introduced by W. M. Latimer andW. H. Rodebush 1 to cover a species of molecular interaction the qualitativeeffects of which have been extensively observed. These effects are generallymost pronounced when one of the participants is an O-H or N-H groupand the other is an 0, N, F, or C1 atom. As the properties of many im-portant families of organic compounds are intimately related to the presenceof the former groupings, the hydrogen bond has come to play a large r61ein many topics of organic chemistry.2 Here an attempt will be made tosummarise some of the more significant physical studies of this particularmolecular interaction.The magnitude of the interaction can be given by its energy value,measured by the chemist as A H , in kcal.per g.-mol. per bond. Despitethe extensive discussion of hydrogen bonds, it appears that satisfactorydeterminations of this key factor are far less numerous than might bedesired. Table I summarises those determined from equilibrium studies.Estimates from heats of dilution,3 heats of vaporisation,4 and similar generalprocesses, whilst possibly indicating the order of magnitude, cannot berelied upon for accuracy, for the number of hydrogen bonds broken is oftenundetermined and the allowance to be made for many other factorsinvolved in the changes is uncertain. To take equilibrium constants foundin different solvents and combine them to provide a AH value is clearlynot justifiable.A number of the uncertainties in the spectroscopic deter-mination of AH in solution have been indicated.6It is doubtful whether the particular “ bond ” ascribed to these pro-cesses is the sole factor contributing to A H . Apart from the assumptionof simple equilibria which may not always be strictly correct, the valuessuch as that for the aniline association should be compared with the heatJ . Amer. Chem. SOC., 1920, 42, 1419.L. Hunter, this vol., p. 141.K. L. Wolf, inter alia, Trans. Paraday SOC., 1937, 33, 179.(a) M. L. Huggins, J . Org. Chem., 1937, 1, 407; ( b ) L. A. K. Staveley, J. H. E.Jeffes, and J. A. E. Moy, Trans. Faraday SOC., 1943, 39, 5.H. M. Glass and W. M. Madgin, J ., 1933, 193, 1431.M. M. Davies and G. B. B. M. Sutherland, J. Chem. Physics, 1938, 6, 767WELLS : CRYSTAL GROWTH. 79only along lines, or even at points. In any case, the picture of two crystalsfitting perfectly together over a plane surface of union is probably far fromthe truth, as will be evident from the remarks in the next section on theprobable structure of actual crystal faces.( 5 ) The Perfection of Internal Structure and Faces of CrystaEs.-Theconcept of the mosaic structure of crystals was introduced by Darwin in1914, since when it has been discussed in a large number of papers, particu-larly in the Zeitschrift fur Kristullographie (1934, 89). Although a detaileddiscussion of mosaic structure is not possible here, it is relevant to considerits origin in terms of the mechanism of crystal growth.A difference betweenthe lattice parameters in the surface layers of a crystal and in the interior(the Lennard-Jones effect) was postulated by F. Zwicky 73 and later calcul-ated by J. E. Lennard-Jones and B. M. Dent 74. As the size of a crystalis reduced the volume of the external layers increases in proportion to thevolume of the whole crystal, so that for very small crystals it becomesjustifiable to speak of the parameter of the crystal as it whole, this being amean value. It was shown 75 that the parameter of very small crystalsmust be greater than normal in the case of ionic crystals but less than normalfor homopolar crystals. This effect has been verified experimentally forcertain metals (nickel,76 copper and iron 77).As a crystal grows, theexternal layers become internal ones and in the process the interatomicdistances therefore require readjustment. This readjustment can only goto completion if the mean thermal energy of the atoms or ions of the latticeis sufficient to enable them to adopt their equilibrium positions. If thisdoes not happen, however, the deviation of the structure from the idealcannot continue indefinitely. At some time the formation of a new nucleuswill be more advantageous from the energy standpoint, and therefore morelikely, than the further growth of the existing crystal with the deformedlattice. Thus the growth of the first crystal ceases and the new unstrainedcrystal begins to grow, i.e., the crystal growth is intermittent and leads toa structure consisting of separate (mosaic) blocks.The intermittent natureof the crystallisation of metallic crystals has been confirmed in the case ofcrystals grown from the vapour 78 and deposited electrolytically. Photo-micrographs of electrolytically deposited nickel,79% 80 cobalt,81 copper,s2etc., show a layer structure, the individual layers having a thickness ofaround cm. According to R. Suhrmann and H. S~hnackenberg,~~ the73 Physikal. Z., 1923, 24, 131.75 J. E. Lennard-Jones, 2. Krist., 1930, 79, 215.7 7 N. A. Shishakov, J. Exptl. Theoret. Physics U.S.S.R., 1940, 10, 1450.79 A. W. Hothersall and G. E. Gardam, Metal Ind., London, 1939, 55, Nos. 21 and80 E. Raub and M. Wittum, 2.EEektrochem., 1940, 46, 71.*1 G . A. Moore, Trans. Electrochem. SOC., 1937, 71, 247.82 V. Mattacotti, Metal Ind., N.Y., 1939, 37, 259.1x3 2. Elektrochem., 1941, 47, 277.74 Proc. Roy. SOC., 1928, A , 121, 347.H. BOOCBS, Ann. Phyaik, 1939, 35, 333.M. Straumanis, 2. physikal. Chern., 1931, B, 13, 316; 1932, B, 19, 63.2280 GENERAL AND PHYSICAL CHEMISTRY.energy of activation U of the ordering process (the readjustment mentionedabove) ranges from 150 cals./g.-atom for bismuth to 800 cals./g.-atom fornickel, and is very much less than for processes involving change of placeof atoms in the crystal. The number of atoms n capable of passing fromstates of non-equilibrium to states of equilibrium, when their total numberis N , will be given by n = Ne-V’kT.If crystallisation takes place at atemperature v U / k (the temperature of rest) then deformation of thelattice should not occur. It is also necessary that the rate of crystallisationbe not greater than the rate of the ordering process. M. Renninger ** showedthat in crystals grown from the melt by the Kyropoulos method there isno pronounced mosaic structure, in contrast to natural crystals of rock-salt.Stressesof the third kind arise, and are counterbalanced, within a particular mosaicblock, owing to the difference between the parameters of the internal layersand the surface layers. Stresses of the second kind arise because contiguousexternal layers of neighbouring blocks have different parameters, for theplane a t which the growth of one crystal block finishes (hence that farthestremoved from the state of equilibrium) touches the plane a t which growth ofthe next block commences (hence the plane nearest to the state of equil-ibrium). Just as a singlemosaic block is built up of layers, so the whole crystal is built up of mosaicblocks, and Joff6 supposes that if a, is the parameter of the internal layersand a2 that of the free surface of the crystal, then the parameter al of theinternal surface of the crystal will have some value intermediate betweena, and a2.For an ionic crystal a,>a&a,, and for a homopolar or metalliccrystal ao<ar<az. By analogy with the stresses of the third kind thereshould arise stresses of the first kind, counterbalanced within the limits ofvolumes comparable with the volume of the whole crystal. These stresseswould be oriented and capable, on reaching a certain magnitude, of causingsplitting or disruption of the crystal.Hence, on reaching a certain size amosaic crystal should become mechanically unstable, and disruption oflarge crystals grown from solution has been observed.86 It would thereforebe of some interest, as has been pointed out elsewhere in another connec-t i ~ n , ~ ’ ~ 88t 89 to have information about the largest known crystals ofdifferent substances, particularly if the maximum size could be correlatedwith the mode of growth and degree of mosaic structure. It is interestingthat in a number of cases it has been shown that if an impurity is addedto the solution much larger crystals can be grown.Joff6 suggests thatmany of the abnormal types of crystal growth should be explicable in termsof his picture of “ real ” crystals. A detailed description of many types ofV. S. Joff6 85 distinguished three types of stress in real crystals.These stresses are also counterbalanced locally.84 2. Krist., 1934, 89, 344.86 A. V. Shubnikov, “ How Crystals Grow,” Moscow, 1935.8 5 Uspekhi Khimii, 1944, 13, 144.C. Palache, Amer. Min., 1932, 17, 362.C. FrondeI, ihid., 1935, 20, 469.8s J. W. Retgers, 2. physikal. Ghem., 1892, 9, 278.no W. E. Gibbs and W. Clayton, Nature, 1924, 113, 492WELLS : CRYSTAL GROWTH. 81abnormality has been given by D. B. Gogoberid~e.~~ According to F.Bernauer 92 the bifoliate type of spherulite arises by growth in the directionof the long axis of the crystal at a constant rate accompanied by splittingat a constant angular velocity.In the above picture a real crystal, grown at too low a temperature, isin a metastable condition and not in true thermodynamic equilibrium.In contrast to this, D.Balarew 93 has developed a theory of “ growth con-glomerates ”, based on two postulates : first, that a crystal with perfectsurfaces and possessing edges and corners can never be in thermodynamicequilibrium with its environment, and second, that a large perfect crystalmust pass over spontaneously into one with mosaic structure. He supposesthat definite conditions of crystallisation give rise to a particular crystallineconglomerate and that the intermittent growth of crystals leads to a growthconglomerate comprising separate layers which is in thermodynamic equi-librium.The theory appears to be founded on a misinterpretation of theThomson-Gibbs equation as applied to crystals. For a liquid, this equation,vix., p, = p,e2Va rRT, relates the vapour pressure of a droplet of radius rt o the surface free energy per unit area (o), molecular volume ( V ) , and thevapour pressure of a plane liquid surface. When this is applied to a crystal,r becomes the central distance of the plane face (distance from the (‘ Wulffpoint ”), but Balarew 94 assumes it to mean the radius of curvature andregards corners and edges as having very great curvature, ( ( of atomicdimensions ”. The theory that crystals grow or dissolve “block byblock ” seems to rest on very doubtful experimental evidence.For example,in one of his experiments Balarew claims to show that the solubility ofgypsum depends on the direction of the ~tirring.~5 As I. N. Stranskig6points out, in a critical review of Balarew’s work, it is difficult to imaginehow the forces between blocks of the size suggested (some lo-* cm. side)could be adequate to orient the blocks in the formation of a single crystal,and moreover the mode of formation of the blocks has not been explained.Further references are given to Balarew’s work.97The shape of a crystal may, for many purposes, be described as a convexpolyhedron, and it was the perfection of many crystal faces which madepossible the development of crystaIlography as a science.However, thereare many ways in which crystals depart from the above description. First,there are the cases in which the crystal is still essentially a convex polyhedronbut (a) the simple faces are replaced by vicinal faces, ( b ) the ‘( face ” isactually formed into ridges caused by the alternation of faces of two types,91 Usp. Fiz. Nauk., 1940, 2, 242. 92 “ Gedrillte Kristalle ”, Berlin, 1929.93 “ Der disperse Bau der festen Systeme ”, Dresden, 19.39.94 Kolloidchem. Beih., 1930, 30, 258; 1931, 32, 203; 1933, 37, 184; 2. Krist., 1934,95 D. Balarew and N. Kolarew, ibid., 1939, 101, 156.9 7 D. Balarew, ibid., 1938, 100, 167; Zentr. Min., 1941, 228; Kolloidchem. Beih.,1939, 50, 178; 1940, 51, 123; 1941, 52, 45; Kolloid-Z., 1939, 88, 161, 268; 1940, 92,82; 1942, 98, 43.89, 268; 1936, 93, 166.Ibid., 1943, 105, 9182 GENERAL AND PHYSICAL CHEMISTRY.(c) the crystal is tapered, (d) the whole face is curved, or ( e ) there are localisedimperfections on an otherwise plane face.The last three phenomena appear,at least in many cases, to be associated with the presence of impurities inthe solution, as, for example, in the case of the low conical hillocks on (011)faces of potassium perchlorate crystals grown in the presence of certaindyes.98 The same phenomenon may be observed on the tetrahedron facesof sodium chlorate crystals grown from solutions containing sodium thio-sulphate. In the second large group come the more radical departuresfrom normal growth as a single crystal, such as spherulitic, dendritic, andtwinned structures.If a solution of sodium carbonate is allowed to diffuseslowly into a gel containing barium chloride (prepared from commercialgelatin and allowed to set) the precipitation of the barium carbonate takesplace in layers, and a variety of crystal forms is observed. These rangefrom needles, through " sheaves " to spherical aggregates. The structuresand optical properties of these spherulites have been studied recently insome detail, particularly by H. W. Morse and his co-worker~.~~ The growthof the practically spherical aggregates and of the intermediate forms can beaccounted for if it is postulated that crystallisation radiates from a centralnucleus in a limited solid angle only.It is assumed that growth is fastestin one direction, that every point at the surface of the growing cone offibres can act as a new starting point for further radiating growth, and thatthe spatial extent of the latter is controlled by the possible angle of apertureof the cone and by the mechanical obstruction of the existing fibres. Asgrowth proceeds, new fibres radiate from points reached by those formedearlier. The sheaf then opens out' in fan-like manner until an approximatelyspherical shape is reached, when presumably the process stops owing toexhaustion of material in the environment. A somewhat similar explan-ation has been given 100 for the two-dimensional spherulites of substancessuch as malonamide and resorcinol grown between glass plates.Betweencrossed Nicols the three-dimensional spherulites show in parallel light aninterference figure similar to that of a uniaxial crystal cut perpendicularto the optic axis and viewed in convergent light.In considering the genesis of twin crystals, which he classifies into growthtwins, transformation twins and gliding twins, M. J. Buerger emphasisesthe close relation of twinning to polymorphism, and suggests that growthtwinning is more likely, other things being equal, the greater the degree ofsupersaturation. Thus the condition causing supersaturation twins is mostlikely to arise just once-as the crystal nucleus forms-and not again, SOthat nuclei supersaturation twins are often characteristically simple pairs.This simple treatment does not account for the extraordinarily regularstructure of some lamellar twins, such as those of potassium &lorate grownD* H.E. Buckloy, Z . Krist., 1934, 89, 221.DD Bull. Soc. franq. Min., 1931, 54, 19; A m r . J . Sci., 1932, 23, 421, 440; 1933, 25,494; Amer. Min., 1933, 18, 66; 1936, 21, 391.loo B. Popoff, Latv. Farm. Zurn., 1934, 1.Amer. Min., 1945, 30, 469WELLS : CRYSTAL GROWTH. 83from supersaturated solution. To quote R. W. Wood,2 " a plate whichstarts with twin planes 0.0002 mm. apart apparently builds up seven hundredlaminz of the same thickness, while another plate starting with a different' grating constant ' sticks to it to the end." In other words, after a distancecorresponding to some 300 unit cells, the orientation of the crystal changes,and this change takes place regularly at intervals of about 2000 A.In a paper on the surface motion of particles in crystals and the naturalroughness of crystal faces J.Frenkel3 begins by pointing out that vicinalfaces with very high indices are not to be regarded as planes of high specificsurface free energy (compare Miers's paradox,44 that the faces actuallypresent on a growing crystal of alum are those with very low densities ofatoms per unit area), as is often assumed to be the case, In fact they con-sist of steps, the flat portions of which are planes of low indices [e.g., (111)in the case of the vicinal faces on alum]. For the two-dimensional analogue,a staircase-like line with identical steps n units in length and 1 unit inheight, the additional free energy per unit length is simply Nw, where w isthe additional energy per step and N = l / a n = ( l / a ) tan+, a being thelattice constant and + the angle of inclination of the vicinal face to the basicface.Since the surface free energyof the vicinal face is only slightly greater than that of the basic face itfollows that the surface of a crystal in statistical equilibrium consists, notof a plane surface, but of a series of vicinal faces which arise spontaneouslyas the result of thermal fluctuations. This fluctuating roughness can becharacterised by the ratio hla where A is the mean length of the separatesteps. To account forthe variations in the areas of the terraces it is supposed that atoms canmove freely over the horizontal portion of each terrace without interactionone with another.With respect to the " plane gas phase " adsorbed on agiven terrace, the next terrace, lying at a higher level, plays the r81e of thecondensed phase, and there exists a continuous exchange of atoms betweenthe two plane phases, leading to fluctuations in the areas of the separateterraces. This concept is further extended to the edges of the terraces, theatoms linearly adsorbed on the rectilinear portion of each edge behaving asa kind of linear gas, so ensuring the possibility of a reshaping of the outlinesof the separate terraces without changing their areas. The growth ofa crystal is visualised as taking place by the random deposition of particleson the growing face, in general on the flat portions of the atomic terraces,thereby passing into the two-dimensional gas phase.Later, some of thembecome attached, still in a perfectly random way, to the vertical stepsbounding the terraces (passing thus into the one-dimensional gas phase),and they move along until they become firmly attached at an angle (corner),as in the Kossel picture. This generalisation of the Kossel-Stranski theoryis also applicable to vaporisation, dissolution or melting, when the aboveprocesses take place in the reverse order. A mechanism of this type hasThus o = oo + w N = o0 + (w/a) tan$.Assuming ~ > n , it is found that A/U = 4eW'kT.a Phil. Mag., 1909, 18, 535. J . Physics, U.S.S.R.,1945, 9, 39284 GENERAL AND PHYSICAL CHEMISTRY.been suggested by P.Lukirsky to account for the development of vestigialcrystal faces on the surface of a crystalline body ground initially in the formof a sphere, and subjected to more or less prolonged heating.It might a t first sight appear that certain observations on the move-ment of layers across the faces of growing crystals are in conflict with theabove picture of crystal growth. Observations of the interference coloursof thin crystals of m-toluidine 69 6 indicate layers only a few moleculesthick. The layers mentioned by C. W. Bunn and H. Emmett must havea thickness of the order of the wave-length of visible light (some 103 atomsthick). They are observed only towards the edges of faces and presumablyare the result of thin layers overtaking one another.Observations havealso been made on layers spreading across faces of growing crystals of alkalihalides,s and interpreted as supporting the Kossel-Stranski theory of thegrowth of ionic crystals. M. Volmer has commented on the interpretationof some of these experiments. It seems likely that the above effects areobserved only under conditions (e.q., of rapid growth from supersaturatedsolutions) such that external factors-concentration gradients and diffusioneffects-are important, and that they are not relevant to the case of acrystal growing slowly in a well-stirred solution. The former conditions,and also the presence of suitable impurities in certain cases, are known tolead t o the formation of vicina.1 or curved faces, or tapered crystals.In allthese cases the surface is not a normal face but the contour of the edges oflayers, and the different types of divergence from normal plane faces of lowindices represent different relations between the rate of spread of layers andthe frequency of init’iation of new layers.S. Tolansky lo has studied the topography of crystal faces by means of amultiple beam interferometric method. A highly reflecting film of silverabout 500 A. thick is deposited on the crystal face, which is placed near,and parallel to, an optical flat of quartz. Interference fringes are producedusing a parallel beam of monochromatic light at normal incidence, and theyshow many interesting features of the structure of the crystal face.Ex-amination of a (100) face of quartz, of high optical quality, showed the faceto consist-not of a simple plane surface-but of vicinal faces inclined a tangles varying from 0.50 to 9.00 minutes of arc and mostly curved, withradii of curvature from 20 to 60 metres. There were also sub-microscopictetrahedral projections about 450 A. high, which may represent nuclei fromwhich subsequent growth would have started. A study of cleavage surfacesof mica and selenite 1’9 12 showed steps on the surface of the former down to40 A., all the steps being niultiples of 20 A., the c spacing of mica as determinedby X-ray diffraction. These steps are presumably the same as those in-4 Compt. rend. Acad. Sci. U.R.S.S., 1945, 46, 300.5 R. Marcelin, Ann. Physique, 1918, 10, 185.L.Kowarski, J . Chim. physique, 1935, 32, 303, 395, 469.Nature, 1946, 158, 164.‘‘ Kinetik der Phasenbildung,” p. 55.11 S. Tolansky, ibid., p. 51.8 Z. Gyulai, 2. Krist., 1935, 91, 142.lo Proc. Roy. Soc., 1945, A , 184, 41.l2 Idem, ibid., 1946, A , 186, 261WELLS : CRYSTAL GROWTH. 85ferred to exist on some mica surfaces from experiments made by Friedel onthe orientation of ammonium iodide crystals on such surfaces.It is not possible to reviewhere all the work done in the last few years on supersaturation and nucleusformation. The early work of Miers and others appeared to supportOstwald’s view that a t a given temperature there is a definite concentrationbelow which crystals are not formed spontaneously (it being possible tomaintain the solution indefinitely in this metastable state), whereas athigher concentrations spontaneous crystallisation occurs.The experi-ments of Miers, from which the actual “ supersolubility ” curve, betweenthe metastable and labile regions, was plotted, only show that under theconditions of these experiments there was a fairly sharp boundary betweenthe concentrations at which nucleus formation took place rapidly or fairlyslowly. Later work showed that the area of the “ metastable ” region canbe reduced by increasingly vigorous stirring or by the presence of foreignsolid particles. Comparable results were obtained with melts, though insome cases if the rate of cooling is very great nuclei are not formed but aglass results. Although far less importance would now be attached to theprecise position of Miers’s supersolubility curve, since this has been shownto depend on the experimental conditions, it is generally agreed that justbelow the saturation point there is a region in which the probability of nucleusformation is small (“ metastable ” region), but that this probability in-creases rapidly beyond a certain degree of supersaturation.For a super-cooled liquid L. C. de Coppet l3 gave a simple kinetic explanation.In technical crystallisation processes it is important to avoid excessiveformation of nuclei on cooling surfaces. Rapid agitation does not over-come this difficulty as mechanical shocks cause nucleation in the body ofthe solution. One way in which this has been overcome is to carry out thesupersaturation in one part of the apparatus and to allow crystal growthto take place in another vessel containing seed crystals, as in the Oslocrystalliser.14* l5 The supersaturation of the solution travelling from theevaporator is insufficient for appreciable nucleus formation to take placebut, of course, sufficient to cause growth of the seed crystals in the crystal-lising compartment.A kinetic derivation of the rate of nucleus formationfrom the vapour state has been given by I. N. Stranski and R. Kaishev.16Nucleus formation in supersaturated solutions can apparently be verycapricious. For example, it was found in some experiments that by intro-ducing seed crystals a t the saturation temperature and then cooling, growthfirst occurred only on the seed crystals, then a t a lower temperature a fewnew nuclei appeared, but only a t a still lower temperature did nuclei formin large numbers throughout the solution.17 Such effects are, however,(6) Miscellaneous.-(a) Nucleus formation.l3 Ann.Chim. Phys., 1907, 10, 457.l4 F. Jeremiassen and H. Svanoe, Chem. Met. Eng., 1932, 39, 594.l6 H. Svanoe, I n d . Eng. Chem., 1940, 32, 636.l6 Z. physikal. Chem., 1934, B, 28, 317.H. H. Ting and W. L. McCabe, Id. Eng. Chem., 1934, 20, 10086 GENERAL AND PHYSICAL CHEMISTRY.very dependent on the size and total number of seed crystals, rate of cooling,speed of stirring, etc. Some recent papers on supersaturation and nucleusformation in solution are noted.l* Brief reference only can be made toother recent work on crystallisation or recrystallisation processes.Fromstudies of the kinetics of the crystallisation of sucrose solutions, A. vanHook l9 concludes that the rate of growth of the crystals is determinedprimarily by some interfacial reaction rather than an interboundary re-action, i.e., that processes occurring at the crystal face (orientation andincorporation of molecules into the crystal) are more important thandiffusion under the conditions of his experiments. The effect of addedimpurities was also studied.20 The rate of crystallisation from super-saturated solutions of sodium sulphate has been studied.21 According toW. Lotmar,22 thin films of antimony deposited in a vacuum are originallyamorphous, and crystallise spontaneously only if the film thickness exceedsa certain critical value.The growth of crystals during electrodepositionis considered in a theoretical paper by K. M. Gorbunova and P. D. D a n k ~ v , ~ ~and the growth of crystallites in supercooled liquid thymol by G. G .Laemmleh2* P. Laurent 25 has derived formulte for the number of nucleiformed at a given time and for the velocity of crystallisation in allotropictransformations. The crystallisation of salts from thin films of solutionsspread on mercury has been investigated by H. Devaux.26There has been a number ofpapers concerned with the technique of growing large single crystals, asopposed to studies of the way in which the crystals grow (Section 2 ) . Theydescribe modifications of well-known methods.In order to obtain largecrystals (up to 200 g.) of Rochelle salt with preferential development alongthe y and x axes, crystals may be grown between glass plates in a solutionwhich is cooled from 30" at the rate of &lo per day.27 Large crystals ofpotassium dihydrogen phosphate 28 and alkali halides 29 may also be grownfrom aqueous solution. Single crystals of lithium fluoride, potassiumbromide, and sodium chloride weighing up to 35 lbs. have been made 30 bymelting the salt in a conical platinum crucible which is removed very slowlyfrom the furnace into n lower cooler chamber, the crystal growing from the18 K. Neumann and A. Miess, Ann. Physilc, 1942, 41, 319; R. Gopal, J. IndianChem. SOC., 1944, 21, 103, 145; B.S. Srikantan, ibid., 1945, 22, 55; 0. M. "ode, ActsPhysicochim. U.R.S.S., 1940, 13, 617; J. Amsler and P. Schemer, Helv. Physica Acta,1941,14, 318; C. G. Dunn, Physical Rev., 1944, 66, 215.(b) Technique of growing single crystals.18 I d . Eng. Chem., 1944, 36, 1042, 1048; 1945, 37, 782.zO A. van Hook, ibid., 1946, 38, 50.21 E. L. Krichevskaya, J. Physical Chem. U.S.S.R., 1945, 19, 382.22 Helv. Physica Acta, 1945, 18, 232, 369.23 Compt. rend. Acad. Sci. U.R.S.S., 1945, 48, 15.26 Compt. rend., 1944, 219, 205; Rev. met., 1945, 42, 22.26 Compt. rend., 1944, 219, 565.27 L. C. Baker, New Zealand J . Sci. Tech., 1943, 25, B, 62.28 W. Bantle, Helv. Physica Acta, 1943, 16, 207.2s F. Henroteeu, Astronom. J., 1945, 51, 122.3O R. L. Taylor and H.C. Kremers, Chem. and Ind., 1944, 55, 906.z4 Ibid., p. 168WELLS : CRYSTAL GROWTH. 87end of the conical crucible. By allowing the crystallisation of the melt tostart at a surface of a mica sheet, C. D. West 31 has obtained oriented sectionsof single crystals of sodium nitrate. The method is also applicable tosodium, potassium, and rubidium iodides and potassium bromide, whenthe crystal grows with (111) parallel to (001) of the mica. A modificationof the original Verneuil furnace, in which the powdered material is pro-jected into an oxy-hydrogen flame, has been used to obtain syntheticsapphires (single crystals of a-alumina) .32 Fused silica may be convertedinto perfect small crystals of quartz when heated in a solution of sodiummeta~ilicate.~~ Mixed thallous bromoiodide single crystals have beenprepared for use in military infra-red optical instruments.Crystalscontaining 42 moles % of thallous bromide were grown from the melt byusing a, modified Bridgman furnace.35 The melt was held at 470" in afurnace divided into two parts by an insulating baffle, the temperatures inthe two sections being independently controlled, and the baffle serving toproduce a steep temperature gradient in the region where growth tookplace. The best results were obtained witha high temperature gradient and a slow rate of passage through the gradient.Methods of obtaining single crystals, particularly of metals, have beenreviewed by A. Duran 36 (references to 32 papers). The first general methodconsists in slow cooling of the molten material in a crucible, either by re-moving the crucible slowly from the furnace (a method used by P.W.Bridgman3' to obtain single crystals of W, Sb, Bi, Te, Cd, Zn and Sn, andrecently by D. C. Stockbarger for lithium fluoride35) or by slowly coolingthe whole furnace. Various devices are adopted to start the crystallisationfrom a nucleus with the desired orientation,3*9 39 and many designs of furnaceand crucible have been developed.40 The second method is to bring anucleus into contact with the surface of the molten material and to with-draw the crystal slowly,41 a method particularly useful for growing largesingle crystals of certain halides. A third method, recrystallisation in thesolid state, has long been used for preparing mono-crystal wires of metals.Heating combined with compression in a steel mould has also been used.42A conical crucible was used.A.P. W.31 J . Opt. Soc. Amer., 1945, 35, 26.32 K. W. Brown, R. C. Chirnside,tL. A.'_Dauncey, and H. P. Rooksby, Gen. Electric33 N. Wooster and W. A. Wooster, Nature, 1946, 157, 297.34 0. F. Tuttle and P. H. Egli, J . Chem. Physics, 1946, 14, 571.35 Rev. Sci. Instr., 1936, 7 , 133.36 Anal- Pis. Quim., 1941, 37, Supplement, p. 33.37 Proc. Amer. Acad., 1925, 80, 305.3B L. Schubnikow, P ~ o c . K . Akad. Wetensch. Amsterdam, 1930, 33, 327.40 H. Tazaki, J . Sci. Hiroshima Univ., 1940, A , 10, 37, 109; H. E. Farnsworth,Physical Rev., 1935,48,:972; M. F. Hasler, Rev. Sci. Instr., 1933, 4, 656; C.A. Cinnamon,ibid., 1934, 5, 187.(Q.E.C.) Journal, 1944, 13, 63.38 L. Graf, 2. Physilc, 1931, 67, 388.41 s. Kyropoulos, 2. anorg. Chem., 1926, 154, 308.42 H. S . MiiIler, 2. Physik, 1935, 96, 32188 GENERAL AND PHYSICAL CHEMISTRY.4. CRYSTALLOGRAPHY.X-Ray diffraction by crystals is being widely applied to a great variety ofproblems. While the general stereochemical arrangements in molecules ofsome complexity such as penicillin and sucrose are examined and the lesscompletely ordered structures of polymers or soap are studied, preciseinteratomic distances are determined in simpler substances such as methyl-ammonium chloride. Some crystal structures such as that of ice which mightbe considered simple continue to reveal more and more detail as fuller use ismade of all the observable X-ray effects. A mass attack has been made onthe crystal chemistry of the rare earths, thorium, plutonium, neptuniumand, it is presumed, other transuranic elements. As a result of the examin-ation of 150 compounds it was claimed (at the Institute of Physics Conferenceon X-ray analysis during the War) that the crystal chemistry of these ele-ments is now " known " better than that of most other elements.So farthis knowledge is not available in detail. The structures of some complexchlorides of molybdenum have been revealed, but that there are still diffi-culties in structure determination is shown by work on CSCUCI,~. Thisapparently simple structure seems to be based on close packing of czesiumand chlorine ions, but no detailed arrangement has yet been found in agree-ment with the observed diffraction effects.X-Ray examinations continue in use for identification, molecular-weightdetermination, and the testing of proposed molecular formula2 As anexample of identification, the structure determinations of the plutonium andneptunium compounds mentioned above are of some interest.The chemicalidentities of most of the compounds were in this case deduced from theirX-ray diffraction patterns given by very small quantities of materials pre-pared by known methods. The power of the X-ray method to reveal detailsthat are with difficulty determinable by analytical methods is shown in agroup of compounds that might have been supposed to be impure Bi203 butwhich are shown to be built up of approximately spherical units of com-position SiBi,,O,, 3 containing always an atom of silicon a t the centre of thegroup.In another instance 67 the completion of a Fourier electron-densityprojection made possible by the existence of several related structures led tothe revelation of a previously unsuspected molecule of methyl alcohol in thesubstance formerly known as p-quinol but thus shown and subsequentlyconfirmed by analysis to be a compound of composition 3C,H,(OH),,MeOH.Weissenberg photography has been used to show that a sample presumed tobe DDT had a deficiency of one chlorine atom per molecule and to identify itas DDD.*H. P. Klug and G. W. Sears, J. Amer. Chern. SOC., 1946, 98, 1133.E. P. Abraham, D.1\1. Crowfoot, A. E. Joseph, and E. M. Osborn, Nature, 1946,L. G . Sillen; reported at Institute of Physics Conference on War-time Progress inNature,158, 744.X-Ray Analysis, July, 1946 ; see also Arkiv Kemi, Min. GeoE., 1937, A , 12, 18.1945,155, 305.M. Schneider and I. Fankuchen, J. Amer. Chent. Soc., 1946, 98, 2669POWELL : CRYSTALLOGRAPHY. 89B. Strijk and C. H. MacGillavry have examined the structure of a high-temperature modification of sodium nitrite with a view to discover whetheran abrupt change in the temperature coefficients of the cell constants and asimultaneous loss of the original strong piezoelectric effect may be due to theoccurrence of two symmetrical sets of atomic positions in an average structureor to an oscillation of the atoms along one axis.A correction now givenshows that a decision between the two models is not possible from the availabledata.D. A. Hutchinson 6 has used density and X-ray data of calcite, diamond,lithium fluoride, sodium chloride, and potassium chloride to obtain atomicweights. This is done by comparing the molecular weights of two sub-stances calculated from unit cell dimensions and densities. If the atomicweights of some of the elements are assumed, those of others, here calciumand fluorine, may be calculated. The values derived are Ca = 40-0849 50.003, 3' = 18.9967 5 0.0013 and it is concluded that such a determinationis as reliable as other standard atomic weight procedures.Other uses of X-rays include a study of t,he thermal decomposition ofsilver oxalate by means of oscillation and Weissenberg photographs.' Thecrystals are shown to undergo fragmentation in which portions of the originalcrystals break away and assume orientations in which their a axes are notparallel to that of the parent crystal.On further heating, the powder linesof metallic silver appear with definite maxima. This is presumably due tothe orienting influence of the silver oxalate crystals. Many similar reactionscould be investigated in this way.Experimental Methods and Calculations.-A. Turner- Jones and C. W.Bunn have extended the " tilted crystal " method of indexing, and describea method of indexing the reflexions on rotation photographs of a singlecrystal set up in a random orientation.By this method it is possible to takean irregular fragment of a crystal of completely unknown crystallography,set it up on an ordinary X-ray rotation goniometer in any position, take twophotographs, and deduce the unit cell and space-group from these photo-graphs. M. Farquhar and H. Lipson have discussed the general principlesby which improved accuracy may be obtained in the determination of unit-cell dimensions from single-crystal photographs. The principles, based onthose used for powder photographs, applied to an orthorhombic crystalenabled an accuracy of the order of 0.005% to be attained. The integralbreadths of Debye-Scherrer lines for a divergent incident X-ray beam havebeen considered by A. J. C. Wilson.lo The broadening due to the appreciablephase differences between different parts of the crystal, even in the size rangefor which line broadening occurs, is calculated and is shown to be ordinarilynegligible.The accuracy of atomic co-ordinates derived from X-ray data has beenRec. Trau.chim., 1943, 62, 705; 1946, 65, 127.J. Chim. Physics, 1945,13, 383.R. L. GrifEth, ibid., 1946, 14, 408.Proc. Physical SOC., 1946, 58, 200.J . Sci. Imtr., 1946, 23, 177.lo Ibid., p . 40190 GENERAL AND PHYSICAL CHEMISTRY.the subject of theoretical consideration by A. D. Booth.ll By a comparisonof two independent sets of observed F values i t is found that the error inexperimenally observed F’s is independent of the magnitude of F. It isconcluded that this source of inaccuracy in derived atomic co-ordinates is asecondary one and for a particular case the error for a carbon atom isestimated as approximately *0.003 A.The larger error due to the non-infinite limits of Fourier summations is also considered and a possible wayof correcting for it is devised. In a special case the distortion produced isfound to have an upper limit between 0.02 and 0.005 A., experimentallyobserved errors being about 0.02. The effect of thermal agitation is to givea considerable decrease in accuracy, Another paper l1 deals with the problemof determining the maxima in a Fourier synthesis, and is based on examiningthe rapidly varying differential coefficient rather than the function itself.The problem of the steadily increasing magnitude of routine calculationnecessary for any structure determination has received further attention.Forcomputing Fourier series punched-card methods have been used with existingcalculating machines by I?. A. Schaffer, V. Schomaker, and L. Pauling,l2who point out that the method has applications in other fields of molecularstructure determination. Punched cards and a computing service wereemployed in the evaluation of electron densities for penicillin l3 a t intervalsof about 0.25 A. throughout the unit cell. At present this procedure seemscostly. Several machines for performing these calculations have beendesigned or constructed, One described by D. MacLachlan l4 depends on thespreading of layers of sand in sinusoidal waves over a scale plan of the unitcell so that the height of sand at any point is proportional to the electrondensity.An electrical Fourier summation machine has been developed byG. Hagg and T. Laurent.15A. R. Stokes l 6 has described a development of the “ fly’s eye ” whichobviates the calculation of structure amplitudes in the trial-and-error stagesof structure determinations. I n the device described, a regular repeatedpattern representing the structure is produced on a photographic plate by useof a fly’s eye composed of an array of small lenses embossed on the surface of apiece of “ Perspex ” which has been pressed a t its softening temperature intoa copper plate previously indented by means of a steel ballbearing. The dis-advantages of the pin-hole method previously used, ‘uiz., diffuseness of thepin-hole images and blocking of the pin-holes by dust, are overcome.Insteadof a movable lamp to represent the atoms, a uniformly illuminated screenwith a number of opaque discs may be used, so that no negative need be madeand only one exposure is necessary instead of one for each atom.As is well known, the determination of crystal structure by Fouriersynthesis requires the observation of as many X-ray reflections as possiblel1 Proc. Roy. SOC., 1946, A , 188, 77; Trans. Faraday SOC., 1946, 43, 444.l2 J . Chem. Physics, 1946, 14, 648.l3 D. M. Crowfoot and B. W. Rogers, to be published.l4 See Nature, 1946, 158, 260. l6 J . Sci. Imtr., 1946, 23, 155.Proc. Physical Soc., 1946, 58, 306POWELL : CRYSTALLOGRAPHY. 91and the summation of appropriate Fourier series in which the structurefactors, derived easily from these observations, appear as the coefficients.The obstacle to a simple and automatic application of the procedure to anydesired crystal rests in the fact that the structure factor is a complex quantity.The magnitude is derivable from observed quantities but the phase angleescapes observation.At present all the essential work of the determinationis that of discovering these phase angles by a process of trial greatly assistedby a variety of auxiliary means such as the use of physical properties,Patterson methods, introduction of heavy atoms, consideration of pre-viously known structures, and the study of isomorphous or related com-pounds. In the special case of centrosymmetric structures the problemreduces to that of giving the positive or negative sign to the observedstructure factor Phkl for each of the observed hkl reflexions, possibly severalhundred or more in number..If a given arrangement of atoms is considered, it is possible to computethe value of F for all points in reciprocal space, i.e., for a reflexion from aplane of any selected spacing and orientation. For centrosymmetricstructures we may imagine the group of atoms arranged around the originand repeated by simple translations of any desired lengths and directions toform a lattice. The resulting F plot in the reciprocal space is characteristicof the original arrangement and nature of the group of atoms. The value ofF is seen to vary in magnitude from point to point and to undergo changes ofsign. If a continuous variation of spacings could be made without otheralterations in the structure, or at least with only such alterations as could beallowed for, it would be possible to observe a continuous variation in themagnitude of F and to determine the points where it vanished.These wouldcorrespond to changes of sign and hence all the signs could be found. Anapproximation to this procedure was adopted by Perutz l7 in a structurewhere the reflexions from a particular direction in a protein crystal areobservable over a continuous range of spacings due to the taking up ofvariable amounts of liquid between layers. In ordinary practice the valuesof F observed from the Bragg reflexions are only those that correspond to theparticular planes that occur in the crystal under investigation, i.e., at certaincomparatively widely separated points in reciprocal space and without thepossibility of continuous variation.A. D. Booth,18 however, has suggesteda possible limited application of the method by the use of the diffusereflexions. Although it is difficult owing to background to establish theexistence of a point of zero intensity, it may be possible to show that there isno such point in a given region. Thus if a strong streak of diffuse X-rayscattering connects two regions in the reciprocal lattice of a centrosymmetriccrystal the F’s corresponding to those two regions must have the same sign.This, it is suggested, might sometimes help to determine a few signs but wouldnot go far towards solving the general problem.(Mrs.) K. Lonsdale l9l7 J. Boyes Watson and M. F. Perutz, Nature, 1946, 15l, 714.l8 Ibid., 1946, 158, 380. 19 IbicE., p. 68292 GENERAL AND PHYSICAL CHEMISTRY.points out that the argument is sound if the diffuse scattering is due to dis-placement or vibration of those atoms whose diffraction is mainly responsiblefor the reinforcing waves which give the Bragg reflexions, i.e., the scatteringin the streak and the two Bragg spots which it connects must be mainlydue to the same atoms. In ice, however, where the contribution of thecentrosymmetrically arranged oxygen atoms certainly decides the phases,strong diffuse streaks do connect regions where F's are not of the same sign.Moreover, the diffuse pattern is more symmetrical than could be the case ifBooth's rule were satisfied.Any such attempts even at this very limitedcircumvention of sign computation must therefore be made with extremecaution.Inorganic 8tructures.-Crystal chemistry of neptunium and plutonium.20I n the sexa-, quadri-, and ter-valent compounds the crystal radii decrease inthe order uranium, neptunium, plutonium. Tht crystal chemistry of thoriumand especially cerium is closely related to that of uranium, neptunium, andplutonium in the quadrivalent state. In the tervdent state the elementsLa-Sm show a marked similarlity to uranium, neptunium, and plutonium intheir crys t a1 chemistry .Oxides, hydroxides, and basic salts.The cell dimensions of a number ofdouble oxides belonging to the perovskite type of structure have beenaccurately measured by H. D. Megaw.21 This group of compounds includesstructures of very varied but different symmetry, all based on small modi-fications of the same cubic cell. The ideal perovskite type includes SrTiO,,SrSnO,, SrZrO,, BaSnO,, BaZrO,, BaThO,, and BaTiO, above 120". Some,including the usual form of BaTiO,, have a tetragonal cell derived from thecubic structure by simple compression or extension along one of the fourfoldsymmetry axes. Others, including CaTiO, (the mineral perovskite), arederived from the cubic structure by a shear in the 010 plane and a slightextension or compression along the b axis giving a monoclinic pseudo-cellwith the a and c axes equal, so that the lattice is to be described as ortho-rhombic.Changes in some of the atomic parameters cause a doubling of thecell edges. Thepseudo-cell is obtained by a slight compression of the cubic cell along the cubediagonal but the true cell is a multiple of this. The occurrence of the variousstructure modifications is interpreted in a genera1 way by steric considerationsbased on Goldschmidt's ionic radii.Quenselite,22 PbMnO,(OH), has a structure characterised by the super-position of sheets of ions perpendicular to the a axis in the sequence Mn, 0,Pb, OH, Pb, 0, Mn.The decomposition products of lead dioxide at 400" in air have beeninvestigated.23 It was found that lead dioxide samples contained a small2o W.H. Zachariasen reporting a t Institute of Physics Conference on War-timeProgress in X-Ray Analysis, Royal Institution, July 1946; see also ref. (14).21 Proc. Physical SOC., 1946, 58, 133.22 A. Bystrom, Arkiv Kemi, Min. Geol., 1945,19, A, 35.BaTiO, can also be prepared in a rhombohedra1 form.There is a good cleavage parallel to the sheets.A. Westgren and H. Hagg, ibid., 1945-1946, 20, A, 11POWELL : CRYSTALLOGRAPHY. 93amount of water which probably forms part of the anion lattice as hydroxylgroups. The oxygen content cannot be below that corresponding toPbOl.,,. A decomposition product a-PbO, may also be obtained by oxidationof certain preparations of PbO in oxygen at 300-350". This compound hasa range of homogeneity with limits close to the formulae Pb,O, and Pb,O,.The structure is very complicated and not determined with certainty.Thenext step in the decomposition is represented by p-PbO,. The composition isnear to Pb,O, and a structure is proposed in which the lead atoms occupypositions similar to those of the heavy atoms in cubic Bi,O, and cubicSb20,. It is concluded, contrary to the views of M. LeBlanc and E. E b e r i ~ s , ~ ~that the tetragonal and orthorhombic modifications of PbO have no range ofhomogeneity or very narrow ones. Some preliminary data are also givenwhich perhaps represent a third modification of PbO.W. Feitknecht and W. Marti 25 have examined the products of oxidationof manganese( 11) hydroxide and of ammoniacal manganese( 11) salt solutionsby oxygen and hydrogen peroxide, By powder photography the productsare found to be Mn(II),(III) double hydroxide, hausmannite, hydrohaus-mannite, a-, p-, and y-MnO(OH), Mn,O,.Excepting hausmannite andy-MnO(OH), the degree of oxidation of the manganese in all these compoundscan vary within certain limits, i.e., they are non-Daltonian compounds. Themanganites obtained from solutions of Mn(I1) and other metals have adouble layer structure with hexagonal layers of MnO, and disorderedhydroxide layers of the lower-valent metal such as Ca,Mg,Zn. The disorderis shown by varying sharpness of the inner rings or by their absence.W. Feitknecht26 gives some data on basic cadmium sulphate, and W. Lotmar2'has obtained single-crystal data from basic zinc chloride, ZnC12,4Zn( OH),.This has a rhombohedra1 double layer structure, but no detailed parameterdetermination is made.Precision measurements 28 on a sample of exceptionally purelead, 99.999% by spectrographic analysis, give a unit cell dimension,4-9408f.O.0001 kX, slightly higher, as was to be expected, than previousvalues derived from samples that may have contained other atoms which aresmaller than that of lead.Polonium29 is shown to have two crystallineforms, a low-temperature structure described as simple cubic with a = 3.34,and a high-temperature simple rhombohedral form with a 3-36 A., a = 98'13'.The simple structure of graphite with its ababab sequence oflayers was modified by Edwards and Lipson 30 on account of extra lines whichindicate the presence of certain layers in the abcubc order, and J.Gibson 31now reports the appearance of still further faint lines which are not accountedfor by this arrangement. They have been observed in ordinary graphite andElements.Graphite.24 2. physikal. Chem., 1932, A , 160, 69.26 Ibid., p. 1454.28 H. I?. Klug, J . Amer. Chem. SOC., 1946, 98, 1493.3O Nature, 1942, 149, 328; Ann. Reports, 1942, 39, 99.31 Nature, 1946, 158, 752.25 Helv. Chim. Acta, 1945, 28, 149.27 Ibid., 1946, 29, 14.137. H. Beamer and C. R. Maxwell, J . Chem. Physics, 1946, 14, 56994 QENERAL AND PHYSIOAL CHEMISTRY,in very pure artificial graphites. Some of the lines are double, with anangular separation of 0.20". No explanation has been given for these effectswhich might be due to other causes such as impure X-radiation.The term amorphous carbon has been used todescribe more or less impure forms of carbon devoid of any obvious crystallinecharacteristics, but such materials prepared in a variety of ways all giveessentially the same type of X-ray powder photograph with broadeneddiffraction maxima in the same positions.These have been interpreted asdue to graphite-like structure with very small particles and varying disorderof the layers. It is now 32 found that a carbon prepared by carbonisation ofhexaiodobenzene at 5"/min. up to 1000" in an atmosphere of nitrogen givespractically no coherent scattering of X-rays and thus seems to be almostcompletely without any ordered structure. Hexaiodobenzene was selectedsince the large iodine substituents might be expected t o prevent a linking oftwo aromatic residues with their rings coplanar and so favour the formation ofa hypothetical carbon structure in the form of a three-dimensional repetitionof o-tetraphenylene residues.The material obtained is thought to consist ofsuch a cross-linked structure, but highly disordered because of the presence ofoxygen and hydrogen atoms, and it is suggested that small disordered chunksof this type of structure play some part in the building up of chars and cokes.Further evidence is required before this can be regarded as established.The diffuse X-ray scattering obtained fromice crystals gives further information on this structure.33 The diffusepattern is of thermal origin but cannot in the main be due to acousticalvibrations because no combination of elastic constants can give the atar-shaped pattern found.Since the diffuse streaks cannot be due to oxygen(see above) there must be strong vibratory movement of the hydrogennuclei. J. D. Bernal and R. H. Fowler 34 show that the unit cell must be atleast three times as large as the apparent simple cell, while L. P a ~ l i n g , ~ ~from considerations of the residual entropy, has concluded that the watermolecules in ice cannot have definite orientations which would permit aunique crystalline configuration such as that of Bernal and Fowler. Thisnew work by Lonsdale confirms Pauling's suggestion that change from oneconfiguration to another is accomplished by group movements of hydrogennuclei each of which would move from the neighbourhood of an oxygen atomto the next oxygen, or by rotation of water molecules.The small unit cell istherefore a statistical one, and even a t low temperatures the apparent cellmay be small owing to freezing in of different molecular configurations indifferent parts of the crystal. A similar star-shaped diffuse pattern isobtained for ammonium fluoride, isomorphous with ordinary ice. Somehailstones have been shown 36 to contain moderate sized single crystals of theordinary ice form." Amorphous " carbon.Ice and ammonium Jluoride.32 J. Gibson, M. Holohan, and H. L. Riley, J., 1946, 456.33 K. Lonsdale, ref. (19).36 " Nature of the Chemical Bond ", New York, 1939, p. 281.36 K.Lonsdale and P. G. Owston, Nature, 1946, 157, 479.3 4 J . Chern. Physics, 1933, 1, 515POWELL : CRYSTALLOGRAPHY. 95Methylammonium chloride. The unit cell formerly ascribed t o methyl-ammonium chloride was based partly on powder-photograph measurementsand was incorrect. It istetragonal, and the whole structure may be regarded as a somewhat distortedcmium chloride arrangement, in which methylammonium ions are surroundedby the chlorine ions of the top and bottom faces of the cell. The lengths ofthe methylammonium ions which point alternately up and down are parallelto the c axis, and from the Fourier analysis results the distance C-N =1-465&0-01 A. The predicted value is 1-47 if no allowance is made for theformal charge, but with such an allowance it is 1.44, so the formal chargeappears not to have the expected effect although the differences here seem tobe fairly close to the possible errors.I n working out this structure it wasfound necessary to apply separate temperature factors for the methyl-ammonium and the chlorine ions and an anisotropic temperature factor wasused for chlorine with the maximum vibration along the c axis as is suggestedby the form of the corresponding electron-density peak.Halogen-containing complexes. Data concerning a structure deter-mination of aluminium bromide 38 have now become available. Separatemolecules of A]&, are arranged in a monoclinic cell to give a slightlydeformed hexagonal close packing. The molecules are of the type found byPalmer and Elliot in the gaseous state by electron diffraction, i.e., themolecules consist of two tetrahedra of bromine atoms around aluminiumatoms, the tetrahedra sharing an edge. There are some marked differencesin the intramolecular distances derived from the crystal structure and thosegiven by electron diffraction.I n particular the A1-A1 distance 3 . 1 4 ~ . isappreciably shorter than the 3-39 A. found in the gaseous state, and in generalthe values found are closer to those that would be expected for a model con-structed from two regular tetrahedra. The molecule is much less deformedthan in the gaseous state, and it seems that the structure yields less to therepulsive force between the central aluminium atoms. A suggested explan-ation is that it would be impossible to obtain such a good packing with themore deformed molecules and there would be a consequent loss of van derWaals attraction between the bromine atoms.The compound hitherto given the formula Mo3C14( OH),,8H20 has beenexamined.39 Analytical data suggest seven rather than eight water mole-cules, and although the unit-cell dimensions and density agree with sixmolecules of water, it is considered that seven is the more probable figuresince the density determined may be low.From the structure determinationthe formula is now rewritten as [Mo,CI,](OH)~,~~H,O. The [Mo,Cl,] groupis a slightly irregular cube with chlorine a t each corner and with molybdenumatoms at the centres of each cube face but raised slightly, about 0.05 A., abovethe faces.These groups are enclosed in a three-dimensional network ofThe cell now37 found contains two molecules.37 E. W. Hughes and W. N. Lipscombe, J . Amer. Chem. SOC., 1946, 68, 1970.a* P. A. Renes and C . H. MacGillavry, Rec. Trav. chim., 1945,64, 276.C . Brosset, Arkiv Kemi, Min. Geol., 1945-1946, 20 A 796 GENERAL AND PHYSICAL CHEMISTRY.oxygen atoms. Each molybdenum atom has four chlorine neighbours a t2.50, 2.57, or 2-62 A. and one oxygen at 2-29 A. In all, there are 18 oxygenatoms connected with one [Mo,c1,] group. Of these, 4 must be OH and 14must be water, although the 18 atoms are distributed in one group of 6 andone group of 12 equivalent point positions of the hexagonal cell. It issupposed that the 32 hydrogen atoms are distributed statistically among the18 oxygen atoms.The oxygen-oxygen distances, which are not known withgreat certainty, are about 2 . 7 ~ . The compound formerly described as[Mo,C1,,2H20]CI, ,2H20 has a tetragonal structure 39a which contains thesame Mo,CI, group and is now rewritten [MO6C1,](C1,,2H2O). I n the[Mo,Cl,] group the average Mo-Mo distance is 2.64 A.Precipitated potassium cryolite 40 has a variable composition dependingon the fluorine-ion concentration a t precipitation. The general formula isKzAlF3 + z(H20)3 - %, x being between 2.9 and 3. With x = 2-9 the compoundis isomorphous with ammonium cryolite and has a cubic cell a = 8.41, A.The unit cell of K3A1F6 is probably large and derived from a body-centredtetragonal cell a = 5-96, c = 8.46,.In precipitated potassium cryolitesome [All?,] groups may be replaced by [AlF5(H20)] when the fluoride-ionconcentration is not high enough. For every such grcrup replaced onepotassium ion is lost from the lattice.Phosgenite, Pb2C12C03, and the isomorphous bromine compound havebeen e~arnined.4~ A previous structure determination on phosgenitesuggested that there were no carbonate groups in the structure but thearguments used are invalid since the unit cell determined now has the cdimension of the unit cell doubled. The intermediate reflexions thatestablished this are exceptionally weak but are more pronounced in thecorresponding bromide. The positions of lead and bromine have beendetermined and the rest of the structure inferred from packing considerations.It consists of lead, halogen, and carbonate ions.There is no evidence oflinking to form Pb-C1 groups.Organic Crystals (General) .-The general constructional principles under-lying the formation of organic crystals have been examined by W. Nowacki 42who, in presenting the statistics for the compounds that have been suitablyexamined-a fraction of a per cent. only-points out that it remains to con-firm the conclusions on the rest. However, the total number of compoundsis considerable, about a thousand, and it seems unlikely that the high fre-quency of occurrence of certain space-groups which is familiar to workers inthis field is accidental. G . Hagg43 considered that the results might beinfluenced by the inclusion of a great number of space-group determinationswhich have been made on optically active substances, but Nowacki 44 replieswith a table showing the frequencies before and after the subtraction ofcrystals which contain optically active molecules.I n the first case in a totalArkiv KeTni, Min. Geol., 1946, 22, A, 11. 40 Ibid., 1946, 21, A , 9.*? Helv. Chint. Acta, 1943, 26, 459.4 4 Helv. Chirn. Acta, 1945, 28, 664.* l L. G. Sillen and R. Petterson, ibid., p. 13.43 Quoted by Nowacki, ref. (42)POWELL : URYBTBLLOGRAPHY. 97of 914 compounds the group P2, is found for 12%, P2& for 10.5%, andP2,2,2, for 22%. On elimination of 173 crystals with optically activemolecules the statistics are not fundamentally altered the percentages beingrespectively 12,7, and 22.Over 40% of the known organic structures there-fore have these space-groups. Seven other space-groups, viz., PI (2-4),C2 (2.4), C2/c (3.4), P2,2,2 (2*7), Pbcu (2.1), Pnma (3.4) and C4/amm,account each for between 2 and 3.5% and leave about one-third of all thecompounds for distribution among more than 200 remaining space-groups.In explanation of this, Nowacki says that the tendency to close packing,which is so frequently found in inorganic crystals, is certainly not a guidingprinciple, and quotes the 75% of all organic substances so far examined ashaving primitive lattices, with a further 16% having double primitivelattices, whereas a face-centred lattice, fourfold primitive, should lead to amaximum space filling.Although this is clearly so for the simplified case ofcubic close packing of spheres, this part of the argument does not appear tothe Reporter to be a strong one, since any structure may be referred, by asuitable choice of axes, to a primitive lattice, and in monoclinic crystals, forexample, the investigator makes a deliberate choice of axes to avoid theselection of a cell centred in any way except, in some crystals, on (001) faces.Further, when the packing of awkward-shaped molecules is considered, it isfound that by use of suitable symmetry operations the centres of moleculesmay be made to lie in positions closely approximating to those for a face-centred close packing although the structure as a whole is not formallycentred, e.g., in the structure of picryl iodidet5 space-group P4,2,.In this connection also A.Kitaigoro&kyt6 by assuming intermolecularradii for each atom, C 1-70, H 1.18 A,, has calculated the proper volumes of asmall number of aromatic hydrocarbons and compared them with the volumesper molecule in the crystal. Packing fractions between 0.68 and 0.72 areobtained and may be compared with the value 0.74 for closest packing.For molecules which are markedly different in their extensions in differentdirections, centring which involves parallel repetition does not seem soeffective for packing purposes as the use of symmetry operations whichinvolve head-to-tail or similar packing. Apart from this, experience showsthat molecules of the most diverse shapes tend to adopt arrangements inwhich the projecting portions of one fit into the indentations left by thesurrounding molecules in such a way as to achieve a good degree of spacefilling. New structures often appear very striking not only in the mannerwhereby they maintain the familiar van der Waals separations of unlinkedmolecules, but also in the avoidance of any large gaps that would give inter-group separations appreciably greater than the normal.When openstructures appear they are usually attributable to some special circumstancesuch as the directional requirements of hydrogen-bond linkages as in a-resorcinol*' or even more strikingly in quinol.** Nowacki further points out45 G. Huse and H. M. Powell, J., 1940, 1398. '* Acta Phyakochh. U.R.S.S., 1946, 21, 379.47 J.M. Robertson, Proc. Roy. SOC., 1936, A , 158, 79. 48 Ref. (67).REP.-VOL. XLIII. 98 GENERAL AND PHYSICAL CHEMISTRY.that, since the majority of organic molecules have little symmetry of theirown, any higher symmetry of the crystal must result from the arrangementof the molecules and thus selects the 92 asymmorphous space-groups as ofspecial significance for organic crystals. Of all the compounds, 72% arefound to belong to these space-groups. Since many of the molecules havean electric moment, the molecular arrangement will seek to bring about themost effective mutual saturation of dipoles. This is so when the moleculesare arranged in zigzag chains. Only three symmetry elements achieve this,the two-fold screw axis 2,, a network of symmetry centres I, and a glide planeof symmetry c , a, b, d, or n.On the assumptions that the favoured space-groups for organic structures obey the principles of (1) a primitive lattice,( 2 ) asymmorphism, ( 3 ) symmetry elements permissible, are only those statedabove either alone or in suitable combination, those to be expected areP2,, PZ,/c, Pca, Pna, P2,2,2, and Pbca. Some but not all of these occur inthe list of commonly found space-groups, and a further limiting principle isintroduced, that of efficient dipole saturation of one zigzag chain of mole-cules by the others. This requires that a two-fold screw axis may only be per-pendicular to a glide plane, and thus leaves only P2,, P2,/c, and P2,2,2, asthe specially preferred space-groups for organic crystals, i.e., the three firstmentioned as accounting for over 40% of the total.Among the other space-groups the number of examples is too small for any certain conclusions con-cerning their frequency, but some general tendencies can be understood ;e.g., in a comparable set of space-groups the frequency of occurrence increaseswith increase in the number of 2, screw axes as in P222 (0.002~0), P222,(0.003), P2,2,2 (2.7), and P2,2,2, (10.4).C. A. Beevers and W. Cochran49 give apreliminary account of the structure of the sucrose molecule from anexamination of the compound C,,H2,OlI,NaBr,2H,O and the isomorphouschloride. The heavy atoms simplify the phase-angle determinations. Theaccepted structural formula ofsucrose as 1 -a-glucopyranose-2-p-fructofuranose (I) is confirmed. I<:= I l(vo>l Parameters for all atoms are givenI30 \rl’-o- 3’1 1 CH,*OH with an estimated error 0.5 A.for interatomic distances and of(1.) 5” for bond angles.The oxygenatoms attached to carbon atoms 1 and 2 are in the cis-configuration, andsimilarly those of 2’ and 3’. The five atoms of the furanose ring arenot coplanar, atoms 3’, 4’, 5’ being displaced so as to bring the attachedgroups more nearly into the mean plane of the ring. Within the ring themean C-C distance is given as 1 . 4 4 ~ . and the mean angle as 104”. Thepyranose ring is of the Sachse trans-(chair-shaped) form. This result shouldbe compared with that obtained by E. G. Cox and G . A. Jeffrey 50 for glucos-amine hydrobromide where the same form occurs, and by Cox, T.H.Organic Xtructures.-Sucrose.CH,-OH CH,*OHH 6 1-0, H p, HH H HO Hre Nature, 1946, 167, 872. 6o Ibid., 1939,142, 894POWELL : CRYSTALLOQRAPHY. 99Goodwin,51 and A. I. Wagstaff who find the five carbon atoms in a plane withthe oxygen atom out of the plane in methylated aldopyranoses. In thepresent compound each sodium ion is surrounded in a nearly regular octa-hedral manner by one bromine, two water molecules, and three hydroxylgroups, but the surroundings of the bromine are irregular.An earlier attempted structure of m - dini tro benzeneled to a false conclusion through the deceptive character of the crystals whichwere assigned to a too high symmetry class. I n a further examination of thestructure 52 based on the space-group Pbn instead of Pbnm the molecule isfound to be nearly planar.The results of the Fourier analysis are expressedin two diagrams (Fig. 1) projected on the plane of the benzene ring and atm -Dinitrobenxene .1.411-41FIG. 1.(Reproduced by permission from Proceedings of the Royal Society, 1946, A, 188, 59.)right angles to it. This picture is, however, derived from one projection only,and the size and shape of the nitro-group were largely assumed from theresults on other compounds. Some part of the small distortions from thesymmetrical form of the molecule may be spurious. In the molecularcompounds mentioned below the nitro-groups of 4 : 4'-dinitrodiphenyl havea mirror plane passing through the terminal carbon and the nitrogen atomperpendicular to the plane of the benzene rings but the carbon-nitrogen linkis tilted slightly out of the plane of the ring.The determination of structuresof aromatic nitro-compounds has been particularly beset with difficulties andthere is scope for further accurate work.Molecular compounds. Compounds of aromatic polynitro-compounds with61 J., 1936, 1496. IM E. M. Archer, PTOC. Roy. SOC., 1946, A , 188, 61100 QENERAL AND PHYSICJAL CHEMISTRY.other aromatic substances frequently have a 1 : 1 ratio of the two moleculesand this has sometimes been regarded as evidence for an electronic rearrange-ment which provides a chemical link of some kind between the components.It has also been suggested that the association of the two components might beexplained in terms of various interactions (dipole induction effects, dispersioneffect) between one molecule and the other without the necessity for a bond, a i dthat these interactions are most effective if the planes of the aromatic rings areparallel.53 Such a parallelism is observed in many crystalline molecularcompounds of this type.W. S. Rapson, D. H. Saunder, and E. T. Stewart 54have investigated the compounds of 4 : 4'-dinitrodiphenyl with variousdiphenyl derivatives and their results have a bearing on both these supposi-tions. Molecular complexes are formed only with 4-substituted and 4 : 4'-o-00 &-A -0uo IApprox 20A. < bFIG. 2.disubstituted diphenyls. The crystal structures of several of these have beenexamined and are all of the same general type, indicated in Pig.2. In thisidealised structure the dinitrodiphenyl molecules are arranged in planes oneabove the otheq separated by 3.7 A. Running through the structure perpen-dicular to the planes of these molecules are channels in which the other com-ponent molecule, e.g., 4-hydroxydiphenyl, is seen end on with its lengthperpendicular to the plane of the paper. None of the intermoleculardistances is shorter than those normally found in crystals of aromatic nitro-compounds. These results therefore agree with those of H. M. Powell,G. Huse, and P. W. Cooke 55 on other compounds and reveal no localisedbonding between the molecules. Diffuse X-ray reflexions and diffractioneffects due to irregularities somewhat similar to those observed by G .Huseand R. M. Powell 56 in the compounds of hexamethylbenzene with picrylhalides are observed. The molecular ratios in this new set of compounds aredetermined by geometrical considerations. They depend on the number63 D. H. Saunder, Proc. Roy. SOC., 1946, A, 188, 21.'6 Ibid., 1943, 163.~5' J., 1946, 1110.Ibid., p. 436POWELL : CRYSTALLOGRAPHY. 101of dinitrodiphenyl layers that can be accommodated along the length ofthe other component molecule. Thus the length of the 4 : 4’-diacetoxy-diphenyl molecule, after allowance for approach of the next molecule in theend-on position, is 17-18a. This, divided by 3-7, the separation of thenitro-compound layers, gives n = 4-6-4-9 and the compound formed has a5 : 1 ratio of the dinitro-compound to the other molecule.Similar agree-ment is found for the other molecules, the values of n being close to 4,3&, or3 depending on the length of the molecule and in agreement with the com-positions determined by analysis. These structures therefore show thatneither the common 1 : 1 ratio of components nor parallelism of the aromaticrings is essential in these moleuclar compounds.A preliminary communication by D. E. Palin and H. M. Powell 57describes an entirely new type of relationship between the components of amolecular compound. Quinol forms a series of compounds of ideal formula3C,H,(OH),,%f, where M is a small molecule, e.g., sulphur dioxide. Thequinol molecules are linked through hydrogen bonds to form indefinitelyextended cage structures in three dimensions.This structure, of a formimposed by the dimensions of the quinol molecules and the directionalrequirements of the hydrogen bonds, is of such an open character that asecond identical framework structure can completely interpenetrate it.There is thus a mutual multiple enclosure of two giant molecules which haveno direct linkages but are inseparable without the breaking of their ownstructures. This complex of interpenetrating molecules is still not veryclosely packed and contains cavities which are large enough to contain thesmall molecules which form the second component of the molecular com-pound. The formula is determined by the ratio of available cavities to thecage material, and M is restricted to such small molecules as will fit into thespace.The enclosed material once trapped cannot escape despite thevolatile nature of the component in the free state. Whether a given moleculeM will form such a compound is determined, apart from size considerations,by the possibility of obtaining it in sufficient concentration in the samesolution with quinol but does not otherwise depend on the chemical characterof the second component.W. T. Astbury and C. J. Brown 68report that terylene (polyethylene terephthalate) gives a well-oriented fibrediagram with spots that could be indexed on a triclinic unit cell. The fibreaxis has the length of 10-8, A . , which is compared with the 10.9 A. calculatedfor the repeat structureFibres and other complex structures.Increasing disorientation is shown in the usual way by the drawing out ofspots, but terylene is peculiar in that poorly oriented preparations give67 Nature, 1945, 156, 335; see J ., 1947, 208. 68 Ibid., 1946, 158, 871102 GENERAL AND PHYSICAL CHEMISTRY.photographs like those of single crystals rotating about an axis inclined a t asmall angle to the principal axis. Spots are displaced to varying extentsout of the layer lines, and an intense 110 reflexion is seen as two overlappingspots one above and one below the equator. This means that in the drawingprocess it is more difficult to pull 1iO planes into parallelism. From thegreat intensity of this reflexion the chains must be approximately flat andparallel to 110.On drawing, chains or groups are first pulled straight byslipping parallel to this plane, and afterwards, with greater difficulty, theseplanes are themselves pulled into parallelism.A new micro-method for X-ray diffraction of biological objects has beenused by D. Kreger.59 By its means a fibre pattern was obtained from a singlestarch grain. There were a considerable number of spots but the detailedstructure has not been found. Diffraction patterns have previously beenobtained with fairly simple small objects, such as a tungsten thread, and thisextension seems to be of considerable importance.Diffraction patterns of isoprene a t 20'9. and 80" K. show many linesaccording to observations by C. J. B. Clews and A. Schal1amach.m Theseestablish the crystalline character of the material in these conditions butthere is some difficulty in selecting a unit cell. Fibre patterns have beenobtained with filaments of amylose and of amylose containing an uncertain,possibly variable amount of potassium hydroxide.61The diffraction of X-rays by aqueous solutions of hexanolamine oleate 62and of sodium oleate G3 has been studied, and a general structure for themonooleyl disaturated triglycerides has been proposed.64 The structure ofsoap micelles 65 has also been investigated.The X-ray diffraction effects innot too dilute aqueous solution indicate a structure of double layers of soapmicelles with " water" layers between them. In the double layers thehydrocarbon chains are oriented towards each other with the polar endstowards the water. Micelle layer spacings are observed varying from 30 to100 A., and in the plane of the layers there is a nearly constant spacing of 4.5 A.for normal paraffin-chain soaps at all concentrations from 4.5 to 30%.Addition of salts does not materially affect the short spacing, but potassiumor sodium chloride produces a marked effect on micelle layer spacing and onthe intensities of the X-ray pattern. The probable effect is that sodiumchloride makes them smaller.A preliminary report 66 concerning zinc p-toluene-sulphonate and isomorphous substances of type (CH,°C6H4*S03)2Zn,6H,0contains a Fourier electron-density projection which shows all atoms clearlywith the exception of one of the oxygen atoms of the sulphonate group whichoverlaps with the sulphur atom. There is a regular octahedral arrangementOther structures.59 Nature, 1946, 158, 199.6 1 F. R. Senti and L. P. Witnauer, J . Amer. Chem. SOC., 1946, 68, 2407.6a S. Ross and J. W. McBain, ibid., p. 296.6 4 L. J. Filer, S. S. Sidhur, B. F. Daubert, and H. E. Langenecker, ibid., p. 167.65 W. D. Harkins, R. W. Mattoon, and M. L. Corrin, ibid., p. 220.6 6 A. Hargreaves, Nature, 1946, 158, 620.6o Ibid., 1946, 157, 160.63 Ibid., p. 547POWELL : CRYSTALLOGRAPHY. 103of water molecules round each zinc atom. More precise details of the stereo-chemical relationships await a determination of the third atomic co-ordinate for each atom.Unit cell dimensions have been given from two sources 67 for a number ofdiphenyltrichloroethane derivatives. One compound, op’-dichlorodiphenyl-trichloroethane, has a triclinic cell with the unusual number of 20 moleculesper unit cell. There must therefore be at least 10 molecules in the asym-metric unit, a state of things that may perhaps be attributed to the generalawkwardness of the molecular shape for packing purposes. Wild andBrandenberger on the basis of Patterson analysis have suggested atomicpositions for the chlorine atoms in DDT. Schneider and Fankuchen, whohave also studied this substance, conclude that these suggested parametersrequire some modification, but details are not available. The highly sym-metrical form of the quinuclidine molecule might lead one to suppose that itwould form a hexagonal close packing, but this is not the case, since at roomtemperature it forms isotropic cubic crystals with a = 8.977&0.009 A. andfour molecules per unit cell. The translation lattice is face-centred, i.e.,the molecule centres form a cubic close packing. In order to bring thetrigonal symmetry of the molecule into agreement with the cubic symmetrythere must be either free rotation of the molecules about their centres or astatistical disordered structure with the molecular trigonal axes parallel tothe four sets of three fold axes of the cubic unit. On space considerations thelatter is the more probable. H. M. P.MANSEL DAVIES.P. JOHNSON.H. M. POWELL.A. F. WELLS.67 H. Wild and E. Brandenberger, Helv. C?~im. Acta, 1946, 29, 1024; M. Schneiderand I. Fankuchen, J . Amer. Chem. SOC., 1946,68, 2669