CRYSTALLOGRAPHY.A REPORT of this nature cannot claim to deal exhaustively withall the work on crystallography, of direct or indirect interest tochemistry, which has appeared during the year. It is necessaryto limit the scope, so as to be able to deal adequately with thesubjects chosen. We have selected for special treatment the workon the influence of atomic size and chemical constitution on thestructure of crystals, which has been so admirably summarised inthe papers of V. M. Goldschmidt, and also the work on the structureof alloys, which, in the hands of Westgren, PhragmBn, and others,has made considerable advances since it was last dealt with in theseReports.Of great interest to all workers on crystallography is the reportby P. P. Ewald and C. Hermann on all crystlal structures in-vestigated by X-ray methods from 1913 to the end of 1926, whichis at present appearing in serial form in the Zeitschrift fur Kristal-lographie.In Vol. 65, which is just completed, the elements and anumber of binary compounds have been dealt with. The descrip-tions of the structures, given in considerable detail, are very clearand extensively illustrated. The whole, when completed, will forma most valuable compendium.Xixes of Ions in a Crystal Lattice.During the last few years a large amount of work has been doneon the sizes of the atomic domains in the crystal state. The ideaof a definite volume associated with a given atom or ion, which,in compounds of the same type, it always occupies, is becomingincreasingly important as an aid to crystal analysis.For an accountof the work which has been done in this subject up to 1926 referencemay be made to the section entitled " Grosse und Bau der Molekiile "by H. G. Grimm in Geiger and Scheel's Handbuch der Physik, XXII,Quite recently a new estimate of ionic radii has been made byL. Pauling,' who bases his work on the idea that the dimensions ofan ion are conditioned by the radius of the outer electron shell, andthat this in its turn, for ions of similar structure, is inversely pro-Proc. Roy. SOC., 1927, [ A ] , 114, 181; A,, 394; J . Amer. Chem. Soc., 1927,49, 765; A., 399.p. 499274 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.portional to the effective nuclear charge acting on that shell. Heemploys a method based on the wave mechanics t o calculate thiseffective nuclear charge, and is thus able to obtain the ratio of theradii of pairs of ions.To get the actual sizes, he uses as his startingpoint the experimental interionic distances, giving the sum of thetwo “ radii,” in NaF, KCl, RbBr, and CsI, together with an assumedvalue for Li of 0.608. obtained from the experimental distancein lithium oxide. We give in Table I a number of the ionic radii socalculated, compared with the empirical values given by V. M.Goldschmidt.2 It will be seen that the agreement on the whole isvery good.TABLE I.(Ionic radii, in Angstrom units.)Goldschmidt 1.32 1.33 1-52 0.98 0.78 0.67 0.39 0.3-0.4 0.34Pauling ...... 1.40 1.36 0.95 0.65 0.60 0.41 0.34 0.290-8.F-l. Ne. Nal. Mga. AP. Si4. P5. S6.The values used for 0-2 and F-l by Goldschmidt are those deducedby J. A. Wa~astjerna.~ Since, from empirical data from crystalswe cannot obtain the actual radius, but only the sum of two radii,we must assume the radius of at least one ion, and Wasastjerna’svalues are here taken as the starting point. The above table showsonly a few values; many more me given in the papers to whichreference has been made.The Relation between Crystal Strucfure and the Nature of theAtoms taking Part in it.In a series of papers briefly mentioned in last year’s Report,V. M. Goldschmidt has given an interesting survey of the differenttypes of crystal structure formed by the simpler compounds, andof the conditions under which one or other of these types occurs.Although many of the ideas emphasised have been implicit in agood deal of the work on crystal structure, they are summarisedvery clearly and much new matter is included.The whole is basedupon a mass of experimental work, most of which has been carriedout in Goldschmidt’s laboratory at Oslo. Reference may bemade to a good summary of the work, the material of a lecture byGoldschmidt 4 to the German Chemical Society. Goldschmidtpoints out that purely geometrical considerations, based on the ideaof an ionic radius characteristic of each ion, play a very importantpart in determining which type of structure is formed, particularly2 “ Geochemische Verteilungsgesetze der Elemente,” VII and VIII, NorskeVidenskape-Akad.(Mat. Nut. KZ.), 1926, Nos. 2 and 8.2. phyeikal. Chem., 1922, 101, 193; A., 1922, ii, 491,4 Ber., 1927, 60 [B], 1263; A., 611CRYSTALLOQRAPHY. 275when the constituents are simple ions having the inert-gas structure.It is supposed that one important condition for the stability of anionic structure is that anion and kation may touch one another.The number of ions of type X which can surround and touch an ionof type A depends on the ratio of the radii of A and X, supposingeach ion to be a sphere with a definite radius. In Table 11, which istaken from Goldschmidt’s work, are shown, in the first column thenumber of ions X which are supposed to surround and touch an ionA ; in the second the number and arrangement of the ions X aroundA, and in the third the smallest value of the ratio of the radii of theions, Rd/RY, which is permissible in order that such an arrangementmay be possible.It is to be emphasised that the essential point isthe contact of X and A.TABLE 11.Arrangement of X Ions around the Ion A.Number of Limiting ratioions X. Arrangement of X. RAIRx.3 At corners of an equilateral triangle. 0.164 At corners of a tetrahedron (ZnS) 0.224 0.416 0.418 0.73At corners of a square in the plane of A.Along the edges of a cube, A at corner (NaCl) ;At corners of a cube with A in the middle.or at corners of an octahedron.We may now consider the different types of compound AX andAX, with respect to the co-ordination of the ions one to another.In the zinc sulphide lattice, each ion has four neighbours of theopposite kind, in NaCl and NiAs, six, and in CsC1, eight.For lattices of the type AX, there are twice as many ions of theopposite sign around A as there are around X.For the differenttypes of lattice the numbers are as follows : CO,, 2 and 1; SiO,,Cu,O, 4 and 2 ; TiO, (rutile or anatase), CdI,, MoS,, 6 and 3 ; CaF,(fluorite), 8 and 4.Now, so long as we are dealing with simple ionic structures, it isfound that the type of lattice formed by a pair of ions can generallybe predicted by ascribing to each ion one of the radii discussed inthe preceding section, and taking into consideration the limitingratios of the radii for different types of co-ordination. A few ofthe many examples given may be quoted.Of the fluorides of the bivalent metals, MgF,, NiF,, CoF,, FeF,,ZnF,, and MnF, have the rutile structure with co-ordination numbers6 and 3, whereas CdF,, CUP,, HgF,, SrF,, PbF,, and BaF, have thefluorite structure with co-ordination numbers 8 and 4.The seriesas given is arranged in ascending order of RA/Rx. The value ofthe ratio for MnF, is 0.68, and for CdF, 0.77, whereas the limitingvalue of the ratio for the transition from the one type of co-ordin276 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.ation to the other is seen from Table I1 to be 0.73. Further, theoxides, sulphides, selenides, and tellurides of Mg, Cay Sr, and Ba allhave the rock-salt structure (co-ord. number 6) except MgTe, whichhas the wurtzite structure (co-ord.number 4). For the rock-saltstructure the ratio RA/Rx must be between 0.41 and 2.45; MgTe isthe only compound of this whole series in which the ratio fallsoutside these limits, its value being 0.37. The atomic radii cannotbe treated as exactly constant. There is a definite decrease as theco-ordination number decreases, and thus the limits are onlyapproximate; but there is no doubt that for a large class of com-pounds purely geometrical considerations of this kind are moreimportant than chemical considerations in determining the type ofcrystal structure.Geometry is not, however, the only factor. If one of the ions ismuch more readily polarisable than the other, so that it tends tobecome an electric dipole under the action of a field, this may havegreat influence on the actual structure, although geometricalconsiderations will remain as an important factor.Eachcadmium ion lies between six iodine ions, and the iodine has threecadmium ions as nearest neighbours.The crystal forms sheetscomposed of two layers of iodine atoms held together by thecadmium in between them. The iodine ions will be stronglypolarised by the cadmium ions. Each sheet is a very rigid structure.Adjacent sheets, however, are only lightly held together so that thecrystal has a very perfect cleavage. Lattices of this type have beentermed “ Schichtengitter,” or “ layer lattices,” by F. H ~ n d . ~The condition for such a layer lattice appears to be that one of theconstituents should be readily polarisable.This is illustrated bythe following fact. Cadmium fluoride has the fluorite structure.If we replace F’ by OH’ we get a layer lattice.6 Geometrically,OH’ occupies about the same space as F’, but it is a natural dipoleand so the layer lattice is formed. Similarly, if in SnO, or TiO,we replace 0” by S”, which is more readily polarisable, the rutilelattice changes to a layer lattice of the cadmium iodide type.’The lattices so far considered are of the purely ionic type, althoughmodified by polarisation effects. We must now consider brieflysome lattices which are certainly not ionic. One of the types ofAX lattice is typified by nickel arsenide, NiAs. The arsenic atomsare here nearly in hexagonal close-packed array. The nickelatoms lie in the gaps in the structure, between six arsenic atoms,6 2.Physik, 1925, 34, 833; Physikal. Z., 1926, 26, 682; A., 1925, ii, 1132.6 G. Nattrt, Atti R. Accad. Lincei, 1925, [Vi], 2, 495; A., 1926, 228.5 A. E. van Arkel, Physica, 1924, 4, 286; A., 1926, ii, 749,An example is given by the cadmium iodide latticeCRYSTALLOGRAPHY. 277The series of sulphides, selenides, and tellurides of Ca, Mn, Fe, Co,and Ni show a transition from the NaCl structure to the NiAsstructure with increasing atomic number of either ion. There is atthe same time a considerable decrease in the interatomic distancebelow that appropriate to an ionic lattice of the rock-salt type forthe same elements. One remarkable fact about lattices of thistype is that more or less free isomorphous replacement seems totake place between the components.For example, ferrous sulphideand sulphur form an isomorphous mixture in which the excess ofsulphur appears to be able to replace iron in a lattice of the NiAstype.* Goldschmidt and his co-workers found the same thing forCoSe, MnSb, and FeSb, and suggest that the formula of suchcompounds might better be written Fe,Sb, and so on. Suchlattices seem only to be formed when the metallic atom belongs tothe series from scandium to nickel in which there is a deficiency ofelectrons in the M-group. Goldschmidt goes so far as to suggestthat part of the negative charge of the anion either directly orindirectly tends to make good this deficiency. Assuming that adeficiency in an inner electron group in the kation, and a large andreadily polarisable anion are the essentials for this type of structure,Goldschmidt argues that compounds of metals of the platinumgroup with readily polarisable ions should show the NiAs structure.This has been verified for the compound PtSn.Another type of lattice of great interest is that in which eachcomponent has four neighbours, the zinc blende or wurtzite lattice.The geometrical condition for such a lattice is a ratio of radii between0.22 and 4.5, but there seems to be a further condition, which waspointed out by M.L. Huggins and by H. G. Grimm and A. Sommer-feld.1° The condition is that the element A must be as many places(up to three) in the periodic table before one of the elements, C,Si, Ge, Sn, Pb, as the element X is beyond it.The sum of theouter electrons of the two components must therefore be eight.The lattice which is so formed is not a simple ionic lattice, as can beseen by studying the atomic distances in the series given in Table 111,which was investigated by Goldschmidt. Grey tin forms a latticeof the diamond type ; the other compounds in the series are formedTABLE 111.Atomic number. Compound. Lattice constant. Atomic distance.60,50 SnSn 6-46 A. 2-79 8.49,51 InSb 6.452 ,, 2.793 ,,48,52 CdTe 6-463 ,, 2.799 ,,47,63 AgI 6.491 ,, 2.811 ,,N. AlsCn, Geol. F6r. Ftjrh., 1925, 47, 19.Physica2 Rev., 1926, [ii], 27, 286; A., 1926, 458.lo 2. Physik, 1926, 36, 36; A., 1926, 560278 ANNUAL REPORTS ON THE PROGRESS OF CHENISTRY.by increasing the atomic number of one component above thatof tin and decreasing that of the other by the same amount belowit, so that the sum of the atomic numbers remains 100.The mostremarkable thing about the series of compounds so formed, all ofwhich crystallise on the zinc blende (diamond-like) or wurtzitelattices, is the constancy of the interatomic distance. We should notget this constancy in a similar series of compounds of the sodiumchloride type. If we take another of the quadrivalent elementsas the starting point, we get another series, with a different constantatomic distance. We must refer the reader to Goldschmidt’s workfor a complete table of such compounds. The lattice here is not anionic lattice, neither in all probability is it, strictly speaking, atomicor molecular.Goldschmidt concludes that the individuality ofthe single elements matters but little. There seems to be a commonstructure of the whole crystal, the dimensions of which are controlledalmost entirely by the total number of negative charges, andscarcely a t all by the distribution of the positive charges on the singleatomic nuclei. I n the next section we shall see that similar con-siderations are true for alloys and intermetallic compounds. Indeed,both in the NiAs and the wurtzite types of structure many of thecrystals have a metallic lustre and appearance. Such crystals mayrepresent a transition stage between the non-metallic compound andthe true metals.The Crystal Structure of Alloys.In a previous Report l1 some account was given of the work ofA.Westgren and G. Phragmdn on the copper-zinc, silver-zinc,and gold-zinc alloys. These authors have extended this work, andhave found that four types of crystal structure are common to eachof these series of alloys, and to certain other alloy systems.12 Theseare (1) face-centred cubic, (2) body-centred cubic, (3) hexagonalclose-packed, and (4) a complex cubic structure.The face-centred structure is the structure of the pure metals,copper, silver, and gold. When small quantities of zinc, aluminium,or tin are added to these metals no change is produced in the type ofcrystal structure. The atoms of the one kind are replaced by those ofthe other kind, atom by atom, producing an arrangement which, sofar as X-ray analysis can tell, is indistinguishable from that of a puremetal.Such an arrangement is a solid solution, and is character-ised by the fact that atoms of different kinds behave in an identicalA.nn. Reports, 1925, 22, 253.If 2. Metallk., 1926, 18, 279; A., 1926, 1084. Compare also E. A. Owenand G. Preston, PTOC. Physical SOC. London, 1923,36,49 ; M. Andrews, PhysicdRev., 1921, [GI, 18, 245CRYSTALLOGRAPHY. 279manner, being distributed a t random throughout the structure.This arrangement is only possible when the alloy contains largeproportions of the parent metal, d.e., the metal which has thesame structure as the solid solution. With greater quantities of theforeign element, the structure breaks down and the atoms proceedto arrange themselves in quite a different way.One of these alternative structures is a peculiar complex cubicarrangement, which possesses many remarkable features.Thisarrangement is formed by copper, silver, or gold alloyed with zinc,and by copper alloyed with aluminium or tin. Although thestructures are very similar in each case, there is actually a progressiveincrease of complexity in passing from the zinc alloy to thealuminium alloy, and from the latter to the tin alloy.The arrangement of the atoms in the copper-zinc alloy has beendetermined.13 The type of co-ordination is remarkable, each atombeing surrounded by 11, 12, or 13 neighbours at approximatelyequal distances, each neighbouring atom being as far as possible ofthe opposite sort.This structure is stable over a wide range ofconcentrations, the zinc content varying from a value correspondingto the formula Cu,Zn, to one corresponding to Cu,Zn,. The atomsactually appear to be divided in a manner that would correspond tothe formula Cu,Zn8, any excess of zinc atoms replacing individualcopper atoms in a random manner, so that the phase is a solidsolution based on the compound Cu5Zn,. The same is true of thesilver and gold alloys, which are based on the formuls Ag5Zn,and Au 5Zns, respectively.The element manganese,l* in the a-form, bears a striking resembl-ance to these complex cubic alloys. It contains 58 atoms in a cubeof approximately the same size as the unit cube of the alloy, and thereis a somewhat similar disposition of atoms.The distance betweenneighbouring atoms, however, varies considerably. All these factsseem to indicate that a-manganese contains atoms which are in someway different in character, so that the structure is akin to that of analloy rather than to that of a true element.The complex cubic alloys of zinc with copper, silver, and goldall have compositions corresponding to the same atomic percentages,SO that the resemblance is in this case a typical instance of isomor-phism, and presents no unusual features when viewed from thenormal chemical standpoint. The relationship between the alloysof copper with zinc, aluminium or tin is, however, less simple.As the valency of the replacing atom (Zn, Al, or Sn) increases, phasescorresponding to the complex structure become richer in copper.l8 A.J. Bradley and J. Thewlis, Proc. Roy. SOC., 1926, [ A ] , 112, 678; A.,1926, 1084. 14 Idem, ibid., 1927, [A], 115, 456; A,, 814280 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.A similar shift incomposition was found in the case of the hexagonalstructures which Westgren and Phragmen investigated. Theytraced the existence of a hexagonal close-packed type of structurein binary alloys of silver with zinc, aluminium, or tin. The silvercontent of the alloy is found to be greater for tervalent aluminiumthan for bivalent zinc, and still greater for quadrivalent tin.Westgren and Phragmh suggest that the ratio of the number ofvalency electrons to the number of atoms is a significant factor indeciding the nature of the atomic arrangement in such cases as these.This is by no means unlikely, for W.Hume-Rothery l5 has alreadypointed out that the three alloys the empirical compositions ofwhich may be represented by the formulae CuZn, Cu,AI, and Cu5Snhave very similar microstructures, and has suggested that this isdue to the fact that the ratio of valency electrons to atoms is in eachcase 3 : 2. He further suggests that these alloys all possess thebody-centred cubic structure, which Westgren and Phragmkn haveshown to be typical of the p-phases of the alloys copper-zinc, silver-zinc, and gold-zinc. These alloys correspond to the formulaeCuZn, AgZn, and AuZn, so that an arrangement of the atoms as inthe case of CsCl is possible.This czesium chloride structure hasalso been shown by E. A. Owen and G. D. Preston l6 to holdgood in the case of the analogous alloys AuZn and AgMg.Two recent papers by C. H. Johansson and J. 0. Linde,l7 whohave tried to establish a relationship between crystal structure andelectrical conductivity, are of great interest. Copper can bealloyed with gold, platinum, or palladium in all proportions, givinga series of alloys which are ideal solid solutions, consisting only of asingle face-centred cubic lattice with a random distribution of theconstituent elements. I n any such series of alloys the electricalconductivity decreases continuously with a rising percentage of thesubstituent metal, until it finally reaches a minimium and thensteadily rises as the substituent metal becomes the dominant con-stituent.Johansson and Linde show, however, that, when theconstituents occur in certain definite proportions, prolonged anneal-ing at temperatures below 400" produces a remarkable increase inthe electrical conductivity of the alloys. At the same time, new linesappear on the X-ray photographs obtained from the alloys, whichshow quite definitely that a rearrangement of the atoms has takenplace, and that the constituent elements are no longer distributedin a haphazard way. For example, the alloys of copper with gold,lS J . Inst. Metals, 1926, 35, 313; A., 1926, 356.l6 Phil. Mag., 1926, 2, 1266; A,, 1927, 96.Ann. Physik, 1925, 78, 439; 1927, 82, 449; A., 1926, 112; 1927, 400.Compare also E.C. Bain, Chem. Met. Eng., 1923, 28, 21CRYSTALLOGRAPHY. 281platinum, or palladium show a f ace-centred cubic arrangement,with, in general, a random distribution of the elements; but withalloys containing 75 atoms yo of copper, rearrangement takes placeon annealing in such a way that the atoms at the centres of thecube faces are copper, and those a t the cube corners the other metal.The increased conductivity and the regular arrangement of atomsinvariably occur together. Reheating a t a temperature above 400"removes both the extra conductivity and the new X-ray lines.Similar rearrangement takes place when the alloys contain 50atoms yo of each constituent. The crystal structures differ,however, with the different elements, the gold alloy being tetragonal,the platinum alloy trigonal, and the palladium alloy cubic, with acaesium chloride type of structure.According to G.Tammann,l8 any solid solution may be expectedto produce a regularly arranged structure if annealed under suitableconditions; but the work of Johansson and Linde seems to showthat such rearrangement is exceptional and can only occur atcertain concentrations, the resulting structures being in fact inter-metallic compounds. From this point of view, an intermetalliccompound may be merely a special case of a solid solution, in whichthe random distribution has been replaced by a more regular dis-tribution of the atoms of different types.Crystal Structures of Metallic Elements.G. Asahara and T. Sasahara l9 have investigated the crystalstructures of metallic thallium, using single crystals prepared byelectrolysis.They find the structure to be hexagonal close-packed,thus confirming the work of G. R. Levi,Z0 which had been questionedby K. Becker.21The crystal structure of metallic gallium 22 has been found to betetragonal, containing eight atoms per unit cell. There are twoparameters which have not been determined.F. Simon and E. Vohsen 23 have determined the crystal structureof the alkali metals Na, K, Rb, and Cs and find them all to be body-centred cubic. The result for potassium conflicts with that givenby V. M. Goldschmidt, who finds it to be tetragonal.18 " Lehrbuch der Metallographie " (Leipzig), 2nd edn., 1921, p. 329.lo Sci. Papers Inst.Phys. Chem. Rea. Tokyo, 1926,5, 79, 82; A., 1927, 814.Zo Cim., 1924, 1, 1 ; 2. Physik, 1927, 44, 603; A., 1013.21 Ibid., 45, 450; A., 1129.22 F. M. Jaeger, P. Terpstra, and H. G. K. Westenbrink, Proc. K. Akad.28 Natumoiss., 1927, 15, 398.Wetenech. Amsterdam, 1926, 29, 1193; A., 1927, 297282 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.Inorganic Crystals.Co-ordination Compounds.-The present state of the chemicaltheory of the nature of the atomic linkage in co-ordination com-pounds was summarised by N. V. Sidgwick in his PresidentialAddress to the Chemistry Section of the British Association inSeptember 1927. The investigation of these compounds by X-raymethods is a matter of difficulty, since, owing to their complexity,the detailed elucidation of their structures is limited to those ofhigh crystallographic symmetry ; but enough information hasalready been obtained to support the general conclusions as to thestereochemistry of co-ordination compounds originally put forwardby Werner.The following compounds have been examined.FIG. 1.?II*--..--II0Structure of [Co(NR,),]I,, showing unit cell. The large ojin circles representiodine atoms, the large black circles Co(NH,), groups. The partial detail ofthese groups is shown in the smaller diagram. 1 he small black circle representsthe cobalt atom, the small open circles NH, molecules.Hexa-amminocobaltic iodide, [Co(NH,) ,]I,.* The crystal is cubic,the unit cell of side 10.88 8. containing four molecules. Theatomic positions in the unit cell are shown in Fig.1, from which itwill be clear that the structure may be regarded as built on a latticewhich combines the NaCl and CaF, lattices. The lattice pointsaccommodate iodine atoms and co-ordination groups Co(NH,),.One set of iodine atoms and the Co(NH,), groups form a rock-saltlattice, whilst the other two sets of iodine atoms form with the samegroups the CaF, lattice. The ammonia molecules are arranged24 R. W. G. Wyckoff and T. P. McCutcheon, Amer. J . Sci., 1927, [v], 13,223; A., 400; H. Rentschel and F . Rime, Math.-Php. Kl. Suchs. Akad.,1927, '79, 1 ; H. Meisel and W. Tiedjo, 2. anorg. Chem., 1927, 164, 223; A.,923CRYSTALLOGRAPHY. 283octahedrally about the cobalt atom, as anticipated in the co-ordin-ation theory.This type of composite lattice is of frequentoccurrence, and reference is made to it elsewhere in the Report.Of exactly similar structural type is the compound[Co(NH3) 61(C104)3,25the side of the unit cell of the cubic crystal having the length 11.39 8.In this crystal, the oxygen atoms are arranged in fours about thechlorine atom, the perchlorate groups replacing the iodine atoms inFig. 1.An examination of (NH4)2PbC16,26 cubic (a = 10.14 A.), shows theunit cell to contain four molecules. The structure is of the CaF,type in which calcium is replaced by the co-ordination groupPba6-eaCh lead atom being surrounded by 6 chlorine atoms-andfluorine by the ammonium group. The structure is thus similart o that of the analogous salts K2PtC1, and K,SnC16.Of similar type, with obvious structural substitutions, are[ C O ( ~ , ) , ] I , , ~ ~ CS,G~F,,~~ and [N(CH3),]2PtC1,.29 Further ex-amples of co-ordination compounds occur in later sections.Water of Crystallisation.-Owing to the complexity of hydratedcompounds in general, they have not received much attention inX-ray crystallography.E. J. Cuy 30 discusses the tendency of simplecompounds to form hydrates and ammoniates, and the stabilityof such hydrates; he concludes that the question depends on therelative sizes of the ions forming the original compound.With the idea of examining the geometrical significance of waterin hydrated compounds, S. B. Hendricks and R. G. Dickinson31have determined the crystal structures of ammonium, potassium,and rubidium cupric chloride dihydrates (R2CuC14,2H20). Thecrystals, which are tetragonal, have two molecules in the unit cell.The structure is of the calcium fluoride type (the unit cell is almostcubic), in which copper takes the place of calcium and R that offluorine.Four chlorine atoms and two H20 molecules are arrangedoctahedrally about each copper atom, thus forming a cupric chloridedihydrate co-ordination group. The group is, however, somewhatdistorted, the two pairs of chlorine atoms involved being at different25 R. W. G. Wyckoff, S. B. Hendricks, and T. P. McCutcheon, Amer. J.26 R. W. G. Wyckoff and L. M. Dennis, ibid., 1926, [v], 12, 503; A., 1927,27 H. Hentschel and F. Rinne, Math.-Phys. Iil. Sachs. Akad., 1927, 70, 1.28 R.W. G. Wyckoff and J. H. Miiller, Amer. J . Sci., 1927, [v], 13, 347;Sci., 1927, [v], 13, 388; A., 502.97.A., 503.M. L. Huggins, P h y k a l Rev., 1926, [ii], 27, 638; A., 1927, 1014.30 J. Amer. Chem. SOC., 1927, 49, 201; A., 191.a1 Ibid., p. 2149; A., 1013284 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.distances from the copper atom. This distortion is regarded ascorresponding to lack of stability in the co-ordination group.0. Hassel and J. R. Salvesan 32 have examined a series of hetero-polar hexahydrates of the type MG,,LR, where G and R may beH,O and halide, respectively. Thus, in the case of zinc fluosilicate(ZnSiF6,6H,0), the structure is such that one set of ions representinga co-ordination group (Zn,6H20) occupies the corners of a rhom-bohedron of angle 96", the other complex, SiF,, being a t the centreof the rhomb.This rhomb is not, however, the true unit cell;apparently the octahe*al arrangements of the H20 molecules andfluorine atoms about the zinc and silicon respectively are such asto cause the true unit cell to be four times that of the rhomb justmentioned, and the final rhombohedra1 angle to be 112". In addi-tion to this series of compounds, the following were found to possessthe same structure : [co( NH,) ,]Co( CN) ,, [co( NH,) 5,H,0]Co( CN) 6,J. M. Cork33 has recently re-investigated the structure of thealums, KCr(SO4),,12H2O and RA1(S0,)2,12H20, where R is in turn(NH,), K, Rb, Cs, and T1. The unit cell is cubic, of average side12.2 8., and contains four molecules ; the cell dimensions vary littlethroughout the series.The structure may be regarded as beingbuilt on a distorted form of the composite lattice illustrated in Fig. 1.Each metal atom is symmetrically surrounded by six molecules ofwater, and each sulphur atom by four oxygen atoms. The sulphuratoms lie on the trigonal axes of the cell nearer to the tervalentmetal than to the univalent metal.Mixed Crystals.-Several papers have recently appeared on thecharacter and conditions of formation of mixed crystals, but thereis still considerable doubt as to the distribution of the constituentatoms in such crystals. The possibility that a mixed crystal is acomposite of pure crystals of the two constituents is unlikely,since the presence of two different lattices would be revealed byX-rays.Objections of a theoretical nature are put forward byH. G. K. Westenbrink S4 against the suggestion that isomorphoussubstitution takes place atom by atom in a perfectly regular manner.G. Lunde 35 suggests that perfect mixture of the constituents occurs,but that the manner of atomic replacement is purely arbitrary andwithout regularity. The general conclusions to be drawn from theexperimental results appear to be as follows :(a;) Mixed crystals may be formed from constituents whose[Co(NH,),,H2°1Fe(CN)8, [Co(NH,)4,(H,0)21Co(CN)6.32 2. physikal. Chem., 1927, 128, 345; A., 1014.33 Phil. Mag., 1927, 4, 688.34 Rec. trav. chim., 1927, 46, 105; A,, 400.36 BulL SOC. chim., 1927, 41, 304; A., 400CRYSTALLOGRAPHY. 285individual lattices differ considerably in size.For example, T.Barth and G . Lunde 36 were able to prepare series of mixed crystalsfrom halogen compounds of certain heavy metals (large lattices)with those of alkali metals (smaller lattices).( b ) In such cases, in general, the resulting lattice varies in 8,simple manner with the relative proportion of the constituents.Thus, L. Vegard,37 in the case of mercurous chloride and bromide,found a linear increase in the lattice constants as the molecularcontent of the bromide increased from 0 to 100%. He also foundthat the rate of precipitation affected the size of the resulting lattice,the linear law holding for slow rates.( c ) Mixed crystals may be formed from constituents whoselattices differ in character.Thus, T. Barth and G. Lunde 38 foundthat thallous bromide (body-centred cubic) and thallous iodide(rhombic) form mixed crystals the lattice of which may be cubicor rhombic according to the proportion of the constituents, bothtypes existing in the middle of the series. One crystal thus appearsto be able to accommodate itself to the structure of the othercrystal to some extent. This power of accommodation, however,is not necessarily equally shared by the two constituents. Thusin mixed crystals of silver bromide (cubic rock-salt type ; a = 5.76 8.)and silver iodide (cubic zinc-blende type ; a = 6.49 A.) both typesmay occur, but the bromide is able to include in its structure alarge percentage of the iodide, although the converse is not true.(d) In cases where the constituents are coloured, the mixedcrystals often show a deeper colour than either constituent.ThusBarth and Lunde (Zoc. cit.) found this to be true for CuI-AgI andAgBr-AgI. They regard the coloration as due to distortion of theions in fitting into the new lattice.(e) L. Vegard and T. Hauge39 find evidence by X-rays of theformation of mixed crystals when potassium bromide and chlorideor when mercurous bromide and chloride in the solid phase areplaced in contact. They suggest that an exchange of atoms betweenthe crystal lattices occurs.8iZicates.-Reference was made in last year's report to the specialr6le played by the oxygen atoms, owing to their predominant sizeand number, in many of the complex silicates.A general discussionof this subject with examples from recent new work is given in apaper by W. L. Bragg and J. West." The following examples maybe mentioned.36 2. physikal. Chern., 1926, 122, 293; A,, 1926, 895.3 1 2. Physik, 1927, 43, 299; A., 815.39 2. Phyaik., 1927,42, 1 ; A., 604.40 Proc. Roy. Soc., 1927, [A], 114,450; A,, 601 ; Proc. Roy. Inat., 1927,25,302.Norsk Geol. Tidsskrift, 1926,8, 293286 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.Cyanite (one of the forms of N,SiO,). The crystal is triclinic, theunit cell, containing four molecules, being defined by a = 7.15,b = 8.00, c = 5-55 8., a = 90" 54', F = 101" 2', y = 105" 444'.In spite of the irregular character of this cell, it was found possibleto fit it into a scheme of oxygen atoms (diameter 2-70 8.) arrangedin cubic close packing, an arrangement which was verified by anX-ray examination of the crystal.The low symmetry of thestructure is thus due to the complexity introduced by the distribu-tion of aluminium and silicon atoms amongst the interstices in theoxygen arrangement. Although this distribution is not determined,it is anticipated by analogy with other silicates that the aluminiumand silicon atoms are respectively surrounded by groups of six andfour oxygen atoms.The chodrodite series 41 [Chondrodite, Mg( OH),,2Mg2SiO,, mono-clinic ; humite, Mg( OH),,3Mg,Si04, orthorhombic ; clinohumite,Mg( OH),,4Mg,Si04, monoclinic]. The members of this series beara strong crystallographic resemblance to olivine (Mg,SiO,) and,with it, afford an interesting example of morphotropy; for, whilsttwo edges of the unit cell remain practically constant throughoutthe series, the thickness measured perpendicular to these edgesvaries in definite steps which are simply related to each other.Thethree structures may be described as being formed of alternatelayers-parallel to the c face-of Mg(OH), and Mg,SiO,, based onan arrangement of oxygen atoms and hydroxyl groups in hexagondclose packing. In this case, as in that of cyanite, the oxygen atomsappear to determine the dimensional relations, whilst the metaland silicon atoms control the symmetry in the unit cell. Thelayers of Mg,SiO, are found to possess the olivine structure.Phenacite (Be,Si0,).42 The unit cell, which is rhombohedra1 andcontains six molecules, has an angle of 108" 1' and a side of length7.68A.The arrangement of oxygen atoms differs somewhat fromthat in the preceding example in being more open. The trigonalaxes in the structure are contained within narrow channels devoidof atoms, although elsewhere there is close packing. The structuremay be regarded as built up of slightly staggered rows of oxygenatoms in contact parallel to the trigonal axes. These parallel rowsmay be divided into groups of four, arranged to form a new columnof Y-shaped section. The Y-shaped columns are then packedtogether so that one column relative to its neighbours is displacedparallel to its length (and therefore to the trigonal axes) by anamount equal to the radius of an oxygen atom (1.35 A.). The siliconatoms, and probably also the beryllium atoms, lie within groups offour oxygen atoms.4 1 W.H. Taylor and J. West, PTOC. Roy. SOC., 1928, [A], 117, 517.a W. L. Bragg, &bid., 1927, [A], 113, 642; A,, 97CRYSTALLOGRAPHY. 287A recent determination 43 of the space groups of the members ofthe dioptase group-diopfase, phenacite, willemite, and troostife-shows that all four crystals have the symmetry of C&. The simi-larity in the X-ray diffraction patterns suggests that the phenacitestructure is common to the series.An interesting paper by R. W. G. Wyckoff and G. W. MoreyUdescribes an X-ray investigation of compounds in the systemsoda-lime-silica.Of the four silicates of sodium and calcium,two-the orthosilicate, Na,CaSiO,, and metasilicate, Na4Ca(Si03)3-are optically isotropic, the third, Na2Ca2(Si03)3, is slightly doublyrefractive, whilst the fourth, Na2O,3CaO,6SiO,, differs from theothers crystallographically and optically. The X-ray difiractionpatterns of the first three, and especially of the first two, show astrong similarity, although the third is definitely not cubic, thesecond probably only pseudo-cubic, and all three differ widely inchemical composition. Advantage was taken of the high symmetryto examine the structures of the ortho- and meta-silicates. Althoughthat of the latter is not certain, it is considered probable that thesilicon atoms are surrounded by four oxygen atoms.The unit cellof the orthosilicate is cubic, of side 7.50A., and contains fourmolecules. The oxygen atoms are arranged in groups of four abouteach silicon atom. The structure may be regarded as a distortionof a composite lattice of the NaCl and CaF, type (see Fig. 1) in whichthe Ca and SiO, groups are arranged as Na and C1 in rock-salt, andthe Na and SiO, groups as F and Ca atoms in fluorspar. The authorsdirect attention to the frequency of this structure for ionic compoundsconsisting of four groups. From a consideration of such compoundsas [Co(NH,) J13, (NH,),AIF,, and Na,CaSiO,, they conclude that“ there is no obvious connection between the crystal structure of acrystal and the valency of its atoms.”A further attempt to classify the micas 45 illustrates the difficultyof assigning to the more complex silicates formulae having chemicalsignificance. In the present case, the micas are regarded as ‘‘ saltsof an acid with a constant number (six) of silicon atoms.” Thisclassification is based on the observation that the ratio R,O : SiO,=I : 6 is constant throughout the series.Isomorphous Substitution.-The substitution of one set of atomsor group of atoms for another in a series of compounds, is notonly of use in giving information of chemical value, but in the caseof isomorphous series of complex solid compounds it can be a43 G.Gottfried, Neue Jahrb. Min., 1927, [A], 55, 393.44 Arner. J. Sci., 1926, 12, [v], 419; A., 1927, 10.*j *4. F. Hallimond, Min. Mag., 1925, 20, 305; A., 1925, ii, 819; 1926,21, 25, 195; A., 1926, 816288 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.useful aid to the determination of the crystal structure by X-rays.The investigation of the alums quoted above is an example.Afurther example is that of the alkali sulphates of type R,S0,.46 Thesulphates of K, T1, (NH,), and Cs were examined. The smallscattering power for X-rays of the (NH,) group permitted the moredefinite location of the sulphur atoms, whilst the relatively largescattering power of the czesiurn atom aided the location of the Ratoms. The structure, as in other sulphates investigated, contains(SO,) groups; each R atom is surrounded by six oxygen atoms.The unit cell is orthorhombic, contains four molecules, and possessesthe symmetry of Vk6.The atomic arrangement deduced explainsthe pseudo- hexagonal character of these sulphates .Another isomorphous series recently examined is that of thetetragonal scheelite The structures of BaWO,, PbWO,,BaMoO,, and PbMoO, are found to be identical with that ofscheelite (CaWO,), in which the metal atoms may be regarded asarranged in a diamond type of lattice expanded in the direction ofthe c axis, the tungsten atoms being surrounded by four oxygenatoms. The replacement of calcium by barium or lead causes aconsiderable expansion of the scheelite lattice, the effect beinggreater for lead.The series xenotime (YPO,), zircon (ZrSiO,), rutile (TiO,), andcassiterite (SnO,) 48 is interesting as an example of a case wheremorphological isotropy is not necessarily accompanied by structuralsimilarity.The similar structures of the first two crystals arefound to differ from the similar structures of the second two.Colour and Crystal Structure.-0. R. Howell 49 points out that itis in some cases possible to predict the structure of a crystal from itscolour. It has been shown 50 that, when a metallic atom in a colour-less insoluble compound is replaced by cobalt, a pigment is obtainedwhich is blue if the cobalt is surrounded by four other atoms, andred if it is surrounded by six. From the colour of pigments, pre-pared in this way from compounds of unknown crystal structures, itwas possible to predict in some measure the structure of the com-pound from which it was derived.For example, a blue compound isobtained when cobalt replaces zinc in zinc orthosilicate, whereasfrom magnesium orthosilicate a red pigment is obtained. Thestructures of both these silicates have now been determined :46 W. Taylor, Proc. Mancheater Lit. Phil. Soc., 1927 (in the press) ; A. Ogg,Phil. Mag., 1928, 5, 384.47 L. Vegard and A. Refsum, Skr@er Norske Vdenskaps-Akad., 1927, 1,No. 2.48 L. Vegard, ibid., No. 6.4@ J., 1927, 2843.60 R. Hill and 0. R. Howell, Phil. Mag., 1924, 48, 833; A., 1924, ii, 817CRYSTALLOGRAPHY. 289W. Zachariaaen 51 finds zinc orthosilicate to be isomorphous withphenacite, Be,SiO,, in which the beryllium atom is between fouroxygen atoms,& whereas the work of W. L. Bragg and G. B. Brown 52on olivine has shown that in Mg,SiO, each magnesium atom issurrounded by six oxygen atoms.Other examples are given inHowell's paper.Crystal 8tructure of Boron Nit~ide.~~-Prepared crystals of BNwere found to show a similarity in form and structure to graphiteand not to diamond as was previously expected.54 Each nitrogenatom is surrounded by three equidistant boron atoms and vice versa.Solid O~ygerc.~~-X-Ray examination at -252" reveals a body-centred orthorhombic cell of dimensions a = 5.50, b = 3.82, c =3.448., containing two molecules. This is considered to be thelower-temperature modification.Theoretical Determinations of Crystal Par~meters.~~J. E. Lennard-Jones and (Miss) B. M. Dent have extended theirwork on the determination of crystal parameters from the inter-atomic forces, of which an account was given in last ybar's report,to other crystals with one parameter-the rutile group, chloro-stannate and chloroplatinate of potassium, and solid carbon dioxide.Their results for the last are of interest, since they show a distanceof 0.90 8.between carbon and oxygen; this is in fair agreementwith the value obtained by X-ray analysis by J. de Smedt andW. H. M. Keesom,57viz., 1-05 8., but appears to negative the resultsof H. Mark and E. P0hland,~8 who obtained 1.59 8.Organic Crystals.The investigation of the detailed structure of organic crystals ispeculiarly difficult. They are in general of relatively low crystallo-graphic symmetry, the molecules are complicated, and a completedetermination involves the fixing of a large number of parameters.This can only be done by measuring the intensities of the X-rayspectra, and for organic crystals such measurements are usuallynot easy to make (suitable specimens being difficult to obtain),and extremely difficult to interpret.Most of the investigations of51 Nor8k Geol. TicEeskrift., 1926, 9, 65.52 2. Krist., 1926, 63, 638; A., 1926, 995.63 V. M. Goldschmidt and 0. Hwel, Suer. Nor8k Geol. Tids., 1926, 268.64 H. G. Grimm and A. Sommerfeld, 2. Phyeik, 1926, 36, 36; A., 1926,66 J. C. McLennan and J. 0. Wilhelm, Phil. Mag., 1927, [vii], 3, 383; A.,ti6 Phil. Mag., 1927, [vii], 3, 1204; A., 716.67 Proc. K . Akad. Wetensch. Amsterdam, 1924, 27, 839; A , , 1925, ii, 484.68 2. Krist., 1925, 61,293.REP.-VOL. XXIV.K660.297290 ANNUAL REPORTS ON THE PROQRESS OF CHEMISTRY.the structures of organic crystals have not attempted to go beyondthe space group.Space-group determinations may give useful information concern-ing the symmetry of the organic molecules. Of interest in thisrespect is recent work on the structure of a number of methanederivatives. On theoretical grounds a pyramidal structure, havingthe carbon atom at the vertex and the hydrogen atoms all in oneplane, has been assigned to the methane molecule itself.59 Workon the crystal structure of pentaerythritol, C(CH,*OH),, appearedto be in agreement with this; the arrangement of the groupsaround the single carbon atom was stated to be pyramidal,60 andwork on the external symmetry of the crystals61 was supposedto confirm this.Quite recently I. Nitta and S. B. Hendricks 63have published work in which they show that the space group ofthe crystal is Cf and that the molecule may have a fourfold alternat-ing axis of symmetry. This makes a tetrahedral molecule with thecarbon atom in the centre a possibility. Support to this view isgiven by some work of A. Schleede and E. Schneider G4 who concludefrom the growth of single crystals of pentaerythritol that thesymmetry is Sa or tetragonal alternating. The balance of evidenceat present appears to be in favour of a tetrahedral carbon atom inthis compound.In tetranitromethane H. Mark and W. Noethling 65 find that themolecule has a threefold axis. The carbon atom is thus tetrahedral,but only three of the nitro-groups are equivalent.The symmetrycorresponds to the structural formula O*NO*C(NO,),. In tetra-methylmethane they find a tetrahedral group. W. H. George 66has studied the isomorphism of the series carbon, silicon, germanium,and lead tetraphenyl. The crystals are tetragonal, and the unit cell,which contains two molecules, has an alternating fourfold axis ofsymmetry, parallel to the c-axis. The size of the square base of thecell increases and the height decreases with increasing atomicnumber of the quadrivalent element. The phenyl groups are in allcases arranged tetrahedrally about the central atom.V. Guillemin, jun.; Ann. Phy&ik, 1926, 81, 173; A., 1926, 1083.O0 H. Mark and K. Weissenberg, 2.Physik, 1923, 17, 301; A., 1923, i,1055; M. L. Huggins and S. B. Hendricks, J . Amer. Chem. SOC., 1926, 48,164; A., 1926, 227.O1 H. G. K. Westenbrink and F. A. van Melle, 2. Krist., 1926, 64, 648;A. Giebe and E. Scheibe, 2. Phy&k, 1925, 33, 346.O3 Bull. Chem. SOC. Japan, 1926, 1, 62; A., 1926, 665.63 Z. KTiSt., 1927, 66, 131.O4 Natumoise., Dec. 2nd, 1927.66 2. Krist., 1927, 6S, 436.Proc. Roy. Soc., 1927, [A], 113, 686CRYSTALLOGRAPHY. 291Long-chain Cmpounds.-A notable advance has been made byA. Muller 67 in the study of the structure of the long-chain com-pounds. He has succeeded in obtaining rotation X-ray photo-graphs and Laue photographs from small single crystals of stearic,bromostearic, stearolic, and behenolic acids. All the crystals aremonoclinic-prismatic. Chains of carbon atoms exist in all fourcrystals. The chains are packed in the crystal with their axesparallel to one another or nearly so, the distance between carbonatoms in the chains being much less than the distance betweenneighbouring chains. The crystal molecule appears in all casesto be a chain of carbon atoms, the number of atoms in the chainbeing the same as that in the chemical molecule. It will readily beseen that an arrangement of this kind will give parallel sheets ofcarbon atoms very closely and evenly spaced within the unit cell.The true unit spacing perpendicular t o the sheets will be large, butit will be very nearly exactly divided by the sheets of carbon atomsinto a much smaller spacing. Suppose, for example, that the chainconsisted of 19 exactly similar carbon atoms followed by LL carbonatom united with a different group A, and that this was repeatedindefinitely. The true spacing would be from an atom A to thenext atom A, and there would be a large number of orders of spectraon the rotation photograph corresponding to this very long spacing.Had all the carbon atoms been alike, only the 20th, 40th, 60th ofthese spectra would have appeared. Actually the atoms are notall alike, and the intervening spectra do occur, but only those nearthe 20th, 40th, 60th spectra are at all strong, since it is only forthese spectra that the contributions from all the carbon atoms arenearly in phase. Thus, by studying the periodic waxing and waningof the intensities of a large series of spectra, valuable information asto the arrangement of the carbon atoms can be obtained, evenalthough exact measurements of intensity cannot be made.It is interesting to note that the molecular cross-section parallelto the basal plane of the crystal, as determined by Muller, agreesvery closely with Adam’s estimate of the cross-section in his work onunimolecular surface films.In conclusion the authors wish to express their indebtedness toProf. W. L. Bragg, F.R.S., for many helpful suggestions during thepreparation of this Report.R. W. JAMES.J. WEST.A. J. BRADLEY.67 Proc. Roy. SOC., 1927, [A], 114, 642