CRYSTALLOGRAPHY.1. GENERAL.Introduction.-This Report covers the years 1955-56, and follows thebiennial report in the 1954 volume (the special section in 1955, on thecrystallography of proteins, is to be regarded as an intercalation). It isdivided into four sections, one dealing with general topics, two with structures-inorganic and organic-and a fourth giving a short account of recentwork on ferroelectrics.have appeared, covering work published in 194044. The link with thepreceding volumes (1-7) of Strukturbericht is thus completed ; and, whenVol. 14 appears during 1957, the coverage will extend to 1951. A volumeof the Landolt-Bornstein “ Tabellen ’’ 2 issued in 1955 embodies a moreconcise, but remarkably complete, summary of all crystallographic workbefore 1952; the first half of the book (some 500 pages) deals with crystalstructures, the second with spectroscopic data for solids.Volumes of“ Solid State Physics ” are being issued periodically; the first deals mainlywith metals, the second with nuclear magnetic resonance, neutron diffraction,and displacement of atoms by irradiation. “ The Chemistry of the SolidState ” comprises 15 essays on crystal growth, solid reactions, and relatedtopics. Monographs on neutron diffraction and nuclear magnetic reson-ance contain much of interest to the chemist and crystallographer. Kitai-gorodskii’s book deals in particular with the packing of molecules intocrystal lattices. The appearance of the journal KristaZZugraJya betokensthe large amount of crystallographic work being done in the U.S.S.R.-workwhich is not at present adequately known in the West, and which can bebut perfunctorily covered in this Report. Also new is the Journal of thePhysics and Chemistry of the contents of whose first number (Sept.-Oct., 1956) are principally of interest to the crystal physicist.A meetingof the International Union has been reported in summary.1° The FaradaySociety’s Discussion on micro-wave and radiofrequency spectra l1 has sec-tions on paramagnetic and nuclear magnetic resonance, illustrating thevalues of these techniques in the study of crystals, and an informal discussionon melting has been summarised.12 A review summarises the methods forlocating hydrogen atoms in crystals,13 and describes that based on protonicDuring the period under review, Vols.8 and 9 of ‘‘ Structure Reports ”“ Structure Reports,” Vols. 8 and 9, Oosthoek’s Uitgevers, Utrecht.Zahlenwerte und Funktionen, Band I, Teil 4, Berlin, 1954.(Ed.) F. Seitz and D. Turnbull, Academic Press, New York, 1955 etc.G. E. Bacon, “ Neutron Diffraction,” Oxford University Press, 1955.E. R. Andrew, “Nuclear Magnetic Resonance,” Cambridge University Press, 1955. ’ A. I. Kitaigorodskii, “ Organic Crystal Chemistry,” U.S.S.R. .4cademyof Sciences,Published by the U.S.S.R. Academy of Sciences, Moscow.Published by Pergamon Press, New York, 1956.* (Ed.) W. E. Garner, Buttenvorths Scientific Publications, London, 1955.Moscow, 1955.1” A. J. C. Wilson, Nature, 1956, 178, 177.l 1 Discuss.Farada? Soc., 1965, 19.l 2 Tmns. Farads?! Sor., 1956, 52, 882.l 3 I < . E. Richards, vzrarl. Rev., 1956, 10, 480384 CRY STALLOGE4PIIY.resonance in more detail. A translation l4 of a Russian review on thelattice energy of ionic crystals deals in particular with semi-empiricalmethods for assessing these energies and related properties of crystals.In this Report, d(X-Y), or d ( X - - Y), stands for the distance betweenthe bonded, or non-bonded, atoms X and Y, whilst L(X-Y-2) stands forthe bond-angle at Y. Limits of error, when stated, represent standarddeviations (e.s.d.) estimated by a currently accepted procedure for assessingaccuracy.15 The true error is very unlikely to exceed three times e.s.d.‘‘ Analysis ” in the present context means “ crystal structure analysis.”The Phase Problem.-No fundamental advance has been made towards ageneral solution of this critical problem,16 though it has been re-cast into amore satisfactory form by Bertaut.17 (The structure of meyerhofferite,2Ca0,3R,03,7H,0, has been solved by the Hauptman-Karle method ;it contains [B303(OH)J2- ions, with a six-membered ring of alternate boronand oxygen atoms; such a structure could presumably have been solvedby the heavy atom method.) Meanwhile the majority of structures con-tinues to be solved by conventional methods. When all specially favourablefeatures are absent, some form of three-dimensional Patterson synthesis isthe most serviceable method of attack, and is becoming more practicable aselectronic computing aids become more widely available.This develop-ment is also reflected in the increasing proportion of analyses which arebeing refined to a high precision.Absolute Configuration.-This long-standing and formidable problem hasrapidly resolved itself since a method of circumventing Friedel’s law wasintr0d~ced.l~ (A very readable account of the method has recently beenwritten by its discoverer.20) Configurations have been determined for anumber of key-molecules, and thereby absolute configurations are impliedfor a great range of other, stereochemically related systems. The configur-ation of the strychnine molecule lias been shown21 to be the opposite ofthat chosen (arbitrarily) in the original analysis of the hydrobromide. Thescattering of the X-rays from a copper target proved to beMe I ~ sufficiently anomalous at the bromine atom, so that no un-Is-0 orthodox X-ray source was needed.IH...C...H It has been pointed out 22 that the configuration of aIH - C - N H ~ complex molecule can be assigned from a normal X-rayI\o- (,) whose absolute configuration is already known. This principlehas been applied independently23 to a naturally occurringa-amino-acid sulphoxide. Since the configuration in the b-amino-acidgrouping was already known, that for the whole molecule was requiredC analysis, provided the molecule includes an asymmetric group1 4 A. F. Kapustinskii, Quart. Rev., 1956, 10, 288.l5 See, e.g., G. A. Jeffrey and D. W. J. Cruickshank, ibid., 1953, 7, 335.l6 Ann.Reports, 1954, 51, 373.l7 E. F. Bertaut, Acla Cryst., 1955, S , 823; 1956, 9, 769.18 C . L. Christ and J. R. Clark, ibid., 1956, 9, 830.1 9 Ann. Reports, 1951, 48, 361.2O J. M. Bijvoet, Endeavour, 1955, 14, 71.z1 A. I;. Peerdeman, Acln Crysl., 1956, 9, 824.22 A. McL. Mathieson, ibid., 1956, 9, 317.23 R. IIinc and D. Rogers, Chem. and Ind., 1956, 1428SPEAKMAN GENERAL. 385by the X-ray work to be as represented (l).* Thus the stereochemistry atan asymmetric sulphur atom was defined for the first time.makes public forthe first time the Fourier projection derived by Peterson and Levy24 in1953 from their neutron-diffraction study of deuterated ice. This mapshows ‘‘ half-hydrogens ” with d(O+D) = 1.01 A, at each of two positions(very nearly) along the 0 - - - 0 line (d = 2-76 A), and thus graphicallysubstantiates the disordered structure originally proposed by Pauling 25 toaccount for the residual entropy of ice.Objections to this structure onenergetic grounds seem to be removed by a more refined calculation.26 Anumber of acid salts contain short hydrogen bonds which, by crystallo-graphic requirement, are (at least effectively) ~ymmetrical.~~ Sodiumsesquicarbonate, NaHCO3,Na,CO3,2H,O, is a well known case, and thefavourable projection of its structure has been studied by neutron-diff rac-tion,28 and by refined X-ray methods at 18” and at -170°.29 The latterwork reveals a small (and possibly significant) diminution of d ( 0 * - 0) inthe symmetrical bond at lower temperature, though the over-all picture iscomplicated since one of the hydrogen bonds to the water molecule expands.The neutron-diff raction work shows the position of the acidic hydrogen atomwith greater clarity; it appears as a peak centrally placed between the twooxygen atoms, and elongated-though much less so than in KH,P0430-along the direction of the bond.In potassium hydrogen bisphenylacetate,which also possesses a symmetrical bond, neutron diffraction 31 againreveals a centrally placed peak; but now the peak, though considerably‘ I smeared,” shows no elongation along the bond, so that a genuinely sym-metrical bond is not ruled out in this case. On the other hand, the moleculesin solid resorcino132 are linked together by long hydrogen bonds withd(O - 0) = 2.72 A ; here neutron diffraction shows a single hydrogenpeak about 1.02 r f from one oxygen atom.Ubbelohde and Gallagher33have considered the short hydrogen bond in crystals as an acid-basephenomenon, which may imply alternative sites for the proton (e.g.,AH.. . B Z A - . . . HB+), and thus involve co-operative effects ; theyreview a wide range of experimental data from this aspect.Thermal Vibrations--In essence the refinement of a crystal structureimplies minimising the differences between the observed (F,) and calculated(F,) structure amplitudes. In deriving F,-values from the postulatedatomic positions, the atomic scattering functions (f) of the various atoms areHydrogen Bonds.-Vol. 2 of ‘‘ Solid State Physics ”24 S. W. Peterson and H.A. Levy, Phys. Rev., 1953, 92, 1082 ; for a full account of25 L. Pauling, J . Amer. Chem. SOC., 1935, 57, 2680.2G K. S. Pitzer and J. Polissar, J . Ph-ys. Chem., 1956, 60, 1140.2 7 Ann. Reports, 1954, 51, 390; see also Nature, 1948, 162, 695.28 G. E. Bacon and N. A. Curry, Acta Cryst., 1956, 9, 82.29 R. Candlin, ibid., p. 545.30 G. E. Bacon and R. S. Pease, Proc. Roy. SOG., 1953, A , 220, 397.31 Personal communication from Dr. Bacon.32 G. E. Bacon and N. A. Curry, Proc. Roy. Soc., 1956, A , 235, 552.33 A. R. Ubbelohde and K. J. Gallagher, Acta Cryst., 1955, 8, 71.this important work, see Acta Cryst., 1957, 10, 70.* The conventional symbol of a bar alongside represents the lone pair of electrons,in this case on the sulphur atom.REP.-VOL . L III 386 ClCYS'l'Al,l,OGRA PHY.needed. The values of f depend on the distribution of electron-density inthe atom, and they are almost always computed on the assumption that thedistribution is spherically symmetrical, and in fact that obtaining in theisolated atom. These assumptions cannot be valid for a bonded atom,though they work rather well in practice because bonding affects only theouter fringes of the atoms, which make a minor contribution to the totalscattering power. Atoms in a crystal are always vibrating with a mean-square amplitude, s, which in general increases with temperature. Theelectron-density peak is therefore flattened and broadened (" smeared ") ;and this can be taken into account by modifying f with a Debye, or tem-perature, factor, exp [ - (B sin 0) /I2] ; B (often itself referred to as thetemperature factor) is a measure of the smearing and is proportional to 2,and the other symbols have their usual meanings.Various degrees offinesse are then possible in calculating F, : (1) The same parameter, B, canbe used for all the atoms, or for all of the same chemical kind; (2) differentvalues of B can be fitted to each individual atom; either way, the atom,though smeared, still has spherical symmetry; its vibration is taken to beisotropic ; (3) anisotropy of vibration can be introduced by choosing severalvalues of B for each atom ( e g . , along the x-, y,- and z-directions). This lastprocedure implies that the electron-density peak is an ellipsoid, as indeed isoften observed. In its fullest form, it involved introducing up to nine para-meters (three of position, three of anisotropy, and three for its orientation)for each atom in the asymmetric unit; this can be justified only when theexperimental data are adequate in number and accuracy.What has beeiirecognised only recently is the importance of studying the vibrations them-selves in detail. There are two reasons for doing so.First, high accuracyin the atomic co-ordinates is unlikely to be attained until a proper allowancehas been made for vibrations and particularly for their anisotropy if this beconsiderable. When the differences between F, and F, arise mainly froman insufficient recognition of thermal motion, then the normal methods offurther refinement will force errors into the co-ordinates.At one stageduring the analysis of solid benzene this effect led to an erroneous value ofd(C-C), since amended.=The collection of I?,-values at low temperatures is often undertakenbecause more accurate co-ordinates can be determined when thermal motionsare less vigorous.35 Were the vibrations harmonic, the same " mean "structure should be found at any temperature, though the effects of smearingmake atomic peaks harder to locate at higher temperatures. In fact thevibrations are not harmonic (though they are nearly always taken to be soto facilitate theoretical calculations). The mean structures at differenttemperatures therefore differ, but they should converge on the true " rest "structure as temperature falls.It has accordingly been recommended byGilbert and Lonsdale 3G that " complete intensity measurements (should) bemade, at least for simple organic compounds, at more than one temperature,These principles have been understood for some years.s4 E. G. Cox, U. W. J. Cruickshank, and J. A. S. Smith, Nafwre, 1955, 175, 79.35 Anpa. Reports, 1954, 51, 375.36 R . E. Gilbert and K. 1-onsdale, .4cta Cuyst., 1956. 9, 697SPEAKIbl-IN : GENERAL. 387and that a complete structure refinement (should) be carried out at eachtemperature." Most crystallographers would regard this as a counsel ofperfection. These authors and Grenville-Wells 37 have made a thoroughstudy of some of the reflexions from urea crystals at temperatures down to90" K of the thermal motions of its atoms, and of the proper way of allowingfor them.With urea the changes in intramolecular distances with temper-ature appear to be hardly significant, though this may not be generally true.The persistence of zero-point motion limits the usefulness of pursuingmeasurements to very low temperatures, though for typical organic crystalsit should be profitable to go as low as 25" K ; 38 experimental methods forstudying single crystals in this region are being developed.39Secondly, the study of vibrations is now attracting interest for its ownsake. For example, the neutron-diffraction work on KH,PO, at lowtemperatures 40 provides evidence of zero-point vibration. Since neutronsare scattered by the atomic nuclei, a stationary atom should ideally figure inthe derived Fourier map as a point.Because a non-infinite series has to beused, the atom is smeared to a degree that can be calculated. Any furtherspread of the peak is due to thermal motion, whose 2 value can thus beascertained. Extrapolation of 2 for the hydrogen atom indicates a largeamplitude at 0" K. (A similar, but much smaller, effect was recognised inan X-ray study of rock-salt many years Moreover, owing to thesmall mass of the proton, its vibrations are substantially restricted to theground state even at temperatures well above zero. Therefore, " since theFourier plots can be regarded as having been obtained with a neutronmicroscope, [the observed width of the peak] represents a very directdemonstration of the existence of zero-point motion."The electron-density peaks derived from an X-ray study of a covalentnioleciile tend to become lower for atoms far removed from the molecularcentre of gravity.This has been recognised as due to the libration of themolecule as a whole. Higgs 42 has made a quantitative study of this effectin crystals of naphthalene and anthracene. For any atom he divides the2 value (derived from B found experimentally) into two parts : (1) due tointernal vibrations within the molecule, and (2) due to vibrations of thewhole molecule as a rigid body. Calculation shows that (1) accounts foronly about 5% of G, so that it can be neglected for many purposes. Themajor part (2) can be further subdivided into (a) one due to translationalvibration and ( b ) one due to torsional oscillation (libration) ; and these canbe separated since (a) will make the same contribution to 2 for all atoms,whilst ( b ) will contribute the more, the further the atom is from the centre.Thus for naphthalene at room temperature, (G)* is about 0.35 for carbonatoms 9 and 10 (ring junctions), 0.39 for 1, 4, 5, and 8 (w-positions), and0.42 A for 2, 3, 6, and 7 (P-positions). Similar amplitudes have been deduced37 H.J. Grenville-Wells, Acta Cryst., 1956, 9, 709.38 D. W. J. Cruickshank, ibid., p. 1005.Analysis Group ; see Nature, 1956, 177, 1067.4 0 G. E. Bacon and R. S. Pease, Proc. Roy. SOC., 1955, A , 230, 359.4 * I. Waller and R. W. James, ibid., 1927, A , 117, 214.4t P. W. Higgs, A d a Cryst., 1955, 8, 99.E.g., J.H. Robertson's communication to the Oxford meeting of the X-Ra388 CRYSTALLOGRAPHY.for acridine.43 The whole problem has been considered by Cruickshank,awho has developed a systematic procedure for estimating anisotropic Debyefactors during the refinement of the structure, and for expressing the resultsin tensor notation.J. C. S.2. INORGANIC STRUCTURES.The two-year period covered by this Report provides additional and en-couraging evidence of the current resurgence of activity in inorganic crystalchemistry, with over six hundred relevant titles appearing in the literature.'M7e have selected only those papers which contain a significant chemical andcrystallographic contribution, without attempting to be comprehensive.Elements and Simple Molecules.-Recent ly declassified accounts of theinteraction of neutrons with graphite have become available : 45 a detailedmodel of the damage done to the graphite crystal structure is lacking, but itappears that the interstitial atoms or groups produced under irradiation arearranged in a fairly regular array.The allotropes of sulphur continue to bestudied. A redetermination of the molecular parameters of orthorhombicsulphur gives 46 d(S-S) := 2.037 & 0.005 A and L(S-S-S) = 107" 48' 25'in the puckered S, rings. Several other modifications, including the +-,x-, #-, and o-forms, have been shown 47 to possess characteristic diffractionpatterns. The metallic radii of scandium, yttrium, and of all the rare-earthmetals have been remeasured 48 on very pure samples.In the transform-ation of tin, single crystals of the white @-form can produce single crystalsof the grey x-modification , although no regular relationship of orientationbetween the two lattices was found.49 The arguments in the recent contro-versy regarding the structure of @-uranium have beensumrnarised : 50 the general features of the structureare not in doubt, although some bond lengths in thedifferent models appear to differ by about 0.3 A.( I ) The structures of four allotropes of plutonium arenow known : 51 the 10-co-ordinated (1) arrangementin the y-form 52 is unlike that of any other metal.Americium metal, radius 1-82 A, forms a doublehexagonal close packed lattice ; 53 magnetic-susceptibility measurementsindicate three bonding electrons per atom.a-IC1 molecules, d(1-Cl) = 240A, form chains in the crystal,5* withshort I - . - I contacts of 3-05 A (in solid iodine, this distance is 3-54 A) and43 D.C. Phillips, Acla Cryst., 1956, 9, 327.4 4 D. W. J. Cruickshank, ibid., pp. 747, 754.45 G. E. Bacon and B. E. Warren, ibid., p. 1029.46 S. C. Abrahams, ibid., 1955, 8, 661.4 7 J. Schenk, Thesis, Delft, 1966.4 * F. H. Spedding, A. H. Daane, and K. W. Ilerrmann, Acla Cryst., 1956, 9, 659.4 9 K. Kuo and 11'. G. Burgers, Proc. k . m d . Aknd. Wefenschap., 1956, 59, B, 288.50 C. W. Tucker, P. Senio, J. Thewlis, and H. Steeple, Acta Cryst., 1956, 9, 472.5 1 E. R. Jette, J . Chem. Phys., 1955, 23, 365.52 W. 13. Zachariasen and F. H.Ellinger, Acta Cryst., 1055, 8, 431.53 P. Graf, B. €3. Cunningham, C. 13. Dauben, J. C. Wallmann, D. H. Templeton, and54 K. H. Boswijk, J. van der Heide, A. Vos, and E. H. Wiebenga, Acta Cryst.,EI. Ruben, J . Amer. Chesn. Soc., 1966, 78, 2340.19.56, 9. 271ABRAHAMS : INORGANIC STRUCTURES. 389interinolecular I - C1 contacts of 3.00 A. Within the chains there arelinear groups of 3 atoms, I - I-C1, C1- * I-C1, etc., similar to those observedin the 13-, (IC12]-, and [BrIClI- ions. Cyanogen chloride 55 is isostructuralwith the bromide 56 and, like those of the iodide, the molecules form linearchains with rather short distances between molecules along a chain (3.01 Ain NCC1) ; d(N-C) = 1-16, d(C-C1) = 1.57 A. The N, C, and 0 atoms inisocyanic acid 57 are also collinear, d(N-C) = 1.153, d(C-0) = 1.184 A ; themolecules are joined by N-H * N bonds of 3.07 A to form a zig-zag chain,the hydrogen atoms in the bonds being disordered.Hydroxylamine 58probably possesses a tram-configuration, if the third hydrogen atom whichis not involved in hydrogen-bond formation is neglected ; d(N-0) = 1.48 A.Diboron tetrachloride, B,Cl,, forms a planar molecule,59 with a long B-Bbond of 1.80 A, analogous to the long bond in N,0,.60 The hydrogen atomsin ammonia-borine, H3N,BH3,61 probably possess either orientationaldisorder or else rotate; d(B-N) = 1-56 A. The addition product of B2C14and C2H4 is shown62 to be the nearly planar BC12C,H4~BCl, molecule,excluding hydrogen, in which the BC1, groups are in the tram-position andthe boron bonds are trigonally arranged.The sulphur atom bonds in sulphamide 63 form a distorted tetrahedron,with d(S-0) = 1.39 A, an unusually short bond.A very similar structure isfound in sulphamic acid, HS0,*NH,,64 in which one amino-group in sulph-amide is replaced by a hydroxy-group ; d(S-0) = 1-44 if as comparedwith the earlier value of 1.48A. In the phosphorussulphides, P,S, has the same structure (2) in the crys-tal 65 as in the gas state, with d(P-S) = 2.09 andd(P-P) = 2-20 A ; P4S, and P,Slo, with structures pre-viously described in these Reports,66 possess single anddouble P-S bonds, depending on whether they form partof closed rings or not, with d(P-S) = 2.08 and 1.95 A re~pectively.~' InP4S7, d(P-P) = 2-35 & 0.01 A,68 significantly longer than is found in blackphosphorus (2.18 A) or P, (2-21 a).The interesting molecule hexathia-adamantane (CH),S6, has beenshown 69 to possess a structure analogous to hexamethylene tetramine.The trimer of dimethylphosphinoborine io consists of a cyclohexane-like@55 R.B. Heiart and G. B. Carpenter, Acta Cryst., 1956, 9, 889.5 6 S. Geller and A. L. Schawlow, J . Chem. Phys., 1955, 23, 779.5 7 W. C. von Dohlen and G. B. Carpenter, Acta Cryst., 1955. 8, 646.5 8 E. A. Meyers and W. N. Lipscomb, ibid., p. 583.59 M. Atoji, W. N. Lipscomb, and P. J. Wheatley, J . Chem. Phys., 1955, 23, 1176.6o J. S. Broadley and J. M. Robertson, Nature, 1943, 164, 915.61 E. L. Lippert and W. N. Lipscomb, J . Amer.Chem. SOL, 1956, 78, 503; E. W.62 E. B. Moore and W. N. Lipscomb, Acta Cryst., 1956, 9, 668.63 K. N. Trueblood and S. W. Mayer, ibid., p. 628.64 K. Osaki, H. Tadokoro, and I. Nitta, Bull. Chem. SOL. Japan, 1355, 28, 524.6 6 S. van Houten, A. Vos, and G. A. Wiegers, Rec. Trav. chim., 1955, 74, 1167;6 6 Ann. Reports, 1954, 51, 385.6 7 A. Vos and E. H. Wiebenga, Acta Cryst., 1955, 8, 217.69 E. K. Andersen and I. Lindqvist, Arkiv Kemi, 1956, 9, 163.70 W. C. Hamilton, Acta Cryst., 1955, 8, 199.Hughes, ibid., p. 502.Y. C. Leung, J. Waser, and L. R. Roberts, Chem. artd Ind., 1956, 948.Idem, ibid., 1956, 9, 92390 CRYSTALLOGRAPHY.ring of alternating P and B atoms, in the chair configuration, with twomethyl groups attached to each P and two hydrogen atoms to each B atom.Se(SeCN), and S(SCN), are shown 71 to be unbranched non-coplanar mole-cules, taking the cis-form in the crystal.Oxyacids and Acid Salts.-Analyses of two important oxyacids have beenmade : in sulphuric acid 72 the oxygen atoms are arranged in a distortedtetrahedron around the sulphur atom, with L(H0-S-OH) = 103" andL(0-S-0) = 117".There are two kinds of S-0 bond, with d = 1.46 andI-53A, the hydrogen atoms being associated with the longer bonds andforming intermolecular 0 * - 0 contactsof 2-64 and 2.87 A. Phosphoric acid hasbeen the subject of two independent in-vestigations. The PO, group (3) deviates( 3 ) significantly from tetrahedral symmetry; 73 -- L(0-P-0) ~ 1 1 2 " when 0, is involved,otherwise ~ 1 0 6 " ; d(P-0,) = 1-52 & 0.01 A,group is bound by hydrogen bonds of length2.53 A connecting the " keto " 0, with hydroxyl oxygen atoms and 2-84 Ajoining two hydroxyl oxygens.Essentially the same structure with a slightlydifferent set of atomic positions (maximum co-ordinate difference 0.16 A) hasalso been gi~en.~4A study of the infrared spectrum 75 of gypsum crystals reveals two kindsof oxygen atoms in the sulphate group, namely those hydrogen bonded andthose not. The anion in BaTeS40,,2H,O is shown 76 to possess a cis-configuration, in contrast with the tram-configuration observed 77 in(NH,),TeS,O,. The solvate of barium pentathionate with acetone,BaS,0,,H,0,Me,C0,78 has the same internal structure as the correspondingdihydrate, with acetone substituted for a water molecule : the oxygenatoms of the solvate molecules co-ordinate to Ba2+ as do those of the replacedwater molecules. Other recent analyses of acid salts of sulphur, selenium,and tellurium have been described; 79 fuller details of the work on telluriumdibenzenethiosulphonate 8o and on barium pentathionate dihydrate havenow appeared.Redeterminations have been made of the two forms of AlPO,.The veryaccurate intensity measurements on the hexagonal variety indicate 82 thatthe phosphorus atom has two more positive charges than the aluminiumatom. In the tetragonal or low cristobalite form, a regular tetrahedral10, 136.0 HT88 d(P-0) = 1.57 & 0.02 A. Each phosphate71 0. Aksnes and 0. Foss, Acta Chem. Scand., 1954, 8, 1787; 0.Foss, ibid., 1956,72 R. Pascard, Compt. rend., 1955, 240, 2162.i3 S. Furberg, Acta Chem. Scand., 1955, 9, 1667.74 J. P. Smith, W. E. Brown, and J. R. Lehr, J . Amer. Chem. SOC., 1955, 77, 2728.7 5 M. Hass and G. B. B. M. Sutherland, PYOC. Roy. SOC., 1966, A , 236, 427.7 O 0. Foss and 0. Tjomsland, A d a Chem. Scand., 1956,10, 416.7 7 0. Foss and P. A. Larssen, ibid., 1954, 8, 1042.7 8 0. Foss and 0. Tjomsland, ibid., 1956, 10, 424.79 S. C. Abrahams, Quart. Rev., 1966, 10, 407.P. Byum and 0. Foss, Acla Chem. Scand., 1966, 10, 279.81 0. Foss and 0. Tjomsland, ibid., p. 288.82 R. Brill and A. P. de Bretteville, Acla Cryst., 1965, 8, 567ABRAHAMS INORGANIC STRUCTURES. 39 1arrangement is assumed 83 in the PO, group : A1 is co-ordinated to 4 oxy-gen atoms as is Ga in isomorphous GaPO,, with d(A1- - 0) = 1.70 A,d(Ga The PO,group in Ca(H,PO,),,H,O is a regular tetrahedron; 84 d(P-0) = 1.52 A.Each Ca2+ ion is co-ordinated to 8 oxygen atoms, d(Ca * - * 0) = 2.52 A onaverage.In CaHPO, the PO:- ion is again tetrahedral,85 d(P-0) = 1.54 A(mean) : there are two kinds of Ca2+ ion, one co-ordinating with 7, theother with 8, oxygen atoms (Ca - * 0 co-ordination of 6 , 7 , 8 , and 9 is known),d(Ca A cation-oxygen co-ordination of 8, 6, and 6, isreported 86 in ScPO,, InPO,, and TlPO, respectively. The [HP0,I2- ionin MgHP0,,6H20 is tetrahedral 87 with d(P-0) = 1.51 A, and is linkedby hydrogen bonds (2.65-2.86 A) to the octahedral Mg2+(H20), groups.Rubidium metaphosphate, (RbP03),t,88 contains spiral chains of (PO,).heldtogether by Rb+ ions with 7-fold oxygen co-ordination. The chains areformed by tetrahedral PO, groups linked by shared corners; d(P-0) =1.62 A in the chain, otherwise = 1.46 A. Similar arrangements of long andshort bonds have also been observed in chains of (XO,),$, where X = Si, P,As, S, and V. Lithium and sodium polyarsenates form chains of linkedAsO, tetrahedra, with d(As-0) = 1-60-1.68 A and 1-79 A.8s Sodiummetagermanate contains similar chains, d(Ge-0) = 1-84 A. InNH,Cl,As20,,~H,0 double layers of As2O, are interleaved by two layersof NH,Cl; 91 AS-0) = 1-81 A.An electron-diffraction study 92 of basic lead carbonate shows that thecrystal consists of Pb(OH), layers sandwiched between double PbCO,sheets : the sequence of layers varies, giving a disordered structure.Furtherrefinement s3 of the NaNO, crystal structure leads to d(N-0) = 1.236 A,L(0-N-0) = 115.4"; in TINO,, the nitrite ion is probably di~ordered.~,Trigonal pyramidal 10, groups are reportedg5 in the crystal structure ofCe(IO,), and Ce(IO,),,H,O, where d(1-0) = 1.82 A, and L(0-1-0) = (37.2".Trigonal bipyramidal VO, groups share edges to form continuous chains inKVO,,H,O ; d(V-0) = 1.63-1-99 A."Lithium metasilicate 97 contains chains of composition (Si03)7L, similar tothose already described. Among many other silicate analyses are includedthose of d i ~ k i t e , ~ ~ ne~heline,~~ and wadeite.lW0) = 1.78 A, L(A1-O-P) = 145", L(Ga-O-P) = 135".* 0) being 2.46 A.83 R. C.L. Mooney, Acta Cryst., 1956, 9, 728.'.j Idem, ibid., 1955, 8, 579.a 6 R. C. L. Mooney, ibid., 1956, 9, 677, 113.R 7 D. E. C. Corbridge, ibid., p. 991.R9 W. Hilmer and K. Dornberger-Schiff, ibid., p. 87 ; F. Liebau, ibid., p. 811.R 1 M. Edstrand and G. Blomqvist, Arkiv Kemi, 1955, 8, 245.92 J. M. Cowley, Acta Cryst.. 1956, 9, 391.93 G. B. Carpenter, ibid., 1955, 8, 852.94 L. Cavalca, M. Nardelli, and W. Bassi, Gazzettu, 1955, 85, 153.95 D. T. Cromer and A. C. Larson, Acta Cryst., 1956, 9, 1015; J. A. Ibers, ibid.,96 C. L. Christ, J. K. Clark, and H. T. Evans, ibid., 1954, 7, 801.g 7 H. Seemann, ibid., 1956, 9, 251.R. E. Newnham and G. W. Brindley, ibid., p. 759.gD T. Hahn and M. J. Buerger, 2. Kryst.. 1955, 106, 308.G. MacLennan and C.A. Beevers, ibid., p. 187.Idem, ibid., p. 308.Y . Ginetti, Bull. SOC. chim. belges, 1954, 63, 460.p. 225.loo D. E. Henshaw, Min. Mag., 1965, 30, 585392 CRYSTALLOGRAPHY.Oxides, Hydrides, Nitrides, etc.-A review of the structure and propertiesof hydrogen peroxide,lol and a discussion of the oxygen-oxygen bond lengthin terms of bond order 799 lo2 have been made. Two oxides of czsium havebeen examined : Cs,O has a layer-type structure, d(Cs - 0) = 2-86,d(Cs - Cs) = 4.19 A,103 and Cs30 consists of columns of the hypotheticalpyramidal Cs,O+ ion, bound together by " metallic " electrons, in con-formity with the metallic properties of this oxide; d(Cs - - - 0) = 2.89,d(Cs - Cs) = 4.34 It had been reported lo5 that in mercuric oxide,L(Hg-O-Hg) and L(0-Hg-0) were both 109-8", whereas it now appears lo6that the true unit cell should be double, and contains infinite planar zig-zagchains, HgO-HgO - - 0 , with L (HgO-Hg) = log", L (O-HgO) = 179" ;d ( H g - 0 ) = 2-03 A in the chains, and 2-82 A between chains.Essentially thesame dimensions occur in the HgO-Hg-0 chains in 2Hg0,Hg,C1,.107A careful redetermination lo* of the parameters in rutile and anataseleads to d(Ti-0) = 1.946 (4 contacts) and 1-984 (2 contacts) in rutile, and1.937 (4 contacts) and 1.964A (2 contacts) in anatase. The correspondingmetal-oxygen distances in the rutile-type crystals of SnO,, GeO,, MgF,,lo9of VOz,llo and of CrO, ll1 have also been determined. The structure ofV,O,,CaO resembles that of CaTi20,,ll2 the transition metal in both caseshaving an octahedral co-ordination, with Ca2t a t the centres of polyhedraformed by 9 and 6 oxygen atoms respectively.Na, -zVGO1s (x z 1) containszig-zag double strings of VO, octahedra and chains of VO, trigonalbipyramids, the Na+ ions lying in interstitial sites.l13 Each Cu atom inCuCrO, has two near oxygen neighbours in linear array, d(Cu-0) = 1.85 A,and each Cr lies at the centre of a distorted oxygen octahedron, d ( C r 0 ) =1.99 A.114 Endless chains, - Sb-O-Sb-0 - with d(Sb-0) = 2.15 A,are bound together by hydroxyl groups ineach Sb atom is surrounded by four oxygen atoms at the corners of a de-formed trigonal bipyramid, with an unoccupied equatorial corner. Anaccount has been given of the structure of X,O, groups,116 which oftenconsist of two XO, tetrahedra sharing a common oxygen atom, and also ofthe structures of some oxide and hydroxide sulphates and ~hr0rnates.l~~Monograph, No.128, Reinhold Publishing Corp., N.Y., 1055.l o 1 W. C. Schumb, C. N. Satterfield, and R. L. Wentworth, Aaner. Chem. SOC.lo2 S. C. Abrahams and J. Kalnajs, Acta Cryst., 1955. 8, 503.lo3 K.-R. Tsai, P. M. Harris, and E. N. Lassettre, J . Phys. Chem., 1956, 60, 338.lo4 Idem, ibid., p. 345.lo5 W. L. Roth, Acta Cryst., 1956, 9, 277.1 0 6 K. Aurivillius, ibid., p. 685 ; Acta Chern. Scand., 1956, 10, 852.10' S. Sdavnitar, Acta Cryst., 1956, 9, 956.Io8 D. T. Cromer and K. Herrington, J . Amer. Chem. Soc., 1955, 77, 4708.l o 9 W. H. Baur, Acta Cryst., 1956, 9, 515.l 1 0 G.Andersson, Acia CJzem. Scand., 1956, 10, 623.112 F. Bertaut, P. Blum, and G. Magnano, Compt. rend., 1955, 241, 757; E. F.0. Glemser, U. Hauschild, and F. Triipel, 2. anoyg. Chcm., 1954, 277, 113.Ber *taut and P. Blum, Acta Cryst., 1956, 9; 121.113 A. D. Wadsley, ibid., 1955, 8, 695.114 W. Dannhauier and P. A. Vaughan, J . Amer. Chent. Soc., 1115 31. Edstrand, Agfkiv Kemi, 1955, 8, 257.116 G. A. Baxclay, E. G. Cox, and H . Lynton, Chem. and Ind.,1 1 7 G. Lundgren, Rec. Trav. chim.. 1956, 75, 685..955, 77, 896.1966, 178ABRAHAMS INORGANIC STRUCTURES. 393The structures of molybdenum and tungsten compounds containingstructural elements of the perovskite type have been discussed ; 118 M-0 andCu-0 distances are given for compounds of the type M,O,-Cu,O, whereM = Fe, Co, Cr, and Al.l19 A redetermination 120 of the earlier structureof bixbyite (Fe,Mn),O,, gives d[(Fe,Mn) - * 01 = 2-01, 2.67, and 3.00 A inone distorted oxygen octahedron, and 1.90, 1.92, and 2.24A in another.The distorted perovskite GdFeO, has the average d(Gd..*Fe) andd ( G d - * * O ) close to those in an ideal perovskite structure, although in-dividual distances vary by up to 0.4 A from the average : 121 GdFeO, formsthe type structure for a large group of compounds of formula ABO,, whereA is a rare earth and B is a tervalent transition metal element.12, Theferrimagnetic rare-earth ferrites are shown 123 to possess not a pervoskite-type structure with formula AFeO, but instead a garnet-type structure,formula A,Fe,O,,, the iron atoms being distributed over octahedral andtetrahedral sites, in accordance with N@el's theory.12* The shortestd(Fe - * * Fe) between different sites is 3.46 A : d(Fe - - Ooct) = 1-98,d(Fe - Otetr) = 1-86 A.125 Each uranium atom in U,08 is bonded tosix oxygen atoms with d(U-0) = 2.31 A and, in addition, to two otherswith d(U-0) = 2.06 A, the latter forming - - U-0-U-0 - * chains.126A tentative model for a B, hydride (probably B,H,,) has been sug-gested,lZ7 which resembles B1,Hl, with two boron atoms removed and a thirdadded.Magnesium hydride 128 has the rutile-type structure, each Mg atombeing co-ordinated to 6 hydrogen atoms at 1.95 A, d(H - H) = 2.49 and2.76 A (in LiH, the diameter of the H- ion is 2.72 A) : the short H - - Hdistance is characteristic of one anion-anion contact in this type of struc-ture.CuH and CUD have the wurtzite structure 129 while the hydrides ofLa, Ce, Pr, Nd, and Sm all belong to the fluorite type, with compositionMH, (2 < x < 3), the extra hydrogen atoms being distributed over theoctahedral lattice sites. The metallic nature of these rare-earth hydrides isattributed to the presence of valence electrons in excess of the two requiredby the metal atom in M-H bond forrnati0n.1~~ are iso-structural with the alltaline-earth hydrides, although they are not completelystoicheiometric compounds : hafnium forms hydrides and deuterides 132YbD, and EuD,118 A. MagnCli, J. Inorg. Nuclear Chem., 1956, 2, 330.119 C. Delorme, Acta Cryst., 1956, 9, 200.120 H.Dachs, Z. Kryst., 1958, 107, 370.121 S. Geller, J. Chew. Phys., 1956, 24, 1236.lz2 S. Geller and E. A. Wood, Acfa Cryst., 1056, 9, 563; F. Bertaut and F. Forrat,J . Pliys. Radium, 1956. 17, 129.F. Bertaut and F. Forrat, Conzpt. vend., 1956, 242, 382.lZ4 L. NCel, ibid., 1954, 239, 8.lZ5 F. Bertaut, F. Forrat, A. Herpin, and P. M6rie1, ibid., 1956, 243, 808.lZ6 S. Siegel, A d a Cryst., 1955, 8, 617.1 2 7 R. E. Dickerson, P. J. Wheatley, P. A. Howell, and W. N. Lipscomb, J . Chem.128 F. 1-1. Ellinger, C. E. Holley, B. B. McTnteer, D. Pavone, R. M. Potter, E. Starit-129 J. A. Goedkoop and A. F. Andresen, Acta Cryst., 1955, 8, 118.130 C. E. Holley, R. N. R. Mulford, and F. H. Ellinger, J . Phys. Chena., 1955, 59,131 W. L. Korst and J.C . Warf, Acta Cryst., 1956, 9, 452.lsa S. S. Sidhu, L. Heaton, and D. D. Zauberis, &id, p. 607.Phys., 1956, 25, 606.zky, and \V. H. Zachariasen, J . Amer. Chem. Soc., 1955, 77, 2647.1226394 CRYSTALLOGRAPHY.corresponding to Hf Di.63 and Hf D,,,, the former being face-centred cubic,the latter face-centred tetragonal. Zirconium gives analogous hydrides anddeuterides, and titanium apparently forms only the cubic fluorite-typestructure. Like PuO,, PuH,,, is face-centred cubic.133 Aluminium nitride 134departs only slightly from the ideal wurtzite-type structure, and consists ofslightly distorted tetrahedra having atoms of one type at the corners and ofthe other at the centres, d(A1-N) = 1.917 and 1.885 A. Each P atom in Ni3Phas nine Ni neighbours, d(Ni - * P) = 2.30 A, one Ni atom has twelve Nineighbours as in the metal, and the other two have ten Ni neighb0~rs.l~~In CdP,, each P atom has a distorted tetrahedral co-ordination, and eachCd atom a distorted octahedral co-ordination, d(Cd-P) = 2-65-2945 k136Beryllium boride, Be,B, has the fluorite-type structure, d(Be * .- B) = 2-01 Aand d(B - B) = 3-30 A.137 Ga,S, contains the Ga2,+ ion, d(Ga * - - Ga) =2.53 and d(Ga - S) = 2-31 A.138 Stromeyerite, AgCuS, has zig-zagchains of Ag and S atoms, d(Ag - * S) = 2.40 A, L(AgS-Ag) = 113",L(S-Ag-S) = 180°, and triangularly co-ordinated S and Cu atoms,d(Cu - S) = 2.29 (two contacts), 2-26 A (one contact), as building ele-m e n t ~ . ~ ~ ~ Iron carbide, Fe,C, consists of a network of Fe,C tetrahedra,d(Fe-C) = 1.78 A.140 Two independent but mutually consistent analysesof sodamide have been reported.141 The nitrogen atoms form irregulartetrahedra about the sodium atom, d(Na - - N) = 2-44, 2.49 A : there areno hydrogen bonds in NaNH,, as also is true of LiNH,.Halides.-The infrared spectrum of solid NH,F at -195" indicates anaccurately tetrahedral arrangement of F- ions about the NH,+ ion ~ite.1,~The non-planar molecule P,I, has 2/m (C2J symmetry in the solid state,The Ti atom in TiF, lies at the centre of a slightly distorted octahedronof 6 F atoms which are joined together by sharing corners, d(Ti-F) = 1.97 A.The Raman spectrum 145 of fused GaCl, indicates the presence of[Ga]-+[GaCl,]-, there being no evidence for a Ga-Ga bond.Reinvestig-ation 146 of the structure of SnI, shows that a simple distortion of theidealised model is adequate, resulting in SnI, tetrahedra with d(Sn-I) =2.69A. Pyramidal molecules of SbC13 are reported 147 in the crystal,d(Sb-C1) = 2.36, d(C1. - . C1) = 3.49 A, L(C1-Sb-C1) = 95-2", in excellentagreement with the electron-diffraction values. Evidence for a new tellur-d(P-P) = 2.21, d(P-I) = 2.48 A, L(1-P-I) = 102.3", L(I-PAP) = 93*9".la133 F. Brown, H. M. Ockenden, and G. A. Welch, J., 1955, 3932.134 G. A. Jeffrey and G. S. Parry, J . Chem. Phys., 1955, 23, 406.135 B. Aronsson, A d a Chem. Scand., 1965, 9, 137.136 H. Krebs, K.-H. Muller, and G. Ziirn, 2. anorg. Chem., 1956,285, 16.13' L. Ya. Markovskii, Yu. D. Kondrashev, and I. A.Goryacheva, Dokladj' Akad.1 3 * H. Hahn and G. Frank, 2. anorg. Chem., 1955, 278, 340.138 A. J. Frueh, 2. Kryst., 1955, 100, 299.I4O 2. G. Pinsker and S. V. Kaverin, Kristallografiya, 1956, 1, 66.1 4 1 A. Zalkin and D. H. Templeton, J. Phys. Chem., 1956, 00, 821; R. Juza, H. H.142 R. C. Plumb and D. F. Hornig, J . Chem. Phys., 1965, 23, 947.Id3 Y. C. Leung and J. Waser, J. Phys. Chem., 1966, 60, 539.l o 5 L. A. Woodward, G. Garton, and H. L. Roberts, J., 1956, 3723.14R F. Meller and I. Fankuchen, Acta Cryst., 1956, 8, 343.147 I . Lindqvist and A. Niggli, J. Inorg. NucEear Chem., 1966, 2, 346.Nauk, S . S . S . K . , 1955, 101, 97.Weber, and K. Opp, 2. anorg. Chem., 1956, 284, 73.S. Siegel, Acta Cryst., 1956, 9, 684ABRAHAMS INORGANIC STRUCTURES.395ium iodide, TeI, has been offered.148 The I,- ion in CsI, is asymmetricand non-linear, L(1-1-1) = 176.5" & 0*5", d(1-I) = 2-82 -J= 0.02, 3.02 &0.02 A. (cf. the 3-atom sets in a-IC1) : 149 in N(CH,),I,, the V-shaped 1,-ions (apex angle 86.5"), with approximatelylinear arms and structure (4), form sheets withdistances of 3-49 A or more between I,- ions in(4) the sheets.lm NMe; ions and I, molecules liebetween these sheets. There is no evidence forthe existence of an I,- ion in N(C2HJ41,; 151instead there are I,- ions and I, molecules, theNEt, i- ions fitting into the large holes of the iodine lattice. In contrast withthat in CsI,, the 1,- ion is symmetrical and linear, d(1-I) = 2.904 A : in the1, molecules, d(1-I) = 2.735 A.Gold(1) iodide forms infinite chains, - I-Au-I-Au - - -, withL (1-Au-I) = M O O , d(Au-I) = 2.60 a : gold(II1) chloride consists ofplanar Au,Cl, molecules, each gold atom being surrounded by 4 chlorineatoms at the corners of a distorted square, d(Au-C1) = 2.33 (C1 bonded totwo Au atoms), 2-24A (C1 bonded to one Au), L(Au-Cl-Au) = 94.7".Adisordered structure is proposed for PoBr,, with Po in octahedral co-ordination with Br, d(Po-Br) = 2.8 A.The crystal structures of 2HgC12,Hg0,155 of Hg2C1,,2Hg0, lo7 and ofHgC12,2Hg0 156 have been elucidated : the first compound containsthe planar trigonal trischloromercurioxonium group [0( HgCl),] r, withd(Hg-0) = 2.03 A, L(0-HgCl) = 175"; the second contains non-linearHg,Cl, groups with L(C1-Hg-Hg) = 161", d(HgHg) = 2.66 A ; thethird consists of Hg2+ cations and polymeric [OHgClI- anions which linkup to form infinite layers.In mercurous fluoride,15' d(HgHg) = 2-43 A,while in the other halides this distance is 2.53, 8-58, and 2.69 A respectivelyin Hg,Cl,, Hg,Br,, and Hg212, indicating a dependence on the nature of thehalide. The Br- ions in Hg,NHBr, are located 158 in the holes of theslightly puckered [HgJNH),] layers, with [HgBrJ ions lying betweenlayers.form a slightly distorted tetra-hedral arrangement about the central A1 atom, with d(A1-Br) = 2.34,d(A1-S) = 2.40 A. The central atoms in Nb0,F and Ta02F 160 and inTiOF, 161 are octahedrally co-ordinated by randomly distributed 0 and Fl a 8 W. R. Blackmore, S. C . Abrahams, and J . Kalnajs, Acta C y 0 s f ., 1956, 9, 395.'dB H. A. Tasman and K. H. Boswijk, ibid., 1955, 8, 59.*j0 W. J. James, R. J. Hach, D. French, and R. E. Rundle, abid., p. 814.' j l E. E. Havingaand E. H. Wiebenga, Proc. k. ncd. Akad. Mretenscha$., 1955, 58, H ,152 A. Weiss and A. Weiss, 2. Naturforsch., 1956, l l b , 604.153 E. S. Clark, Thesis. Univ. of California, Berkeley, Calif., 1955.154 K. W. Bagnall, R. W. M. D'Eye, and J . H. Freeman, J., 1955. 3039.ls5 S. SCavniEar and D. GrdeniC, Acta Cryst., 1955, 8, 275; A. Weiss, G. Yagorsen,and A. Weiss, 2. anorg. Chew., 1953, 274, 151.156 S. SCavniEar. Acta Cryst., 1955, 8, 379.157 D. GrdeniC and C. DjordjeviC, J . , 1956, 1316.158 K. Brodersen, Acta Cryst., 1955, 8, 723.150 A. Weiss, R. Plass, and A.Weiss, Z. anoug. Chcm., 1956, 283, 390.l a l K. Vorres and J . Donohue, ibid., 1955, 8, 35.2.90 A2-91The four heavier atoms in A1Br,,SH24 1 2 : idem, personal communication.L. K. Frevel and H. W. Rinn, Ada Cryst., 1956. 9, 626396 CRYSTALLOGRAPHY.atoms, forming M(0,F) octahedra, with d(Ta-0,F) = d(Nb-0,F) = 1.95 Aand d(Ti-0,F) = 1.90 A.The halogen atoms in the anions of KBrF, 162 and Cs,CoCl, 163 arearranged in the form of distorted tetrahedra, d(BrF) = 1.81 A andd(Co-Cl) = 2.22-2.41 A, while in K,NiF, the anion consists of NiF,octahedra sharing corners, d(Ni-F) = 2-00 A. Isolated [SbC1,12- ions arereported 165 in (NH,),SbCl,, with a distorted octahedral Sb-Cl bond distri-bution, one of the corners being unoccupied. An octahedral arrangement offluorine atoms has been reported in the anions of a number of compounds offormula ABF,, where B = Zr and Hf,166 As,167 Sb,168 and 0s ; 169 the latticeconstants and structure types of many others have been given.170 Similaranion arrangements are also found in Cs,PoI, and in K4CdC16.172Hydrates.-The complex ion [%r,(OH),J16H,0]8+ is reported 173 in thezirconyl chloride octahydrate crystal ; this complex consists of four Zratoms at the corners of a slightly distorted square linked along each edge bytwo OH groups.Four water molecules are in addition bound to each Zratom, resulting in a distorted square antiprism arrangement for these eightoxygen atoms : there are no Zr-C1 bonds. In HPF,,6H20 174 the watermolecules form cages of 24 oxygen atoms, with the P of the PF, group atthe centre.Two oxygen atoms from water molecules and four from differentdithionate ions, in Na,S20,,2H2O, form 175 the vertices of a distorted octa-hedron of oxygen atoms which contains the Na+ ion. A study176 of thepolarised infrared spectrum of CuC1,,2H20 indicates that the bond betweenH,O and the Cu2+ ion is not ionic, but approaches a covalent link in whichthe oxygen atom has more nearly a tetrahedral bond distribution. Twowater molecules in cupric tetrammine sulphate monohydrate 177 are attachedto each planar Cu(NH,), group, d[Cu - . - O(H,)] = 2-59, 3.37 A, forming adistorted octahedron : each H,O is also linked to two oxygen atoms of anSO, group, d[O * - * O(H2)] = 2.67 A. In chalc~phanite,~~~ ZnMn,0,,3H,0Jthe oxygen and water-oxygen atoms are in irregular octahedral co-ordin-ation with the Zn atom, d(Zn * - * 0) = 1.95, d[Zn * O(H,)] = 2.15 A.The nitrate ions and water molecules in Hg2(N0,),,2H20 together providel m S.Siegel, Acta Cryst., 1956, 9, 493.lBS G. N. Tishchenko and 2. G. Pinsker, Doklady Akad. Nauk, S.S.S.R., 1955, 100,16* D. Balz and K. Plieth, 2. EEeklrochem., 1955, 59, 545.le5 RI. Edstrand, 11. Inge, and N. Ingri, Acta Chem. Scand., 1955, 9, 122.166 H. Bode and G. Teufer, Acta Cryst., 1956, 9, 929; 2. anorg. CJwm., 1956, 283,167 R. B. Roof, Acta Cryst., 1955, 8, 739; J. A. Ibers, ibid., 1956, 9, 967.16E G. Teufer, ibid., p. 539.le9 &I. A. Hepworth, I<. H. Jack, and G. J. Westland, J . Inorg. Nuclear Chem.,170 B.Cox, J., 1956, 876.171 K. W. Bagnall, R. W. M. D’Eye, and J. H. Freeman, ibid., p. 3385.172 G. Bergerhofi and 0. Schmitz-Dumont, 2. anorg. Chem., 1956, 284, 10.173 A. Clearfield and P. A. Vaughan, Acta Cvyst., 1956, 9, 555.174 H. Bode and G. Teufer, ibid., 1955, 8, 611.17j S. Martinez, S. Garcia-Blanco, and L. Rivoir, ibid., 1956, 9, 145.176 R. E. Rundle, K. Nakamoto, and J. W. Richardson, .I. Chew Plays., 1955, 23,177 F. Mazzi, Acta Cryst., 1955, 8, 137.178 A. D. Wadsley, ibid., p. 165.913.18.1056, 2, 79.2450ABRAHAMS INORGANIC STRUCTURES. 397a framework in the holes of which the Hg' ions are located : 17'3 it is sug-gested that a double oxonium ion [H20-Hg-HgH,0]2+ exists in the struc-ture; L(Hg-Hg-0) = 160°, compared with 180" if truly covalent.Co -ordination Compounds.-The recent interest in " sandwich '' com-pounds has been maintained, and the subject reviewed.laO A variety ofcompounds are now known lS1 to be isomorphous with ferrocene, Cr, Co,Ni, Mn, V, and Mg each being able to replace the Fe atom : the pentagonalantiprismatic shape remains throughout, and the metal-carbon distancesare 2.13, 2-22, and 2.30A respectively for the Co, Cr, and V compounds.Dibenzenechromium, Cr(C,H&, forms an analogous " sandwich ''molecule,la2 d(CrC) = 2.19 A.Crystalline K[Co(NH,),(NO,),] is iso-morphous lB3 with Erdmann's salt (in which NH, replaces K) : two NH,molecules in the anion are co-ordinated to Co in the tram-position,d(Co-N) = 2-00 A, and four nitrogen atoms of the NO, groups form a squareabout the Co atom, d(Co-N) = 1-96 A, resulting in an octahedral co-ordin-ation. The Co en33+ ion in DL-trisethylenediaminecobalt (HI) chloridetrihydrate possesses 184 trigonal symmetry, with 6 N atoms of three enmolecules forming a slightly distorted octahedronabout the Co atom.The five-membered Co en ringsare not planar, but are in the " gauche" form.The absolute configuration of the D( +)-[Co en,]3T(5) ion is shown 185 in ( 5 ) . A regular tetrahedralbond distribution about the central Co atomis reported lB6 in di-p-toluidinecobalt dichloride,d(Co-C1) = 2.24, d(Co-N) = 1.92 A. Unlike thetrigonal bipyramidal arrangement about most 5-co-ordinated atoms, a square pyramidal configuration is found in bis-(NN-dimethyldithiocarbamato)nitrosylcobalt(II) ; the central Co atom isabout 4 A above the plane of the four sulphur atoms.lS7The paramagnetic quadricovalent Ni complex bisacetylacetonenickel( 11)is said ls8 to be a trinuclear molecule, Ni,(C5H70,),, the three Ni atomsbeing nearly collinear with d(Ni-Ni) = 2-80 A : the other atoms are un-resolved in the Fourier synthesis.The magnetic moment la9 of the anal-ogous molecule Fe(C5H70,), precludes the use of 3d244s4p3 bond orbitals, butnevertheless there is an octahedral distribution lgo of the Fe-0 bonds,d = 1.95 A. Copper 8-hydroxyquinoline dihydrate, CU(C,H~ON)~,~H,O, isisomorphous lgl with the corresponding zinc salt, and has a square coplanarco-ordination of two oxygen and two nitrogen atoms of 8-hydroxyquinoline,D.GrdeniC, J., 1956, 1312.lSo P. L. Pauson, Qwart. Rev., 1956, 9, 391.l B 1 E. Weiss and E. 0. Fischer, 2. anorg. Chem., 1956, 284, 69.ls2 Idem, ibid., 1956, 286, 142.Y. Komiyama, Bull. Chem. SOC., Japan, 1956, 29, 300.ls4 K. Nakatsu, Y . Saito, and H. Kuroya, ibid., p. 428.Is6 Y . Saito, K. Nakatsu, &I. Shiro, and H. Kuroya, Ada C~yst., 1955, 8, 729.lB6 G. B. Bokii, T. I. Malinovskii, and A. V Ablov, Kristallopajiya, 1956, 1, 49.IB8 G. J. Bullen, ibid., 1956, 177, 537.ls0 F. H. Burstall and R. S. Nyholm, J . , 1952, 3571.ls0 R. B. Roof, Acta Crvst., 195G, 9, 781.lQ1 R. Kruh and C. IV. Dwiggins, J . Atnfr. Chem. Sor., 1955, 77, 806.P. R. H. Alderman and P. G. Owston, Nature, 1956, 178, 1071398 CRYSTALLOGKAPH Y.with two other ligands (H20) weakly bonded in the vertex positions of atetragonal bipyramid.A careful analysis Ig2 of quinquecovalent ter-pyridylzinc dichloride shows that the three terpyridyl nitrogen atoms andthe two chlorine atoms are arranged in the form of a distorted trigonalbipyramid, with two Zn-N bonds in the axial positions; the terpyridylmolecule, which is essentially flat, lies in a plane normal to the equatorialCl-Zn-Cl plane, d(Zn-N) = 2.2, d(Zn-C1) = 2.29 a, L(C1-Zn-Cl) = 112".Similar structures are found for the corresponding cadmium and coppercomplexes, except that in the latter, CuCl,(terpy),2H20, the water moleculeslie in cavities in the structure and do not co-ordinate to the Cu atom. Thesemolecules are probably the first examples of dsp3 bonding for Zn, Cd, or Cuinvolving a chelate group.A study lg3 of bisbenzonitrilopalladium chloride indicates a squarecoplanar complex, the benzonitrile groups being attached through the Natoms in positions trans to each other, d(Pd-C1) = 2-35 A.Each Pt atomin sesquiethylenediaminetrimethylplatinic iodide, Pt (CH3)31, 1 + en, is sur-rounded octahedrally by three N and three C atoms in the cis-configuration,PtA,X3, with d(Pt-C) = d(Pt-N) == 2.45 A on average.l% Dipyridine-mercuric chloride, HgC1,,2C5H,N, has each Hg atom surrounded by four C1and two N atoms, d(Hg-Cl) = 2.34, 3.25 A, d(Hg-N) = 2.60 A, in the formof a distorted 0ctahedr0n.l~~ The Hg-N distance is longer than a covalentbond (ca. 2-03 A) and it is suggested that the pyridine molecules are presentprimarily as solvate of crystallisation.Intermetallic Compounds.-The structure of Li,Pb arid Li,Pb, resemblesthat of lithium metal in which the appropriate number of lithium atoms isreplaced by lead atoms : 196 Li,Pb, is similar although slightly modified.lgiIn KHg and KHg, the mercury atoms tend to assume a square coplanararray, d(Hg-Hg) = 3-00-3.08 A ; lQ8 in KPb, a lattice structure of theMgZn, type is found.lg9 CaSn and CaGe are isotypic ,O0 with CaSi, the Snand Ge bond angles being 96.6" and 100.7" respectively.The structures ofCaZn,, SrZn,, and BaZn, differ although similarities exist : ,01 d(Ca - * - Ca)is 6.5% greater than in the pure alkaline-earth metal while d(Sr - * Sr)is 6.1% less and d(Ba - * Ba) is 11.3% less than in the metal.The com-pound Re,,Ti, occurs in the Re-Ti system,*02 having the a-manganese typeof structure : Nb,X (X = Sn, Os, Ir, Pt), Ta,Sn, and V,Sn have the@-tungsten type of structure,2m for which has been given a set of radii for aneffective co-ordination number of 12.,04 Each Sb atom in Mn,Sb has205lD4 D. E. C. Corbridge and E. G. Cox, J . . 1956, 594.lD3 J. K. Holden and N. C. Baenziger, Acta Cryst., 1966, 9, 194.lD4 M. R. Truter and E. G. Cox, J., 1956, 948.lg5 D. GrdeniC and I. KrstanoviC, Arhiv Kern., 1955, 27, 143.lD6 A. Zalkin and W. J. Ramsey, J . Phys. Chew., 1956, 60, 234.lg7 A. Zalkin, W. J. Ramsey, and D. H. Templeton, ibid.. p. 1275.lD8 E. J. Duwell and N. C. Baenziger, Acta Cryst., 1955, 8, 705.lD9 D.Gilde, 2. anorg. Chem., 1956, 284, 142.P. Eckerlin, H. J. Rleyer, and E. Wolfel, zbzd., 1955, 281, 322.N. C . Baenziger and J . W. Conant, Acta Cryst., 1956, 9, 361.202 W. Trzebiatowski and J. Niemiec, Hocznika Chem., 1955, 29, 277.* O 3 S. Geller, B. T. Matthias, and R. Goldstein, J . Amer. Chem. SOC., 1955, 77, 1502.204 S. Geller, Acta Cryst., 1956, 9, 885.205 Id. Heaton and N. S. Gingrich, ibad., 1955, 8, 207MEGAW : FEKKOELECTKICS AND -1NTIFERROELECTRICS. 3'39four Mn neighbours at 2-75 A, one at 2.79 A, two a t 2.89 A, and one at3.77 A. A shift of electrons from the Mo-Be to the Be-Be bonds in MoBe,,has been suggested to account for the measured interatomic distances.206Recent investigations of the structures of some a-phases 207 indicate thepreference of given kinds of atoms for certain crystallographic sites in theunit cell, leading to a generalisation 208 regarding the nature of this " order-ing '' effect.Analyses of a number of intermetallic compounds of rheniumare reported in Six intermetallic compounds in the Th-A1 systemhave been discovered, and structures suggested.210Compounds of the Transuranic Elements.-The definitive series of papersby Zachariasen on the crystal chemistry of the transuranic elements has nowreached Part 24.52 A full scale review of work in this field is desirable, buta few of the novel structures described may be mentioned here. The(U02F5)3- group in tripotassium uranyl fluoride 211 is pentagonal bipyramidal,the uranyl group (UO,) being collinear, and the five U-F bonds forming anearly regular pentagon normal to the 0-U-0 axis.The (UF7)3- ion inK3UF7, which is isostructural with K,U0,F5, is also a pentagonal bi-pyramid. The uranium atom in U(S0,),,4H20 is surrounded by 8 oxygenatoms in a distorted square Archimidean antiprism.,13 A discussion 214has been given of the crystal chemistry of the (U0J2+, (NPO,)~", (PuO,)~',(Am02)2i, (YuO,)', and (AmO,)' ions, all of which have a symmetricalcollinear shape, the central atoms being able to form additional and longerbonds to 0 or F atoms. The observed bmd lengths can be correlated withthe bond strengths. Collinear uranyl groups have been reported in mag-nesium orthouranate,,15 in (3-uranyl hydroxide,216 in uranyl ~upferrate,~17and in uranyl carbonate.218 Crystals of Cs,ThCl, and Cs2UC1, are iso-structural 219 with Cs,PuCl, : each heavy atom is bonded to 6 chlorine atomsat the corners of slightly distorted octahedra.S.C. A.3. FERROELECTRICS AND ANTIFERROELECTRICS.1ntroduction.-Originally discovered in Rochelle salt,220 ferroelectricityhas now been found in a great variety of different structures; the rate ofdiscovery of new examples shows signs of increasing rather than decreasing.Ferroelectricity consists in a reversible spontaneous polarisation (manifested206 R. F. Raeuchle and F. W. von Batchelder, Acta Cryst., 1956, 9, 691.?07 G. J. Dickens, A. M. B. Douglas, and W. H. Taylor, ibid., 1956, 9, 297; G. Berg-208 J . S. Kasper and R. M. Waterstrat, ibid., 1956, 9, 289.209 S.Geller, ibid., 1955, 8, 15; J . Anzer. Ghem. SOC., 1955, 77, 2641; S. Geller andS. B. Cetlin, Acta Cryst., 1955, 8, 272.210 P. B. Braun and J. H. N. van Vucht, ibid., pp. 117, 246.211 W. H. Zachariasen, ibid., 1954, 7, 783.212 Idem, ibid., p. 792.213 P. Kierkegaard, Acta Chem. Scand., 1956, 10, 699.115 Idem, ibid., p . 788.2 1 6 G. Bergstrom and G. Lundgren, Acta Chem. Scund., 1956, 10, 673.217 W. S. Horton, J. Amer. Chem. SOC., 1956, 78, 897.218 D. T. Cromer and P. E. Harper, Acta Crvst., 1955, 8, 847.21s S. Siegel, ibid., 1956, 9, 827.2p0 J . Valasek, Phys. Rev., 1921, 17, 475.man and D. P. Shoemaker, ibid., 1954, 7, 857.W. H. Zachariasen, Acta Cryst., 1954, 7, 795400 CRYSTALLOGRAPHY.by a dielectric hysteresis loop) which is due to elementary dipoles arrangedso that their resultant dipole moment is not zero.There is characteristic-ally an upper transition temperature at which the dipole moment dis-appears, and there may also be a lower point. The transition is reversiblewithout break-up of the structure, and is displacive in Buerger’s sense,221i.e., it only involves small atomic displacements. It is associated with amarked peak in the dielectric constant and small changes in many otherphysical properties. In many cases, but perhaps not all, the changes arecertainly discontinuous, and the transitions of the first order. Latent heatsvary greatly, e.g., 1150 cal. mole-l in PbTiO, 222 and 12 cal. mole-1 at thelowest transition in BaTi03.223Compounds showing similar transitions without observable spontaneouspolarisation are called antiferroelectrics.First predicted theoretically 224from a rather unreal model, antiferroelectricity is now known in a widevariety of actual structures. They contain elementary dipoles like those ofthe ferroelectrics but so arranged by the symmetry that their resultantmoment is zero. Ferroelectrics may have antiferroelectric properties per-pendicular to their polar axis if the elementary dipoles 225 are not parallelbut are inclined to the axis in an arrangement such that their resultantmoment is not zero; these have been called cone ferroelectrics as distin-guished from Line ferroelectrics with parallel dipoles.Much interesting work, which cannot be surveyed here, has been doneon the physical properties.The chemical interest lies in the nature of thedipoles, the types of structure involved, and the possibility of explainingthem in terms of interatomic forces. Detailed theories,226$ 227 with theexception of Slater’s theory 228 of KH,P04, have all attributed the main r6leto long-range electrostatic forces ; none has proved capable of explaininglater-discovered types of ferroelectrics. Devonshire’s phenomenologicaltreatment 229 has proved stimulating and successful in relating properties 230but cannot help in explaining structures. The question of short-range forcesand the importance of homopolar bonds directed in space has only been dis-cussed q ~ a l i t a t i v e l y . ~ ~ ~ Useful reviews are available of the phenomenologicaltheories,232 of all theories up to about 19!52,227 and of recent experimental andtheoretical work ; 2% a book summarising results and theories is forthcoming.2a221 M.J. Buerger, in “ Phase Transformations in Solids ” (ed. SmoIuchowski),Wiley, New York, 1951.222 G. Shirane and S. Hoshino, J . Phys. SOC. Japan, 1951, 6, 265.223 S. S. Todd and R. E. Lorensen, J . Amer. Ch.em. Soc., 1952, 74, 2043; J. Volger,224 C. Kittel, Phys. Rev., 1961, 82, 729.pP6 L. E. Cross, Phil. Mag., 1956, 1, 76.226 See, for example, W. P. Mason, “ Piezoelectric Crystals,” Van Nostrand, NewYork, 1949; J. C. Slater, Phys. Rev., 1950, 78, 748; J. Pirenne, Physica, 1949, 15, 1019.247 E. T. Jaynes, “ Ferroelectricity,” Princeton Univ. Press, Princeton, 1953.228 J.C. Slater, J . Chem. Phys., 1941, 9, 16.229 A. F. Devonshire, Phil. Mag., 1949, 40, 1040; 1951, 42, 1065.230 W. J. Merz, Phys. Rev., 1953, 91, 513; S. Triebwasser, ibid., 1956, 101, 993;231 H. D. Megaw, A d a Cvyst., 1952, 5, 739; 1054, 7, 187.232 A. F. Devonshire, Phil. Mag. (Suppl.), 1954, 3, 85.233 G. Shirane, F. Jona, and R. Pepinsky, PYOC. Inst. Radio Engrs. N.Y., 1955, 43,234 H. D. Megaw, “ Ferroelectricity in Crvstals,” Methuen, London, 1957.Philips Res. Repoft, 1952, 7, 21.ref. 225.1738MEGAW : FERROELECTRICS AND ANTIFERROELECTRICS. 401A new concept of families of strztctzcres is becoming necessary. Allstructures of a family are derived by different small distortions from thesame high-symmetry form. In one family, two different compounds maybe isostructural, while one compound may have several different structures(it?,, phases) which are truly stable for different ranges of temperature andelectric field but may exist metastably outside these ranges; they may beferroelectric or antiferroelectric or neither.The ideal structure is usuallythe high-temperature form ; the higher its symmetry the greater the possiblevariety of distorted structures. Solid solutions may have phases within thefamily but different from those of either end-member; the possible com-plexity of the phase diagram is thus very great. All transitions within thefamily are displacive.The substances dealt with here fall naturally into two main groups,namely the oxides and the hydrogen-containing compounds.Oxides-The Perovskite family.Detailed analyses, by use of X-rays andneutrons, have been made of tetragonal 235 BaTiO, and the isomorphous 236PbTiO, ; they are qualitatively similar but the displacements are muchlarger in the latter. The oxygen octahedra remain nearly regular, butrelative to their geometrical centres all cations are displaced in the samesense, Ti by 0.12 A and 0.30 A in BaTiO, and PbTiO, respectively, Ba by0.06 A, Pb by 0-47 A. The Ti-0 distances in BaTiO, are 1.87, 2.17, 2-00 Aand in PbTiO, 1.78, 2.38, 1.98A, as compared with 1.96A for the radiussum. The partly homopolar character of the Ti-0 bond in PbTiO, seemscertain, and is evidence for a similar interpretation of the smaller effect inBaTiO,. The relatively large displacement of Pb places it at the apex ofa flat square pyramid, as in PbO, while leaving it close to 4 others of itsoriginal 12 oxygen neighbours.The system KNb0,-NaNbO, has been studied by its electrical and opticalproperties and lattice parameters.225, 237-239 With decreasing temperatureKNbO, is in turn cubic (425"), tetragonal (220") , orthorhombic (- 140" c) ,and rhombohedral, with transition points as indicated ; each structure issmall-cell * and all but the cubic are ferroelectric.NaNbO, is cubic ( ~ 6 4 0 " c),tetragonal small-cell ( * Z O O ) , pseudotetragonal multiple-cell ( ~ 3 6 0 " ) , ortho-rhombic multiple-cell ; all but the cubic are antiferroelectric. Below-120" a new ferroelectric phase can be produced 239 by the application ofa large field in a certain direction; once produced it remains stable up to-55". Another, probably different, phase is produced by a differentlydirected field at or below room temperature but this is never stable withoutthe field. The room-temperature structure 240 shows tilting of octahedra235 B.C . Frazer, H. R. Danner, and R. Pepinsky, Phys. Rev., 1955, 100, 745.236 G. Shirane, R. Pepinsky, and B. C. Frazer, Acta Cryst., 1956, 9, 131.237 G. Shirane, H. Danner, A. Pavlovic, and R. Pepinsky, Phys. Rev., 1954, 93, 672;G. Shirane, R. Newnham, R. Pepinsky, ibid., 1954, 96, 581 ; H. Francombe, Acta Cryst.,1956, 9, 256.238 F. Jona, G. Shirane, and R. Pepinsky, Phys. Rev., 1955, 97, 1584.239 L. E. Cross and B. J. Nicholson, Research Correspondence, 1954, 7, S30; Phil.Mag., 1955, 46, 453.240 P.Vousden, Acla Cryst., 1951, 4, 545. * A small-cell structure can be referred to a primitive unit cell of approximatelythe same dimensions as that of the ideal structure: in a multiple-cell structure the trueprimitive unit cell consists of two or more nearly identical sub-units of that size402 CKYSTALLOGKAYHY.such that Na has probably 6 near oxygen neighbours instead of 12; it alsoshows antiparallel displacements of Nb within the octahedra along one face-diagonal of the original cube. Solid solutions with very small amounts ofKNbO, give structures characteristic of KNbO,. Solid solutions betweenNaNbO, and Cd,Nb,O, also show perovskite-type structures at the NaNbO,end.*1SrTiO, (cubic small-cell) has no transition 242 down to 8" K, but its di-electric constant behaves like that of materials approaching a ferroelectricCurie point.Below 4" K a ferroelectric phase can be induced by a field.2&CaTiO, (distorted, multiple-cell) is somewhat similar electrically,2u but nolow-temperature transition has yet been reported; that z45 at 1260" c ispresumably to a cubic form.Solid solutions of PbTiO, and PbZrO, with each other, or with Ba, Sr,or Ca replacing Pb, give a very complex series of phases. Between PbTiO,(ferroelectric, tetragonal, small-cell) and PbZrO, (antiferr~electric,~~~ ortho-rhombic,23* multiple-cell) there is a Zr-rich ferroelectric rhombohedralwhich can also be induced by an applied field outside its normalcomposition range ; 248 it is isomorphous with rhombohedral BaTiO,, and hasa relative cation displacement of 0.14 I t also occursin (Pb,Ba)21-0,.~~~ The structure of the other phases remains unknown.The high-temperature (tetragonal) form of WO,, which is antiferroelectric,has been studied in Qualitatively it closely resembles BaTiO,with the barium atoms omitted and half the titanium displacements reversedin sense. The displacement of tungsten relative to the centre of symmetryis 0.23 A.The room-temperature form has been re-investigated; 251 it ismonoclinic, but the atomic parameters are not known. A low-temperatureform has been reported as rhombohedral and ferr~electric.,~~LiNbO,, formerly thought to have an ilmenite struc-ture, has now been shown 2% to be a type of its own.The oxygen array, asin ilmenite, approximates to hexagonal close-packing, but the sequence ofcations in octahedral sites parallel to the c-axis is : Li, Nb, empty, Li, Nb,empty. . ., which is compatible with polar symmetry and the reportedferroelectricity. The niobium atoms are displaced 0.28 A from the centresof the octahedra. There is a topological relationship with the perovskitestructure.(cf. 0.17 A in PbTiO,).Lithium niobate.241 B. Lewis and E. A. D. White, Acta Cryst., 1955, 8, 849.242 J. K. Hulm, Proc. Phys. Soc., 1951, 63, 1184.243 H. Granicher, Helv. Phys. Acta, 1956, 29, 211.a44 H. Granicher and 0. Jakits, Nuovo cim. (SuppZ.), 1954, 11, 480.246 B. F. Naylor and 0. A. Cook, J . Amer. Chem. Soc., 1946, 68, 1003.2413 G.Shirane, E. Sawaguchi, and Y . Takagi, Phys. Rev., 1951, 84, 476.247 G. Shirane and A. Takeda, J . Plzys. SOC. Japan, 1952,7,5 ; G. Shirane, K. Suzuki,g4a E. Sawaguchi, ibid., 1953, 8, 615.24s G. Shirane, Phys. Rev., 1952, 86, 219; G. Shirane and S. Hoshino, Acta Cryst.,260 W. L. Kehl, R. G. Hay, and D. Wahl, J . A$$. Phys., 1952, 23, 212.251 C. Rosen, E. Banks, and B. Post, Acia Cryst., 1956, 9, 475; G. Andersson, Acta252 B. T. Matthias and E. A. Wood, Phys. Rev., 1961, 84, 1255.z53 P. Bailey, Thesis, Bristol, 1953, quoted by H. D. Megaw, Acta Cryst., 1954,and A. Takeda, ibid., 1952, 7, 12; G. Shirane and K. Suzuki, ibid., 1952, 7, 333.1954, 7, 203.Chew. Scand., 1953, 7, 154.7, 187hIEGhW FERRUELECTRICS AN 1) ANTIFEHKOELEC lX1CS.403Yyochzlores. Cd,Nb,O,, ferroelectric below about 180" K, has apyrochlore structure at room temperature. This, like perovskite, has aframework of octahedra linked by shared corners, the seventh oxygen atombeing linked only to cadmium. The phase transition makes remarkablylittle difference to the X-ray pattern,255 being detectable only by a veryslight splitting of the highest-angle lines. The ferroelectric phase is probablytetragonal, possibly orthorhombic, but certainly not rhombohedral.Pb2Nb,0,, with a multiple-cell variant of the same structure,2M is anti-f erroelect ric.Though oxides with some oxygen deficiency retain the yyrochlore struc-ture, Cd,Nb,O, has the columbite structure and is not ferroelectric; 255PbNb,06 has been reported with an orthorhombic ferroelectric form,256and with a perovskite form.257Hydrogen-containing Compounds.-New work on Rochelle salt 233 sug-gests that the hydrogen-bond system must be radically revised ; detailedco-ordinates and bond lengths are not yet available.Very careful refine-ment of both high 30 and low-temperature 409 258 forms of KH,PO, has beencarried out, and the reversal of the structure accompanying reversal of thespontaneous polarisation has been elegantly demonstrated. The low-temperature form of ND4D,P0, (presumably isomorphous with NH,H,PO,)has been shown 259 to be antiferroelectric ; the difference in detailed arrange-ment between this and KH2P0, may be attributed2,O to the bonding re-quirements of the NH, group.The periodates Ag2H,I06, (NH,),H,IO,, and(ND,),D,IO, are antiferroelectric ; 261 they have transitions a little belowroom temperature, at which the a-edge is doubled in all three compounds andthe c-edge also in Ag,H,IO,. There is some formal resemblance to KH,PO,,with trigonal symmetry replacing tetragonal and octahedra replacingtetrahedra.Very interesting new ferroelectrics and antiferroelectrics occur aniongthe sulphates. The first group is typified by guanidine aluminium sulphatehexahydrate,262 (CH,N,)Al(SO,),,GH,O. ' I Isomorphous " compounds occurwith Cr, Ga, or V replacing Al, and Se replacing S. These materials areferroelectric at room temperature and remain so up to about 300" c, whenthey decompose. Another interesting family is that of the alums,AJA*1T(S0,),,12H20 ; these have long been known to possess several differenthut closely-related structures at room temperature, and recent work 263 shows264 W.R. Cook and H. Jaffe, Phys. Rev., 1952, 88, 1426; 1953, 89, 1297.y 5 5 F. Jona, G. Shirane, and R. Pepinsky, ibid., 1956, 98, 903.2 5 6 G. Goodman, J . Amer. Ceram. SOC., 1953, 36, 368.257 M. H. Francombe, Acla Cryst., 1956, 9, 683.258 H. A. Levy and S. W. Peterson, Phys. Rev., 1954, 93, 1121,259 E. A. Wood, W. J. Merz, and B. T. Matthias, ibid., 1952, 87, 544.K. 0. Keeling and R. Pepinsky, 2. Krist., 1955, 106, 236.261 G. Busch, W. Kanzig, and W. M. Meier, Helv. Phys. Ada, 1953, 26, 385; H.Granicher, W. M. Meier, and W. Petter, ibid., 1954, 27, 216; D. Aboav, H. Granicher,and W.Petter, ibid., 1955, 28, 299.262 A. N. Holden, B. T. Matthias, W. J. Merz, and J. P. Remeika, Phys. Rev., 1955,98, 546; A. N. Holden, W. J. Merz, J. P. Remeika, and B. T. Matthias, ibid., 1966,101,962 ; J. P. Remeika and W. J. Merz, ibid., 1956, 102, 295.263 For a survey, see for example, K. D. Bowers and J. Owen, ReFort Progr. Ph-ys.,1955, 18, 304404 CRYSTALLOGRAPHY.a very complex series of transitions at low temperatures. Some alums havenow been found to be ferroelectric, e.g., (CH3*NH,)Al(SO,),,12H2O below176" K, and some antiferroelectric.za Other ferroelectric sulphates are 265(NH,),SO, and 266 (NH,),Cd,(SO,), (the latter cubic at room temperature)with Curie points at 223" K and 87" K respectively.Ferroelectricity is also reported in ~olemanite,2~~ CaB,O,(OH),,H,O,below - 2.5".Both room-temperature 268 and low-temperature structuresare monoclinic.Generalisations.-The oxides all have saturation moments about 10-30 PC crn.-,, as compared with 0.1-1-0 PC cm.-2 for compounds of hydrogen.They all contain one of the " cations " Ti4+, Z P , Hf4+, Nb5+, Ta5+, or W6+in octahedral co-ordination, the octahedra being linked by corners. In allthose examined in detail, the octahedra are little distorted, but the " cations "are displaced appreciably from their geometrical centre. It seems likelythat this octahedral group constitutes the elementary dipole, the polaris-ation of the oxygen atoms shielding each from the others. Whether the" cation " is displaced towards a corner, edge, or face of the octahedronseems to depend mainly on the identity of the cation and the temperature,but it is also affected by the polarising power of the other cation present,or, in BaTiO,, by its large size which strains the TiO, framework; nearthe limits of its stability range it may also be influenced by an appliedfield.Tilting of the octahedra about their shared corners is common in themultiple-cell structures.This puckering changes the co-ordination of thesecond cation; the change, so far as available evidence goes, is that re-quired by Goldschmidt's rules of ionic packing, e.g., Na becomes 6- insteadof 12-co-ordinated. There is a tendency for the two framework bonds tooxygen to be non-collinear, as one would expect if they were partly homo-polar. In adjacent octahedra the relative sense of the displacements, andhence of the dipole moments, depends on the bond angle at the oxygenatom.The choice between ferroelectricity and antiferroelectricity thusdepends on how the octahedra can be built together to satisfy the bondangle at the oxygen atom and the packing requirements of the secondcation.The hydrogen compounds have in general more complicated structures,where the symmetry by itself is not as informative as in the oxides, andexcept for KH,PO, none is known in sufficient detail. They all containhydrogen bonds, but these range from short (2-49A in KH,PO,) to long(2.87 A in the alums) and include N-H. . . 0 in (NH,),SO, as well asO-H . . . 0 in many of the others.It seems that the polarisation of eitheror both of the oxygen atoms involved in the bond is important, but inKH,PO, the displacement of phosphorus relative to its neighbours suggeststhat the PO,(OH), group as a whole is the dipole.264 R. Pepinsky, F. Jona, and G. Shirane, Phys. Rev., 1956, 102, 1181.*68 F. Jona and R. Pepinsky, ibid., 1956, 103, 1126.267 J. W. Davisson, Actu Cryst., 1956, 9, 9 ; G. J. Goldsmith, Bull. Amer. Php. SOC.,268 C . I,. Christ, J . R. Clark, and H. T. Evans, A d a Cryst., 1954, 7, 453.B. T. Matthias and J . P. Remeika, ibid., 1956, 103, 262.1956, 1, 322SPEAKMAN ORGANIC STRUCTURES. 405These generalisations, tentative as they are, suggest that the short-rangeor chemical forces play an important part, and that further work in thisfield, especially if it can be made quantitative, will be of considerablechemical interest.H. D.M.4. ORGANIC STRUCTURES.Carboxylic Acids and Related Compounds.-For some years long-chaincompounds have been isolated in a state of high purity a t Uppsala, andphysical measurements on the normal fatty acids have now been sum-marked in two papers by Stenhagen and von S y d o ~ . ~ ~ ~ The first dealswith the melting points and transition points of the acids from C,, to C29;the second with the polymorphic forms and their structures. Six forms areknown with certainty : A, B, and C with acids whose molecules contain aneven number of carbon atoms, and A', B', and C' with the odd members-though all three forms are not necessarily known for every acid.Thestructures of these forms are described, as are also the sub-cells whichcharacterise the two types of packing of the parallel polymethylene chains.The well-known alternation of melting-points (Le., of the C or C' forms) isnot due to any inherent difference in molecular structure; it can be con-vincingly explained as due to differences in crystal structure, which lead tocloser van der Waals contacts between layers of terminal methyl groups inthe even acids (C-form). The molecules of (-+)-9-methyloctadecanoicacid,270 CH,*[CH,],*CHMe*[CH,],CO,H, are much more tilted (72") fromthe normal to the plane occupied by the carboxyl groups than are those ofany other known fatty acid; this is clearly due to the necessity for accom-modating the methyl group, protruding from the middle of the chain, in thegap at the end of the neighbouring molecule.Magnetic measurements 271on cupric laurate and stearate suggest that pairs of copper atoms lie closetogether, and hence that the structure resembles that of cupric acetatedih~drate.,~,The acid, C,H40,,2H,0, formerly supposed to be dihydroxymaleic, isnow thought to be dihydroxyfumaric and this is confirmed in a partialX-ray analysis.273 Acid fumarates of composition M,H,A3 (M = K, Rb;A = fumarate) have been studied.274 One fumarate residue is required tobe centrosymmetric, but, since hydrogen atoms were not located, it is notclear whether the formulation should be BMHA,H,A or M,A,2H& Tiglicacid 275 proves to have the trans-configuration (cis-methyls) (1).Thisimplies that angelic acid, work on which is in progress, has the alternativeconfiguration.The structure of benzoic acid has been determined with considerable268 E. Stenhagen and E. von Sydow, Arkiv Kemi, 1953, 6, 309; 1956, 10, 231.2 T o S. Abrahamsson, Acta Cryst., 1956, 9, 663.2 7 1 R. C. Herron and R. C. Pink, J . , 1956, 3948.272 Anit. Reports, 1954, 51, 390.273 M. P. Gupta, .I. Amer. Chem. Soc., 1953, 75, 612; Canad. J . Chem., 1955, 33,274 Idem, Acta Cryst., 1956, 9, 263.2 7 5 A. L. Porte and J. M. Robertson, Nature, 1965, 176, 1116.1450406 CRYSTALLOGRAPHY.accuracy; 276 and the bond lengths shown to be in good accord with theresults of molecular-orbital calculations.277 Dimeric molecules (2) also existin phenylpropiolic The planar molecules are bisected by a crystallo-graphic plane of symmetry parallel with their length.The two C-0 bondstherefore appear to be equivalent, and the hydrogen atoms more symmetricallylocated than appears in formula (2). This unacceptable conclusion, thoughsupported by a good agreement between F, and Fc, was evaded by the dis-covery in the structure of disorder, allowance for which made the agreementbetter; dimeric molecules lie a t random with respect to the alternativeorientations (2) and (3), and the observed symmetry is merely a statisticalone. [In a similar way the molecule of naphthazarin (4) has been foundto be crystallographically centrosymmetrical by two independent workers.279]Effects of this kind seem to be fairly common ; and crystallographers oughtto be on their guard against being misled by them.9-Aminosalicylic acid 280has been analysed with sufficient accuracy for the hydrogen atoms to belocated, with reasonable certainty, at positions which prove that this aciddoes not adopt the zwitterionic structure generally found in aliphatic amino-acids. A preliminary report 281 has been made of the full-scale analysis ofFeist's acid; the structure now accepted for this compound is also indicatedby nuclear magnetic resonance.282 Silver perfluorobutyrate 283 consists ofdimers, the two carboxyl groups being linked via two silver atoms into eight-membered rings.According to a fairly precise analysis,284 formamidoxime has a planarmolecule. Donohue 285 has cited this work in evidence against the suggestedpolar structure ( R2C=AH-6) for oximes.The structures of succinimide 286and succinamide 287 have been studied, the latter with a precision sufficientto locate the hydrogen atoms and hence to confirm the amide (rather thanthe imidol) grouping. A study of the unstable form of chloroacetamide 288includes a survey of bond lengths and angles in various amides; in all casesL(C-C-N) is less than L(C-C-0), as-in analogy with carboxyl-is to beexpected for the amide group. An analysis of the stable form of chloro-276 G. A. Sim, J. M. Robertson, and T. H. Goodwin, A d a Cyi.d., 1955, 8, 157.277 T. H. Goodwin, J., 1955, 4451.278 J. S. Rollett, Acta Cryst., 1955, 8, 487.279 C. Billy, Compt. rend., 1955, 240, 887; 0.Borgen, A d a Chrnz. Scuud., 1956, 10,280 F. Bertinotti, G. Giacomello, and A. M. Liquori, Acta Cryst., 2954, 7, 807.281 D. R. Petersen, Chem. and Ind., 1956, 904.282 A. S. Kende, ibid., 1956, 437.283 A. E. Blakeslee and J . L. Hoard, J . Amey. Che~n. Soc., 1956, 78, 3029.284 D. Hall and F. J. Llewellyn, Acta Cryst., 1956, 9, 108.285 J. Donohue, J . Amer. Chem. Soc., 1956, 78, 4172.286 R. Mason, Acta Cryst., 1956, 9, 405.287 D. R. Davies and R. A. Pasternak, ibid., p. 334.Z B R M. Katnyama, ibid., 1956, 9, 986.867SPEAKMAN ORGANIC STRUCTURES. 407acetamide led to angles which would have made this substance an excep-tion, but a brief report of a rather more accurate analysis 290 gives anglesthat conform.A study of N-chlorosuccinimide 291 has also been brieflyreported.Though not isomorphous, benzeneseleninic acid (5) 292 and its fi-chloro-derivative 293 have very similar structures, that of the former having beenbeen studied with higher accuracy. The three bonds roundPh-Se /OH the selenium atom are arranged pyramidally, the angles allbeing near to 100"; the two SeO bonds differ in length,d(Se-OH) being 1.765 and d(Se-0) 1.707, each &0.015 A ;the molecules are linked together by strong hydrogen bonds d(OH . . , 0) =2.52 L f , so as to form infinite spiral chains round the 2,-axis. An accurateanalysis of dibenzyl hydrogen phosphate,294 which is of interest as a modelcompound for nucleic acids, shows that d(P-0) = 1.469 -& 0.004 A for theunicovalent oxygen atom, and d(P-0) = 1.545, 1.545, and 1.566A for theother three oxygens.Aromatic Hydrocarbons.-Ant hracene now holds the palm as best illus-trating the evolution of X-ray methods.So long ago as 1921, a comparisonof its unit-cell dimensions with those of naphthalene enabled W. H. Braggto suggest an orientation for the molecule. In 1933 Robertson 295 measuredabout 80 F,-values and used them to compute one of the earliest sets ofelectron-density projections, which clearly showed the molecule and itsposition in the cell, but was not accurate enough to detect differences inbond-lengths. The same author and his collaborators published in 1950 anaccount 296 of a three-dimensional study : nearly 700 F, values had beenmeasured, an electron-density section in the molecular plane (see A m .Reports, 1950, 47, 433) was derived, and bond-lengths were given with anaccuracy estimated at &O.Ol A.(The lengths were later compared withthose calculated by various wave-mechanical procedures.297) The sameexperimental data have now been used by Cruickshank298 in the mostthorough refinement yet applied to a structure of this kind; and thereemerges an extremely detailed picture of the molecule in its crystallineenvironment. The final bond-lengths and angles (e.s.d. & 0.004 A and& 12') are given in Fig. 1. With one exception the lengths differ surprisinglylittle from those estimated in 1950, though the precision is now higher andmore firmly based. The slight deviations of the atoms from their meanplane-also shown in the Fig.-are now highly significant ; and they can bereasonably attributed to the stresses exerted on the various parts of themolecule by identifiable contacts with its neighbours.The vibrations of the\O28B J. Dejace, Acta Cryst., 1955, 8, 851.2D0 B. R. Penfold and W. S. Simpson, ibid., 1956, 9, 831.291 R. N. Brown, ibid., p. 193.292 J . H. Bryden and J . D. McCullough, ibid., 7, 833.2B3 Idem, ibid., 1956, 9, 528.2Br J. D. Dunitz and J . S. Rollett, ibid., p. 327.295 J . M. Robertson, Proc. Roy. Soc., 1933, A , 140, 79.2B6 A. McL. Mathieson, J. M. Robertson, and V. C. Sinclair, Acta Cvyst., 1950, 3, 245.297 C. A. Coulson, R. Daudel, and J. M. Robertson, Proc. Roy. Soc., 1951, A , 207,2BB D.W. J. Cruickshank, Acta Cryst., 1956, 9, 915; for some minor emendation see306.Ada Cvyst., 1957, in the press408 CRYSTALLOGRAPHY.atom can be resolved into translational movements with r.ni.s. amplitudesof 0.20, 0.16, and O*lSA parallel to the respective molecular axes, L, M,and N, and into librations of 2-3" about these axes. The first of thesetranslations is probably significantly greater than the other two, and itcorresponds to movement in the direction in which the molecule might wellFIG. 1.civcles represent the deviations (in 0.001 A) of the atoms f r o m their mean molecular plane.Axis M aBond-lengths (A) and angles i?$ the anthracene molecule. The figures within theexperience least resistance. The final " difference map " shows negativeareas at the centres of the rings and between the " spokes" of the C-Hbonds.It is tempting to ascribe this to the lateral contraction of theatomic orbitals when they enter into a o-bond (see p. 411). Theoreticalcalculations of the electron-density over the benzene molecule do not revealsuch electron-deficient areas,299 but the contraction may not be properlyreproduced in the usual L.C.A.O. approximation.have nowbeen analysed by two-dimensional methods, but with sufficient accuracy toshow that the molecular dimensions do not differ seriously in the two forms.The space-group of azulene (6) was formerly thought to require the moleculeto be effectively centrosymmetric, which would imply randomness of orient-ation in the crystal. But more detailed studies, briefly reported from twolaboratories,301 indicate a different space-group and show projections inwhich the five- and seven-membered rings are easily recognisable.Theimportant question of bond-lengths cannot yet be answered. Analyses ofchrysene 302 and 3 : 4-benzopyrene 303 show these molecules to be planar,or very nearly so. Although the molecule of 9 : 10-dihydroanthracene is" folded " about the line of atoms 9 and 10, that of the related compound (7)appears to be centrosymmetric, and hence presumably planar.304Other work on aromatic hydrocarbons can be considered in relation toovercrowding.305 Projections of certain overcrowded molecules have beenBoth polymorphic forms of 1 : 2-5 : 6-dibenzanthracene299 N. H. March, Acta Cryst., 1952, 5, 187; W.Cochran, ibid., 1956, 9, 924.3OO J. M. Robertson and J. G. White, J., 1947, 1001; 1956, 925.301 J. M,. Robertson and H. M. M. Shearer, Nature, 1956, 177, 885; Y . Takeuchi302 D. M. Burns, Acta Cryst., 1056, 9, 173.303 J. Iball and D. \V. Young, Nature, 1956, 177, 985.804 Personal communication from Dr. Iball.Ann. Reports, 1954, 51, 393.and R. Pepinsky, Science, 2956, 124, 126.(It was there stated that the structures of m- andp-xylylenes were first revealed by X-ray analysis: so far as the m-compound is con-cerned, this is erroneous-see W. Baker, J. F. W. McOmie, and J. M. Norman, J., 1951,11 14.SPEAKMAN : ORGANIC STRUCTURES. 409derived from intensity data at low temperatures; 306 on the maps thus"sharpened" the hydrogen atoms can often be located, and this helpsconsiderably in understanding the stereochemical details of the strain.Anaccurate low-temperature study of diphenyloctatetraene , Ph*[CH:CH],-Ph 307shows the benzene rings to be slightly out of the plane of the zigzag goly-methine chain, a result attributed to repulsion between the ortho-hydrogenatoms and those on the terminal CH-groups; the mean L(C=C-C) =124.2" &- 0.2". Pentacene probably has a planar molecule, as also hascircumanthracene (1 1, the third member of the coi-onene-ovalene series) ; 308but the intermediate compounds (8, 9, and 10) are considerably distorted.3og3 : 4-Benzophenanthrene is well known to have an overcrowded molecule,but, when the interfering atoms are bonded in 2 : 13-benzofluoranthene (la),the molecule becomes planar,31° though the new bond [d(C-C) = 1.49 A]must cause considerable disturbance of the aromatic ring-system.Heterocyclic Systems.-Four important molecules containing nitrogenatoms have been studied with high accuracy.s-Triazine (13) 311 has thehigh molecular symmetry Fm, which is fully used in the crystal structure-arare occurrence. Only four parameters are therefore needed to define the(static) structure, and they may be expressed as d(C-N) = 1.319 & 0.005,d(C-H) = 1.00 A, L(N-C-N) = 126.8" & 0-4", and L(C-N-C) = 113.2" If:0.4". s-Tetrazine (14) has a centrosymmetric which does notdeviate significantly from coplanarity, and whose dimensions correspondclosely with those of triazine : d(C-N) = 1.334 0.007 (mean of two),116.0" & 0.3" (mean of two). Phenazine (15) has been studied in its a-form.313 This molecule too is centrosymmetric, and it does not deviateH(N-N) = 1.321 & 0.010 A, L(N-C-N) = 127.4" & 0*3", L(C-N-N) =306 F.L. Hirshfeld and G. M. J. Schmidt, Acta Cryst., 1956, 9, 233.307 W. Dreuth and E. H. Wiebenga, ibid., 1955, 8, 755.308 E. Clar, W. Kelly, J. M. Robertson, and M. G. Rossmann, J., 1956, 3878.309 Personal communications from Prof. Robertson, Dr. Rossmann, and Mr. Trotter310 H. W. Ehrlich and C . A. Beevers, Acta Cryst., 1956, 9, 602.311 P. J. Wheatley, ibid., 1955, 8, 224.31a F. Bertinotti, G. Giacornello, and A. M. Liquori, ibid., 1696, 9, 610.313 F. H. Herbstein and G. M. J. Schmidt, ibid., 1956, 8, 399, 406610 CRYSTALLOGRAPHY.significantly from mmm symmetry, though this is not a crystallographicrequirement ; L(C-N-C) = 116.6" & 0.6", and the structurally distinctC-C bonds differ in length, in a sense generally in accord with molecular-orbital calculations.Acridine (16) crystakes in a number of polymorphicforms, and that designated I11 has now been analysed in great detail.314Antiparallel pairs of dissymmetric molecules front one another across centresof symmetry ; the polar stresses imposed by this arrangement presumablyaccount for the appreciable and complex molecular distortion from the idealplane. (C-N-C) = 117.2" -j= 0*4", and the bond-lengths are in fair agree-ment with the results of theoretical calculations.Rut, as Phillips pointsout, the observed lengths of corresponding C-C bonds in anthracene, acridine,and phenazine agree amongst themselves strikingly, andthan with the theoretical values.much more closelyAn accurate analysis of 4-nitropyridine 1-oxide has been recently de-scribed; 315 L(C-N-C) = 115.4" -j= 12", and the molecule is strictly co-planar. The molecule of 2 : 2'-dipyridyl is also planar, and has the trans-configuration with respect to the nitrogen though in complexformation it must adopt the cis-form; L(C-N-C) = 116.7". The structureof pteridine (17) has been surveyed by two-dimensional methods,317 and thebond-lengths have been compared with the results of molecular orbitalcalculations.318 The crystal structure, like the molecule, has no centre ofsymmetry, so that refinement proved difficult.The maximum atomic dis-placement from the mean plane was found to be as much as 0.06 A ; butthis is not claimed as significant. The mean of the four L(C-N-C) = 117",compared with 120" for the eight angles at carbon atoms.A fuller account of work on parabanic acid has appeared.319 Difficultiesof refinement limited the accuracy attained with dialuric acid (18) ; 320it is probable that the atoms of the ring are coplanar and that the moleculeadopts the tautomeric form shown, though the hydrogen atoms were notdirectly located. In an analysis of 4 : 5-diamino-2-chloropyrimidine 321314 D. C . Phillips, Acta Cryst., 1956, 9, 237.315 E. L. Eichorn, ibid., 1956, 9, 787.317 T.A. Hamor and J. M. Robertson, J., 1956, 3586.318 T. H. Goodwin and A. L. Porte, J., 1966, 3695.3lS D. R. Davies and J . J . Blum, Acta Cryst., 1956, 8, 129.360 L. E Alexander and D. T. Pitman, ibid., 1956, 9, 501.at1 N. E. White and C . J . B. Clews, ibid., 1956, 9, 586.L. L. Merritt, jun., and E. D. Schroeder, ibid., 1956, 9, 801SPEAKMAN : ORGANIC STRUCTURES. 41 1on the other hand, the positions of the hydrogen atoms unequivocally indi-cate the formula (19). The purine analogue, xanthazole (20), has beenexamined as its d i h ~ d r a t e . ~ ~ ~ The evidence presented makes it probablethat the hydrogen atoms are situated as shown, implying a semi( ?)mesoionicstructure. The paper includes a survey of molecular data for a number ofpurines and pyrimidines.Correlation of the various data leads to the generalisation that thenitrogen valency-angle in a six-membered ring is always less than 120" whenthe ring is of aromatic type (--N=) and nearly always greater when it isnot (-NR-).The former part of this rule was pointed out by Bertinotti,Giacomello, and Liquori,312 in relation to compounds (13)-( 15) and melamine,and attributed to the steric repulsion exerted by the bulkier lone-pair ( ~ $ 2 )orbital on the two more condensed bonding orbitals. The idea323 that abonding orbital may be more restricted in space than was the non-bondedatomic orbital, or than the usual L.C.A.O. calculation implies, is supportedby several lines of evidence (see p. 408). The latter part of the rule is atpresent less well established; if it proves generally true, it may be attribut-able to the fact that, in an unconjugated system, the bonds to >NH willbe considerably shorter than those to >CH2.There is now a more detailed account 324 of work on the mesoioniccation (21).Except for the hydrogen atoms of the methyl groups, themolecule is strictly co-planar ; and the same appears to be true of the relatedsubstance, 5-amin0-2-rnethyltetrazole.~~~ Fuller accounts have been givenof the structures of indigo, thioindigo, and selenoindigo 326 (22 ; X = NH,S, and Se). All three molecules adpot the trans-configuration shown;L (C-X-C) = 1 loo, 92O, and SO", respectively. Similar results have beenreported from U.S.S.R.327 for the first two substances.The eight-memberedring in cydotetramethylenetetranitramine (23) is centrosymmetric andpuckered,328 with L(C-N-C) = 123-124" and L (N-C-N) = 109-1 12".,4 similar eight-membered ring occurs in (CMe2*Si0),,329 in whichL(Si-0-Si) = 142.5". 1 : 4-Dithian wo has a chair-form molecule withd(S-C) = 1.81, d(C-C) = 1-49 A, and L(C-S-C) = 99". A recent accurateanalysis of thianthren confirms the " folding '' of this molecule about theS . . . S-line,=l with L(C-S-C) = 100" 5 1.0" and d(S-C) :-= 1.76 0.01, a.312 W. Nowacki and H. Biirki, Z . Krist., 1955, 106, 339.333 C . E. Mellish and J. W. Linnett, Trans. Faraday SOC., 1954, 50, 667.324 J. H. Bryden, Acta Cryst., 1955, 8, 211.325 Idem, ibid., 1956, 9, 874.326 H. von Eller, Bull. SOC. chim. France, 1955, 1426, 1429, 1433, 1438, 1444.317 Y e .A. Gribova, G. S. Zhdanov, and G. A. Gol'der, Kristallografiya, 1956, 1, 53.328 P. F. Eiland and R. Pepinsky, 2. Krist., 1955, 108, 273.12D H. Steinfink, B. Post, and I. Fankuchen, Acfa Cryst., 1955, 8, 420.3Jo R. E. Marsh, ibid., p. 91.a31 H. Lynton and E. G. Cox, J., 1956, 4886; see also I. Rowe and B. Post, ActaCvyst., 1956, 9, 82741 2 CRYSTALLOGRAPHY.Miscellaneous Compounds.-In the monoclinic form of n-hexatriacontane,C,,H,,, the molecule adopts the form of a regular planar so thatthe mean values of d(C-C) = 1.534 5 0-006 A, and L (C-C-C) = 112"1' & 21', could be assessed with precision. Similar mean values of 1.639 &0.013 and 112-7" -+ 1.0" have been found in ll-aminoundecanoic acidhydrobromide.= Dimethylacetylene possesses a very simple structure thathas been analysed with high accuracy; d(C-C) = 1.457 -J= 0.010,d(C-C) = 1.211 & 0.017 A ; methyl groups of contiguous molecules areseparated by only 3-54 A, so that some " interlocking " of rotating groups ispresumed. The compound, " Rongalite C," made by reducing a mixtureof formaldehyde and sodium hydrogen sulphite, has been shown335 tocontain the anion (24) in which the bonds round the sulphur atom are/O-\O(24) HO*CH,-SMeSOa\,C=C=N-Me (25)PhSOaarranged pyramidally, and the values of d(S-0) = 1.495 & 0.010 A, donot differ appreciably.Di-$-tolyl telluride, selenide, and sulphide formisomorphs, which have been carefully a n a l y ~ e d . ~ ~ ~ The angle at the hetero-atom increases with diminishing atomic number : 101" & 2.7" (Te), 106" &1.9" (Se), and 109" & 1.9" (S) ; and this trend is continued in diphenyl ether(116" & 4°).337 Though diphenyl sulphone and sulphoxide have quitedifferent (though related) unit-cell dimensions, so that strict ismorphism isnot possible, over 90% of the sulphone can be replaced by sulphoxide withoutchange of the lone-pair on the sulphur atom adequately takingthe place of the missing osygen atom.A second vinylideneamine (25) isbeing examined by Wheatley ; 339 it also has a C-C-N-C-chain that is nearlylinear, though in this case L (C-N-C) is significantly less than 180".Unlike that of keten itself, the dimer of dimethylketen has a carbocyclicstructure (26), and this has been confirmed by X-ray diffraction.a0 Themolecular symmetry in the crystal is 21972 and hence the ring is planar,though large out-of-plane vibrations may occur.The structure of cyclo-hexylammonium chloride has been determined with considerable accuracy.a1The ring has the chair-form with d(C-C) averaging 1.55 & 0.02 A, andL(C-C-C) 108" & 2"-a direct confirmation of the Sachse structure in amolecule where the carbon atoms are not overshadowed by heavier sub-stituents. (cycLoHexane itself has a highly disordered crystal structure.a2)In benzene iodochloride, PhIC12,3d3 and its 9-chloro-derivative 344 the332 H. M. M. Shearer and V. Vand, Acta Cryst., 1956, 9, 379.333 G. A. Sim, ibid., 1955, 8, 833.334 E. Pignataro and B.Post, ibid., 1955, 8, 672.338 hl. R. Truter, J.. 1955, 3064.336 \V. R. Blackmore and S. C. Abrahams, Acta Cryst., 1955, 8, 317, 323, 329.337 N. J . Leonard and L. E. Sutton, J. Amer. Chew. SOC., 1948, 70, 1564.338 S. C. Abrahams and J. V. Silverton, Acta Cryst., 1966, 9, 281.33s Personal communication.340 P. H. Friedlander and J . M. Robertson, J., 1956, 3083.341 A. Shimada, Y. Okaya, and M. Nakamura, Acta Cryst., 1955, 8, 819.342 T. Oda, Structure Reports, 1947-48, 11, 611.343 E. M. Archer and T. G. D. Schalkwyk, A d a Cryst., 1953, 6, 88.344 D. A. Rekoe and R. Hulme, Naiure, 1956, 177, 1230SPEAKMAN : ORGANIC STRUCTURES. 413ICl,-group is linear, symmetrical, and nearly perpendicular to the plane ofthe benzene ring; d(1-C1) = 2.45 fi.The chemical properties of di(hydr-oxydury1)methane (27) suggest that there is steric stress at the methylenegroup, and analysis 345 shows that d(Cap-CH2) = 1.60 and L(Ch-C-Car) =119'. The h e r of phenyl isocyanate (28) has been carefully analysed,346 thes;'/ c \'C'Me,C CMeZMe Me Me MeH O ( - J - C H , 0 0 "Me Me Me Me(27)II0 ( 2 8 )phase problem being solved by use of the fact that the dimer is isostructuralwith $-terphenyl. The centrosymmetric molecule has H(C-N) = 1-42,1-49 0.014A and L(N-C-N) = 87", L(C-N-C) = 93" & 1.5" in the four-membered ring, and d(C-0) = 1.15, d(N-Ck) = 1.41 & each somewhat outof the plane of the ring. Unlike some other nitroso-compounds, p-iodo-nitrosobenzene is monomeric, with a planar molecule, which may bestabilised by a polarisation bond, d(I .. . 0) = 3.2 A, between successivehead-to-tail molecules.The very careful analysis of sodium tropolonate has been described inmore detail.s48 The atoms of the anion deviate from planarity only by smalldistances, the greatest of which (0.03 A) is ofdoubtful significance, and can in any case be(&0-013 a) are shown in formula (29) ; they(29) nearly correspond to the anion's having aplane of symmetry, normal to the paper, sothat greater reliance can be placed on the''b 1.379 mean values for pairs of corresponding bonds.The bond between the CO-groups is certainlylonger, and the adjacent C-C bonds are probably longer, than the rest. Allthe hydrogen atoms were located, with d(C-H) = 1-03 (mean).In thetropolonium cation,3qs the C-0 bonds are also equal in length, though longer(1.41 a), whilst in tropolone itself 350 they probably differ (1.26, 1.34 A).Molecular Compounds.-Studies of a number of complexes containingdioxan (D) have been briefly reported by Hassel and his co-workers:D,Br2,351 D,ICl,352 D,HgC12.353 In all there is a close approach between anoxygen atom and a halogen : e.g., d(O . . . Br) = 2.7, d ( 0 . . . I) = 2-6 A.Similar compounds occur with amines-e.g., between hexamethylene-tetramine and Br2,354 with d(N . . . Br) = 2.3 A. These distances are much6-t s-0 \fig 7-+.. %b+ attributed to crystal forces. Bond-lengths20345 B. Chaudhuri and A. Hargreaves, Acta Cryst., 1956, 9, 793.3*0 C.J. Brown, J., 1955, 2931.347 M. S. Webster, J., 1966, 2841.348 Y . Sasada and I. Nitta, Acta Cryst., 1956, 9, 205.*4B Y . Sasada, K. Osaki, and I. Nitta, ibid., 1954, 7, 113.350 M. Kimura and M. Kubo, Bull. Chem. SOC. Japan. 1953, 26, 250.351 0. Hassel and J. Hvoslef, Acta Chem. Scand., 1954, 8, 873.352 Idem, ibid., 1956. 10, 138.353 Idem, ibid., 1954, 8, 1953.354 Idem, ibid., 1056, 10, 1394 1 1 CKYS I’.ILLOCKAPHY.less than the sums of the van der Waals radii, and strong “ polarisationbonds ” are presumably present. [On the other hand, the abnormal inter-molecular contact, d ( N 0 , . . . CH) = 2.6 A, found in fi-nitroaniline hasnow been amended : 355 there is an ambiguity in the structure, and whenthis is correctly resolved, y-co-ordinates of neighbouring molecules becomeinterchanged, with the result that, though intramolecular distances remainas before, all intermolecular contacts are changed, and the anomaly dis-appears.] The lower-melting product of the reaction between 2 : 3-di-chlorodioxan and ethylene glycol was shown by X-ray work not to be theexpected na~hthadioxan.~~~ The higher-melting product did not crystalliseconveniently for X-ray study; but a projection derived from its complexwith HgCl, 357 clearly reveals the presence of a naphthadioxan molecule.Inthe 2 : 1-compound between hexamethylbenzene and c h l ~ r a n i l , ~ ~ ~ pairs ofmolecules of the former sandwich roughly parallel molecules of the latter.Natural Products and Related Compounds.-A review of the X-ray methodfor the direct determination of the structures of moderately complex organiccompounds has appeared,359 and it is illustrated by reference to the analysesof a number of natural products. A full account has now been given of theuse of generalised (“ modulus ”) projections in the analysis of isocrypto-leurine met hiodide .3wThe related structures of morphine (30) 361 and codeine 362 have beenelucidated by studies of their hydrohalide salts.Each consists of two ring-systems (1-11, III-IV) approximately at right angles to one another so as toyield an inverted T-shaped molecule. The stereochemical arrangementsuggested on chemical grounds is confirmed, including the cis-fusion ofrings I1 and 111. A note 363 gives a complete picture of the structure andconformation of the cation in de(oxymethy1ene)lycoctonine hydriodidehydrate.A projection of the quinine molecule can be seen in a preliminaryreport 36* on analyses of the hydrated sulphate and selenate.3 6 5 J. Donohue and K. N. Trueblood, Acta Cvyst., 1956, 9, 960 (see also ibid., p. 966).356 Ann. Reports, 1952, 49, 373.357 0. Hassel and C. Ramming, A d a Chewz. Scand., 1956, 10, 136.358 T. T. Harding and S. C. Wallwork, Acta Cryst., 1955, 8, 787.350 A. McL. Mathieson, Rev. Pure Appl. Chew. (Australia), 1955, 5, 113.360 J. Fridrichsons and A. McL. Mathieson, Actu Cryst., 1955, 8, 760 (see also -4nit.361 M. Mackay and D. C. Hodgkin, J., 1955, 3261.362 J. M. Lindsey and W. H. Barnes, Acta Cryst., 1955, 8, 227.363 M. Przybylska and L. Marion, Canad. J . Chem., 1956, 34, 185.3~ H. Mendel, Proc. k . ned. Akad. Wetenschap., 1055, 58, B, 132.Reports, 1954, 51, 398)Hydroxydihydroeremophilone 365 has the structure represented by (31),which agrees with Simonsen's suggestion and supplies some other stereo-chemical information : there is a cis-fused decalin system; and, since theabsolute configuration of part of the eremophilone molecule has been de-d ~ c e d , ~ ~ ~ the configuration of the whole can now be inferred from formula(31). A more detailed report 367 of the work on (3-caryophyllene chloride isnow available. The structure deduced by chemical methods i s confirmed--in an analysis which is independent of chemical information-whilst thefour-membered ring is shown to be trans-fused to the seven-membered.A number of peptides and amino-acids have been studied, two of themwith high precision, viz., histidine hydrochloride hydrate 368 and glycyl-1,-tryptophan d i h ~ d r a t e . ~ ~ ~ The cation of the former has the tautomericform shown (32 with mesomers) ; d(C-NH,-') = 1.52 0.01 a, and a similarexcess over the standard length (1.47 A) has been noted for this bond ininany other such compounds. There is a preliminary account of a fairlyaccurate analysis of glycyl-L-alanine hydrochloride hydrate.370 The struc-ture of a new (P-)form of L-glutamic acid has been described.371 Thehydrogen atoms were located only with some uncertainty, but their probablepositions agree with other evidence in indicating the zwitterionic structureshown (33). A comparison with glutamine and glutamic acid hydro-chloride shows differences of conformation in these three closely relatedI ~ C - C H I CHI N HT 1. CO; HO,C-CH~.CH,.CH(NH~~ )-co~'+HC=NH( 3 2 ) HN-CH ( 3 3 )molecules, presumably attributable to differing crystalline environments.There is a progress report 372 on the analysis of the tripeptide, glutathione;the two peptide groups are nearly planar, as usual, and mutually at right-angles. Work on methylguanidinium nitrate 373 and nitroguanidine 374 maybe mentioned here; both structures are essentially coplanar, and the latterpossibly includes a bifurcated hydrogen bond.The X-ray analysis of vitamin B,, and related substances 375 is nownearing a phase of completion. According to a report issued in July, 1956,376the molecular formula is almost certainly C63H,,0,4N,,PCo, and the posi-tions found for these atoms are probably essentially correct [Fig. 21. Somewater molecules, which occupy spaces within the structure in both wet andair-dried crystals, are yet to be located. " The molecule that appears is365 D. F. Grant and D. Rogers, Chem. and Ind., 1956, 578.366 W. Klyne, J., 1953, 3072.367 J. M. Robertson and G. Todd, J . , 1055, 1254.368 J. Donohue, L. R. Lavine, and J. S. Rollett, .-lciu Cr?ist., 1956, 9, 655.369 H. A. Pasternak, ibid., 1956, 9, 341.370 T. C. Tranter, Nature, 1956, 177, 37.371 S. Hirokawa, Acta Cryst., 1955, 8, 637.374 W. B. Wright, Chem. and Ind., 1956, 437.373 R. M. Curtis and R. A. Pasternak. Acta Cryst., 1955, 8, 675.374 J. H. Bryden, L. A. Burkhardt, E. W. Hughes, and J. Donohue, ibid.. 1956,9, 573.3 7 5 Ann. Reports, 1954, 51, 399; 1956, 52, 403.y7(r D. C . Hodgkin, J. Kamper, M. Mackay, J. Pickworth, K . N. Trueblood, and5. CT. White, Nature, 1956, 178, 64416 CRYSTALLOGRAPHY.beautifully composed, not far from spherical in form, with all the morechemically reactive groups on its surface. . . ; . . . the atomic positions foundconform in a most convincing way with the stereochemical rules established.! A(Reproduced, with permission, from D. C . Hodgkin et al., Nature, 1956, 178, 65.)by the study of simpler molecules.” There are probably six double bondsin the pseudo-porphin nucleus, and it seems possible that the interventionof the cobalt atom enables them to constitute a resonating system (34, etc.).This ring system is nearly planar, but not quite; and the deviation is perSPEAKMAN ORGANIC STRUCTURES. 417haps due to overcrowding caused by the benziminazole residue co-ordinatedto the cobalt atom on the underside.This work represents the summit of achievement in X-ray analysis sofar. It is understood that a full account is being prepared and that it endswith the sentence : “ And this is not the limit.”J. C . S .S. C . ABRAHAMS.H. D. MEGAW.J. C . SPEAKMAN.REP.-VOL. LIII