ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.THIS Report marks a transition stage. Reports for recent years aimedat a comprehensive stock-taking of work carried out over a period of yearsin selected topics. In future Reports, the aim will be to give a generalperspective of the main developments during the year reviewed. The paperscited have been selected so as to give preference to those likely to interestchemists outside the immediate circle of specialists. Since the generalplan is to give an account of trends in the various branches of Chemistry,the treatment of individual topics is more by reference and much less self-contained than hitherto. Topics under active controversy have beenincluded.As in other transition states, a certain time-indeterminacy is inevitablein the present Report.The range of publication dates covered is furtherwidened by the fact that publications made during the war in manyEuropean countries have in some cases only recently become available toBritish readers. Sections 11 and 12, on the subjects of which there hasbeen much recent discussion and some controversy, are more self-containedand are dealt with separately. The remainder of the Report includestopics from publications which in the main have been abstracted betweenAug. 1948 and July 1949, inclusive, though it is not wholly restricted tothis field. A. R. U.1. GENERAL THERMODYNAWCS AND THE EVALUATION OFTHERMODYNAMICAL FUNCTIONS FOR GASES.1. A number of theoretical papers have been published which refer tothe general thermodynamics of irreversible processes. Irreversible ‘‘ entropyproduction ” in processes such as viscous flow and thermoelectric effectsare discussed by various authors.1 One main stimulus to theories of irrever-sible processes arises from the success of the thermal-diffusion method ofseparation of isotopes.K. Schafer suggests that in the separation of gasmixtures by thermal diffusion the entropy and heat conductivity of thecomponents rather than their molecular weights are of controlling importance.Some experimental evidence is described for nitrogen-hydrogen mixturesR. C. Tolman and P. C. Fine, Rev. Mod. P h y s h , 1948, $30, 51; I. Prigogine,‘‘ gtude thermodynamique des Phhomknes irreversibles,” Dunod, Paris, 19478 GENERAL AND PHYSICAL CHEMISTRY.containing dinitrogen tetroxide.2 Other work on thermal diffusion includesgeneral theoretical calculations,3 and measurements of the Soret effect inaqueous solutions of sucrose.* The rate of entropy increase in anelasticprocesses has been discussed by C.Eckart.5 Experiments on " steady-state " irreversible processes include reports on the separation of com-ponents by thermo-osmosis of liquids through porous materials and ofgases through a membrane. Thermo-molecular pressure differences havebeen measured in hydrogen, deuterium, helium, and neon at pressuresranging from 0.01 to 0.09 em. and temperature gradients from 390" to roomtemperatures.* Thermal-diffusion potentials have been studied in cellswith silver/silver halide electrodes, and various electrolytes in which atemperature gradient was maintained.g The biological implications ofirreversible processes have been discussed.l*2.A second main stimulus in the study of the general thermodynamicsof irreversible processes arises from the remarkable thermo-mechanicalproperties of liquid helium below the ?,-point .I1 Papers include a deductionof London's relation for the " fountain " effect,12 experiments on thedifferences in behaviour between 3He and 4He atoms in the liquid,13 andobservations and calculations on " second sound " in liquid helium inrelation to the high thermal conductivity of He 11.14 A high absorptioncoefficient has been observed in liquid He, near the h-point, with ultrasonicvibrations. l53.Finally, the bold suggestion of utilising the heat gradient from thesurface to the interior of the earth as a source of power by means of thermo-artesian wells l6 may be noted.4. In the systematic evaluation of thermodynamic functions for im-portant chemical species by calorimetric and spectroscopic means new data2 K. Schafer, Angew. Chem., 1947, 59, A , 83.I. Prigogine, Physica, 1947, 13, 319. 6 . R. de Groot, J . Phys. Radium, 1947, 8,129, 188.4 J. van Dranen and F. Bergsma, Physica, 1947,13, 558.6 C. Eckart, Physical Rev., 1948, 73, 373.6 H. P. Hutchinson, I. S. Nixon, and EL. G. Denbigh, Paraday SOC. Discussions, 1948,7 K. G. Denbigh, Nature, 1949, 163, 60.8 A. van Itterbeck and E. de Grande, Physica, 1947, 13, 422.* H.J. V. Tyrrell and G. L. Hollis, Trans. Paraday SOC., 1949, 45, 41 I .10 I. Prigogine and J. M. Wiame, Experientia, 1946,11, 11.11 Cf. Repts. Progr. Physics, 1949, 12, 280.12 S. R. de Groot, Physica, 1947, 13, 555.l3 H. A. Fairbank, C. T. Lane, L. T. Aldrich, and A. 0. Nier, Physical Rev., 1948,73, 256, 729; J. G. Daunt, R. E. Probst, and H. L. Johnston, ibid., p. 638.l 4 V. Peshkov, J . Phys. U.S.S.R., 1946, 10, 389; W. Band and L. Meyer, PhysicalRev., 1948, 73, 226 (cf. The statistical mechanical calculations of W. Band, J . Chem.Physics, 1948, l$, 343); D. V. Gogate and P. D. Pathak, Proc. Physical Xoc., 1947,59, 457; L. Tisza, Physical Rev., 1947, 72, 838; R. B. Dingle, Proc. Physical Soc.,1949, 62, 154; H. S. Green, Nature, 1948, 161, 391.3, 86-16 J. R.Pellam and C. F. Squire, Physical Rev., 1947, 72, 1245.G. Claude and A. G. Claude, Compt. r e d . , 1949, 228, 544UBBELOHDE : ISOTOPE CHEMISTRY. 9include those for carbonyl chloride,17 ethyl chloride,ls hexaflu~roethane,~~vinyl chloride, bromide, and iodide,20 buta-1 : 2-diene,21 and benzene.22The potential barriers hindering internal rotation about the single C-Cbond is computed to be 4-7 kcals./mole for ethyl chloride, 4.35 kcals./mole €orhexafluoroethane, and 1-6,&0.4 kcals./mole for the methyl group in buta-1 : 2-diene. In solid carbonyl chloride there is evidence of random orient-ation of the molecules at low temperatures, and of “ premelting.” Furthercalculations on the thermodynamics of the internal rotator have beenp~blished.,~ (For other aspects of potential barriers hindering rotation,cf.section 3, 11 .)5. Calculations of equilibria in terms of the thermodynamic functionsand fundamental constants have been published for various systems,including saturated hydrocarbons,24 processes related to butadiene synthesis,25and the system Br, + C1, 2BrC1.26 General methods for the computa-tion of complex equilibria in gaseous systems have been proposed.27Miscellaneous thermodynamical studies of general interest includework on the “ supercritical ” state of liquids, with special reference to theirsolvent power.28 Much of this work has been stimulated by the attemptto grow large crystals of optically pure quartz,29 and by problems 30 in thehydrothermal production of minerals.Equations of state for gases and solids a t pressures up to lo5 atmospheresand at temperatures up to lo* degrees have been studied in connection withdetonation phenomena in explo~ives.~~ A.R. U.2. ISOTOPE CHEMISTRY.1. A large range of stable and radioactive isotopes is potentiallyavailable.32 It is not yet fully clear how far radio-tracer chemistry canl7 W. F. Giauque and W. M. Jones, J. Amer. Chem. Soc., 1948,70, 120.l6 J. Gordon and W. F. Giauque, ibid., p. 1506.l9 E. L. Pace and J. G. Aston, ibid., p. 566.21 J. G. Aston and G. J. Szasz, J. Amer. Chem. SOC., 1947, 69, 3108.22 G. D. Oliver, M. Eaton, and H. M. Huffin, ibid., 1948, 70, 1502.23 J. C. Halford, J. Chem. Physics, 1948, 16, 560.24 33.Zeiss, Oel u. Kohle, 1944, 40, 242.25 F. G. Brickwedde, M. Moskow, and J. G. Sston, J , Res. Nut. Bur. Stand., 1946,26 K. Butkow, Rec. Truv. chim., 1948, 67, 551.27 F. J. Krieger and W. B. White, J. Chern. Physics, 1948, 16, 358.2o R. E. Richards, J., 1948, 1931.37, 263.G. A. M. Diepen, Chem. WeekbZud, 1948, 44, 137; Klinkenberg, ibid., p. 138;W. Tomassi, Roczn. Chem., 1948, 22, 191.29 A. C. Swinnerton, G. E. Owen, and J. F. Corwin, Furuduy SOC. Discumions, 1949,5, 172; G. van Praagh, ibid., p. 338; L. A. Thomas, Nora Wooster, and W. A.Wooster, ibid., p. 341.30 Jean Wyart, ibid., p. 323; R. M. Barrer, ibid., p. 326.31 J. L. Copp and A. R. Ubbelohde, Trans. Furuduy Soc., 1948, 44, 1 ; P. Caldirola,J. Chem. Physics, 1946, 14, 738; S.Paterson, ibid., 1948, 16, 159.32 “ Radioactive and stable isotopes,” Isotope Information Office, Harwell, Didcot,Berks; Proc. Conf. Nuclear Chem., May, 1947, Chem. Inst. Canada; F. A. Paneth,Quart. Reviews, 1948, 2, 9310 GENERAL AND PHYSICAL CHEMfSTICY.be used in any laboratory with good general equipment, and how far thespecial safety precautions required or the short life of suitable tracersrestricts the use of certain radio-isotopes to laboratories with very specialfacilities. The chemical effects accompanying nuclear transformationshave been reviewed recently.33 Discussions have also been published ofpossible applications of stable and radio-isotopes to chemical problems.34Experimental data on a few of the more versatile radio-isotopes includethe following which have a bearing on possible applications in physicaland general chemistry :The half life of tritium, 3H, has been estimated to lie between 10.7 and12.7 years.35 Its use for evaluating (low) solubilities of water in organicsolvents has been discussed.36The half lifeof 1% has been estimated by various authors to lie in the range 5100-7200 years ; 37 its nuclear spin appears to be zero.38 Various biochemicaland chemical problems the study of which is made possible by use of thisradio-isotope have been reviewed.39 Methods of preparing barium carbonatewith high specific activity have been de~cribed.~* An interesting differencein radioactivity has been claimed between methane from sewage gas, whichgives 10.5 disintegrations/min./gC., and methane from petroleum deposits,which is inactive.41 The geochemistry of the non-radioactive isotope 13Chas also been discussed.42 Experiments on the formation of llC continueto be reported.43Much work continues on the radio-isotopes of carbon.The diffusion of 24Na into glass has been investigated.4435S has been used in the measurement of transfer constants45 and theincorporation of radio-sulphur in benzylpenicillin has been de~cribed.~~33 Ann.Reports, 1948, 45, 1 ; cf. Symposium on Radiation Chemistry, J . Phys.Colloid Chem., 1948, 52, 437.34 J. W. T. Spinks, Proc. Conf. Nuclear Chem. May, 1947, Chem. Inst. Canada, p. 134(radio-isotopes); M. Lounsbury, ibid., p. 153 (stable isotopes); 0. Holm, Angew.Chem., 1947, 59, A, 2; 0.Erbacher, ibid., p. 6.36 M. Goldblatt, E. S. Robinson, and R. W. Spence, Physical Rev., 1947, 72, 973.A. Novick, ibid., p. 972.36 G. G. Joris and H. S. Taylor, J . Chem. Physics, 1948, 16, 45.87 L. D. Norris and M. G. Inghram, Physical Rev., 1948, 73, 351 ; R. C. Hawkings,R. F. Hunter, W. B. Mann, and W. R. Stevens, ibid., p. 696; L. Yaffe and J. M.Grunlund, ibid., p. 696.38 F. A. Jenkins, ibid., p. 639.3B W. W. Miller and T. D. Price, Nucleonics, 1947, 1, 11 ; 0. Beeck, J. W. Otvos,D. P. Stevenson, and C. D. Wagner, J . Chem. Physics, 1948,16, 255.40 L. D. Norris and A. H. Snell, Physical Rev., 1948, 73, 254.41 E. C. Anderson, W. F. Libby, S. Weinhouse, A. F. Reid, A. D. Kirshenbaum, I4a G. E. Hutchinson, Amer. J . Sci., 1949, 247, 27.43 E.M. McMillan and H. F. York, Physical Rev., 1948, 73, 262; W. Heckro44 J. R. Johnson, J . Appl. Physics, 1949,20, 129.46 C. Walling, J . Amer. Chem. SOC., 1948, 70, 2361.I* Y. Sato, G. I'. Barry, and L. C. Craig, J . Biol. Chem., 1948,174, 217.A. V. Grosse, ibid., 1947, 72, 931.and P. Wolff, ibid., pp. 264, 265; E. M. McMillan and R. D. Miller, ibid., p. 80.tUBBELOHDE : ISOTOPE CHEMISTRY. 11The use of radioactive phosphorus in biochemical research introduces someunexpected diffi~ulties.~'Radioactive argon 4* and arsine 49 have been used in adsorption measure-ments.Measurements of self-diffusion in solids were amongst the first applicationsof tracer technique, but the solid isotopes of natural radio-elements wereonly of comparatively restricted interest. Self-diffusion measurementswith isotopes newly available promise to be of major importance in metal-lurgical research.Experiments with radio-isotopes of transition metalshave shown an unexpected result with 01- and y-iron. Self-diffusion ina-iron which is stable below 910" is 100 times as fast as in the y-metal whichis stable above the transition point, when both are extrapolated to 910".The diffusion coefficients are Da.Fe = 34,000 exp (-77,20O/RT) and D,+ =0.00104 exp ( -48,000/RT).51 Exchange reactions between complex ionsof Fe have been investigated using 59Fe and 56Fe.52 The exchange betweenradio-active Mn" in solution and manganese dioxide has been studied.53Radio-copper has been used in studying various exchange processes 54between copper or copper amalgam and cupric ions in solution.Theapplication of radio-tracers to friction studies has been discussed. Radio-bromine and radio-iodine have been used in measuring the velocitycoefficients of exchange reactions.55 Ethyl iodide has been used tocompare weak neutron fluxes by an estimation of the radioactive iodineproduced. 562. A number of fundamental investigations have been made with stableisotopes on the influence of mass on physical properties, especially thoseinvolving kinetic and thermodynamic differences. Some general aspectsof the differences which arise in physico-chemical properties with isotopeshave been re~iewed.~'In the gaseous and liquid states, tests on differences between the knownproperties of hydrogen compounds and deuterium compounds includemeasurements of the activity of dissolved cadmium iodide 58 in dideuteriumoxide, the kinetics of the thermal decomposition of deuterium iodide andmeasurements of the equilibrium 2DI =+ I, + D2,59 and the associationSelf-diffusion in gaseous argon has also been studied.5047 W.D. E. Thomas and D. J. D. Nicholas, Nature, 1949, 163, 719.** B. P. Burtt and J. D. Kurbatov, J . Amer. Chem. Xoc., 1948, 70, 2278.4e J. W. Hickey and E. 0. Wiig, ibid., p. 1574.61 G. E. Birchenall and R. F. Mehl, J . AppE. Physics, 1948, 19, 217.64 R. C . Thompson, J . Amer. Chem. Soc., 1948, 70, 1045.6s B. Pullman and M. Haissinsky, J . P h p . Radium, 1947, 8, 36.64 M. Quintin, P. Sue, and M. Bizouard, Compt.rend., 1948, 226, 1723; G. ICayas,65 C. C. Evans and S. Sugden, J., 1949, 270.66 P. I?. D. Shaw and C. H. Collie, ibid., p. 1217.67 H. Urey, J., 1947, 562; J. Mattauch, Angew. Chem., 1947, 59, A, 37; K.6a E. C. Noonan, J . Amer. Chem. Soc., 1949,71, 102.T. Hutchinson, PhysicaE Rev., 1947, 72, 1256.ibid., p, 2144.Schaefer, &bid., p. 42.N. F. H. Bright and R. P. Hagerty, Tram. Paraday Xoc., 1947, 43, 69712 GENERAL AND PHYSICAL CHEMISTRY.of liquid deuterium fluoride. 6o Thermodynamic properties of methylalcohol have been compared with those of methyl deuteroalcohol.61 Thesmaller molecular volume and smaller intermolecular forces of dideuteriumoxide compared with water have been investigated.62 Differences betweenthe lattice parameters in uranium trihydride, a = 6.6310 & 0.0008 A., andin uranium trideuteride, a = 6.620 If.0.002 A.63, confirm the observationswith other solid hydrides and d e ~ t e r i d e s . ~ ~In the crystalline state, isotope effects for a number of acid salts, suchas ammonium dihydrogen phosphate 65 and potassium dihydrogen arsenate,66have been measured. Transitions in the solid state below the melting pointhave been reported for deuterium chloride, bromide, and iodide. The chloridediffers in behaviour from the other two, showing only one transition whereasdeuterium bromide and iodide have twos6' A. R. U.3. BOND STRUCTURE AND BOND PROPERTIES.A large range of physical properties of molecules continues to be studiedwith the general aim of increasing the body of quantitative informationabout chemical binding.1.Amongst bond problems which continue to attract much researchmay be noted the structure of the association bonds in HF, (FHF)', and inthe corresponding deuterium compounds. The potential energy of (HF)zhas been calculated for various molecular configurations. 68 Experimentsinclude measurements of the vapour pressures of liquid hydrogen fluoride,69the dielectric polarisation of the vapo~r,~O and the Raman spectra ofpotassium hydrogen difl~oride,~l and studies on the complex salts CsF,(HF),where thermal analysis indicates the values n = 1, 2, 4, and 6.7z2. Experiments and theoretical studies on the hydrides of boron continueto be published.733. Evidence has been adduced that the tendency of boron to act asacceptor in co-ordination compounds in the series boron trifluoride, tri-6o J.H. Hildebrand and A. Gee, J. Amer. Chem. Soc., 1948,70,427.62 K. Wirtz, Angew. Chem., 1947,59, A , 138.63 R. E. Rundle, J. Amer. Chem. SOC., 1947, 69, 1719.6d A. R. Ubbelohde, PTOC. Roy. SOC., 1937, A , 159, 306.65 A. R. Ubbelohde and I. Woodward, Proc. Roy. Soc., 1942, A , 179, 399,66 D. H. W. Diekson and A. R. Ubbelohde, Actq Cryst., 1950, 3, 6.6 7 K. Clusius and G. Wolf, 2. Naturforsch., 1947, 2a, 495.68 G. E. Evans and G. Glockler, J. Chem. Physics, 1948, 16, 324.70 R. A. Oriani and C. P. Smyth, J. Amer. Chem. SOC., 1948, '70, 125.71 L. Couture and J. P. Mathieu, Compt. rend., 1949, 228, 555.72 R. V. Winsor and G. H. Cady, J.Amer. Chem. SOC., 1948, 70, 1500.L. A. K. Staveley and A. K. Gupta, Trans. Paraday Soc., 1949,45,50.Cf. S. R. de Groot andM. M. Biedermann, Physica, 1941,8, 905.See ref. 60.G. Silbiger and S. H. Bauer, ibid., p. 115; J. S. Kasper, C. M. Lucht, and D.Harker, ibid., p. 881; R. E. Rundle, ibid., 1947, 69, 2075; J. Goubeau, Angew.Chenz., 1945, 60, A , 78; cf. R. I?. Bell and H. J. Emelhius, Quart. Reviews, 1948, 2, 132.Cf. ref. 133UtBBELOHDE : BOND STRUCTURE AND BOND PROPERTIES. 13chloride, tribromide, and tri-iodide increases with increasing electro-negativity of the halogen atom, which accompanies increased electrophilicproperties of the boron atom.?* The structure and thermodynamic pro-perties of the co-ordination compound NH3,BF3 have been further in-vestigated, 75 and it has been estimated from Raman-spectrum frequenciesthat the co-ordination of nitrogen to aluminium in NH,,AlCl, lowers theN-H binding energy in this compound by 25%.764.Data on the co-ordination of iodine with molecules of various solventswith donor properties have been reviewed.77 The iodine in the brownsolutions appears to be much more reactive than that in the violet solutions.Absorption spectra 78 suggest the complex C6H6,12 in benzene solutions,which is thought to be analogous with the ion 13'.The results of spectrophotometric investigation of the interaction betweenthe ions Sb+++ and Sbffff* in solution in concentrated hydrochloric acidconcur with the evidence from the crystal Rb2SbC1, in indicating some formof bonding between the ion pair (111) and (V), which is associated withintense colour.795. In spectroscopic methods, the development of techniques 80-83for measurements on absorption spectra in the '' micro-wave " region(centimetre waves) has yielded important information on pure rotationalspectra. Molecules for which data of high precision on rotationaf-energylevels have been obtained include NH3,s** 82y 84* 85 N,0,86* 87 H20,88 ICl,s9,OCS,91 BrCN and ICN,s7~ 92 CH31,92 and CH,:CF2.93The hyperfine splitting of the energy levels of a polar diatomic molecule74 D. R. Martin, Chena. Reviews, 1948, 42, 581.7 5 A. W. Laubengayer and G. F. Cordike, J . Amer. Chem. SOC., 1948,70, 2274.76 J. Goubeau and H. Siebert, 2. anorg. Chem., 1947, 254, 126.77 J.Kleinberg and A. W. Davidson, Chem. Reviews, 1948, 42, 601 ; F. Fairbrother,7 8 K. A. Benest and J. H. Hildebrand, J . Amer. Chem. Soc., 1948,70, 2832.79 J. Whitney and N. Davidson, ibid., 1947, 69, 2076.$0 C. K. Jen, PhysicaE Rev., 1947, 72, 986.81 R. H. Hughes and E. B. Wilson, ibid., 1947, 71, 562; R. J. Watts and D.82 H. H. Nielson and D. M. Dennison, ibid., 1947, 72, 1101.S4 J. W. Simmons and W. Gordy, Physical Rev., 1948, 73, 713; D. Williams, ibid.,85 R. L. Carter and W. B. Smith, ibid., p. 1053; T. A. Pond and W. F. Cannon,8 6 D. K. Coles, E. S. Elyash, and J. G. Gorman, ibid., 1947, 72, 973.a 7 A. G. Smith, H. Ring, W. V. Smith, and W. Gordy, ibid., 1948, '43, 259, 633.S. Golden, T. Wentink, R. Hillger, and M. W.P. Strandberg, ibid., p. 92.89 R. T. Weidner, ibid., 1947, 72, 1268; 1948, 73, 254; C. H. Tomes, F. R.J . , 1948, 1051.Williams, ibid., 1948, 72, 980.W. D. Hershberger, J . Appl. Physics, 1948, 19, 411.1947, 72, 974.ibid., 1947, 72, 1121.R. S. Henderson, ibid., 1948, 73, 107.Merritt, and B. D. Wright, ibid., 1948, 73, 1334.J. Bardeen and C. H. Tomes, ibid., p. 627.91 A. Roberts, ibid., p. 1405.O2 0. R. Gilliam, H. D, Edwards, and W. Gordy, ibid., p. 635.93 A. Roberts and W. F. Edgell, J . Chem. Physics, 1949, 17, 74214 GENERAL AND PHYSICAL CHEMISTRY,in an electric field (the Stark effect) can give important information on theinteraction between nuclear spins and nuclear quadrupole moments, andthe rotational-energy le~els.80-~4* 86-94 An illustration of particular interestto chemists arises in the micro-wave spectra of methyl cyanide and iso-cyanide 95 in which the hyperfine structure of the rotational-energy levelsshows that the nuclear interaction effects are considerably larger in thecyanide.A further interesting feature is that the energy absorption bya gas in the neighbourhood of a resonance line in the micro-wave regionshifts the population of energy states in the gas from that at thermalequilibrium to a distribution where marked saturation effects have beenobserved, 8 5 9 966. Advances in the interpretation of Raman and ultra-violet absorptionspectra have made possible the study of increasingly complex problems ofmolecular constitution. A general review includes the interpretation ofstructures such as borine and he~amethyldialuminium,~~ the height of thebarrier opposing cis-trans-isomerisation in eth~lene,~s the effect of resonatingdouble bonds on electronic levels in polyatomic molecules,99 the ionisationpotential of chromophores as affected by substituents,lW the role of hyper-conjugation in near ultra-violet spectra,lOl electronic transitions in simpleunsaturated hydrocarbons,102 and steric hindrance to the planarity of dyemolecules and in cis-decalin .lo3 The ul t ra-viole t spectra of nitro- su bs titu tedorganic molecules lo4 and of anthracene compo~nds,1~~ and the ultra-violetand vacuum ultra-violet spectra of a wide variety of other organic sub-stances lo6 and of hydrogen-bridged alcohols and amides in solution havebeen systematically studied.7.Theoretical €ormuh for the absorption spectra of cyanine dyes andcarotenoids, based on simple electron models, give good agreement withexperimental values. 108 The metallic model for conjugated polyenes hasO4 W. A. Nierenberg, I. I. Rabi, and M. Slonick, Physical Rev., 1948, 73, 1430;J. Bardeen and C. H. Tomes, ibid., p. 97.H. Ring, H. Edwards, M. KessIer, and W. Gordy, ibid., 1947, 72, 1262.96 P. I. Richards and H. S. Snyder, ibid., 1948, 73, 269, 1178; R. Karplus and J.O 7 R. S. Mulliken, Ch,em. Reviews, 1947, 41, 207.O8 R. S. Mulliken and C. C. J. Rothaan, ibid., p. 219.Oe K. F. Herzfeld, ibid., p. 233.Io2 E. M. Carr, ibid., p. 293.loS L. G. Brooker, F. L. White, R. H. Sprague, S.G. Dent, and G. van Zandt, ibid.,lo* W. H. Rodebush, Chem. Reviews, 1947, 41, 317.lo6 R. N. Jones, ibid., p. 353.lo* L. W. Morrison, Id. Chem., 1947, 23, 817; L. N. Ferguson, Chem. Reviews,1948, 43, 385; E. R. Blount, M. Fields, and R. Karplus, J . Amer. Chem. Soc., 70, 194;E. R. Blount and M. Fields, ibid., p. 189 ; J. R. Platt, H. B. Klevens, and W. C. Price,J. Chem. Physics, 1949, 17, 466; C. H. Miller and H. W. Thompson, ibid., p. 845;Ta-Kong Liu and A. B. F. Duncan, ibid., p. 241.Sehwinger, ibid., p. 1020; R. Karplus, ibid., pp. 1027, 1120.loo W. C. Prince, ibid., p. 257.F. A. Matsen, W. W. Robertson, and R. L. Chuoke, ibid., p. 273.p. 325; D. H. R. Barton, J., 1948, 340.lo' G. A. Hanslow, Hsi-Teh-Hsieh, and R. C. Shea, ibid., p.426.lo8 H. Kuhn, Helv. Chim. Acta, 1948, 31, 1441; W. Kuhn, ibid., p. 1780UBBELOHDE : BOND STRUCTURE AND BOND PROPERTIES. 15also been discussed by N. S. Bayli~s.1~~ Regularities in the fluorescencespectra of a wide range of polycyclic aromatic hydrocarbons in solutionhave been described.l1°8. Much progress continues to be made in purely mathematical calcul-ations of bond structures, particularly of aromatic molecules.ll1 Thisbranch of mathematical chemistry is rapidly attaining major importance.Studies include the construction of molecular diagrams of bond length andbond character in systems such asII IIand a wide range of nitrogenous heterocyclic c0mpounds.~13 Calculationsof the electronic structure and dipole moments of pyridine 114 and electronicdiagrams for a range of conjugated nitrogenous compounds 115 have alsobeen published.A theoretical study of the oxidation-reduction potentialsof quinones has correlated these with the resonance of the x electrons.1lsThe electron distribution has been calculated in relation to the acidic andbasic strengths of indole, pyrrole, carbazole, aniline, diphenylamine, andtriphenylamine.ll7 Computations have been made on the excited electroniclevels in naphthalene, anthracene, and homologues,lls on the electronicstructure and bond lengths of coronene and pyrene,llg and on the electronicstructure of some aza-naphthalenes, -anthracenes, and -phenanthrenes.120Calculation has been made of charge diagrams for styrolene and o-, m-, andp-divinylbenzene.121 Charge distributions and bond orders have beencomputed for 4-aminostilbene and related molecules,122 and a correlation hasbeen attempted of calculated electronic structure with carcinogenic activityof the former.123 A moleoular-orbital treatment of the ultra-violet spectra ofbenzene and borazole has been p~b1ished.l~~ The electronic structure ofthiophen compounds has been compared with that of the benzene ana10gues.l~~On the basis of theoretical calculations it is claimed that several non-lo9 N.S. Bayliss, J . Chem. Physics, 1948, 16, 287.ll1 C. A. Coulson, Quart. Reviews, 1947, 1, 144.lla 0. Chalvet, L. Henriet, and E. Lesein, Compt. rend., 1947, 225, 1010.1lS M. Martin, ibid., 1948, 227, 1237.116 M. G. Evans, J. Gergely, and J.de Heer, Trans. Paraday Soc., 1949,45, 312;11' G. Berthier and B. Pullman, Compt. rend., 1945,228, 1725.11* C. A. Coulson and H. C. Longuet-Higgins, Proc. Physical SOC., 1948, 60, A , 78.lx9 W. E. Moffitt and C. A. Coulson, ibid., p. 309.120 H. C. Longuet-Higgins and C. A. Coulson, J., 1949, 971.lz1 G. Berthier and B. Pullman, Compt. rend., 1948,226, 488.lZ2 C. A. Coulson and I. Jacobs, J., 1949, 1983.123 A. Pullman, Compt. rend., 1948, 226, 486.ls4 C. C. J. Rothaan and R. S . Mulliken, J . Chem. Phy&cs, 1948,16, 118.R. Schoental and E. J. Y. Scott, J., 1949, 1683.11* J. Ploquin, ibid., 1948, 226, 245.0. Chalvet and C. Sandorfy, ibid., 1949, 228, 566.cf. M. Diatkina and J. Syrkin, Acta Physicochim. U.S.S.R., 1946, 21, 921.33, C, Longuet-Higgins, Trans.Faraday SOC., 1949, 45, 17316 GENERAL AND PHYSICAL CHEMISTRY.benzenoid aromatic hydrocarbons so far unknown should be reasonablystable once they were formed.126 An empirical equation and theoreticalcalculations have been proposed for the resonance energy of polycyclicaromatic hydrocarbons.12'9. Experimental studies on the general electronic and structural pro-perties of aromatic compounds include a variety of other techniques inaddition to those listed ab0ve.~~-l0* Bond-length variations in aromaticsystems have been reviewed; 128 the C-H bond energy in toluene and thexylenes has been estimated.lZ9 Permanent dipole moments in benzene ordioxan solutions have been reported for fused aromatic hydrocarbons suchas acenaphthene (1.6 D.) and perylene (1.9-2 D .) ; anthracene and naph-thacene have zero dipole m0rnent~s.1~0 Co-ordination in solution has beenpostulated between iodine and benzene 78 and in the coloured complexwF6*C6H6.131 Deviations from coplanarity in halogen-substituted benzeneshas been claimed, on the basis of electron diffraction experiments, for themolecules o-dichloro-, o-dibromo-, 1 : 2 : 3 : 5-tetrabromo-, hexachloro-, andhexabromo-ben~ene.~~~ The basic strengths of 14 mononitronaphthyl-amines have been measured in aqueous solution ; 3-nitro-2-naphthylamineis 10,000 times stronger than 1-nitro-2-naphthylamine, providing further /yy evidence for the substantial contribution of the Erlenmeyer formula 1\A/in the s t r ~ c t u r e . 1 ~ ~ Experimental and theoretical studies of the Mills-Nixon effect have been reviewed.134The preparation and properties of BBB-trimethylborazole have beendescribed.135 Although this compound has certain similarities withmesitylene it breaks up more easily. The reactionsCH3 of NNN- trimethylborazole indicate that the B-HB link is less stable to hydrolysis than B-Me./ \ Cryoscopic determinations of the molecular weightof free phthalocyanine and of the copper, lithium, HT SJHB-cH3 and silver derivatives in concentrated sulphuricacid give values which are in agreement with thoseH r expected for fully ionised single molecules.Theebullioscopic molecular weight of lithium phthalo -cyanine in ethyl alcohol indicates the presence of the m0n0rner.l~~126 R.D. Brovn, Trans. Faraday Xoc., p. 296; D.P. Craigand A,Maccoll, J., 1949,964.137 P. G. Carter, Trans. Faraday SOC., 1949, 45, 597.126 J. M. Robertson, Act& Cry&, 1948, 1, 101.12* M. Swarc, J . Chem. Physics, 1948, 16, 128.130 H. Lumbroso, Compt. rend., 1947, 225, 1003.131 H. F. Priest and W. C. Schumb, J . Arner. Chem. floe., 1945, '40, 2291.132 0. Bastiansen and 0. Hassel, Acta Chem. Scand., 1947, 1, 489.133 A. Bryson, Trans. Faraday Soc., 1949, 45, 257.134 H. D. Springall, G. C. Hampson, C. G. May, and H. Spedding, J., 1949, 1524.136 E. Wiberg, K. Hertwig, and A. Bolz, 2. anwg. Chem., 1948, 256, 177.136 M. V. Sirur, M. S. Muthanna, S. K, Bhattacharyya, and (Sir) J. C. Ghosh, Proc.cH3-B\ /Nat. Inst. Sci. India, 1947, 13, 141UBBELOHDE : BOND STRUCTURE AND BOND PROPERTIES.17Semi-conductor properties of phthalocyanines have been detected bymeasurements of the conductivity a t various t e r n p e r a t ~ r e s . ~ ~ ~Calculations of the molecular packing and heat of sublimation of aromatichydrocarbons 13* and measurements of the heat capacity, heat of fusion,and entropy of benzene 139 indicate normal intermolecular forces and normalthermodynamic behaviour of solid benzene.Various studies on cyclooctatetraene show that this molecule has lessresonance stability than would correspond with an aromatic resonance“pool ” of e1e~trons.l~~ Its heat of isomerisation to liquid styrene is-34-3, -+ 0-34 kcals./mole at 25”.10. The configuration and vibrational spectra of aliphatic long-chainmoleculks continue to arouse d i s c ~ s s i o n .l ~ ~ - ~ ~ ~ In problems of hydro-carbon reactivity, such as the reaction with molecular oxygen, it is not atpresent clear whether n-paraffins are mainly coiled or stretched in the vapour144 Raman spectra indicate that the dimethyl-zinc, -cadmium,and -mercury, and methylmercury halide molecules are straight andthat dimethyl disulphide has predominantly a cis-configuration of themethyl groups with considerable restriction of rotation about the S-Sbond.14611. Whereas studies on aromatic and conjugated-bond systems followmethods which have been discussed fairly extensively, for saturated mole-cules the basic electronic problems are less easily formulated with quantitativeprecision.Valuable collections of numerical data on the physical constants ofhydrocarbons include measurements of boiling point, freezing point, dp/dt,refractive index, density, viscosity, heat of vaporisation, infra-red andultra-violet absorption spectra, heat of formation, free energy andequilibrium constant of formation, entropy, and heat capacity.147 Listsof dissociation energies of carbon bonds have been c0mpi1ed.l~~ Carbon-la7 D. D, Eley, Nature, 1948, 162, 819.138 A. J. Kitaigorodski, Bull. Acad. Sci. U.X.S.R., Cl. Sci. Clzirn., 1946, 103.139 G. D. Oliver, M. Eaton, and H. M. Huffman, J. Amer. Chem. SOC., 1948, ‘SO,1502.140 E. J. Prosen, Mi. M. Johnson, and F. D. Rossini, ibid., 1947, 69, 2068; G.Berthier and B. Pullman, Trans, Faraday Soc., 1949, 45, 484; R.C. Pink and A. R.Ubbelohde, ibid., 1948, 44, 708 (where other references are given).141 J. Barrio1 and J. Chapelle, J. Phys. Radium, 1947, 8, 8 ; L. KelIner, Nature,1949, 163, 877.142 R. P. Bell, Trans. Paraday Soc., 1949, 45, 946.143 A. R. Ubbelohde, Rev. Inst. Franc. Pe‘trole Ann. Cornbust. liq*, 1949, 4,144 W. J. Taylor, J. Chern. Pliysics, 1948, 16, 257.145 F. Feher, W. Kolb, and L. Leverenz, 2. Naturforsch., 1947, 2a, 454.lp6 H. Gerding and R. Westrik, Rec. Trav. chim., 1942, 61, 412.147 “ Physical constants of hydrocarbons,” U.S. Dept. Commerce, Nat. Bur.Stand., 1949; Cf. N. Corbin, M. Alexander, and G. Egloff, J. Phys. Colloid Chem.,1948, 52, 387; H. Wiener, ibid., p. 425.448.148 J. S. Roberts and H, A. Skinner, Trans.Faraday SOC., 1949, 45, 33918 GENERAL AND PHYSICAL CHEMISTRY.halogen-bond strengths have been evaluated by a number of authors,14@and the Fox-Martin rule for the energy of carbon bonds has been reviewed.150The origins of the potential barrier hindering rotation in ethane and relatedsubstances have been investigated in terms of electrostatic interactionenergies.151 Difficulty is found in reconciling the measured entropy andspecific-heat values of 1 : 2-dichloro- and 1 : 2-dibromo-ethane with anysimple type of rotational barrier.152 Raman spectra have been used toevaluate the proportions of the different configurations assumed by moleculesthrough rotation about single bonds, i.e. the " rotational isomers " of liquidhydrocarbons 153, 154 and of dihal0genoethanes.1~5 Infra-red observationsgive similar r e ~ u 1 t s .l ~ ~ Electrostatic interactions, including quadrupoleeffects in ethane, methylamine, methyl alcohol, and dimethylacetylene,appear to account for the observed barrier to r0tation.1~~The problem of changes of reactivity in a homologous series of n-hydro-carbons continues to provoke discussion and experiment.l*2+ 143 As thenumber and distribution of C atoms changes, there are systematic trendsin molecular polarisability and other physical properties. The possibilityof coupling of the vibrations of individual bonds may affect transmissionof activation energy to a specific bond and may explain effects of structureon reactivity.143 Calculations have been made which suggest that thedecomposition of unsaturated hydrocarbons and of aliphatic free radicalstakes place a t the bond having the lowest free-valency i n d e ~ .1 ~ ~ Ionisationpotentials show a systematic decrease with increasing chain-length inparaffins and A1- and A2-olefins.159 A systematic decrease in depolarisationof scattered light with increase in chain branching of paraffin moleculeshas also been claimed.160Calculations have been made of the bond lengths of single bonds inhydrogen halides ; 161 bond dissociation energies of group I1 halides have149 A. S. Carson and H. A. Skinner, J., 1949, 936 ; H. Mackle and A. R. Ubbelohde,J., 1948, 1161. 0. H. Gellner and H. A. Skinner, J., 1949, 1145 ; A. G. Evans, " TheReactions of Organic Halides in Solution," Manchester Univ.Press, 1946; J. A.Ketelaar and G. W. van Oosterhout, Rec. Trav. chim., 1946, 65, 7.E. C. Baughan, Trans. Faraday Soc., 1948, 44, 545.151 E. N. Lassettre and L. B. Dean, J. Chem. Physics, 1948, 16, 151.15% W. D. Gwinn and K. S. Pitzer, ibid., p. 303.153 J. G. Aston, D. H. Rank, N. Sheppard, and G. J. Szasz, J. Amer. Chert%. SOG.,1948, 70, 3525.154 D. H. Rank, N. Sheppard, and G. J. Szasz, J. Chem. Physics, 1949, 17, 83;N. Sheppard and G. J. Szasz, J. Chem. Physics, 1949,17, 86, 93 ; San-ichiro Mizushimaand Hiroetsu Okazaki, J. Amer. Chem. Soc., 1949, 71, 3411.155 San-ichiro Mizushima, Yonezo Morino, Itaru Watanabe, Takehiko Simanouti,and Shigeto Yamaguehi, J. Chem. Physics, 1949, 17, 591; H. J. Bernstein, ibid.,pp.256, 258, 262.156 D. W. E. Axford and D. H. Rank, ibid., p. 430.1 5 7 E. N. Lassettre and L. B. Dean, ibid., p. 317.168 G. Berthier and B. Pullman, Corn@. rend., 1948, 226, 2146.159 R. E. Honig, J. Chem. Physics, 1945,16, 105.160 I. Fabelinsky, J. Phys. U.S.X.R., 1948, 10, 231.E. Warhurat, Trans. Paraday Soc., 1949, 45, 461UBBELOHDE : STRUCTURE AND PROPERTIES OF LIQUIDS. 19been discussed; 162 and bond lengths in some inorganic molecules havebeen reviewed and it has been pointed out that a number of bonds areunexpectedly short, as in silicon tetrafluoride, phosphorus trifluoride,M-0 in many oxy-ions and molecules, M-C in metallic carbonyls, andM-N in phtha10cyanines.l~~ The intervalency angles of 0 and S in cyclicmolecules have been re-assessed from the dipole moments.16412.Experimental techniques for investigating the mechanism of organicreactions have become progressively more rigorous from the physico-chemical standpoint, and increasing attention has been paid to quantitativedata on the various bond parameters involved. Brief mention may bemade of systematic studies where the results appear to be of a nature whichcan be correlated closely with quantitative bond structure.165 Fresh datahave also been obtained for the heats and entropies of ionisation of someorganic acids 166 in relation to their molecular structure. A. R. U.4. THE STRUCTmCE AND PROPERTIES OF LIQUIDS.1. Measurements of the surface tension and of its temperature coeficientcontinue to be made as an aid to the elucidation of the structure of liquids.A number of papers refer to the surface tension of liquid metals.Theoreticalcalculations of the surface tension of liquid argon and liquid mercuryindicate a linear temperature coefficient. 167 A general theoretical dis-cussion on the temperature coefficient of the surface tension of liquidmetals168 has been published, and a proposal has been made to evaluatethe magnitude of the surface tension of liquid metals on the basis of theSornmerfeld theory of electrons in metals.16s The temperature coefficientof surface tension has been measured for molten selenium 17* and for anumber of alicyclic hydrocarbons.171 Measurements of the surface tensionand density of lead-antimony and cadmium-antimony alloys suggest thepersistence of the compound CdSb in the liquid ~ t a t e .1 ~ ~ Restrictedmiscibility in the liquid metals AI-In and Ga-T1 contrasts with completemiscibility in the liquids Ga-Si, Ga-Ge, In-Si, In-Ge, and T1-Ge.1732. The distribution of atoms in molten Pb, TI, In, Au, Sn, Ga, Bi, andGe, and the alloy Au-Sn have been evaluated by means of Fourier analysesof X-ray diffraction spectra and have been compared with the arrangements162 H. A. Skinner, Trans. Faraday Soc., 1949, 45, 20.163 A. F. Wells, J., 1949, 55.16* K. E. Calderbank and R. J. W. Le FBvre, J., 1949, 199.166 C . K. Ingold et al., J., 1948, 812, 1283, 2038.T. L. Cottrell, G. W. Drake, D. L. Levi, K. J. Kelly, and J. H. Wolfenden, J.,1948, 1016, 1019.167 G. Jura, J . Phys.Colloid Chem., 1948, 52, 40.16* A. S. Skapski, J . Chem. Phys.ics, 1948, 16, 386, 389.16* A. Kh. Breger and A. A. Zhukhovitsky, J . Phys. Chem. U.S.S.R., 1946,20, 355.170 K. Astakhov, N. Penin, and E. Dobkina, ibid., p. 403.171 W. Hiickel and H. Harder, Chenz. Ber., 1947, 80, 357.172 H. T. Greenaway, J . Inst. Metals, 1947, 74, 133.173 W. Klernm, L. Klemm, E. Hohmann, H. Volk, E. Orlamunder, and H. A. Klein,2. anorg. Chem., 1948, 256, 23920 GENERAL AND PEYSICAL CHEMISTRY.of atoms in the corresponding solids. In melting Pb, T1, In, and Au theaverage number of nearest neighbours decreases and the average inter-atomic distance decreases ; in melting Sn, Ga, Bi, and Ge the reverse effeGtsare 0b~erved.l~~3. Applications of ultrasonic measurements to the investigation of thestructure of liquids continue to be fairly numerous.175 Observationsinclude determination of the acoustic velocity, evaluation of the temperaturecoeficient of velocity, and measurements of the absorption ~0efficients.l~~Structural influences have been investigated in a series of liquid Al-olefins(C7-15) a t 15--30°.177 In water the velocity temperature coefficientand the absorption coefficient are abnormal, ' probably owing to internalrelaxation effects 178 associated with the special structure of liquid water.Peaks in the absorption of ultrasonic vibrations are sometimes foundwhen the absorption coefficient is plotted against the composition of aliquid mixture, particularly when one of the components is water; thesemay be due to molecular association in the liquid mixture, and suggest thatdevelopments of ultrasonic techniques may build up a valuable body ofinformat ion about the structure of 1 i q ~ i d s .l ~ ~4. Ultrasonic measurements have also given interesting informationabout molecular motions in liquids composed of macro-molecules. Struc-tural influences on the value of the ratios, velocity/density, have been studiedfor various hydrocarbons -and polymers as liquids or solutions. 180 Shearwaves and longitudinal waves of ultrasonic frequencies have been studiedin polyisobutene liquid polymers with viscosity ranging from 0.3 to 1700centipoises at 25". The polymers act as Maxwellian relaxing liquids, andthe shear elastic constants increase with increasing chain length and withfalling temperature.lsl Ultrasonic measurements a t 30" and 50.7" havealso been made on a range of polydimethylsiloxanes, SiMe3*[O*SiMe2],*O*SiMes.The unusually high compressibilities found for these liquids correlate with thelow cohesive forces and low boiling point, and with large-amplitude oscillationsof the methyl groups.ls2 Hysteresis effects in viscosity determinationswith glycerol and mineral lubricating oils, when the pressure is suddenlychanged, probably arise from analogous relaxation effects in such 1 i q ~ i d s .l ~ ~174 H. Hendus, 2. h7aturforsch., 1947, 2a, 505.175 A bibliography of references (to 1939) is given by W. T. Richards, Rev. Mod.176 E. Bauer, Proc. Physical Xoc., 1949, 62, 141. J.R. Pellam and J. I(. Gab, J .177 R. T. Lagemann, ibid., 1948, 16, 247.Physics, 1939, 11, 36; cf. Repts. Progr. Physics, 1948, 11, 217.Chem. Physics, 1946, 14, 608.G. W. Willard, J . Acoust. Xoc. Amer., 1947, 19, 235; L. Hall, Physical Rev.,179 R. Parshad, J . Acoust. Soc. Amer., 1948, 20, 66; F. H. Willis, ibid., 1947, 19,18* G. Natta and M. Baccaredda, J . Polymer Sci., 1948, 3, 829.le1 W. P. Mason, W. 0. Baker, H. J. McSkimin, and J. Heiss, Physical Rev., 1948,1948, 73, 775.242; C. J. Burton, ibid., 1948, 20, 186.73, 1074.A. Weissler, J . Amer. Chem. SOC., 1949, 71, 93.lE3 F. Charron, Compt. rend., 1947, 225, 919UBBELOHDE : LIQUID AND SOLID DIPLECTRICS. 21Attempts have been made to correlate the energy of vaporisation and cohesionwith the viscosity of liquids.lM5.Systematic studies of the effect of molecular structure on the thermalconductivity of liquids give evidence for the participation of the internaldegrees of freedom in heat cond~ction.1~~ Attempts have been made tocorrelate the thermal expansion of organic liquids with their molecularstructure.ls6 The density of liquid selenium at different temperatures isof some interest in camparison with that of sulphur.lS7 A. R. U.5. THE PHYSICAL CHEMISTRY OF LIQUID AND SOLID DIELECTRICS.1. The dielectric losses of liquid chlorobenzene, bromobenzene, ethylchloride, butyl alcohol, and butyl bromide have been measured a t micro-wave frequencies (A - 3 cm.).lS8 Formuls for the internal field strengthof a dielectric show discrepancies with experiment in a number of cases.For example, the molecular polarisation Pm of a non-polar gas like carbondioxide passes through a maximum at about 250 atmospheres, and thepolarisation of ionic crystals changes when they are powdered.ls9 A newequation for the internal field strength has been claimed to be superior toOnsager’s equation.lgo The dielectric relaxation in high polymers has beencorrelated with the ability of the molecules carrying dipoles to rotate freely ; lglthe dielectric losses in rubber swollen with non-polar and with polar solventssuggest independent movement of the dip01es.l~~ Solid solutions of aliphaticlong-chain polar compounds such as ketones or esters in long-chain hydro-carbons, e.g. n-hexacosane, continue to provide important systems in whichdielectric relaxation can be correlated with detailed information about thestructure .1932.Much work continues to be published on (‘ ferro-electric ” solids such asRochelle salt, potassium dihydrogen phosphate, and barium metatitanate, inwhich the dielectric constant attains very high values below a critical tempera-ture or (‘ Curie point.’’ The term ‘( ferro-electric ’’ is used to indicate thatthe high dielectric constant is due to a co-operative effect between themolecular dipoles, which has certain analogies with the production of ferro-magnetism by co-operative effect between molecular magnetic moments.Ferro-electric domains in single crystals of Rochelle salt below the CurieILE4 L. Grunberg and A.H. Nissan, Trans. Paraday Soc., 1947,45, 125.lS6 L. Riedel, Mitt. Kaltestech. Inst., Karlsruhe, 1947, No. 2, 45 pp.le7 K. V. Astakhov, N. A. Penin, and E. I. Dobkina, J . Gen. Chem. Russia, 1947,lB8 G. E. Crouch, J . Chem. Physics, 1948, 16, 364.G. Steensholt, Phil. Mag., 1946, 37, 357.1’7, 378.E. J. Verwey, Chem. Weekblad, 1947, 43, 662; J. Icil. Bijvoet, ibid., p. 631;C. A. h i s s i n k , ibid., p. 633.loo C. J. Bottcher, ibid., p. 652.lgl W. Kiihn, Helu. Chim. Acta, 1948, 31, 1259.lg2 A. Schallamach and P. Thirion, Trans. Furaday SOC., 1949, 45, 605;lg3 R. J. Meakins, Nature, 1948, 162, 994.cf. W. C.Carter, M. Magat, W. C. Schneider, and C. P. Smyth, ibid., 1946, 42, 21322 GENERAL AND PHYSICAL CHEMISTRY.point can apparently give rise to reflexions of ultrasonic waves (10 mc./sec.).l9*The effect of the lattice constants of Rochelle salt on the electromechanicalproperties has been discussed.lg5 According to one theory, contractionof short hydrogen bonds in the crystal, due to mechanical or thermal effects,leads to a shift of the proton towards the midpoint of the hydrogen bondwith consequent changes in the polarisability.196g 197 Various studies on thecrystal domains in Rochelle salt and potassium dihydrogen phosphate havebeen p~b1ished.l~~~ lg8 Ferro-electric domains in barium metatitanate havebeen distinguished by the appearance of single crystals under the microscope,with polarised light, and by other physical properties.199 Photographs ofhysteresis loops produced on a cathode-ray oscillograph when a singlecrystal of barium metatitanate is placed in an electric field also give evidenceof ferro-electric domains.200 Methods for growing barium metatitanatecrystals have been described201 and the crystal structure has been dis-cussed.202 The properties of mixed barium-strontium titanate have alsobeen investigated .203 A. R. U.6. THE PHYSICAL CHEMISTRY OF TffE SOLID STATE.Many developments of routine crystallographic analysis are now beingpublished in the Acta Crystallogruphica.1. Though the discussion of crystallographic techniques in detail fallsoutside the scope of this section (see section 12 and the Report on Crystal-lography), mention may be made of the diffraction of neutron beams bycrystals, including sodium chloride, diamond, aluminium, sodium, sodiumbromide, sodium fluoride, sodium hydride, and sodium deuteride. It isinteresting to note that in sodium hydride the proton scatters neutronswith negative scattering amplitude, in contrast to the deuteride in whichthe deuterons scatter with positive amplitude.204 Limitations in the useof Geiger counters for the measurement of Bragg and diffuse scatteringfrom small single crystals have been disc~ssed.20~ The location of hydrogenlo* W.J. Price, Physical Rev., 1948, 73, 1132.lo6 R. M. Lichtenstein, ibid., 1947, 72, 492 ; cf. W. P. Mason, ibid., p. 976.lo6 A. R. Ubbelohde and I. Woodward, Proc. Roy. SOC., 1946, A , 185, 448.lS7 A. R. Ubbelohde, J . China. p h y e u e , 1949, 46, 429; W. P. Mason, PhysicalRev., 1947, 72, 854.lo* J.H. Thorn and If. E. Buckley, Acta Cryst., 1949, 2, 333; S. Miyake, Proc.Physico-Math. SOC., Japan, 1941, 23, Aug. and Oct. ; J . Phy8ical SOC. Japan, 1947,2,98.lo9 B. Matthias and A. Hippel, Physical Rev., 1948, 73, 268, 1378 ; cf. B. Matthias,Nature, 1948, 161, 325; H. D. Megaw, Proc. Roy. SOC., 1947, A , 189, 261 ; G. C.Danielson, Acta Crystall., 1949, 2, 90.2oo A. de Bretteville, Physical Rev., 1948, 73, 807.*01 B. Matthias, ibid., p. 809; H. F. Kay, Acta Cryst., 1948, 1, 229.H. F. Kay, If. J. Wellard, and P. Vousden, Nature, 1949, 163, 636; H. T.Evans and R. D. Burbank, J. Chem. Physics, 1948,16, 634.203 J. G. Powles, Nature, 1948, 162, 655.R. J. Finkelstein, Physical Rev., 1947, 72, 907; C. G. Schull et al,, i b a ., 1948,73, 527, 830, 842.*06 K. Lonsdale, Acta Cryst., 1948, 1, 12TTBBELOHDE: PHYSICAL CHEMISTRY OF THE SOLID STATE. 23atoms in crystals by X-ray diffraction may become possible in certainorganic compounds by the use of sufficiently precise methods for obtainingelectron-density contours in molecules.2062. Amongst new crystal structures with more than a specialised interestthe following may be noted : potassium and rubidium hydroxides,207sodium cyanate,208 the ionic layer structure in aluminium chloride,209 andthe bond-lengths in certain polysulphides.210 Preparation of non-cubic(graphitic) silicon 211 and of colourless carborundum 212 has been claimed.3. Studies of the vibration frequency and vibration amplitudes of atomsand groups in crystals continue to be published, for crystals of even greatercomplexity.The Raman spectra of crystals such as diamond, sodiumchloride, magnesium oxide, lithium fluoride, potassium chloride, caesiumchloride, aluminium oxide, ammonium chloride, calcium carbonate, andcertain metals have been recorded and interpreted theoretically in a seriesof papers. As might be expected from considerations of bond anharmo-nicity (cf. reference 19?), temperature coefficients of lattice frequencies aremuch larger than those of intramolecular frequencies in calcium carbonate.The variation of Raman spectra of ammonium chloride may be correlatedwith various transitions in the ~rystal,~13 The Debye temperature of sodiumnitride, as computed from specific heat data, is 460" & 15" K., comparedwith 505" 15" K.computed from variations of the intensity of X-rayreflections.214 Rotational vibrations have been postulated in hexamethylene-tetramine crystals to explain the change of X-ray diagrams with tem-p e r a t ~ r e . ~ ~ ~ Root-mean-square amplitudes of atomic vibrations have beentabulated for 20 elements and 24 compounds crystallising in the cubicsystem.216 Fresh theoretical calculations have been made on the zeropoint energies of lithium hydride and deuteride,217 which are evaluateda t 5.4, and 4-3, kcals. respectively.4. Crystal ion radii for tervalent and quadrivalent ions of the elementsthorium, uranium, neptunium, plutonium, and americium have beenevaluated.218 Correlation of ionic radii with solid-solution limits and withzo* J.D. Morrison, W. P. Binnie, and J. M. Robertson, Nature, 1948, 162, 889.207 T. Ernst and R. Schober, Arzgew. Chem., 1948, 60, A , 77.Zo8 hf. Bassi&, Hem. Serv. Chim. de I'Etat, 1943, 30, 30.209 J. A. Ketelaar, C. H. MacGillavry, and P. A. Renes, Rec. Trav. chim., 1947,66,501.I. M. Dawson, A. McL, Mathieson, and J. M. Robertson, J., 1948, 322.211 F. Heyd, 3'. Kohl, and A. Kochanovska, Coll. Czech. Chem. Comm., 1947,12, 502.212 R. Iley and H. L. Riley, Nature, 1947, 160, 468.213 (Sir) C. V. Raman, R. S. Krishnan, K. G. Ramanathan, and P. K. Narayaswamy,214 M. Bassidre, Mem. Sew. Chim. de Z'Etat, 1943, 30, 33.216 P. A. Shaffer, J . Amer. Chem. Soc., 1947, 69, 1557.216 K. Lonsdale, Acta Cryst., 1948, 1, 142; for other effects of temperature onX-ray scattering see E.A. Owen and R. W. Williams, Proc. Roy. Soc., 1947, A , 188,509, and G. H. Begbie, ibid., p. 189.Proc. Indian Acad. Sci., 1947, 26, A , 339.217 S. R. de Groot and M. M. Biedermann, Physica, 1941,8,905.W. H. Zachariasen, Physical Rer., 1948, '73, 110424 GENERAL AND PHYSICAL CHEMISTRY.crystal-compound formation has been made in a number of simple ioniccrystals. The solid-solution limit a t room temperature of zinc oxide in cubicmagnesium oxide is a t 33% of zinc, and that of zinc oxide in nickel oxideat 35% of zinc. Results are also given for solubilities of zinc oxide inhexagonal cadmium and cobalt m0noxides.~19 A complete range of solidsolutions is observed in the alkaline-earth carbonates barium-strontiumcarbonates and calcium-strontium carbonates, but only limited rangeswhen the differences in ionic radii are larger, as in barium-calcium carbonates(aragonite).The solid solutions rich in calcium crystallise in the aragonitestructure in the first instance, but are transformed into the calcite structureon storage.220 A predominant influence of ionic radius is apparent in thesystems formed by the salt pairsor RbCl *ac7 or KCI with MgCl, and Nal] with Mg12Thermal and X-ray analyses have indicated crystal compounds withcongruent melting points with the following formuh :Type ABX, : NaMgF,or KIKMgF3 KMgCl,RbMgF, RbMgCl,Type A2BX4 :K2MgC14Rb2MgF4 R b2MgC14and mixed crystals of sodium iodide-magnesium iodide which disintegrateat lower ternperatures.,,l Solid solutions of potassium chloride-potassiumbromide and lithium chloride-rubidium chloride have been studied.222In the system potassium nitrate-ammonium nitrate solid solution occurseven when the two salts are ground together at 40°.223 The solubility oflead dichloride in silver chloride at 270" is first decreased and then raisedby increasing amounts of dissolved cadmium5.Interstitial solid solutions have been further investigated in a numberof systems. Uranium trihydride and trideutride have been prepared ; theyare electrically conducting and have m. p. >600°, indicating a special typeof binding of the hydrogen.225 In palladium-hydrogen and cognate systemsit has been claimed that part of the hydrogen is not truly interstitial but isoccluded in rifts.226 Studies are reported on carbides MgC, and Mg2C,.227R.Rigamonti, Gazzetta, 1946, 76, 474.220 R. Faivre and G. Chaudron, Compt. rend., 1948, 226, 903.*21 W. Klemm, Angew. Chem., 1948,60, A , 57; 2. anorg. Chem., 1948,256, 25..222 J. A. Wasastjerna, Acta SOC. Sci. Penn., 1944, 3, No. 8.223 J. Whetstone, Canadian J . Res., 1948, 26, 23, 499.224 C. Wagner and K. E. Zimen, Acta Chem. Scand., 1947, 1, 539.225 R. E. Rundle, J . Amer. Chem. SOC., 1947, 69, 1719.226 D. P. Smith, Phil. Nag., 1948, 39, 477.a27 F. Irrrnann, Helv. Chim. Acta, 1948, 31, 1584UBBELOHDE : PHYSICAL CHEMISTRY OF THE SOLID STATE. 25The monocarbides (MC) of titanium, zirconium, vanadium, niobium, andtantalum are cubic, but that of tungsten and M0,C are hexagonal.Con-tinuous solid solutions are formed by metal-carbide pairs in the temperaturerange 1600-2100" as follows : Ti/V, Ti/Nb, Zr/Nb, Nb/Ta, (Ta, Nb)/V,V/Ta, Ti/Ta and probably Ti/Zr. Solubility is limited in the pairs : V/Zr ;W/Zr, V, Nb, Ta; Mo/Zr, V, Nb, Ta.,,* An electronic interpretation ofinterstitial metallic carbides, nitrides, and oxides with cubic sodiumchloride structure has been proposed, in terms of electron-deficient bondstructures in which the non-metal forms more bonds than it has orbitals.229" De-fect oxides " with stoicheiometric composition MOO, (n = 0.10 to 2-97) andwith a number of different crystal phases have been synthesised, and havebeen examined by X-rays and by electrical-resistance measurements.23oVariation of the partial pressure of oxygen over cadmium oxide at differenttemperatures gives a reversible variation of thermoelectric power, owing tothe reversible filling of lattice defects.231 Measurements of the electricalconductivities of solid oxides, zinc oxide, Fe,03, Cr203, ZnFe,04, ZnCr,O,,MgFe,O,, and MgCr,O,, have been made over a range of temperatures upto lOOO", in atmospheres of air, oxygen, hydrogen, and carbon monoxide.It has been shown that zinc oxide, Fe203, ZnFe,O,, and MgFe20, are electronconductors, whereas Cr203, MgCr20a, and ZnCr204 are positive-hole con-ductors. At temperatures between 0-5 and 0-25 Tm (T, = m.p. in OK.) theconductivity varies reversibly with oxygen pressure.The relation of theseobservations to different mechanisms of electrical conductivity in the solidsand to their chemical reactivity has been discussed.232 For SnS233 andPbS 234 the Fowler-Wilson semi-conductor theory seems insufEcient toexplain the temperature coefficients and the absolute magnitude of thethermo-electric power. X-Ray, pyknometric, and magnetochemical studiesindicate a range of defect structures in Ti(Se), and Ti(Te), (n = 2.00 tol.00).235 The conductivity and thermoelectric effect in cuprous oxide havebeen further in~estigated.,~~Periodic faults have been detected in the crystal lattices of some mole-cular complexes of 4 : 4'-dinitrodiphenyl with other diphenyl derivatives.2377. Various studies on temperature effects in crystals have been reported,which have a bearing on the thermodynamics of the solid state.Sharpanomalies in the thermal expansion and specific heat of chromium sesqui-6. Defect crystal structures continue to receive much attention.228 H. Nowotny et al., Metallf., 1947, 2, 257, 265.229 R. E. Rundle, Acta Cryst., 1948, 1, 180.Z3O 0. Glemser and G. Lutz, Angew. Chem., 1948, 60, A , 69.231 C. A. Hogarth and J. P. Andrews, PhiE. Mag., 1949, 40, 273; C. A. Hogarth,232 D. J. M. Bevan, J. P. Shelton, and J. S. Anderson, J., 1948, 1'1.29.233 J. S. Anderson and M. C. Morton, Trans. Faraday SOC., 1947, 43, 186.234 M. C. Morton, ibid., p. 194.236 P. Ehrlich, 2. angew. Chem., 1948, 60, A , 68.236 N. IN. Greenwood and J. S. Anderson, Nature, 1949, 164, 346.237 R.W. James and D. H. Saunder, Acta Cryst., 1948, 1, 81.ibid., 1948, 39, 26026 QENERAL AND PHYSICAL CREMXSTRY.oxide have been detected in the range 31-33°.238 Titanium sesquioxideexhibits anomalous thermal expansion and electrical conductivity around200".239 Specific-heat anomalies have been detected in deuterium chloride,bromide, and i0dide.6~ Nickel monoxide tends towards cubic symmetrysmoothly as the temperature rises towards 300". The fact that the latticeshows distorted cubic symmetry a t lower temperatures is attributed to theatomic-size ratio Nil0 being just too small a t room temperature for a stableface-centred cubic structure. As the temperature rises, the nickel atomsoccupy more space. Solid solutions of small quantities of iron and cobaltin nickel oxide give stable cubic structures at room temperature, apparentlybecause of the larger atomic radius of bivalent iron or cobalt comparedwith ni~ke1.~4* An important review of different types of thermal trans-formation in solids involves a classification on the basis of the thermo-dynamic treatment evolved by Ehrenfest .241 A crystallographic inter-pretation of the distinction between continuous and discontinuous thermaltransitions in solids has been proposed, on the basis that in continuoustransitions the new structure appears, not as a distinct crystal phase, butas a sub-crystalline hybrid structure in the original single crystals.242Studies of the temperature variation of the elasticity modulus of a range ofmetals from -180" to +lOOO" have been Generally themodulus falls with rising temperature, but where there are allotropicmodifications or Curie points discontinuities may arise.8.Various kinetic aspects of changes in the solid state are receivingincreasing attention from the physico-chemical standpoint. The growthof crystals has been the subject of a Faraday Society Discussion.244 Theaccommodation coefficients for vapour-solid transitions in benzene, iodine,camphor, and water are estimated to be 0.62, 0.94, 0.17, and 0.068, re-spectively, which appear to be of the same order as for the correspondingvapour-liquid transitions.245 This supports the view that the first state ofcondensed molecules on a solid surface is akin to a liquid in structure.Ithas been suggested that the surface distribution of atoms in solids is akinto the liquid state.246 Fresh evidence has been brought forward that heatinga liquid or solution above the equilibrium crystallisation temperature T,can increase the subsequent interval between T, and the temperature ofspontaneous crystallisation TT,.247 A review of reactions in the solid state238 J. Jaffray and J. Viloteau, Compt. rend., 1948, 2MY 1701.239 111. Foex and J, Loriers, ibid., p. 901.240 H. P. Rooksby, Acta Cryst., 1948, 1, 226.241 J. Jaffray, Ann. Phgsique, 1948, 3, 5 ; cf. Quart. Reviews, 1949, 3, 65.242 A. R. Ubbelohde and I. Woodward, Proc. Roy. Xoc., 1947, A , 188, 358.243 W. Koster, 2. Metallk., 1948, 39, 1.244 Faraday SOC. Discussions, 1949, 5.245 BI.K. Baranaev, J. Phys. Chem. Russia, 1946, 20, 399. Cf. J. Birks andR. S. Bradley, Proc. Roy. Xoc., 1949, A, 198, 226; R. S. Bradley and A. D. Shellard,ibid., p. 239.246 C. Gurney, Proc. Physical Soe., 1949,62, A, 642.247 R. Gopal, J . Indian Chem. Soc., 1947, 24, 279UBBELOHDL : PHYSICAL CHEMISTRY OF THE SOLID STATE. 27has been published.248 Publications on kinetic processes in the solid stateinclude evidence that dissolved water increases the rate of reaction betweenFe,O, and other oxides in the temperature range 300-700".249 Theactivation energy for diffusion of neutral coupled pairs of positive- andnegative-ion vacancies in alkali halide crystals has been calculated.25o Itis suggested that this process may be more important than the diffusionof single vacancies.251 Measurements from -40" to 120" of the specificconductance of rapidly frozen aqueous solutions of various electrolytes areinterpreted on the view that rotation of water molecules in the lattice canfacilitate transfer of H+ and OH-.252 Measurements of the internal frictionas a function of temperature and concentration of impurities in solid solutionhave been correlated with crystallographic results in the case of tantalumand z i n ~ .~ ~ 3 In solid solutions of nitrogen in iron, a new phase has beendiscovered by plotting the temperature of maximum internal friction againstcomposition.254 The transformation in the solid state for nitrito- ---+nitro-pentamminocobaltic nitrate has been investigated.2559.Some correlation of chemical reactivity or catalytic efficiency with thearrangement of atoms in various crystal faces of a solid has been achievedin a number of cases. For crystals of copper heated at 900" the rateof oxidation of the different faces is in the sequence (210), (221) > (211),(110) > (111) > (100) > 123. Measurements have also been published onthe oxidation of crystals of iron a t 850".256 Comparisons of the catalyticcombination of hydrogen with oxygen on single crystals of copper in thetemperature range 360-440" showed that at low partial pressures ofoxygen the combination rate on the crystal face (100) was twice as large ason (lll), and that the face (100) remained smooth whereas (111) wasroughened.At higher partial pressures of oxygen the activity of (111) increased.Copper powder formed rapidly on all crystal faces at mol.fractions of oxygengreater than 5%.257 In the catalytic decomposition of carbon monoxideon single crystals of nickel at 550" selective deposition of carbon was observedon the (111) faces.258 The catalytic production of (ethylene + hydrogenchloride) from ethyl chloride on crystals of barium chloride, manganouschloride, lead( 11) chloride, silver chloride, and various mixed crystals24s G. Cohn, Chem. Reviews, 1948, 42, 527.24s C. Haasser and H. Forestier, Compt. rend., 1947, 225, 240.250 G. J. Dienes, J . Chem. Physics, 1948, 16, 620.251 For refs. see Mott and Gurney, " Electronic Processes in Ionic Crystals," Oxford252 S. I. Weissmann, Nature, 1948, 161, 241.Univ. Press, 1940.Tantalum : T'ing-Sui Ke, Physical Rev., 1948, 74, 9, 16. Zinc : C.A. VVert,264 C. Zener, " Elasticity and Anelasticity of Metals," Unir. Chicago Press, 1948,a56 B. Adell and G. Tholin, Acta Chem. Scad., 1947, 1, 624.256 J. B6nard and J. Talbot, Compt. rend., 1947, 225, 411.257 H. Leidheiser and A. T. Gwathmey, J . Amer. Chem. SOC., 1948, 70, 1200.J . Appt. Physics, 1949, 20, 29.p. 120.Idem, ibid., p. 120628 GENERAL AND PHYSICAL CHEMISTRY.has been studied in relation to the dipole moment of the "activedoublet." 259The activation energy for the catalytic activity of a range of gold-cadmium alloys in the decomposition of formic acid at 225-350" has beencorrelated with the Brine11 hardness.260 A.R. U.7. ADSORPTION AND SURFACE CHEMISTRY.A great volume of work on adsorption and surface chemistry continuesto be published.1. Interest in the physical chemistry of aerosols appears to have beenstimulated by a number of wartime and agricultural applications, as wellas by the possibilities of " rain-making " by condensing droplets from airsupersaturated with m o i s t ~ r e . ~ ~ l - ~ ~ ~ Various possible nuclei for " rain-making " include sodium chloride 262 and silver iodide.263 The growth ofparticle size with time in aerosols has been discussed by various authors.2642. Measurements on the adsorption of gases on solids have been used inmany cases to calculate the available surface of the absorbent by theBrunauer-Emmett-Teller m e t h ~ d .~ ~ ~ a - f Discrepancies from these authors'adsorption theory have been n ~ t e d . ~ ~ ~ ~ , b Another main objective has beenthe evaluation of integral and differential heats of adsorption.266a-b Othersinclude the measurement of dielectric constants of vapours of ethyl chloride,butane, and ethyl ether on silica, which indicate that adsorbed ethylchloride acts as a non-polar compound owing to restricted mobility of themolecule carrying the dipole in the adsorbed layer.267 The heat capacityof nitrogen adsorbed on titanium dioxide in the temperature range 20-430" K.is slightly below that of bulk nitrogen in the gas phase.266e Phase changes259 G. A. Schwab and A. Karatras, J . Phys. Colloid Chenz., 1948, 52, 1053.260 G. A. Schwab and S.Pesmatjoglou, ibid., p. 1046.261 E. B. Kraus and P. Squires, Nature, 1947, 159, 489.262 H. Dessens, Compt. rend., 1948, 226, 506.263 B. Vonnegut, Chem. Reviews, 1949, 44, 277.264 I. S. Artemov, J . Phys. Chem. RZGSS~Q, 1947, 20, 553 (mineral oil aerosols);P. S. Prokhorov and V. N. Yashin, Colloid J . U.S.S.R., 1948, 10, 122 (water droplets).D. W. E. Axford, K. F. Sawyer, and T. M. Sugden, Proc. Roy. SOC., 1948, A, 195, 13(hygroscopic aerosols).265 ( a ) R. T. Davis and T. W. De Wtt, J . Amer. Chem. SOC., 1948, 70, 1135; (b)S. J. Gregg and J. Jacobs, Trans. Faruday SOC., 1948, 44, 574; J. F. Duncan, sibid.,1949, 45, 879; (c) P. H. Emmett, Chem. Reviews, 1948, 43, 69; ( d ) M. A. Cook, J . Amer.Chem. SOC., 1948, 70, 2925; ( e ) M. Dole, J .Chem. Physics, 1948,16, 25; (f) A. G. Foster,Faraday SOC. Discussion, 1948, 3, 41.266 ( a ) L. G. Joyner and P. H. Emmett, J . Amer. Chem. SOC., 1948, 70, 2359; (b)idem, ibid., p. 2353; (c) J. Perreu, Compt. rend., 1948, 226, 907; (d) V. A. Crawfordand F. C. Tompkins, Trans. Paraday SOC., 1948, 44, 698; ( e ) J. A. Morrison and G. J.Szasz, J . Chem. Physics, 1948, 16, 280 ; (f) C. Pierce and R. N. Smith, J . Phys. ColloidChem., 1948, 52, 1111, 1115; (9) J. Perreu, Compt. rend., 1948, 226, 492, 2138; 1949,228, 1429; ( h ) P. R. Basford, (3. Jura, and W. D. Harkins, J . Amer. Chem. SOL, 1948,'20, 1444.267 R. McIntosh, H. S. Johnson, N. Hollies, and L. McLeod, Canadian J . Res.,1947, 25, B, 566UBBELOHDE : ELECTROCHEMISTRY AND IONIC CBEMISTRY. 29have been postulated in films of vapour adsorbed on solids to explain thevariation in surface compressibility with surface pressure .268 Sorption-desorption isotherms of water vapour on silica gel indicate that the sorbedliquid does not freeze a t -5°.2693.Various aspects of the surface chemistry of liquids have been discusseda t a recent Faraday Society meeting.270 The variation of surface viscositywith surface pressure has been measured for various unimolecular layers.271The phenomena of electrocapillarity have been reviewed.272 Adsorptionfrom solutions has a most important application to the technique ofchromatographic separation of components. Most developments of thistechnique merely have applications in view, but theoretical discussionsand interpretations have been proposed by a number of authors.273A. R.U.8. ELECTROCHEMISTRY AND IONIC CHEMISTRY.Several main objectives can be recognised in publications on electro-chemistry and ionic chemistry during the period under review.1. The main interest of new investigations of ions in aqueous solutionhas concentrated on new types of molecules giving colloidal ions by theassociation of smaller molecules into a micelle 274 or because of the poly-merisation of a large number of ionising groups into a macro-molecule.2752. Studies of molten electrolytes include the determination of viscosityisotherms from 580" to 690" for mixtures of cadmium chloride and cadmiumbromide. The derived activation energy is about 1.7 times the activationenergy for ionic migration calculated from the electrical conductivity.276From observations on the electrolytes or cryolite-alumina baths it has beensuggested that the primary ionic process is the electrolysis of sodiumoxide.277 Electrode processes in molten electrolytes have been reviewedfor molten alkali sulphates, phosphates, carbonates, silicates, fluorides, andwith special reference to the oxygen over-potential a t a smoothplatinum anode.The electrical conductivity has been measured for silicatemelts containing calcium, manganese, and aluminium.279268 S. J. Gregg and F. A. P. Maggs, Trans Faraday SOC., 1948, 44, 123.269 W. 0. Milligan and H. H. Rachford, J. Amer. Chem. SOC., 1948, 70, 2922.270 Faraday SOC. Discussions, 1948, 3.271 M.Joly, J. Chim. physique, 1947, 44, 206, 213.272 D. C. Graham, Chem. Reviews, 1947, 41, 441.273 Chromatographic Adsorption, Faraday SOC. Discussions, 1949, in the press.274 (Only a selection of papers on micelle formation is given; cf. An?&. Reports,1948, 45, 33.) (a) G. L. Brown, P. F. Grieger, A. C. Kraus, and H. S. Young, J. Airier.Chem. SOC., 1949, 71, 95, 309; (b) W. D. Harkins, J . Chem. Physics, 1948, 16, 156;R. W. Mattoon, R. S. Stearns, and W. D. Harkins, ibid., p. 644.275 R. M. Fuoss and U. P. Strauss, J. Polymer Sci., 1948, 3, 246, 602, 603.276 H. Bloom, B. S . Harrap, and E. Heymann, Proc. Roy. SOC., 1948, A, 194, 237.277 R. Gadeau, Bull. SOC. frang. &ect., 1947, 7, 640.278 H. Flood and T. Ferland, Faraday Xoc. D ~ S G U S S ~ O ~ S , 1947, 1, 302,279 J.O'M. Bockris, J. A. Kitchener, S. Ignatowicz, and J. W. Tomlinson, ParadaySOC. Discussions, 1948, 4, 26530 GENERAL AND PHYSICAL CHEMISTRY.3. Studies on ionic processes in non-aqueous systems have a numberof features of general interest. These include the study of ionic reactionsin liquid hydrogen cyanide.280 Conductance measurements have beenmade on various salts dissolved in nitrobenzene,281 including the mixedsalt system NaCI-A12Br,-C6H,*W02.282 Although acetic anhydride is itselfpractically non-conducting, conducting solutions are obtained with a widevariety of salts, which include arsenic trichloride and antimony trichloride,with or without added potassium chloride, zinc chloride, bismuth chloride,cobaltous iodide, triphenylmethyl chloride, or tetramethylammoniumIn liquid sulphur dioxide a maximum in the conductance isfound when equimolecular proportions of an acid chloride and aluminiumchloride or antimony pentachloride are present.Apparently new types ofcation are formed.284 Proposed equations areCH,*COCI + SbC1, ---+ CH,*CO+ + SbC1,-NOCl + AICI, --+ NOf + AIC1,-The ionisation of triphenylmethyl bromide by the additions of stannicbromideCPh,Br + SnBrdhas been measured in benzene, chlorobenzene, bromobenzene, ethylenedibromide, and ethyl bromide.285 Liquid dinitrogen tetroxide has beenstudied as an ionising solvent.286 In ethyl ether the E.M.F. of cells of thetypePh,C* + SnBr,-Ag,AgBrlLiBr in Et,O/LiBr in Et,OlAgBr,AgC1 c2has been measured, with the addition of lithium perchlorate to fix activityfactors .287 Velocity coefficients have been determined for exchangereactions between lithium bromide and alkyl bromides in anhydrous acetonesolution.288 These indicate incomplete dissociation of lithium bromide.Incomplete dissociation of hydroxides of sodium, potassium, rubidium,calcium, barium, and thallium in aqueous solution has been measured byreaction-kinetic methods.289 Acid-catalysed alcoholysis in toluene and ina number of polar solvents has been studied.290 The structure of nitricacid has been studied in solvents such as chloroform and ether,291 and theS8O G.Jander and B. Gruttner, Chem. Ber., 1948, 81, 102, 114.281 E. G. Taylor and C. A. Kraus, J . Amer, Chem. Soc., 1947, 69, 1731.s8P I.S. Bigich, J. Qen. Chem. Russia, 1946,16, 1783.288 H. Schmidt, I. Vry’ittkop, and G. Jander, 2. anorg. Chesn., 1948, 256, 113.%a4 F. See1 and H. Bauer, 2. Naturforsch., 1947, 2b, 397286 C. C. Addison and R. Thompson, J., 1949, S1, 211.287 U. Berglund and L. G. Sillen, Acta Chem. Scad., 1948, 2, 116.F. Fairbrother and B. Wright, J., 1949, 1058.C. C. Evans and S. Sugden, J . , 1949, 270.R. P. Bell and J. E. Prue, ibid., p. 362.%SO M. F. Carroll, ibid., p. 2188.sD1 R. Dalmon, Mem. Serv. Chim. de l’gtat, 1943, 30, 141UBBELOHDE : KINETIC STUDIES. 31dissociation of hydrogen chloride has been studied in alcohol, acetone, anddioxan by optical methods.2924. Much interest has continued to be shown in the properties of solutionsof alkali metals and alkaline earths in liquid ammonia.The molar volumeof sodium in liquid ammonia has been evaluated.293 Measurements onsodium-ammonia at low temperatures 294 give no evidence for super-conductivity or anomalous magnetic properties. Phase diagrams ofpotassium, lithium, calcium, strontium, barium, and calcium in liquidammonia have been investigated in relation to the electrical conductivity,magnetic susceptibility, and dielectric constants of the systems 295 (cf.section 11).The polarography of solutions of alkali metals and of tetraethyl-,tetrapropyl-, and tetrabutyl-ammonium iodide in liquid ammonia hasbeen studied. The results are interpreted in terms of a cathodic dissolutionof electr0ns.~~65. Ionic processes at electrodes, especially the phenomena of over-voltage, have been discussed by various authors a t a Faraday Societymeeting.297 The standard electrode potentials of the elements have beenreviewed .297a A.R. U.9. KINETIC STUDIES. PHOTO-REACTIONS AND AUTOXIDATION.Of the publications in these two special sections of kinetic studies, anumber of general interest may be referred to.1. The photochemical oxidation of cyclohexene, 1 -methylcyclohexene,2 : 6-dimethylocta-2 : 6-diene, and ethyl linoleate has been studied. Theprimary act is postulated to be the dissociation of the 0-0 bond in theperoxide ROOH. All four oxidations have thermal activation energiesranging from 6 to 8 k ~ a l s . ~ ~ ~ The photochemistry of aldehydes298a andketones 299 has been reviewed.Photo-sensitisation reactions includestudies of the role of metal vapours such as zinc, cadmium, and mercury ingas reactions.300 Photo-sensitisation of reactions by fluorine and chlorine,and probably by bromine, is attributed to the formation of atoms.301Photo-formation of atoms from hydrogen chloride is also assumed to explain292 E. A. Braude and E. S. Stern, J., 1948, 1971, 1976.293 A. J. Stosick and E. B. Hunt, J. Amer. Chem. SOC., 1948, 70, 2826.2g4 L. Giulotto and A. Gigli, Physical Rev., 1947, 71, 211 ; A. J. Birch and D. IC. C.295 A. J. Birch and D. K. C. MacDonald, ibid., 1948, 44, 735.2B6 H. A. Laitinon and C. J. Nyman, J . Amer. Chem. SOC., 1948,70,2241, 3002.297 Faraday Xoc. Discussions, 1947, 1.297u J. O’M. Bockris and J.F. Herringshaw, Faraday SOC. Discztssions, 1947, 1, 328.2B8 L. Bateman and G. Gee, Proc. Roy. SOC., 1948, A, 195, 376.29*u F. A. Blacet, J. P h p . Colloid Chem., 1948, 52, 534.29Q W. A. Noyes, ibid., p. 546.sOO E. UT. R. Steacie, Canadian J. Res., 1948,28, B, 609.301 J. W. T. Spinks, Canadian. J . Res,, 1948,26, B, 629.MacDonald, Trans. Paraday SOC., 1947, 43, 792.L. B. Thomas and W. D.Gwinn, J. Amer. Chem. Soc., 1948, 70, 264332 GENERAL AND PHYSICAL CHEMISTRY.the vapour-phase addition of hydrogen chloride to ethylene initiated byultra-violet light .302 The photolysis of dimethylmercury in the presenceof hydrogen to produce methyl radicals has been re-in~estigated.~~~2. A number of photo-reactions involving more complex molecules,such as fluorescent dyes and chlorophyll, have been interpreted wit~h theaid of the " exciton " hypothesis.304 Investigations of the photo-voltaiceffect a t electrodes of zinc, cadmium, and silver have exhibited the profoundinfluence of dissolved oxygen.305One typical proposed structure is :3.Investigations continue on oxygen-carryingCH,---C€€, I N=CH I HC==NInitiation of oxidations by atomic hydrogen has beenThe autoxidation of tetralin 308 and of olefins 309 has been further studiedcobalt compounds.306further in~estigated.~~'in terms of the peroxide radicals taking part in the reaction mechanism.Hydrogen peroxide has been isolated as calcium peroxide octahydrate fromthe oxidation products of pr0pane.~1~ Reference may be made to threerecent symposia on hydrocarbon oxidation,311 and to various papers onthe oxidation of hydrocarbons and related molecules in the gas phase.312Studies of the emission spectra from flames a t low pressures have giveninteresting information about effective rotational and translational tem-peratures of the molecules.313 A.R. U.10. THE PHYSICAL CHEMISTRY OF MACRO-MOLECULES.1. In connection with statistical studies on rubber-like molecules, newexperimental tests and theoretical discussions have been published on the302 J. H. Raley, F. F. Rust, and W. E. Vaughan, J. Amer. Chem. SOC., 1948, 'SO, 2767.303 M. K. Phibbs and B. de B. Darwent, Trans. Faraday Soc., 1949, 45, 541.304 G. 0. Schenk, Naturwiss., 1948, 35, 28; R. Livingston, J. Phys. Colloid Chem.,1948, 52, 527; R.Livingston and R. Pariser, J. Amer. Chem. Soc., 1948, 70, 1510;T. Forster, 2. Naturforsch., 1947, 2&, 174.305 J. M, Blocher and A. B. Garrett, J. Amcr. Chem. Soc., 1947, 69, 1594.306 H. Diehl et al., Iowa State Coll. J . Sci., 1947, 21, 271, 278, 287, 311, 316, 326.307 E. J. Badin, J. Amer. Chem. Soc., 1948, 70, 3651, 3965.308 A. Robertson and W. A. Waters, J., 1948, 1574, 1578, 1585.309 L. Bateman and G. Gee, Proc. Roy, Soc., 1948, A , 195, 391.310 P. L. Kooijman, Rec. Trav. chim., 1947, 66, 217.311 Faraday SOC. Discussions, 1947, 2; cf. Rev. Inst. Frang. Pe'trole Ann. Combust.liq., 1949, 4; Third Symposium on Combustion Flame and Explosion Phenomena,Williams and Wilkins Go., Baltimore, 1949.312 M. F. R. Mulcahy, Trans.Farday Soc., 1949, 45, 537, 575; G. A. McDowelland J. 33. Thomas, J., 1949, 2208, 2217; (Sir) A. Egerton, E. J. Harris, and G. H. S.Young, Trans. Faraday Soc., 1948, 44, 745.313 A. G. Gaydon and H. G. Wolfhard, Proc. Roy. Soc., 1948, A , 194, 169; 1949,199, 89UBBELOHDE : THE PHYSICAL CHEMISTRY 03 MAORO-MOLECULES. 33structure and thermodynamic functions of rubber, “ Polythene,” andrubber-liquid Acoustic determinations of the physical constantsof rubber-like materials have given data on the velocity of sound, and theattenuation coefficient from which Young’s modulus and the associatedviscosity coefficient have been calculated.315 The thermo-elastic behaviourof certain plant tissues has been ~ t u d i e d . ~ f ~2. Various physico-chemical studies on the sorption of water by proteinshave been published.Differential and integral free energy, entropy, andheat changes have been evaluated for the sorption of water by silk, wool,ovalbumin, collagen, gelatin, and lactoglobulin. The differential entropychange, a t low vapour pressures, suggests that the initial stages of sorptionof water may be accompanied by re-arrangement of protein chains.317Measurements of the dielectric constant of keratin show that, as the amountof water absorbed increases, the dielectric constant increases, probablybecause of an increased freedom of rotation of polar groups in the macro-m0lecule.3~~ Results have also been published for the effects of sorptionof n-propanol and acetone.319 Desorption isotherms have been publishedfor the removal of water from benzoylated casein.320Thermodynamic measurements of the binding of copper by bovineserum albumin 321 and on the combination o f Orange-I1 acid with woolkeratin322 have been interpreted in terms of the molecular structures ofthe protein.X-Ray studies of single crystals of tomato bushy-stunt virusgive further insight into the effects of partial removal of water from acrystalline protein, which leads to a slight disorientation of the internalcrystalline regions.323 The attractions, a t distances of several thousand A.,between macro-molecules in liquids have been further ons side red.^^ Adiscussion on lipoproteins was held in August, 1949, by the Paraday Society.Energy transport in proteins has been associated with the giant networkof hydrogen bonds.3253.Miscellaneous studies of the physico-chemical properties of macro-molecules include measurements of the infra-red spectra of the silicones.32sA. R. U.314 D. G. Fisher, Proc. Physical SOC., 1948, 60, 99; G. Gee, Trans. Faraday SOC.,1946, 42, B, 33; J . Chim. physique, 1947, 44, 66; R. Kubo, J . Colloid Sci., 1947,2, 527; H. Kuhn, ReZv. Chim. Acta, 1948, 31, 1677; W. Parks and R. B. Richards,Trans. Faraday Soc., 1949, 45, 203.316 A. W. Nolle, J . Acoust. SOC. Amer., 1947, 19, 194.316 0. Treitel, J . Coll, Sci., 1947, 2, 453.317 S. Davis and A. D. McLaren, J . Polymer Sci., 1948, 3, 16.318 G. King, Trans. Faraday Soc., 1947, 43, 601.320 E. F. Mellon, A. H. Korn, and S.R. Hoover, J . Amer. Chern. SOC., 1948, ‘SO, 1144.811 I. M. Klotz and H. G. Curme, J . Amer. Chern. Soc., 1948, 70, 939.322 A. B. Meggy, Trans. Faraday SOC., 1947, 43, 502.823 C. H. Carlisle and K. Dornberger, Ackc Cryst., 1948, 1, 194; cf. (Turnip Yellow324 J. Winter, Compt. rend., 1948, 226, 704.326 K. Wirtz, 2. Natur-wsch., 1947, 2b, 94.826 R. E. Richards and H. W. Thompson, J., 1949, 124.31s Idem, ibid., p. 552.Mosaic Virus), J. D. Bernal and C. H. Carlisle, Nature, 1948, 162, 139.REP.-VOL. XLVI. 34 GENERAL AND PHYSICAL CHEMISTRY.11. MAQNETOCHEMISTRY.1. Magnetochemical Aspects of Cata&is.-It has long been thoughtthat some relation may exist between catalytic activity and the phenomenonof paramagnetism. Obvious parallelisms exist between the pronouncedmagnetic properties of the transition-group metals and their catalyticeffects, the non-uniform fields in the neighbourhood of paramagnetic centreshaving been invoked by several workers as one of the main causes of generalcatalytic It is not wholly decided whether paramagnetismaccompanies catalytic activity, merely because the free valencies which areeffective for catalysis involve paramagnetic orbita.ls, or whether intenselocal magnetic fields have a catalytic effect by lifting the quantum restrictionson certain changes of bonding.The examples which follow illustrateboth possibilities.(a) The ortho-para-Hydrogen Conversion.-The discovery of the catalyticortho-para-hydrogen conversion presented the first clear example of thelifting of quantum restrictions by intense magnetic fields.Early work 328showed that, at low temperatures, conversion was much more rapid oncatalysts exhibiting paramagnetism. such as chromium sesquioxide andgadolinium oxide. Weakly paramagnetic oxides such as cerium dioxide,and diamagnetic oxides, were relatively ineffective. The conversion involvesisolated molecules and is effected by the non-uniform magnetic forces in theneighbourhood of the paramagnetic ions.328 At higher temperatures, e.g., onmetal wires, magnetic forces need not be inv0ked.~30 ortho-para-Conversionis thought to proceed by an exchange of atoms between a hydrogen moleculein an absorbed monolayer and a hydrogen atom in the underlying stablechemisorbed layer. Experiments by Burstein 331 indicate that this exchangemechanism may be the main route on charcoal even a t 80” K., contrary to theview 332 that in this case (‘ surface paramagnetism ” is the responsible factor.The observed inability of NN-diphenyl-N‘-picrylhydrazyl to catalyse theortho-para-conversion 333 in spite of its undoubted paramagnetism appearsto be due to its non-adsorptive properties, which prevent intimate contact ofhydrogen with the region of intense non-uniform magnetic field.Whenintimately mixed with a suitable adsorbent such as zinc oxide this free radicalhas strong catalytic activity.( b ) Mixed Oxides and Solid Solutions.-Evidence for the existence of arelation between catalytic activity and magnetism has been obtained by327 R.Kuhn, in Freudenberg’s “ Stereochemie,” F. Deuticke, Leipzig, 1933,p. 917 ; cf. P, W. Selwood, Chem. Reviews, 1946, 38, 52, 55, for other refs.328 H. S. Taylor and H. Diamond, J. Amer. Chem. Soc., 1933, 55, 2613.32* A. Farkas, “ Light and Heavy Hydrogen,” Cambridge Univ. Press, 1935,530 J. K. Roberts, Proc. Roy. SOC., 1935, 152, 445; D. D. Eley, ibid., 1941, 178,331 R. Burstein, Acta Physicochim. U.S.S.R., 1938, 8, 857.332 P. W. Selwood, Chem. Reviews, 1946, 38, 51.333 J. Turkevich and P. W. Selwood, J . Amer. Chem. Soc., 1941, 83, 1077.p. 95.452; Trans. Paraday Soc., 1948, 44, 216PINK : MACINETOCHEMISTBY. 35G. F. Huttig and his co-workers from studies on mixed 0xides.3~~ Oneexample is provided by mixtures of zinc oxide and chromium sesquioxide.These show striking changes in catalytic activity when heated, which areclosely paralleled by changes in the magnetic susceptibility of the mixtures.For the equimolecular mixture the activity for the thermal decompositionof methanol reached a sharp maximum a t 400°, a steep rise in susceptibilitywith incipient ferromagnetism being observed a t approximately this tem-perature.Above 400" a decrease in activity with a simultaneous loss offerromagnetism occurred. In explanation, the formation of intermediatecompounds is suggested, but their exact nature is not certain and thequestion must remain open.332V. Cirilli335 has studied the magnetic behaviour of a number of solidsolutions of metallic oxides. The susceptibility x for alumina-ferric oxidesystems treated a t 600" and 850" showed a striking increase with increased[Fe,O,] owing to the presence of strongly magnetic y-Fe203 held in solidsolution by y-A1203.For any proportion of ferric oxide in excess o f 67%,x drops considerably owing to formation of the weakly magnetic rhombo-hedral form corresponding to cc-Fe,O,. Only small paramagnetic sus-ceptibilities were observed in the system chromium sesquioxide-aluminairrespective of chromium content and temperature of heating.Mixed oxides in the form of '' supported " catalysts have been studiedextensively by P. W. Selwood and his c o - w ~ r k e r s . ~ ~ ~ Measurements of x a tdifferent temperatures for catalysts comprising chromium sesquioxide ony-Al,03 and molybdenum dioxide on y-A120, showed that the magneticproperties of the catalyst approached those of a magnetically dilute com-pound; i.e., one in which interaction between the magnetic centres is at a,minimum.With increasing [Cr3+] an increase in the Weiss constant wasobserved. There is evidence that the surface in these catalysts is onlypartly covered by a chromium sesquioxide layer.The Weiss constant for manganese oxide catalysts supported on aluminashows a striking variation with concentration, reaching a sharp maximuma t -8% of manganese. It is suggested that the crystal lattice of aluminaexerts an inductive effect on manganese oxides which tend to conformto the lattice structure of the support even to the extent of a changeof valency. The presence of MnlI1 a t low, and %Iv at high, concentrationswas confirmed by analysis.Support for this hypothesis was obtainedby demonstrating that manganese oxides supported on rutile, which isisomorphous with manganese dioxide, exhibit no anomalies of the kinddescribed.(c) Adsorbed Substances and Catalytic Poisons.--The magnetic propertiesof adsorbed substances frequently exhibit anomalies. Pioneer work ins34 G. F. Huttig, KolEoi&-Z., 1942, 99, 262; 1942, 98, 263; 1941, 97, 281; 1941,94, 137, 258; for other refs. see Selwood, ref. 332.535 V. Cirilli, Qazzettu, 1947, '77, 255.ss6 P. W. Selwood et d., J . Anzev. Chern. SOC., 1946, 68, 2055; 1947, 69, 1590;1948, 70, 2145, 2271 ; 1949,71, 693,252236 GENERAL AND PHYSICAL CHEMISTRY.this field is due to S.S. Bhatnagar, K. N. Mathur, and P. L. K a p ~ r , ~ ~ ’ whoshowed that the salts of many transition-group metals become diamagneticafter adsorption on charcoal.338 This change in magnetic susceptibilityprovides strong evidence for the formation of complexes on the surface ofthe charcoal, in which the unpaired electrons responsible for the para-magnetism of the ion take part in covalent binding with the substrate.Recent work 339 throws light on these ‘‘ chemisorptive bonds.’’ Sus-ceptibility measurements by the Sucksmith method on a palladium catalyston which dimethyl sulphide had been adsorbed revealed a significantdecrease in the paramagnetism of the catalyst. Alkyl sulphides are powerfulpoisons for palladium and are strongly adsorbed. It is inferred that thebinding involved in this adsorption is of a type in which electrons from thed-band of the palladium take part.The authors compare this effect withthe effect of hydrogen atoms on the d-band of the metal in palladium-hydrogen systems. In previous work, E. B. Maxted and R. MT. D. Morrish 340had shown that poisoning by compounds containing sulphur or phosphorusdepended on the presence, in the valency shell of the toxic element, of freeelectron pairs, Thus, organic sulphides and thiols are toxic, whereas thecorresponding sulphones and sulphonic acids are not.R*C :;: H .. Toxic : ROC :g: OR’ . *0 00 0ROC :*i OH .. ROC : K: C*R‘ .. Non-toxic :On the basis of the magnetic evidence it is suggested that a chemisorbedmolecule transfers an electron to a vacant surface d-orbital, the para-magnetic susceptibility of the surface palladium atoms being therebyreduced to zero.A survey of other work341 also showed that the only metal ions whichare toxic to hydrogenation catalysts such as platinum are those in whichthe d-orbitals of the toxic ion are occupied by either electron pairs or singleelectrons.If unoccupied d-orbitals are present or if no d-orbitals arepossible, toxicity is not observed. The possibility that the binding in thecase of the adsorbed metallic ions involves electrons excited into the un-occupied s- and p-orbitals appears to be precluded by further observations.Strong toxic action towards a platinum catalyst was observed with dimethyl-mercury, trimethylindium, and tetrameth~l-lead.~~~ With the lead compound337 S.S. Bhatnagar, K. N. Mathur, and P. L. Kapur, lndiun J . Physics, 1928, 3,338 Cf. A. Boutaric and P. Berthier, J . Chim. physique, 1942, 39, 129; Chem. Zentr.,s3e M. H. Dilke, D. D. Eley, and E. B. Maxted, Nature, 1948, 161, 804; cf. E. B.340 E. B. Maxted and R. W. D. Morrish, J., 1940, 252.s41 E. B. Maxted and A. Marsden, ibid., p. 469.342 E. B. Maxted and K. L. Moon, J., 1949, 2171.53.1943, I, 1456.Maxted, J., 1949, 1987PINK : MAGNETOCHEMISTRY. 37all four of the s- and p-orbitals are engaged in covalent-bond formationwith carbon (if the usual structure for these compounds is accepted).Excitation of electrons into these levels cannot, therefore, be a necessityfor chemisorptive binding.Reduction to the metal on the catalyst surfaceof the ions themselves or of the metallo-organic compounds seems to beexcluded. Metallic salts which are poisonous for catalytic hydrogenationsare also toxic for oxidation and reduction of the metallo-organiccompounds does not occur to a significant extent under the experimentalconditions.344 The close connection between catalytic activity and magneticsusceptibility for the metallic ions is shown in the following table. Catalyticactivity rises to a maximum with palladium and platinum, the two metalswith maximum x, and falls to a low or even zero activity with the diamagneticmetals, silver and gold.Metal Ru Rh Pd Ag 0 s Tr Pt AuAtomicno. (44) (45) (46) (47) (76) (77) (78) (79)The views expressed by Maxted and his co-workers are interconnectedwith earlier experiments by G.-IM.Schwab and his who obtainedaccurate measurements of the activation energy for formic acid dehydro-genation by catalysts consisting of alloys of silver, gold, or copper with awide range of other metals. A general relation was claimed between theactivation energy for this reaction and the degree of completion in anyparticular alloy of the first Brillouin zone, the activation energy increasingwith the degree of electron saturation of the zone. This led directly to theconcept that catalytic activation consists in a transition of electrons fromthe substrate to the metallic catalyst. As might be expected on this view,a sharp maximum in activation energy was observed for y-phases, in parallelwith the striking minimum in their electrical conductivity.A magneticstudy of the alloys used by Schwab might well prove of great interest inthis connection.The magnetic properties of oxygen adsorbed on charcoal continue toattract interest. It now seems well established that the adsorbed gas hasthe same susceptibility a t room temperature as gaseous oxygen. Variousauthors346 observed a slow diminution with time of the paramagnetism ofthe charcoal-oxygen system as a result of carbon dioxide formation. Theirwork has been confirmed by C . Courty347 who found a steady decrease inx during almost a year. According to Courty the first stage in carbondioxide formation is the production of oxygen atoms on the charcoal surface.Xg.-at.+51*8 +114*2 $476.2 -21.6 $9.5 +29*0 +214*7 -29.6343 E. B. Maxted, J . , 1922, 1760.344 V. N. Ipatiew, G. Rasurvajew, and I. F. Bogdanow, Ber., 1930, 63, 335.345 G.-M. Schwab et al., Trans. Faraduy Xoc., 1946, 42, 689; Ber., 1943, 76, 1228;Naturwiss., 1943, 31, 27, 345; 2, anorg. Chem., 1944, 252, 205; 2. Elektrochem., 1944,50, 204.346 J. Aharoni and F. Simon, 2. physikal. Chem., 1929, B, 4, 175; R. Juza andR. Langheim, Nuturwiss., 1937,25, 522 ; R. Juza, R. Langheim, and H. Hahn, Angew.Chem., 1938, 51, 354; R. Juza and R. Langheim, 2. Elektrochem., 1939, 45, 689.347 C. Courty, Colioque sur l'adsorption, Centre Nat. Recherche Scient., Paris, 194938 GENERAL AND PHYSICAL CHEMISTRY.9. Structural Problems in Organic C?hemistry.-(a) Structure and driagneticSwceptibility of Organic Compounds.-Applications of the magneticmethod t o structural problems continue to attract interest.Molecularcompounds of s-trinitrobenzene with hydrocarbons and phenols have beenexamined.348 In each case the molecular compound is less diamagneticthan the sum of the diamagnetism of its components, the maximumanomalies occurring with anthracene and phenanthrene. However, only arelatively slight deviation from additivity is found for naphthalene picrate,in support of the assumption that the components are linked togetheronly by weak electrostatic f0rces.3~~ Susceptibilities of the tautomericforms of 8-hydroxyquinoline have been measured.350 Measurements ofx for solutions in benzene, pyridine, and quinoline suggest that in thesesolutions two-thirds of the hydroxyquinoline exists in the phenolic and one-third in the ketonic form.The fact that the isomeric pairs of p-chloro-, p-bromo-, and' p-nitro-benzenediazocyanide, and the two known forms of diphenyl-4 : 4'-bis-diazocyanide, have susceptibilities only slightly different has been taken inconjunction with other evidence as indicative of cis-trans-isomerism asdistinct from the cyanide-isocyanide relati0nship.3~1 C.M. French 352 hasdetermined x for a series of aliphatic acids and esters and evaluated Axm forthe methylene group, and W. R. Angus and G. Stott report values for aseries of isomeric aldehydes and ketones.353 The aldehydes are morediamagnetic than the ketones but the differences are small.Measurementsof the diamagnetic susceptibility of cyclooctatetraene support 8 cyclicstructure with conjugated double bonds rather than an aromatic type ofsystem, in agreement with infra-red and Raman spectra.140 J. R. Lacher 354has pointed out marked deviations in the experimental values, for poly-halogen derivatives of methane, from Pascal's additivity rule and haspresented an empirical interpretation on the assumption that the molecularsusceptibility is the sum of the atomic susceptibilities and six interactionterms directed along the edges of a tetrahedron. Evidence obtained byX-ray study of urea has been used355 to calculate its susceptibility by themethod of F. W. Gray and T. H. Cr~ikshank.3~~ No agreement wasobserved between the calculated and experimental values either for ureaor for its derivatives. Magnetic measurements on di-2-benzthiazolyldisulphide and di-(9-ethoxy-lO-phenanthryl) peroxide 357 show that the348 R.C. Sahney, S. L. Aggarwal, and 3%. Singh, J. Indian Chem. SOC., 1946, 23,335.349 F. G. Baddar md H. Mikhail, J., 1949, 2927.350 &I. Seguin, Bull. Soc. chim., 1946, 13, 566.361 D. Anderson, M. E. Bedwell, and R. J. W. Le FBvre, J., 1947, 457.352 C. M. French, Trans. Faruduy SOC., 1947, 43, 356.35s W. R. Angus and G. Stott, Nature, 1946, 158, 705.354 J. R. Lacher, J. Amer. Chem. Soc., 1947, 69, 2067.365 S. K. Siddhanta, J . Indian Chem. SOC., 1947, 24, 21.366 F. W. Gray and J. H. Cruikshank, Trans. Furaday SOC., 1935, 31, 1491.a67 H.C. Cutforth and P. W. Selwood, J . Amer. Chem. SOC., 1948, 70,278PINK : MAGNETOCHEMISTRY. 39former is dissociated to a considerable degree in toluene, but that the latteris diamagnetic in all cases and shows no temperature coefficient of sus-ceptibility. The magnetic method has also been applied to the study of thedisproportionation of diphenyl-p-t0lylmethy1.~~~ Measurement of thetemperature coefficient gives a value for the activation energy of 13.1 kcals.per mole of free radical. An interesting observation was made in the courseof this study : the free radical solution remained strongly coloured afterdisproportionation when the reaction was carried out in the dark; in thelight, however, colour and paramagnetism decreased in parallel.Themagnetic properties of bi-radicals have been reviewed.3593. Diamagnetism of Liquid Mixtures.-From measurements on the sus-ceptibilities of mixtures of aniline with ethyl, n- and iso-propyl alcoh01,~~~evidence has been obtained for the formation, in solution, of amine-alcohol‘‘ salts.” With methanol, however, the susceptibility is additive. Notabledepartures from additivity for mixtures of ethyl alcohol with o- and m-toluidine, pyrrole, pyridine, and quinoline have also been observed.361Similarly results have been obtained for mixtures of chloroform with aseries of ketones.362 The susceptibilities are additive except in the caseof acetone, where the slight anomaly may be explained by hydrogen bonding.Investigations of this kind might in principle be of value in elucidatinginstances of chemical interaction in solution, but it seems evident that theexpectation that data might become available which would be suitablefor tests of theories of the structure of liquids has not been realised.W. R.Angus and D. V. Tilston363 have surveyed the published work on liquidmixtures accumulated since the pioneer observations of A. W. Smith andA. W. Smith.364 Many of the data have been recalculated by a method,previously used by Angus and W. K. Hill,365 designed to bring out clearlyany real deviations from additivity. The conclusion is that although thebulk of the qualitative evidence supports small but real deviations fromadditivity, no quantitative measure of any accuracy can be derived.Itwould seem that much of the early work in this field has unfortunately beencarried out with materials whose purity has not been above suspicion.4. Magnetic Susceptibilities of Inorganic Compounds.-E. Grillot 366 hasconcluded that the law of additivity of magnetic susceptibilities is notapplicable to a series of twenty-three compounds of bivalent lead. P.Pascal, A. Pacault, and A. Tchakirian367 claim that, provided that thereis no marked structural constraint, the law of additivity is applicable to a356 W. Byerly, H. C. Cutforth, and P. W. SsIwood, J . Amer. Chem. SOC., 1948, 70,359 F. L. J. Sixma, Chem. Weekblad, 1947, 43, 437.360 S. Hatem, Compt. rend., 1947, 225, 332.361 Idem, ibid., p. 296.363 W. R. Angus and D. V. Tilston, Trans. Paraday SOC., 1947, 43, 221.364 A.W. Smith and A. W. Smith, J . Amer.*Chem. Soc., 1918, 40, 1218.s65 W. R. Angus and W. K. Hill, Trans. Paraday Soc., 1940, 36, 923.366 E. Grillot, J . Chim. physique, 1946, 43, 169.367 P. Pascal, A. Pacault, and A. Tchakirian, Compt. rend., 1948, 226, 849.1142.M. Seguin, ibid., 1947, 224, 92840 GENERAL AND PHYSICAL CHEMISTRY.series of germanium compounds. The main difficulty in evolving forinorganic chemistry anything comparable to the Pascal system of constantsin the organic field is that insufficient homologous series are available forcomparison and evaluation of atom and group susceptibilities. Usefulapplications of the magnetic method in the inorganic field neverthelesscontinue to accumulate. Magnetic measurements have shown that theperiodates of copper, nickel, cerium, and yttrium are true salts of theperiodic acids and not complexes.36s A magneto-chemical study of thepotassium chlorostannites 369 indicates that the hydrates of these com-pounds and stannous chloride itself are not simple molecular associationsof water and the corresponding salts.The molecular susceptibility ofpotassium stannichloride dihydrate agrees with the view that this compounddiffers from [SnC14(H20),]K2 only in the insertion of a molecule of water inthe crystal lattice. Interesting results have been obtained370 in a studyof nickel diformyldiethylenedi-imine-camphor. This compound is dia-magnetic in the solid state and in solution in benzene and acetone, butparamagnetic in methanol and other solvents.In a recent series of papers 371Sugden and his co-workers have reported x values for the ions of yttrium,samarium, gadolinium, and thulium. The rare earths were purified byfractional crystallisation controlled by measurements of magnetic sus-ceptibility. Crystallisation was continued until a series of successivefractions give the same x values. Measurements were made in solutionwith a Gouy apparatus for which an accuracy of a t least 1 part in 600 withdiamagnetics is claimed. This degree of accuracy is readily attainable atroom temperatures. A decrease of diamagnetism has been found, in thecase of lead bromide, from -0.275 x to -0.249 x after exposureto At the same time the salt loses 0.03-0.1% of bromine.This phenomenon may be associated with the photosensitivity of leadbromide. Susceptibilities are reported of cuprous nickelsalts in solution,374 potassium ferricyanide a t high ternperat~res,~’~ andcopper potassium sulphate a t temperatures below 1 O K.3765.Micro-wave Paramagnetic Resonance Absorption.-The discovery 377-379of the phenomenon of paramagnetic resonance absorption provides anew and direct method for the investigation of closely spaced energy368 R. Sahney, S. L. Aggarwal, and 31. Singh, J . Indian Chem. Soc., 1947,24, 193.368 E. Grillot, Compt. rend., 1948, 226, 496.37f S. Sugden et al., J., 1949, 131, 135, 136, 137, 139.378 I. Delgery, Compt. rend., 1947, 225, 398.373 M. L. Khanna, J . Xci. I d . Res. India, 1947, 6, B, 4.374 J.M. Alameda, An. real. Xoc. esp. Fds. Quim., 1947, 43, 689, 711.375 H. Masson, Compt. rend., 1947, 224, 1277.376 D. de Klerk, Physica, 1946, 12, 513.377 C. J. Gorter, ibid., 1936, 3, 503, 1006.378 E. Zavoisky, J . Phys. U.S.S.R.;1945, 9, 211; 1946,10, 197; R. L. Cummerow87* R. L. Cummerow, D. Halliday, and G. E. Moore, ibid., 1947, 72, 173 ; C. KittelI. Lifschitz, Rec. Trav, chim., 1947, 66, 401.and D. Halliday, Physical Rev., 1946, 70, 433.and J. M. Luttinger, ibid., 1948, 73, 162PINK : MAGNETOCHEMISTRY. 41levels in paramagnetic materials. Early experiments in this field 377were limited by unavailability of oscillators of sufficiently high fre-quency, a want remedied by the great war-time advances in micro-wavetechnique. In a typical experimental arrangement,378) 380 the absorptionis measured as a function of the magnitude of a static magnetic field appliedin a direction perpendicular to a magnetic field, fluctuating with a frequencyof 9375 mc./sec.The salt is placed in a circuit element situated betweenthe poles of the electromagnet. As the static field is varied, the powerabsorption of the salt is found to pass through well-defined maxima. Suchparamagnetic losses have been investigated for salts of the iron group381and for chromic ammonium a l ~ m . 3 ~ ~ Extension of such measurementsshould throw light on the existence and prevalence of magnetic exchangecoupling between ions. Theoretical aspects have been dealt C.Kittel has discussed the theory of ferromagnetic resonance a b s o r p t i ~ n .~ ~Developments in this field may be awaited with great interest.6. Miscellaneous Problems.-The effect of cold-working on the magneticsusceptibility of copper and aluminium has been examined.385 The dia-magnetic susceptibility of copper decreases rapidly to 15% below theannealed value and then rises slowly with increased cold working. Theparamagnetic susceptibility of aluminium decreases similarly to a similarextent. The effects appear to be associated with lattice distortion andgrain fragmentation. Negative results were obtained 386 in experimentsaimed at the detection of super-conductivity in rapidly cooled solutions ofsodium in liquid ammonia at 78" and 195" K. by measurement of x for thesolutions by the Gouy method.Measurements of the magnetic anisotropy are reported on rn~lybdenite~~'on nickel ions in ~rysfals,38~ and on a large number of crystals and naturallyoccurring substances including m i ~ a .3 ~ ~ A synthetic mica has been found 390to be quite strongly paramagnetic, but the paramagnetism is attributed toinclusions of Fe304 since the susceptibility decreases with increasing fieldstrength and much of the iron content can be removed by dilute sulphuricacid. The diamagnetic susceptibilities of alkali-metal salts dissolved infused borax were claimed 391 to be greater than for the pure salts, pointing380 P. R. Weiss, Physical Rev., 1948, 73, 471.381 R. L. Cummerow, D. Halliday, and G. E. Moore, ibid., 1947, 72, 1233.382 P. R. Weiss, C. A. Whitmer, H.C. Torrey, and J. S. Hsiang, ibid., p. 975;D. M. S. Bnguley and J. H. E. Griffiths, Nature, 1947,160, 532; R. Bleaney and R. P.Penrose, Proc. Physical Soc., 1948, $0, 395.383 C. Kittel and J. M. Luttinger, Physical Rev., 1948, 78, 162; C. J. Gorter andJ. H. Van Vleck, ibid., 1947, 72, 1128.384 C. Kittel, ibid., 1947, 71, 270; 1948, 73, 155.386 T. S. Hutchison and J. Reekie, ibid., 1948, 73, 517.386 R. B. Gibney and B. L. Pearson, ibid., 1947, 72, 76; cf. refs. 294, 295.s87 A. K. Dutta, Indian J . Physics, 1945, 19, 225.s88 A. Mookherji, ibid., 1946, 20, 9.380 P. Nilakantan, J . Indian I n s t . Sci., 1941, 23, G, 1, 41, 59, 95, 100, 161.380 J. T. Kendall and D. Yeo, ATature, 1948, 161, 476.3g1 S. K. Majumdar and R. P. Banerjee, Indian J .Physics, 1946, 20, 21842 GENERAL AND PIXYSICAL CHEMISTRY.to increased electronic orbits or an enlargement of the crystal lattice. Thisconclusion is not confirmed by molecular refraction and X-ray diffractionstudies.experiments have been described BB3 in whichthe polymerisation of pure vinyl chloride was followed by susceptibilitymeasurements. In this connection another effect has been noted 394 whichmay be of general significance. Polyindene fractions polymerised to differentdegrees (2.45-7.39) were measured by the cylinder method, The plot ofx against degree of polymerisation shows a distinct maximum at a mediumdegree of polymerisation (-5). The rise in x is easily explained in terms ofthe decrease in double bonds with increasing polymerisation, but the originof a paramagnetic component leading to a fall in x a t higher degrees ofpolymerisation is not so readily explained.Eollowing earlierR.C. P.12. METALS AND ALLOYS. THE PAULING HYPOTHESIS.1. Introduction.-In recent years much interest has been aroused by aseries of papers by L. Pauling in which attempts are made to develop atheory of metals and alloys from a viewpoint different from that usuallyadopted. The non-specialist reader may find it difficult to distinguishbetween the real conclusions or predictions of the theory on the one hand,and its empirical or ad hoc assumptions on the other, and the present reportis an attempt to clarify the position.The early theories of Drude and Lorentzin which the electrons were treated as particles of a gas obeying the classicallaws led to the well-known difficulty that the observed specific heats ofmetals could not be reconciled with the presence of electrons to a numberof the same order as that of the atoms, this number being required by theelectrical and optical properties.The first step towards the removal of this impasse was taken in 1928 bySommerfeld who treated the electrons as particles of a gas obeying theFermi-Dirac statistics.In this case the small mass of the electrons meansthat if they are present to the extent of 1 - 4 electrons per atom, the resulting" electron gas " is almost completely degenerate 397 at room temperatures,and has a very small specific heat which is approximately proportional tothe absolute temperature.In this way the presence of a number of electronsof the order to be expected from the normal valencies of the metals could bereconciled with specific heats accounted for almost entirely * by the thermal398 J. Farquharson, Trans. Paraday SOC., 1936, 32, 210; J. Farquharson and P.Ady, Nature, 1939, 143, 1067; S. S. Bhatnagar, P. L. Kapur, and G. Kaur, J .Indian Acad. Sci., 1949, 10, A , 468: J . Indian Chem. Soc., 1940, 17, 177.The free-electron gas theory.393 0. Tanaevsky, Compt. rend., 1947, 225, 1069.39* W. Schutzner, Nature, 1949,164, 364.397 For an elementary description of these ideas and a general review of the electrontheories of metals, see W. Hue-Rothery, " Atomic Theory for Students of Metallurgy "(Institute of Metals Monograph Series).* At very low temperatures the electronic specific heat is a relatively greaterfractionHUME-ROTHERY : METALS AND ALLOYS.43oscillations of the atoms. The Sommerfeld theory still required free pathsmuch longer than were really consistent with the mathematical treatment,but the introduction of the ideas of the Fermi-Dirac statistics marked animmense advance.The idea of an electron gas was clearlytoo simple, and in the later developments of the theory associated with thenames of Bloch, Brillouin, Mott, and Jones the methods of wave-mechanicsare applied to the motion of electrons in a 3-dimensional periodic fieldwhose periodicity is that of the crystal lattice. In this case, if, as at theabsolute zero, the periodicity of the field is perfectly regular, the wave-likecharacteristics of an electron enable it to move unimpeded through thelattice,? and the long free-paths indicated by the electrical conductivitiescan be understood. The state of an electron in a crystal lattice can beexpressed by its wave-number 1 / A , where h is the associated wave-length.I n practice it is customary to multiply the wave-number l / h by 2x, andthe quantity - is called the waue-number k ; it is a vector quantity whichcan be used to describe the state of an electron.The wave-like charac:teristics of an electron then mean that, for electrons whose states lie in anyone direction of k, there will be certain values of k for which the electronicwave-length satisfies the conditions for a Bragg reflection by atomic planeswithin the crystal.Electrons in such states cannot move freely throughthe crystal, and the effect of this is that for each direction of k: there areranges of forbidden energies which separate the bands or zones of permittedelectron energies. These developments have led to a successful interpret-ation of the three main types of substance, insulators, semi-conductors, andnormal conductors, and have thrown much light on the electrical propertiesof metals, and on the structures of some alloys.398* 399Calculation of physical properties. It is desirable to emphasise theextent to which the electron-band theory of metals, using the very minimumof assumptions, has led not only to a general explanation of a wide rangeof phenomena, but to quantitative calculations of the physical constantsof crystals.In some of the more refined calculations using a Hartree self-consistent field method, the atomic field is calculated by assuming onlythe mass and charge of the electron, and the atomic number of the atomThe electron-band theory.*2xh3Q8 For an elementary account of this work see ref. 397, Part V, p. 179, and A. H.Cottrell, “ Theoretical Structural Metallurgy,” Edward Arnold.3Q8 For more detailed treatments see N. F. Mott and H. Jones, “The Theory ofthe Properties of Metals and Alloys,” Oxford Vniversity Press.* For abbreviation we use the term electron-band theory to include both thesimple Brillouin zone theories and the more detailed theories in which the atomicfield is considered, and a, p , or d functions are introduced.t It can be shown that this conclusion is not affected by the zero-point energy ofthe atomic vibrations.$. In the free-electron theory the direction of k is the direction of motion of theelectron, but in a periodic field the electron does not always move in the same directionas k44 GENERAL AND PHYSICAL CHEMISTRY.or ion concerned. This atomic field is then introduced into a calculationof the Wigner-Seitz 400 type in which the only additional assumption madeis that of the type of structure in which the metal crystallises. With noassumptions other than these the theory has been able to calculate thelattice spacings, binding energies, and compressibilities of the alkali metals,lithium and sodium, and of the bivalent metal, beryllium.H. Jones401has also shown that the theory accounts satisfactorily for some propertiesof close-packed hexagonal crystals, and particularly for the variation oflattice spacing with composition in alloys. It is thus reasonable to saythat by assuming nothing but the mass and charge of the electron, theatomic number, and the type of crystal structure, the theory has permittedthe calculation of a wide range of physical properties.* I n the alkali metalsthe ions are small compared with the shortest distances between the atoms.Such metals may be called “ open ” metals in contrast to “ full ” metals,such as copper, where the electron clouds of the ions in the metallic crystaloverlap to such an extent that the compressibility is determined more bythe ionic overlap than by the valency electrons.For copper Fuchs’stheoretical calculations 402 are in reasonable agreement with the observedcompressibility although the calculations here involve the introduction ofsome empirical assumptions, and are thus not so completely fundamentalas those referred to above. For elements of higher valency the calculationsbecome increasingly difficult but approximate solutions have been obtainedfor alumini~rn,~O3 iron>@ and tungsten.405 All this represents a substantialachievement of quantitative theory. The theory has failed to explain thephenomenon of supraconductivity. Otherwise there is little in contradictionto it as regards the properties of the perfect crystal lattice, and for theseproperties the general impression is that further development is a matter ofovercoming the mathematical difficulties.The mechanical properties ofmetals outside the elastic range depend largely on the secondary structureof the actual crystal, Le., the structure involving mosaics, dislocations,lattice defects, etc., and it is a weakness of the theory that it does not lenditself readily to the calculation of such effects.2. The Pauling Hypothesis.-The first paper by Pauling406 on metallicbonds appeared in 1938 and was concerned mainIy with the metals frompotassium to copper, and with the corresponding elements of the later400 E. Wigner and F. Seitz, Physical Rev., 1933, 43, 804; 1934, 46, 509; E.Wigner,Physical Rev., 1934,46, 1002 ; J. Bardeen, J . Chem. Physics, 1938, 6, 367. For generalreviews see refs. 397 and 399.401 H. Jones, PhySicu, 1949, 15, 13 (Discussion 21).402 K. Fuchs, Proc. Roy. SOC., 1935, A , 151, 585; 1936, A , 153, 622.403 Z . Matyas, Phil. Mug., 1948, 39, 429; 1949, 40, 324.404 M. F. Manning, Physical Rev., 1943, 63, 190; J. B. Greene and M. F. Manning,*05 M. F. Manning and M. I. Chodorow, ibid., 1939, 56, 787.406 L. Pauling, ibid., 1938, 54, 899.* It will be appreciated that the elastic constants permit the calculation of theibid., p. 203.characteristic temperature of a crystalHTJME-ROTHERY : METALS AND ALLOYS. 45periods of MendelGev’s table. I n each Long Period there is a markeddecrease in atomic diameter * on proceeding from the alkali metal to themetals in Groups 11, 111, IV, and V.On passing to Group VI the atomicdiameter still decreases although to a lesser extent, and then in Groups VIIand VIII the atomic diameters become approximately constant, and showa slight increase on passing to copper, silver, and gold in Group IB. Thesegeneral effects are summarised in Fig. 1, and clearly suggest that the firm-ness of the atomic binding in the metallic crystals increases to a maximumin the region of Groups VI-VII.The same general conclusion is reached by a study of the melting pointsof the elements which in all three Long Periods reach a maximum inGroup VI.The reciprocal of the compressibility, which may be called the incom-pressibility of a metal, indicates the difficulty with which the atoms can bepulled apart, and is thus a measure of the strength of binding.I n theelements of the Long Periods the incompressibilities rise to maxima in theregion of Group VI, and thus again suggest that the atomic binding isstrongest in this region.In the electron-band theory of metals the assembly of electrons is con-sidered as a whole, and the mathematical treatment develops from theconsideration of the properties of the assembly in a uniform potential (free-electron theory) to that of their behaviour in a simple periodic field, andthen to more complicated developments in which the wave-functions in theregion of the atoms are assumed to have symmetry characteristics resemblingthose (s, p , d functions) of free atoms.Each electron is represented by awave-function extending over the whole crystal, and the emphasis is on thecrystal and the assembly as a whole. I n contrast to this the Pauling theoryapproaches the problem by considering the behaviour of the electrons inthe immediate vicinity of each atom, and deals particularly with the numberof electrons concerned in binding an atom to its immediate neighbours.Ideally, each method of approach if pushed sufficiently far would lead to acomplete solution of the problem of the structure of metals.In Pauling’s fmt paper406 the conclusion is reached that the metallicbond is closely related to the ordinary covalent or electron-pair bond. Thisconclusion had previously been advanced by V.M. Goldschmidt 407 whoregarded the typical covalent diamond structure as commensurable withthose of the metals. The alkali metals crystallise in the body-centredcubic structure in which each atom has eight close neighbours at a distance0.866 a (where a is the side of the unit cell) and six further neighbours a t adistance a. In these metals, according to Pauling, the atomic bondinginvolves four orbitals of each atom (one s and three p ) , and the metallicbond results from resonance between all the possible arrangements of the*O7 V. M. Goldschmidt, 2. physikal. Chem., 1928, 133, 397.* The atomic diameter is taken to be the closest distance of approach betweentwo atoms in the crystal of the elementFIG. 1.(b)7st Long period, 5K4343i,@Bod’- centped cubic structure.face -centred cu6ic structure. @The interatomic distances of the elements.[The crystal structure of a-manganese is complex, and the interatomic distances vary[Reproduced, with permission, from @‘Electrons, AtomsHUME-ROTHERY : METALS AND ALLOYS. 47available electrons in one- or two-electron bonds between the 14 closeneighbours of each atom.The transition elements are those in the free atoms of which an octet(w2, np6) of electrons expands into a group of 18 electrons (m2, np6, &lo)by the building up of a sub-group of ten d electrons. Pauling assumes thatin the crystals of these elements the bonding involves the d orbitals, sothat there are altogether 9 orbitals to be considered (one s, three p , andfive d).* Pauling then interprets the characteristics of Figs.l ( a ) and l(6)by assuming that on passing from potassium to vanadium the numbers ofbonding electrons increase in unit steps from 1 to 5 per atom with a regularincrease in the number of covalent bonds between which resonance canoccur, and consequently with a steady increase in the strength of thecohesion. Since the covalent bonds involve paired electrons of oppositespin this interpretation accounts for the fact that the metals concerned areneither strongly paramagnetic nor ferromagnetic in spite of the presence ofan incomplete d shell.In order to account for the existence of an almost constant atomicdiameter after Group VI (see Fig. 1) Pauling assumes that some of the dorbitals are not available for bond formation, and from a consideration ofthe saturation moments of the ferromagnetic metals, iron, nickel, and cobalt,he concludes t that of the five 3d orbitals, 2.56 are concerned in bond forma-tion, whilst the remaining 2.44 orbitals are atomic d orbitals which do not takepart in binding the atoms together, and in which the electrons enter so asto have the same spin as long as this is possible, in accordance with theprinciple of maximum multiplicity.These non-integral numbers or orbitalsrepresent a situation in some ways the same as if at a given instant someatoms were in one state and some in another, the fractional number beinga time-average. Pauling assumes that in chromium 0.22 electrons per atomAtomic d orbital.- Metal.+Cr ......... 0.22 0Mn ......... 1.22 0Fe ........ 2-22 03.22&CO ......... 2.44 0.784.22 - Ni ......... 2.44 1.78Total numberSatn. moment, of electrons in Totalbonding 3d number ofassumed. observed. hybrid orbital. electrons.0.22 - 5.78 61-22 - 5.78 72-22 2.22 5.78 81.66 1.61 5.78 90.66 0.61 5-78 10have entered the atomic orbitals, and that this number increases by unityfor each step along the Periodic Table. In this way the above scheme is408 &I. F. Manning and H. M. Krutter, Physical Rev., 1937, 51, 761.* Manning and Krutter 408 had previously shown that for calcium in the First LongPeriod the approach of the atoms is sufEciently close for the 49, 4p, and 3d bands tooverlap, so that the valency or bonding electrons are in hybrid 9, p , d states.t This section describes the first of Pauling’s papers and the details are slightlymodified later (see p. 49)48 GENERAL AND PHYSICAL CHEMISTRY.drawn up for the electronic distribution in the crystals of the elements con-cerned. This scheme requires the number of bonding electrons to be roughlythe same in the whole series of elements from chromium to nickel. It showsthat (subject to the empirical assumptions of the numbers involved) on pass-ing from chromium through manganese to iron the numbers of electrons peratom in the atomic d orbitals will be less than the number of orbitals (2-44),so that all these electrons can have the same spin with a correspondingincrease in the saturation moment. On passing to cobalt the number ofelectrons to be distributed among the d orbitals (3.22 per atom) is greaterthan the number of orbitals (2.44), and so some of the atomic 3d electronswill be paired, with a resulting saturation moment 2.444.78 = 1.66,whilst on passing to nickel the saturation moment is 2.44-1.78 = 0.66.The scheme requires a maximum saturation moment to be shown at23% of the way between iron and cobalt, and experimentally the atomicsaturation moment of iron-cobalt alloys rises to a maximum a t 26 atomic-%of cobalt.It must be emphasised that the choice of these numbers is a purely adhoc assumption made in order to agree with the observed saturation moments.The general idea that the number of electrons per atom involved in bondingincreases from 1 to 5 per atom on passing from Group IA to Group VA isit reasonable and straightforward interpretation, but the scheme gives noexplanation of the maximum cohesion observed in Group VIA.Thesplitting of the d band was not a new idea since it had been shown as longago as 1928 by BetheM9 and is an inevitable consequence of the assemblyof the atoms into a crystal structure. The Pauling theory interprets butdoes not explain the magnetic properties, since the assumptions were chosenso as to agree with the experimental facts. Pauling assumes that thebonding 3d electrons are those whose wave-functions overlap appreciably,whilst the atomic 3d orbitals overlap less and can consequently give riseto the positive exchange integral involved in ferromagnetism.This generalpicture of the building up of an inner core of 3d electrons on passing fromGroup VI to Group VIII appears very probable. It provides a differencebetween atoms of nearly the same atomic radius, and this may be one of thereasons 4lO why superlattices are formed in solid solutions in these elements.This fact could not be understood in terms of older theories because thewide solid solution in the systems Fe-Co, Fe-Ni, and Co-Ni suggested aclose similarity of the atoms, and some difference was needed to explainwhy the ordered structures were formed.The Pauling view of the transition elements was thus an attractiveinterpretation, and the idea that the d orbitals are concerned in the metallicbonding is confirmed not merely by the more refined band theories4M*405in which d functions are introduced, but also by the chemistry of co-ordination compounds which has been successfully interpreted in terms40B H.Bethe, Ann. Physik, 1928, 87, 55; 1929, 3, 133.*lo W. Hwne-Rothery and J. W. Christian, PhiE. Mag., 1946,36, 835HUME-ROTHERY : METALS AND ALLOYS. 49of hybrid s, p , d orbitals. More doubt exists about the extension of thetheory to copper, silver, and gold which was dealt with only very brieflyin the first paper 406 but developed in detail later (see below).3. Co-ordination Number and Bond Radii of the Metal Atoms.-In thelater extension of the Pauling theory the essential assumption made isthat in copper, silver, and gold, and in the succeeding elements in thePeriodic Table, the outermost d electrons of the ions are still involved in themetallic bonding, so that in zinc, for example the bonding electrons are inhybridised ( 3 4 48, 4p) orbitals.By means of the empirical methodsdescribed below, which are based on the interpretations of observed bondradii, it is then concluded that the valencies (i.e. the numbers of electronsper atom involved in resonating covalent bonds) of the elements in Groups IB,IIB, and IIIB are 5.44, 4.44, and 3.44, respectively. This is in completecontradiction to all earlier theories and it seems doubtful whether a valencyof 4.44 for zinc can be reconciled with the data of Beardea et d 4 1 1 for softX-ray absorption and emission, since these results suggested that the 3delectrons were too deep down in the atom to be affected by alloying. Inview of the satisfactory quantitative theory of the zinc crystal in terms ofthe normal valency of 2, the new valencies should be regarded with suspicionuntil they receive quantitative confirmation ; that they are not impossibleis shown by the existence of co-ordination compounds of copper in which(spd) hybrid orbitals are involved.In Pauling’s second paper 412 an equation is used to express the relationbetween the apparent atomic radius and the bond number (which may befractional), the bond number being the number of shared electron pairsinvolved.The equation iswhere n is the bond number, Le., the number of shared electron pairsinvolved in the bond. This is empirical although the type of law has apartly theoretical basis in terms of the number of canonical structures.The value of C is empirical and may not be constant. This relation is thentested by comparison between the bond lengths (i.e.the distances betweenclosest neighbours) in the face-centred cubic and body-centred cubicmodifications of iron, titanium, zirconium, and thallium which crystallise inboth structures. If the co-ordination number of the body-centred cubicstructure is taken to be 8, the empirical relation is not confirmed, and thisis taken to indicate that an individual atom is bonded not merely to its8 closest but also to the 6 next closest neighbours. Attempts to obtain anempirical equation which covers all the data are unsuccessful, and Paulingtherefore drops the empirical equation, and uses the data from the abovefour elements to construct a curve from which the radius for co-ordinationnumber 12 can be deduced when an element crystallises in the body-centred4l1 J.A. Bearden and H. Friedman, Physical Rev., 1940, 58, 387; J. A. Beardenand W. W. Beeman, ibid., p. 396.418 L. Pading, J . Anaer. Chena. Soc., 1947,6$, 642.R, - 22% = C lo50 GENERAL AND PHYSICAL CHEMISTRY.cubic structure. This procedure means, of course, that the finer detailsof the atomic radii which are later deduced are not related to fundamentalcovalent-bond theory but are based on arbitrary relations deduced frommetallic structures themselves. A further objection to Pauling’s procedureis that the four elements used to deduce the correction curve are all of variablevalency, and there is no reason why the different allotropic forms shouldrefer to atoms with the same number of valency electrons.Subject to the above assumption, Pauling then deduces a series of metallicradii, R12, for co-ordination number 12, and a corresponding series of single-bond radii, R,, obtained from the empirical equation by assuming that thebond number is vf12 where v is the valency of the element.In this partof the paper there appears to be confusion between observation, interpret-ation, and theory. I n the case of a- and p-manganese, for example, thecrystal structures are abnormal with several close interatomic distances,and ever since the original work of A. J. Bradley413 in 1927 it has beensuggested that these structures contain atoms in two or more electronicstates. Pauling assumes the existence of the abnormal structures, and byapplying his empirical relations to the varying inter-atomic distances is lednaturally to the conclusion of the existence of atoms of differing valencies.He then states that, “This fact explains the occurrence of this unusualatomic arrangement.” The circular nature of the argument is a t onceobvious. The only established fact is the abnormal crystal structure; theremainder of the discussion is empirical assumption or interpretation.Thecase of chromium which is assumed to crystallise in both body-centredcubic and close-packed hexagonal structures is discussed in detail but israther unconvincing because the careful work of Grube and Knabe *14makes it probable that this metal crystallises only in the body-centred cubicstructure ; the supposed modification with a close-packed hexagonal struc-ture is presumably caused by the presence of hydrogen absorbed duringelectrolytic deposition.*In the later part of the second paper 412 Pauling compares the single-bond radii deduced as described above with other atomic radii (tetrahedralradii, octahedral radii, radii from metal hydrides, etc.).In the series of413 A. J. Bradley and J. ThewIis, Proc. Roy. SOC., 1927, A, 115, 456.4 l 4 G. Grube and R. Knabe, 2. Elektrochem., 1936, 42, 793.415 A. J. Bradley and E. F. Ollard, Nature, 1926, 117, 122.d f 6 H. Sasaki and S . Sekito, Tram.Electrochem. Soc., 1931, 59, 437.* The resistance/temperature c m e was determined by Grube and Knabe up to1800” and showed a very slight irregularity a t about 1580”. The discussion in thepaper makes it clear that this was almost certainly connected with the oxide contentof the metal, and did not indicate a polymorphic transformation. The hexagonalmodification was first described by Bradley and Ollard415 and later by Sasaki andSekit0.4~~ Both these observations were made on electrodeposits, and in the dis-cussion on the paper of Sasaki and Sekito the suggestion was made that the hexagonalform occurs only in the presence of hydrogen, and that the body-centred cubic form isproduced when the hydrogen is given off. The hexagonal modification is included inmost collected tables of crystal structures, but is clearly not sufficiently well establishedfor the pure metal to justify a detailed discussion of interatomic distancesHUME-ROTHERY : METALS AND ALLOYS.51elements Na to Cl, the new single-bond radii are in good general agreementwith the other radii, but in the series Li to F, and in the later elements ofthe Periodic Table, there are discrepancies which are explained only byintroducing assumptions which are as numerous as the facts explained.The second paper by Pauling thus emphasises what was only brieflyreferred to in the first paper, namely the high valencies ascribed to copper(5.44), zinc (4.44), and gallium (3.44). The paper contains little whichconfirms these arbitrary assumptions, and little or nothing which explains,predicts, or generalises the data in a useful way, and none of the doubtfulpoints contained in the 1938 paper is removed.4.BrilIouin Zones and Alloy Structures.-In the band theory thesymbol N(E) is used to denote the number of electronic states per unitvolume of metal with energies between E and E + dE, and diagrams aredrawn in which N(E) is plotted against E, and the region of states occupiedN(E) 1 AFIG. 2.a t the absolute zero is shaded. We may imagine the electron states to beshown in a 3-dimensional wave-number diagram with the components(&, k,, kz) of the wave-number k as co-ordinate axes. In the free-electrontheory the states occupied by electrons at the absolute zero occupy a spherein the wave-number diagram, and the surface of this sphere is called thePermi Surface.It can readily be shown that this sphere of occupied statesleads to the relation N(E)ccE* and the N(E) curves of the free-electrontheory are thus of the form shown in Fig. 2(a). As explained above(p. 43), the wave-like characteristics of the electron mean that for eachdirection of the wave-number, there are critical wave-lengths which satisfythe condition for reflection by planes of atoms within the crystal, and it canbe shown that as the wave-number is increased there is a sudden increasein energy a t each of these critical wave-numbers. The critical wave-numbers lie on planes in E-space, and these planes bound the so-calledBrillouin Zones. If now we represent the electron states in a 3-dimensionalk-space diagram we find the latter divided into a number of polyhedralzones; inside these zones the energy increases continuously with the wave52 GENERAL AND PHYSICAL CHEMISTRY.number, whilst there is an abrupt increase in energy on passing from a statejust within the zone to one lying just outside.It follows therefore that onincreasing the number of electrons per unit volume, the Fermi surfaceexpands until it touches the surface of the first Brillouin zone. At thisstage the abrupt increase in energy on passing through the zone boundarymeans that on further increasing the number of electrons they do not atfirst pass into states lying outside the zone; this naturally produces a fallin the N(E) curve which takes the forms of Fig.2(b) or (c). If the energygap a t the surface of the zone is sufficiently large, an increasing number ofelectrons will result in the whole of the states of the first zone being occupiedbefore any electrons enter the states of the second zone, and the curves forthe two zones will be separated as shown in Fig. 2(b). If, on the other hand,the energy gap is relatively small, the lowest states of the second zone mayhave lower energies than the highest states of the first zone, and in this casethe two N(E) curves overlap as shown in Fig. 2(c). This second kind ofcurve is characteristic of most metallic structures.In a pure metal the number of electrons per atom is fixed, but if we alloya metal with one of higher or lower valency we can increase or decrease theaverage number of valency electrons per atom, and in this way can producea variation analogous to that referred to above.Referring to Fig. 2 it canreadily be seen that on increasing the number of electrons so that theoccupied states increase from A to B, the rapid fall in the N(E) curve willmean that a larger increase in energy is involved for each electron added.*In H. Jones’s theory 417 it was therefore concluded that, on adding an elementof higher valency to one of lower valency, a given crystal structure wouldtend to become relatively unstable when the electron concentration (ie., thenumber of electrons per atom) reached the value denoted by the region A-B inFig. 2, because if all other possible crystal structures were considered therewould probably be one of them whose N(E) curve remained high, and whichcould therefore accommodate the electrons with a lower energy.In the sameway a structure whose N(E) curve rose to a pronounced peak as a t A inFig. 2 would tend to be stable a t this electron concentration because thehigh N(E) curve would mean that the electrons were accommodated with alow energy. The Jones theory can be summarised by saying that, so far asthe electronic energy is concerned, alloys tend to assume structures whoseN(E) curve is high 7 and which can therefore accommodate the electronswith a low energy. This theory was applied with conspicuous success tothe structure of y-brass. It so happens that for this structure the shape ofthe first Brillouin zone is not very different from that of a sphere, with theH.Jones, Proc. Roy. SOC., 1934, A , 147, 225, 396; Proc. Physical SOC., 1937,49, 250. * The Jones theory applies only to alloy systems where the constituent atoms areof similar size and electrochemical characteristics, so that the structure is determinedpredominantly by the electron concentration.-f A high N(E) curve means a large number of energy states of the value concernedso that a given increase in the number of electrons involves a relatively small increasein the maximum energyHUME-ROTHERP : METALS AND ALLOYS. 53result that the N(E) curve (Fig. 2) falls very steeply from A to B to C, andthe number of electron states per atom in the complete zone is not muchgreater than that corresponding to the peak at A .This led to a mostunfortunate position in which the Jones theory was misunderstood as beingone which indicated that stability would be produced by a number ofelectrons suflicient to fill a zone completely. The true position is as explainedabove, and in metallic structures there is nothing to suggest that anystability is conferred by a number of electrons which suffice to fill a zone.*In the third development of the Pauling hypothesis, Pauling andE ~ i n g , ~ ~ ~ attempts are made to extend the Jones theory to the structureof @-brass, y-brass, a-manganese, and @-manganese by assuming that theelements exert the valencies of the Pauling hypothesis (Cu 5.4, Zn 4.4,Ga 3.4) instead of the usual valencies (Cu 1, Zn 2, Ga 3).The use of thevalencies deduced from the interatomic distances in crystal structures ofthe elementis involves the assumption that these valencies are constants ofthe elements and independent of the crystal structure. This appearsimprobable if the non-integral values are to be interpreted as averages ofwhole-number valencies.It is well known that in the so-called electron compounds a phase of a givenratio of valency electrons to atoms when the elements are given their normalcrystal structure tends to occur at definite valencies (e.g., Cu 1, Zn 2, Ga 3).Pauling and Ewing show what had not previously been appreciated, namelythat the principle would still apply if the valencies of the same elementsdiffered by steps of - 1 (e.g., Cu 5-4, Zn 4.4, Ga 3.4), instead of by +1 onpassing along the series.?The use of Pauling valencies does not therefore invalidate the empiricalrelation between crystal structure and electron concentration, but thearbitrary procedure by which some of the d electrons are included in thezones whilst others are omitted has been criticised by N.F. Mott.*19 Apartfrom this, most of Pauling and Ewing’s discussion is unfortunately basedon the assumption that the number of electrons required to fill a zone isthe significant quantity. For y-brass where the properties indicate anearly full zone this misunderstanding is not serious. For @-brass it is,*18 L. Pauling and F. J, Ewing, Rev. Mod. Physics, 1948, 20, 112.*l9 N. F. Mott, “ Discussion at Amsterdam Conference on Metals,” 1948.* I f a substance is an insulator with an N(E) curve of the type of Fig.2 ( b ) , a structurewith a completely filled first zone may be regarded as more stable than one with a fewmore electrons, because of the abrupt increase in energy from A to B. In the genera1case of overlapping zones, there is no reason why the number of electrons required tofill a zone should be significant.t Thus the &brass structure occurs a t composition CuZn, Cu5Ga, CuSSn, and ifCu, Zn, Ga, and Sn are assigned valencies of 1,2,3, and 4 respectively, these compositionscorrespona to an electron : atom ratio of 3/2. If the valencies had been taken as Cu,5.4, Zn = 4.4, Ga = 3-4, and Sn == 2.4 the electron : atom ratios of the above com-position would be16.2 + 3.4 = 4.9, Cu,Sn - 27 + 2.4 4.9.4 6 CuZn = 5*4 = 4.9, ~ u , ~ a =54 GENERAL AND PHYSICAL CHEMISTRY.however, most unfortunate that the theory of Jones which predicts thepeak on the N(E) curve of Fig. 2 a t the observed electron concentrationof 1.48 should be dismissed by Pauling and Ewing because this value doesnot correspond to a completely filled zone. The attempts to show that largezones can be obtained which are nearly filled at the electron concentrationrequired by the high valencies are thus of little significance. Apart fromthis, Pauling and Ewing’s treatment is inconsistent in that the zone for@-manganese is regarded as associated with reflections weaker than thosewhich are completely ignored in dealing with other structures.Paulingand Ewing 418 are also incorrect in suggesting that the concept of a sphericalFermi surface can be reconciled with the high valencies of their assumptions.The assumption of a spherical Fermi surface is a reasonable approximationwhen the number of electrons is small and they are essentially of an s type.It is, however, well established 419 that, when p and d functions are incor-porated, the Fermi surface is often entirely different from that of a sphere.It does not seem unreasonable to say, therefore, that Pauling and Ewing’sapproach involves misunderstandings and inconsistencies which preventit from providing any real confirmation of the Pauling hypothesis.5. Metallic OPbitals.-In the later developments of the Pauling hypothes-is, the picture is slightly modified.The number of atomic non-bonding dorbitals is still assumed to be 2.44 per atom. Since the total number of(s, p , d ) hybrid orbitals is 9 per atom, this leaves 9 - 2.44 = 6-56 orbitalsper atom to be accounted for. The figures given previously indicate thatnot all of these orbitals are used, and in the later papers * 420, 421 Paulingassumes that 5.78 orbitals per atom are involved in the formation of stable(spd) bonding orbitals, and that the remaining 0-78 orbitals per atom, whichare called metallic orbitals, are a characteristic of metals and are necessaryto permit unsynchronised resonance between the individual valency bonds.In all cases the fractional numbers are to be interpreted as averages, so thatin the structures concerned about three quarters of the atoms possess theextra metallic orbital.This concept is used to discuss the structure ofwhite tin in which the interatomic distances are markedly greater than ingrey tin (diamond structure). The conclusion is reached that in white tinthe valency is less than 4, a suggestion which had been made from simplerconsiderations as long ago as 1936.422 The picture of white tin presentedby Pauling involves the existence of (a) neutral bivalent atoms, (b) ter-covalent tin atoms with a negative charge, and (c) uni-covalent atoms witha positive charge. This is essentially an interpretation of the interatomicdistances and is not supported by any other quantitative evidence.020 L. Pauling, Proc. Roy. Soc., 1949, A , 196, 343.4z1 L. Pauling, J., 1948, 1461.422 W. Hume-Rothery, “ The Structure of Metals and Alloys,” Institute of MetalsMonograph Series, 1936.* Some confusion in publication appears here since in the 1949 paper 420 it is statedthat this conclusion was reached in the earlier papers 40% 412 whereas actually thesecontain no references to the metallic orbital, although it can be seen from the 1947paper 412 that a11 the orbitals were not being usedHUME-ROTHERP : METALS AND ALLOYS. 55The implications of the assumption of the ‘‘ metallic ” orbital have beendealt with fully by Pauling in his 1949 paper a20 vhich begins by discussingthe relative proportion of s and p character in the bonding orbitals of thediatomic molecules Li,, Na2, K,, Rb,, and Cs,, and of the orbitals in thecorresponding metals as interpreted by the resonance-bond hypothesis.This discussion is interesting and suggestive. In the remainder of thispaper increasing emphasis is placed upon the interpretation of the fractionalvalencies of the earlier papers as being averages of integral valencies, andspeculations are made regarding the actual valencies of which the fractionalvalues represent the average. The further hypothesis is then advancedthat a special stability will be found if the resonance results in a simpleratio of the number of bonds to the number of positions, so that a specialstability is associated with bond numbers which are simple fractions (i,4, 8, . . .); the importance of a bond number equal to Q had previouslybeen emphasised by Rundle.*,3 These considerations are then used todeduce a system of single bond radii, and of metallic radii for the metallicatoms in different valency states. This treatment requires slight modific-ations to be made to the valencies described in ( b ) and (c), but the generalpicture remains unchanged. It is legitimate to claim that the radii deducedform a consistent scheme, but it should be emphasised that the numericalvalues are often essentially the observed experimental values modified byrelations which are largely empirical and are sometimes adjusted directlyto fit the observed facts.In the same paper the structures of a few intermetallic compounds arediscussed, but the number of these is too small to enable any conclusion tobe drawn as to whether the new hypothesis will permit any useful generalis-ation, and the treatment is essentially an interpretation which provides noevidence in support of the hypothesis.6. Conclusion.-From the above description it will be seen that thePauling hypothesis is at present essentially a discussion of known experi-mental data in terms of empirical assumptions for which no independentevidence is available. The papers may properly be called an interpretationof the facts, but the number of arbitrary assumptions is so great that littlehas really been explained or calculated, whilst no useful generalisationshave yet resulted. At the same time, the general method of approach tothe problem, namely by considering the electronic characteristics in theimmediate vicinity of the individual atom, is extremely suggestive and offersa useful alternative to that of the accepted theories. It seems highlyprobable that Goldschmidt’s original suggestion of the resemblance betweenthe covalent and metallic bonds is essentially correct, and the extensionof this idea in terms of orbital and resonance theory is desirable. Theoriginal hypothesis of Pauling that the number of electrons involved inbonding increases from one to between five and six per atom on passingfrom potassium to chromium seems highly probable, and seems to emphasis0429 R, E. Rundle, J . Amer. Chem. Soc., 1947, 69, 1327, 171956 GENERAL AND PHYSICAL CHEMISTRY.the part which may be played by d eIectrons in the cohesion of the earliertransition elements. The postulate of non-integral numbers of bondingelectrons per atom is purely arbitrary, but the interpretation in terms ofaverages of atoms in different states is almost certainly correct, and mayprovide a useful clue towards the understanding of the characteristics ofthe alloys of the transition metals. At the same time it should be recognisedthat this interpretation makes it probable that the average valency of themetals concerned will be different in different crystal structures. So longas one is dealing with the normal metallic structures (face-centred cube,body-centred cube, and close-packed hexagonal) it is reasonable to assumethat the average valency of a given metallic atom, in the Pauling sense,will be approximately constant. There is, however, no reason to supposethat the same average valencies will hold in completefy different structuresand the attempts made by some writers to interpret the structure of inter-mediate phases in alloys by assuming a constant series of Pauling valenciesare unconvincing and premature until the hypothesis has been more firmlyestablished. For this purpose the need at the moment is not for furtherdiscussions of structures; what is required is either the calculation ofphysical properties by fundamental methods which do not assume the valuesof the properties concerned, or alternatively the generalisation of facts toa number substantially greater than the assumptions involved.W. HUME-ROTEERY.R. C. PINK.A. R. DBBELOHDE