作者: William Jackson Pope,  


期刊: Annual Reports on the Progress of Chemistry  (RSC Available online 1908)
卷期: Volume 5, issue 1  

页码: 258-279




年代: 1908




出版商: RSC


数据来源: RSC



CRYSTALLOGRAPHY.THE modes in which the behaviour and properties of crystallinesubstances can influence chemical theory may be roughly classifiedunder two headings. First, including those in which, with ourpresent knowledge, no special interest attaches to the crystallinenature of the solid substance; into this category fall all questions ofthe solubility of crystalline substances, and of the equilibriumbetween liquid and crystalline phases, or between two crystallinephases. Questions of this kind are not discussed in thepresent Report, because their experimental treatment has not yetprogressed so far as to render of importance the differences insurface character presented by the various kinds of crystal facesoccurring on one substance, and also because they properly formpart of the report on physical chemistry.The second categoryembraces the relation between the crystal structure and thechemical nature of substances, and to this subject alone the presentReport is confined.As a result of the study of crystalline structure, both in its ex-perimental and theoretical aspects, during the past hundred years,it may be stated that the whole of the physical, geometrical, andmechanical properties of crystalline substances are in harmony withthe following geometrical definition. A crystalline structure is ahomogeneous one, that is, a structure the parts of which are uni-formly repeated throughout, corresponding points having everywherea similar environment. The correspondence between this statementand the facts is so complete as to prove definitely that the charac-teristic which distinguishes crystals from all other bodies is this homo-geneity of structure.From the principle of structural homogeneitymay be a t once deduced the various forms in which the empiricallyobserved fundamental law of crystallography has been stated, suchas the law of zones, the law of rational indices, etc., and it is to beconcluded that the distinguishing feature of external regularity ofform assumed by a crystalline substance is correlated with theclass of homogeneous structure to which it belongs.An investigation into the structure of crystalline substances, aCRYSTALLOGRAPHY. 259defined above, may be regarded as involving two distinct inquiries.The first of these is concerned with the kinds of homogeneousstructure geometrically possible, and the second, with the natureof the units of which the homogeneous structure is built up.Thefirst inquiry, regarded as a purely geometrical one, has now beenprosecuted to a stage approaching finality. The second inquiryinvolves the application of geometrical methods to specific cases'which have been experimentally investigated ; its pursuit isattended with much difficulty, and it is but in the early stages ofdevelopment.The work which has been done on the possible kinds ofhomogeneity of structure has been well summarised in a report tothe British Association on the structure of crystals,' so that itwill suffice now to indicate very briefly and roughly the successivestages by which our present highly complete knowledge of thesubject has been attained.(1) Bravais (1850) effected an exhaustive inquiry into the variousways in which small identical regular bodies can be distributeduniformly throughout unlimited space, so that every one of themhas the remainder of the assemblage arranged about it in anidentical manner, and with the same orientation. The last con-dition involves the property that a linear translation of the entireassemblage, the length an4 direction of which are those of a linejoining the centres of any two of the bodies, produces coincidenceof the moved assemblage with the assemblage as it stood beforethe translation; the centres of the bodies consequently form aparallelopipedal network or a so-called " space-lattice.'' Bravaisshowed that fourteen kinds of such space-lattices exist, and thatthese correspond in their symmetry with the seven large crystalsystems.It may be noted that any movement or operation, such asthe translation just mentioned, which, after performance, leavesthe assemblage identical in aspect with its original, is convenientlytermed a '' coincidence movement "; in addition t o the linear trans-lations, some of the Bravajs space-lattices possess other coincidencemovements which are rotations about axes. The occurrence ofrotations about an axis as coincidence movements is expressed bynaming that axis one of symmetry, and, if the angular rotationproducing coincidence is 36Oo/m, the axis is described as one ofn-fold symmetry. The axial ratios of a crystalline substance, statedin the customary form of the value of a : b : c , represent the ratio ofthree linear translations of the space-lattice distributed in three-dimensional space.(2) Sohncke (1876) determined the possible kinds of homogeneousThese stages are three in number.Brit.Assoc. Report, Glasgow, 1901, 297.s 260 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRYarrangement derivable by enlarging Bravais’s definition, the modifi-cation consisting in the abandonment of the condition that thesimilar environments of the units must be similarly orientated.This change of definition abolishes the necessity for attributing anyaxial crystal symmetry to the unit itself, and renders possible thegeometrical dissection of every symmetrical Bravais unit intoidentical smaller units devoid of axial symmetry.Substitutingmere points or small spheres for Bravais’s small regular bodies, andmaking the former as numerous as the coincidence movements,axial and translational, of the system under consideration, Sohnckemakes the configuration, namely, the coincidence movements ofhis systems of points, express all the identical repetition of partspresent. He discriminates sixty-five types of homogeneous structure,and these are known as Sohncke systems; in addition to the kindsof crystal symmetry exhibited by the Bravais space-lattices, theSohncke systems furnish types corresponding in symmetry withmost of the thirty-two crystal classes into which the seven largecrystal systems are subdivided.(3) The final step soon followed Sohncke’s important develop-ment of the possible ways of deducing homogeneous structures.It was perceived that the coincidence movements of a Sohnckesystem represent only identical repetition of parts, and leaveenantiomorphous likeness (or mirror-image resemblance) of parts tobe expregsed by some added condition.Bravais had modified theSymmetry of some of his space-lattices to meet this requirement byattributing to his small bodies the lower symmetry needed forcorrespondence with the facts. To avoid the necessity for any suchunsatisfactory contrivance, a further modification of the conditionof similar environment was now resorted to; it was seen that twopoints in an assemblage are similarly, although not iaentically,environed if the arrangement of the unlimited assemblage aboutone of them is the mirror-image of its arrangement about theother ; also that coincidence operations about centres of symmetryor planes of symmetry then perform the function fulfilled in theSohncke systems by the coincidence movements, and express therelation between similar points enantiomorphausly related.Fedoroff, Schonflies, and Barlow independently investigated theadditional forms supplied by this enlarged conception of similarityof environment, and proved that the admission of coincidenceoperations connecting similar points, the environments of whichpresent mirror-image similarity, leads to the discrimination of manymore types of symmetry ; the latter now provide representativesof all the thirty-two classes of crystal symmetry.The investigatorsjust named are agreed that the total number of types of symmetricaCRYSTALLOGRAPHY. 261.structure made possible by the further enlargement of definitiondefined above is 230, and these are described as the 230 types ofpoint-systems. As no kind of operation, other than such as areemployed in the Sohncke systems and the systems derived fromthem by mirror-image duplication, can form a component of acoincidence operation consistent with homogeneity of structure, thefirst part of the inquiry into crystal structure, that dealing withthe mode of arrangement of the parts, is virtually ended.A simple illustration will make clear the distinction betweenthe three kinds of similarity of position of members of a flock ofsimilar parts just described. Consider a stack of cubes, such as areused by children, built up in the ordinary way, so that the cubesare in face contact, and so that throughout the stack each cubecorner makes contact with seven other cube corners.The assemblageof points formed by the cube corners is a Bravais space-lattice.Each point in this space-lattice is common to twelve cube faces,each cube face being also common to two cubes in contact. Replaceone point of the space-lattice by a cluster of twelve points, onelying on each diagonal of a cube face drawn from the originalpoint, and all being equidistant from the original point.Repeatthis process throughout the system until each point of the space-lattice is similarly and symmetrically replaced by a cluster oftwelve. The assemblage built up by this symmetrical repetitionthroughout space of the cluster of twelve points about the originalcube corners of the space-lattice is a Sohncke system, and consistsof twelve interlaced space-lattices which are related by simple axialrotations: all the points are identically related to the entireunlimited assemblage.Next displace each point in a cluster of twelve from the planeof the cube face in which it lies, all the twelve being movedsimilarly, symmetrically, and in the corresponding direction, topoints just within the cubes; this operation can be so performedthat the resulting twelve-point cluster is no longer identicalwith its mirror-image.Treat an adjacent cluster in the sameway, but making the arrangement identical with the mirror-imageof the first, and repeat these operations symmetrically and alter-nately throughout space until all the original twelve-point clustershave been appropriately displaced; one of the 230 point systemsis thus generated. It consists of a Bravais space-lattice in whicheach point is replaced by a twelve-point cluster of enantiomorphousform disposed about the original point ; one-half of the clm tershave the right-handed, the others the left-handed, configuration.The assemblage may be also regarded as an interpenetration of aright- and a left-handed Sohncke system, one, namely, whicb i 262 ANNUAL REPORTS ON THE PROGRESS OF CHEMlSTRY.derived by a mirror-image repetition of either the right- or theleft-handed component Sohncke system.After this necessarily brief and incomplete sketch of the resultsarrived a t in the inquiry as to the mode of arrangement of partsholding in crystalline structures, attention may be directed towardsthe second kind of problem involved, that, namely, of the natureof the parts which are arranged.During the past century exactdata concerning the crystalline forms of some thousands of sub-stances have been obtained, and these are now being collected andrepublished by Paul Groth.2 Although until very recently nocomprehensive scheme had been advanced for reconciling thecrystalline form and chemical nature of substances in general,several results obtained, and conclusions drawn, stand out beyondothers as indications for the construction of such a scheme. Thefact that certain definite laws are revealed in the enormous numberof observations made of crystalline forms has led to the convictionthat the geometrical and physical properties of a crystalline materialare absolutely characteristic, and are, consequently, functions of thechemical composition, constitution, and configuration of the sub-stance: the discovery by Mitscherlich (1819) of the general factsof isomorphism, and that substances of the same chemical typeexhibit almost identical crystalline forms, has greatly strengthened,not, as was originally anticipated, weakened, this conviction.Pasteur’s law, that substances of enantiomorphous molecular con-figuration affect enantiomorphous crystalline structures, and thatthe crystal structures assumed by enantiomorphously related mole-cular configurations are themselves enantiomorphously related, hasbeen the subject of considerable controversy.3 The law may nowbe regarded its vindicated, and possesses importance in connexionwith the interdependence of crystalline form and chemical con-~ t i t u t i o n .~ Groth placed the subject of morphotropy on a soundbasis by pointing out that derivatives of benzene, which are not soclosely related as to be isomorphous, frequently exhibit markedquantitative resemblances in crystalline form ; this, again, indicatedthe existence of a function connecting crystalline form andchemical constitution.All these discoveries now form parts of thehistory of chemical crystallography, and have proved the basis ofimportant developments. No less importance attaches to severalmore recent extensions of our knowledge, which may now be brieflydiscussed.Chemische Krystallogrphie, Leipzig, 1806, c t seq.Wnlden, Bw., 1896, 29, 1692 ; A . , 1896, ii, 553 ; Kipping and Pope, Trans.,Pope and Harvey, Trans., 1901, 79, 828.1897, 71, 989 ; Barlow, Phil. Mag., 1897, [v], 43, 110CRYSTALLOGRAPHY. 263Tschermak has pointed out5 the frequent occurrence of astriking relation between the numerical proportions in which atomsof different elements are present in the molecule of a substanceand the nature of the symmetry presented by the crystalline form.He notes that compounds in the molecular formulz of which thenumbers 2 and 3 or 6 occur as denoting the nu;mbers of atoms ofvarious elements present, tend to crystallise in the rhombohedra1 orthe hexagonal system ; these crystalline systems are characterisedby the possession of axes of two- and three- or six-fold symmetry.As instances may be quoted the compounds of the following com-positions ; Fe203, FeCl,, A1C13,6H,0, Ag3SbS3, (C,H,),C*OH,SrCl,,GH,O, PI,, and CHI,.Similarly, those substances in themolecular formuh of which the number 4 occurs, but not thenumber 3, in a large proportion of cases crystallise in the tetragonalsystem ; this system possesses axes of two-fold and four-fold symmetry,but not of three-fold symmetry. As typical examples, the followingsubstances may be noted : ZrSiO,, G1S0,,4H20, (C,H,),Si, andC(CH,*OH),.I n the same way, compounds in the molecular com-positions of which the numbers 4 and 3 cccur tend to crystallisein the cubic system, this system possessing axes both of three- andof four-fold symmetry ; as illustrations the compositions of thefollowing cubic substances may be quoted : 3KF,ZrF,, Ag,PO,,As406, and K,S04,A1,S0,,24H,0. Tschermak’s conclusions are ofgreat significance as condemnatory of the view still occasionallyadvanced that the individuality of the atom is entirely lost whenit enters into molecular combination.The axial ratios by means of which the crystalline form of acrystalline substance are described are the ratios of some of thetranslations occurring in the homogeneous structure of the crystal.I n passing from a given substance to one isomorphous with it,the axial ratios in general change to a greater or less extent;but inasmuch as each set of axial ratios consists merely of ratios ofthe actual dimensions of the corresponding homogeneous structure,the comparison of the axial ratios of two isomorphous substancesdoes not reveal the change in dimensions which has accompaniedthepassage from one substance to the other.The three translations,the ratios alone of which are given by the axial ratios a : b : c, ingeneral all change during such a transition. More informationcan, however, be obtained by the consideration of a solid figure ofwhich the volume is the molecular volume, M , of the substance,and the iinear dimensions, x, I), and w, are in the ratio, a : b : c,of the axial ratios; the linear dimensions of the solid figure,measured in the three axial directions, indicate for a series ofTsch, Illi?~, Mitt., 1903, 22, 393264 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.isomorphous substances the absolute changes in magnitude ofcorresponding translations of the homogeneous structure commonto the substances which occur in passing from one member of theseries to another.I n either of the rectangular systems the values ofx, +b, and o, which are termed the ‘topic parameters’ or the‘ molecular distance ratios,’ are the following :$+,ac aFurther, x$w = M, and cc : b : c = x : $ : o.The molecular dis-tance ratios were introduced by F. Becke,6 and measure the absolutechanges in dimensions which a definite parallelopipedal molecularunit of the structure undergoes during the passage from onecrystalline substance to another or others isomorphous with it.They were applied by W. Muthmann7 to the investigation of thealkali permanganates, and from the differences between correspond-ing molecular distance ratios observed amongst the various saltsof the series, the conclusion was drawn that the unit of thecrystalline structure is composed of four chemical molecules. Theextension of this work to the alkali perchlorates, which are iso-morphous with. the permanganates, has furnished T. V.Barker 8with results which are not in agreement with Muthmann’:,conclusion. The way in which the axial ratios and the moleculardistance ratios are related is shown in the following table, whichgives the values for the alkali permanganates:a : b : c. M. x : q i : w .KMnO, ......... 0.7972 : 1 : 0.6491 58.526 3.8554 : 4-8360 : 3.1350RbMn0, ...... 0.8311 : 1 : 0.6662 63.228 4.0322 : 4.8517 : 3.2312CsMnO, ...... 0.8683 : 1 : 0.6853 70’042 4.2555 : 4.9009 : 3.3584NH,MnO, ... 0.8164 : 1 : 0.6584 62.126 3’9767 : 4.8711 : 3.2071It will be seen that whilst the axial ratios only measure therelative dimensions of translations in the homogeneous structurein the case of any one substance, because one axial dimension, thatof the axis b , is taken as unity, the molecular distance ratiosindicate, in addition, the relative dimensions of correspondingtranslations in the several members of an isomorphous series.The molecular distance ratios have been very systematicallyapplied by A; E.H. Tutton to the investigation of a long series ofsalts,S and the kind of information which they are capable ofyielding is well illustrated by this author’s numbers for the alkalisulphates and selenates.Sitzungsber. K. Akad. FViss. Wien, 1893, 30, 204.7 Zeitsch. Kryst. Min., 1894, 22, 497 ; A., 1894, ii, 181. * 16id., 1907, 43, 529.Trans., 1894, 65, 688 ; 1905, 87, 1183CRYSTALLOGRAPHY. 265x : J , : w .I<,SO, ........................ 3.88'10 : 3'8574 : 4.99644.0340 : 4.0039 : 5.23664.2187 : 4.1849 : 5.2366K,8e04 .......................4.0291 : 4.0068 : 5.1171Cs,SeO,. ....................... 4'3457 : 4.3040 : 5.6058Rh,SO, ........................cs,so, ........................Rh,Se04 .................... 4'1672 : 4'1315 : 5.3461The comparison of these figures shows that in passing from thesulphate or the selenate of one alkali metal to that of its neighbourin the periodic classification, the greatest change in the moleculardistance ratios is in o, which is measured in the vertical directionof the axis c ; the horizontally measured dimensions x and $Iexperience much less change. In passing from a sulphate to thecorresponding selenate, variation in the opposite sense is observed ;the values of x and $I change more than does that of o. Fromthese results Tutton concludes that the molecules of the alkalisulphates and selenates are so disposed in the crystal structure thatone atom of sulphur or selenium lies between two of the alkalimetal, and that all three are extended in the direction of thevertical axis c or of o.He claims that the further analysis ofhis results enables him to identify the particular point system ofthe 230 which characterises the crystal structure of these salts.In order that the notion of molecular distance ratios may besuccessfully applied to series of isomorphous substances, it isessential that the axial ratios used in their calculation should bethe ratios of corresponding translations in the crystal structure,cof a type common to the several members of the series; the knowncondition that the axial ratios of isomorphous substances approxi-mate closely to each other, in general renders it easy to ensure this.The molecular distance.ratios have, however, also been extensivelyapplied to morphotropically related substances, and here it isfrequently difficult to ensure that the axial ratios, and even theaxial directions, selected for the calculation, refer to correspondingdirections and dimensions in the homogeneous structures of theseveral members of the morphotropic series. The series of valuesstated in the following table are given by F. Slavik.10Crystal NH,I. NMe,I. NEt,I. NPr,I.ill ........... 57 -51 108.70 162.91 235-95x ............ 3.860 5.315 6-648 6.093I/I ........... 3'860 5.319 6'648 7.851w ............ 3 860 3.842 3.686 4.933system.Cubic. Tetragonal. Tetmgonsl. Orthorhombic.These numbers suggest that on replacing the four hydrogen atomsin ammonium iodide by four methyl or four ethyl groups, the mainlo ZeitsA. Kryst. Min., 1902, 36,'ZSS ; A., 1902, ii, 661266 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.change in dimensions of the crystal structure occurs in the direc-tions of the axes a and 6, in which the dimensions x and I) aremeasured; it is not, however, immediately evident that the values ofthe axial ratios, a : b : c, have been so chosen in the case of tetra-propylammonium iodide as to correspond with those used in thecase of the other members of the series. Another interesting seriesof alkyl derivatives, those of carbamide, has been worked out byG.Mez.11 In connexion with this question, it may be remarkedthat the practice, now very general, of publishing the moleculardistance ratios of isolated substances is useless, as the values onlypossess significance when compared with appropriately selectedmolecular distance ratios of related compounds.During the past twenty years Tutton has carried out a remark-able series of crystallographic measurements, the results of whichare, for the most part, published in the Transactions of theChemical Society. He has studied, in the majority of cases withthe aid of specially designed measuring instruments, the ortho-rhombic sulphates and selenates of potassium, rubidium, czesium,ammonium, and thallium, and many members of the series ofmonosymmetric double salts of the general compositionin which R is K, Rb, Cs, or NH,, M is Mg, Zn, Fey Ni, Co,Mn, Cu, or Cd, and D is S or Se.I n addition to the determinationof the crystalline form and the refraction constants, the coefficientsof expansion by heat, and other properties of these materials havebeen ascertained in the different principal directions of the crystalstructure. Amongst the principal conclusions which Tutton hasdrawn are that in each case the crystalline form and other proper-ties of the rubidium salt are intermediate between those of thecorresponding potassium and caesium salts; and that, in the caseof the double salts, the alkali metal exerts a predominant influencein determining the crystalline form; it is also shown that theeffect of introducing the ammonium radicle in place of a potassiumatom is nearly the same a,s that of similarly substituting a rubidiumfor a potassium atom.Tutton summarises his conclusions in ageneral law which states that,l2 in an isomorphous series in thestrictest sense, where the interchangeable elements belong to thesame family group of the periodic classification, the whole of theproperties of the crystals, morphological, optical, thermal, andphysical, in general are functions of the atomic weights of theseelements ; the sulphates and selenates of potassium, rubidium, andcaesium, of which the molecular distance ratios are quoted on p. 265,l1 Zeitsch. h-ryst. Men., 1902, 35, 242 ; A., 1902, i, 86.Proc.Boy. Soc., 1907, 79 A 381 ; A., 1907, ii, 688.RM(DO,),,6H@CRYSTALLOGRAPHY. 267belong to such a series, which, for the purpose of distinguishing thecloseness of the relations connecting its several members, is termeda (( eutropic series.” Thallium sulphate and selenate and ammoniumsulphate are only isomorphous with the previously mentionedeutropically related salts in a less rigid sense; this may be expressedby saying that thallium and ammonium are capable of changingplaces with potassium, rubidium, and czsium without alteringthe crystal system and without causing angular and structuralchanges of much greater magnitude than those produced by theinterchange of members of the same family group of elements. Anisomorphous series, in this wider sense, is defined as one the membersof which bear some definite chemical analogy and crystallise accord-ing to the same system and in the same class of that system, anddevelop the same forms inclined a t angles which only differ by afew degrees, rarely exceeding 3O. A eutropic series is one in whichthese small angular differences, and also the structural and physicalproperties of the crystals, obey the law of progression according tothe atomic weights of the interchangeable elements which give riseto the series and which belong to the same family group.Thusthallium sulphate and selenate and ammonium sulphate belong tothe isomorphous orthorhombic series, R,( S,Se)O,, whilst the sul-phates and selenates of potassium, rubidium, and caesium belong,not only to this isomorphous series, but also to the more exclusiveeutropic series included within it.The intimate relationship thusexhibited between potassium, rubidium, and caesium is of similarnature to that expressed by associating these three metals togetheras one Dobereiner triad in the periodic classification. Two generalpropositions, which could not previously be substantiated, areestablished by Tutton’s work. First, that goniometric measurementscan be made on carefully prepared materials of high purity, whichpossess a degree of accuracy comparable with that of atomic weightdeterminations. Secondly, proof is repeatedly found that the sub-stitution of one particular element by another produces a quantita-tively similar change in dimensions of the crystal structure, inwhatever salt the substitution is made; this result constitutes a greatadvance, because it shows that each atom entering into a crystallinestructure produces a definite and constant crystallographic effect,and indeed indicates the mode in which attempts should be madeto define that effect as a constant of the element concerned.The need for some distinction, such as that drawn by Tuttonbetween a eutropic and an isomorphous series, has also been recog-nised by T. V.Barker,l3 who has investigated the mode in whichl3 Trccns., 1906, 89, 1143 ; Jfi7~. Hug., 1307, 14, 235 ; 1908, 15, 42 ; A . , 1907,ii, 240 ; 1908, ii, 366268 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.substances crystallise from solution upon surfaces consistingof crystalline plates of other materials. T'he crystals whichseparate from the solution are in many cases found to assumea definite orientation with respect to principal crystallographicdirections in the crystalline surface upon which they form; theone substance is then said to form parallel growths upon the other.Examination of this property, that of forming solid solutions, anda number of others, as exhibited by the cubic cyanides and halogensalts of ammonium and the alkali metals has led Barker to classifythese compounds in two " isostructural " groups, the memberswithin either of which are especially closely related to each other.It is concluded that no direct connexion exists between the forma-tion of parallel growths and of solid solutions, although the twoproperties are favoured by the same factor, namely, similarity ofmolecular volume.Attention may now be directed to a mode of treating the secondkind of crystallo-chemical problem distinguished earlier in theReport, which offers a systematic scheme for the quantitativecorrelation of crystallographic facts of chemical importance, anddefines the relation subsisting between crystalline form andchemical composition, constitution, and configuration.W. Barlowand W. J. Pope 14 have adopted, for motives of convenience, a methodof regarding the whole of the volume occupied by a crystallinestructure as partitioned out into polyhedra, which lie packed togetherin such a manner as to fill the whole of that volume without inter-stices.The polyhedra can be so selected that each represents thehabitat of one component atom of the material, and are termedthe spheres of atomic influence of the constituent atoms. Up tothis point no assumption is made other than that clearly indicatedby the results of crystallographic measurements, namely, that eachatom present in a crystalline structure exerts a distinct morpho-logical effect--or, what is the same thing, appropriates a certaindefinite volume. The assumption is next made that the crystallinestructure, which is resolvable into individual molecules and ulti-mately into individual atoms, exists as such by reason of equili-brium set up between opposing attractive and repulsive forcesoperative between the component atoms, and that this equili-brium results in the polyhedra representing the spheres of atomicinfluence assuming shapes which are as nearly as possible spherical.The application of the new method of treatment and the assumptiondefined are shown to bring immediately into quantitative corre-spondence a great variety of crystallographic data which could notTrans., 1906, 89, 1675 ; 1907, 92, 1150 ; 1908, 93, 1528CRYSTALLOGRAPHY.269previously be interpreted, and to lead to noteworthy conclusionsrespecting valency and chemical constitution, which can be, andhave since been in part, verified by purely chemical methods.In harmony with the assumption that the spheres of predominantatomic influence tend towards sphericity, the polyhedra thus arriveda t may be regarded as derived by compression of a close-packedassemblage of deformable incompressible elastic spheres, the com-pression sufficing for the practical extinction of the interstitialspace.When such an assemblage is released from pressure it isevident that in place of polyhedra, the shapes of which approximateas closely as possible to the spherical, closely-packed spheres are pre-sented; the distances between the sphere centres can be sub-stantially in the same ratios as the distances between the centres ofthe corresponding polyhedra in the unexpanded mass, and theequilibrium condition of maximum sphericity of the polyhedra willbe represented in the expanded mass of spheres by the existenceof the maximum number of contacts between spheres.The wholemethod of treating the primary assumption thus resolves itself intofinding close-packed assemblages of spheres of various sizes repre-senting by their relative volumes the spheres of influence of thecomponent atoms of any particular crystalline structure.For illustrative purposes, the comparatively simple case presentedby the crystalline elements may be presented. I f the atoms of anelement are all similar, and if their grouping into molecular com-plexes does not appreciably affect the relationship existing betweenneighbouring atoms, the crystalline form assumed by the elementshould have the symmetry and dimensions of the closest-packedassemblage of equal spheres. There are, however, two such closest-packed assemblages,l5 one of cubic symmetry, in which thesymmetry defines all the dimensions, and the other of hexa-gonal symmetry, in which the ratio of a horizontal translation,a, to a vertical translation, c, is a:c=l:1*6330 or 1 :1'4142.Of the crystalline elements, 50 per cent.are cubic and 35 per cent.are hexagonal, and, so far as data have been collected, the axialratios of the hexagonal elements approximate to the values of a : cquoted above.Suppose, however, that some complicating factor is operative indetermining the crystalline form of the element, such, for instance,as a molecular aggregation holding certain sets of atoms togetherin positions of some restraint; this should disturb the simplicity ofthe relation indicated above, and should result in the crystallineform departing to a greater or lesser extent from the closest-packedl5 Trans., 1907, 91, 1159270 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.cubic or hexagonal arrangement of equal spheres.Those elementswhich are neither cubic nor hexagonal would therefore be expectedto assume crystalline forms approximating closely to the cubic orhexagonal arrangement indicated. An inspection of the geometricaldata for the few elements which are neither cubic nor hexagonalshows that they are all so closely allied to the forms indicated thata very slight distortion would make them wholly cubic or hexagonal.It is further very significant that those elements which exhibitcharacteristics usually associated with particular types of molecularaggregation, such as colour, existence in allotropic modifications,etc., are the ones which differ niost markedly in crystallineform from the simple cubic and hexagonal structures indicated;thus, whilst ordinary phosphorus and diamond are cubic, red phos-phorus and graphite are respectively orthorhombic and mono-symmetric. Consideration of the crystalline structure and thetwinning of diamond, together with its relations to graphite, haveled W.J. Sollas l6 to suggest the cubic closest-packed arrangementof equal spheres as representing the crystal structure of diamond,and the tetrahedrally arranged groups of four spheres, into whichthat arrangement is homogeneously partitionable, as representingthe molecules of this allotropic form of carbon.17On turning to the binary compounds, such as NaC1, KI, AgI, andZnO, a further advance is indicated. The molecules of nearly allbinary compounds consist of two atoms of undoubtedly equalvalency, and of these 68.5 per cent.are cubic and 19.5 per cent.hexagonal, the axial ratios of the latter in every case approximatingvery closely to the theoretical value of a : c = 1 : 1.6330, indicatedabove. Whilst, however, the crystal forms of the cubic and hexa-gonal elements nearly all belong, so far as is known, to the holohedralcrystal classes, those of the binary compounds belong to the lesssymmetrical hemihedral, tetartohedral, or hemimorphous classes ofthe two systems. By allocating, in the cubic or hexagonal closest-packed assemblage above referred to, one-half of the polyhedralcells, appropriately selected, to the one kind of component atoms,and the remainder to the other element present in the compound,the cubic or hexagonal crystalline form, with its appropriate corre-sponding hemi- or tetarto-hedrism or hemimorphism, can be preciselyimitated.Other peculiarities of the crystalline structure, such asthe existence of gliding planes in the alkali halogen compounds andthe interconversion of the cubic and hexagonal modifications ofsilver iodide, can also be exactly simulated. Each of the assemblagesl6 Proc. Boy. Xoc., 1901, 67, 493.I7 Compare also Sci. Proc. Roy. UuJZ. Soc:., 1897, 8, 542, and Tram., 1906, 89,1741CRYSTALLOGRAPHY. 271thus devised can be geometrically partitioned into similar unitscomposed of two adjoining spheres of atomic influence, one of eachelement; these, it may be premised, represent the molecules of thebinary compound as they occur in the crystal structure.The close imitation of the crystalline behaviour of the binarycompounds by the closest-packed assemblages of polyhedra or spheres,briefly described above, points to a conclusion of a novel kind, the cor-rectness of which has been repeatedly confirmed in the course of thework now under review. The conclusion is that the volumes appro-priated by the polyhedra representing the spheres of atomic influencein any crystalline structure are approximately proportional to thenumbers representing the valencies of the respective elements con-cerned.Further investigation seems to show that in every casehitherto studied the valency thus exhibited by an element is thelowest which its chemical behaviour assigns to it; this valency isconveniently distinguished as the fundamental valency of theelement. The crystalline forms of the substances CsI,, Tl13, andCsI,, for example, are all in accordance with the view that theconstituent elements are fundamentally univalent. The law thusenunciated is termed the law of valency volumes.It is not indicated that the volumes of the spheres of atomicinfluence are rigidly proportional to the whole numbers repre-senting the fundamental valencies ; on the contrary, the volumesonly approximate to the whole number ratios, and an analysis ofthe data for the crystalline trihalides of the alkali metals showsthat throughout the measured series of sixteen salts, the volumeof the sphere of atomic influence increases slightly in passing frompotassium to rubidium to czsium, and from chlorine to bromine toiodine.The sphere of atomic influence of thallium in thallic iodideis almost identical in volume with that of rubidium in rubidium tri-iodide. The indication thus obtained of the invariability of magni-tude of the sphere of atomic influence of any particular elementis in complete agreement with the general result drawn fromTutton’s work, namely, that the dimensional influence exercised onthe crystal structure by a particular atom is constant. The closeapproximation to identity between the volumes of the spheres ofatomic influence of rubidium and thallium in the salts TlI, andRbI, is striking in view of Tutton’s demonstration that rubidiumand thallous sulphates have almost the same crystallographic dimen-sions.18The law of valency volumes noted above indicates that a veryclose relationship exists between the crystalline form of a substanceand the fundamental valencies of the component elements.It shouldl8 h o e . Roy. Soc., 1907, 79, A, 351 ; A., 1907, ii, 688272 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.consequently be possible to elucidate by its aid all those morphotropicsimilarities between the crystal forms of substances of allied con-stitutions which in the past have been a t once so striking and somysterious; this can, indeed, be done by substituting, in the cal-culation of the molecular distance ratio;, the molecular volume bythe sum of the valencies of the atoms constituting the molecule.By this means a method is obtained of comparing the dimensionsof translations in the crystalline structures of a series of morpho-tropically related substances, on the assumption that, under suchconditions, each atom throughout the series reserves for its ownoccupation a volume proportional to the number representing itsfundamental valency.The sum of the valencies of the atoms com-posing the molecule, the so-called “ valency volume,” being W , therequired translation ratios, or the equivalence parameters,” x, y,and z, are given in the rectangular crystalline systems by :x=$?, 3 - F -..=37The further relations hold that xyz = W and x : y : z =a : b : c.If morphotropic relationships are correlated by means of theequivalence parameters, it is evident that strong confirmation ofthe truth of the law of valency volumes is obtained. The study ofa number of cases shows this prediction to be amply verified,lg andthe following may be quoted in order to show the nature of therelation established.d-Camphoric anhydride, Cl0Hl4O3, and the additive compound ofd-camphoric acid with acetone, C,,H,,0,,+(CH,)2C0, are bothorthorhombic, and are closely related through their axial ratios ;the latter values and those of the corresponding equivalence para-meters are stated below :w. a : b : c.2 : y : z .d-C,,H,,O, .. . . . . . . . . . .. .d-Cl,H,,O,, $Mr,CO . . .The axial ratios show that the whole of the morphological effectof introducing the elements of H,O,~Me,CO into the moleculeof camphoric anhydride is exerted in the direction of the axis a ;the equivalence parameters show that the magnitude of this effectis proportional to the sum of the valencies of the increment thusintroduced. Bther instances of the kind are found amongst thehumite mineralsF0 and the substances related to ‘‘ saccharin.” F. M.Jaeger has also demonstrated 21 that predictions concerning the60741’0011 : 1 : 1‘72701.2386 : 1 : 1‘71723-265 : 3’262 : 5.6334.043 : 3.265 : 5.606l9 T r a m , 1906, 89, 1680.21 B i d . , 1008, 93, 517.2o Ibid., 1686 ; 1908, 93, 1559CRYSTALLOGRAPHY.273existence of morphotropic relations, based on the considerations justput forward, are verified in actual practice.Whilst a large mass of results such as the above definitely provethe truth of the new crystallographic law of valency volumes, it isinteresting that independent evidence establishing a relationbetween valency and volume has recently been brought forwardfrom quite another source. G. Le Bas has shown22 that the mole-cular volumes of a series of normal paraffins in the liquid stateat the melting point can only be interpreted on the assumption thatthe atomic volume of carbon is four times that of hydrogen; themelting points are approximately equal fractions of the criticaltemperatures, and Le Bas has also demonstrated that the samerelation holds in a series of paraffins when examined at some otherseries of corresponding temperatures.The molecular volumes, M, ofthe normal paraffins containing from 11 to 35, or n, carbon atoms inthe molecule, in the liquid state a t the melting point, are given bythe expression :M = 2.970(6n + 2 ) = 2.970 W :W being the valencs volume; the quantity 2.970 represents theatomic volume of hydrogen in the hydrocarbons under the condi-tions specified. Somewhat similar results have been obtained byI. Traube,23 as regards the proportionality, not only of valency andatomic volume, but also of valency and atomic refraction. I n alater paper,24 Le Bas extends his conclusions to olefinic andacetylenic hydrocarbons.The definite demonstration which Le Bas has furnished of therelation between the atomic volumes of hydrogen and carbon inliquid hydrocarbons and the valency of these two elements is ofimportance in connexion with the nature of liquids; it indicatesthat the principle of close packing of the molecular aggregates stillapplies in liquids, the,main difference between the liquid and thecrystalline states being probably that, whiIst both are close-packedconditions, the latter is a structurally homogeneous state, and theformer is not.Further, since in liquids the valency volume is onlyproportional to the molecular volume under corresponding condi-tions, it is suggested that throughout series of crystalline substancesthe molecular volumes would be proportional to the valency volumesif the former values could be determined at corresponding tem-peratures.No means of defining corresponding temperatures, inthe sense of the van der Waals gas equation, for crystalline sub-stances, are as yet available, but in the light of the results now22 Trans., 1907, 91, 112 ; Phil. Mag., 1907, [vi], 14, 324 ; A., 1907, ii, 754.23 Ber., 1907, 40, 723 ; A., 1907, ii, 205.24 Phil. Mag., 1908, [vi], 16, 60 ; A , , ii, 667.REP.-VOL. V. 274 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.reviewed it would seem likely that, measured at corresponding tem-peratures, the molecular distance ratios would be directly propor-tional to the equivalence parameters throughout series of crystallinesubstances. This probability seems likely to render unfruitfulattempts to ascertain the nature of specific crystal structures bycorrelating the crystalline form, the atomic volumes of the componentelements, and the changes in molecular volume which accompanypolymorphous changes in the materials concerned.Much work ofa very suggestive character has, however, been done on this subjectby W. J. sol la^.^^As indicating the probability of the transient existence in liquidsthroughout molecularly large tracts of homogeneously arrangedaggregates of molecules, the work of 0. Lehmann, D. Vorlander,F. M. Jaeger, and others on the so-called ‘‘ liquid crystals” maybe quoted. A number of substances, many of which exhibit closeconstitutional relationships, are now known which throughoutdefinite ranges of temperature exist in liquid phases exhibitingdouble refraction and other behaviour ordinarily attributed tocrystalline structures ; in certain cases the occurrence of dimorphismand of sudden changes of optical orientation can be distinctlyobserved.As has been remarked above, the partitioning of a crystal struc-ture into close-fitting polyhedral units, each of which representsthe sphere of influence of a constituent atom, is equivalent to, andis conveniently replaced by, the building up of a system of spheresin contact with each other.The equilibrium condition-that thepolyhedra shall assume shapes as nearly spherical as possible-isimitated by arranging the spheres in close-packing; that is to say,so that the assemblage presents the maximum number of contactsbetween spheres.I f the assemblage of spheres is compressed fromall sides so as to eliminate the interstices, each sphere becomesflattened to polyhedral shape.26The construction of a model which shall represent in dimensionsand structure the crystalline form of any given substance conse-quently resolves itself into the construction of a close-packedassemblage of spheres of volumes proportional to the fundamentalvalencies of the several elements contained in the substance, theproportion in which the various kinds of spheres are used beinggiven by the molecular composition. The assemblage thus producedmust be characterised by symmetry and translations identical withthose of the crystalline substance, and must be capable of partitioninto units, each of which represents in composition, constitution,and configuration a chemical molecule.These conditions narrowly25 Proc. Roy. SOC., 1898, 63, 291. 26 Trans., 1907, 91, 1157CRYSTALLOGRAPHY. 275limit the possible assemblages of spheres which may be presentedfor any particular case.The investigation of the case of benzene in the manner justindicated has led to the production of a model which is in accord-ance with the crystalline form of the hydrocarbon, and which maybe partitioned into units, each of the composition C,H,, and posesessing a definite configuration of a novel character.27 The modelof the benzene molecule thus derived accords with the generalbehaviour of the hydrocarbon, and possesses certain advantages overthe older models; thus it shows how the ortho-para law of substitu-tion operates, it indicates why optical activity is not exhibited bycertain of the di-derivatives of benzene, and offers a very simplemechanism representing the production of benzene or its homologuesfrom the corresponding acetylene derivatives.28 In similar mannermodels representing naphthalene and anthracene have been devised.It should, perhaps, be emphasised that in constructing close-packedassemblages representing crystalline benzene or any other substanceno suggestion is made that the component atoms are packed closelytogether; the close-packing of the spheres of atomic influencemerely means that the whole of the space occupied by a crystallinematerial is occupied by the constituent atoms in the sense that anypoint chosen within it is subject to the predominant influence of someone atom and that each atom thus influences a domain which isapproximately spherical in shape.Two important questions relating to substitution and multi-valency are conveniently considered in connexion with close-packed assemblages of the same or different sizes.Firstly, if, in ahomogeneous and close-packed assemblage of spheres, homogeneouslysituated spheres each of volume m are each replaced by a group of twoor more spheres having the total volume m, a slight distortion ofthe assemblage, which does not change the grouping of the un-changed spheres, suffices for the restoration of close-packing.Thisis termed the first geometrical property of close-packed homogeneousassemblages, and indicates that in the assemblages representing thecrystal structures of substances of some molecular complexity, onekind of sphere of a certain magnitude may be replaced by severalothers of the same total magnitude, or vice versa, without neces-sitating any considerable rearrangement or " remarshalling " of theassemblage as a whole. It indicates, for instance, that if all thenitrogen spheres, each of volume 3, in the assemblage representingtriphenylamine are replaced, each by three spheres of volume 1,'77 T~mzs., 1906, 89, 1692.28 Compare J. 13. Tingle and F. C . Blanck, J. A7ner. Chenz. Soc., 1908, 30,1596 ; A., i, 893.T 276 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.representing hydrogen, close-packing can be restored to the modifiedassemblage by a slight distortion, which leaves the groups of spheresrepresenting the phenyl radicles of unchanged configuration.Thesecond point of importance arises in connexion with the so-calledsecond geometrical property of close-packed homogeneous assemblages.This states that if, in such an assemblage as that of triphenylamine,the nitrogen spheres of volume 3 are each replaced by a carbonsphere of volume 4, close-packing can only be restored by distortionunaccompanied by remarshalling, if for each extra unit of volumethus added yet another extra unit of volume is introduced. So thatif the nitrogen spheres are substituted by carbon spheres as justsupposed, the restoration of the close-packing can only be broughtabout without profound rearrangement of the assemblage by intro-ducing a sphere of volume 1 with each carbon sphere; the relationsbetween the assemblages and the molecular compositions of tri-phenylamine and triphenylmethane are thus indicated.The modesin which substitutions, such as those of iN by iCH, or of OH by *OH,*NH,, *CH,, or GN, occur whilst some large radicle in the assem-blage preserves its original configuration are thus elucidated.The second geometrical property has, however, still wider applica-tions. The replacement of the nitrogen sphere of volume 3 by thecarbon sphere of volume 4 is, under the conditions explained, geo-metrically equivalent to introducing with it another sphere ofvolume 1, such as a hydrogen sphere; and by the same argumentas before, it is necessary, in order to restore close-packing withoutremarshalling, to associate yet another sphere of volume 1 with thenitrogen sphere.By selecting a chlorine sphere of unit volume forthe latter purpose a mode is indicated by which the assemblage forammonia or tin amine can be converted into ammonium chloride orone of its alkyl derivatives, and generally by which the valency ofan element can be caused to increase by two, or a whole multiple oftwo, units.29 Further, the application of the second geometrical pro-perty elucidates immediately the well-known relationship betweenthe crystal forms of calcite, CaCO,, and sodium nitrate,NaNO,.The crystalline structures of those two substances arehighly characteristic and present striking peculiarities ; theyare of identical symmetry and of almost the same relative dimen-sions, and yet no correspondence exists between calcium and carbonon the one hand, and sodium and nitrogen on the other. The secondgeometrical property indicates, however, that if the nitrogen spheresof volume 3 present in the sodium nitrate assemblage are replacedeach by a carbon sphere of volume 4, an extra unit of volume mustbe introduced for each sphere so substituted in order that close-‘Ly Tyans., 1907, 91, 1204CRYSTALLOGRAPHY. 277packing may be re-established without remarshalling ; the similaritybetween the two crystalline substances indicates that they have thesame marshalling, and the extra unit of volume thus called for ip1introduced by, a t the same time, replacing each sodium sphere ofvolume 1 by a calcium sphere of volume 2.Incidentally it isindicated that the molecules of calcium carbonate and sodium nitratehave the same configuration. The crystalline structures of thesetwo rhombohedra1 substances have been worked out in detailto asalso have those of the similarly related but orthorhombic aragonite,CaCO,, and potassium nitrate. Several other morphotropic rela-tionships of similar kind have been recently discussed by F. M.Jaeger with the aid of the equivalence parameter^.^^Comparatively few cases of morphotropic relationship between theseveral polymorphous modifications of any particular substance havebeen recorded, but by examining the crystalline forms of such com-pounds; under the aspects suggested by the new mode of regardingcrystal structure, numerous analogies are revealed.The mode ofoccurrence of polymorphism is best illustrated by aid of a simpleexample. The cubic and hexagonal crystal structures of silveriodide have been imitated by the construction of cubic and hexa-gonal closest-packed systems of spheres of the same size; in theseconstructions equal numbers of triangularly-arranged layers ofspheres of the same sizes are packed together in two alternativemanners. The one kind of layer contains three times as manyspheres representing silver atomic domains as of those representingiodine; the other kind of layer contains three times as manyiodine as silver spheres.The arrangement of equal numbers ofthese two kinds of layers which gives the cubic closest-packedassemblage is one in which the layers are so stacked one uponthe other that the fourth layer comes exactly over the first, thefifth over the second, and so on; in the hexagollal arrangementthe layers are so stacked that the third lies over the first, thefourth over the second, and so on. The conversion of the cubicmodification into the hexagonal one is equivalent to convertingthe cubic assemblage into the hexagonal one by sliding each thirdlayer in the stack into the appropriate position. Both assemblagesare capable of geometrical partition into identical units represent-ing the molecule AgI, and so may be regarded merely as differentmodes of packing together identical molecular units.I f this iscorrect, and if polymorphously related crystal structures are to beregarded as made up of identical layers packed together in alterna-tive ways, it should, in general, be possible to determine identicalsets of translations in the several such crystal structures. This selec-3d Trans., 1908, 93, 1528. 31 Ibid., 517278 ANNUAL REPORTS ON THE PROGRESS OF CHENIISTRY.tion is obviously possible in the cubic and hexagonal assemblagespresented for silver iodide, because the horizontal translations withinthe layers are the same in both cases, and the vertical translations,or the distances between the planes of sphere centres in two adjoin-ing layers, are also the same.The morphotropic relation thusindicated, namely, the possibility of calculating the axial ratiosof one substance from those of a polymorphously related substanceby some simple change in the axial directions, has been discoveredin a number of instances. Thus, by merely changing the axialdirections in the hemimorphously rhombohedral silver antimonysulphide, Ag,SbS,, for which Miers gives the values u : c = 1 : 0.7892,axial ratios are obtained of the values a : b : c = 1.9007 : 1 : 1.0971,p = 90° ; these correspond closely with the axial ratios, a : b : c =1-9465 : 1 : 1-0973, P = 90°, given for the monosymmetric mineralof the same composition.32 Cases of isopolymorphism may be dealtwith in the same way.Thus the transposition of the axial ratios,a : c = 1 : 0.8276, of the rhombohedral sodium nitrate yields theaxial ratios, a : b : c = 1.7320 : 1 : 0.7151, values almost identical withthose stated by Jaeger 33 for the orthorhombic rubidium nitrate,namely, u : b : c = 1.7366 : 1 : 0.7106.The treatment of crystal structures as close-packed assemblagesand the interpretation of the crystal measurements by the aid ofthe equivalence parameters suggests wide developments of the wholesubject of morphotropic relationships; one of these has been fol-lowed up with success. I n the assemblage representing crystallinebenzene and in those for the simple benzene derivatives, the carbonspheres are found arranged in columns; each joint in the latterconsists of three carbon spheres arranged in triangular contact.34The presence of these columns keeps the translation measuredin their direction the same in the various assemblages inwhich they occur; in benzene itself the value of thistranslation is that of the equivalence parameter a=2.780.Itwould consequently be expected that this value should occuramongst the equivalence parameters of any benzene derivative theassemblage of which contains the columns remarked. On calcu-lating the equivalence parameters of twelve derivatives of picricand styphnic acids, it has been found that one of the three equival-ence parameters in each case assumes a value closely approaching t othe vaIue z=2.780, for benzene.35 The prediction as t o theexistence of this particular morphotropic relation has thus beenamply verified, and an indication has been obtained that the32 Trans., 1908, 93, 1531.34 Trans., 1906, 89, 1693.35 G. Jerusalem and W, J. Pope, Proc. Roy. Sot. 1908 80, A, 557 ; A . ii, 674.33 Zcifsch. Kryst. Miv., 1907, 43, 588Cli I' ST A L J,O GR A PH Y. 279occurrence in the crystal structure of the columns of carbon spheresreferred to is a general property of benzene derivatives. Theinterpretation to be placed upon the general occurrence of thecolumns is that, in the passage from crystalline benzene to somecrystalline derivative, the columns of carbon spheres move apartto a sufficient extent to allow of the introduction of the substitut-ing groups, the increase of volume thus rendered available foroccupation by spheres of atomic influence being proportional tothe increase in valency volume caused by the substitution.The fixity of arrangement of part of the crystalline structureduring changes amongst comparatively small substituting groupsin large molecular complexes, as well its the operation of the firstand second geometrical properties which are observed in the caseof the above substances, is also well exemplified by the nearapproximation to identity of the axial ratios of dibenzyl, stilbene,tolane, and azobenzene.36 The precision with which the changes ofthe equivalence parameters accord with the changes of compositionin such series of related substances as the above proves definitelythat the volumes of the spheres of atomic influence in any given com-pound are approximately proportional to the fundamental valenciesof the elements concerned. This also involves the conclusion thatwhen a considerable increase of molecular volume attends the sub-stitution of one atom by another of the same valency, as, forexample, the replacement of hydrogen by chlorine in benzene, eachcomponent sphere of atomic influence is proportionally enlarged ;the volumes appropriated in the chlorobenzenes by hydrogen,chlorine, and carbon still stand in the ratio of their respectivefundamental valencies, although those for hydrogen and carbonare actually greater than in benzene itself.WILLIAM JACKSON POPE.313 Zirngiel)I, Zc%ihc'). Kryst. Mi7t.., 1902, 36, 117 ; A . , 1902, ii, 496


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