CRYSTALLOGRAPHY.*THREE important advances are to be noted in the province of X-rayinvestigation, so far as concerns this Report. The first is the inde-pendent and almost simultaneous development, by Debye andScherrer in Germany and Hull in America, of an ingenious methodof investigating crystal aggregates ; this method was just mentionedin a previous Report, but. requires further notice now that theoriginal literature is available.The nature of the second advance can best be described by aquotation from Hull’s paper on the structure of iron.2 “It is verydiffimlt to conceive of any arrangement of point atoms which will[account for the experimental data]. We are forced, I think, t o lookfor the explanation in the internal structure of the atoms. If it isassumed that all the twenty-six electrons .. . are displaced from thecentre of the atom along the cube diagonals in four groups of 3,8, 8, 8 a t distances 1/32, 1/16, 118, and 114 respectively ofthe distance to the nearest atom, all the observed facts are accountedfor within the limits of experimental error.” It may be added thatthe same degree of penetration is characteristic of Debye andScherrer, who believe they have proved that salts are ionised in thecrystalline state.The third advance relates to the application of X-ray methods tothe study of amorphous substances, including colloids. Debye andScherrer have shown that aharcoal is really crystalline, andScherrer3 has proved that colloidal particles of silver and gold, asalso gels of silicic and stannic acids, are in reality ultramicroscopiccrystals.Apparently the only substances which may be neglectedThe Reporter regrets that owing to lack of space the consideration ofsome important mineralogical researches has had t o be postponed. It ishoped t o treat these adequately in the 1920 Report. Miss M. W. Porterhas kindly drawn some of the figures, and Mr. R. C. Spiller has assistedgreatly in the preparation of the manuscript, and the writer would take thisopportunity of thanking them for their kind co-operation.A. W. Hull, Physical Rev., 1917, [ii], 9, 84.3 P. Scherrer, Nachr. Ges. Wiss. G6ttinge?a, 1918, 96 ; A., ii, 274.19198 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.by the crystallographer are glass, and such organic materials ascelluloid, collodion, gelatin, albumin, cellulose, and starch.X-Ray methods of exploring crystal structure appear t o havereached a definite stage of development, so that a general apprecia-tion may not be altogether devoid of interest.One matter of detailmay be mentioned immediately. The face-centred lattice and itsderivatives (the diamond “lattice,” the blende and pyrites struc-tures, and so on) no longer wholly represent the family of cubicstructures, for there are now several examples of the cube-centred1 a ttice.The fifth and coiicluding volume of Groth’s inyaluable Chein-ische Krystallographie ” has appeared.It has, of course, long been known that silver or copper is just aseasily attacked by nitric acid as gold is resistant; also that anadmixture of gold (erroneously believed to be 25 per cent.--“ quar-tation”) protects silver or copper from action.As a result ofpatient tests with more varied reagents, Tammann has proved theexistence of reaction-limits, a t such definite metal concentrations asare expressible by simple multiples of 118. Apparent.ly, there areseveral degrees of nobility in the silver-gold and copper-gold seriesof alloys, the investigation of which has not only told us much con-cerning the chemical properties of a space-lattice, but has also ledto an interesting interpretation of a variety of properties, rangingfrom optical anomalies in mixed crystals t o the temper of a metal.Two commemorations have been celebrated. The first, in honourof the 175th anniversary of the birth of the Abb6 Haiiy, has beenacwmpanied by the issue of a special number of the Americanil_lin,eralogist containing many interesting portraits, facsimile letters,and scme eight essays by American mineralogists.The centenaryof the foundation of the American Journal of Science has also beenwoithily sigiialised by the appearance of a special number: contain-ing historical accounts of the development of world science ingeneral and of American science in particular. Apparently the firstAmerican Xineralogical Society was founded in 1799.The gradual transformation undergone by the science of miner-alogy during the last fifty years has been eloquently described inrecent accounts by Sir H, A. Miers 6 and G.T. Prior.6 The progressof crystallography is not less amazing. Crystal strudure is becom-ing incre and more a happy hunting ground for all kinds of physi-cists; and i t seems not impossible that the complexities of thegaseous and fluid conditions (which appear t o be relatively simple,since they are merely studied in the aggregate) will only be un-4 “ A Century of Science in America,” Amer. J . Sci., 1918, [iv], 46, 1.T., 1918, 113, 363. Geol. Nag., 1919, [vi], 6, 10CRYSTALLOGRAPHY. 199ravelled when crystal structure shall have been profoundlyelucidated.X-Ray Methods of h’xploring Crystal Structure. The Debye-Scherrer-Hull Method of X-Ray Exploration.This ingenious method of studying crystal structure, when thematerial is an irregular aggregate of tiny crystals, not necessarilyendowed with plane faces, was independently and almost simultane-ously devised by Debye and Scherrer 7 and Hull.* Although formallythe method is an extension of the original Laue photographicmethod, all interpretations have, of course, been really renderedfeasible by the spectrometric researches of W.H. and IV. L. Bragg.The following account was compiled in the first instance from Hull’sFIG. l a . FIU. lb.Rpaper became it was more accessible. It will be seen later thatDebye-Schemer and Hull only differ in subsidiary details.Suppose (Fig. l a ) a monochromatic beam of X-rays, A B (whichhas already passed a series of fine slits), be allowed to impingeon thecube face of a crystal of potassium chloride, a t the correct glancingangle, $, for the first order “ reflection,” and the rays be receivedon a narrow photographic film, YEP’, bent to the form of a semi-circle with centre B , then the film on development will show a muchover-exposed line, E, due to the undeviated beam, and a line k’, dueto cumulative reflection, the distance of which from E is determinedby the arc 28,.If now the glancing angle be increased to a newvalue, 8, (the appropriate angle for the second order reflection), a7 P. Debye and I?. Scherrer, Physikal. Zeitsch., 1916, 17, 277 ; 1917, 18,291 ; A., 1917, ii, 437.A. W. Hull, Physical Bev., 1917, [ii], 10, GG1200 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.new line, G, will make its appearance, the arc BG' being measuredby 28,; and so on for a third or still higher order.I n all cases the glancing angles of intense reflection are related tothe distance, c&,, between successive structural planes, by the equa-tions, h=2cl.sin 8, 2h=2d. sin 8,, 3h=2d. sin 8,, and so on.9If, again, dodecahedra1 and octahedral plates be subject to experi-ments, new lines will appear, in positions involving the new gratingdistances dl10 and d,,,.Now consider what will happen if some very finely powderedpotassium chloride be placed at B (instead of a crystal plate) andan exposure taken without troubling about any particular glancingangle (Fig. l b ) . There will simultaneously be a considerable numberof minute crystals having the same orientation as the first crystaiconsidered above, but these will oiily constitute the members of alarger group, making the same angle with the incident beam, butlying in all azimuths.The I ' reflected " beams from crystals of thisgroup will form a hollow cone of total angle 48,, and will interceptthe film in symmetrical positions P and 3''. There will be manyFJG. 2.G F E F'333 330 222 300 220 200 I l l 110 100 100other crystals having the second kind of orientation, which will give'rise to the hollow cone GRG', and so on. (If a plane, film, R, wereused concentric circular impressions would result, but a plane filmof manageable diniensions would only register cones up to 48, where8=22io'). After the semi-circular film has been unbent anddeveloped, the lines on the portion El' for the first three orderreflections will be in the positions given in Fig.2, in which theindices (222) signify a second-order reflection from (lll), and so on.It will be realised that the linear distance of any line from E is asini-ple function of (1) the radius of the bent film, (2) the wave-length of the X-rays used, (3) the order of the reflection, and (4) thefundamental grating distance, d , of the1 atomic strata, responsiblefor that line.I n the actual case of potassium chloride there would, of course,be more than nine lines. 'The number of lines is dependent on thewave-length of the monochromatic X-rays employed, for, althoughthe number of possible structaral planes is infinite, only those planes0 The Reporter regrets the slip involved in a previous Report (,47an.Report, 1914, p.240, lilies 22-27)CRYSTALLOGRAPHY. 201can reflect any energy the distances apart of which are greater thanA / Z . Thus, there is a limit to the number of lines, depending onboth structure and wave-length employed. The following tablerefers to the diamond.No. of linesX-Rays used. Wave-length. theoretically possible.Tungsten doublet ............... 0-212 x 10-8 More than 100.Rhodium doublet ............... 0.617 30.Iron doublet ..................... 1-93 Only 3, namely, fromMolybdenum (K,-doublet) ... 0-712 27.{llli, j l l O l , 1311;.From the method of experiment’ation it will, perhaps, be obviousthat a form { 311) of the diamond, consisting of twelve structuralplanes, will only give one line.The existence of the twelve planesmerely enhances by twelve the chance that a crystal shall have thecorrect orientation ; accordingly, the intensity of the line is propor-tionately increased. This property constitubes an advantage in thestudy of planes of the general indices { h k l } , for the co-operation ofthe twentg-four planes (of a cubic crystal), each of which will havea subordinate reflectivity, may lead, so to speak, to a combinedcreditable effort.The principles and routine of the interpretation are clearlyexpounded by Hull and applied to the analysis of ten crystal aggre-gates, one of which, the diamond, was purposely selected as a check.In theory, nothing need be known about the system or “crystalelements,” but, in practice, if these are known the burden ofanalysis is greatly lightened.The crystal powder (0.005 gram, or, if necessity compels, one-tenth of that) is best contained in a thin-walled tube of 1 mm.dia-meter. The material of the tube. must naturally be amorphous(glass, celluloid, or collodion). Perfeot irregularity of the crystalgrains is desirable for uniform results, and can be ensured byrotating the tube during the exposure.In order t o render t.he X-rays more monochromatic, Hull alwayspasses them through a suitable screen, which absorbs stray wave-lengths. If molybdenum rays are used, the screen should bezirconium or a compound like zircon.10I n a later paper the author11 shows that his method can beemployed successfully as a method of chemical analysis (that is,identification of substances the characteristic linw of which arealready known).For example, a specimen of ‘‘ chemically pure ”sodium fluoride was found to exhibit the characteristic lines, both ofsodium fluoride and sodium hydrogen fluoride, NaHF2. It is alsolo A. W. Hull and (Miss) ISI. Rice, ibid., 1916, [ii], 8, 326.l1 A. W. Hull, J . Amer. Chem. SOC., 1919,41, 1168; A., ii, 470.H202 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.evident that a mixture of sodium fluoride and potassium chloridecan be readily distinguished from a mixture of the same bulk com-position of sodium chloride and potassium fluoride, for the molecularvolumes (and therefore grating distances) of the four compounds aredifferent.Debye and Scherrer press the powder into the form of a rod, and,if necessary, give it a coating of collodion to prevent disintegrationduring the radiation.The photographic film they arrange in theform of a cylinder, with axis perpendicular to the incident beam.The various cones intersect the film in curves represented schemati-cally in Figs. 3 and 4, the1 last-mentioned figure representing halfthe unbent film. Of course, the linear distances only need bemeasured along the symmetry trace X Y .FIG. 3. FIG. 4.X YThe method is absolutely trustworthy up to the point a t whichThis point will be illustrated later under the interpretation begins.‘‘ graphite ” (p. 203).The reconstructions or models offered by the various workers sincethe appearance of the last Report will now be considered.The listwill be restricted to models which are relatively final, as space doesnot admit of any discussion of the less satisfactory cases. Gratingdistances are in al1,cases given in Angstrom units, and must accord-ingly be considered as multiplied by 1 0 - 8 om.Cubic System.‘‘ Cubic ” lattic2 ......... None so far dkcovered.Centred lattice ............ Tungsten (Debye*) ; a=3.18 (length of cubeletedge).a = 2-86a = 4-30.a==3.50 (author not entirelyIron (Hull) ;Sodium (Hull) ;Lithium (Hull) ;satisfied).* P. Debye, Physikal. Zcitsch., 1917, 18, 483 ; A., 1917, ii, 571CRYSTALLOGRAPHY. 203C‘*t~bic: System (continued).Centred lattice . ........... Nickel (Hull) ; a=2.76 Hull believes to bedimorphous, but heFace-centred lattice ...Nickel (Hull) ;Diamond “ lattice ” ...a= 3-52 (is not sure).Aluminium (Hull) ; a=4.05.,, (Schemer*) ; n=4.07.Diamond (Hull) ; absolute agreement with W. H.Silicon (Debye and Scherrert) ; a= 5.46.Grey tin (theu = 6.46.Lithium fluoride (Debye and Scherrers) ; a=,4-14.Lithium fluoride, sodium fluoride, potassiumfluoride, magnesia (Hull 11) ; distances not stated.and W. L. Bragg.9 , (Hull) j‘ a= 5.43.tin-pest ’’ : Bijl and Kolkmeijer;)Rock-salt structure .. .* P. Schemer, Physikal. Zeitsch., 1918, 19, 23; A., 1918, ii, 113.t P. Debye and P. Schemer, Physikal. Zeitsch., 1916, 17, 277.Z A. J. Bijl and N. H. Kolkmeijer, Proc. K . Akad. Wetensch. Amsterdam,8 P. Debye and P. Schemer, PhysikaE.Zeitsch., 1918, 19, 474 ; A., ii, 20.II A. W. Hull, J. ,4iner. Chem. SOC., 1919, 41, 1168; A., ii, 470.1919, 21, 501 ; A., ii, 161.Hexagonal System.Magnesium.-This interesting structure, unravelled by Hull, canbe most simply described as Barlow’s close-packed hexagonal systemof spheres, slightly deformed. More precisely stated, there are twotriangular, prismatic lattices 12 (a = 3.22, c = 5.23) so interposed thatone centres the other.Graphit e.-This substance has been examined by Debye andScherrer 13 and by Hull,14 who suggest slightly different models.The former workers interpret the structure as an interpenetration oftwo facecentred rhombohedra (of edge 4-48), so that the vertex ofone lattice lies one-third the full vertical distance (10.23) below theother.The vertical distances bebween successive horizontal layersof atoms is accordingly 3.41 (agreeing very well with W. H. Bragg’spreliminary determination, 3‘42) ; the crystallographic constant ofthe f ace-centred rhombohedra1 lattice, a, is 68O26’.Hull’s analysis takes the form of “ a n hexagonal structure, com-posed of four simple lattices of triangular prisms, each of side2.47 and height 6.80, the atoms of the third lattice being directlyabove those of the first a t a distance of one-half the height of thel2 The term “ triangular lattice ” is a useful- variant of “ 120°-prismlattice,” for it obviates circumlocution in describing certain cases of inter-penetration.l3 P. Debye and P. Schemer, Physikal. Zeitsch., 1917,18, 291 ; A ., 1917,ii, 437.lP A. W. Hull. Phaysicd Rev., 1917, [ii], 10, 661.H* 204 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.prism, those of the second and fourth lattices being above thecentres of alternate triangles of the first, a t distances 1 / 14 and 8/ 14respectively of the height of the prism.”A comparison of the above two models may well be given here,because the differences are so small as to make it improbable thatthe real solution will be agreed on before the lapse of several years.Debye and Scherrer used a copper anti-cathode and Hull one ofmolybdenum. This made i t necessary to calculate all Debye andScherrer’s grating distances in order t o eliminate inessentials duet o different wave-lengths. The experimental results were thenfocnd to be in substantial agreement, both with regard to gratingdistances and intensities.Hull’s reflections go far beyond the rangeof Debye and Scherrer’s owing to the shorter wavelength of themolybdenum rays, and incidentally include a reflection, beyondDebye and Scherrer’s observed lines, which will fit in with theirunrepresented (O$a).l5 On the other hand, Hull is not quite satis-fied with his model because certain reflections are missing, theabsence of which he refers to some special dist.ribution or other ofthe electrons‘within the atom. The writer finds that all thesereflections are represented in Debye and Scherrer’s list of lines,with the possible exception of one line, which is attributed by themto the P-radiation of copper.If this line is in reality an a-line (theallocation of “ a ” or “ P ” appears to be sometimes a matter ofopinion rather than exactness) all Hull’s missing lines are accountedfor, and presumably there need be no appeal to a special electronicdistribution.For simplicity of comparison Hull’s refined estimates of level,1/14 and 8/14, must be arbitrarily altered t o 0/14 and 7/14 (with-out, of course, implying that his model is in any way incorrect).I n each model atoms are then arranged in horizontal planes accord-ing to a bee-cell pattern. Moreover, the edge of the hexagon isthe same within the errors of experiment, say, 1.45. The, bee-cellpattern will therefore be adopted as a medium of expression. Thedistancw between successive layers is the same (3.40-3.42).Theonly difference, is that Hull’s third layer of bee-cells is verticallyabove the first layer, whilst in Debye and Scherrer’s model everyfourth layer is above the first. Plans of the two structures aregiven in Figs. 5 and 6, in which the various layers are distinguishedby different kinds of lines and by the adoption of point-circles andcircles of different radii for the atoms. Only two. and three layersneed be shown respectively in the two figures.l5 Debye and Scherrer’s stated reflection (022) is really a first order reflectionIts absence would have seriously undermined their model-a point ( O i l ) .which they appear to have overlooked.CRYSTALLOGRAPHY. 205It is of interest t o note that Debye and Scherrer regard thediamond as the prototype of aliphatic compounds (owing t o thetetrahedral environment of each atom), and graphite as the proto-type of aromatic compounds, since it can be held to illustrate threeprincipal valencies in a horizontal plane and an unique valency,directed up or down, serving to interlock the various strata(compare, however, p.208).Charcoal.--“ Amorphous ” charcoal from most varied sourcesyields three lines, all of which are coincident with specific graphitelines. Debye and Scherrer have accordingly concluded that charcoalFIG. 5 . FIG. 6.consists of polyatomic (‘ molecules ” (containing 20 or 50 at,oms),these ‘‘ molecules ” being tiny fragments of the graphite structure.Tetragonal System.C‘halcopyrit e , CuFeS,.-This interesting mineral has been investi-gated by the Bragg method by C.L. Burdick and J. H. Ellis,l6 whooffer the model shown in Fig. 7, in which the copper and ironatoms taken collectively form what may be loosely described as aface-centred cubic lattice (the axial ratio c :a= 0.985). The sulphuratoms are found to occupy the centres of half the smaller “cubes,’7selected tetrahedrally. The calculated intensities of the variousreflections fit in very well with the observed valueg. A cursoryglance at the figure will show that the structure is that of zincblende, in which half the zinc atoms are replaced by copper atomsand half by iron atoms. Yet in spite of this great similarity zincblende has a perfect dodecahedra1 cleavage, whilst chalcopyrite hasnone ; moreover, an octahedral cleavage is characteristic of theJ .Amer. Chem. Soc., 1917, 39, 2518; A., 1918, ii, 46206 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.related diamond structure. The property of cleavage is evidentlyas mysterious as the development of plane faces on a crystal. TheReporter finds the structure to be an example of the Fedorov pointsystem 33s (Xchonflies, VL; Barlow, 59&; Hilton, Did).White Tin.-As in the case of the grey modification, the exam-ination 17 was carried out by means of the, Debye-Scherrer method,and led to the result that a structural tetragonal cell (with dimen-sions u=5*84 and c=2.37) has its vertical sides centred; that is,there are three interpenetrating tetragonal lattices.Now the struoture demands a value for the ratio c :u=0‘406, which incidentallyinvolves that the only common form, p { 111 1, should have theindices { 403j. This perversion of form development is unexampled.FIG. ‘1.If the accuracy of the analysis is unquestionable, it signifies thatlittle is definitely known about the correlation of form and struc-ture.Rhonabohedral System.Curb orwzdum, CSi .-A thorough examination 18 of t,his substanceresults in the following interpretation. The crystal is pseudo-cubicfor the angle a=89O56/. The silicon and carbon atoms each furnisha ‘‘ face-centred rhombohedra1 lattice,” l9 the two lattices interpene-l7 A. J. Bijl and N. H. Kolkmeijer, Proc. K. Akad. Wetensch. Amsterdam,1919, 21, 494 ; A., ii, 161.C.L. Burdick and E. A. Owen, J . Amer. Chem. SOC., 1918, cu), 1749;A . , ii, 62.l9 It is, perhaps. worth while pointing out that tha term “face-centredrhombohedra1 lattice ” used by X-ray workers is one of convenience, anddoes not imply the existence of more than one Bravais lattice in the rhomboCRY STALLOGRAPRY. 207trating with a comnion vertical axis and in such a way that a hori-zontal layer of carbon atoms is displaced vertically through 0*36d,where d signifies the distance between successive horizontal layersof carbon or of silicon atoms.dcZde?zda.-The model offered by Vegard and Schjelderup 20 forthe alum group has been refuted by Niggli,21 who in turn offers amodel, which cannot be considered for reasons of time and space.Several theoretical papers require a brief notice. The interpretationof the results of the Debye-Scherrer-Hull method is also discussedmathematically by C.Ruiige22 and by A. Johnsen and 0. T0eplitz.~3General explanatory papers and books on the relationship of X-raywork to the theory of crystal structure are becoming more nunier-ous. The excellence of Kreutz’s24 book is only marred by t,he factthat he practically ignores the Fedorov-Schonflies point systems.Voigt25 in an interesting paper is incline,d to weigh t’he relativemerits of Sohncke and Fedorov-Schonflies. It does not seem to begenerally recognised that there is no question of a comparison ofthe Sohncke theory or of a somewhat halting, because ad-hoc-extended, later Sohncke theory with the Fedorov-Schtinflie theoryhedral system.Any rhombohedral lattice can be described either as rhombo-hedral or as a centred-rhombohedra1 or as a face-centred rhombohedrallattice, each variant implying a specific axial ratio or fundamental angularconstant a. Any particular choice is one of taste, in just the same way asis the allocation of the indices (110; or (100; or {ill) to, say, the cleavage,rhombohedron of calcite. It is interesting to note that, if the allocation ofindices were consequential instead of conventional, the X-ray exploration ofcalcite demands the indices fl00) for the steep rhombohedron f f l l l } . Thelatter transformation was indeed suggested long ago by Goldschmidt, pro -ceeding from what is really a principle of simplicity of indices which wassubsequently developed by Fedorov and then abandoned because it wm notsufficiently exact for the purposes of crystallo-chemical analysis.Evenmore radical transformations of indices have been advocated by Fedorov.It seems t o the writer, however, that transformations are never expedientin conventional descriptions of crystal morphology, for they are liable to createconfusion. On the other hand, in the practice of crystallo-chemical analysisall questions of taste or opinion have naturally to be rigorously subordinatedto uniform principles, covering both the deduction of the space-la$tice andthe erection and orientation of that lattice. The tendency of Fedorov’sand Go1dschmidt)’s highly original work is to create barriers between the“ old ” and the “ new ” crystallography.These barriers are really built upof inessentials ; their eventual removal will presumably lead to a fusion ofthe more reasonable elements of the conservative and progressive sectionsof crystallographers.2o L. Vegard and H. Schjelderup, Ann. Physik, 1917, [ii], 54, 146; A . ,1918, ii, 156.21 P. Niggli, Physikal. Zeitsch., 1918, 19, 225 ; A., 1918, ii, 315.2 2 Ibid., 1917, 18, 509.24 S. Kreutz, “ Element8 der Theorie der Krystallstruktur ” (1915).25 W. Voigt, Physikal. Zeitsch., 1918, 19, 237.23 Ibid., 1918, 19, 47208 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.-however geiielrally i t is concedeid in other branches of geometrythat t'he whole necessarily includes the part.Debye and Scherrer o n Atomic Structure in a Crystal.A recent paper by Debye and Scherrer26 may, perhaps, beregarded as the present' high-water mark of X-ray investigation.The authors advance certain theoretical considerations which serveto harmonise Braggs' principle (that the arnplihde of reflectedX-rays is proportional to the atomic weight) and Barkla's con-clusion that the atomic weight is proportional to the intensity(square of the amplitude1),27 and they conclude that the inteasityof radiation depends on the number (Moseley number) and posi-FIG.8. FIG. 9.tion of the electrons in the atom. The authors believe that theirmethod of X-ray expelrimentation is delicate enough to examinetwo questions of t5he greatest import.The first of these questions rdatw to the mechanism of theattachment between atoms in a crystallised element.For example,in the diamond structure each carbon atom is environed tetra-hedrally by four carbon atoms. Are the four atoms held bywhat may be termed chemical valencies? Now the chemicalvalency between the) two atoms of a hydrogen molecule is a t p r esent int'erpreted mechanically as due to a midway dielectronic ringwith a plane of rotation perpendicular to the valency bond. Ifthis were also true for thel diamond structure, the crystal wouldhave the diagrammat'ic structure represented by Fig. 9, in whichonly two out of the six Moseley electrons of each carbon remain26 P. Debye and P. Scherrer, Physikal. Zeitsch., 1918, 19, 474 ; A., ii, 20.27 W. H. and W. L.Bragg, " X-Rays and Crystal Structure," p. 49CRYSTALLOGRAPHY. 209in the atom, and each of the other four, joined by one more fromone of the four nearest atoms, rotates round a point which islocated half-way between a pair of atomic centres. The differencesbetween the new and the original Bragg structure (Fig. 8) aresufficiently great as to allow of a definite decision one way or theother, by means of a careful analysis of the inte'nsities of the curvesin a Debye-Scherrer X-radiogram. Amongst other things, thereshould be a strong second-order relflection from the octahedralplanes. The result decisively negatives the subsistence of chemicalvalencies due to electronic rings and substantiates anew the Braggstructure. Moreover, other examples (of elements ? not specified)have been investigated, and the authors have not been able to finda single case in which electronic rings serve as bonds in a crystal.The second question relates to the possibility of ionisation incryst?als of electrolytes.Since the reflecting power of an atomdepends on the number of electrons, the power will be correspond-ingly modified by the loss or gain of an electron due t o ionisation.As a result of a careful analysis of the X-radiogram of lithiumfluoride (co-structural with the sodium chloride group), Debye andScherrer conclude that the lithium has lost and the fluorine gaineda negative electron. Itis again assumed that the diffracting power of an atom is elqua1 t othe number of negative electrons as given by the Moseley number,namely, Li=3, F = 9 .I n all the structural planes of lithiumfluoride having three odd indices, for example, (1111, {113},{ 133}, planes are alternately ,wholly lithium and wholly fluorine ;the effective reflecting values will either be 2 and 10 or 3 and 9,accordingly as the structure is ionised or not. The authorsconclude that the crystal is ionised.28The method of reasoning is as follows.General Conclusions : A Suggestion.It has now become fairly evident that the X-ray method ofexploring crystal structure is really a (I sub-chemical " method.2s The above conclusion was not easily deduced, for sodium fluoride,if ionised, should present no first order reflections from planes havingthree odd ,indices. Such planes did, in fact, give weak reflections.The way out of this difficulty involved theoretical considerations, in-cluding estimates of the disturbances due to temperature (subsequentlyapplied to lithium fluoride), the objective value of which the presentwriter feeIs he is not competent t o estimate.In view of the fundamentalimportance of the subject, most crystallographers would feel happier if theresults of any future comparative investigation of the whole co-structuralgroup of alkali haloids mutually confirmed each other, for there would thenbe a reasonable certainty that the theoretical considerations are congruentwith the workings of nature210 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.Whilst it probes the structure more profoundly than a purelychemical method ever sets out to do, it does not a t the presentmoment give any information on chemical properties or structure.For example, although the similarity of structure of carbon(diamond), silicon, and tin can be held t o have chemical signifi-cance, and although we are possibly on the eve of absolutely trustpworthy information concerning the existence or no of " ionisation "in crystals, there is, so far, no real information from X-ray sourceson the mechanism of such chemical unions as are implied by theformula CH,, or the formula (SO,) of the sulphate radicle, or bythe commas characteristic of the formulz MgS04,7H,0,and 2KF,SiF,, or the significance of a happier variant of thelatter, K,[SiF,]. It would appear that chemical information onall these points can only accrue by the X-ray method in so faras the unions are1 brought about by the1 transfer of one or moreX-ray diffracting electrons.During recent years there has been a tendency to jump to theconclusion that molecules disappear in a crystal and become partsof an indefinitely extended crystal molecule.X-Ray physicistshave never claimed that their work decides the question one wayor the other, although the close approach of the three oxygen atomsin the calcite structure could be interpreted, perhaps, as a signthat the (CO,) group exists as an entity. A t the present momentsomet-hing more than mental inertia compels the view that mole-cules or ionic groups persist in a crystal; i t will be time to revisethe view when, say, i t is the usual thing for a crystal of an ortho-ccmpound to give a mixture of ortho- and para-derivatives on melt-ing, or vice versa.A celrtain amount of pooling of affinity mayexist in a cryst'al (and so lead t o a very shadowy, indefinitely ex-tended " molecule "), but t o a degree that is a t present quitel vagueand scarcely susceptible of discussion.So far as crystallography is concerned, the result of the X-raywork is the proof that the abstract theory of crystal structure(built up by the efforts of Hauy, Frankenheim, Bravais, Sohncke,Fedorov, and Schonflies) faithfully embodies a concrete reality.The present interpretation is an atomic interpretation, becausemolecules are, so to speak, outside the terms of reference of theX-ray inquiry.Work on the infra-red29 is susceptible of a molecular interpretation, but possibly other methods will have to be29 C. Schaefer and M. Schubert, Ann. Physilc, 1916, [iv], 50, 283, 339 ;1918, [iv], 55, 397, 577 ; 1919, [iv], 59, 583 ; A., 1916, ii, 505 ; 1918, ii, 282,315 ; K. Rrieger, ihid., 1918, [iv], 57, 287 ; A., ii, 37.&SO4,MgSO4,6H20CRYSTALLOGRAPHY. 211found before the molecular aspect of crystal structure becomes fullyrevealed.The results already obtained are of such superlative importanceas to make it desirable thatl the X-ray work shall continue alongcrystallographic lines and not altogether take other directions.There are signs, however, that future developments may not beso rapid. It would seem that the simpler cases are being exhaustedand that great difficulties stand in the way of future progress.Many of the cases which have been examined defy any trustworthyinterpretation.Although further result-s can be expected from a more refinedinvestigation of the simpler cases already elucidated, investigationson slightly less simple cases is the obvious next step. How arethese cases t o be selected? Past results have supplied an answer,but only on the negative side.Degree of complication evidentlydepends on two main factors, complexity of chemical compositionand lack of crystal symmetry. The two factors are mysteriouslyinterwoven, and may only be separated in a tentative manner forillustrative purposes. The orthorhombic sulphur and thehexagonal ( 1 ) graphite are less simple than any cubic element, butthey are also less simple than the rhombohedra1 calcite.Thetetragonal cassiterite (complicated enough) is simpler than thecubic garnet. The orthorhombic potassium sulphate, K,SO,, ismore complicated than the cubic spinel, Al,MgO,. When the twofactors are regarded singly, it appears likely that complexityincreases in a kind of geometrical progression with the number ofkinds of atoms and with degradation of symmetry. No successfulinterpretation has yet been offered for a substance containing fourkinds of atoms (with the possible exception of Niggli’s alum model)or for an orthorhombic, monoclinic, or anorthic crystal.I n the past, the proper choice of material for investigation wasperhaps fairly obvious ; elements and simple compounds crystal-lising in the cubic system invited inquiry.More recently, theselections have not been so fortunate. The selections have,perhaps, been guided by physical rather than chemical instincts.The present writer believes that a proper regard to both chemistryand physics is more likely to lead to happy selections, and that thereal finger-post is symmetry.Although inany exceptions are known, it is, nevertheless, astatistical truth that everything strives towards symmetry in sofar as the environment will allow. Chemical molecules take upsymmetrical configurations-otherwise 99 per cent. would betheoretically resolvable into enantiomorphous configurations212 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.Again, the arrangement in a crystal tends towards symmetry.Most elements crystallisel in the cubic, hexagonal, tetragonal, andrhombohedral systems.Binary molecules, like sodium chloride,possessing a rotational axis of symmetry, group themselves in highlysymmetrical ways (the grouping possibly being facilitated byionisation). Organic chemical molecules, which configurationallyrarely possess more than a plane or centre of symmetry, generallyarrange themselves during crystallisation according t o a highersymmetry (45 per cent. in each of the orthorhombic and monoclinicsystems). Unfortunately, this higher symmetry is frequentlyaccompanied by grave complications, inte)rpene;tration of molecularor ionic space lattices giving rise to more general point systems, theelucidation of which becomes accordingly difficult. There is, how-ever, a fairly well-represented class of Substances in which the mostprobable stereochemical configuration has the same symmetry asthe crysbal form.Such structures are less likely to be compli-cated ; the number of structural parameters should be relativelysmall. These are the substances which appear t o be worthy of theimmediate attention of X-ray workers. A few typical exampleswill serve as illustrations.I n the province1 of organic chemistry, molecules of carbon tetra-bromide and tetraiodide, silicon tetraiodide, and hexamethylene-tetramine, N,(CH,),, have the symmetry of a regular tetrahedron,and the substances crystallise in the cubic system (carbon tetra-bromide above1 4 7 O ) .The e1ucidat”ion should be easier than thatof garnet. I n inorganic chemistry, there are many compounds,like potassium platinochloride and periodatel, which are “ tetra-gonal ” configurationally and in crystallisation. I n the rhombo-hedral system, in addition to calcite, theire are numerous groups ofcompounds, of which the following formulae illustrate examples :Mg,SiF,,6H20, MgPtI,,SH,O, MgPtBr,,12H20. I n all these cases,the natural configurations for the separated parts, say,[Mg,GH,O]++ and [SiF,] - -, are rhombohedral, and the structureswill presumably involve two or four parameters more than in thecase of calcite. However complicated the formuh may appear, thestructures can scarcely be as difficult as in a case like potassiumsulphatel, where a tetragonal molecule1 or SO, group is degraded t ofit in with an orthorhombic type1 of symmetry.With regard to the question whether the1 exploration of, say,carbon tetrabromide should reveal the quadrivalent nature ofcarbon, it seems certain that an appeal to a transfer of electronswill not help matters, for relative intensities can scarcely sub-stantiate an assumption (transfer of electrons) concurrently withthe value of the bromine parameterCRYSTALLOGRAPHY.213Tammarm's ll'orlc on Biffusioit and Reaction Limits : Chemicaland Galvanic.It may be stated a t once that the work capitalises the interestthat has always been attached to the property of diffusion in thesolid state,30 and has, no doubt, considerable metallurgical signifi-cance.Tammann31 shows that cast, untempered alloys, or, whatamounts t'o the same thing, tempered alloys which have been sub-sequently subjected tto harsh treatment (rolling, drawing into wire,hammering, and so forth), tend t o behave incoherently towardschemical reagents, whilst tempered alloys take on themselves someof the properties of a compound. He presents a mass of experi-mental data which a t least goes a long way towards proving thatmixed crystals (not compounds in the formal sense) in certainsimple, definite proportions resist chemical action in the samedegree as is exhibited by the more dour constituent. Thisorganised resistmame is ref erred to an intimate atomic equilibrium,sejt up as a result of diffusion, whereby the structural space latticeloses the properties of a conglomerate and acquires that perfectionof design which is characteristic of the structure of an uncon-taminated metal or pure chemical compound.So much by wayof introduction; we may now consider a few details, almost whollyrestricted to gold alloys.Chemical Behaviour of Well-t empered ,4 Iloys.-At bokh ordinaryand at slight*ly elevated €emperatures, well-tempered copper-goldand silver-gold alloys remain uncorroded in general and do notbring about any deposition of metal from solution when digestedfor a prolonged period with solutions of palladous chloride,platinous chloridei, yellow ammonium sulphide, sodium disulphide,sulphur dissolved in carbon disulphide, sodium diselenide, picricacid, or alkaline solutions of sodium tartrate, provided the alloycontains 25 molecular per cent..or more of gold; i f , however, thegold content sinks t o 24 per cent., chemical reaction takes place.Again, with the silver-gold series of w ell-annealed mixed crystals,the limit of reaction for solutions of gold chloride, chromic, per-manganic, and nitric acids lies sharp a t the 50 molecular per cent.composition. Further, a t t.he, ordinary temperature, moist air coii-taining hydrogen sulphide has no action on copper-gold alloys con-taining a t least 25 molecular per cent. gold, but a t t,emperatureshigher than looo, alloys of all compositions are gradually attacked,30 Compare " Diffusion in Solfds," by C.H. Desch, Brit. Assoc. Reports,1912, 348.31 G. Tammann, Zeitsch. anorg. Ghem., 1919, 107, 1-239 ; Nachr. Ges. WZ'SA.Gdttingen, 1916-1919 ; A., 1917-1919, ii214 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.with the formation of oxide or sulphide of copper. This reactivityTammann attributes to the enhanced rate of diffusion of copperand gold atoms, so that action is no longer restricted to the finestpossible surface layer. Mercurous salts also attack the wholecopper-gold series (pure gold excepted), even a t the ordinarytemperature; there is, however, a reaction limit in the matter ofa precipitation of mercury from mercuric chloride a t the composi-tion 25 molecular per cent. gold. There is also a limit in thereaction of solutions of silver salts; in this case, itn is not so sharplydefined, lying between the limits 8-15 molecular per cent.gold.Presumably, by analogy, Tammann considers the upper limit aslying at 1 / 8 gold (12.5 molecular per cent.).With some reagents there is not merely an absolute resistancelimit-there is also a relative resistance limit. Thus, boiling nitricacid removes the whole of the copper or silver from a’gold alloyprovided the gold content is less than 318 mol. ; if the com-position lies between 3/8 and 4/8 gold, only part of the less noblemetal can be extracted; if the composition lies between 418 and 8/8gold, the specimen, as stated above for many other reagents, iswholly unattacked.Chemical Beha8viowr of Unt empered A 1Zoys.-Several series ofcomparative experiments were made on the effect of temperingcopper-gold alloys (having compositions close to the 418 limit) onthe sharpness of the limit of reaction.The reaction selected wasthe deposition of finely divided gold from a solution of aurouschloride. The reactants were sealed up in tubes and inspectedfrom time to time, and the strips of alloy were subsequentlytempered and digested afresh with solution. The results seem veryconvincing. Untempered strips ranging up to a 51 molecular percent. gold content became stained in patches, owing to parts of thespecimen having a less percentage composition than 50. Iftempered a t 900° for forty hours, an alloy containing 50.5 mole-cular per cent. of gold remains bright, whereas equally temperedalloys containing 49.5 per cent.or less become brown. It must,accordingly, be concluded that the reaction limit for the homo-geneous mixed crystal lies a t 50 molecular per cent.The deleterious effect of cold-working a previously tempered“soft” alloy on the sharpness of the reaction limit is illustratedby a series of experiments on the action of sodium sulphide, onsilver-gold alloys. Well-tempered plates (0.5 mm. thick? exhibita reaction limit within the narrow range 24.5-25.5 molecular percent. gold. When the same plates had been rolled and beaten outto an order of thickness represented by 0.01 mm., discolorationtook place even with a gold content of 55 molecular per centCRY STALLOGRAPHS. 215Galvanic PoterttiuZ.-The application of thermodynamic theoryto a study of the dependence of polarisation potential on the com-position of an alloy presupposes that the several kinds of met’allicatoms can inter-diffuse with great rapidity.This condition is,however, not fulfilled at ordinary temperatura, so that mixedcrystals may be expected to betray a de’finite resistance limit. Thisexpectation was realised, for example, in the copper-gold andsilver-gold series of alloys. The polarisation potential for “soft ”t’empered gold-silver alloys in an alloy I AgNO, solution I Ag elementhas the constant value 0.808 volt for all mixed crystals varyingfrom 100 to 50 molecular per cent. gold, whilst the much lowervalue 0.71 volt is suddenly found €or mixed crystals cont’aining49 per cent.gold. On the other hand, “hard ” untempered alloys(non-homogeneous), whilst showing something of a break a t the50 per cent,. composition, do not exhibit the constant value 0.808volt for gold-rich series, but values fluctuating between 0.703 and0.739. A series of investigations was made at higher temperatures.In the case of the element-AgAu, 1 AgNO, I glass I NaN03,KN03,AuC13 1 Au+,i t was found that the potential varies greatly with the tempera-ture and changes with the time. The galvanometer readings firstbecame independent of the time at 320°, and at this temperaturethe values showed no break at 50 per cent. composition, but variedcontinuously for the whole series of Au-Ag alloys. This funda-mental difference of behaviour a t low and high temperatures is inharmony with the differences already mentioned f o r “ chemical ”reactivities; they indicate that, at temperatures a t which an activeprocess of diffusion is out of the question, the chemical propertiesof metallic mixed crystals change discontinuously a t certain definiteconcentrations.Tammann emphasises the point that these changescannot be referred to1 the formation of chemical compounds in theformal sense, for the substances in question are miscible in all pro-portions and chemically similar. It may be added that theocclusion of hydrogen by mixed crystals of palladium and platinumreveals corresponding discontinuities.32Behuviour of Mixticres of Sodium Chloride and Silver Clzloricle.-Although such mixed cryst-als cannot be obtained from aqueoussolution, for obvious reasons, they are readily obtainable in anyproportion from mixed fusions.33 The process of leaching thesemixed crystals has been studied by Tammann and Schmidt.34 The32 G.Tammann, Nachr. Ges. Wiss. Grittingen, 1918, 72 ; A., ii, 293.33 C. Sandonnini, A t t i R. Accad. Lincei, 1911, [v], 20, i, 758; A., 1911, ii, 800.3 4 G . Tammann and K. W. Schmidt, Nachr. Ces. IYiss. Gottingen, 1918,296 ; A., ii, 396216 ANNUAL REPORTS ON THE PROGRESS O F CHEMISTRY.results depend greatly on whether the mixed crystals have or hawnot been tempered (that is, rendered homogeneous by holding a ta temperature well below the melting point for a considerable time).Well-tempered crystals (powdered to a size less than 0.05 mm.)refuse t o yield any so’dium chloride provided the composition isa t least 6/8AgC1, whilst crystals ranging between 5/8AgCl andpure NaCl give up the whole of the sodium chloridel.I n theinterval, 6 / 8-5 i 8AgC1 part of the sodium chloride is extractable.Synopsis of Results.-The following table will indicate the com-prehensive nature of Tammann’s investigations and their generalresults. I n every case the fraction refers to the second memberof the metallic pair of components :Components.Ag-Au ........................CU-AU ...........................Fe-V .............................Ag-Mn ........................Ag-Mg ........................*Zn-Ag ...........................*Zn-Au ...........................Pd-Au ........................Pd-Ag ...........................Chemical and galvanicreaction limits.- 218 418- 218 418118218 -1/8 -218 -- 218 418418418418- ----- -- -* The alloys containing zinc appear t,o be complicated owing to the existenceof “ intermetallic compounds. ”Tammann’s Theoretical Interpretation.-The interpretation ofthe above interesting observations is naturally of a geometricalorder. Only the sketchiest description can be given here. Thereare three space lattices in the cubic system: the cube (Tammann’s“ &point lattice ”), the centred cube ((( 9-point lattice ”), and thefacecentred cube ( ( r 14-point lattice ”). F o r each of these latticesthe most regular distribution (“ welll-tempered ” distribution) canbe worked out for two components, A and B (say, gold and copper,or gold and silver), or for three components, A , B, and C (say,sodium, silver, and chlorine), when present in the definite amountsimplied by 1/8, 2/8, 3 / 8 , and 4/8.Thus, in the case of a 2/8mixed crystal of gold and silver (for example, Au : Ag = 1 : 3), theregular distribution for the facecentred lattice is that in whichone of the four component cubic lattices is wholly occupied by goldatoms. It is apparently only in a well-tempered state t>hat nobleatoms will be in a position to protect less noble atoms, under whichf avourablel conditions, for every noble atom present, the protection(which is not individually, but socially, organised) may extendbeyond the limits 1 : 1 (4/8) and reach the limits 1 : 3 (2/8).Theefficiency of the protection is worked out with a wealth of ingenuityCRY STALLOQRAPHY. 217it partly depends on the chemical nature of the dissolvent andpartly on the nature of the space lattice. If properly protected,i t is only the surface atoms which are within reach of the dissolvent.If, however, the temperature is sufficiently high, the boundary layerof noble atoms may lose their protective powers, on account of thehigh rate of inter-diffusion of spacelattice components, with theresult that the structure is eventually deprived of its less nobleelements.General Con,cZtcsions.-In a comparison of the behaviour of alloysand mixed crystals of salts, Tammann points out that, diffusion inthe latter is extremely slow.Alloys can be thoroughly tempereda t several hundred degrees below the melting point, but mixedcrystals of compounds, as, for example, mixtures of sodium chlorideaqd silver chloride, require more prolonged treatment’ at tempera-tures relatively nearer the melting point. The comparatively slowrate of diffusion of isomorphous compounds can also be demon-strated visually by selecting substances (say, azobenzene anddibenzyl) in which the rate of interpenetration can be measuredby the advance of the coloured border. It is also pointed out thatthe anomalous double refraction of isomorphous mixtures of bariumand lead or strontium nitrates is referable! t o the fact’ that. deposi-tion from aqueous solution occurs at’ temperatures so far belowthe melting points of the constituents that true equilibrium cannotbe subsequently attained by a process of diffusion.Many kinds ofobservations are quoted showing thatl ordinary mixed crystals arescarcely ever homogeneous; this implies that< the laws of dilutesolutions are not rigorously applicable to “ solid solutions.” 3535 The above digest, somewhat inadequate for lack of space, was compiledfrom the only available original source, the paper printed in the Zeitschriftfur anorganische und allgemcine Chenzie. A comparison of that comprehensivereview with the abstracts of his numerous papers in the GGttingen Nachrichtenreveals the fact that a certain amount of revision has been undertaken byTammann ; thus, the previous statement that solutions of vanadic acid revealan intermediate reaction limit for gold-copper mixtures at 3/8-gold appears tohave been tacitly withdrawn.Again, earlier statements that “ with thehexagonal Sb-Bi mixed crystals the rate of action of different reagents altersabruptly at multiples of 1/6 ” is likewise dropped ; in the general interpretationsuggested by Tammann, the stages, if any, should follow the rule of “ eightp,’’not of “ sixths,” since the lattice can scarcely be hexagonal, but is ratherrhombohedra1 and pseudo-cubic. Moreover, i t is difficult to see how aninterpretation which holds for alloys typified by gold-silver, the constituentsof which have the same space lattice, can be regarded as satisfactory in sucha case as magnesium-silver in which the two-constituents exhibit fundament a1cliff erences of structure218 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.Some Crystallographic Eesearches.The examination of the double selenates of the general formulaeR$’e(SeO&$H,O and R2Co(Se0,),,6H20, in which R representspotassium, rubidium, msium, and ammonium, has been carried outby Tutton.36 The investigation of the iron series was rendered verydifficult owing to1 the instability of ferrous selenate.The work hadto be carried out a t as low a temperature as possible. The resultsconfirm all the author’s previous conclusions concerning the regularprogressive effects of potassium, rubidium, and cesium, and alsothe close similarity of the ammonium salts. On the, other hand,doubts have been expressed by I.Langmuir 37 concerning the innateisomorphous replaceability of potassium and the ammonium radicleas being a t variance with one of the deductions from his “octettheory ” of electronic distribution.3s The author attributes theisomorphism of potassium and ammonium sulphates to the mass-effect of the sulphate radicle, and he appeals to the, difference iiistructure, as revealed by X-rays, of the cubic chlorides. It may benoted here that a similar appelal to the iodides neutralises the valueof this evidence. Langmuir’s paper, however, mainly deals withthe more general aspects of iso’morphism. Thus, he is led to expectisomorphism, as a reeult of similarity of electronic arrangement,between the following pairs of compounds, which, i t will be observed,present the same general similarity of composition as Fedorov’s“ isotectonic ” and Barker’s “ unusual ” cases : NaF,MgO,MgF,,N+O, KCl,CaS, CaCl,,K,S, RbBr,SrSe, SrBr2,Rb2Se,CsI,BaTe, Ba12,Cs2Te, N,,CO, KCNO,KN,, NaHSO,,CaHPO,,KHSO,,SrHPO,, NaC103,CaS03, KHS03,SrHP0,, Na,S,O,,C~P,O,,Na,S,07,C+P,07, MnSe0,,2HzO, FeAs0,,2H,O.Relatively few ofthe above compounds appear to have been crystallographicallyexamined, but Langmuir gives fairly convincing evidence in thecases already known. For example, Hull has a t his suggMtiondefinitely proved by means of X-rays that magnesia has the samecubic structure as sodium fluoride and rock salt.A brief paper by Bowen39 serves to clear up the apparentlyirregular optical behaviour of the mineral torbernite,which under crossed Nicols only yields red and purple interference36 A.E. H. Tutton, Phil. Trans., 1919, [A], 218, 395; A., ii, 346; Proc.37 J . Amer. Chem. SOC., 1919, 41, 1543 ; A., ii, 506.38 Idem, ibid., 868 ; A., ii, 328.39 N. L. Bowen, Anzer. J . Sci., 1919, [ivl, 48, 195.c u (UO,), (PO,),, 1 2 H,O,Boy. SOC., 1919, [A], 96, 156 ; A., ii, 417CRYSTALLOGRAPHY. 218tints, even when the sections are so thin that' grey of the first orderwould be expected. It is found that the mineral is negative forshort wave-lengths and positive for longer wave-lengths, the wave-length for isotropism being 0.515 p.An elegant study of the natural and artificial etching figures oncrystals of the calcite group of minerals 40 admirably illustrates thelaw of symmetry; in all cases, the symmetry of form and dispositionof the figure is in accordance with true rhombohedra1 symmetry.Comparative experiments on cleavage plates betray degrees ofresemblance represented by calcite, niagnesite, rhodochrosite ;chalybite; .. . calamine. Apparently not cognisant of the workof Goldschmidt and Wright, the author records some observatioiiswhich illustrate the law of polarity.41The rotatory power of sodium chlorate crystals, both when pureand when coloured with " extra China-blue," has been determinedby P e r ~ c c a , ~ ~ who observed in different azimuths variations in therotatory value of the1 coloured crystals which amounted to some25 per cent. Variations were also observed for the pure crystals;the mean value for [u]: is + 3 O 7 1 .A crystal of sulphur from a unique source (a mixture of a hotalcoholic solution of ammonium polysulphide, beiizonitrile, hydroxyl-ainine hydrochloride, and ether) has been identified, and measuredby F. R. von Bichowsky,43 who also contributes a valuable statisticalsummary of the various forms which have been observed. Theauthor remarks on the prevalence of odd numbers in the indicesat the expense of even numbers, the interpretation of which hasbeen given by G . Friedel44 as a striking example of the Bravaisprinciple.A paper by G. F. H. Smith and R . H. Solly 45 on the perplexingform development of sartorite raises fundamental questions ofcrystal structure. The authors conclude that the crystals betraythe interpenetration of three distinct space lattices, one of which ismonoclinic, the other two anorthic. No doubt the authors haveexamined the question whether the simpler interpretation, offeredby Fedorov46 for the somewhat similar case of calaverite, is relevantor no; but, in any case, it seems to the Reporter that one of thecrystals (preferably No. 1) should bel crushed up and submitted toX-radiation by the Debye-Scherrer-Hull mebhod-the angular4O A. P. Honess, Amer. J . Sci., 1918, [iv], 46, 201.41 Ann. Report, 1917, 247.4 2 E. Perucca, Nuovo Cim., 1919, [vi], 18, ii, 112 ; A., ii, 487.43 J . Washington Acad. Sci., 1919, 9, 126; A., ii, 189.4 1 Bull. Soc. franc. illin., 1907, 30, 365.45 illin. Mag., 1919, 18, 259.4F Z'eitsch. Xmjst. dilin., 1903, 37, 611220 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.differences in the space lattices, inferred by the authors, mightallow of a definite substantiation of the correctness of theirinterpretation.The announcementl, some, nine months ago, of the death of Pro-fessor E. s. Fedorov, of Petrograd, came as a heavy blow to hismany admirers. A brief appreciation is postponed from thisReport in the hope that he may still be with us, actively further-ing the progress of science by his rare genius.T. V. BARKER