CR,YSTALLOGRAPHY AND MINERALOGY.THE striking renewal of activity in the subjects under review in thisReport is all the more gratifying because they were among the firstto suffer from the outbreak of war. The volume of work to be notedis, indeed, so considerable that space will not allow some investi-gations to be treated in accordance with their intrinsic merits. !Thisis especially the case perhaps in the province of crystal-structure.In the first place, there are to be noted two books of more thanordinary value. The one by Niggli1 not only contains a full andclear account of all the point-systems, but also brings the subjectup to date iq the light of X-ray methods and results. Sommerfeld’sbciok2 is more general, covering, in fact, recent developments in awide field of physical discovery and interpretation, to which thestudy of crystals has contributed so powerfully.Then there are twoimportant contributions to the related subjects of atomic distancesand volumes, and also many successful reconstructions of crystals,all of which will receive due notice. On the other hand, an ingeni-ous development of X-ray technique must be disposed of here some-what summarily. The method depends essentially on the study ofa sequence cf Laue photographs, the crystal being turned through aknown number of degrees, by the help of a special tvo-circle gonio-meter, between the various exposures. m e photographs are thenanalysed by the help of a new instrument termed a ‘(cyclometer,”and the direction of a structural plane of symmetry, if such bepresent, is thereby located.Fresh exposures on the goniometerlead to a determination of the ‘‘ X-ray class of symmetry,” that is,the real class to which has been added a centre of symmetry; and aset of crystal-elements can also be deduced. I n other words, theinvestigation oan be evidently carried t o the same stage as is custom-P. Niggli, “ Geometrische Krystallographie des Diskontinuums,” 1919,a book that arose from an analytical investigation of the cubic-point systemby the same author, Jakrb. Min. Beil-Bd., 1919, 43, 1.A. Sommerfeld, “ Atombau und Spektrallinien.”a R. Gross, Gentr. Min., 1920, 52.19CRYSTALLOGRAPHY AND MINERALOGY. 199ary by orthodox geometrical methods, but the crystal need have noplane faces. The method has already been applied to crystals oftungsten,4 and also, without an actual publication of details, to tri-dymite and hzmoglobin.What appears to be a final determination of the symmetry-class ofthe mineral benitoite may well be mentioned here, as illustratingthe meaning of the term X-ray class of symmetry.According toF. Rinne,s there are only three symmetry-classes which are worthyof a consideration : (1) trigonal equatorial, (2) ditrigonal equatorial,and (3) ditrigonal polar, each of which by addition of a centre ofsymmetry happens to lead t o a distinct class, namely, (1) hexagonalequatcrial, (2) dihexagonal equatorial, and (3) dihexagonal alter-nating. Laue photographs of homogeneous portions of a crystalunmistakably rule out the first and third alternatives, and benitoiteis accordingly the first representative of the ditrigonal equatorialclass.Theoretical discussions of the finer details of crystal structure arebecoming more frequent.The effect of various possible types ofelectronic arrangement on the general symmetry of the diamond,rock-salt, and sylvine has been worked out by H. Thirring.6 Withregard to the much-vexed question of the chemical aspect of crystalstructure, opinion would seem to have taken a welcome, if belated,turn in the German literature-perhaps on account of Wiilstatter’s 7expressed opinion that the disappearance of the molecule in a crystalcannot be reconciled with the immense body of well-established factsof organic chemistry.Two papers by A. Reis 8 are also suggestivein this connexion. An allusion may also be made here to the impor-tant work, which has been carried on during the last twenty-fiveyears, on the hehaviour of crystals to infra-red radiation-work thatis disseminated in various journals and worthy of a complete Reportin itself. In a sense, the work has more chemical interest thanX-ray work, for infra-red radiation would seem to be a molecular asopposed to an atomic probe. All carbonates, for example, exhibitan intense reflection for infra-red rays of a specific wave-length, nomatter whether they are in the state of fusion, solution, or crystal.Quite recently there have been numerous attempts to correlate theextreme wave-lengths (residual rays--(-( Reststrahlen ”) , selectivelyreflected by crystals, with the elastic and other constants.An im-portant paper by H. Rubens and H. von Wartenberg 0 is the key toR. Gross and N. Blassman, Jahrb. Min, Beil-Bd., 1919, 42, 728.Centr. Min., 1919, 193.Ph?ysikal. Zeitsch., 1920, 21, 281 ; A., ii, 477. ’ R. Willstatter, Zeitsch. angew. Chem., 1919, 32, 331.Zeitsch. Elektrochem., 1920, 26, 408, 412.Sitzungsber. Preuss. A k d . Wiss. Berlin, 1914, 189 ; A., 1914, ii, 236200 A."UAL REPORTS ON THE PROURESS OF CHEMISTRY.some of the earlier papers. Some supplementary references 10 tomore recent papers may be useful to those who are interested. Itmust be noted that the conclusions about fluorspar are vitiated byan arithmetical mistake. An early publication of the new compu-tations is promised.As the portion devoted to Mineralogy is supposed to cover aperiod of three gears, it will be realised that no space can beallotted to the results of chemical analysis and descriptions of newmineral species; further, that little attention can be devoted towhat may be termed the observational side of the science.Fortun-ately, these aspects are already well cared for in special journals.A recent list of new minerals, for example, has been given bySpencer,ll and a new venture on the part of the MineralogicalMagazine-the publication of abstracts-would seem t o be justifiedby results. Several important American investigations of mineralsystems are to be noted, which emphasise the desirability of thefoundation on this side of something of the nature of a Petrophysi-cal Institute; which, without being an exact copy of the Americanoriginal, could fruitfully co-operate with it in the advancement ofpure and applied science.Without some such centre there arealmost insuperable difficulties in the way of any serious Europeancontributions t o experimental mineralogy, for the problems thereinvolved require such special resources as are scarcely within thepower of a University laboratory to provide. One department ofsuch an Institute might well be devoted to the manifold chemicalproblems connected with crystals. The future of crystallo-chemicalanalysis, in particular, would seem to require something more thanthe spasmodic support of individuals.The simplification of themethod, and the reduction to a unified system of the numerouscompounds described within the last six years, not to speak of thelimitless compounds of the future, would require some form oforganised effort. Chemists could then be encouraged, not only tosend their new crystalline compounds to be investigated and regis-tered, but also to expect help, as a matter of course, in the identi-lo H. Rubens, Ber. Deut. physikal. Ges., 1915, 17, 315 ; Sitzungsber. Preuss.Akad. Wiss. Berlin, 1917, 43 ; H. P. Rollnagel, Physical Rev., 1918, 11, 135 ;M. Born, " Dynamik der Kristallgitter," 1915 ; Ber. Deut. physikal. Ges.,1919, 21, 533; M. Born and 0. Stern, Sitzungsber. Preuss. Akad. Wiss.BerZin, 1919, 48, 901 ; M. Born, ibid., 1918, 604 ; A., ii, 401 ; M.Born andA. Land6 Ber. Deut. physikal. Ges., 1918, 20. 210; A., 1919, ii, 188; A.LanZt, ibid., 1918, 20, 217 ; 1919, 21, 644 : K. Fajans, ibid., 1919, 21, 539,714; A.. ii, 21; M. Born, ibid., 1919, 21, 533; Ann. Physik, 1920, [iv], 61,87 ; A . , ii, 227 ; M. Born and E. Bormann, ibid., 1930, 62, 218 : W. Voigt,dbid., 1919, 60, 638.l1 I,. J. Spencer, Min. Mag., 1919, 18, 373CRYSTALLOGRAPHY AND MINERALOGY. 201fication of complex products of reaction, especially in those casesin which they are hampered by a paucity of material.Atomic Distances and Volumes.Two recent attempts to carry our knowledge of atomic volumesbeyond the stage represented by Lothar Meyer's well-known curvewould seem to indicate substantial progress towards a solution ofthe simpler problems connected with this most difficult subject.The first paper to be noted deals not so much with volumes aswith atomic distances in crystals.As a result of a critical survey ofthe numerous structures which have been successfully determinedby various X-ray workers, W. L. Bragg12 finds that the distancebetween contiguous atomic centres of any given pair of elements,A and B, is almost constant for all crystals. Now, if the atoms beregarded as spherical, this distance can be regarded as made up ofthe sum of the radii of the two atoms, and if the radius of atom Abe known then the radius of atom H can be obtained by subtrac-tion. In this way, by making use of the X-ray data referring tosuch crystalline elements as carbon, silicon, and various metals, theauthor is subsequently able to deduce preliminary values for theatomic radii of such elements as oxygen, nitrogen, sulphur, and thehalogens, which have so far only been investigated in the form ofcompounds.These preliminary estimates are then mutuallyadjusted by an elaborate series of cross-checks, the result being atable of mean radii or diameters, in agreement as a rule with indi-vidual observations within the limits k10 per cent. Further, it ispossible to deduce diameters for certain other elements from com-parisons of the molecular volumes of isomorphous substances. Theresults are given in the form of a curve (with atomic diametersplotted against atomic numbers), which is here reproduced as far asthe element strontium (see Fig.1). It is seen that the diameters,as thus deduced from the established structures of crystallineelements and compounds, are of the same periodic character as theso-called atomic volumes of the Lothar lleyer curve. (Paren-thetically, it may be here added that the ionic radii for the halogensand alkali metals have been deduced in another way by A. Land6,13who attributes a greater radius to a halogen ion than to an ion ofthe alkali metal immediately following it in the list of the elements.A similar view is held by K. Fajans.l* This want of agreementbetween Bragg and Land6 and Fajans cannot be discussed here, itsthe more important of the German papers are not available.)la Phil. Mag., 1920, [vi], 40, 169; A., ii, 537.l3 Zeitsch.Physik, 1920, 1, 191 ; A., ii, 540.l4 Ibid., 2, 309; Zeitsch. Elektrochern., 1920, 26, 502.H202 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.Bragg’s paper must be consulted for a discussion of the physicalsignificance assigned to these diameters. The immediate objectwould seem t o be strictly practical. “The way of regarding theatoms as spheres packed tightly together is useful in constructingmodels of crystalline structures . . . and, it is hoped, will help infuture investigations . . . by limiting the number of possiblearrangements.” An example of this practical usefulness will begiven below under casium dichloroiodide. The writes would alsomention that the application of the method to the cassiterite groupand to anatasel5 points t o the need of a revision of the modelswhich have hitherto been offered.The second investigation refers to the volumes of elementaryatoms. Setting out from the current view that the elements typi-fied by sodium, magnesium, aluminium, and silicon respectivelypossess 1, 2, 3, and 4 outer electrons, and a corresponding effectiveFiQ.1.number of positive charges on the nucleus, Sommerfeld 16 examinesthe attractive effects of these successive increases in nuclear chargeon the radius of the outer electronic ring, and he deduces that theatomic radii of the four elements specified should exhibit the ratios1:0*57:0.42:0-33. He also points out (as will be indicated pre-sently) that these values are in fair agreement with the valuesobtained by dividing atomic weight by specific gravity.Now W. L.Bragg has emphasis4 the fact that the structural details of acrystal must be taken into account; that the packing of sphericalatoms is closer in some elements than in others; in other words,that the old meaning of atomic volume is of the nature of a fiction.It is therefore interesting t o bring into the comparison the valuesof the true absolute volumes (for which the writer is responsible),l5 Ann. Reports, 1917, 14. 233. l6 A. Sommerfeld, op. cit., 105CRYSTALLOGRAPHY AND MINERALOGY. 203and also their ratios.lowing table.The various results are embodied in the fol-Table of Volume Constants.Na. Mg. Al. Si.Hull's abso1ute"distances (p) ......... 3-72 3-22 2.86 2-35 x cm.True absolute spherical volumes..26.9 17.5 12.2 6.79 x C.C.True atomic-volume ratios ............Sommerfeld's theoreticd ratios ......Sommerfeld's cited ratios ................1-00 : 0-65 : 0-45 : 0.251-00 : 0.57 : 0.42 ; 0.331-00 : 0.57 : 0.41 : 0.51It is seen that the true atomic-volume ratios are in general agree-ment with Sommerfeld's theoretical values, and do not exhibit thegreat discrepancy 0-51 with respect to silicon-an apparent but nota real anomaly, which is simply due to the relatively open packingof the silicon (or diamond) structure. The general agreement is nodoubt due to the relative simplicity of the problem of atomicvolumes in the particular case of chemically uncombined elements.*Recent Structural Models.In view of the novelty and high degree of importance attachedto the X-ray method, an attempt has always been made in theseReports to give complete lists of those models which appear to bewell established.This custom will be adhered to on the presentoccasion.Some Cubic and Hexagonal Elements and Compounds.-Thlereare some fifteen substances which can be disposed of in the form* A brief note on the more salient aspects of atomic volumes in compoqdsmay not be out of place. It might seem a t the outset that the conversi,onof W. L. Bragg's absolute " atomic diameters " into corresponding sphericalvolumes (whereby the fluctuations naturally become of the order +_ 30 percent.) might throw light on such a perplexing problem as the undoubtedvolume equality of ammonium and rubidium compounds-a problem towhich neither atomic weights nor atomic numbers bring any solution.Now the radius of the ammonium radicle can scarcely be greater than thesum of the radius of nitrogen and the diameter of hydrogen.As the latterdiameter is generally accepted by physicists to be 10-8 cm., the radius of theradicle comes out to be 1-65( x 10-8 cm.), which is much lower than 2.25,the radius of the rubidium atom. The corresponding spherical volumes are,of course, much further away from the expected ratio 1 : 1, being by calcula-tion in the proportion 1 . 2-5. The nearest interpretation of this discrepancyis that an initially spherical or (as some mathematical physicists prefer)cubical atom suffers a deformation on entering into chemical union ; but theobvious difficulties which stand in the way of any precise definition of thenew shapes, added to the possibility that atoms may change their volumeon combination owing to a rearrangement or an actual transfer of electrons,would seem to demand the discovery of new methods of experimentationbefore real progress can be made.H* 204 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.of a table. With the exception of thorium and nickel (determinedby H.Bohlin)," all the values given below are due t o Hu11,18 whosays, apropos cobalt : " A finely powdered sample produced by rapidelectrolysis showed a mixture of cubic and hexagonal close-packingin nearly equal ratio. After annealing in hydrogen at 600°, thissample showed only the cubic form.Another sample, composed offilings from pure cast metal, showed slight traces of hexagonal pack-ing, due presumably to straining. It is possible that the otherclose-packed metals will behave in a similar manner, but this ques-tion has not been studied." According t o Hull, ductility in ametal is a result of a face-centred cubic arrangement.Table of some Cubic and Hexagonal Structures.Distance be-Arrangement Grating distance tween atomicof atoms. of cube planes. centres.Cobalt (dimorphous). .. Face-centred cube(cubic close-packed).Thorium .................. Do. 2.56 3.62Nickel ..................... Do. 1.765 2-50Rhodium ............... Do. 1.9 1 2.70Platinum ............... Do. 2.01 2-86Chromium ...............Centred cube 1.455 2-52Molybdenum ............ Do. 1.576 2.7 3Magnesium ............ Hexagonal close- - 3.222.84 Zinc ..................... Do.3-15 Cadmium ............... Do.Cobalt (dimorphous). .. D O . - 2.53Lithium fluoride* ...... Simple cube 2.01 2.01Sodium fluoride* . . , , . . Do. 2.31 2-3 1Potassium fluoride* ... Do. 2.69 2-69Magnesium oxide* ... Do. 2-11 2-111.785 x lo-* cm. 2.52 x 10-8 cm.packed. --* In these four cases the arrangement of like atoms is, of course, given bythe face-centred cube.,4n.timony.lg-The nature of this structure is perhaps best graspedas follows. Suppose the familiar rock-salt cell, of Fig. 2, be set upwith a solid diagonal vertical and then extended along it until theoriginal cubic 9O0-angle has attained the value 9 2 O 53'.The edgeof the cell must now be taken t o be 3.10 x 10-8 cm.; the correspond-ing length of the vertical diagonal is 5.64. Now let 'the centresof the chlorine atoms be shifted through a vertical distance of 0.42(exaggerated in Fig. 3), and finally suppose all the atoms to be re-placed by antimony; the result is the antimony structure, which isthe first example among eleaents of a '' hexahedral " structure, thatl7 Ann. Physik, 1920, [hl, 61, 421 ; A., ii, 214.ID R. W. James and N. Tunstall, Phil. Mag., 1920, [vi], 40, 233 ; A.. ii, 648.A. W. Hull, Proc. Arner. Inst. Electrical Engineers. 1919, 38, 227CRYSTALLOQRAPHY AND MINERALOGY. 205is, one in which each atom is closely environed by six other atoms.Ir, all previous cases of elementary substances the environment hasalways been tetrahedral, octahedral, or dodecahedral.Zincite,20 Zn0.-The crystal structure of this well-known dihexa-gonal polar mineral provides one of the few cases in which a verbaldescription is better than a diagram.Isomorphous with green-ockite, CdS, and wurtzite, ZnS, it exhibits an interesting structuralcontrast t o the commoner form of zinc sulphide-zinc blende. I nboth minerals the zinc atoms are essentially arranged in accordancewith the principle of close-packing, the difference being that in zincblende the “ cubic ’’ style of close packing is affected, in zincite the(( hexagonal ” style. I n both structures the zinc (or cadmium)atoms are environed tetrahedrally by the sulphur (or oxygen) atoms.FIG.2. FIG. 3.The absolute vertical distance in zincite between successive layersof similar atoms is 2.60, whilst the horizontal interval betweenadjacent atomic centres is 3’22. It is of interest to recall the factthat E. S. Fedorov 21 showed that two different structures are recon-cilable with the preliminary observations recorded in W. H. andW. L. Braggs’ well-known book, one of them demanding atomicpolarity, the other being the structure finally adopted by W. L.Bragg.The Calcite Group.-An X-ray study that has some bearing onthe question of the existence of groups of atoms in crystals we oweto R. W. G. WyckoffyB2 who has subjected calcite, rhodochrosite,chalybite. and magnesite (as also sodium nitrate23) to an investiga-2o W.L. Bragg, Phil. Mag., 1920, [vi], 39, 647; A , , ii, 433.a1 Bull. Acad. Sci. Petroqrad, 1916, 10, 377.aa Amer. J . Sci., 1920, [iv], 50, 317.23’Idem., PhyRicaZ Rev., 1920, [ii], 16, 149 ; A., ii, 756206 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.tion by the Nishikawa method-essentially an ingenious combina-tion of the Laue and de Broglie methods. The nature of some ofthese compounds has been previously elucidated by W. H. andW. L. Bragg, who explained their results in terms of a face-oentredlattice, but the structures are, perhaps, best visualised as beingthe sodium ohloride structure, which has been deformed along athreefold axis until the cleavage cube has acquired the angles ofthe cleavage rhombohedron, the sodium and chlorine atoms beingthen regarded as substituted by calcium atoms and carbonate groupsrespectively. An inspection of Fig.4 (which is drawn true to scale)will show t>hat triads of oxygen atoms are relatively close to indi-vidual carbon centres. The main result of the new investigation ist:, show that these triads are a t a constant distance of 1.22 Ang-strom units from their corresponding carbon atoms, although allother atomic distances vary considerably in passing from one car-FIG. 4. FIG. 5.nbonate to another-the distances between adjacent carbon andmetallic atoms, for example, being 3.04 and 2.83 A.U. in calciumand manganese carbonates respectively. This can be interpreted asevidence of the persistence in the crystal structure of the C0,-groups, the internal details of which are, so to speak, no concernof the externally placed metallic ion.Caesium DichEoroiodide, CsC1,I.-The elucidation of this rhombo-hedral substance has been successfully accomplished by the sameauthor24 by means of the Nishikawa method.The lattice can beregarded as derived from the rock-salt type of structure, by a com-pression along a three-fold axis, until the cubic 90° angle hasacquired the rhombohedra1 SOo 12’ value. The absolute dimensionof this vertical length is 6-06 x 10-8 cm.; czesium and iodine atomsare placed alternately a t the corners. A chlorine atom is locatedR. W. G. Wyckoff, J . Amer. Chsm. SOC., 1920, 42, 1100; A., ii, 489CRYSTALLOGRAPHY AND MINERALOGY. 207on the principal axis of this cell at a distance equal to 0.62 timesthe celldiagonal, from either the msium or the iodine atom.* Theorigin of this ambiguity lies in a circumstance peculiar to thechemical composition ; the reflecting powers of the horizontal strataof msium and iodine atoms are approximately equal (on account ofthe close atomic weights or numbers of the elements concerned), andthe strata are accordingly indistinguishable from each other bymeans of X-rays.. , . The writer therefore thought it would beinteresting t o examine the two questions : (1) whether the structureas determined by Wyckoff is reconcilable with W. L. Bragg”s valuesof atomic diameters, and (2) whether the application of theseatomic diameters serves to remove the ambiguity concerning theposition of the chlorine atoms.The answers to both these ques-tions would seem t o be emphatic affirmatives. Figs. 6-7 representFIU. 6. Fqa. 7 .uertical elevations on the plane (il0). In Fig. 6 W. L. Bragg’smean ualues, Cs =4*74 ; I = 2.80 ; C1= 2- 10, have been adopted;although there is a slight interpenetration of the iodine and chlorinespheres of influence, the spacial accommodation for the variousspheres can be regarded as satisfactory. This interpenetration canbe avoided and the general fit improved, without tampering withWyckofYs data, if some such amended values as Cs=5*36, 1=2.70,and C1=1*90 be adopted (compare Fig. 7). In both figures thechlorine-centres have been taken as lying nearer to iodine than tomsium; if the chlorine-centres lay nearer to czsium, they wouldfall inside the e s i u m atoms.* Since emh of the corner-atoms of the cell is really common to eightcells in an idnitely extended structure, and since the chlorine atom bslongswholly to the cell illustrated, it follows that the total cell-composition ia${Cs,T,)Cl, which is equivalent to CsICl,208 A ~ A L REPORTS ON THE PROGRESS OF CHEMISTRY.Physical Crystallography.This important branch of physics is poorer by the loss of ProfessorW. Voigt, of Gottingen, so celebrated for his experimentalresearches io 'elasticity and the many other abstruse properties ofcrystals requiring a highly mathematical treatment.EZectroZytic Conduction.-The many experimental difficultieswhich have long stood in the way of an exact study of electrolyticconduction in crystals have been recently overcome by Tubandt,26who has thereby opened up a new field of investigation (the abstractmust be consulted for an account of the general method of experi-mentation).Since the specific conductivities of the compoundsexamined are very low a t ordinary temperatures, the experimentswere carried out in a stream of an indifferent gas at as high a tem-perature as practicable. This immediately led to the interestingobservation that the specific conductivity of the cubic form of silveriodide (stable above 144'6O) is 3000 times as great as in the caseof the hexagonal modification (both measured near the transitiontemperature), and if the measurement be effected close t o themelting point the value is actually much higher for the solid thanfor the fused substance.Crystals of silver chloride, bromide, andiodide were found to behave as unidirectional electrolytes, permit-ting freely the migration of silver ions (in amounts which rigor-ously obey Faraday's law), but preventing all movement of halogenions in the reverse direction. Lead chloride, however, behaves inexactly the opposite way, the negative chlorine ions migratingfreely. The author points out that these trustworthy results ofcareful experiment are difficult to reconcile with a view that thecrystal ions of binary compounds are held in equilibrium by elec-trostatic forces. The investigation of silver sulphide, of whichthere are two forms, /3 (179O)a, revealed a new point of interest.The high temperature a-modification behaves just like the halogensalts of silver, but with the &form there is simultaneously an elec-tronic conduction in the opposite direction, so that the crystalexhibits both electrolytic and metallic conduction. The author isdisposed to refer this to the presence in the B-form of two kindsof molecules.Ultramicroscopic inclusions in Crystals.-It will be rememberedthat inorga& ultra-microscopic '' colloidal " particles have beendefinitely proved to be crystalline by the use of the Debye-Scherrer-Hull method of X-ray exploration.26 The investigation of minuteC.Tubandt, Mitt. Naturjor8ch. Ges. HaZEe, 1917, 4, 21 ; C. Tubandt andS. Eggert, Zeitsch. anorg. Chern., 1920, 110, 196 ; A., ii, 279; C.Tubandt,Zeitsch. Elektrochern., 1920, 26, 360. es Ann. Rep&, 1919, 16, 197CRYSTAXLOQRAPHY AND MINERALOGY. 209particles in crystals by the help of the ultramicroscope is now pro-ceeding. The beginnings of this work apparently lie in a suite ofpapers 27 on the nature of nietal-fogs in crystals. It has been foundthat absolutely pure crystals of lead chloride, silver chloride, andbromide (that is, crystals of the ordinary substances which havebeen recently treated with halogen to transform any trace of freemetal into haloid) are ultramicroscopically transparent. I f thismaterial is melted and treated with a trace of free metal or of areducing agent like potassium cyanide, a metallic fog is producedin the re-solidified material.Novel results are obtained in the caseof lead chloride, for owing to the strong double refraction of thecrystal each speck of light, arising from an ultramicroscopio par-ticle, is doubled and plane-polarised. Thallium ohloride andbromide could not be obtained clear, since they cannot be treatedwith halogen without the formation of higher haloids.The method has been more recently applied28 to a study of theorigin of opalescence in mixed crystals of sodium and potassiumchloride, occasionally erupted by Vesuvius. The previous investi-gation of the binary system, NaCl-KCl by Nacken 29 was, of course,invaluable. m e opalescence is due to a separation of the twocomponents consequent on the temperature falling below the pointof complete miscibility for a given mixture.It was instructive toobserve the process in laboratory products of various compositions,as it gradually unfolded itself under the ultramicroscope. Thecrystal becomes doubly refracting, due to strains ; then the sepa-rated particles reveal their existence, and finally strains and thedouble refraction disappear. The author proposes to attack thesystem orthoclase-albite, in which a primary homogeneous mixedcrystal (“ anorthoclase ”) will no doubt eventually yield a micro- orcryptoperthitic structure.Specific Beats of Minerals.-A monumental research on thespecific heats of the various modifications of silica and of the moreimportant silicates has been published by White,so who within thelast few years has greatly improved the general technique of hightemperature measurement.The constants directly determined were‘‘ interval-specific heats,” that is, average specific heats over suchranges of temperature as 0-looo, 0-300°, 0-500°, and so on.From these values the specific heat a t any desired temperature wasdeduced by two new methods, which gave perfectly consistent27 R. Lnrenz and W. Eitel, Zeitsch. anorg. Chem., 1915, 91, 46, 57, 61;A., 1915, ii, 260.2 8 W. Eitel, Centv. Mia., 1919, 173.R. Nacken, S~tzungsber. Preuss. AEad. Wi.~s. Berlin, 1918, 192: A.,1919, ii, 281.$0 W. P. White, Amer. J . Sci., 1919, [iv], 47, 1 ; A., 1919, ii, 133210 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.results, and this when multiplied by the factor M / n (where M isthe molecular weight, and n the number of atoms in the molecule),finally yields the mean atomic heat.At the ordinary tempera-ture the value of the lastrmentioned constant is of the order 3-3 forsilica and 3.75 for silicates; it increases with rise of temperature, a tfirst quite rapidly and then more gradually as it approaches alimiting value in the neighbourhood of 6-0. The results will nodoubt have great significance in the future study of certain geologi-cal proeesses, but it may be noted that tkey have already animportant bearing on various questions of great theoretical. interest.The atomic heat a t constant volume, for example, can be computedfrom the observed atomic heat. a t constant pressure by the help ofa well-known thermodynamic formula, involving compressibility,thermal expansion, and density, but the computed value for cristo-balite (according to Fenner 31 the stable modification of silica above1470O) cannot be reconciled with generally accepted theoreticalideas, which must accordingly rest on a faulty basis.Moreover,the results obtained from a study of the various modifications ofsilica oan be used as a test of the reasonableness of Smits’ theoryof dynamic sllotropy,s2 and as a result of his painstaking work ofprecision the conclusion is drawn by White that it is possible toover-estimate the value of that theory.Optics.-Attention must be called t o a paper33 on the generaloptical properties of amyrolin, C,,H,,O,. This monoclinic substanceexhibits an abnormally high birefringence (apparently onlyexceeded by calomel), and is also very noteworthy on account of astrong dispersion of the conical refraction.Two papers by A.Ehringhaus 34 on the dispersion of the birefringence of manysubstances are also worthy of a careful perusal.Corn para t iue Chemical Cry st allogra ph y .The progressive nature of the effects produced by a mutual sub-stitution of the elements potassium, rubidium, and caesium, as wellas the close similarity of rubidium and ammonium compounds,which has been largely emphasised by Tutton’s investigations dur-ing the last thirty years, is now so well known that iC is onlynecessary to place on record a recent paper by this indefatigabhworker35 dealing with the compounds typified by the formula31 C .N. Fenner, Trans. SOC. Qlass Technology, 1919, 3, 116.32 Ann. Reports, 1914, 11, 268.33 H. Rose, Jahrb. Min., 1918, 1 ; A., 1918, i, 266.34 Ibid., Be&-Bd., 1916, 41, 342 : 1920, 43, 557.35 A. E. H. Tutton, PYOC. Roy. SOC., 1920, [A], 98, 67 : A., ii, 690ORYSTALLOGRAPHY AND MMEIEALOGIY. 211R,Cu(SeO,),,GH,O. There are also two papers to be noted refer-ring to series of organic compounds. m e first, by A. Ries,% dealswith an extensive series of mono-, di-, tri- and tetra-alkyl deriv-atives of ammonium picrate, some of which have been previouslyexamined by Jerusalem. The main results of this work are two innumber: first, the prevalence of polymorphism in organic com-pounds (many of the substances appearing in three or four forms),and secondly, the regularity with which one of the modifications ofevery tetra-substituted picrnte is either strictly hexagonal orpseudo-hexagonal.The theoretical interpretation of this regu-larity would have been easy if the substances concerned had beentri-substituted. The second paper 37 deals with the series of com-pounds, typified by the general formula R,N*HgI,, in which Rrepresents various alkyl, aryl, or alphyl groups. One result is toprove that the raceniic compound, dl-Ph(CH,Ph)MeEtNHgI,, isisomorphous with the corresponding diethyl oompound, whichnecessarily consists of identical and symmetrical molecules. Perhapsthe most noteworthy features of the paper, however, are the omis-sion of all computed angles, as being unnecessary to any futurepurpose, and also the description of the methods devised in recentyears, which serve to reduce the routine work of crystal descriptionto about one-third of that formerly required.Methods of Investigating Opaque Substances.Although opaque minerals are not relatively very numerous, theyrepresent a highly important class of compounds, if only becauseof their supreme economic value.In the pasf the identification ofopaque compounds has had to depend on such simple physical testsas density, cleavage, hardness, and streak (supported by themethods of chemical analysis), since the ordinary optical methodsare only applicable to transparent substances; but in recent yearsmore and more attention has been paid to those special microscopicmethods introduced by Sorby, which have been developed more andmore in connexion with metallography.This technique has beenapplied t o minerals (notably in America). The new method hasbeen recently expounded in at least two books,38~~ and a generalaccount, together with a most valuable bibliography, has also been36 Zeitsch. Kryst. Min., 1920, 55, 454 : A., i, 715.3 7 T. U. Barker and (Miss) M. W. Porter, T., 1920, 117, 1303.3 8 J. Murdoch, ‘‘ Microscopical Determination of the Opaque Minerals, ”3 3 W. M. Davy and C. M. Farnham, “Microscopic Examination of Ore1916.Minerals,” 1920212 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.given by a German worker.40 The method has been variouslynamed '' Mineralography," " Opakography," and " Minera-graphy "-terms which are perhaps less pronounceable than " Chal-cography " (suggested by Brauns).The method consists essentially of the examination, under amicroscope fitted for side-illumination, of the upper surface of aspecimen which has been ground, polished, and possibly etched withvarious reagents.Both ordinary and plane polarised light areemployed. In the latter case any opaque mineral that does notbelong to the cubic system may reflect two plane or ellipticallypolarised rays, one of which is somewhat retarded (not, in general,to the same extent as in the case of transparent substances). Theprinciples underlying the various optical effects have been recentlytreated very thoroughly by Wright:' who has also done much toperfect the finer technique.42 The method has obviovsly a greatfuture, not least on the purely scientific side, for it promises tolead t o a revision of many opaque mineral species.It should alsoprove useful in the examination of dyes and lakes.Thermal Studies of Mineral Systems.Thermal studies of mineral systems are becoming so numerousthat they cannot all be described with a fullness proportionate t otheir deserts. I n making a selection, the writer is compeIled torestrict himself to some relatively simple investigations, and, infer-entially, to omit any consideration of the complex ternary system,43Ca0-Mg0-SO,, as also of Niggli's work 44 on certain mixed fusionsinvolving the oxides of sodium, potassium, calcium, aluminium,carbon, silicon, and titanium.It is believed that the relativelysimple cases will give a general idea of the significance of thepresenbday Lype of work, which is presumably the main object ofthis Report.Binary Systems involving Barytes, Getestine, and Anhydrite.-In continuation of his previous work,45 in which it was proved thatbarytea, celestine, and anhydrite pass into other modifications(probably monoclinic) a t high temperatures, Grahmann 46 hasinvestigatz? the miscibility relations of the substances over a vastH. Schneidwhtihn, Jahrb. Min. Bed.-Bd., 1920, 43, 400.41 F. E. Wright, Proc. Amer. Phil. SOC., 1919, 58, 401.42 Idem, Mining and Metallurpt, 1920. No. 158.Is J. B. Ferguson and H. E. Merwin, Amer. J . Sci., 1919, [iv], 4$, 81, 165;44 P.Nigqli, Z0;tsch. csnorg. Chem., 1916, 98, 241 ; A . , 1917, ii, 211.4.5 Ann. Reports, 1913, 10, 256.4 G W. Grahmann, Jahrb. Min., 1920, i, 1.A . , 1919, ii, 401, 459CRYSTALLOGRAPHY AND MINERALOGY. 213range of temperatures. The method adopted was that of coolingcurves, supplemented by density determinations and by a study ofthe optical properties in thin sections. It is found that each pairof the a(high temperature)-modifications yields an uninterruptedseries of mixed crystals. This is also true for the ~ ( I o w tempera-ture)-modifications of barium and strontium sulphates-in otherwords, for barytes and celestine. On the other hand, the misci-bility of the &modifications of calcium and strontium sulphates(anhydrite and celestine) is limited even a t the high temperatureof 1000c, and becomes more restricted a t the ordinary temperature.Anhydrite can take up 42 mol.per cent. of strontium sulphate, andcelestine up to 12 per cent. of calcium sulphate-the mixturesbeing isodimorphous in Retgers’ sense. Anhydrite and barytespresent a similar behaviour, but the miscibility is much morerestricted, each being able to take up about 6 per cent. only ofthe other. The research is, of course, of considerable mineralogicalinterest, for it reveals miscibility possibilities far in excess of thoseactually observed in nature, as determined by mineral analyses.Binary System A’Icermanite-Gehlenite.4~--The investigation ofmixtures of these two compounds may be regarded as an excellentexample of the experimental method of studying a perplexingmineral problem.Two distinct species-gehlenite,3CaO,Al2O3,2SiO2,and melilite, Na,O,l 1 (Ca,Mg)0,2 (A1,Fe),03,9Si02-are usuallyrecognisecl as belonging to the tetragonal “ melilite group.” Witbthese must be reckoned the closely related iikermanite, an impor-tant constituent of furnace slags, which, according to Vogt, is essen-tially a calcium silicate, 4Ca0,3Si02. Now a well-defined com-pound, 2Ca0,Mg0,2Si02, was found by Ferguson and Merwin toplay an important r61e in the ternary system, Ca0-Mg0-SiO,, andthey concluded it to be Akermanite in its purest form; moreover,since a compound, 2Ca0,Al,03,Si0,, deemed to be pure gehlenite,had been previously prepared by Rankin and Wright, the investi-gation of the equilibrium relationships of gehlenite and iikermanitesuggested itself as a method of attacking the difficult problem ofthe melilite group.It is found that the two isomorphous compon-ents form an uninterrupted series of mixed crystals exhibiting aminimum melting point (Roozeboom’s type 111). As gehlenite andAkermanite are respectively negative and positive optically, oneof the mixtures (55 per cent. of kkermanite) is isotropic. (As amatter of fact, this inversion of optical character was observed byVogt in the case of certain furnace slags, which he regarded as47 J. B. Ferguson and A. F. Buddington, Amer. J. 8 c i . , 1920, [iv], 50,131 ; A., ii, 621214 ANNUAL REPORTS ON THE PROQRESS OF CHEMISTRY.mixtures of gehlenite and hkermanite.) Another interesting itemis that akermanite glass has a higher density and refractive indexthan the crystalline modification.The authors hope to continuetheir work, so auspiciously begun, and there can be little doubt,that the correct interpretation of the melilite group will not be longdelayed.Ternary Systent,*8 Mg0-A120,-Si0, .-The investigation of thissystem was beset with much difficulty owing to th8 high tempera-tures involved, which were frequently beyond the limits of theplatinum furnace. The various binary compounds have been eluci-dated in previous researches and noted in these Reports. T'he onlyterhary compoutld is apparently a simplified cordierite,2Mg0,2A120,, 5 SiO,,a phase which decomposes a t a temperature lower than its meltingpoint, but which can crystallise out of a complex mixture a t some-what lower temperatures. The compound is best prepared byholding a glass of like composition a t temperatures lying between900° and 1400O; an unstable form begins to appear a t 900°, whichgoes over at a somewhat higher temperature to the stable form.The equilibrium relationships of this cordierite are somewhat com-plicatetl by the fact that it forms solid solutions wit.h spinel,MgA1,0,, and sillimanite, Al,SiO,.Natural cordierite containswater, and part of the magnesia is replaced by ferrous oxide, butthe general similarity in optical properties is sufficiently close toestablish its identity with the synthetic, iron-free cordierite.The Dehydration Process in Crystals (" Eflorescence ").The results of a comprehensive investigation of this process havebeen recently published by Gaudefroy.49 Although not generallysusceptible to ocular proof under the microscope, loss of water isalmost certainly accompanied by a temporary local liquefaction.Byway of a general suppopt to this conclusion, Gaudefroy sta€es thatalmost any finely powdered hydrate can be transformed into acoherent cake by simply allowing it to remain in a desiccator for afew hours. This behaviour he attributes to a temporary solutionof the solid in the water which it is about to lose by evaporation.In at least one case a periodic liquefaction and solidification isdirectly observable under the microscope. Under certain conditionsa crystal of the heptahydrated zinc sulphate becomes covered withmonoclinic crystals of the hexahydrated salt, which extend their4 8 G.A. Rankin and H. E. Merwin, Amer. J . SC~., 1918, [iv], 4-5, 301 ; A.,1918, ii, 199.4 9 C. Gaudefroy, Bull. SOC. Jranc. Min., 1919, 42, 284CRYSTALLOGRAPHY AND MINERALOGY. 215boundaries in a rhythmic manner. A t various stages a tiny crystalof the hexahydrate is surrounded by a zone of liquefaction, intowhich it grows as water is eliminated. The loss of one mo'iecide ofwater of crystallisation is accompanied by a contraction equal toabout one-tenth of the original molecular volume; and the surfaceof the new crystal consists of a concentric system of furrows andridges as a result of this periodic shrinkage.Another general point of interest is that the inception of dehy-dration and consequently the local fo?mation of a dehydrationfigure can be readily brought about by inoculation with a frag-ment either of the actual product of dehydration or of a substanceisomorphous with it. T'hus if an orthorhombic crystal of mag-nesium chromate, MgCr04,7H20, be simply touched by a crystal ofthe anorthic copper sulphate, CUSO,,~H,O, dehydration of thechromate to the pentahydrate begins immediately, and proceeds atsuch a rate as to be visible to the naked eye.Many hydrated substances lose water of crystallisation in morethan one well-defined stage.To each stage there corresponds acharacteristic dehydration figure. Thus, ferrous sulphste,FeS0,,7H20, either loses three m3leculss of water or one; in theformer case the figures are elliptical, whilst in the latter case theboundaries are rectilinear, being, in fact, either triangles ortrapezia.With many substances two or more kinds of transforma-tion take place simultaneously, so that it becomes impossible bymeans of a chemical ahalysis to correlate each type of dehydrationfigure with the specific amount of water lost There are, however,other ways of deducing the composition of the different products.Thus the hept'ahydrated cobalt sulphate, unlike its isomorphferrous sulphate, does not give the elliptical type of dehydrationfigure, but only the rectilinear type, and as the product can beproved by chemical analysis to be the hexahydrate, the same mustbe reasonably true of the corresponding type of figure given byferrous sulphate.A oonfirmatory test is to drop small fragmentsof the dehydrated salt into a saturated solution of another salt; ifthe fragments grow isomorphously, their composition is therebysatisfactorily determined. This test is particularly trustworthy inthe case of tlhe vitriols, which have been so thoroughly investigatedby previous workers from almost every conceivable point of view.Following is a brief summary of the various types of dehydrationfigure revealed by Gaudefroy's researches.Rectilinear Figures Determined by the Crystals under Dehydra-tion.-Figures of this class are quite numerous, being, in fact, givenin 54 per cent. of the substances examined. The dehydrationtakes place most favourably along certain selected planes of th216 ANNUAL REPORTS ON THE PROGRESS OF CHEMlSTRY.structural lattice, with the result that the dehydration figures onany given face are bounded by traces on that face of other impor-tant structural planes.By a study of the forms of the dehydrationfigure on the best developed faces of a crystal the “dehydration-polyhedron ” can be determined, from which the dehydration figurefor any other face can be deduced in the usual way. I n the case ofthe monoclinic heptahydrated’ sulphates of iron and cobalt, thedehydration polyhedron is bounded by the forms {OOl}, (110}, and{ 101j. The material within the boundaries of a given dehydrationfigure is a t first limpid, but soon becomes opaque; during thelimpid stage i t can be proved optically to consist of an irregulararrangement of minute crystals.Rectilinear Figures Determined by the Product of Dehydration.-Each of these figures, in their simplest form, represents a singlecrystal of the new hydrate. The figures on any given face haveaccordingly no precise orientation. A good example is the hexa-hydrated decomposition product of ordinary zinc sulphate, whichhas already been mentioned as growing rhythmically.Figures Exhibiting a Diuision into FOUT Sectors.-These areespecially common in gypsum, the anorthic and orthorhombicvitriols, and the ferrocyanides. Opposite sectors are optically simi-lar. The diagonals of the sectors are generally more distinct thanthe external boundaries, and have a definite orientation on eachcrystal face. The fine structure of the sectors is sometimes verycomplicated, but as a rule each sector is made up of a parallelbunch of fibres.EUipticaZ Pigures.-These figures are characterised by an extra-ordinarily fine texture of component particles arranged with everypossible orientation. The figures are generally very deep-seated,and the internal surfaces are also curved. Wherever several kindsof dehydration figure are given by the same substance, the ellipticalfigures are characteristic of that chemical change which involves thegreatest loss of water, and the excessively minute size of the com-ponent particles is attributed to the powerful disruptive effects ofthe correspondingly great contraction of molecular volume. It isicteresting to note that the ratios of the ellipsoidal axes may differwidely in isomorphous substances. In zinc vitriol, for example, theratios are 1.1 : 1 : 1.4, whilst in the corresponding magnesium saltthe ellipsoid practically becomes a sphere, and the figures on allthe faces are substantially circles and not ellipses. In a monocliniccrystal one of the three ellipsoidal axes is always coincident withthe symmetry axis, and in a uniaxial crystal the ellipsoid is one ofrotation.T. V. BARKER