March, 1925 CRYSTAL STRUCTURES OF HEMATITG, ETC. 78 1 volve the use of any organic solutions containing perchloric acid. Any remote danger of violent reaction resulting from the use of such solutions is eliminated. Gooch filtering crucibles with asbestos mats can be used wherever plati- num-sponge filtering crucibles are mentioned in this paper. Summary 1. The correct drying temperature of the insoluble alkali perchlorates has been found to be 350’. 2. The occlusion of perchloric acid by these salts has been studied. 3. Previous procedures for the perchloric acid separation of the alkali metals by extraction are shown to be faulty and an improved method is described. URBANA,ILLINOIS [CONTRIBUTION FROM THE GATESCHEMICAL LABORATORY,CAIJFORNIA INSTITUTE OF TBCHNOLOGY,No. 561 THE CRYSTAL STRUCTURES OF HEMATITE ’AND CORUNDUM BY LINUSPAULING AND STERLING B. HENDRICKS RECEIVEDJANUARY 12,1926 PUBLISHEDMARCH 6,1925 Introduction Hematite, Fe203,and corundum, A&&, form crystals which have been assigned,’ on the basis of observed face development, to the holohedral class of the rhombohedral system, with the rhombohedral angle a: equal to 85’ 42’ and 85’ 42$‘, respectively. Spectrometric measurements have been made2of the reflection of X-rays from three faces of ruby, A1403, and two of hematite. Utilizing the hypothesis that in ruby each aluminum atom is equidistant from six oxygen atoms, and each oxygen atom equi- distant from four aluminum atoms, a possible structure has been devised* which is not incompatible with these spectrometric observations. This structure has been used in a theoretical consideration of the influence of atomic arrangement on birefringen~e,~and in the explanation of the ob- served variation with temperature of the intensity of reflection of X-rays from faces of crystals of ruby and ~apphire.~An exact knowledge of the arrangement of the constituent atoms in ruby would make the arguments of these papers much more convincing. Powder photographic data from aluminum and ferric oxides prepared Groth, “Chemische Krystallographie,” Engelmann, Leipzig, 1908, Vol. 1, p. 105. * W. H. and W. L. Bragg, “X-Rays and Crystal Structure,” G. Bell and Sons, London, 1915, p. 171. W. H. and W. L. Bragg, “X-Rays and Crystal Structure,” 4th edition, G. Bell and Sons, London, 1924, p. 183. W. I,. Bragg, Proc. Roy. Soc., 106,346 (1924). 6 I. Backhurst, ibid., 102, 340 (1922). 782 LINUS PAWING AND STERLING B. HENDRICKS VOl. 47 under different conditions have been published;s but no attempt has been made to deduce their structures from them. The dimensions of units of structure of aluminum, ferric, and chromic oxides which are said to agree with unpublished powder photographic data have been reported.? We have, therefore) made a thorough X-ray study of crystals of hematite and of corundum, utilizing the results of the theory of space groups to interpret the data obtained from Laue and spectral photographs and considering all possible structures. Well-formed natural crystals of hema- tite, transparent faintly blue crystals of Ceylon corundum,* and sections cleaved from massive corundum were used. The X-ray data were ob- tained by the usual photographic methods described by Wy~koff.~The investigation was aided financially by a grant made to Professor A. A. Noyes by the Carnegie Institution of Washington. The Structure of.Hematite Photographic Data.-The data obtained from spectral and Laue photographs are presented in the usual way in Tables I and 11, respec- tively. The Unit of Structure.-A spectral photograph of the K-radiation of molybdenum reflected from the face (100)’ of hematite (planes denoted by primes refer to the axes used by Groth) gave, as shown in Table I, the value 3.682 f 0.010 8. for d/n. If n is one, this corresponds to a unit of structure with a = 3.70 A., and Q! = 85’ 42’. With one Fez08 in this unit, the density calculated from the X-ray data is 5.25, in good agree- ment with the observed values,’ which range from 5.15 to 5.30. TABLEI SPECTRALPHOTOGRAPHIC DATA FROM (110) OF HEMATITE Angle of d.0 Intensity of Line5 Order reflection n reflectionb P n 4O 54‘ 3.693 A. W a! 1z 5 31 3,700 m Y 2n 9 41 3.683 vw P 2n 9 52 3.678 in 011 212 11 5 3.686 S ffZ 212 11 9 3.681 ms a In Tables I and 111, y indicates MoKy, X = 0.6197 A.; 6, MoKP, X = 0.6311; al,MoKa1, X = 0.7078; az, MoKora, X = 0.7121; a,mean of a1 and a~,X = 0.710. ‘The abbreviations signify: s, strong; ms, medium strong; m, medium; mw, medium weak; w, weak; vw, very weak; vvw, very very weak. 6 Hedvall, Z.unovg. Chem., 120,327 (1922). 7 Davey and Hoffman, Phys. Rev., 15,333 (1920). Davey, ibid., 21,716 (1923). 8 We wish to thank Professor Charles Palache of Harvard University for the Ceylon corundum. 9 Wyckoff, “The Structure of Crystals,” The Chemical Catalog Co., New York, 1924, pp. 109-116 and 161-164. March, 1925 CRYSTAL STRUCTURES OP HEMATITE, ETC. 783 TABLEI1 LAUS PHOTOGRAPHIC DATAFROM HEMATITE Incident beam normal to (110). Structure factors calculated for u = 0.292, w = 0.1050. dhkZ nX Estimated hkl A. A. intensity Sl Sa sa -032 1.415 0.34 1 1.16 1.16 1.16 -131 1.215 .32 2 1.88 1.88 1.88 315 0.971 .44 2.5 1.88 1.88 1.88 322 .932 .28 0.4 1.59 1.59 1.59 053 .927 .32 1.3 1.36 1.98 2.60 -154 .go9 .30 6 5.33 6.42 7.51 326 .870 .38 0.03 0.61 0.61 0.61 456 .862 .42 .06 2.44 2.44 2.44 405 ,808 .30 .2 1.84 1.84 1.84 567 .732 .43 2.5 2.17 3.06 3.95 275 .717 .43 8 5.63 6.76 7.89 174 .678 .41 0.05 1.16 1.09 1.02 578 .636 .30 .6 3.32 4.25 5.18 -678 .623 .40 .1 2.44 2.44 2.44 172 ,586 .33 .2 1.73 2.35 2.97 497 .567 .42 .6 2.61 3.54 4.47 736 .560 -40 1.3 2.94 3.73 4.52 789 .559 .39 1.6 5.94 7.08 8.22 717 .552 -43 1.5 3.64 4.73 5.82 is1 .534 .42 0.3 1.87 2.49 3.11 194 .527 .39 1.5 5.26 6.39 7.52 3.10.7 .504 .34 0.4 5.89 6.82 7.75 E27 .497 .35 .3 3.78 4.87 5.96 536 .495 .32 .05 1.02 1.64 2.26 862 .493 .35 .04 2.54 2.54 2.54 9.9.10 .489 .42 .4 4.76 5.83 6.90 EOCi .488 .35 .6 5.70 6.83 7.96 5.i.m .469 .33 .04 3.14 3.63 4.12 &.$,E .461 .33 .I 3.76 4.65 5.54 BlTj .439 .28 .04 1.96 3.09 4.22 Upon assigning indices to the spots on a Laue photograph and calcu- lating values of nX on the basis of this unit, a number of forms, including (5% ] ’, {531]‘ and {91T}’, were found to have nX less than 0.24 A,, the lower wave-length limit of X-rays present in the incident radiation. This unit is accordingly eliminated. The corresponding hexagonal unit, as well as any hexagonal unit with the same value of d00.1,is also eliminated by these data. However, the hexagonal unit with twice this value for d00.1 does account for the Laue data. Similarly the rhombohedral unit containing two FeaOa obtained by taking new axes along the diagonals of the faces (loo)’, (010)’ and (OOl)’, accounts for all the Laue data, and is the smallest rhombohedral unit that does this. The hexagonal unit is improbable, for all planes of the ’large 784 LINUS PAULING AND STJ3RLING B. HeNDRICKS VOl. 47 class for which 2H + I + L, -H + I t- L, and -H-21 + L are not all divisible by three are found to give only third-order reflections, and it is difficult to explain the absence of first- and second-order reflections. Accordingly, the rhombohedral unit with a = 55’ 17’ and a = 5.42 =t0.01 fi., containing two FezOs, is taken to be correct. Indices (hhl) used in this paper refer to the axes of this unit. The Space Group.-Laue photographs show the symmetry of point group Dad; the structure is, accordingly, isomorphous with one of the point groups CavlDS and DSd. The only space groups fulfilling this requirement and based on a rhombohedral lattice are C:v, C:v, D:, D:d and DZ. Each of these space groups provides one or more arrangements of two E’ezOa in the unit of structure.1° Those afforded by CX, D: and D:d are improbable because they do not account for the observed absence of all planes of the type (hhl) with I odd, many of which were in positions favorable to reflection. Of the two remaining space groups Ctv and D3Bd the latter is taken as correct, for the crystallographic data strongly indi- cate the structure to be isomorphous with point group DSd. The Atomic Arrangement.-The possible arrangements allowed by D$ are Fe at (a) 000, )$+-- and (b) tit $2, or at (e)www, www, )-w )-w +-w, w+$ w+t w++, with 0 at (4 at% 8tb 9tt itt, 8tt, 2% or at (e) uii0, iiOu, Ouii, 3-u u++ +, u+4 + i-u, $ 3 -u u++.