Araki, Takaharu

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RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:The Crystal Structure of Wulfenite,PbMoO_4Araki, TakaharuAraki, Takaharu. The Crystal Structure of Wulfenite, PbMoO_4. Memoirsof the College of Science, University of Kyoto. Series B 1957, 24(2): 155-1601957-10-15http://hdl.handle.net/2433/258497       MEMOIRS OF THE COLLEGE OF SCIFNCE, UNIVERSITY OF KYOTO, SERIES B,             Vol. XXIV, Ne. 2 Geology and Mineralogy, Article 3, 1957          The Crystal Strncture of WulÅíenite, PbMo04                                   By                            Takaharu ARAKI             GeologiÅëal and Mineralogical Institute, University of Kyoto                           (Received July 25, 1957)                                 Abstraet    The crystal $tructure of wulfenite, PbMoO, was determined by means of X--ray oscillation                                                oephotographing. The unit cell has the dimensiensof a--5.47A, c =12.18A and the space groupis C46h-I4i/a. There are four chemical units of PbMoO, in Åíhe unit cell. The coordinatesof atems were found by two dimensional Fourier synthesis and those of oxygen atoms werefurther refined by the difference synthesis.                               Introauetien    Hitherto several authors have determined lattice constants, numbers of chemicalunlt, space groups and atomic coordinates of the minerais of schee!ite type structure.But, only a few resuits of X-ray stgdies on wulfenite have so far been reported.DicKiNsoN (1920) was the first to examine the structure of wulfenite and soon afterVEGARD and REFsuM (1927). The atomic coordinates of oxygen atoms in thestructure were, however, not fully determined. On the other hand, SILLEN andNyLANDER (l943) found coordinates of oxygen atorns of this mineral, applying therigid sphere method which based on certain assumption. It is desirab}e, however,that these coordinates are checl<ed X-ray crystallographically.                              Experimental    Specimens found in Bolivia, South Amerlca, were submitted to the presentstudy. X-ray photegraphings were carried out using unfiltered Cu-K radiationsthroughout.    The lattice constants were determined by the a- and c-axis rotation photograph-ings. The lattice constants thus obtained are as follows:                                  eo           a==5.47Å}e.01A c=12.18Å}O.02Athe annexed errors being the probable errors. The result is in good agreementwith that reported by previous authors. The ratio, a:c=1:2.226 is also in goodagreement with aXiai ratio given in th'e Dana's System of Mineralegy. The number156 Takaharu ARAI<Iof chemical unit of PbMeo, in the unit celi is 4. The space group is CX,-I4i/a,hfel refiexions being present only wheR h-!. lg '. l=2?t, hho refiexions only when lv--2n,Ie :=2n and Oel reflexions only when l--4n. The resuks are also in good agreementwith those reported by the previous authors.                            Structure analysis    Intensities of the reflexions on the oscillatien photographs were estimated!2gelS$S•pt• '  grs 'ljevtmpz2iEililllFig. 1.Do0   aElectronContoursdensity in theat intervals ofc>oN....wwN $sllgeSl!l._.__.rmLa_......_......{IIIL)ts__.._._L'rOIO] projection, lo e.A-2. zereobtainedCOntellrSmarethe final broken.summation.The Crystal Structure of Wttlfenite, PbMoO, 157visually with the aid of intensity edge and corrected fer the Lorentz and polariza-tion factors, but not for absorption nor ternperature factors. The corrected intenskies,which approximately proportional te the structure factors were then converted to aset of numbers.    It was proposed by the previous authors that metal atoms of some compoundsof scheelite type structure were }ocated on the speclal positions and in the presentcase it was confirmed that heavy atems were located on that posltlons Åírom theobservation of streng refiexions. 'I'herefore, the signs of Fe's whose values wererelatively large could be easily found. At the outset, the electron densities in the[010] and the [OOI] projectlons were evaluated by means of two dlmensionalFeurier synthesis using Fe's whose signs could be determined, and the maxima inthe electron density rnaps, which represent the positions of heavy atoms, werefound to coincide exact}y wlth the specia} positions, Subsequently, the coordinatesof oxygen atoms were searched for by the method of trial and error using theintensities of reflexions, to which heavy atoms do not contribute. Then, the appro-xirr}ate structure of wulfenite could be found.    For the refinement of the coordinates of atoms, two dimensienal Fourier sum-matioRs were carried out using Fo's at first, whose signs were settled from theapproximately determined structure, iat intefvals of 1/60 of the cell edgeswitk tke aid of Beevers and Lipsonstrips. But, final summation were atintervais of 1/60 and 1/l20 of a-and c-cell edge respectively. Forscattering factors Thomas-Fermi'svalues for heavy atoms and Viervoiland Ogrim's values for oxygen atomswere used. After repeating the sum-mation several times, giving neces-sary corrections for the coordinatesof oxygen atoms, the maxima in theelectron densky map, wliich representthe pesitions of oxygen atoms, almostcoincided wlth coordinates of theatoms. In Fig. 1 are shown theelectron density in the [010] projec-tion, obtained in the final sumrnation.   For further fefinement of the eoor-dinates of oxygen atoms, differencesynthesis was then carried out, us-ing the differences between Fo's andF(Pb, Mo)'s. Where, F(Pb, Mo)'sare the calculated structure factors4Zo-N\iN''x'xN s )'"yx NN_.__ "x'x-Nxtb:;yi' t-Nt"  xlvnv..itt(xx'1N'N'x' s slxtx,N•x 11Itt,lN.c//:1-t 't{t    XEIectron density in the [010] projection,ebtained in the final difference synthesis.Contours at intervals of 4e.Anv2. zerocontours are broken, negative contoursdotted. Positions of Pb and Mo atomsare rnarked by selid circle and crossrespectively.lzFig. 2.158 Takaharu ApLAi<xto which oniy Pb and Mo atoms contribute. After repeating this synthesis severaltimes, giving necessary corrections, the maxima in the electron densky map satis-factorily coincided with the coordinates of oxygen atoms cho$en. In Fig. 2 areshown the electron density in the [010] projection, obtained in the final differencesynthesis.    The coordinates of atoms found in the fina! structure are given in Tabie 1. Thetermination errors of the atomic coordinates in the [0101 projection are given inTable 2.Table 1. Coordinatesstructure ofof atoms in thewulfenite. Table 2. Termination errors.AtomPbMooINurnber in theof atomsunit cell4416x/ao.oooo.ooo0.247ylb zlc Atom0.250     0.6250250     0.1250.342     O.040PbMoo   ex (A)o.oooo.oooO.O03   ey (A)   O.O05I   oz (A)so.eoeo.oooo.o2e    In Table 3 are summarized Fo's and F.'s. F.'s are calcu!ated with atomic eoor-dinates finally obtained and Fe's are rendered, at the finai stage of the analysis,comparab}e on an approximately absolute scale by rnultiplying a facter which mini-mumizes the sum of differences between corresponding Fo and Fc.Table 3. Observed and calculated structure factors for hleO and hel regexions.ehfel Fo02004006020022022024024026026o4oe420420440440460lI 246  287  299  245  224i 273. 23!  310  315  271  279  266  310  252s 252  235iFc- 376 326- 213 376- 335-  335 326 332- 259- 254 326- 331- 326 232 232- 223llfell46e600620620640640O04O08OO1210i10310510710910.llFe202265235271235202273307328 25 32 69 97 81 87Fc- 221 213- 254- 259 22i 223- 362 304- 316 -95  73 133- 122 -63  66Ihlel i F,10.13le.1520220420620820.1020.1220.143013e330530730930.11 55 48 21188232 38207 23102 84 31 34 62 80Fc  66 -56 -61- 388  -3 319  29- 246  24 -96  93  79 -76 -77  71lllItII{Il•ifels30.134024044064084e.lo40.12.5015035e5507509602604606liFe 72 57264191 22191 87 86 84 55 64264Fc  66  45- 297   3 266 -28- 242 -78  90  50 -49 -81 -1- 266   oThe Crystal Structure of Wulfenite, PbMoO, 159The reliability numbers, R="Y}llFoI-1F.Il=lFoI, are 0.20 for hleO and 0.29 for hOlreflexions.Description of the strtteture   The structure of wulfenite is il!ustrated inscheelite type structure reported by the previouscoordinates of oxygen atoms with those obtained Fig. 3.attthors.by the  It is essentiaily of the Nowever, comparing therigid sphere method, thereCaFig.oO    Mo Pb3. The crystal  (elO) plane.  expressed by   ostructure ef wulfenite, projected onNumbers denote the heights of atomsthe percentage ef b-translation.16eare appreciable diffeyences espe-cially iR y-coordinate and withthose of scheelite and BaW04,there are also considerable dif-ferences in coordinates.    Mo atom is situated at thecenter of tetrahedron of four ex-ygen atoms, whereas Pb atom issurrounded by eight oxygen atomswhich form somewhat irregularpolyhedron. Each 0 atom is shar-ed by one Mo and two Pb atoms.Interatomic distances are given inTable 4.Tal<aharu ARAI<I  Table 4. Interatomic distances.Atom AtomMo-OPbi 0Pb2 OOI 02Ol 03o, o.,02 0302 04Q3---O,01 Os'Distance  e (A)lli1.772.492.822.882902.902.9e2.902.882.90IAtomiAtomIEl01 02iOi 0601 0701 07iOl 08Ol 09'ol OleOl----03'Ol Oll''Distance   o  (A)2.943.283.343.404.024.034,254.324.53                             Acknowiedgment    The writer wishes to express his sincere thanks to Prof. Dr. T. ITo and Mr.T. UEDA wlio }<indly gave him advice in this work. He is also indebtecl to Dr. KSAKuRAI who sent him preciotts specimens used in the present experiment. He isalso grateful to Dr. K ']]ANAKA, and to Messrs. Y. FuJiwARA, T. SFJTo who affordedfaci!ities in taking X-ray photographs.                                References                          /Dici<iNsoN, R. G. (1920): J. Am. Chem. Soc., 42, 85.SiLLSN, L. G. and NyLANDER, A. (1943): Arkiv. Kem. Min. Geol., Z7 A, No. 4, 1.VEGARD, L. and REFsvM, A. (1927): Norsk. Geol. Tidsskr., 9, 24.

The Crystal Structure of Wulfenite, PbMoO_4

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The Crystal Structure of Wulfenite, PbMoO_4

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