American Mineralogist, Volume 64, pages 1265-1271, 1979 Structure and symmetryof CuS, (pyrite structure) Husnnt E. KING, JR.' eNo Cnenres T. PREWITT Departmentof Earth and SpaceSciences State Universityof New York StonyBrook, New York 11794 Abstract X-ray diffraction data collectedon a single-crystalspecimen of CuS2show that despiteits optical anisotropyCuS, apparentlyhas the cubic pyrite structure,with a: 5.7891(6)A.pre- cessionand Weissenbergphotographs fail to reveal any reflections which violate the require- ments for space group Pa3. Such reflections, however, Wereobserved in four-circle di-ffrac- tometer measurements,but they are shown to result from multiple di-ffraction,effects. Reflement of the structurein spacegroup Pa3 using 209 intensity data givesa weightedre- sidual of 0.014and x(S) : 0.39878(5).A comparisonof the refined structurewith other pyrite structuressuggests that copper in CuSz has a formal valenceof 2+ and three antibonding electrons.Also, the CuSeoctahedron is only slightly distorted,which is in contrastwith the square-planarcoordination usually found for Cu2*. Introduction spect to the X-ray diffraction studies on FeS'. Fin- Disulfides of the transition elementsMn through klea et al. (1976) found no deviations from cubic Zn crystalllz,ein the pyrite structure. The Mn, Fe, symmetry,but Bayliss (1977)concluded that at least Co, and Ni membersof this group occur as minerals, sone pyrite crystalsare triclinic. Becauseoptical ani- and their structures have been refined. CuS, and sotropy has always been observedfor CuS, we de- ZnS.' are not found in nature, but they have been cided to investigate its crystal structure to provide synthesizedat high temperaturesand pressures.This further information on this intriguing problem. paper reports the results obtained in study a of the Experimental crystal structure and optical propertiesof CuSr. CuS, is of interestfor two reasons.First, its crystal The CuS, crystal used is a small (0.13 x O.l2 x chemistry is unique. Nakai et al. (1978)have shown 0.08 mm) rectangular prism selectedfrom material through X-ray photoelectronspectroscopy that most reported by Bither et al. (1968). Although polished copper sulfidescontain only Cu*; however,our crys- sectionsof thesecrystals are anisotropic in reflected tal-chemical evidenceindicates that copper in CuS, light, long-exposureprecession and Weissenberg is divalent. The copper is coordinated by six sulfur photographs failed to reveal any diffraction spots atoms in a trigonal antiprism slightly distorted from which are inconsistent with the requirements for an octahedron,rather than in its usual square-planar space group Pa3. This crystal was mounted on a coordination. Second,optical evidencefor non-cubic Picker four-circle diffractometer and its lattice pa- symmetry has been reported (Taylor and Kullerud, rameters were determined from twelve automati- 1972),btt not explainedin terms of the crystal struc- cally-centeredreflections s5ing MoKc radiation. The ture. Similar, but less intense, optical effects have least-squaresrefinement of the orientation matrix been reported for FeS, (Stanton, 1975; Gibbons, (Tichj, 1970)provides an unconstrainedestimate of 1967).These authors disagreeas to whether the ani- all unit-cell lengthsand angles;with the precisionob- : sotropy is entirely a surface feature or intrinsic to the tained, the geometry of the cell is cubic with a crystal structure.There is also disagreementwith re- 5.7891(6)A.This value agreeswell with previous de- terminations gsing X-ray powder diffraction tech- : I Presentaddress: IBM T.J. Watson ResearchCenter, P.O. Box niques: a : 5.7898A (Bither et al., 1968) and a 218, Yorktown Heights,New York, 10598. 5.7897 A (Taylor and Kullerud, 1972). oo03-.wx/79/ I I 12-1265$02.00 1265 1266 KING AND PREWITT: STRUCTURE OF CUS' we observed,as Baylisshad for FeSr,several forbid- den reflections(an efample for 500 is shown in Fig. la). However, all the forbidden reflections we ob- served could be eliminated by rotating the crystal around the diffraction vector to some arbitrary V angle (Fig. lb). i{, is a right-handed rotation whose zero is defined with or : 0 with m (hkl) plane in dif- fracting position. Further information was provided by making integrated intensity measurements at every 0.5o in V from -90 to *90o and plotting the results as I"*/2o, vs. V (Fig. 2). This figure shows that, even though the diffracted intensity is abovethe detection limit (1"o"/2o,= I in this figure) at some V values,it is below that limit at many other V values. Becausea Bragg reflection'sintensity should not be- come undetectableat any V value, we conclude that \ all such observed reflections, forbidden for space group Pa3, are the result of multiple diffraction ef- \", fects. We also believe that, although Bayliss (1977) may have beenworking with non-cubicFeS, crystals, Fig. l. A-20 scans for 400, 500 and 600 at two positions around he did not give sufficientinformation to elininate the : the diffraction vector: 9:0'(la) and V 15l' (lb). iP is a right- possibility that the extra reflectionshe observedwere handed rotation whose zero is defined when or : 0 with at (hklt plane in diffracting position. caused by multiple di-ffraction. Coppens (1968) discussedcriteria for the occur- With the crystal mounted on the diffractometer, rence of multiple Bragg scattering, and concluded we again tested for reflections which violated Pa3 that reciprocal lattice points within 0.003A-' of the symmetry. To minimize multiple diffraction effects, Ewald spherecould satisfythe requirementsfor mul- we used graphite monochromated MoKa radiation tiple di-ffraction.In order to test the applicability of and an arbitrarily-oriented crystal ([,0.1,03] was ap- this idea to FeS, and CuSr,we calculatedthe number proximately parallel to the O axis). Ttie 0-20 scan of reciprocal lattice points which meet this criterion mode was used.Even with this arbitrary orientation. for various setsof diffraction conditions.For the 100 Fig. 2. Results of integratedintensity measurementsat every 0.5o around the diffraction vector from -90 to 90'. The intensity is normalized to the detectionlimit (2o7);thus, a value >l is consideredto be observed. KING AND PRETI/ITT: STRUCTURE OF CuS2 1267 Table l. Refinementresults tions during the course of the data collection. In- tensities were corrected for Lorentz and polarization Spacegroup ^c t ^'l ^6 effectsas wel as absorption.The absorption correc- No. of reflections 251 tion was computedusing a modified versionof Burn- No. of observedreflections* 209 ham's (1966)program with the massabsorption coef- Wtd. r, all data** 0.014 ficients of Cromer and Liberman (1970). This n, a1| data+ 0.019 program also calculatesa geometric factor (Zachaia- Wtd. r, observedreflections 0.014 sen, 1967)used in the extinction correction. n, observedreflections 0.013 ^++ Refinement J I .75 The program RrINe4 (Finger and Prince, 1975) Reffecxions with I < 2aI are not was used for full-matrix least-squaresrefinement. incLuded in the observed refTect.ions, ** 2,1/2- Neutral scattering factors of Cromer and Mann wtd. r = r,2 ,---^ . tLw{1po1-lFcl)- /EwFo-l-' (1968) along with anomalousdispersion coemcients *n = rI lr^l-lr^llttlr^1. of Cromer and Liberman (1970)were used. Equiva- Standard deviation of an observation lent reflectionswere not averagedto allow for refine- weL9ttc. ment of anisotropicextinction. Only reflectionswith I > 2o, were used in the refinement. The structurewas refinedin spacegroup Pc3 using and 300 reflectionsof CuS, (MoKa radiation), there starting parametersfrom previous unpublished re- are many reflections within 0.003A of the Ewald finements.In the pyrite structure, the metal atom is spherein any orientation tried thus far. When b* is at the origin and the nonmetal one at x, x, x; thus, initially parallel to the X-ray beam and c* is normal there is one variable positional parameter.The start- to the equatorial plane, there are 47 other reciprocal ing model was one having isotropic temperaturefac- lattice points near the spherewhen 100is in diffract- tors and no correction for secondaryextinction. Sub- ing position. Similar results are obtained for FeSr. sequentmodels included anisotropicthermal motion Therefore,it would be extremelydifficult, using four- and both isotropic (Zachariasen, 1967) and ani- circle geometry, to prove that the extra reflections are sotropic (Coppens and Hamilton, 1970; Thornley a result of causesother than multiple diffraction. and Nelmes, 1974)secondary Qxtinction corrections. Diffraction intensities for structure refinement The final model containedcorrections for anisotropic were measuredon a Picker four-circle diffractometer thermal motion and anisotropic type 2 extinction. at the GeophysicalLaboratory (Washington, D.C.), These refinement results are shown in Table l, and using Nb-filtered MoKa radiation with the difrac- the observed and calculated structure factors are tometer operating n t};Le0-20 scan mode. 253 reflec- available.' Table 2 gives the final positional pa- tions were measuredrepresenting all with h, k, I > O rameters, anisotropic temperature factor coem- and 0o <20 < 60o,except for certain ft&Owhich were inadvertently omitted. Scan rates and background 2 To receivea copy of this material, order Document counting tirnes were adjusted for each reflection AM-79- I 14 from the BusinessOffice, Mineralogical Societyof America, (Finger et al.,1973) to producea value of 0.01 for o,/ 2000 Florida Avenue, N.W., Washington, D.C. 20009. Please L Referencereflections