American Mineralogist, Volume 66, pages 1250-1253, 198i,

Electronic structure of thiospinel minerals: results from MO calculations

Devro J. VeucHer-t Department of Geological Sciences University of Aston in Birmingham Birmingham 84 7ET, England

eNo Jonr A. Tossnll Department of Chemistry, University of Maryland College Park, Maryland 20742

Abstract

Molecular orbital calculations employing the SCF-X" scattered-wavecluster method have been used to model the electronic structures of the thiospinel minerals linnaeite (ColSa),carrollite (CuCozSl)and greigite (Fe:S+).The results, which are in agreementwith previously postulated qualitative models, support mixing of highest energy occupied orbitals (octahedral site e* and tetrahedral site e orbitals) in CqSa and CuCo2Sawith consequent metallic conductivity and temperature independent (Pauli) paramagnetism. This contrastswith FerSoin which spin-splittingof the orbitals in the valenceregion results in localized outermost electrons and ordered magnetism. The physical properties of thiospinels can be understood in terms of these molecular orbital models.

Introduction in good agreementwith experimental data Sulfides with the form a from spectra, have become available (Vaughan er large group of solids with interesting electrical and al., 1974;Tossell, 1977, for example).In this paper, magnetic properties (von Philipsborn, 1974).Natu- the results of such quantitative calculations have rally occurring thiospinels, although much fewer in been used to model the electronic structures of number (Vaughan and Craig, 1978),form a diverse CuCo2Sa(carrollite), Co3SaGinnaeite) and Fe3Sa group of minerals which exemplify problems of (greigite). Models derived from the calculations are more general interest in mineralogy. The then compared with the qualitative models and the systematics of the spinel structure-type have re- properties of thiospinel minerals considered in the cently been reviewed by Hill et al. (1979) and light of thesenew models. further data on the properties, phase relations and crystal chemistry of certain thiospinel minerals are Quantitative calculations-methods and results provided by Vaughanand Craig (1978). The Self-Consistent-Field )L Scattered-Wave Qualitative molecular orbital and band theory Cluster method (abbreviated"SCF-)L-SW") is a models have been applied to gain an understanding molecular orbital method which yields results in of the chemical bonding in thiospinels by Gooden- good quantitative agreement with experiment for ough (1969)and by Vaughan et al. (1971),The latter many chemical and mineralogical systems (John- authors also showed how such models may be son, 1975;Messmer, 1977; Rosch,1976; Tossell et employed in order to understand the composition al., 1974;Vaughan et a|., 1974;Tossell, 1978a). limits, variation in cell parameters,microhardness, The method is based on the division of a crystal- reflectanceproperties, relative stabilities and hence line structure into component polyatomic clusters geological occurrence of the mineral thiospinels. such as the CoSn6 tetrahedral unit which can be Since publication of the qualitative models, meth- usedto representthe tetrahedralsite Co2* in Co3Sa. ods for the quantitative calculation of molecular The spacewithin and around the cluster is geomet- orbitals, which give results for transition metal rically partitioned into atomic sphere regions cen- 0003-m4>v81iI I l2-1250$02.00 1250 VAUGHAN AND TOSSELL: THIOSPINEL MO CALCULATIONS t25l tered on the metal and anion nuclei, with spheresin The choice of oxidation state and spin-statefor the contact and completely enclosed within an outer cation employed in the calculation was based on sphere beyond which is an extramolecular region. evidence available from electrical and magnetic Within the outer spherebut between atomic sphere studies, neutron diffraction, Mossbauerspectrosco- regions is the interatomic region. The electrostatic py and electron spectroscopy (see Vaughan and potential of the remaining atoms in the crystal Craig, 1978,for further information). lattice is approximated by a spherical shell of posi- Although the calculations provide data on the tive charge (the Watson Sphere) passing through relative energiesof all valence and core orbitals, it the anion nuclei. is only the highest energy orbitals of the valence The potential energy in the various regions is region which are significant for understanding evaluated using electrostatics together with the X" bonding models and the properties of the sulfides. statistical approximation of Slater; the potential is In these , and sulfides, it is then simplified and used to solve numerically the orbitals dominantly of metal 3d character which one-electron Schr

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Fig. 1. Orbital energy level diagram showing results ofSCF-X"-SW calculationson the clusters CoS;e, CoSa6,CuSt7, FeS;5, FeSflo and FeSfe for the relative energiesofoutermost (valence)orbitals. For those systemscontaining unpaired electrons the efects of spin-splitting into spin-up ( t ) and spin-down ( J ) MO's is shown. 1252 VAUGHAN AND TOSSELL: THIOSPINEL MO CALCULATIONS

3d type orbitals) at the top ofthe valenceband. For emphasizesthe importance of spin-splitting of the 3d configurations in which unpaired electrons oc- orbitals in the valence region. A previous study of cur, a further effect to consider is that of spin- Fe3Oa(Tossell, 1978b)yielded a qualitatively similar splitting of the MO energy levels into spin-up and cluster MO diagram.Studies on Fe3Oa(see Shuey, spin-downsets as shown in Figure 1. 1975) have shown that its conductivity increases greatly above its Verwey temperature(119K), at Comparisonof quantitative and qualitative which the Fe ions in the octahedral site become approaches indistinguishable. In this state, the t2, octahedral The orbital energy diagramsshown in Figure 1 for site orbital is close in energy to the e tetrahedralsite CoSf e and CoSa6 indicate that the empty esorbitals orbital and so strong mixing and metallic conductiv- of the octahedral cluster will be close in energy to ity ensues.Such may also be the casefor greigite. the partially filled e orbitals of the tetrahedral cluster. Since the energy of interaction between Electron structure modelsand the propertiesof orbitals varies inversely with their energy difer- thiospinels ence, we would expect the octahedral site e, and The qualitative models outlined by Yatghan et al. tetrahedral site e orbitals to mix substantially. A (1971)were used to show how variations in unit cell band of energy levels would thus be formed with a parameter, microhardness,and reflectancecould be width greater than the original er-e separation. explained for the mineral thiospinels in terms of This will lead to metallic conductivity and weak bonding models. In terms of smaller overall unit cell temperature independent (Pauli) pararnagnetismof parameters and metallic properties, thiospinels Co3Sa.The resulting band energy level diagram will such as Co:S+, CuCo2Sa,Ni:S+ and FeNi2Saare be very similar to those postulated by Goodenough considered to form a group characterizedby delo- (1969)and Vaughanet al. (1971). calization of the outermost (essentially metal 3d) In extending in composition to CuCozS+,overlap electrons. The calculationssupport this approachto can again be envisagedbetween empty e* orbitals the electronic structure of Co3Saand CuCo2Saand on octahedral site cobalt atoms and e and tz orbitals give confidence in its application to the other thio- of the tetrahedral site copper. Although the as- . Variations of physical properties and in sumed oxidation state of copper is Cu2* we have stabilities of membersof this group can be interpret- reason to expect from other calculations (Tossell, ed on the basisofthe numberofelectrons occupy- 1978a)and spectroscopicdata (Nakai et al.,19781' ing the band formed from the e, and e orhital Folmer and Jellinek, personal communication) that overlap. the oxidation state of copper approaches Cu+r. In contrast to the metallic group of thiospinels, Again CuCo2Sais a metallic Pauli paramagnetand greigite and a number of other minerals including the qualitative orbital diagram proposed on the daubr6elite show evidence of having localized va- basis of observed properties (Goodenough, 1969; lence electrons. The unit cell parameters of mem- Vaughan et al., l97l) is supportedby the results of bers of this group are appreciably greater and calculations. The clusters chosen as approximate evidence of stable solid solution series not seen; models for CuCo2Sa are CoSfe and CuStT for observationswhich can be explainedon the basis of reasons discussedabove. Such a set of electron the major differences in electronic structure ob- configurations suggestsa deficiency ofelectrons on served between members of the two groups and the S anions. An alternative assumption of a d5 well shown for the case of greigite in Figure L configuration on octahedral Co would stabilize the Further evidence will be presented elsewhere t2, orbital so much that it and the Cudrot2 would no (Vaughan and Craig, in preparation) to show that longer be close in energy and would interact only greigite is metastable. Examination of Figure l. weakly leading to nonmetallic behavior. suggeststhat the occupancy of highly destabilized Greigite, Fe3Sa, in contrast to the other two antibonding orbitals by electrons would causesuch thiospinels, has ferrimagnetic and semiconducting instability. properties and the Mcissbauer spectrum suggests high-spin Fe3* in tetrahedral and octahedral sites Acknowledgments (Vaughan and high-spin Fe2* in octahedralsites and Cathy Kennedy is thanked for typing the manuscript and Ridout, 1970;Hulliger, 1968).The model for the Beverley Parker for drafting the figure. The authors acknowl- electronic structure of greigite shown in Figure I edge the support ofNero grant No. 1509. VAUGHAN AND TOSSELL: THIOSPINEL MO CALCULATIONS 1253

References structure of Cu in tetrahedraland triangular coordination with S. Physicsand Chemistryof Minerals2,225-236. Goodenough, J. B. (1969) Descriptions of outer d electrons in Tossell, J. A. (1978b) Self-consistant field X- study of one- thiospinels. Journal of Physics and Chemistry of Solids 30, electron energy levels in Fe3Oa.Physics Review Bl7 . 26r-280. ,484487 Tossell, J. A., Vaughan,D. J. and Johnson,K. H. (1974)The Hill, R. J., Craig, J. R. and Gibbs, C. V. (1979)Systematics of electronic structure of rutile, wiistite and hematitefrom molec- the spinel structure type. Physicsand Chemistry of Minerals 4, 317-339. ular orbital calculations. American Mineralogist 59, 319-334. Vaughan, D. J., and Craig, J. R. (1978)Mineral Chemistry of Hulliger, F. (196E)Crystal chemistry of the chalcogenidesand Metal Sulphides. Cambridge University Press, Cambridge, pnictides of the transition elements.Structure and Bonding 4, 82-229. England. Vaughan,D. J. and Ridout, M. S. (1971)Mdssbauer studies of Johnson, K. H. (1975) Quantum chemistry. Annual Review Physicsand Chemistry26,39-57. some sulphide minerals. Journal of Inorganic and Nuclear Chemistry33,741J47. Messmer, R. P. (1977)The molecular cluster approach to some Vaughan, D. J., and Burns, R. G., and Burns, V. M. (1971) solid state problems. In G. Segal, Ed., Modern Theoretical Geochemistryand bonding of thiospinel minerals.Geochimica Chemistry Vol. E, p. 215-246,Plenum Fress, New York. CosmochimicaActa 35, 365-3E1. Nakai, I., Sugitani,Y., Nagashima,K., and Niwa, Y. (197E)X- Vaughan,D. J., Tossell,J. A., and Johnson,K. H. (1974)The ray photoelectron spectroscopic study of copper minerals. bonding offenous iron to sulphur and oxygen: a comparative Journal of Inorganic and Nuclear Chemistry 40,789-791. study using SCF-X. scatteredwave molecular orbital calcula- Rosch, N. (1976) The SCF-X. scattered-wave method with tions. Geochimica CosmochimicaActa 38, 993-1005. application to moleculesand surfaces.In P. Phariseauand L. Von Phillipsborn, H. (1974)Zur Kristallchemie von Sulfide and Scheire, Eds., Electrons in Finite and Infinite Structures,p. l- Selenid Spinellen. Fortschrift Mineralogie 51, 2Ol-239. 143,Plenum Press, New York. Shuey, R. T. (1975) Semiconducting Ore Minerals. Elsevier, Amsterdam. Manuscript received, November 24, 1980; Tossell, J. A. (1978a) Theoretical studies of the electronic acceptedfor publication,June 5, 1981.