Hostname: page-component-7dd5485656-bvgqh Total loading time: 0 Render date: 2025-10-31T16:35:47.683Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermodynamics of (Zn,Fe)S sphalerite. A CVM approach with large basis clusters

Published online by Cambridge University Press:  05 July 2018

A. I. Balabin  and
R. O. Sack
A. I. Balabin
Affiliation:
Department of Geological Sciences, Box 351310, University of Washington, Seattle, WA 98195/1310, USA
R. O. Sack*
Affiliation:
Department of Geological Sciences, Box 351310, University of Washington, Seattle, WA 98195/1310, USA
*
*E-mail: chukchi@u.washington.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We have developed a cluster variation method (CVM) model based on cuboctahedral and octahedral basis clusters containing 13 and 6 atoms, respectively, and applied it to the analysis of the thermodynamic mixing properties of (Zn,Fe)S solid solutions. The model, in which the internal energy of the lattice is approximated by next to nearest neighbour (nnn) pair interactions and many-body interactions associated with nearest neighbour (nn) equilateral triangles, describes the FeS contents of sphalerites equilibrated with pyrrhotite and pyrite, and with pyrrhotite and iron metal within experimental uncertainties. The model predicts moderate deviations from ideality; the mean values of the Lewis and Randall activity coefficient of FeS and ZnS are, 1.48 and 1.03, respectively. Predictions of the model are in qualitative agreement with cell-edge data. The model also predicts that sphalerites undergo long-range ordering to lower-symmetry structures at temperatures only slightly below those investigated experimentally, a result in agreement with inferences from an existing Mössbauer investigation of synthetic sphalerites.

More realistic models in which interactions are ascribed to larger species (nn triangular and centred square species) predict that such long-range ordering occurs at even higher temperatures and underscore the need for better characterization of the structures of (Zn,Fe)S minerals.

Keywords

sphaleritethermodynamicscluster variation methodpyrrhotitepyrite

Information

Type
Research Article
Information
Mineralogical Magazine , Volume 64 , Issue 5 , October 2000 , pp. 923 - 943
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anzai, S. and Ozawa, K., 1974. Effect of pressure on the Neel and ferrimagnetic Curie temperatures of FeS1+δ . Phys. Stat. Sol, 24, K31–4.CrossRefGoogle Scholar
Arnold, R.G. (1962) Equilibrium relations between pyrrhotite and pyrite from 325° to 743°C. Econ Geol., 57, 72–90.CrossRefGoogle Scholar
Balabin, A.I. and Urusov, V.S. (1995) Recalibration of the sphalerite cosmobarometer: Experimental and theoretical treatment. Geochim. Cosmochim. Acta, 59, 1401–10.CrossRefGoogle Scholar
Barker, J.A. (1953) Methods of approximation in the theory of regular mixtures. Proc. R. Soc., A216, 45.Google Scholar
Barton, P.B. Jr., and Toulmin, P. III, (1966) Phase relations involving sphalerite in the Fe-Zn-S system. Econ. Geol., 61, 815–49.CrossRefGoogle Scholar
Barton, P.B. Jr., Bethke, P. M. and Roedder, E. (1977) Environment of ore deposition in the Creede mining district, San Juan Mountains, Colorado: Part III. Progress toward interpretation of the chemistry of the ore-forming fluid for the OH vein. Econ. Geol., 72, 1–24.CrossRefGoogle Scholar
Bloc, S., Piermarini, G.J., Munro, R.G. and Fuller, E. (1989) Isothermal phase behavior of silver antimony sulfide (Ag3SbS3), zinc germanium phosphide (ZnGeP2) and zinc sulfide. Physica A, 156, 341–52.Google Scholar
Benbattouche, N., Saunders, G.A., Lambsom, E.F. and Hönle, W. (1989) The dependences of the elastic stiffness moduli and the Poisson ratio of natural iron pyrites FeS2 upon pressure and temperature. J. Phys. D: Appl. Phys., 22 670–5.CrossRefGoogle Scholar
Boorman, R.S. (1967) Subsolidus studies in the ZnS-FeS-FeS2 system. Econ Geol., 62, 614–31.CrossRefGoogle Scholar
Boorman, B.S., Sutherland, J.K. and Chernyshev, L.V. (1971) New data on the sphalerite-pyrrhotite-pyrite solvus. Econ. Geol., 66, 670–5.CrossRefGoogle Scholar
Borredon, R, Laffite, M. and Moury, R. (1983) Composition des sphalerites du district mineral de Hualgayoc (Perou). Min. Deposita, 18, 437–42.CrossRefGoogle Scholar
Bronshtein, I.N. and Semendiyev, K.A. (1979) Handbook of Mathematics. Teubner, GDR (in Russian).CrossRefGoogle Scholar
Browne, P.R.L. and Lovering, J.F. (1973) Composition of sphalerites from the Broadland geothermal field and their significance to sphalerite geothermometry and geobarometry. Econ. Geol., 68, 381–7.CrossRefGoogle Scholar
Bryndzia, T.L., Scott, S.D. and Spry, P.G. (1988) Sphalerite and hexagonal pyrrhotite geobarometer: Experimental calibration and application to the metamorphosed sulfide ores of Broken Hill, Australia. Econ Geol., 83, 1193–204.CrossRefGoogle Scholar
Burgman, E. Jr., Urbain, G. and Fronberg, M.G. (1968) Contribution à l’étude du systéme fer-soufre limité au domaine du mono-sulfure de fer (pyrrhotine). Mem. Sci. Rev. Métall., 65, 567–78.Google Scholar
Chao, G.Y. and Gault, R.A. (1998) The occurrence of two rare polytypes of wurtzite, 4H and 8H, at Mont Saint-Hilaire, Quebec. Canad. Mineral., 36, 775–8.Google Scholar
Chernychev, L.V., Anfilogov, V.A., Pastushkova, T.M. and Suturina, T.A. (1968) Hydrothermal investigation of the system Fe-Zn-S. Geologiya Rudnykh Mestorozhdeniy, 3, 50–64 (in Russian).Google Scholar
Chernychev, L.V., Afonina, G.G. and Berestennikov, M.I. (1969) Cell-edge dimensions of iron-bearing sphalerites synthesized under hydrothermal conditions. Geologiya Rudnykh Mestorozhdeniy, 6, 85–9 (in Russian).Google Scholar
Chuang, Y.Y., Hsieh, D.-C. and Chang, Y.A. (1985) Thermodynamic and phase relationships of transition metal sulfur systems: Part V. A re-evaluation of the Fe-S system using an associated solution model for the liquid phase. Metall. Trans. B, 1613, 277–85.CrossRefGoogle Scholar
Cromwell, P.R. (1997) Polyhedra. Cambridge University Press, Cambridge, UK.Google Scholar
Dicarlo, J., Albert, M., Dwight, K. and Wold, A. (1990) Preparation and properties of iron-doped II-VI chalcogenides. J. Solid State Chem., 87, 443–8.CrossRefGoogle Scholar
Finel, A. (1994) The cluster variation method and some applications. Pp. 495–450 in: Statics and Dynamics of Alloy Phase Transformations (Turchi, P.E.A and Gonis, A., editors). Plenum Press, New York.CrossRefGoogle Scholar
Finel, A. and Tetot, R. (1996) The Gaussian cluster variation method and its application to the thermodynamics of transition metals. Pp. 197–203 in: Stability of Materials (Ginis, , editor). Plenum Press, New York.CrossRefGoogle Scholar
Fleet, M.E. (1968) On the lattice parameters and superstructures of pyrrhotites. Amer. Mineral., 53, 1846–55.Google Scholar
Fleet, M.E. (1975) Thermodynamic properties of (Zn,Fe)S solid solutions at 850°C. Amer. Mineral., 60 466–70.Google Scholar
De Fontaine, D. (1975) k-Space symmetry rules for order-disorder reactions. Acta Metall, 23, 553–71.CrossRefGoogle Scholar
De Fontaine, D. (1994) Cluster approach to orderdisorder transformations in alloys. Solid State Phys., 47, 33–176.CrossRefGoogle Scholar
Guggenheim, E.A. (1937) Theoretical basis of Raoult’s law. Trans. Faradary. Soc., 33, 151–79.CrossRefGoogle Scholar
Hijmans, J. and de Boir, J. (1955) An approximation method for order-disorder problems I. Physica, 21, 471–84.CrossRefGoogle Scholar
Hollenbaugh, D.W. and Carlson, E.H. (1983) The occurrence of wurtzite polytypes in eastern Ohio. Canad. Mineral., 21, 697–703.Google Scholar
Hutchison, M.N. and Scott, S.D. (1983) Experimental calibration of the sphalerite cosmobarometer. Geochim. Cosmochim. Acta, 47, 101–8.CrossRefGoogle Scholar
Keller-Besrest, F. and Collin, G. (1990) Structural aspects of the α-transition in stoichiometric FeS: Identification of the high-temperature phase. J. Solid State Chem., 84, 194–210.CrossRefGoogle Scholar
Kikuchi, R.D. (1951) A theory of cooperative phenomena. Phys. Rev., 81, 988–1003.CrossRefGoogle Scholar
Kikuchi, R. (1973) Superposition approximation and natural iteration calculation in cluster-variation method. J. Chem. Phys., 60 1071–80.CrossRefGoogle Scholar
King, H.E. Jr., and Prewitt, C.T. (1982) High-pressure and high-temperature polymorphism of iron sulfide (FeS). Acta Crystallogr., B38, 1877–86.CrossRefGoogle Scholar
Kruse, O. (1990) Mössbauer and X-ray study of the effects of vacancy concentration in synthetic hexagonal pyrrhotites. Amer. Mineral., 75, 755–63.Google Scholar
Libowitz, G.G. (1972) Energetics of defect formation and interaction in nonstoichiometric pyrrhotite. Pp. 107–15 in: Reactivity of Solids (Anderson, J.B., Roberts, M.W. and Stone, F.S., editors). Chapman & Hall, London.Google Scholar
Loucks, R.R. (1984) Zoning and ore genesis at Topia, Durango, Mexico. PhD Thesis, Harvard Univ., Cambridge, Massachusetts.Google Scholar
Lusk, J. and Ford, C.E. (1978) Experimental extension of the sphalerite geobarometer to 10 kbar. Amer. Mineral, 63, 516–9.Google Scholar
Massalski, T.B. ed. (1986) Binary Alloy Phase Diagrams. American Society for Metals, Metals Park, Ohio.Google Scholar
Mizuta, T. (1988) Interdiffusion rate of zinc and iron in natural sphalerite. Econ. Geol., 83, 1205–20.CrossRefGoogle Scholar
Niwa, K. and Wada, T. (1961) Thermodynamic studies of pyrrhotite. Metall. Soc. Conf., 8, 945–61.Google Scholar
Novikov, G.V., Sokolov, Ju.A. and Sipavina, L.V. (1982) The temperature dependence of the unit-cell parameters of pyrrhotite Fe1−xS. Geochem. Int., 19, 184–90.Google Scholar
Novikov, G.V., Egorov, V.K. and Sokolov, Ju.A. (1988) Pyrrhotites: Crystal and Magnetic Structure. Phase Transformations. Nauka, Moscow (in Russian).Google Scholar
Oates, W.A., Zhang, F., Chen, S.-L. and Chang, Y.A. (1999) Improved cluster-site approximation for the entropy of mixing in multicomponent solid solutions. Phys. Rev. B, 59, 11221–25.CrossRefGoogle Scholar
O’Leary, M.J. and Sack, R.O. (1987) Fe-Zn exchange reaction between tetrahedrite and sphalerite in natural environments. Contrib. Mineral. Petrol., 96, 415–25.CrossRefGoogle Scholar
Osadchii, E.G. and Sorokin, V.I. (1989) Stannite- Containing Sulfide Systems. Nauka, Moscow (in Russian).Google Scholar
Pankratz, L.B. and King, K.G. (1965) High-temperature heat contents and entropies of two zinc sulfides and four solid solutions of zinc and iron sulfides. Bureau of Mines Report of Investigations, 6708, 1–8.Google Scholar
Platonov, A.N., Shadlun, T.N., Polyakova, O.P., Dobrovol’skaya, M.G. (1969) Polytypes of sphalerites and their typomorphic importance. Geologiya Rudnykh Mestorozhdeniy, 11, 3–16 (in Russian).Google Scholar
Rau, H. (1976) Energetics of defect formation and interaction in pyrrhotite F1−xS and its homogeneity range. J. Phys. Chem. Solids, 37, 425–9.CrossRefGoogle Scholar
Rosenqvist, T. (1954) A thermodynamic study of iron, cobalt and nickel sulfides. J. Iron Steel Inst., 176, 37–57.Google Scholar
Saati, Th.L. and Bram, J. (1964) Nonlinear Mathematics. Dover Publications, New York.Google Scholar
Sanchez, J.M., Ducastelle, F. and Gratias, D. (1984) Physica A, 128, 334.CrossRefGoogle Scholar
Sanchez, J.M. and de Fontaine, D. (1980) Ordering in fee lattices with first- and secopnd-neighbor interactions. Phys. Rev. B, 21, 216–28.CrossRefGoogle Scholar
Schlijper, A.G. and Westerhof, J. (1987) Improved cluster variation approximations by extention of local thermodynamic states. Phys. Rev. B, 36, 5458–65.CrossRefGoogle Scholar
Schneeberg, E.P. (1973) Sulfur fugacity measurements with the electrochemical cell AglAgIlAg2+xS. Econ. Geol, 68, 507–17.CrossRefGoogle Scholar
Scott, S.D. and Barnes, H.L. (1971) Sphalerite geothermometry and geobarometry. Econ. Geol., 66, 653–69.CrossRefGoogle Scholar
Scott, S.D. (1973) Experimental calibration of the sphalerite geobarometer. Econ. Geol., 68, 466–74.CrossRefGoogle Scholar
Scott, S.D. and Kissin, S.A. (1973) Sphalerite composition in the Zn-Fe-S system below 300°C. Econ. Geol., 68, 475–9.CrossRefGoogle Scholar
Skinner, B.J. (1962) Thermal expansion of ten minerals. USGS Prof. Paper, 450-D, 109–12.Google Scholar
Sorokin, V.I. and Bezmen, N.I. (1973) The sulfide system Zn-Fe-S in equilibrium with chloride solutions at 600 °C and 1000 kg/cm2 . Ocherki Fiziko-ximicheskoy Petrologii, 3, pp. 36–43. Nauka, Moscow (in Russian).Google Scholar
Sorokin, V.I. and Chichagov, A.V. (1974) Sulfides from the system Zn-Fe-S in equilibrium with water solution of NH4Cl at 400°C and 1000 kg/cm3 . Ocherki fiziko-ximicheskoj petrologii, 4, 176–85. Nauka, Moscow (in Russian).Google Scholar
Sorokin, V.I., Gruzdev, V.S. and Shorygin, V.A. (1970) Variation of the a o parameter with the content of iron in sphalerite obtained under hydrothermal conditions. Geochem. Int., 7, 361–3.Google Scholar
Sorokin, B.I., Novikov, V.K., Egorov, V.K., Popov, V.I. and Sipavina, L.V. (1975) An investigation of Fe-sphalerites by means of Mössbauer spectroscopy. Geochimiya, 9, 1329–35.Google Scholar
Taylor, L.A. (1969) Low-temperature phase relations in the Fe-S system. Carnegie Inst. Wash. Yearb., 62, 175–89.Google Scholar
Toulmin, P. III, and Barton, P.B. Jr., (1964) A thermodynamic study of pyrite and pyrrhotite. Geochim. Cosmochim. Acta, 28, 641–71.CrossRefGoogle Scholar
Toulmin, P. III, Barton, P.B. Jr., and Wiggins, L.B. (1991) Commentary on the sphalerite geobarometer. Amer. Miner., 76, 1038–51.Google Scholar
Turkdogan, E.T. (1968) Iron-sulfur system. Part 1: Growth of ferrous sulfide in iron and diffisivities of iron in ferrous sulfide. Trans. Metall. Soc. Amer. Ins. Min. Metall. Pet. Eng., 242, 1665–72.Google Scholar
Udodov, Yu.,N. and Kashayev, A.A. (1970) An isothermal section (400°) of the state diagram of pyrrhotite. Trans. (Doklady) U.S.S.R. Acad. Sci.: Earth Sci. Sect., 187, 103–5.Google Scholar
Vaks, V.G. and Samolyuk, G.D. (1999) On accuracy of different cluster models used in describing ordering phase transitions in fee alloys. JETP,, 88, 89–100.CrossRefGoogle Scholar
van Aswegen, J.T.S. and Verleger, H. (1960) Röntgenographishe untersuchung des systems ZnS-FeS. Die Naturwissenschaften, 47, 131.CrossRefGoogle Scholar
Vinograd, V.L. and Putnis, A. (1999) The description of Al, Si ordering in aluminosilicates using the cluster variation method. Amer. Mineral., 84, 311–24.CrossRefGoogle Scholar
Zunger, A. (1994) First-principles statistical mechanics of semiconductor alloys and intermetallic compounds. Pp. 361–419 in: Statics and Dynamics of Alloy Phase Transformations (Turchi, P.E.A. and Gonis, A., editors) Plenum Press, New York.CrossRefGoogle Scholar