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Evaluation of Standard Free Energies of Formation of Clay Minerals by an Improved Regression Method

Published online by Cambridge University Press:  28 February 2024

Chandrika Varadachari ,
Mahammad Kudrat  and
Kunal Ghosh
Chandrika Varadachari
Affiliation:
Department of Agricultural Chemistry and Soil Science, University of Calcutta, 35 B.C. Road, Calcutta 700 019, India
Mahammad Kudrat
Affiliation:
Department of Agricultural Chemistry and Soil Science, University of Calcutta, 35 B.C. Road, Calcutta 700 019, India
Kunal Ghosh
Affiliation:
Department of Agricultural Chemistry and Soil Science, University of Calcutta, 35 B.C. Road, Calcutta 700 019, India
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Abstract

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An improved regression method for the evaluation of standard free energies of formation (ΔG°f) of clay minerals is here proposed in an attempt to remove some of the limitations of the earlier method (Chen, 1975). Particularly, this method suggests a procedure for the assignment of rankings for Σ ΔG°f, i values. Moreover, an iterative least-squares fitting technique is applied to solve the exponential equation to obtain the estimated ΔG°f. The estimated ΔG°f data for the various standard clay minerals are derived and compared with data available in the literature; in general, there is good agreement between the values. It is also shown how the regression method can be extended to clay minerals of variable composition. The ΔG°f's for several such minerals have been evaluated; a large number of combination equations required for such computations have been listed, so that for other similar minerals the process of evaluation of ΔG°f is greatly simplified.

Keywords

Clay mineralsFree energies of formationRegression method
Type
Research Article
Information
Clays and Clay Minerals , Volume 42 , Issue 3 , June 1994 , pp. 298 - 307
Copyright
Copyright © 1994, Clay Minerals Society

References

Aagaard, P., and Helgeson, H. C., (1983) Activity composition relations among silicates and aqueous solutions: II. Chemical and thermodynamic consequences of ideal mixing of atoms on homological sites in montmorillonites, illites and mixed-layer clays: Clays & Clay Minerals 31, 207–217.CrossRefGoogle Scholar
Barany, R., and Kelley, K. K., (1961) Heats and free energies of formation of gibbsite, kaolinite, halloysite and dickite: U.S. Bur. Mines Report Investigation 5825, 1–13.Google Scholar
Bricker, O. P., Nesbitt, H. W., and Gunter, W. D., (1973) The stability of talc: Amer. Mineral. 58, 64–72.Google Scholar
Chen, C., (1975) A method of estimation of standard free energies of formation of silicate minerals at 298.15°K: Am. J. Sci. 275, 801–817.CrossRefGoogle Scholar
Christ, C. L., Hostetler, P. B., and Siebert, R. M., (1973) Studies in the system MgO-SiO2-CO2-H2O (III): The activity product constant of sepiolite: Am. J. Sci. 273, 65–83.CrossRefGoogle Scholar
Draper, N. R., and Smith, H., (1981) Applied Regression Analysis: John Wiley & Sons, New York, 458–465.Google Scholar
Fritz, B., (1985) Multicomponent solid solutions for clay minerals and computer modeling of weathering processes: in The Chemistry of Weathering, Drever, J. L., ed., D. Reidel, Dordrecht, 19–34.Google Scholar
Grim, R. E., (1968) Clay Mineralogy: McGraw-Hill, New York, 86 pp.Google Scholar
Harary, F., (1972) Graph Theory: Adison-Wesley, Reading, Mass., 32–42.Google Scholar
Helgeson, H. C., (1969) Thermodynamics of hydrothermal systems at elevated temperatures and pressures: Am. J. Sci. 267, 729–804.CrossRefGoogle Scholar
Helgeson, H. C., Delany, J. M., Nesbitt, H. W., and Bird, D. K., (1978) Summary and critique of the thermodynamic properties of rock forming minerals: Am. J. Sci. 278A, 1–220.Google Scholar
Huang, W. H., and Keller, W. D., (1973) Gibbs free energies of formation calculated from dissolution data using specific mineral analysis. III. Clay minerals: Amer. Mineral. 58, 1023–1028.Google Scholar
Jackson, M. L., (1965) Chemical compositions of soils: in Chemistry of the Soil, Bear, F. E., ed., Oxford & I.B.H., Calcutta, pp. 95–100.Google Scholar
Karpov, I. K., and Kashik, S. A., (1968) Computer calculation of standard isobaric-isothermal potentials of silicates by suitable regression from a crystallochemical classification: Geochem. Internatl. 6, 706–713.Google Scholar
Kittrick, J. A., (1971a) Stability of montmorillonites: I. Belle Fourche and Clay Spur montmorillonites: Soil Sci. Soc. Am. Proc. 35, 140–145.CrossRefGoogle Scholar
Kittrick, J. A., (1971b) Stability of montmorillonites: II. Aberdeen montmorillonite: Soil Sci. Soc. Am. Proc. 35, 820–823.CrossRefGoogle Scholar
Lippman, F., (1977) The solubility products of complex minerals, mixed crystals and three-layer clay minerals: Neues. Jahrb. Mineral Abh. 130, 243–263.Google Scholar
Lippmann, F., (1981) The thermodynamic status of clay minerals: in Proc. 7th Internatl. Clay Conf., Olphen, H. van and Veniale, F., eds., Elsevier, Amsterdam , 475–485.Google Scholar
Mattigod, S. V., and Sposito, G., (1978) Improved method for estimating the standard free energies of formation of smectites: Geochim. Cosmochim. Acta 42, 1753–1762.CrossRefGoogle Scholar
Mukherjee, A., (1979) Gibbs free energy of phlogopite—a discussion with reference to the reaction: Biotite + 3 quartz = K-feldspar + 3 orthopyroxene + H2O: Am. J. Sci. 279, 1083–1086.CrossRefGoogle Scholar
Nriagu, J. O., (1975) Thermochemical approximations for clay minerals: Amer. Mineral. 60, 834–839.Google Scholar
Reesman, A. L., (1974) Aqueous dissolution studies of illite under ambient conditions: Clays & Clay Minerals 22, 443–454.CrossRefGoogle Scholar
Reesman, A. L., and Keller, W. D., (1968) Aqueous solubility studies of high-alumina and clay minerals: Amer. Mineral. 53, 929–942.Google Scholar
Robie, R. A., Hemingway, B. S., and Fisher, J. R., (1978) Thermodynamic properites of minerals and related substances at 298.15°K and 1 atmosphere pressure and at higher temperatures: U.S. Geol. Survey Bull. 1452, 1–456.Google Scholar
Rouston, R. C., and Kittrick, J. A., (1971) Illite solubility: Soil Sci. Soc. Am. Proc. 35, 714–718.Google Scholar
Scarborough, J. B., (1976) Numerical Mathematical Analysis: Oxford & IBH, New Delhi, 545–547.Google Scholar
Slaugher, M., (1966) Chemical binding in the silicate minerals. Part I. Model for determining crystal-chemical properties. Part II. Computational methods and approximations for the binding energy of complex silicates. Part III. Application of energy calculations to the prediction of silicate mineral stability: Geochim. Cosmochim. Acta 30, 299–313, 315–339.CrossRefGoogle Scholar
Sposito, G., (1986) The polymer model of thermochemical clay mineral stability: Clays & Clay Minerals 34, 198–203.CrossRefGoogle Scholar
Tardy, Y., and Fritz, B., (1981) An ideal solid solution model for calculating solubility of clay minerals: Clay Miner. 16, 361–373.CrossRefGoogle Scholar
Tardy, Y., and Garrels, R. M., (1974) A method of estimating the Gibbs energies of formation of layer silicates: Geochim. Cosmochim. Acta 38, 1101–1116.CrossRefGoogle Scholar
Tardy, Y., Duplay, J., and Fritz, B., (1987) Stability fields of smectites and illites as a function of temperature and chemical composition: in Geochemistry and Mineral Formation at the Earth Surface, Clemente, R. R., and Tardy, Y., eds., CSIC, Granada, 462–494.Google Scholar
van Heeswijk, M., and Fox, C. G., (1988) Iterative method and Fortran code for nonlinear curve fitting: Comput. Geosci. 14, 489–503.CrossRefGoogle Scholar
Varadachari, C., (1992) Constructing phase diagrams for silicate minerals in equilibrium with an aqueous phase: A theoretical approach: Soil Sci. 153, 5–12.CrossRefGoogle Scholar
Weaver, C. E., and Pollard, L. D., (1973) The Chemistry of Clay Minerals: Elsevier, Amsterdam , 10–11.Google Scholar
Zen, E.-An., (1972) Gibbs free energy, enthalpy and entropy of ten rock-forming minerals: Calculations, discrepancies, implications: Amer. Mineral 57, 524–553.Google Scholar