Abstract
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.
Similar content being viewed by others
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.
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.
Bricker, O. P., Nesbitt, H. W., and Gunter, W. D. (1973) The stability of talc: Amer. Mineral. 58, 64–72.
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.
Christ, C. L., Hostetler, P. B., and Sieben, R. M. (1973) Studies in the system MgO-SiO2-CO2-H2O (III): The activity product constant of sepiolite: Am. J. Sci. 273, 65–83.
Draper, N. R. and Smith, H. (1981) Applied Regression Analysis: John Wiley & Sons, New York, 458–465.
Fritz, B. (1985) Multicomponent solid solutions for clay minerals and computer modeling of weathering processes: in The Chemistry of Weathering, J. L. Drever, ed., D. Reidel, Dordrecht, 19–34.
Grim, R. E. (1968) Clay Mineralogy: McGraw-Hill, New York, 86 pp.
Harary, F. (1972) Graph Theory: Adison-Wesley, Reading, Mass., 32–42.
Helgeson, H. C. (1969) Thermodynamics of hydrothermal systems at elevated temperatures and pressures: Am. J. Sci. 267, 729–804.
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.
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.
Jackson, M. L. (1965) Chemical compositions of soils: in Chemistry of the Soil, F. E. Bear, ed., Oxford & I.B.H., Calcutta, pp. 95–100.
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. Internat!. 6, 706–713.
Kittrick, J. A. (1971a) Stability of montmorillonites: I. Belle Fourche and Clay Spur montmorillonites: Soil Sci. Soc. Am. Proc. 35, 140–145.
Kittrick, J. A. (1971b) Stability of montmorillonites: II. Aberdeen montmorillonite: Soil Sci. Soc. Am. Proc. 35, 820–823.
Lippman, F. (1977) The solubility products of complex minerals, mixed crystals and three-layer clay minerals: Neues. Jahrb. Mineral Abh. 130, 243–263.
Lippmann, F. (1981) The thermodynamic status of clay minerals: in Proc. 7th Internatl. Clay Conf, H. van Olphen and F. Veniale, eds., Elsevier, Amsterdam, 475–485.
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.
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.
Nriagu, J. O. (1975) Thermochemical approximations for clay minerals: Amer. Mineral. 60, 834–839.
Reesman, A. L. (1974) Aqueous dissolution studies of illite under ambient conditions: Clays & Clay Minerals 22, 443–454.
Reesman, A. L. and Keller, W. D. (1968) Aqueous solubility studies of high-alumina and clay minerals: Amer. Mineral. 53, 929–942.
Robie, R. A., Hemingway, B. S., and Fisher, J. R. (1978) Thermodynamic properites of minerals and related sub-stances at 298.15°K and 1 atmosphere pressure and at higher temperatures: U.S. Geol. Survey Bull. 1452, 1–456.
Rouston, R. C. and Kittrick, J. A. (1971) Illite solubility: Soil Sci. Soc. Am. Proc. 35, 714–718.
Scarborough, J. B. (1976) Numerical Mathematical Analysis: Oxford & IBH, New Delhi, 545–547.
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.
Sposito, G. (1986) The polymermodel of thermochemical clay mineral stability: Clays & Clay Minerals 34, 198–203.
Tardy, Y. and Fritz, B. (1981) An ideal solid solution model for calculating solubility of clay minerals: Clay Miner. 16, 361–373.
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.
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, R. R. Demente and Y. Tardy, eds., CSIC, Granada, 462–494.
van Heeswijk, M. and Fox, C. G. (1988) Iterative method and Fortran code for nonlinear curve fitting: Comput. Geosci. 14, 489–503.
Varadachari, C. (1992) Constructing phase diagrams for silicate minerals in equilibrium with an aqueous phase: A theoretical approach: Soil Sci. 153, 5–12.
Weaver, C. E. and Pollard, L. D. (1973) The Chemistry of Clay Minerals: Elsevier, Amsterdam, 10–11.
Zen, E-An (1972) Gibbs free energy, enthalpy and entropy of ten rock-forming minerals: Calculations, discrepancies, implications: Amer. Mineral 57, 524–553.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Varadachari, C., Kudrat, M. & Ghosh, K. Evaluation of Standard Free Energies of Formation of Clay Minerals by an Improved Regression Method. Clays Clay Miner. 42, 298–307 (1994). https://doi.org/10.1346/CCMN.1994.0420308
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1346/CCMN.1994.0420308