The distribution of divalent trace elements between sulfides,oxides, silicates and hydrothermal solutions: I. Thermodynamic basis

Experimental data for the standard Gibbs free energies of formation from the elements of a wide variety of metal sulfides and oxides, spinels, olivines and pyroxenes at 25°C and 1 bar define linear correlations, within about ±900 cal·mole^?1, with the corresponding conventional standard partial molal Gibbs free energies of formation of the aqueous M²⁺ cations of the form where a_MaZ and b_MaZ are empirically determined constants characteristic of the structure M_nZ. The only exceptions to correlations of this type are compounds of the heavy alkaline earths Ca, Sr and Ba, which appear to follow correlations with cation radius instead. The linear free energy correlations enable prediction of standard Gibbs free energies of formation of compositional end-members of a particular structure M_nZ provided that a_MaZ and b_MaZ are known accurately. When only the free energy of the Mg end-member is known, the standard Gibbs free energy of formation at 25°C and 1 bar of the Fe endmember, and hence a_MaZ and b_MaZ Can be predicted from the temperature independence of and estimated entropies and heat capacities for the Fe end-member. Using this approach, the free energies of ferrosilite, hedenbergite and annite at 25°C and 1 bar were predicted to within ±1000 cal·mole^?1 of the helgesonet al. (1978) values. Free energies of formation of talc (M₃Si₄O₁₀(OH)₂), clinchlore (M₅Al₂Si₃O₁₀(OH)₈), and tremolite (Ca₂M₅(Si₄O₁₁)₂(OH)₂)-type compounds where M is Mg, Mn, Zn, Fe, Co, or Ni were then predicted at 25°C and 1 bar.Calculation of the equilibrium distribution of Mg, Zn and Sr between galena and hydrothermal solution, and Zn, Mg, Fe and Mn between chlorite and hydrothermal solution demonstrates: (1) that the Sr contents of low temperature galenas (e.g. Mississippi Valley-type) should be negligible (reported analyses of Sr content and Sr isotopic composition of such galenas are probably attributable to fluid inclusions or carbonate inclusions); and (2), that the Zn contents of hydrothermal chlorites in a model of the midoceanic ridge hydrothermal systems are sensitive to temperature, to complexing in the aqueous phase, and to the overall Fe/Mg ratio of the chlorite.