For the reaction: 1 diopside+3 dolomite ?2 forsterite+4 calcite+2 CO
2 (14) the following
P total?
T-brackets have been determined experimentally in the presence of a gasphase consisting of 90 mole%CO
2 and 10 mole%H
2O∶1 kb, 544°±20° C; 3kb, 638°±15° C; 5kb, 708°±10° C; 10kb, 861°±10° C. The determination was carried out with well defined synthetic minerals in the starting mixture. The MgCO
3-contents of the magnesian calcites formed by the reaction in equilibrium with dolomite agree very well with the calcite-dolomite miscibility gap, which can be recalculated from the activities and the activity coefficients of MgCO
3 as given by Gordon and Greenwood (1970). The equilibrium constant
K 14b was calculated with respect to the reference pressure
P 0=1 bar using the experimentally determined
\(P_{total} TX_{CO_2 }\) brackets, the activities of MgCO
3 and CaCO
3 (Gordon and Greenwood 1970; Skippen 1974) and the fugacities of CO
2 Holloway (1977) considering the correction of Flowers (1979). Results are plotted as function of the absolute reciprocal temperature in Fig. 1. For the temperature range of 530° to 750° C the following linear expression can be given for the natural logarithm of K
14b:
(g) $$[ln K_{14b} ]_T^P = - \frac{{18064.43}}{{T\left( {^\circ K} \right)}} + 38.58 + \frac{{0.308(P - 1 bar)}}{{T\left( {^\circ K} \right)}}$$ where
P is the total pressure in bars and
T the temperature in degrees
Kelvin. Combining Equation (g) with the activities of MgCO
3 and CaCO
3 gives the equilibrium fugacity
\(f_{CO_2 }\) :
(i) $$[ln f_{CO_2 } ]_T^P = - \frac{{11635.44}}{{T\left( {^\circ K} \right)}} + 21.09 + \frac{{0.154(P - 1 bar)}}{{T\left( {^\circ K} \right)}}$$ Equation (i) and the fugacities of CO
2 permit to calculate the equilibrium data in terms of
\(P_{CO_2 }\) and
T (see Fig. 3) or
P total,
T and
\(X_{CO_2 }\) (see Fig. 5). Combining the
\(P_{total} TX_{CO_2 }\) equilibrium data of the above reaction with those of the previously investigated reaction (Metz 1976): 1 tremolite+11 dolomite ?8 forsterite+13 calcite+9 CO
2+1 H
2O yields the stability conditions of the
four-mineral assemblage: diopside+calcian dolomite+forsterite +magnesian calcite and the stability conditions of the
five-mineral assemblage: tremolite+calcian dolomite+forsterite +magnesian calcite+diopside both shown in Fig. 6. Since these assemblages are by no means rare in metamorphic siliceous dolomites (Trommsdorff 1972; Suzuki 1977; Puhan 1979) the data of Fig. 6 can be used to determine the pressure of metamorphism and to estimate the composition of the CO
2-H
2O fluid provided the temperature of the metamorphic event was determined using the calcite-dolomite geothermometer.
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