ALBERT

Notes: Abstract Three Al-Cr exchange isotherms between Zn(Al, Cr)2O4 spinel and (Al, Cr)2O3 corundum crystalline solutions have been studied experimentally at 900°, 1100°, and 1300° C, at a total pressure of 25 kbar. Employing data on the equation of state of corundum (Chatterjee et al. 1982), the experimental results were evaluated thermodynamically. It was found that the thermodynamic mixing properties of Zn(Al, Cr)2O4 spinels are best described in terms of a symmetric Margules equation. The T- and P- dependence of the Margules Parameter, W G Sp , and of ΔG* of the exchange reaction, 1/2 ZnAl2O4 + 1/2 Cr2O3 = 1/2 ZnCr2O4+1/2 A12O3, are found to be ΔG *=1493−2.869·T+0.0081·P and W G Sp (J/mol)=23456+0.0386·P, with T given in K and P in bar.

Notes: Abstract The system MgO-Al2O3-SiO2(MAS) comprises 88–90% of the bulk composition of an average peridotite. The MAS ternary is thus a suitable starting point for exploring peridotite phase relations in multicomponent natural systems. The basic MAS phase relations may be treated in terms of the reactions (see list of symbols etc). (1) py (in Gt)=en (in Opx)+mats (in Opx), (2) en (in Opx)+sp (in Sp)=mats (in Opx)+fo (in Ol), and (3) py (in Gt)+fo (in Ol)=en (in Opx)+sp (in Sp). Extensive reversed phase equilibria data on these three reactions by Danckwerth and Newton (1978), Perkins et al. (1981), and Gasparik and Newton (1984) employing identical experimental methods in the same laboratory have been used by us to deduce the following internally consistent thermodynamic data applying the technique of linear programming:ΔH 298(1) 0 = 2536 J, ΔS 298(1) 0 =− 6.064 J/K;ΔH 298(2) 0 = 29435 J, ΔS 298(2) 0 = 8.323 J/K; andΔH 298(3) 0 =−26899 J, ΔS 298(3) 0 =−14.388 J/K.These data are also found to be consistent with results of calorimetry. Figure 2 shows the calculated phase relations based on our thermodynamic data; they are consistent with the phase equilibria experiments. Successful extension of the MAS phase relations to multicomponent peridotites pivots on the extent to which the effects of the “non-ternary” (i.e. other than MAS) components can be quantitatively handled. Particularly hazardous in this context is Cr2O3, although it barely makes up 0.2 to 0.5 wt% of such rocks. This is because Cr+3 fractionates extremely strongly into Sp. This study focuses on the peridotite phase relations in the MgO-Al2O3-SiO2-Cr2O3 (MASCr) quaternary. Thermodynamic calculations of the MASCr phase relations have been accomplished by using ΔH 298 0 and ΔS 298 0 values for the reactions (1) through (3) indicated above, in conjunction with data on thermodynamic mixing properties of a) binary Sp (sp-pc) crystalline solution (Oka et al. 1984), b) ternary Opx (en-mats-mcts) crystalline solution (this study), and c) binary Gt (py-kn) crystalline solution (this study). The results are shown in P-T projections (Figs. 3a and b) and isobaric-isothermal sections of MASCr in a projection through the component fo onto the SiO2-Al2O3-Cr2O3 ternary (Figs. 4a and b). The most important results of this work may be summarized as follows: 1. With increasing incorporation of Cr+3 into Sp and Gt, the X mats isopleths of the reactions (1) and (2) are shifted to higher temperatures (Fig. 3a); simultaneously, the spinel-peridotite to garnet-peridotite phase transition is moved to higher pressures (Fig. 3b). 2. At identical P and T, the X mats values of Opx coexisting in equilibrium with Ol and Sp is strongly dependent upon the X pc value in the latter phase (Figs. 4a and b). Accurate correction for the composition of Sp is, therefore, a necessary precondition for geothermometry of the spinelperidotites. 3. The discrepant temperatures reported by Sachtleben und Seck (1981, Fig. 5) from the spinel-peridotites of the Eifel area (systematically too high temperatures as a function of X pc in Sp) are demonstrated to be the result of ignoring the nonideality in the chromian spinels.

Notes: Abstract Modified Redlich-Kwong (MRK) equations of state have been derived for the pure fluid species H2 and H2O by expressing the parametera as a function ofT andP, andb as as a function ofP only. These equations are valid above 0° and 0.01° C, respectively. For H2O, the prediction of volumes is successful not only in the supercritical, but also in the subcritical range. As a result of this, the saturation curve of H2O can be calculated with a maximum deviation of ±1.4 bar in the range 100–350° C. Between 350° C and the critical point (374.15° C), the uncertainty increases somewhat; this is due to a fundamental inadequacy of the Redlich-Kwong equation itself. These equations of state permit extrapolations to pressures of 100 kbar for H2 and at least 200 kbar for H2O and are, therefore, eminently suited for geochemical applications. Formulation of the MRK of the binary H2-H2O mixtures was achieved by assuming the quadratic mixing rule for the parametersa mix andb+mix. To derive the cross coefficients,aH2-H2Oandb H 2-H 2O, adjustable corrective factors ɛ and τ had to be introduced. TheT- andP-dependences of ɛ and τ are based onP-V-T-X H 2 data (Seward and Franck 1981) to 440° C and 2500 bar. The resulting equation of state very satisfactorily reproduces the volumes observed experimentally at various sets ofT,P, andX H 2. At a total pressure of 2 kbar, positive deviation from ideal mixing behaviour is still perceptible at as high a temperature as 1000° C. At some temperature around 380° C, phase separation sets in, an aqueous solution with dissolved H2 coexisting in equilibrium with an H2-rich fluid with dissolved H2O. The computedP-T-X H 2 surface of this two-phase region agrees well with that observed in Seward and Franck's (1981) experiments. An independent proof of the validity of this equation of state is the accuracy with whichH m ex can be predicted. Calorimetric measurements ofH m ex (Smith et al. 1983, Wormald and Colling 1985) compare excellently with those predictions. This is indicative of the fact that theP-V-T-X H 2 measurements by Seward and Franck (1981) are mutually consistent with the calorimetricH m ex data reported by Smith et al. (1983) and by Wormald and Colling (1985). Extrapolation of the equation of state for the H2-H2O mixture is not recommended to pressures far beyond those for whichP-V-T-X H 2 data are available at present. Despite this, it sets the stage for rigorous thermodynamic treatment of some redox equilibria of interest to geochemistry, which was not possible hitherto because of lack of such data.