A new technique, Pd-oxide equilibration, has been developed for the experimental determination of theactivities of oxide components in melts and minerals using the equilibrium between Pd alloy, oxygen, and the oxide component in the sample of interest. Due to theextraordinary stability of dilute alloys of Pd with Mg, AI, and Si, these metals dissolve into Pd in equilibrium with oxide-based materials in amounts easily measured with the electron microprobe at f_O_2's that can be achieved with conventional gas-mixing techniques. Activity-composition relations for Pd-Mg, -Al, and -Si alloys were determined by equilibrating Pd at fixed f_O_2 and T with periclase,corundum, and cristobalite (a_(oxide)≡1). Because Mg, Al, and Si have constant activity coefficients in Pd at low concentrations, the activity of the oxide of each metal is asimple function of the ratio of the concentration of the metal in Pd in equilibrium with the sample to that in Pd in equilibrium with the pure oxide. Therefore, if Pd plus amelt or mineral and Pd plus pure oxide standards are equilibrated simultaneously at fixed T and f_O_2 theprecision of the analytical technique is the major limitation on the determination of oxide activities. With Pd-oxide equilibration, all measurements of thermodynamic properties reflect equilibration at the temperature of interest, so no phase, ordering, or structural changes upon quenching influence the results. In addition, the method can be precise, since the only measurements involved in the determination of activities are the concentrations of various metals in the Pd, and there is no need for accurate knowledge of T or f_O_2.
The technique of Pd-oxide equilibration was used to determine activities of MgO and Al_2O_3 and ∆G_f°'s in stoichiometric MgAl_2O_4 spinel at 1150 to 1400°C. The results are in good agreement with those of JANAF (1985) but are distinct at the 1σ level from the ∆G_f°'s of Helgeson et al. (1978), Holland and Powell (1990), Berman (1988), and Hallstedt (1992), and at the 2σ level from Robie et al. (1978). This implies a larger residual entropy upon quenching than is accounted for by most compilations ofthermodynamic data. These differences were accounted for by applying Landau theory corrections to the calorimetric heat contents (Bonnickson, 1955) using neutron diffraction measurements of the equilibrium amount of disorder in spinel as a function of temperature (Peterson et al., 1991). The corrected heat contents and measured ∆G_f°'s have been used to produce a new, self-consistent C_p function that can account for all experimental data. The results imply that nonconfigurational entropy contributionsare important in spinel.
Pd-oxide equilibration was also used to measure the activities of MgO, Al_2O_3, and SiO_2 In melts in the five-component system CaO-MgO-Al_2O_3-SiO_2-TiO_2(CMAST). Five bulk compositions were studied, including synthetic analogs of Type B, Type C, and forsterite-bearing Ca-Al-rich inclusions (CAls) and one synthetic analogof an average Group 2 plagioclase-olivine inclusion (POI) from carbonaceous chondrites. Correlated variations between activity coefficient and liquid composition are observed in the melts, which may give insight into the relationships between thermodynamics and structure. The measured activities agree to within 10-35% of those calculated using Berman's (1983) model and are therefore generally consistent with known phase equilibrium data in CMAS. Measured activities indicate that liquids of CAl and POI composition would be out of equilibrium with a solar gas and should volatilize Mg, SiO, and lesser Ca if they melt in such a gas.
The technique of Pd-oxide equilibration was also used to measure the activities of MgO and Al_2O_3 in spinel solid solutions in the MgAl_2O_4-Al_(8/3)O_4 compositional system at 1400°C. Eight compositions were studied, ranging from stoichiometric MgAl_2O_4 to corundum-saturated spinel. Activities of MgAl_2O_4 and γ-Al_(8/3)O_4 were calculated from the experimental values of a_(Mg)O and a_(Al)_2O_3 using the free energy expressions of Chamberlin et al. (l993b) and Navrotsky et al. (1986). The MgAl_2O_4activities are approximately Raoultian, whereas the γ-Al_(8/3)O_4 activities show a strong positive deviation from ideality. A plausible model for spinel solid solution at 1400°C based on Landau theory (Carpenter et al., 1993a,b) is set forth, with an assumed cation and vacancy distribution. The similarity between the free energies of mixing calculated from the activities and the enthalpies of mixing measured by Navrotsky et al. (1986) imply that entropies of mixing are virtually zero and that the solid solution is affected by significant short-range order. The∆G_f° of spinel increases with increasing alumina content, indicating that excess alumina does not increase the condensation temperature of spinel in the solar nebula. However, the high P_(Al) in the solar nebula and the fact that ∆G_f° remains relatively constant at low alumina contents imply that the first spinel condensates would be somewhat aluminous.
Finally, Pd-oxide equilibration was used to measure the activities of MgO and SiO_2 in forsterite and protoenstatite. Four compositions were studied: nominally pure forsterite, forsterite in equilibrium withprotoenstatite, and forsterites that crystallized from liquids of two different bulk compositions in the system CMAST (POI and FOB). Measured oxide activities and ∆G_f°'s vary systematically with Ca content. The ∆G_f°'s are consistent with the literature values of Robie et al. (1978), Berman (1988), JANAF (1985), and Gillet et al. (1991) in this temperature range except in FOB, where they are lower. The free energy of formation (∆G_f°) of protoenstatite from the oxides determined from the MgO and SiO_2 activities agrees with that of Berman (1988) to 1 kJ/mole. Low levels of Ca dissolved in forsterite may increase the number of point defects in the lattice and thereby decrease the mechanical strength of the mineral. The Pd-oxide equilibration technique, with its potential for directly and precisely determining oxide activities in melts and mineral solutions and free energies of formation of minerals, could be of considerable value in refining the existing thermodynamic data base.
