Numerical models for igneous activity on any planet must be based on thermal properties and melting relationships for realistic multicomponent systems. A consistent model for the composition of the earth's mantle may be obtained by considering a mixture of basalt and dunitc, as postulated by Ringwood and others, if the uranium, thorium, and potassium concentrations of the basalt are similar to that of basalts dredged from the deep ocean floors. Present evidence does not indicate that the bulk composition of the moon is appreciably different from that of the earth's mantle.On the basis of a review of existing phase equilibria and high pressure studies, we predict melting behavior as a function of pressure and temperature for a composition equivalent to 1 part basalt and 3 parts dunitc. The specific heat and fusion properties of the important minerals in this system are reviewed. The implications of these data for an understanding of magma generation are discussed.A review of the factors influencing the thermal conductivity of rocks indicates that when considering the details of heat conduction under conditions likely to be encountered within the earth's upper mantle and the moon, a model invoking constant phonon conductivity and temperature independent photon mean free path may be unrealistic. A more likely, but still oversimplified, model has a phonon conductivity inversely proportional to temperature, and, unless scattering dominates, a photon mean free path directly proportional to temperature over the range of interest. Pressure should not significantly affect the thermal conductivity within the upper mantle, except by changing the stable mineral assemblage. of the moon at the time of its formation were 0øC and the uranium content were 0.05 ppm, with Th/U and K/U in the ratio 3.7 and 10', respectively, melting would have begun about 1.5 X 10 • years after formation, the intensity being largely controlled by the thermal conductivity. At lower U, Th, and K contents, the onset of volcanism would have been delayed or suppressed completely, depending on the conductivity. Properly selected samples of the moon's surface rocks should thus make it possible to determine its initial temperature. The total thickness of extrusive and intrusive igneous rocks is shown to be critically dependent on the efficiency of radiative heat transfer in removing heat from the interior.
The a-c and d-c resistances for tetragonal zirconia were measured over the temperature range of 1100~176 and pressure range of 1 to 10 -14 atm oxygen. Polarization studies indicated that in oxygen atmospheres an oxygen electrode reaction occurs at the platinum-zirconia interface so that it is not possible accurately to separate ionic and electronic conduction components from the resistance data. However, the data do indicate a significant ionic conduction component within the pressure and temperature range studied. Assuming that oxygen transport accounts for the ionic conduction some order of magnitude values for oxygen diffusion in zirconia at 1400~ were calculated.Most chemical processes of interest in the fabrication and use of materials at high temperatures involve heterogeneous systems, and the kinetics of these processes are more often than not transport-controlled. However, experimental data on high-temperature diffusion processes is very limited, and we are not yet able to predict transport behavior.In conjunction with recent studies in our laboratories, on the kinetics of oxidation of zirconium carbide and boride in the 1000~176 range, we desired data on the mass transport properties of the ZrO2 that can form as a surface coating during the oxidation process. In particular, information was sought on the diffusion of oxygen, the defect structure of the oxide, and the effect of temperature, atmosphere, and impurity content on the defect structure. As a result of this interest, we initiated a study of the a-c and d-c electrical conductivity of tetragonal zirconia in an attempt to provide some of the desired information.From a-c and d-c resistance measurements we expected to be able to calculate transport numbers and separate ionic and electronic conduction components. From accurate knowledge of these components a defect structure model can be developed. In addition, knowledge of ionic conduction will permit the calculation of diffusion data for oxygen, providing that oxygen is the only ionic species contributing significantly to the ionic conduction.Previous work on tetragonal zirconia has been extremely limited. Kofstad and Ruzicka (1) found that the direct current conductivity of tetragonal zirconia had a complex oxygen dependence. They proposed as a possible explanation for this behavior that zirconia is an ionic conductor with a coupled transport of oxygen vacancies and interstitials and pointed out that to confirm this explanation it would be desirable to study the relative importance of ionic and electronic conduction as a function of the partial pressure of oxygen. Vest and Tallan (2) have been studying tetragonal as well as monoclinic zirconia concurrently with this study utilizing a polarization technique. Their results have not yet been reported in detail.
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