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A model of solute partitioning in a finite body under conditions of continuous cooling is developed for the determination of cooling rates from concentration profile data, and applied to the partitioning of zirconium between ilmenite and ulvospinel in the Apollo 15 Elbow Crater rocks. Partitioning in a layered composite solid is described numerically in terms of concentration profiles and diffusion coefficients which are functions of time and temperature, respectively; a program based on the model can be used to calculate concentration profiles for various assumed cooling rates given the diffusion coefficients in the two phases and the equilibrium partitioning ratio over a range of temperatures. In the case of the Elbow Rock gabbros, the cooling rates are calculated from measured concentration ratios 10 microns from the interphase boundaries under the assumptions of uniform and equilibrium initial conditions at various starting temperatures. It is shown that the specimens could not have had uniform concentrations profiles at the previously suggested initial temperature of 1350 K. It is concluded that even under conditions where the initial temperature, grain sizes and solute diffusion coefficients are not well characterized, the model can be used to estimate the cooling rate of a grain assemblage to within an order of magnitude.

The process of breccia formation by viscous sintering in the absence of pressure, advanced by Simonds (1973), is examined in detail. The limitations on the standard model for such sintering are considered. The competing process of crystallization is analyzed kinetically in terms of time-temperature-transformation curves corresponding to various degrees of crystallinity. The analysis is applied to Lunar Composition 15418 to illustrate the approach. The results indicate that close constraints can be placed on the thermal histories of lunar breccias, particularly breccias with modest degrees of crystallinity, from microstructural observations and kinetic measurements.

The process of clastic breccia formation by viscous sintering in a stress-free environment is analyzed by treating crystallization and sintering as concurrent, competing processes. The kinetic analysis of crystallization is based on the construction of continuous cooling curves corresponding to the degree of crystallinity observed in the matrix of the breccia. These curves are obtained from corresponding time-temperature-transformation curves, which in turn are constructed from measured values of the crystal growth rate together with calculated values of the nucleation frequency. The kinetic analysis of sintering is based on a modification of the Frenkel (1945) treatment of viscous sintering appropriate for conditions of continuous cooling. The analysis is applied to Lunar Composition 70019 to illustrate the approach. It is shown that it is possible from the kinetic analysis to estimate both the rate at which a given breccia cooled and the minimum temperature at which the matrix particles came in contact. The results obtained for Lunar Composition 70019 seem physically reasonable and suggest that this sample cooled on the surface of the moon in its present form rather than buried in an ejecta blanket from which it was later excavated.

The diffusive isothermal partitioning of solute in a layered two-phase material has been analyzed to help elucidate the phenomenon of solute partitioning in multiphase lunar and terrestrial materials and to estimate the cooling history of samples. After reviewing the physical chemistry of partitioning and the case of an infinite one-dimensional diffusion couple, we solve in analytic form the case of a finite one-dimensional couple. The solution can be used to estimate cooling histories or to interpret laboratory experiments on partitioning. A sample calculation is included.

The equilibrium stability criterion for diffuse interfaces in a two-component solution with a miscibility gap requires that the interdiffusion flux vanish. If the system is continuously deformed, convective fluxes disrupt the equilibrium in the interface regions and induce a counter diffusive flux, which is dissipative and contributes to the apparent viscosity of the mixture. Chemical free energy is recoverably stored, causing viscoelastic phenomena. Both effects are significant.

The kinetics of crystal growth have been determined over a wide range of temperature, from 800 to 1219 C, for lunar compositions 14259 and 14310. At all temperatures for both compositions the extent of crystal growth is found to be a linear function of time. For both materials, the growth rate versus temperature relations exhibit the form generally found with glass-forming materials. At all temperatures measured, the crystal growth rate of composition 14259 is smaller than that of composition 14310. The maximum growth rate for both compositions occurs at a temperature of about 1120 C. The growth rate data are combined with viscosity data obtained on the same compositions to construct the reduced growth rate versus undercooling relations.

The work investigates experimentally the conditions required to form glasses out of a number of lunar compositions. Viscous flow and crystallization behavior of several compositions were studied over a wide range of temperature. These data exhibit the form generally found for glass-forming liquids. Combining growth rate with viscosity data, the fraction of preferred growth sites on the crystal-liquid interfaces is found to increase with increasing undercooling for all lunar compositions. The detailed forms of the kinetic data are predicted by recent computer simulations of crystal growth. Calorimetry studies indicate that lunar orange soil was formed under conditions of much slower cooling rate than 1000 deg K per sec.

Calculations of the expected crystallization behavior of selected lunar compositions (60095 and 14259) are presented. Knowledge of this behavior combined with measurements of the state of crystallinity in partially devitrified lunar samples permits the determination of the thermal history of the samples. The state of crystallinity of a specimen is described by a statistical crystal distribution function psi. The heat flow problems of a plate of opaque glass quenched on an aluminum block and of a semi-transparent glass sphere cooling by radiation are analyzed. The results are combined with laboratory measurements of the crystal growth velocity and the viscosity, and with theoretical expressions for the nucleation frequency (homogeneous and heterogeneous) to obtain psi. It is found that the calculated psi is much too large in comparison with laboratory experiments on lunar samples. Possible reasons for the discrepancy are discussed, and the most likely cause is that the assumed nucleation barrier is too small. It also appears likely that these materials have relatively few nucleating heterogeneities.

The flow characteristics of lunar compositions 15555 and 68502 have been determined over a wide range of viscosity. The temperature ranges covered by the measurements are 1201-1410 and 622-695 C for the 15555 composition and 1261-1515 and 725-840 C for 68502 composition. Reliable data could not be obtained over the intermediate ranges of temperature because of the occurrence of crystallization. The experimental data in the high temperature regions are found to be in close agreement with predictions of the semiempirical model of Bottinga and Weill. The results on these compositions are compared with previous data on other lunar compositions and on anorthite; and the importance of the flow behavior in interpreting lunar flows and phase morphologies is emphasized. Data are also reported on the kinetics of crystallization of the 15555 composition over the temperature interval from 700 to 1020 C.