Search

Abstract—Type B coarse‐grained calcium‐aluminum‐rich inclusions (CAIs) are the oldest known materials to have formed in the solar system and are a unique source of information regarding conditions and processes in the protoplanetary disk around the young sun. Recent experimental results on the crystallization and evaporation of type B‐like silicate melts allow us to place the following constraints on the conditions in the protoplanetary disk during the formation of type B CAIs. 1) Once type B CAIs precursors have been condensed from a solar composition gas, they were reheated at 1250–1450 °C, as is indicated by their igneous texture. 2) The melilite mantles characteristic of type B1 CAIs could be formed by crystallization of magnesium‐ and silicon‐depleted melt in the outer part of the partially molten droplets. Such depletion can arise when evaporation is fast compared to chemical diffusion in the melt. This requires the pressure of the surrounding solar composition gas to be at least 10−4bars during the initial crystallization of melilite mantle. Type B2 CAIs with uniform distribution of melilite are expected to form at pressures less than 10−5bars. 3) Evaporation calculations are used to place bounds on the thermal history of the type B CAIs. Observed compositional zoning in melilite suggests that the temperatures in the protoplanetary disk where the type B CAIs resided after crystallization could not have exceeded ˜1000 °C for more than a few tens of thousands of years. A recent calculation of the physical conditions associated with nebular shocks produced transient temperatures and gas pressures very much like what we find is required to melt reasonable CAI precursors and evaporate these sufficiently quickly to make a type B1 CAI.

Kelvin's estimate of about $$10^{8}$$years for the age of the earth, based on the time required for an initially uniform and hot thermal structure to decay to the presently observed surface temperature gradient, is briefly reviewed. The later realization that the earth was at least several billion years old ($$4.5 \times 10^{9} years$$) posed a dilemma: How to reconcile thermal evolution with this great age? Radiogenic heat production alone is demonstrably insufficient to effect the reconciliation and, in the end, it is mantle convection, with its ability to exploit the entire internal heat of the earth, that provides the way out. The present usefulness of thermal structure as a measure of age (age now taken to mean local as opposed to global age) is reviewed for oceanic and continental regions. As for Kelvin, he was quite right in arguing that the earth's age was not only finite but measurable, measurable however by methods he did not anticipate.

Plots of Sr and Nd isotopic ratios, and La/Sm ratios of MORB from the Pacific and Atlantic oceans show a decrease in variability with increasing spreading rate, a decrease in the average value of the Sr isotopic ratio and La/Sm ratio, and an increase in the average Nd isotopic ratio. Pb isotopic ratios do not exhibit a similar correlation. In modeling this data we assume a mantle source for MORB that is heterogeneous in concentration, isotope ratios, and melting on a scale much smaller than the region from which melts are drawn. Viewed on a larger scale the mantle source would appear homogeneous by averaging over a fixed distribution of heterogeneous material. The Sr isotopic composition of melt derived from such a source is calculated using a simple sub-ridge melting and segregation model. If increasingly incomplete extraction of sub-ridge melt correlates with an increase in spreading rate, this model generates Sr isotopic variations similar to those seen in the MORB data set. This illustrates that melt extraction processes may well significantly modify mantle isotopic signatures, which has important implications for deciding whether isotope and REE ratios seen to vary in MORB should be attributed to process (i.e., melt extraction) or to the mantle source.

Empirical models for multicomponent diffusion in an isotropic fluid were derived by splitting the component's dispersion velocity into two parts: (a) an intrinsic velocity which is proportional to each component's electrochemical potential gradient and independent of reference frame and (b) a net interaction velocity which is both model and reference frame dependent. Simple molecules (e.g., M pO q) were chosen as endmember components. The interaction velocity is assumed to be either the same for each component (leading to a common relaxation velocity U) or proportional to a common interaction force (F). Uor Fis constrained by requiring no local buildup in either volume or charge. The most general form of the model-derived diffusion matrix [D] can be written as a product of a model-dependent kinetic matrix [L] and a model independent thermodynamic matrix [ G], [D] = [L] · [ G]. The elements of [ G] are functions of derivatives of chemical potential with respect to concentration. The elements of [L] are functions of concentration and partial molar volume of the endmember components, C ioand V io, and self diffusivity D i, and charge number z iof individual diffusing species. When component nis taken as the dependent variable they can be written in a common form L ij= D jδ ij+ C io[V noD n− V joD j)A i+ (p nz nD n− p jz jD j)B i] where the functional forms of the scaling factors A iand B idepend on the model considered. The off-diagonal elementL ij(i≠ j) is directly proportional to the concentration of component i, and thus negligible when iis a dilute component. The salient feature of kinetic interaction or relaxation is to slow down larger (volume or charge) and faster diffusing components and to speed up smaller (volume or charge) and slower moving species, in order to prevent local volume or charge buildup.

Chemical diffusion profiles in molten CaOAl2O3SiO2have been measured over a large range of compositions at 1500°C and l GPa. The diffusion profiles have been inverted for effective binary diffusion coefficients (EBDCs) and for the chemical diffusion matrix. The EBDCs are shown to depend strongly on both composition and direction of diffusion in composition space. The dependence of EBDCs on direction in composition space, which for the system studied here can be as large as a factor of seven, severely limits the applicability of EBDCs to interdiffusion in any direction other than the one used to derive the EBDCs.

Self diffusion coefficients of calcium (DCa), aluminum (DAl), silicon (DSi), and oxygen (DO) were measured in molten CaOAl 20 3SiO 2at 1500°C and 1 GPa over a range of melt compositions, using the isotope tracer method. For all but one composition, the measured self diffusion coefficients decrease in the order DCa> D Al> D O> D Si, with D Ca∼ 4–19 D Si, D Al∼ 2D Si, and D O∼ 1–2 D Si. The relative uncertainties, based on replicated experiments, are 8% for DCa, 27% for DAl, 28% for DSi, and 18% for DO. Although the self diffusion coefficients of calcium, aluminum, silicon, and oxygen increase with the decrease of melt viscosity, they do not obey the Stokes-Einstein equation or the Eyring equation. The compositional dependence of the self diffusion coefficients of calcium, aluminum, and oxygen were parameterized in terms of melt viscosity (Pa · s) via the power law relation: DCa= (115.141/viscosity 0.389) × 10 −12m 2s −1DA1= (47.302/viscosity 0.800) × 10 −12m 2s −1DO= (33.080/viscosity 0.722) × 10 −12m 2s −1

A numerical model which describes oxygen isotope exchange during burial and recrystallization of deep-sea carbonate is used to obtain information on how sea surface temperatures have varied in the past by correcting measured δ18O values of bulk carbonate for diagenetic overprinting. Comparison of bulk carbonate and planktonic foraminiferal δ18O records from ODP site 677A indicates that the oxygen isotopic composition of bulk carbonate does reflect changes in sea surface temperature and δ18O. At ODP Site 690, we calculate that diagenetic effects are small, and that both bulk carbonate and planktonic foraminiferal δ18O records accurately reflect Paleogene warming of high latitude surface oceans, biased from diagenesis by no more than 1°C. The same is likely to be true for other high latitude sites where sedimentation rates are low. At DSDP sites 516 and 525, the effects of diagenesis are more significant. Measured δ18O values of Eocene bulk carbonates are more than 2% lower at deeply buried site 516 than at site 525, consistent with the model prediction that the effects of diagenesis should be proportional to sedimentation rate. Model-corrections reconcile the differences in the data between the two sites; the resulting paleotemperature reconstruction indicates a 4°C cooling of mid-latitude surface oceans since the Eocene. At low latitudes, the contrast in temperature between the ocean surface and bottom makes the carbonate δ180 values particularly sensitive to diagenetic effects; most of the observed variations in measured δ18O values are accounted for by diagenetic effects rather than by sea surface temperature variations. We show that the data are consistent with constant equatorial sea surface temperatures through most of the Cenozoic, with the possible exception of the early Eocene, when slightly higher temperatures are indicated. We suggest that the lower equatorial sea surface temperatures for the Eocene and Oligocene reported in other oxygen isotope studies are artifacts of diagenetic recrystallization, and that it is impossible to reconstruct accurately equatorial sea surface temperatures without explicitly accounting for diagenetic overprinting.

A mathematical formulation for the buoyancy-driven segregation of a light fluid from a deformable matrix is applied to a geometrically simple system to illustrate its dynamical and chemical evolution. A layer with initially uniform fluid content contained above and below by impermeable boundaries, if sufficiently deep, displays three regimes: a compacting boundary layer at its base, a non-compacting interior regime, and a growing pure fluid layer at the top. Various other initial conditions are discussed, including cases with linearly decreasing fluid content and with locally large (in relative terms) fluid content. The chemical evolution of the segregating fluid is also described. Having illustrated some of the properties of fluid segregation by matrix compaction, we use it as a framework for discussing the secular changes in $$^{143}Nd/^{144}Nd$$and Sm/Nd of Hawaiian basalts.

A series of idealized models for determining the balance of forces in plate tectonics are presented and the question of the driving mechanism is reduced to evaluating several integrals that represent the forces on the bounding surfaces of the lithospheric plates and the total buoyancy of the downgoing slab. The value of the integrals are plotted as a function of depth along the downgoing slab to graphically represent the complete balance of forces, thus showing the relative importance of the different terms and also giving a measure of the internal stresses within the downgoing slab. The models that best explain the observed velocity of plates and the distribution of stresses within the downgoing slabs as inferred from focal mechanisms require the viscosity in the upper mantle to increase with depth by a factor of about 20. The primary balance of forces in these models is between the negative buoyancy of the downgoing slab and the nonhydrostatic pressure acting on its base. The significant role of the nonhydrostatic pressure is the principal new result of these calculations.

A finite amplitude, numerical model of convective motions through a phase boundary is studied. The phase change is assumed to occur over a finite vertical transition zone in the fluid and thus a continuously stratified model is considered. The motions are driven by horizontal temperature gradients on the boundaries or super-critical vertical stratification. In the case of Rayleigh instability, the numerical results reproduce the neutral curve previously obtained in the analytic solution of the linearized problem. When the parameters of the problem are chosen to simulate the olivine-spinel transition in the upper mantle, the following results are obtained: (1) the vertical scale of motion is the entire depth of the fluid; (2) the horizontal scale is not significantly changed from the case of a single phase fluid; (3) the amplitude of the motion is not significantly changed, due to buoyancy changes at the phase boundary being offset by corresponding sources and sinks of latent heat; and (4) the phase boundary varies in depth by as much as 30 km when the vertical velocities are of the order of 10−1 cm yr−1.