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At least 739 records · Page 41

The thickness of eucritic crust in the HED parent body

Because cumulate eucrites are generally thought to be located at the lower part in eucritic crust on a diogenitic mantle in the HED parent body, the burial depth of cumulate eucrites gives information on the thickness of the eucritic crust. We estimated the burial depth and cooling rate of cumulate eucrites, Serra de Mage and Moore County on the basis of the width of augite lamellae and compositional gradients of Ca in pyroxenes by numerically solving the diffusion equation. We obtained the burial depth of the eucrites of 7-8 km and cooling rate of 0.00016-0.0002 degrees C/yr.

Miyamoto, M.↗

Growth kinetics of the (001) face of TGS below the ferroelectric transition temperature

The growth rates of the (001) face of triglycine sulfate (TGS) from aqueous solutions were measured at 33.55 C in an apparatus which produced a laminar flow of solution past the crystal. The data of growth rate as a function of relative supersaturation were compared with the results of two well-known models: the Burton-Cabrera-Frank (1951) surface diffusion model and the birth-and-spreading growth model. Both models produced good fits to the growth rate data. However, on the basis of the qualitative aspects of the experimentally-observed growth, it is suggested that the correct growth model for these crystals is the Burton-Cabrera-Frank model.

Reiss, D. A.↗

MOCVD of GaAs in a horizontal reactor - Modeling and growth

A two-dimensional model for metalorganic chemical vapor deposition of GaAs in a horizontal reactor is presented. The model is characterized by the following parameters: reactor geometry and operating pressure, thermal boundary conditions, ratio of reactants, chemical reactions, total inlet gas flow rate, as well as molecular weights, thermal conductivities, heat capacities, viscosities, and binary diffusion coefficients of the gas-phase species. Film thickness profiles predicted by the model are compared with those of GaAs thin films grown in the modeled reactor. Results obtained show a good agreement between the predictions and data over the entire length of the deposition region for the low pressure and high flow rate run. Attention is also given to the reactor design and growth conditions.

Clark, Ivan O.↗

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Li, Jianzhong↗

Parameterization of linear wave chemical transport in planetary atmospheres by eddy diffusion

Two-dimensional transport by linear waves is parameterized by wave velocity and temperature correlations and nonconservative properties of the atmosphere in a residual Eulerian framework. Explicit expressions derived for the eddy tracer flux vector are written in eddy diffusion tensor form, but it is demonstrated that strong coupling of chemistry and temperature through the rate constants, as is the case for ozone, requires additional terms proportional to the mixing ratio and not to its gradient. A variety of limiting cases are discussed. In the residual Eulerian framework the K(yz), K(zy) components are nonzero for a nonconservative atmosphere and/or a reactive tracer. Tracers have common transport coefficients in the limit where their chemistry is negligible in comparison to transience. It is shown that the usual one-dimensional vertical eddy diffusion continuity equation is rigorously valid only when the temperature dependence of the rate constants is negligible and the tracer has strong vertical stratification relative to its horizontal variability.

Strobel, D. F.↗

Permeation Rate Equations for Hydrogen and Deuterium in a Palladium-Silver Alloy

Mass transfer of a gas through a selective, solid membrane is an effective method for separation of desired species. This selective permeability is evident in the flow of hydrogen and the isotope deuterium through palladium-silver metal alloy media. In this study, based upon Sieverts’s law and the Arrhenius diffusion equation, an empirical correlation was developed to determine the steady-state permeation rate R, dependence on media temperature T, gas supply pressure p(sub S), and gas backpressure p(sub B) on the lower pressure side. Because of an extensive range of experimental conditions and complete reporting of raw data, the research by Ackerman and Koskinas was used as a source for data allowing empirical equation fitting. Unfortunately, those authors reported best-fit equations that poorly represented their own results. To improve the modeling of the original data and demonstrate the quality of the measurements, the current study develops improved hydrogen and deuterium permeation rate equations: P = 4.22×10(exp −6) A[exp(−704/T)](sq. root p(sub S) − sq. root p(sub B))/t for hydrogen P = 2.12×10(exp −6) A[exp(−468/T )](sq. root p(sub S) − sq. root p(sub B))/t for deuterium for values of cross-sectional area A (sq.cm), medium thickness t (cm), pressure p (psia), and temperature T (Kelvin), giving a permeation rate in mole/minute. These equations model permeation rate data more closely than do several other existing literature sources.

Smith, Phillip J.↗

Dendritic solidification. III - Some further refinements to the model for dendritic growth under an imposed thermal gradient

Some further refinements to a simple model for dendritic solidification in a binary alloy melt under an imposed positive thermal gradient are presented. Two new expressions for the dendrite tip undercooling have been obtained and shown to yield a limiting value of Delta T sub 0 and very small growth rates. Here Delta T sub 0 is the equilibrium solidification range of the alloy. At very large growth rates, all three tip undercooling expressions reach the same limiting value depending on the value of a dimensionless parameter lambda which is related to the effective diffusion distance ahead of the dendrite tip. The predicted tip undercoolings are, however, somewhat lower at intermediate growth rates. An improved calculation for the solute buildup at the dendrite tip due to curvature effects is also included.

Laxmanan, V.↗

Ion beam microtexturing of surfaces

Some recent work in surface microtecturing by ion beam sputtering is described. The texturing is accomplished by deposition of an impurity onto a substrate while simultaneously bombarding it with an ion beam. A summary of the theory regarding surface diffusion of impurities and the initiation of cone formation is provided. A detailed experimental study of the time-development of individual sputter cones is described. A quasi-liquid coating was observed that apparently reduces the sputter rate of the body of a cone compared to the bulk material. Experimental measurements of surface diffusion activation energies are presented for a variety of substrate-seed combinations and range from about 0.3 eV to 1.2 eV. Observations of apparent crystal structure in sputter cones are discussed. Measurements of the critical temperature for cone formation are also given along with a correlation of critical temperature with substrate sputter rate.

Robinson, R. S.↗

Loci/STREAM Sharp Interface Model Validation of Cryogenic Propellant Tank Self-Pressurization

This paper documents a model validation effort for the prediction of cryogenic propellant tank selfpressurization physics using the Loci/STREAM sharp interface CFD model developed at NASA MSFC. Cryogenic fluid management (CFM) applications for long duration spaceflight missions require accurate modeling of heat transfer and thermodynamics. Therefore, detailed validation of those physics is important to ensure simulation accuracy. In the past, the MSFC Propulsion Fluid Dynamics Branch has validated and used the Loci/STREAM Volume of Fluid (VOF) module extensively for propellant slosh applications, which are dominated by fluid motion. For cases where the interface gas/liquid interface is essentially static, the Loci/STREAM sharp interface was developed for more rapid and efficient CFM analysis. In the present study, Loci/STREAM sharp interface simulations were compared with the NASA K-site self-pressurization experiment of a flight weight, partially full, LH2 tank in normal gravity. This study investigated several parametric effects and made a number of important observations on the performance of the Loci/STREAM sharp interface method: - First, a homogeneous model was derived to verify the CFD model. The homogeneous model assumes both gas and liquid phases are uniform and are at saturation temperature. The predicted pressure rise rates at 3.5 W/m2 and 2.0 W/m2 with a 49% fill level are all lower than the experimental measurement. This is expected due to the observed temperature stratification near the gas-liquid interface during testing. - The k-w and k-e turbulence models predict comparable pressurization rates, which are much lower than the experiment measurement. On the other hand, the pressure values and pressurization rates from both models are almost the same as those of the homogeneous model. The current turbulence model is too diffusive and is not capable of capturing the thermal stratification in the liquid and ullage. - When using the laminar flow model, the pressurization rate is found to be very close to the experimental value when a quasi-steady flow field is allowed to develop by continuously venting the tank prior to pressurization as was done during testing. On the other hand, without initial venting, the rate is not constant. Additionally, the development time to reach a quasi-steady flow field differed from the experiment due to the lack of turbulent mixing away from the gas-liquid interface that is expected in reality. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 15% of the experimental value for 49% fill level at 3.5 W/m 2 and is within 18% for 2.0 W/m 2 heat loading. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 18% of the experimental value for a 29% fill level and within 15% for an 83% fill level.

H. Q. Yang↗

High-Subsonic Performance Characteristics and Boundary-Layer Investigations of a 12 10-Inch-Inlet-Diameter Conical Diffuser

Performance and boundary-layer data were taken in a 12 degree 10-inch inlet-diameter conical diffuser of 2:1 exit- to inlet-area ratio. These data were taken for two inlet-boundary-layer conditions. The first condition was that of a thinner inlet boundary later (boundary-layer displacement thickness, delta* approximately equal to 0.034) produced by an inlet section approximately 1 inlet diameter in length between the entrance bell and the diffuser. The second condition was a thicker inlet boundary layer (delta* approximately equal to 0.120) produced by an additional inlet section length of approximately 6 diameters. Longitudinal static-pressure distributions were measured fro wall static orifices. Transverse total- and static-pressure surveys were made at the inlet and exit stations. Boundary-layer velocity distributions were measured at seven stations between the inlet and exit. These data were obtained for a Reynolds number (based on inlet diameter) range of 1 x 10(exp 6) to 3.9 x 10(exp 6). The corresponding Mach number range was from M = 0.2 to choking. At the maximum-power-available condition supersonic flow was obtained as far as 4.5 inches downstream from the diffuser inlet with a maximum Mach number of M approximately equal to 1.5. The total-pressure loss through the diffuser in percentage of inlet dynamic pressure was approximately 2.5 percent for the thinner inlet boundary later and 5.5 percent for the thicker inlet boundary later over the lower subsonic range. These valued increased with increasing flow rate- the values for the thicker inlet boundary later more than those for the thinner inlet boundary layer. The diffuser effectiveness, expressed as the ratio of the actual static-pressure rise to the ideal static-pressure rise, was about 85 percent for the thinner inlet boundary layer and about 67 percent for the thicker inlet boundary later in the lower subsonic range. These values decrease with increasing flow rate. Separated flow was observed for both inlet-boundary-layer conditions in the region of adverse pressure gradient just downstream of the transition curvature from inlet section to diffuser. The flow for the thinner-inlet-boundary-layer condition did not fully re-establish itself along the diffuser walls. The thicker inlet-boundary-layer flow, while not completely re-establishing the normal flow pattern downstream of the separated region, did re-establish more successfully than the thinner inlet boundary layer.

Little, B. H., Jr.↗

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

VanOverbeke, Thomas J.↗

The effect of prewhirl on the internal aerodynamics and performance of a mixed flow research centrifugal compressor

The internal three-dimensional steady and time-varying flow through the diffusing elements of a centrifugal impeller were investigated using a moderate scale, subsonic, mixed flow research compressor facility. The characteristics of the test facility which permit the measurement of internal flow conditions throughout the entire research compressor and radial diffuser for various operating conditions are described. Results are presented in the form of graphs and charts to cover a range of mass flow rates with inlet guide vane settings varying from minus 15 degrees to plus 45 degrees. The static pressure distributions in the compressor inlet section and on the impeller and exit diffuser vanes, as well as the overall pressure and temperature rise and mass flow rate, were measured and analyzed at each operating point to determine the overall performance as well as the detailed aerodynamics throughout the compressor.

Bryan, William B.↗

Landscape Evolution, A Comparison of Form and Process

This project's goals were to collect, analyze and interpret 3-dimensional physiographic data for understanding the processes responsible for landscape modification. The primary landforms to be studied were Neogene cinder cones in Arizona (San Francisco Volcanic Field (SFVF), Coconino and Kaibab National Forests, Arizona). We also obtained and are still analyzing digital topographic data for the Long Valley-White Mountains area of California, which display Quaternary normal fault scarps, as well as extensive evidence of degradation. The work resulted in a large database of measured rates of downslope transport of slope debris. It was hypothesized that the work would increase our understanding of process-response models of hillslope degradation, and of the effects of climate change and other parameters on degradation rates. In greater detail, our primary goal was to compare evolutionary sequences of hillslopes, as exemplified by the topography of landforms of the same type but of different ages, with measurements of the surficial processes active on the landforms. Assuming that other parameters, such as hillslope materials and vegetation are held constant, and that the effects of changing climate are negligible, then the sediment transport rates measured today on the landforms should be the same as those calculated from the inversion of landform topography by use of a diffusion-type model. However, if the effects of changing climate or other factors are not negligible, then the observed transport rates would differ from those which must be invoked to explain the current topography. We hypothesized in fact that because degradation on the event scale is highly transient and localized, we would find a wide divergence between modern, measured transport rates, and rates calculated by global landform inversion or modeling. Because of the length of time involved in collection of sufficient data on current degradation rates, we are still continuing to analyse and interpret the data. Completion of the work will increase our understanding of the potential effects of anthropogenic climate and surficial change on the Earth's solid surface, and possibly allow us to constrain paths of hill-slope evolution following anthropogenic modifications, as well as compare the short-term with the long-term rates of hillslope degradation.

Bursik, Marcus I.↗

Experimental Investigation of Centrifugal Compressor Stabilization Techniques

Results from a series of experiments to investigate techniques for extending the stable flow range of a centrifugal compressor are reported. The research was conducted in a high-speed centrifugal compressor at the NASA Glenn Research Center. The stabilizing effect of steadily flowing air-streams injected into the vaneless region of a vane-island diffuser through the shroud surface is described. Parametric variations of injection angle, injection flow rate, number of injectors, injector spacing, and injection versus bleed were investigated for a range of impeller speeds and tip clearances. Both the compressor discharge and an external source were used for the injection air supply. The stabilizing effect of flow obstructions created by tubes that were inserted into the diffuser vaneless space through the shroud was also investigated. Tube immersion into the vaneless space was varied in the flow obstruction experiments. Results from testing done at impeller design speed and tip clearance are presented. Surge margin improved by 1.7 points using injection air that was supplied from within the compressor. Externally supplied injection air was used to return the compressor to stable operation after being throttled into surge. The tubes, which were capped to prevent mass flux, provided 9.3 points of additional surge margin over the baseline surge margin of 11.7 points.

Skoch, Gary J.↗

An experimental study of the ice column habit transitions

The influence of supersaturation on column growth of ice crystals forming from atmospheric water vapor was investigated. A high density of crystals was generated on a glass fiber cooled by liquid N2 in a thermal diffusion chamber. Attention was focused on a neighbor-free hollow prism during a stepwise decrease in supersaturation while the crystal temperature was maintained constant. Another experiment involved epitaxial growth of ice crystals on CuS, where nonthickening crystals could only be grown below -7 C. A critical supersaturation was found to be necessary for growth of the basal plane. Beyound the critical value, surface kinetics do not control the growth rate, which is then dominated by the penetration of water molecules through the diffusion field surrounding the crystal.

Cho, N.↗

Immiscible phase incorporation during directional solidification of hypermonotectics

Solidification processes in immiscible samples were investigated by directly observing the events taking place at the solid-liquid interface during directional solidification. Visualization of these events was made possible through the use of a transparent metal analog system and a temperature gradient stage assembly fitted to an optical microscope. The immiscible transparent analog system utilized was the succinonitrile-glycerol system. This system has been shown to exhibit the same morphological transitions as observed in metallic alloys of monotectic composition. Both monotectic and hypermonotectic composition samples were directionally solidified in order to gain an improved understanding of the manner in which the excess hypermonotectic liquid is incorporated into the solidifying structure. The processing conditions utilized prevented sedimentation of the excess hypermonotectic liquid by directionally solidifying the samples in very thin (13 microns), horizontally oriented cells. High thermal gradient to growth rate ratios (G/R) were used in an effort to prevent constitutional supercooling and the subsequent formation of L(sub 2) droplets in advance of the solidification front during the growth of fibrous composite structures. Results demonstrated that hypermonotectic composites could be produced in samples up to two weight percent off of the monotectic composition by using a G/R ratio greater than or equal to 4.6 x 10(exp 4) C(s)/mm(sup 2) to avoid constitutional supercooling. For hypermonotectic samples processed with G/R ratios below 4.6 x 10(exp 4) C(s)/mm(sup 2), constitutional supercooling occurred and resulted in slight interfacial instability. For these samples, two methods of incorporation of the hypermonotectic liquid were observed and are reported. The correlation between the phase spacing, lambda, and the growth rate, R, was examined and was found to obey a relationship generally associated with a diffusion controlled coupled growth process. For samples with compositions ranging from the monotectic composition up to 2 percent off of the monotectic composition, data indicated that the square of the phase spacing (lambda) varied linearly with the inverse of the growth rate (R).

Andrews, J. Barry↗

Thermodynamic and Diffusion Model Estimates on Metamorphic Temperatures and Timescales for Basaltic Eucrite GRA 98098

Introduction: HED meteorites are thought to rep-resent igneous rocks from Vesta’s basaltic crust and preserve evidence of early crustal metamorphism. Determining the temperatures and timescales of thermal metamorphism is important for reconstructing crustal evolution in the early solar system. Here, we study basaltic eucrite Graves Nunataks (GRA) 98098, which has been identified as a highly metamorphosed eucrite [1]. We present new estimates on metamorphic temperatures determined via thermodynamic modeling as well as the initial results from diffusion models constraining timescales of thermal metamorphism. Sample Description: GRA 98098 is an unbrecciated eucrite with a granoblastic plagioclase and pyroxene mineralogy. Millimeter to cm-long lathes of tridymite cross-cut and poikilitically enclose plagioclase and pyroxene [1,this work]. Pyroxene grains have exsolved into Ca-rich (~Wo38En29Fs33) and Ca-poor (~Wo4.5En36Fs59.5) lamellae. Both unzoned and zoned plagioclase grains are observed. Unzoned plagioclase grains are found solely with tridymite laths. These grains have ~An92 compositions. The cores of the zoned plagioclase grains have the same composition and thin, relatively sodic rims (~An67), (Fig. 1). The bulk sample is unusually enriched in highly in-compatible elements and has one of the most fractionated REE patterns reported [1]. Maximum metamorphic temperatures of 985±78°C have been estimated using two-pyroxene thermometry [2]. Methods: Thermodynamic modeling. Thermodynamic models were constructed using the software Perple_X, which employs a Gibbs free energy minimization in order to determine the most stable phase assemblage for a given bulk rock composition [3]. Bulk composition was calculated using mineral com-positions acquired via EMPA (this study) and the observed abundancies present in the thin section. Two bulk compositions were estimated; 1) includes all phases present in the thin section, (assumes that all phases are present during metamorphism), 2) excludes tridymite from the bulk calculation (assumes that tridymite was not present during metamorphism). In order to determine whether metamorphic equilibria was achieved and estimate temperatures of metamorphism, we compared measured pyroxene compositions with thermodynamically predicted compositions [4, Fig. 2]. Diffusion Modeling. Several time-temperature de-pendent diffusion profiles were calculated in order to determine the best match for XAn chemical profiles observed at the edges of the zoned plagioclase (Fig. 3). We assumed that the start condition was a stepwise gradient at the plagioclase/pyroxene interface. We also assumed an average diffusion coefficient (D) and a constant temperature using the equation in [5]. D was determined for two temperatures (T = 1060ºC; near eucrite solidus [6] and T = 985ºC; metamorphism reported in [4]) and then XAn was calculated as a function of distance from plagioclase core to rim using an error function solution to Fick’s second law. Results: Thermodynamic model results are summarized in Fig. 2. For a bulk composition that includes all phases in the thin section, pyroxene endmember compositions plot in the following temperature ranges: Fs ~660-860ºC, En~1000ºC & 1150ºC, and Wo~760-900ºC (Fig. 2a). For a bulk composition that excludes tridymite from the peak metamorphic assemblage (i.e., the bulk composition minus the contribution from tridymite), a temperature range could not be determined for the Fs component of pyroxene. For Wo, T~760-900ºC and En, T~1000ºC & 1150ºC (Fig. 2b). Fig. 3 summarizes the diffusion model results. For T = 1060°C & 985°C, the most appropriate time interval was estimated based on which diffusion curve most matched (solid lines, Fig. 3) the EMPA data. For T = 1060°C, the best looking match was t = 500 ka. For T = 985°C, the best match was t = 7 Ma. Discussion and future work: Temperature estimates from thermodynamic models are not conclusive because the temperature ranges determined for pyroxene endmember stability do not overlap (colored fields in Fig. 2), thus implying that there is disequilibrium between pyroxene crystals and the bulk composition considered [4]. Thus, additional exploration is needed to define a metamorphically equilibrated do-main that accurately records peak temperature. The utility of defining metamorphically equilibrated do-mains to improve the accuracy and level of detail elucidated regarding the petrogenetic history of metamorphose samples has been demonstrated previously [4,7]. We suggest that in the case of Fig. 2a, the thin section composition is not representative of the length scales over which metamorphic equilibrium was achieve and in the case of Fig. 2b, the assumption that tridymite was not present during metamorphism was incorrect. However, results from thermodynamic models can provide insight into the relative timing of mineral and compositional textures. For example from texture alone, it is unclear whether tridymite was igneous in origin and represents the last bits of melt in a crystallizing magma chamber, or if it formed during (and possibly initiated) open system thermal metamorphism. The latter could be consistent with a partial melt hypothesis [8,9] while the former implies that simple fractional crystallization can yield the textures present in GRA 98098. The lack of coincidence be-tween pyroxene endmember compositions in Fig. 2b suggest that the bulk composition minus tridymite was not the assemblage in equilibrium with the pyroxene, suggesting that tridymite was present during metamorphism and formed during igneous crystallization. We conclude that the development of the Na-rich plagioclase rims likely occurred during or immediately after peak thermal metamorphism, because eucrites of similar metamorphic grade and texture have unzoned plagioclase (~An92) [2,4,8], and Na zoning is only observed in the plagioclase not included in the tridymite. This suggests that the zoning formed after tridymite formation, and therefore after igneous crystallization. Thus, the timescales calculated via diffusion modeling possibly represent the time interval over which thermal metamorphism occurred. Cooling rates approximated for the Vestan crust predict that the crust cooled below 300°C around 35-40 Ma after formation[10]. This is consistent with our modeling results that predict formation of the Na rich plagioclase rims occurring at higher temperatures over a period of 0.5 to 7 Ma years. Future work. Additional thermodynamic modeling work will focus on selecting an equilibrated bulk rock domain in which to elucidate metamorphic conditions. Diffusion models currently provide a minimum time-scale, since diffusion slows down as the system cools. Future work with will focus on integrating cooling into the diffusion models and constraining the depth at which thermal metamorphism occurs because it could be used to determine whether the range of time-scales calculated for thermal metamorphism are consistent with the geologic environment.

J S Gorce↗