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Structure from Motion Photogrammetry and Micro X-Ray Computed Tomography 3-D Reconstruction Data Fusion for Non-Destructive Conservation Documentation of Lunar Samples

Our team is developing a modern, cross-disciplinary approach to documentation and preservation of astromaterials, specifically lunar and meteorite samples stored at the Johnson Space Center (JSC) Lunar Sample Laboratory Facility. Apollo Lunar Sample 60639, collected as part of rake sample 60610 during the 3rd Extra-Vehicular Activity of the Apollo 16 mission in 1972, served as the first NASA-preserved lunar sample to be examined by our team in the development of a novel approach to internal and external sample visualization. Apollo Sample 60639 is classified as a breccia with a glass-coated side and pristine mare basalt and anorthosite clasts. The aim was to accurately register a 3-dimensional Micro X-Ray Computed Tomography (XCT)-derived internal composition data set and a Structure-From-Motion (SFM) Photogrammetry-derived high-fidelity, textured external polygonal model of Apollo Sample 60639. The developed process provided the means for accurate, comprehensive, non-destructive visualization of NASA's heritage lunar samples. The data products, to be ultimately served via an end-user web interface, will allow researchers and the public to interact with the unique heritage samples, providing a platform to "slice through" a photo-realistic rendering of a sample to analyze both its external visual and internal composition simultaneously.

Beaulieu, K. R.↗

NASA Tech Briefs, October 2007

Topics covered include; Wirelessly Interrogated Position or Displacement Sensors; Ka-Band Radar Terminal Descent Sensor; Metal/Metal Oxide Differential Electrode pH Sensors; Improved Sensing Coils for SQUIDs; Inductive Linear-Position Sensor/Limit-Sensor Units; Hilbert-Curve Fractal Antenna With Radiation- Pattern Diversity; Single-Camera Panoramic-Imaging Systems; Interface Electronic Circuitry for an Electronic Tongue; Inexpensive Clock for Displaying Planetary or Sidereal Time; Efficient Switching Arrangement for (N + 1)/N Redundancy; Lightweight Reflectarray Antenna for 7.115 and 32 GHz; Opto-Electronic Oscillator Using Suppressed Phase Modulation; Alternative Controller for a Fiber-Optic Switch; Strong, Lightweight, Porous Materials; Nanowicks; Lightweight Thermal Protection System for Atmospheric Entry; Rapid and Quiet Drill; Hydrogen Peroxide Concentrator; MMIC Amplifiers for 90 to 130 GHz; Robot Would Climb Steep Terrain; Measuring Dynamic Transfer Functions of Cavitating Pumps; Advanced Resistive Exercise Device; Rapid Engineering of Three-Dimensional, Multicellular Tissues With Polymeric Scaffolds; Resonant Tunneling Spin Pump; Enhancing Spin Filters by Use of Bulk Inversion Asymmetry; Optical Magnetometer Incorporating Photonic Crystals; WGM-Resonator/Tapered-Waveguide White-Light Sensor Optics; Raman-Suppressing Coupling for Optical Parametric Oscillator; CO2-Reduction Primary Cell for Use on Venus; Cold Atom Source Containing Multiple Magneto- Optical Traps; POD Model Reconstruction for Gray-Box Fault Detection; System for Estimating Horizontal Velocity During Descent; Software Framework for Peer Data-Management Services; Autogen Version 2.0; Tracking-Data-Conversion Tool; NASA Enterprise Visual Analysis; Advanced Reference Counting Pointers for Better Performance; C Namelist Facility; and Efficient Mosaicking of Spitzer Space Telescope Images.

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Improved Pyrotechnic Shock Scaling Method Based on Shock Response Spectrum and Statistical Energy Analysis

It has been more than forty years since the pyrotechnic shock scaling method was introduced. The scaling method estimates the attenuation of the Shock Response Spectrum (SRS) based on the distance from the source, structural configurations, types of structural joints and interfaces, and intervening structure [1]. The method has been successfully used in the spacecraft community countless times and still is frequently used to develop pyrotechnic shock requirements at various levels of assembly of a spacecraft. However, since the method was derived empirically from a limited set of shock test data [2], the aerospace community has been looking for an alternative approach. In this paper, a computational scaling method based on Statistical Energy Analysis (SEA) is re-visited. SEA is traditionally used as a method for investigating the diffusion of acoustic and vibratory energies of a system at steady-state [3]. Previously, an approach using the SRS as an acceleration constraint condition to the SEA model was introduced to estimate the attenuation from a shock source [4,5]. In the current investigation, additional examples are provided to further validate the approach. In addition, responses in the time domain are produced by the Local Modal Phase Reconstruction (LMPR) approach which was recently introduced to the community [6].

Fernandez, Juan P.↗

A Hybrid Parachute Simulation Environment for the Orion Parachute Development Project

A parachute simulation environment (PSE) has been developed that aims to take advantage of legacy parachute simulation codes and modern object-oriented programming techniques. This hybrid simulation environment provides the parachute analyst with a natural and intuitive way to construct simulation tasks while preserving the pedigree and authority of established parachute simulations. NASA currently employs four simulation tools for developing and analyzing air-drop tests performed by the CEV Parachute Assembly System (CPAS) Project. These tools were developed at different times, in different languages, and with different capabilities in mind. As a result, each tool has a distinct interface and set of inputs and outputs. However, regardless of the simulation code that is most appropriate for the type of test, engineers typically perform similar tasks for each drop test such as prediction of loads, assessment of altitude, and sequencing of disreefs or cut-aways. An object-oriented approach to simulation configuration allows the analyst to choose models of real physical test articles (parachutes, vehicles, etc.) and sequence them to achieve the desired test conditions. Once configured, these objects are translated into traditional input lists and processed by the legacy simulation codes. This approach minimizes the number of sim inputs that the engineer must track while configuring an input file. An object oriented approach to simulation output allows a common set of post-processing functions to perform routine tasks such as plotting and timeline generation with minimal sensitivity to the simulation that generated the data. Flight test data may also be translated into the common output class to simplify test reconstruction and analysis.

Moore, James W.↗

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗

International Space Station 2A Array Modal Analysis

On December 9th 2009, the International Space Station (ISS) 2A solar array mast experienced prolonged longeron shadowing during a Soyuz undocking. Analytical reconstruction of induced thermal and dynamic structural loads showed an exceedance of the mast buckling limit. Possible structural damage to the solar array mast could have occurred during this event. A Low fidelity video survey of the 2A mast showed no obvious damage of the mast longerons or battens. The decision was made to conduct an on-orbit dynamic test of the 2A array on December 18th, 2009. The test included thruster pluming on the array while photogrammetry data was recorded. The test was similar to other Dedicated Thruster Firings (DTFs) that were performed to measure structural frequency and damping of a solar array. Results of the DTF indicated lower frequency mast modes than model predictions, thus leading to speculation of mast damage. A detailed nonlinear analysis was performed on the 2A array model to assess possible solutions to modal differences. The setup of the parametric nonlinear trade study included the use of a detailed array model and the reduced mass and stiffness matrices of the entire ISS being applied to the array interface. The study revealed that the array attachment structure is nonlinear and thus was the source of error in the model prediction of mast modes. In addition, a detailed study was performed to determine mast mode sensitivity to mast longeron damage. This sensitivity study was performed to assess if the ISS program has sufficient instrumentation for mast damage detection.

Laible, Michael↗

NASA Tech Briefs, September 2013

Topics include: ISS Ammonia Leak Detection Through X-Ray Fluorescence; A System for Measuring the Sway of the Vehicle Assembly Building; Fast, High-Precision Readout Circuit for Detector Arrays; Victim Simulator for Victim Detection Radar; Hydrometeor Size Distribution Measurements by Imaging the Attenuation of a Laser Spot; Quasi-Linear Circuit; High-Speed, High-Resolution Time-to-Digital Conversion; Li-Ion Battery and Supercapacitor Hybrid Design for Long Extravehicular Activities; Ultrasonic Low-Friction Containment Plate for Thermal and Ultrasonic Stir Weld Processes; High-Powered, Ultrasonically Assisted Thermal Stir Welding; Next-Generation MKIII Lightweight HUT/Hatch Assembly; Centrifugal Sieve for Gravity-Level-Independent Size; Segregation of Granular Materials; Ion Exchange Technology Development in Support of the Urine Processor Assembly; Nickel-Graphite Composite Compliant Interface and/or Hot Shoe Material; UltraSail CubeSat Solar Sail Flight Experiment; Mechanism for Deploying a Long, Thin-Film Antenna From a Rover; Counterflow Regolith Heat Exchanger; Acquisition and Retaining Granular Samples via a Rotating Coring Bit; Very-Low-Cost, Rugged Vacuum System; Medicine Delivery Device With Integrated Sterilization and Detection; FRET-Aptamer Assays for Bone Marker Assessment, C-Telopeptide, Creatinine, and Vitamin D; Multimode Directional Coupler for Utilization of Harmonic Frequencies from TWTAs; Dual-Polarization, Multi-Frequency Antenna Array for use with Hurricane Imaging Radiometer; Complementary Barrier Infrared Detector (CBIRD) Contact Methods; Autonomous Control of Space Nuclear Reactors; High-Power, High-Speed Electro-Optic Pockels Cell Modulator; Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors; Enigma Version 12; Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program; Spitzer Telemetry Processing System; Planetary Protection Bioburden Analysis Program; Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2); ISSM: Ice Sheet System Model; Automated Loads Analysis System (ATLAS); Integrated Main Propulsion System Performance Reconstruction Process/Models. Phoenix Telemetry Processor; Contact Graph Routing Enhancements Developed in ION for DTN; GFEChutes Lo-Fi; Advanced Strategic and Tactical Relay Request Management for the Mars Relay Operations Service; Software for Generating Troposphere Corrections for InSAR Using GPS and Weather Model Data; Ionospheric Specifications for SAR Interferometry (ISSI); Implementation of a Wavefront-Sensing Algorithm; Sally Ride EarthKAM - Automated Image Geo-Referencing Using Google Earth Web Plug-In; Trade Space Specification Tool (TSST) for Rapid Mission Architecture (Version 1.2); Acoustic Emission Analysis Applet (AEAA) Software; Memory-Efficient Onboard Rock Segmentation; Advanced Multimission Operations System (ATMO); Robot Sequencing and Visualization Program (RSVP); Automating Hyperspectral Data for Rapid Response in Volcanic Emergencies; Raster-Based Approach to Solar Pressure Modeling; Space Images for NASA JPL Android Version; Kinect Engineering with Learning (KEWL); Spacecraft 3D Augmented Reality Mobile App; MPST Software: grl_pef_check; Real-Time Multimission Event Notification System for Mars Relay; SIM_EXPLORE: Software for Directed Exploration of Complex Systems; Mobile Timekeeping Application Built on Reverse-Engineered JPL Infrastructure; Advanced Query and Data Mining Capabilities for MaROS; Jettison Engineering Trajectory Tool; MPST Software: grl_suppdoc; PredGuid+A: Orion Entry Guidance Modified for Aerocapture; Planning Coverage Campaigns for Mission Design and Analysis: CLASP for DESDynl; and Space Place Prime.

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'The surface management system' (SuMS) database: a surface-based database to aid cortical surface reconstruction, visualization and analysis

Surface reconstructions of the cerebral cortex are increasingly widely used in the analysis and visualization of cortical structure, function and connectivity. From a neuroinformatics perspective, dealing with surface-related data poses a number of challenges. These include the multiplicity of configurations in which surfaces are routinely viewed (e.g. inflated maps, spheres and flat maps), plus the diversity of experimental data that can be represented on any given surface. To address these challenges, we have developed a surface management system (SuMS) that allows automated storage and retrieval of complex surface-related datasets. SuMS provides a systematic framework for the classification, storage and retrieval of many types of surface-related data and associated volume data. Within this classification framework, it serves as a version-control system capable of handling large numbers of surface and volume datasets. With built-in database management system support, SuMS provides rapid search and retrieval capabilities across all the datasets, while also incorporating multiple security levels to regulate access. SuMS is implemented in Java and can be accessed via a Web interface (WebSuMS) or using downloaded client software. Thus, SuMS is well positioned to act as a multiplatform, multi-user 'surface request broker' for the neuroscience community.

NASA Discipline Neuroscience↗

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗

Hydrogen (H) Isotope Composition of Type II Kerogen Extracted by Pyrolysis-GC-MS-IRMS: Terrestrial Shale Deposits as Martian Analogs

Described here is a technique for H isotope analysis of organic compounds pyrolyzed from kerogens isolated from gas‐ and liquids‐rich shales. Application of this technique will progress the understanding of the use of H isotopes not only in potential kerogen occurrences on Mars, but also in terrestrial oil and gas resource plays. H isotope extraction and analyses were carried out utilizing a CDS 5000 Pyroprobe connected to a Thermo Trace GC interfaced with a Thermo MAT 253 IRMS. Also, a split of GC‐separated products was sent to a DSQ II quadrupole MS to make qualitative and semi‐quantitative compositional measurements of these products. Kerogen samples from five different basins (type II and II‐S) were dehydrated (heated to 80 C overnight under vacuum) and analyzed for their H isotope compositions by Pyrolysis‐GC‐MS‐TC‐IRMS. This technique takes pyrolysis products separated via GC and reacts them in a high temperature conversion furnace (1450 C), which quantitatively forms H2. Samples ranging from ~0.5 to 1.0mg in size, were pyrolyzed at 800 C for 30s. and separated on a Poraplot Q GC column. H isotope data from all kerogen samples typically show enrichment in D from low to high molecular weight. H2O average delta D = ‐215.2 per mille (V‐SMOW), ranging from ‐ 271.8 per mille for the Marcellus Shale to ‐51.9 per mille for a Polish shale. Higher molecular weight compounds like toluene (C7H8) have an average delta D of ‐89.7 per mille, ranging from ‐156.0 per mille for the Barnett Shale to ‐50.0 per mille for the Monterey Shale. We interpret these data as representative of potential H isotope exchange between hydrocarbons and sediment pore water during basin formation. Since hydrocarbon H isotopes readily exchange with water, these data may provide some useful information on gas‐water or oil‐water interaction in resource plays, and further as a possible indicator of paleoenvironmental conditions. Alternatively, our data may be an indication of H isotope exchange with water and/or acid during the kerogen isolation process. Either of these interpretations will prove useful when deciphering H isotope data derived from kerogen analyses. Understanding the role that these H‐bearing compounds play in terrestrial shale paleo‐environmental reconstruction may also prove useful as analogs for understanding the interactions of water and potential kerogen/organic compounds on the planet Mars.

Socki, Richard A.↗

Mars Science Laboratory Navigation Results

The Mars Science Laboratory (MSL), carrying the Curiosity rover to Mars, was launched on November 26, 2011, from Cape Canaveral, Florida. The target for MSL was selected to be Gale Crater, near the equator of Mars, with an arrival date in early August 2012. The two main interplanetary navigation tasks for the mission were to deliver the spacecraft to an entry interface point that would allow the rover to safely reach the landing area, and to tell the spacecraft where it entered the atmosphere of Mars, so it could guide itself accurately to close proximity of the landing target. MSL used entry guidance as it slowed down from the entry speed to a speed low enough to allow for a successful parachute deployment, and this guidance allowed shrinking the landing ellipse to a 99% conservative estimate of 7 by 20 kilometers. Since there is no global positioning system in Mars, achieving this accuracy was predicated on flying a trajectory that closely matched the reference trajectory used to design the guidance algorithm, and on initializing the guidance system with an accurate Mars-relative entry state that could be used as the starting point to integrate the inertial measurement unit data during entry and descent. The pre-launch entry flight path angle (EFPA) delivery requirement was +/- 0.20 deg, but after launch a smaller threshold of +/- 0.05 deg was used as the criteria for late trajectory correction maneuver (TCM) decisions. The pre-launch requirement for entry state knowledge was 2.8 kilometers in position error and 2 meters per second in velocity error, but also smaller thresholds were defined after launch to evaluate entry state update opportunities. The biggest challenge for the navigation team was to accurately predict the trajectory of the spacecraft, so the estimates of the entry conditions could be stable, and late trajectory correction maneuvers or entry parameter updates could be waved off. As a matter of fact, the prediction accuracy was such that the last TCM performed was a small burn executed eight days before landing, and the entry state that was calculated just 36 hours after that TCM, and that was uploaded to the spacecraft the same day, did not need to be updated. The final EFPA was 0.013 deg shallower than the -15.5 deg target, and the on-board entry state was just 200 meters in position and 0.11 meters per second in velocity from the post-landing reconstructed entry state. Overall the entry delivery and knowledge requirements were fulfilled with a margin of more than 90% with respect to the pre-launch thresholds. This excellent accuracy contributed to a very successful and accurate entry, descent, and landing, and surface mission.

navigation↗

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↗