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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Assessment of DSN Communication Coverage for Space Missions to Potentially Hazardous Asteroids

A communication coverage gap exists for Deep Space Network (DSN) antennas. This communication coverage gap is on the southern hemisphere, centered at approximate latitude of -47deg and longitude of -45deg. The area of this communication gap varies depending on the altitude from the Earth s surface. There are no current planetary space missions that fall within the DSN communication gap because planetary bodies in the Solar system lie near the ecliptic plane. However, some asteroids orbits are not confined to the ecliptic plane. In recent years, Potentially Hazardous Asteroids (PHAs) have passed within 100,000 km of the Earth. NASA s future space exploration goals include a manned mission to asteroids. It is important to ensure reliable and redundant communication coverage/capabilities for manned space missions to dangerous asteroids that make a sequence of close Earth encounters. In this paper, we will describe simulations performed to determine whether near-Earth objects (NEO) that have been classified as PHAs fall within the DSN communication coverage gap. In the study, we reviewed literature for a number of PHAs, generated binary ephemeris for selected PHAs using JPL s HORIZONS tool, and created their trajectories using Satellite Took Kit (STK). The results show that some of the PHAs fall within DSN communication coverage gap. This paper presents the simulation results and our analyses

Kegege, Obadiah↗
NASA NTRS2015

Determine Optimal Stimulus Amplitude for Using Vestibular Stochastic Stimulation to Improve Balance Function

Sensorimotor changes such as postural and gait instabilities can affect the functional performance of astronauts when they transition across different gravity environments. We are developing a method, based on stochastic resonance (SR), to enhance information transfer by applying non-zero levels of external noise on the vestibular system (vestibular stochastic resonance, VSR). Our previous work has shown the advantageous effects of VSR in a balance task of standing on an unstable surface [1]. This technique to improve detection of vestibular signals uses a stimulus delivery system that provides imperceptibly low levels of white noise-based binaural bipolar electrical stimulation of the vestibular system. The goal of this project is to determine optimal levels of stimulation for SR applications by using a defined vestibular threshold of motion detection. A series of experiments were carried out to determine a robust paradigm to identify a vestibular threshold that can then be used to recommend optimal stimulation levels for sensorimotor adaptability (SA) training applications customized to each crewmember. The amplitude of stimulation to be used in the VSR application has varied across studies in the literature such as 60% of nociceptive stimulus thresholds [2]. We compared subjects' perceptual threshold with that obtained from two measures of body sway. Each test session was 463s long and consisted of several 15s long sinusoidal stimuli, at different current amplitudes (0-2 mA), interspersed with 20-20.5s periods of no stimulation. Subjects sat on a chair with their eyes closed and had to report their perception of motion through a joystick. A force plate underneath the chair recorded medio-lateral shear forces and roll moments. Comparison of threshold of motion detection obtained from joystick data versus body sway suggests that perceptual thresholds were significantly lower. In the balance task, subjects stood on an unstable surface and had to maintain balance, and the stimulation was administered from 20-400% of subjects' vestibular threshold. Optimal stimulation amplitude was determined at which the balance performance was best compared to control (no stimulation). Preliminary results show that, in general, using stimulation amplitudes at 40-60% of perceptual motion threshold significantly improved the balance performance. We hypothesize that VSR stimulation will act synergistically with SA training to improve adaptability by increasing utilization of vestibular information and therefore will help us to optimize and personalize a SA countermeasure prescription. This combination may help to significantly reduce the number of days required to recover functional performance to preflight levels after long-duration spaceflight.

Goel, R.↗
NASA NTRS2015

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

Liou, Frank↗
NASA NTRS2016

Design Considerations for a Stopped-Rotor Cyclocopter for Venus Exploration

This paper considers the use of a cycloidal blade system as a means of providing lift and propulsive thrust as well as combined with a stopped rotor system, to create a stopped-rotor cyclocopter vehicle, during a mission to Venus. This stopped-rotor cyclocopter will be capable of flying at all atmospheric levels of Venus as well as landing on the surface for scientific investigation. Three reference conceptual designs with different stopped-rotor cyclocopter yaw angles are tested in RotCFD as well as a model of a hovering cyclorotor for comparison with past work in the literature and innovative study for future projects.

Husseyin, S.↗
NASA NTRS2017

Modeling of Different Fiber Type and Content SiC/SiC Minicomposites Creep Behavior

Silicon Carbide based Ceramic Matrix Composites (CMCs) are attractive materials for use in high-temperature applications in the aerospace and nuclear industries. However, creep damage mechanism in CMCs is the most dominant mechanism at elevated temperatures. Consequently, the tensile creep behavior of Hi-Nicalon, Hi-Nicalon Type S SiC fibers and Chemical vapor infiltrated Silicon Carbide matrix (CVI-SiC) were characterized and creep parameters were extracted from creep experiments. Some fiber creep tests were performed in inert environment at 1200 C on individual fibers. Creep behavior of different fiber content pristine and precracked Hi-Nicalon and Hi-Nicalon Type S reinforced minicomposites with BN interphases and CVI-SiC matrix were then modelled using the creep data found in this study and the literature and compared with creep experiments results for the pristine and precracked Hi-Nicalon and Hi-Nicalon Type S minicomposites. Finally, the effects of load-sharing and matrix cracking on CMC creep behavior will be discussed.

ceramic matrix minicomposites↗
NASA NTRS2017

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang↗
NASA NTRS2018

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget.

shock wave/boundary-layer interactio↗
NASA NTRS2022

Charging Experiments and Filtration Testing on Facemask Materials: Towards Goals of Full Performance Restoration of Used N95 Masks and Enhancement of Common-Fabric Facemasks

Different techniques have been developed for sanitizing N95 masks while retaining whatever charge remains on them. However, these sanitizing methods do not address the fact that the electrical charge, filtration efficacy, and breathability of such masks may be expected to degrade during long-term use based on mechanisms known in the literature. In this study, approaches to electrically (re)charging facemask filter materials were explored in response to the COVID-19 induced shortage of N95 masks. The effort consisted of charging experiments followed by filtration testing conducted at the coupon level during a month-long period (May 2020). The main focus of the work was to develop a recharging technique which could eventually be adapted and used as part of a broader full-performance restoration process for used N95 masks, e.g., which might employ simple washing by alcohol or soapy water as a preceding step for sanitization and declogging. Most tested coupons were therefore nonwoven meltblown fibrous polypropylene (PP) filter media extracted from decades old N95 masks. Keeping in mind commonly used cloth facemasks, limited trials were also performed with some commercially available fabrics. Charging was done at elevated temperature and was followed by cooling to freeze in the applied charges produced from corona discharges using different electrode configurations and parameter combinations, or from triboelectric rubbing. Charging was also focused on using potentially scalable equipment, e.g., Van de Graaff generators or consumer ionic hair products. Some degree of success was achieved with one of the fabrics and the PP filter media which was first purposefully discharged to have typical filtration efficiency (FE) of ~35%. Numerous attempts at corona charging discharged media resulted in filtration efficiency (FE) ≥ 80 – 85%. Some measure of charge robustness was also established via stable performance during loading testing. However, results where FE ≥ 90% were not reliably repeatable and no results met the FE ≥ 95% goal due to shortcomings of the charging process. The best three trials for PP media statistically met the FE ≥ 90% criteria, amounted to a small percentage of the trials relying on an ionic hair dryer, and are attributed to good embedding of charges via aerodynamic force. Triboelectric charging significantly enhanced the viability of one of the polyester fabrics –measured FE increased from 19% up to 46% while maintaining a reasonably low pressure drop.

N95↗
NASA NTRSDate not supplied

Wall-Modeled Large-Eddy Simulations for High-Lift Configurations using FUN3D

Wall-modeled large-eddy simulation (WMLES) capability has recently been implemented into FUN3D, an unstructured, node-centered, finite-volume solver developed at the NASA Langley Research Center. In this paper, WMLES is assessed for two configurations that are representative for high-lift applications. The first configuration is a nominal two-dimensional multielement airfoil that has been extensively studied in the literature. WMLES solutions are computed for four angles of attack and compared with previously reported solutions. Good agreement of integrated forces, surface pressures, and boundary-layer velocity profiles is shown with available experimental data especially at lower angles of attack. WMLES solutions are also computed for the NASA High-Lift Common Research Model over a large range of angles of attack. Forces, pitching moments, and pressure distributions are favorably compared with the experimental data up to the maximum lift, including the angle of attack where the maximum lift is obtained experimentally. Eddy visualization techniques of q-criterion and density-gradient magnitude illustrate the resolved content.

High-Lift flows↗
NASA NTRSDate not supplied

Constraints on triple oxygen isotope kinetics

Triple oxygen isotope measurements have been used as tracers for classifying meteorites, as indicators of atmospheric chemistry and as a proxy for primary productivity among other uses. These utilities rely on the mass dependency of most chemical reactions: δ17O is proportional to δ18O by roughly a factor of 0.5. However,in detail it is known that mass-dependency factorsvary. Constraints on mass dependency are well established for equilibrium isotope effects, but similar constraints for kinetic isotope effects are lacking.Here, we provide constraints for isotope effects generated by unidirectional chemical reactions (i.e. kinetic isotope effects, KIEs). A simplified Monte Carlo model is used to estimatethe range of kinetic isotope effects. It is found that the range of KIEs exceeds the range of equilibrium isotope effects such that some mass dependent kinetic isotope effects could be mistaken for being mass-independent. For the16O-17O-18O system,Δ′17Ovariations as large 0.8‰ can be generated from a single reaction step. Two case studies from published literature, on the thermal decomposition of calcite (CaCO3) and brucite (Mg(OH)2), are used to test the extreme limits of the modeled results. Isotope fractionationsgenerated fromdensity functional theory models of the surface reaction steps are shownto match the published data. The fractionation models are strictly mass dependent thus this result suggests thermal decomposition of calcite is also mass dependent. Although oxygen is the focus here, our approach applies to any system with more than two isotopes.

J. A. Hayles↗
NASA NTRSDate not supplied

Silicon Partitioning Between Iron-Rich Metal and Silicate Melt: New Constraints From Aerodynamic Laser Levitation Furnace Experiments

The partitioning of light elements (e.g., Si, C, H, etc.) between silicate melts and iron metal alloys as a function of pressure and temperature is a critical constraint in defining the compositional evolution of planetary interiors. While there are a significant number of experimental studies in the literature that examine the various influences of oxygen fugacity, temperature, pressure, and composition on the metal-melt partitioning of silicon, it is difficult to disentangle the effects of each variable due to the nominally independent parameters (e.g., pressure, temperature, composition) being collinear. To better test for the independent effects of pressure, temperature, and melt composition on the partitioning of silicon between iron alloy and silicate melt, new high temperature (1800°–2500°C), rapid quench (~700°C/s) aerodynamic levitation laser-heating experiments in the Fe-Si-Mg-O (En65-Fa5-Si3-Fe27) system were conducted. This high temperature, low pressure method is ideal for these experiments because it eliminates the metal container as a sink for elements of interest to partition into, and it has a rapid quench rate that minimizes potential exsolution of silicon from the metal phase during quench cooling. Given the short run times of the levitation experiments (30–60 seconds), a time series at a lower temperature (1700°C) in a vertical gas-mixing muffle tube furnace was also conducted to assess equilibrium times of the bulk composition. All successful runs were imaged using back-scatter electron imaging and analyzed for phase composition using a JEOL 8530F field emission microprobe. These new data were added to a comprehensive and internally consistent data set created from published experiments, and subsequently modeled using parameters designed to minimize collinearity (e.g., optical basicity is used as a proxy for melt composition). High collinearity is found in the data set however between temperature and oxygen fugacity, precluding any model that contains both as nominally independent variables. The resulting model demonstrates a statistically significant effect of pressure, temperature, and melt composition on the partitioning of silicon in Fe-rich metal, which has implications for the formation of planetary cores in rocky planets and provides important constraints on potential bulk core compositions.

Metal↗
NASA NTRS2022

SatNet: A Benchmark for Satellite Scheduling Optimization

Satellites provide essential services such as networking and weather tracking, and the number of near-earth and deep space satellites are expected to grow rapidly in the coming years. Communications with terrestrial ground stations is one of the critical functionalities of any space mission. Satellite scheduling is a problem that has been scientifically investigated since the 1970s. A central aspect of this problem is the need to consider resource contention and satellite visibility constraints as they require line of sight. Due to the combinatorial nature of the problem, prior solutions such as linear programs and evolutionary algorithms require extensive compute capabilities to output a feasible schedule for each scenario. Machine learning based scheduling can provide an alternative solution by training a model with historical data and generating a schedule quickly with model inference. We present SatNet, a benchmark for satellite scheduling optimization based on historical data from the NASA Deep Space Network. We propose formulation of the satellite scheduling problem as a Markov Decision Process and use reinforcement learning (RL) policies to generate schedules. The nature of constraints imposed by SatNet differ from other combinatorial optimization problems such as vehicle routing studied in prior literature. Our initial results indicate that RL is an alternative optimization approach that can generate candidate solutions of comparable quality to existing state-of-the-practice results. However, we also find that RL policies overfit to the training dataset and do not generalize well to new data, thereby necessitating continued research on reusable and generalizable agents.

Wilson, Brian↗
NASA NTRS1999

Publication Bias ( The "File-Drawer Problem") in Scientific Inference

Publication bias arises whenever the probability that a study is published depends on the statistical significance of its results. This bias, often called the file-drawer effect since the unpublished results are imagined to be tucked away in researchers' file cabinets, is potentially a severe impediment to combining the statistical results of studies collected from the literature. With almost any reasonable quantitative model for publication bias, only a small number of studies lost in the file-drawer will produce a significant bias. This result contradicts the well known Fail Safe File Drawer (FSFD) method for setting limits on the potential harm of publication bias, widely used in social, medical and psychic research. This method incorrectly treats the file drawer as unbiased, and almost always miss-estimates the seriousness of publication bias. A large body of not only psychic research, but medical and social science studies, has mistakenly relied on this method to validate claimed discoveries. Statistical combination can be trusted only if it is known with certainty that all studies that have been carried out are included. Such certainty is virtually impossible to achieve in literature surveys.

Scargle, Jeffrey D.↗
NASA NTRSDate not supplied

Venous Gas Embolism: Review to Quantify a Safe Volume of Air in Intravenous Fluids Bags for Spaceflight Applications

INTRODUCTION: The ability to create intravenous fluids (IVF) in-situ from the potable water supply of a spaceflight vehicle or habitat is a desired capability for an exploration medical system. In order to define an acceptable volume of air in IVF bags, an understanding of the volume of venous gas embolism as it relates to negative outcomes is needed. The purpose of this study is to review the literature to determine if there is a known volume of gas that contributes to mortality and/or morbidity that could be used to define requirements for rapid IVF infusion in microgravity. METHODS: A literature review was conducted of the PubMed database using the syntax: (Venous) AND (Gas OR Air) AND (Embolism) AND (Morbidity) AND (Mortality) AND (Volume) as well as manual review of references from relevant articles. 151 articles were screened excluding partial text and pediatric articles. Studies were reviewed for identification of volume of venous gas embolism associated with morbidity and/or mortality, which identified 27 articles. RESULTS: Reviewed literature included animal studies, case reports, and review articles. A high variation of proposed volumes contributing to mortality was reported. The limited human data values ranged from 20 ml to 200 ml of infused air with mortality estimated to be 48 – 80%. No studies evaluated human morbidity in any capacity. DISCUSSION: The lack of consensus on the safe volume of infused air has potential ramifications for IVF use in spaceflight as current technologies to create IVF from potable water may introduce air in IVF bags. While current microgravity infusion protocols call for the use of inline air removal filters, commercially available options have flow rate limitations that preclude rapid infusion in a resuscitation scenario. Such filters may be used in parallel to increase flow rate, but the time required to set up such a system may exclude its use during a medical emergency. Additionally, these consumable filters drive up the overall mass and volume of the medical system. Identification of a safe volume of air in IVF would allow for guidelines for the in-situ production of IVF in future spaceflight vehicles/habitats.

Christopher R Woodard↗
NASA NTRS2021

Wake Instability Behind Isolated Trip Near the Leading Edge of the BOLT-II Configuration

The BOLT-II (Holden Mission) configuration is an extended version of the BOLT flight article and depicts hypersonic boundary-layer transition in the presence of multiple and potentially interacting instability mechanisms. Several numerical studies of the boundary-layer instabilities over these configurations have been reported in the recent literature, including our previous studies of the modal instability characteristics of boundary-layer streaks adjacent to the minor-axis symmetry plane of the BOLT configuration and the wake instabilities behind a diamond planform (“pizza-box”) trip along the symmetry plane on the secondary side of the BOLT-II configuration. The present work extends the latter study to a scaled version of the same trip that is located in the region of nonzero crossflow in the vicinity of the leading edge at X/L = 0.5. Collectively, the trips along the symmetry plane and near the leading edge are the focus of the NASA roughness experiment on the secondary side of the BOLT-II configuration. The laminar basic state computation at the nominal flight design condition of Re ∞ = 5.44 x 10 6 /m and Re ∞ = 2.5 x 10 6 /m shows that the leading-edge trip with k/δ ≈ 0.70 and planform-side-length-to-height ratio of b/k = 3.0 induces multiple asymmetric, longitudinal streaks within the trip wake. The most prominent streak among these resembles a finite amplitude crossflow vortex, and it supports the amplification of multiple families of unstable modes. The application of multi-dimensional instability analysis to the wake flow reveals that the most amplified unstable mode can achieve a peak N-factor of up to 20 by X/L = 0.80, indicating that the onset of transition is more than likely to occur within eighty percent of the model length. To the best of our knowledge, the present study represents the first analysis including nonparallel and curvature effects on hypersonic tripwake instabilities in the presence of boundary-layer crossflow over a three-dimensional configuration.

Boundary layer transition↗
NASA NTRS1975

Correlation of displacement effects produced by electrons, protons and neutrons in silicon

The correlation of displacement effects produced by electrons, protons, and neutrons in silicon is studied. Available data from the literature is employed. In particular the scope of the study is limited to the degradation of excess carrier lifetime and device electrical parameters directly related to it. The degree to which displacement effects may be correlated in order to predict semiconductor device response based on response data to another type of radiation is discussed. Useful ranges of the correlation factors (lifetime damage constant ratios) as a function of device majority carrier type, device resistivity, and injection level are presented. A significant dependence on injection level for the correlation factors is found.

Van Lint, V. A. J.↗
NASA NTRS1976

Gaseous emissions and toxic hazards associated with plastics in fire situations: A literature review

The hazards of plastics in fire situations, the gases emitted, the factors influencing the nature of these emissions, the characteristics of toxic gases, and the results of laboratory studies, are discussed. The literature pertaining to the pyrolysis and oxidation of plastics was reviewed. An effort was made to define the state of the art for determining the toxic gases emitted by plastics under fire conditions. Recommendations are made and research needs defined as a result of this review.

Junod, T. L.↗
NASA NTRS2014

Vaporization Studies of Olivine via Knudsen Effusion Mass Spectrometry

Olivine is the major mineral in the Earth's upper mantle occurring predominantly in igneous rocks and has been identified in meteorites, asteroids, the Moon and Mars. Among many other important applications in planetary and materials sciences, the thermodynamic properties of vapor species from olivine are crucial as input parameters in computational modelling of the atmospheres of hot, rocky exoplanets (lava planets). There are several weight loss studies of olivine vaporization in the literature and one Knudsen Effusion Mass Spectrometry (KEMS) study. In this study, we examine a forsterite-rich olivine (93% forsterite and 7% fayalite, Fo93Fa7) with KEMS to further understand its vaporization and thermodynamic properties.

Planetary atmospheres↗