Search NASA⌕ Search

SEARCH · Search NASA

Results for “Entropy Production”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

Microwave Imaging on Metal Objects

This final report for the project discusses the attempts to model, using different methods, microwave image reconstruction. Maximum Entropy Method was not successful. Attempts to use Singular Value Decomposition (SVD) got some good results after initial failure. SVD is based upon a theory of linear algebra, to the effect that any M X N Matrix A whose number of rows M is greater than or equal to its number of columns, N can be written as the product of an M X N column-orthogonal matrix U, an N X N diagonal Matrix, W, with m positive or zero elements (the singular values) and the transposition of an N X N orthogonal matrix V. In microwave imaging, the scattered fields can be expressed by the induced current distribution. The SVD method required more contiguous computer memory than was available. Work was also done on the Conjugate Gradient Method (CGM), which didn't work well when tried earlier. It was found that separation of the imaginary part and the real part during calculation may work. This work was considered incomplete as of the end of the grant period.

Tolliver, C. L.↗

Lightning and Other Influences On Tropical Tropospheric Ozone: Empirical Studies of Covariation

Tropical and subtropical tropospheric ozone are important radiatively active species, with particularly large effects in the upper third of the troposphere. Temporal variability of O3 has proved difficult to simulate day by day in process models. Thus, individual roles of lightning, biomass burning, and other pollution in providing precursor NO(x), radicals, and chain carriers (CO, hydrocarbons) remain unquantified by simulation, and it is theoretically reasonable that individual roles are magnified by a joint synergy. We use wavelet analysis and Burg-algorithm maximum entropy spectral analyses to describe time-scales and correlation of ozone with proxies for processes controlling its concentration. Our empirical studies link time variations apparent in several datasets: the SHADOZ (Southern Hemisphere Additional Ozonesondes) network stations (Nairobi, Fiji), and auxiliary series with power to explain ozone-determining processes, with some interpretation based on the TTO (Tropical Tropospheric Ozone) product derived from TOMS (the Total Ozone Mapping Spectrometer). The auxiliary series are The OTD/LIS(Optical Transient Detector/Lightning Imaging Sensor) measurements of the lightning NO(x) source, the OLR (Outgoing Longwave Radiation)measurement of high-topped clouds, and standard meteorological variables from the United States NCEP (National Centers for Environmental Prediction) and Data Assimilation Office analyses. Concentrating on equatorial ozone, we compare the statistical evidence on the variability of tropospheric ozone. Important variations occur on approximately two-week, two-month (Madden-Julian Oscillation) and annual scales, and relations with OLR suggest controls associated with continental clouds. Hence we are now using the Lightning Imaging Sensor data set to indicate NO(x) sources. We report initial results defining relative roles of the process mentioned affecting O3 using their covariance properties.

Chatfield, Robert B.↗

Crystallization behavior of anorthite

The growth rate of anorthite crystals from the melt is studied as a function of temperature with undercooling in the ranges 52-152 and 402-652 degrees C. The triclinic form is invariably observed as the crystallization product, growth is preferentially in the c direction, and the interface morphology is faceted. Significant growth rate anisotropy is indicated. The maximum growth rate of anorthite from the melt is higher than for anorthite-rich lunar compositions. Recent computer studies are combined with experimental data to estimate the heat of fusion of anorthite as 28000-45000 cal/mol; the corresponding range for entropy of fusion is (7.8-12)R (where R is the gas constant). The observations and kinetic data support Jackson's predictions concerning materials with large entropies of fusion and his suggestion that entropy of fusion is an important parameter for characterizing the crystal-liquid interface and the nature of the crystallization process.

Klein, L.↗

Environmental Effects on the Metallicities of Early-Type Galaxies

We have completed and published two papers based on research from this grant. Our first paper "SN IA Enrichment in Virgo Early-type Galaxies from ROSAT and ASCA Observations" was published in the Astrophysical Journal (vol 539,603) reported on the properties of nine X-ray bright elliptical galaxies in the Virgo cluster observed by ROSAT and ASCA. We measured iron abundance gradients as a function of radius in three galaxies. We found that the magnesium and silicon abundance gradients were in general flatter than those of iron. We suggest this is due to a metallicity dependence in the metal production rates of SN Ia's. We calculate SN Ia rates in the center of these galaxies that are comparable to those measured optically. Our second paper "ASCA Observations of Groups at Radii of Low Overdensity: Implications for Cosmic Preheating" also was published in the Astrophysical Journal (vol 578, 74). This paper reported on the ASCA spectroscopy of nine groups of galaxies. We found that the entropy profile in groups is driven by nongravitational heating processes, and could be explained by a short period of preheating by galactic winds.

Jones, Christine↗

Environmental Effects on the Metallicities of Early-Type Galaxies

In this multi-year project to investigate the metal enrichment of early-type galaxies, we have used ROSAT, ASCA and now Chandra observations to study samples of galaxies. We have published two papers and a third paper that incorporates Chandra archival observations is nearing completion. Below, we briefly describe our findings. Our first paper "SN IA Enrichment in Virgo Early-type Galaxies from ROSAT and ASCA Observations" was published in the Astrophysical Journal (vol 539, 603) reported on the properties of nine X-ray bright elliptical galaxies in the Virgo cluster observed by ROSAT and ASCA. We measured iron abundance gradients as a function of radius in three galaxies. We found that the magnesium and silicon abundance gradients were in general flatter than those of iron. We suggest this is due to a metallicity dependence in the metal production rates of SN Ia's. We calculate SN Ia rates in the center of these galaxies that are comparable to those measured optically. Our second paper "ASCA Observations of Groups at Radii of Low Overdensity: Implications for Cosmic Preheating" also was published in the Astrophysical Journal (vol 578, 74). This paper reported on the ASCA spectroscopy of nine groups of galaxies. We found that the entropy profile in groups is driven by nongravitational heating processes, and could be explained by a short period of preheating by galactic winds. The third paper (in preparation) uses a sample of about 200 galaxies from both ROSAT and Chandra observations. In this paper we characterize both the nuclear and the extended X-ray emission for this sample. We will use these observations to determine the "on-time" of the X-ray emitting AGN and the fraction of "fossil groups" as well as to investigate how large AGN outbursts can sweep the galaxy of its hot ISM, thus leading to changes in the ISM metal enrichment.

Oliversen, Ronald J.↗

Nonlinear shock acceleration. III - Finite wave velocity, wave pressure, and entropy generation via wave damping

The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity (V sub ph) of the scattering waves through the background fluid, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to 1/E sq are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of V sub ph, so that earlier results concerning its value remain valid for finite V sub ph. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, approximately greater than 4 and less than 6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.

Eichler, D.↗

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗

The delayed-detonation model of a type Ia supernovae. 1: The deflagration phase

The nature of the 'delayed detonation' mechanism of Khokhlov for the explosion of Type Ia supernovae is investigated by using two-dimensional numerical hydrodynamics simulations. A new algorithm is used to treat the deflagration front. Assuming that it propagates locally at the laminar flame speed, the deflagration is insufficient to unbind the star. Expansion shuts of the flame; much of this small production of iron group nuclei occurs at lower densities, which reduces the electron-capture problem. The burning front does become wrinkled, but the wavelength of the instability is much larger than the computational grid size and is resolved; this is consistent with previous analysis. Because the degenerate star has an adiabatic exponent only slightly above 4/3, the energy released by deflagration drives a pulsation of large amplitude. During the first expansion phase, adiabatic cooling shuts off the burning, and a Rayleigh-Taylor instability then gives mixing of high-entropy ashes with low-entropy fuel. During the first contraction phase, compressional heating reignites the material. This paper deals with the deflagration phase, from the onset of burning, through expansion and quenching of the flame, to the first contraction.

Arnett, David↗

The Application of Nonstandard Analysis to the Study of Inviscid Shock Wave Jump Conditions

The use of conservation laws in nonconservative form for deriving shock jump conditions by Schwartz distribution theory leads to ambiguous products of generalized functions. Nonstandard analysis is used to define a class of Heaviside functions where the jump from zero to one occurs on an infinitesimal interval. These Heaviside functions differ by their microstructure near x = 0, i.e., by the nature of the rise within the infinitesimal interval it is shown that the conservation laws in nonconservative form can relate the different Heaviside functions used to define jumps in different flow parameters. There are no mathematical or logical ambiguities in the derivation of the jump conditions. An important result is that the microstructure of the Heaviside function of the jump in entropy has a positive peak greater than one within the infinitesimal interval where the jump occurs. This phenomena is known from more sophisticated studies of the structure of shock waves using viscous fluid assumption. However, the present analysis is simpler and more direct.

Farassat, F.↗

Isentropic Compression of Multicomponent Mixtures of Fuels and Inert Gases

In selected aerospace applications of the fuels hydrazine and monomethythydrazine, there occur conditions which can result in the isentropic compression of a multicomponent mixture of fuel and inert gas. One such example is when a driver gas such as helium comes out of solution and mixes with the fuel vapor, which is being compressed. A second example is when product gas from an energetic device mixes with the fuel vapor which is being compressed. Thermodynamic analysis has shown that under isentropic compression, the fuels hydrazine and monomethylhydrazine must be treated as real fluids using appropriate equations of state. The appropriate equations of state are the Peng-Robinson equation of state for hydrazine and the Redlich-Kwong-Soave equation of state for monomethylhydrazine. The addition of an inert gas of variable quantity and input temperature and pressure to the fuel compounds the problem for safety design or analysis. This work provides the appropriate thermodynamic analysis of isentropic compression of the two examples cited. In addition to an entropy balance describing the change of state, an enthalpy balance is required. The presence of multicomponents in the system requires that appropriate mixing rules are identified and applied to the analysis. This analysis is not currently available.

Barragan, Michelle↗

GRX-810: NASA High Temperature Alloy Development for Additive Manufacturing

High-entropy alloys, and by extension, medium entropy alloys are an exciting new class of materials due to their impressive mechanical properties, especially at cryogenic and elevated temperatures. In this study, a novel oxide dispersion strengthened (ODS) NiCoCr-based alloy is presented which exhibits exceptional high temperature properties compared to conventional wrought superalloys. This new ODS alloy, GRX-810, leverages additive manufacturing to disperse nanoscale Y2O3 particles throughout the microstructure without the use of resource intensive processing steps, such as mechanical alloying. Microstructural and mechanical characterization confirms the successful incorporation and dispersion of nano-scale oxides throughout the build volume. As a result, this recently discovered processing route presents a new alloy design and production path that is synergistic between additive manufacturing and dispersion strengthening, possibly enabling a new generation of high-performance alloys.

Tim Smith↗

Excitation of solar p-modes

We investigate the rates at which energy is supplied to individual p-modes as a function of their frequencies nu and angular degrees l. The observationally determined rates are compared with those calculated on the hypothesis that the modes are stochastically excited by turbulent convection. The observationally determined excitation rate is assumed to be equal to the product of the mode's energy E and its (radian) line width Gamma. We obtain E from the mode's mean square surface velocity with the aid of its velocity eigenfuction. We assume that Gamma measures the mode's energy decay rate, even though quasi-elastic scattering may dominate true absorption. At fixed l, E(Gamma) arises as nu(exp 7) at low nu, reaches a peak at nu approximately equal 3.5 mHz, and then declines as nu(exp 4.4) at higher nu . At fixed nu, E(Gamma) exhibits a slow decline with increasing l. To calculate energy input rates, P(sub alpha), we rely on the mixing-length model of turbulent convection. We find entropy fluctuations to be about an order of magnitude more effective than the Reynolds stress in exciting p-modes . The calculated P(sub alpha) mimic the nu(exp 7) dependence of E(Gamma) at low nu and the nu(exp -4.4) dependence at high nu. The break of 11.4 powers in the nu-dependence of E(Gamma) across its peak is attributed to a combination of (1) the reflection of high-frequency acoustic waves just below the photosphere where the scale height drops precipitously and (2) the absence of energy-bearing eddies with short enough correlation times to excite high-frequency modes. Two parameters associated with the eddy correlation time are required to match the location and shape of the break. The appropriate values of these parameters, while not unnatural, are poorly constrained by theory. The calculated P(sub alpha) can also be made to fit the magnitude of E(Gamma) with a reasonable value for the eddy aspect ratio. Our resutls suggest a possible explanation for the decline of mode energy with increasing l at fixed nu. Entropy fluctuations couple to changes in volume associated with the oscillation mode. These decrease with decreasing n at fixed nu, becoming almost zero for the f-mode.

Goldreich, Peter↗

Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

Kiely, Aaron↗

Noise produced by fluid inhomogeneities

In an actual engine system, one mechanism for production of hot spots is the burning of various fluid elements at various different mixture ratios. Variable mixture ratio means variable temperature, and this is the effect that has been studied insofar as a noise source is concerned. However, variable mixture ratio also implies variable molecular weight and heat capacity. The paper investigates whether either of these last two variations may be responsible for a significant noise source. The analysis is made within the context of one-dimensional unsteady flow as in the work of Candel (1972). A mixture of thermally perfect gases is assumed as the working fluid, and the fluid composition consists of species 1 and a small and variable mole fraction of species 2 which has different molecular weight and specific heats as compared with species 1. In the absence of changes in the ratio of specific heat (gamma), the entropy variations due to temperature and molecular weight variations are equivalent as a sound source. The portion of sound called 'gamma prime' noise is discussed.

Strahle, W. C.↗

Maximum entropy modeling to identify physical drivers of shallow snowpack heterogeneity using unpiloted aerial system (UAS) lidar

Understanding the spatial variability of the snowpack is valuable for hydrologists and ecologists seeking to predict hydrological processes in a cold region. Snow distribution is a function of interactions among static variables, such as terrain, vegetation, and soil properties, and dynamic meteorological variables, such as solar radiation, wind speed and direction, and soil moisture. However, identifying the dominant physical drivers responsible for spatial patterns of the snowpack, particularly for ephemeral, shallow snowpacks, has been challenging due to the lack of the high-resolution snowpack and physical variables with high vertical accuracy as well as inherent limitations in traditional approaches. This study uses an Unpiloted Aerial System (UAS) lidar-based snow depth and static variables (1-m spatial resolution) to analyze field-scale spatial structures of snow depth and apply the Maximum Entropy (MaxEnt) model to identify primary controls over open terrain and forests at the University of New Hampshire Thompson Farm Research Observatory, New Hampshire, United States. We found that, among nine topographic and soil variables, plant functional type and terrain roughness contribute up to 80% and 76% of relative importance in the MaxEnt framework to predict locations of deeper or shallower snowpacks, respectively, across a mixed temperate forested and field landscape. Soil variables, such as organic matter and saturated hydraulic conductivity, were also important controls (up to 70% and 81%) on snow depth spatial variations for both open and forested landscapes suggesting spatial variations in soil variables under snow can control thermal transfer among soil, snowpack, and surface-atmosphere. This work contributes to improving land surface and snow models by informing parameterization of the sub-grid scale snow depths, down-scaling remotely sensed snow products, and understanding field scale snow states.

Eunsang Cho↗

Bryce Canyon Water Resources: Monitoring Vegetation Health and Water Availability in Bryce Canyon National Park for Drought Stress Mitigation Planning

Bryce Canyon National Park is home to groundwater-dependent ecosystems (GDEs) that are threatened by a multidecadal drought and increased groundwater extraction due to a spike in tourism. These ecosystems contain unique species that are only found in areas where near-surface groundwater is present, such as aspen groves and fens. These species contribute to the high biodiversity found in Bryce Canyon, which boosts an ecosystem’s productivity and the services it provides to the park. Unfortunately, many of these GDEs are too small to identify with traditional Earth observation platforms and are difficult to physically reach for monitoring purposes. This project partnered with the National Park Service to identify springs and seeps as a proxy for GDEs within Bryce Canyon from 2013–2022. Furthermore, this project tested the feasibility of various methods to detect and monitor springs and seeps and therefore facilitate the partner’s efforts to conserve these ecologically valuable GDEs in Bryce Canyon. The team mapped groundwater discharge with high resolution National Agriculture Imagery Program (NAIP) and assessed park vegetation trends with Landsat 8 Operational Land Imager (OLI) and PlanetScope imagery. In-situ precipitation data and the Western Land Data Assimilation System (WLDAS) were used to produce time series of climatic variables. Seeps and spring locations were predicted using random forest classification and maximum entropy machine learning models.

Groundwater dependent ecosystems↗

Control of Combustion-Instabilities Through Various Passive Devices

It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.

Frendi, Kader↗

Stability of Pseudobrookite-Type Titanium Oxides

Orthorhombic, (Bbmm), (Al, Fe, Cr, Ti)(sub 2) TiO5-(Mg, Fe)Ti2O5 solid solutions (pseudobrookites, s.l.) are found either as an oxidation product of ilmenite and/or spinel or a primary crystallizing phase in igneous and metamorphic rocks on Earth (e.g., basalt flows, crustal and mantle xenoliths, hornfels), and basaltic rocks on the Moon. Moreover, orthorhombic oxides are often part of the crystalline matrix in glass/ceramics with useful applications, and play a major role in the industrial production of TiO2. To fully exploit the potential of these compounds as petrogenetic indicators and/or useful materials we need to quantitatively understand the factors controlling their properties and stability, and thus, to extrapolate beyond the calibrating experiments. For that purpose, we need to combine thermochemistry, phase equilibrium, and in situ P-V-T-cation disorder experimental data that presently either are incomplete or lacking. Perhaps, the most complete data set is that for MgTi2O5 (karrooite) which allows the calibration of models for the Gibbs free energy of the MgTi2O5 as a function of pressure, temperature, and the Mg2+-Ti4+ distribution between the two nonequivalent octahedral sites. Consequently, the effect of cation disorder on MgTi2O5 stability, and the phase relations among MgTi2O5, other titanium oxides, and silicate minerals can be examined. Calculated phase relations in the Mg-Ti-Si-O system and phase equilibrium experiments in Fe-bearing compositions suggest that pseudobrookite-type oxides may be a more common in rocks than previously realized. However, homogeneous and heterogeneous equilibria, and crystallization paths likely affect their stability. For example, isobaric increases in temperature favor disordering and thus entropy-stabilization, in contrast, isothermal increases in pressure have the opposite effect. Although, currently, the potential effect of composition to cation disorder cannot be fully explored, it appears that enrichment in trivalent cations probably enhances entropy-stabilization and thus may increase the stability of (Al, Fe, Cr, Ti)-rich pseudobrookites relative to that of (Mg, Fe)-rich ones. In addition, high-temperature, nearly isothermal, decompression paths of olivine+orthopyroxene+oxide assemblages may favor pseudobrookites (s.l.) over rutile and/or ilmenite, in contrast, cooling at low pressures seems to favor ilmenite and/or rutile. In the case of crustal and mantle xenoliths, the presence or absence of orthorhombic oxides is probably controlled by reactions with olivine, orthopyroxene, ilmenite, and rutile. In oceanic mantle xenoliths such reactions may also involve a TiO2-enriched but not SiO2-enriched melt/fluid, because pseudobrookites (s.l.) would react with the SiO2-enriched melt/fluid to form orthopyroxene and rutile. Parenthetically, experiments and model calculations in the Mg-Ti-Si-O system suggest that low degree partial melting of low-TiO2 bulk compositions may produce Ti-enriched liquids in equilibrium with olivine, orthopyroxen ad=nd MgTi2O5, rutile or ilmenite.

Xirouchakis, Dimistrios↗