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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Time-resolved spectroscopy of the Mercury 6 3P1 state

The time-resolved fluorescence was observed from the Hg 6 3P1 state under the influence of the earth's magnetic field and with applied fields of up to 14 G. Modulation of the fluorescence decay signal was observed as a function of both time and space and can be interpreted in terms of a classical precession of the excited atom about the magnetic field or as quantum beats resulting from interference between coherently populated Zeeman sublevels. This modulation was studied for each of the five resolvable components of the hyperfine structure separately. The fluorescence from the even isotopes was determined to be almost completely modulated while the fluorescence from the odd isotopes was only partially modulated. The frequency of modulation of the fluorescence from the mercury-202 isotope was observed as a function of the applied magnetic field and a value for the Lande factor of 1.46 + or - 0.03 was obtained. This is within experimental error of the accepted value of 1.486. In addition, the frequency of modulation as a function of applied magnetic field was determined for each of the three resolvable components with more than one contributing isotopic hyperfine line. An investigation of the effect of radiation trapping on the degree modulation was also made.

Halstead, J. A.↗
NASA NTRS2004

Estimating Basic Preliminary Design Performances of Aerospace Vehicles

Aerodynamics and Performance Estimation Toolset is a collection of four software programs for rapidly estimating the preliminary design performance of aerospace vehicles represented by doing simplified calculations based on ballistic trajectories, the ideal rocket equation, and supersonic wedges through standard atmosphere. The program consists of a set of Microsoft Excel worksheet subprograms. The input and output data are presented in a user-friendly format, and calculations are performed rapidly enough that the user can iterate among different trajectories and/or shapes to perform "what-if" studies. Estimates that can be computed by these programs include: 1. Ballistic trajectories as a function of departure angles, initial velocities, initial positions, and target altitudes; assuming point masses and no atmosphere. The program plots the trajectory in two-dimensions and outputs the position, pitch, and velocity along the trajectory. 2. The "Rocket Equation" program calculates and plots the trade space for a vehicle s propellant mass fraction over a range of specific impulse and mission velocity values, propellant mass fractions as functions of specific impulses and velocities. 3. "Standard Atmosphere" will estimate the temperature, speed of sound, pressure, and air density as a function of altitude in a standard atmosphere, properties of a standard atmosphere as functions of altitude. 4. "Supersonic Wedges" will calculate the free-stream, normal-shock, oblique-shock, and isentropic flow properties for a wedge-shaped body flying supersonically through a standard atmosphere. It will also calculate the maximum angle for which a shock remains attached, and the minimum Mach number for which a shock becomes attached, all as functions of the wedge angle, altitude, and Mach number.

Luz, Paul L.↗
DOE OSTI2023

Structural and thermodynamic effects of hydration in Na-zeolite A (LTA) from low-temperature heat capacity

Zeolite A (Linde Type A; LTA) is an industrially important porous mineral that has recently been shown to exhibit framework flexibility upon changes in hydration level. Here, to investigate the flexibility transition from a thermodynamic perspective, we have performed heat capacity measurements on sodium zeolite A at seven incremental hydration levels ranging from zero to equilibrium with ambient air. Excess low-frequency vibrations beyond the predictions of the Debye model are found in all samples, and the frequency of these vibrations increases as a function of hydration level. This suggests that an increase in hydration causes a decrease in at least one type of framework flexibility for sodium zeolite A. In addition, a subtle excess heat capacity contribution from 150 to 280 K is observed only for low and intermediate hydration levels, which may arise from a transformation tied to framework flexibility previously observed in zeolite A via gas absorption calorimetry. Values of the standard thermodynamic functions C p,m °, Δ 0 T S m °, Δ 0 T H m °, and Φ m ° are also reported.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

The Mass Function of GX 339–4 from Spectroscopic Observations of Its Donor Star

We obtained 16 VLT/X-shooter observations of GX 339−4 in quiescence during the period 2016 May–September and detected absorption lines from the donor star in its NIR spectrum. This allows us to measure the radial velocity curve and projected rotational velocity of the donor for the first time. We confirm the 1.76 day orbital period and we find that K {sub 2} = 219 ± 3 km s{sup −1}, γ = 26 ± 2 km s{sup −1}, and vsin i = 64 ± 8 km s{sup −1}. From these values we compute a mass function f(M) = 1.91 ± 0.08 M{sub ⊙}, a factor ∼3 lower than previously reported, and a mass ratio q = 0.18 ± 0.05. We confirm the donor is a K-type star and estimate that it contributes ∼4%--50% of the light in the J- and H-bands. We constrain the binary inclination to 37° < i < 78° and the black hole (BH) mass to 2.3 M{sub ⊙} < M{sub BH} < 9.5 M{sub ⊙}. GX 339−4 may therefore be the first BH to fall in the “mass-gap” of 2–5 M {sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

The effect of self-interaction error on electrostatic dipoles calculated using density functional theory

Spurious electron self-interaction in density functional approximations (DFAs) can lead to inaccurate predictions of charge transfer in heteronuclear molecules that manifest as errors in calculated electrostatic dipoles. Here we show the magnitude of these errors on dipoles computed for a diverse set of 47 molecules taken from the recent benchmark study of Hait and Head-Gordon. We compare results of Perdew-Wang local spin density approximation (PW92), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriatedly normed (SCAN) meta-GGA dipole calculations, along with those of their respective self-interaction-corrected (SIC) counterparts, to reference values from accurate wave function-based methods. The SIC calculations were carried out using the Fermi-Löwdin orbital (FLO-SIC) approach. We find that correcting for self-interaction generally increases the degree of charge transfer, thereby increasing the size of calculated dipole moments. The FLO-SIC-PW92 and FLO-SIC-PBE dipoles are in better agreement with reference values than their uncorrected DFA counterparts, particularly for strongly ionic molecules where significant improvement is seen. Applying FLO-SIC to SCAN does not improve dipole values overall. In addition, we show that removing self-interaction improves the description of the dipole for stretched-bond geometries and recovers the physically correct separated atom limit of zero dipole. Finally, we find that the best agreement between the FLO-SIC-DFA and reference dipoles occurs when the molecular geometries are optimized using the FLO-SIC-DFA.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1984

A note on the variational method of Stokes and DeMarcus for radiative transfer in planetary atmospheres

A generalization of the variational principle of Stokes and DeMarcus (1971) by the construction of two bifunctionals is proposed. The equation of radiative transfer is obtained by imposing the stationary condition on such functionals, and the reflectivity and transmissivity at arbitrary angle are given by their extremum values. Further simplification is possible when trail functions are used that are linear in the variational parameters, in which case the source function derived from the method of Stokes and DeMarcus can give the reflectivity at arbitrary emergent angle to second order. The usefulness and limitations of these variational priinciples are explored with extensive numerical results.

Chow, K. S. K.↗
NASA NTRS1989

Robust computer-aided synthesis and optimization of linear multivariable control systems with varying plant dynamics via AUTOCON

AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.

Lefkowitz, C. P.↗
NASA NTRS1994

Global shortwave energy budget at the earth's surface from ERBE observations

A method is proposed to compute the net solar (shortwave) irradiance at the earth's surface from Earth Radiation Budget Experiment (ERBE) data in the S4 format. The S4 data are monthly averaged broadband planetary albedo collected at selected times during the day. Net surface shortwave irradiance is obtained from the shortwave irradiance incident at the top of the atmosphere (known) by subtracting both the shortwave energy flux reflected by the earth-atmosphere system (measured) and the energy flux absorbed by the atmosphere (modeled). Precalculated atmospheric- and surface-dependent functions that characterize scattering and absorption in the atmosphere are used, which makes the method easily applicable and computationally efficient. Four surface types are distinguished, namely, ocean, vegetation, desert, and snow/ice. Over the tropical Pacific Ocean, the estimates based on ERBE data compare well with those obtained from International Satellite Cloud Climatology Project (ISCCP) B3 data. For the 9 months analyzed the linear correlation coefficient and the standard difference between the two datasets are 0.95 and 14 W/sq m (about 6% of the average shortwave irradiance), respectively, and the bias is 15 W/sq m (higher ERBE values). The bias, a strong function of ISCCP satellite viewing zenith angle, is mostly in the ISCCP-based estimates. Over snow/ice, vegetation, and desert no comparison is made with other satellite-based estimates, but theoretical calculations using the discrete ordinate method suggest that over highly reflective surfaces (snow/ice, desert) the model, which accounts crudely for multiple reflection between the surface and clouds, may substantially overestimate the absorbed solar energy flux at the surface, especially when clouds are optically thick. The monthly surface shortwave irradiance fields produced for 1986 exhibit the main features characteristic of the earth's climate. As found in other studies, our values are generally higher than Esbensen and Kushnir's by as much as 80 W/sq m in the tropical oceans. A cloud parameter, defined as the difference between clear-sky and actual irradiances normalized to top-of-atmosphere clear-sky irradiance, is also examined. This parameter, minimally affected by sun zenith angle, is higher in the midlatitude regions of storm tracks than in the intertropical convergence zone (ITCZ), suggesting that, on average, the higher cloud coverage in midlatitudes is more effective at reducing surface shortwave irradiance than opaque, convective, yet sparser clouds in the ITCZ. Surface albedo estimates are realistic, generally not exceeding 0.06 in the ocean, as high as 0.9 in polar regions, and reaching 0.5 in the Sahara and Arabian deserts.

Breon, Francois-Marie↗
DOE OSTI2021

In-depth understanding of molecular mechanisms of aldehyde toxicity to engineer robust Saccharomyces cerevisiae

Aldehydes are ubiquitous electrophilic compounds that ferment microorganisms including Saccharomyces cerevisiae encounter during the fermentation processes to produce food, fuels, chemicals, and pharmaceuticals. Aldehydes pose severe toxicity to the growth and metabolism of the S. cerevisiae through a variety of toxic molecular mechanisms, predominantly via damaging macromolecules and hampering the production of targeted compounds. Compounds with aldehyde functional groups are far more toxic to S. cerevisiae than all other functional classes, and toxic potency depends on physicochemical characteristics of aldehydes. The yeast synthetic biology community established a design–build–test–learn framework to develop S. cerevisiae cell factories to valorize the sustainable and renewable biomass, including the lignin-derived substrates. However, thermochemically pretreated biomass-derived substrate streams contain diverse aldehydes (e.g., glycolaldehyde and furfural), and biological conversions routes of lignocellulosic compounds consist of toxic aldehyde intermediates (e.g., formaldehyde and methylglyoxal), and some of the high-value targeted products have aldehyde functional group (e.g., vanillin and benzaldehyde). Numerous studies comprehensively characterized both single and additive effects of aldehyde toxicity via systems biology investigations, and novel molecular approaches have been discovered to overcome the aldehyde toxicity. Based on those novel approaches, researchers successfully developed synthetic yeast cell factories to convert lignocellulosic substrates to valuable products, including aldehyde compounds. Here, we highlight the salient relationship of physicochemical charac- teristics and molecular toxicity of aldehydes, the molecular detoxification and macromolecules protection mechanisms of aldehydes, and the advances of engineering robust S. cerevisiae against complex mixtures of aldehyde inhibitors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h -1 Mpc) 3 Horizon hydrodynamic simulation to a (1 h -1 Gpc) 3 N -body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving n q ≈ 10 -5 h 3 Mpc -3 placed either in massive haloes or randomly. On scales of 10–30 h -1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ 123 /(ξ 12 ξ 13 + ξ 12 ξ 23 + ξ 13 ξ 23 ) ≈ -4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h -1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q . For λ = 100 or 50 h -1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ -3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1–2.6. At r = 10 and 20 h -1 Mpc, we predict a signal-to-noise ratio (SNR) of ~9 and ~7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ~37 and ~25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h -1 Mpc the predicted SNR is lower by a factor of ~3–5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.

Astronomy & Astrophysics↗
DOE OSTI2017

BOSS Great Wall: morphology, luminosity, and mass

Galaxy superclusters are the largest systems in the Universe that can give us information about the formation and evolution of the cosmic web. Here, we study the morphology of the superclusters from the BOSS Great Wall (BGW), a recently discovered very rich supercluster complex at the redshift z = 0:47. Methods. We have employed the Minkowski functionals to quantify supercluster morphology. We calculate supercluster luminosities and masses using two methods. Firstly, we used data about the luminosities and stellar masses of high stellar mass galaxies with log( M * /h -1 M ⊙ ) ≥ 11.3. Secondly, we applied a scaling relation that combines morphological and physical parameters of superclusters to obtain supercluster luminosities, and obtained supercluster masses using the mass-to-light ratios found for local rich superclusters. The BGW superclusters are very elongated systems, with shape parameter values of less than 0.2. This value is lower than that found for the most elongated local superclusters. The values of the fourth Minkowski functional V 3 for the richer BGW superclusters ( V 3 = 7 and 10) show that they have a complicated and rich inner structure. We identify two Planck SZ clusters in the BGW superclusters, one in the richest BGW supercluster, and another in one of the poor BGW superclusters. The luminosities of the BGW superclusters are in the range of 1-8 x 10 13 h -2 L ⊙ , and masses in the range of 0.4-2.1 x 10 16 h -1 M ⊙ . Supercluster luminosities and masses obtained with two methods agree well. The BGW is a complex of massive, luminous and large superclusters with very elongated shape. The search and detailed study, including the morphology analysis of the richest superclusters and their complexes from observations and simulations can help us to understand formation and evolution of the cosmic web.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1981

The ultraviolet properties of dust in the Orion Nebula

The continuum in the Orion Nebula was observed with the IUE at 16 positions varying from 30 arcsec to 5 arcmin in angular separation from the central star Theta(1) Orionis C. The atomic continuum was estimated from the H-beta brightnesses. The remaining scattered starlight was analyzed by multiple-scattering models in which the main parameters are: (1) the albedo of the dust; (2) the scattering phase function parameter, the averaged cosine of the angle of scattering; and (3) the density of dust grains at small distances from the star. It is found that (a) dust must be depleted near the star; (b) the albedo is fairly well determined and is constant across the 2200 A extinction feature; and (c) grains are quite forward-throwing at 1300 A, as they have been found at 4600 A earlier. The scattering is more isotropic at 2400 A. However, the absolute value of the scattering phase function parameters at all wavelengths is quite uncertain because it depends sensitively upon the density of grains close to the star.

Mathis, J. S.↗
DOE OSTI2017

Bonding, elastic and vibrational properties in low and high pressure synthesized diamond-like BCx phases

Recent studies demonstrate that low pressure chemical vapor deposition at 950 K leads to the synthesis of diamond-like boron carbides with high concentrations of boron (0.66 < x < 4) in which the sp 2 fraction depends on the boron concentration [1]. This indicates that the graphitic BC3 (g-BC3) phases obtained by chemical vapor deposition materials are mixtures of diamond-like and graphitic BCx phases. This finding allows us to revise the interpretation of the x-ray diffraction (XRD) patterns of the g-BC3 phases discussed previously [2, 3]. To support the new interpretation, we conducted a laser heating experiment of the g-BC3 phase. We found that after laser heating at 1100 K and 25 GPa in a diamond anvil cell (DAC) almost all graphitic layers of the g-BC3 transform into a cubic structure. The XRD pattern of the cubic BC3 phase (c-BC3) can be indexed with a cubic unit cell a = 3.619 (0.165) Å. Measurements of the equation of state of the g-BC3 phase demonstrated that boron atoms were incorporated into the graphitic B-C network. The linear compressibility along the c axis can be characterized by the value of the linear modulus Bc = 29.2 ± 1.8 GPa. Linear fitting of the experimental data for the a/a o parameter as a function of pressure gives us the value of the linear elastic modulus along the a axes: Ba = 800 ± 75 GPa.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

Solar wind variations and geomagnetic storms - A study of individual storms based on high time resolution ISEE 3 data

Two independent methods are employed to determine the relationship between the parameter epsilon and total energy dissipation rate of the magnetosphere U sub T by selecting disturbed periods from the same data d set used by Baker et al. (1983). Specifically, four storms are examined in detail, since the accuracy of estimating U sub T is significantly improved during disturbed periods. The first method assumes that U sub T = M sub A exp.2- alpha(epsilon) where M sub A is the Alfven Mach number and alpha varies with time. The second method considers a linear, time-invariant dynamic system with epsilon as input and U sub T as output. This means that U sub T = W(asterisk)epsilon where asterisk is the convolution and W is a transfer function characteristic of the system. It is found that alpha values fluctuate mainly between 0 and -0.25. The transfer function analysis indicates that W often resembles a delta-function or a narrow rectangular impulse. Both results give the same implication (namely that U sub T is approximately equal to epsilon) and thus are consistent with the view that the magnetosphere is primarily a directly driven system during disturbed periods.

Akasofu, S.-I.↗
NASA NTRS1992

A genetic algorithms approach for altering the membership functions in fuzzy logic controllers

Through previous work, a fuzzy control system was developed to perform translational and rotational control of a space vehicle. This problem was then re-examined to determine the effectiveness of genetic algorithms on fine tuning the controller. This paper explains the problems associated with the design of this fuzzy controller and offers a technique for tuning fuzzy logic controllers. A fuzzy logic controller is a rule-based system that uses fuzzy linguistic variables to model human rule-of-thumb approaches to control actions within a given system. This 'fuzzy expert system' features rules that direct the decision process and membership functions that convert the linguistic variables into the precise numeric values used for system control. Defining the fuzzy membership functions is the most time consuming aspect of the controller design. One single change in the membership functions could significantly alter the performance of the controller. This membership function definition can be accomplished by using a trial and error technique to alter the membership functions creating a highly tuned controller. This approach can be time consuming and requires a great deal of knowledge from human experts. In order to shorten development time, an iterative procedure for altering the membership functions to create a tuned set that used a minimal amount of fuel for velocity vector approach and station-keep maneuvers was developed. Genetic algorithms, search techniques used for optimization, were utilized to solve this problem.

Shehadeh, Hana↗
NASA NTRS2015

Phase-Based Adaptive Estimation of Magnitude-Squared Coherence Between Turbofan Internal Sensors and Far-Field Microphone Signals

A cross-power spectrum phase based adaptive technique is discussed which iteratively determines the time delay between two digitized signals that are coherent. The adaptive delay algorithm belongs to a class of algorithms that identifies a minimum of a pattern matching function. The algorithm uses a gradient technique to find the value of the adaptive delay that minimizes a cost function based in part on the slope of a linear function that fits the measured cross power spectrum phase and in part on the standard error of the curve fit. This procedure is applied to data from a Honeywell TECH977 static-engine test. Data was obtained using a combustor probe, two turbine exit probes, and far-field microphones. Signals from this instrumentation are used estimate the post-combustion residence time in the combustor. Comparison with previous studies of the post-combustion residence time validates this approach. In addition, the procedure removes the bias due to misalignment of signals in the calculation of coherence which is a first step in applying array processing methods to the magnitude squared coherence data. The procedure also provides an estimate of the cross-spectrum phase-offset.

Combustion↗
DOE OSTI2022

The low-temperature heat capacity and thermodynamic properties of greigite (Fe 3 S 4 )

Heat capacity measurements provide important insights into the energetic, thermodynamic, and magnetic properties of materials. Herein we report the heat capacity of greigite (Fe 3 S 4 ) from 1.8 to 300 K. Greigite is a magnetic spinel mineral and through a ferromagnetic magnon term, C fsw = B fsw T 3/2 , ferrimagnetic ordering is observed in the low-temperature heat capacity. Using a set of theoretical fits of the experimental data, we calculate the thermodynamic functions, including the standard entropy ($Δ_{0}^{T}$S m °). Greigite is important in iron sulfide formation and reaction pathways in environmental, ore-forming, and technological settings and previous work has measured enthalpies $ΔH_{r}°$ of formation and decomposition to neighboring phases. In this work, the stability of greigite relative to the elements is demonstrated with a negative Gibbs energy ($ΔG_{r}°$) of formation and the stability relative to decomposition products of pyrrhotite (FeS 1.092 ) and pyrite (FeS 2 ) is demonstrated with a positive Gibbs energy ($ΔG_{r}°$) of decomposition. Values of the standard thermodynamic functions C p,m °, $Δ_{0}^{T}$S m °, $Δ_{0}^{T}$H m °, and Φ m ° are tabulated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Heat capacity and thermodynamic functions of transition metal ion (Cu 2+ , Fe 2+ , Mn 2+ ) exchanged, partially dehydrated zeolite $\mathrm{A}$ ($\mathrm{LTA}$)

Here we have measured the heat capacity from 1.8 to 300 K of partially dehydrated zeolite A (LTA), fully exchanged with Cu 2+ , Fe 2+ , and Mn 2+ ions. The samples have a broad excess heat capacity contribution centered around 4 K, which we attribute to local electric fields splitting the magnetic moments of the cations. The excess heat capacity is modelled using a sum of several Schottky anomalies. From these models, we conclude that the cations in the Cu 2+ zeolite reside in at least four distinct coordination environments, and that some of the coordination environments in all three zeolites are highly asymmetric. We also report theoretical fits of the heat capacity data, and values of the standard thermodynamic functions C P,m , Δ 0K T S m ° , Δ 0K T H m ° , and Φ m ° at smooth temperatures. The standard molar entropies at 298.15 K are 71.8 J·K -1 ·mol -1 for Cu-zeolite A (Cu 0.22 Al 0.49 Si 0.51 O 2 1.04 H 2 O), 71.1 J·K -1 ·mol -1 for Fe-zeolite A (Na 0.01 Fe 0.23 Al 0.50 Si 0.51 O 2 ∙0.77 H 2 O), and 66.0 J·K -1 ·mol -1 for Mn-zeolite A (Mn 0.26 Al 0.49 Si 0.50 O 2 ∙0.53 H 2 O).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗