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At least 811 records · Page 45

Delta Method Application for the Correlation of IR Detector Thermal Parasitic Loads with Statistically Accurate Results

The Linear Etalon Imaging Spectral Array (LEISA) is a cryogenic IR detector that is passively cooled below 110K. LEISA is part of the L’Ralph instrument, which is going on the Lucy mission, with planned flyby’s of the Trojan asteroids around 5.5 AU. One of the primary thermal challenges is to successfully quantify each significant parasitic heat flow value with statistical certainty.Simulation of flight-like thermal environments and correlation of thermal models is an important part of this challenge, which can be critical for thermally sensitive systems such as cryogenic detectors that are passively cooled. It is common practice during TVAC to achieve several thermal balance points and then to correlate several design variables in order to achieve the closest match to all balance points tested. This approach lends itself to high levels of uncertainty in the correlated values due to the cumulative effect of absolute temperature uncertainty and differences between the sensors used for the measurement. Accuracy can be improved with the use of more accurate sensors, by calibrating all sensors with respect to each other, and by using Zero-Q methodologies, all of which add cost and complexity to the test.The Delta Method uses the difference in temperature caused by the changes in the boundary conditions to calculate heat flows and/or thermal resistances across temperature differentials. This eliminates the problem of high uncertainties with absolute temperature measurements, and yields statistically accurate results down to the sensor resolution of 1mK at < 100K, by taking the sensor’s calibration errors out of the equation. During testing, this method relies on parametric variations around an initial balance point, by varying the boundary conditions of the different parasitic heat sources. The Delta Method, as well as its application on the LEISA thermal test, will be discussed in detail.

Daniel G. Bae↗

A Gaussian process autoregressive model capturing microstructure evolution paths in a Ni–Mo–Nb alloy

Additive manufacturing is increasingly being employed to produce components of complex geometries in structural alloys because of the expected energy savings associated with the near-net-shape capability and the ability to build in novel internal features that are not possible with many conventional manufacturing approaches. However, because of the extreme thermal conditions encountered, the non-equilibrium microstructures produced during powder bed-based additive manufacturing processes must be subjected to custom post-heat treatment processes to recover the target mechanical properties. Phase-field models and simulation techniques have matured to a state where the microstructure evolution paths, and the morphologies of the resulting precipitate phases can be predicted reasonably accurately, considering alloy-specific thermodynamic and kinetic aspects of the nucleation and growth processes. However, phase-field simulations are computationally intensive, which precludes the ability to apply the simulations directly to the length scale of the entire component. Therefore, it is highly desirable to develop low-computational-cost surrogate models that effectively capture the physics at the microstructural length scale, while facilitating the design of optimized processing conditions resulting in location-specific targeted microstructures at the component scale. The work presented here demonstrates the application of the materials knowledge system framework to develop a surrogate model that effectively captures the microstructural path during annealing of a Ni–Mo–Nb alloy containing different Mo and Nb compositions known to segregate during solidification under additive manufacturing conditions. Specifically, the surrogate model built in this work is based on a Gaussian process autoregressive model informed by statistical representation of simulated microstructures using two-point correlations and dimensionality reduction through principal component analysis. In conclusion, this surrogate model is shown to capture the bifurcation of the microstructural path during precipitation, which yields a microstructure dominated by the $\gamma^{\prime\prime}$ phase at high Nb concentrations and the $\delta$ phase at low Nb concentrations.

36 MATERIALS SCIENCE↗

Comparison of source-location algorithms for atmospheric samplers

Numerous algorithms have been developed to determine the source characteristics for an atmospheric release, e.g., (Bieringer et al., 2017). This study compares three models that have been applied to the data collected by the International Monitoring System operated by the Comprehensive Nuclear-Test-Ban Treaty Preparatory Commission to estimate source event parameters. Each model uses a different approach to estimate the parameters. A deterministic model uses a possible source region (PSR) approach (Ringbom et al., 2014) that is based on the correlation between predicted and measured sample values. An unnamed model developed at Pacific Northwest National Laboratory (herein called BAYEST) uses a Bayesian formulation (Eslinger et al., 2019; Eslinger et al., 2020; Eslinger and Schrom, 2016). The FREAR model uses a different Bayesian formulation (De Meutter and Hoffman, 2020; De Meutter et al., 2021; Pieter De Meutter, 2021). The performance of the three source-location models is evaluated with 100 synthetic release cases for the single xenon isotope, 133 Xe. The release cases resulted in detections in a fictitious network with 120 noble gas samplers. All three source-location models use the same sampling data. The two Bayesian models yield more accurate location estimates than the deterministic PSR model, with FREAR having slightly better location performance than BAYEST. Samplers with collection periods of 3, 6, 8, 12, and 24-h were used. Results from BAYEST show that location accuracy improves with each reduction in sample collection length. The BAYEST model is slightly better for estimating the start time of the release. The PSR model has about the same spread in start times as the FREAR model, but the PSR results have a better average start time. The Bayesian source-location algorithms give more accurate results than the PSR approach, and provide release magnitude estimates, while the base PSR model does not estimate the release magnitude. This investigation demonstrates that a reasonably dense sampling grid will sometimes yield poor location and time estimates regardless of the model. The poor estimates generally coincide with cases where there is a much larger distance between the release point and the first detecting sampler than the average sampler spacing.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Demonstration and technoeconomic analysis of dodecanol production from acetate using metabolically engineered Escherichia coli

In a circular bioeconomy, the one-way conversion of petroleum to chemicals and CO 2 is replaced with processes that reduce CO 2 to energy carriers and useful materials that are returned to CO 2 upon combustion. A circular bioeconomy that relies on photosynthesis to generate sugars as the chief energy carrier and precursor to chemical building blocks has yet to overcome many recalcitrant aspects of plant-based photosynthesis, namely, high feedstock costs, arable land scarcity, food competition, and fertilizer overuse. Acetate is a potential sustainable energy carrier because it can be produced from CO 2 either electrocatalytically or by acetogens via the Wood-Ljungdahl pathway. Here, in this work, we conducted a metabolic engineering study of Escherichia coli 's ability to convert acetate into dodecanol as a model oleochemical product. We performed techno-economic and life cycle analyses to determine break-even points with alternative fossil fuel-based strategies and identified critical process performance parameters for supporting an industrial acetate-based bioprocess. These analyses showed that oleochemical yield is the primary driver of minimum oleochemical selling price and carbon intensity. Therefore, to increase yield on acetate, we deleted the aceBAK operon, which facilitates funneling of acetate into biomass instead of product. We performed additional strain engineering to increase flux towards dodecanol and increase acetate uptake. Finally, we demonstrated increased yield in controlled bioreactors, improving from 13% of the maximum theoretical yield to 37%. Rigorous uncertainty analyses assuming a range of market conditions and future technological performances resulted in 88% and 37% of simulated scenarios having lower carbon intensities than fossil fuel-based routes and lower minimum selling prices than the market price.

Acetate↗

Fluctuations in the entropy of Hawking radiation

We use the gravitational path integral (GPI) to compute the fluctuations of the Hawking radiation entropy around the Page curve in a two-dimensional model introduced by Penington Before the Page time, we find that δ S = e − S / 2 , where S is the black hole entropy. This result agrees with the Haar-averaged entropy fluctuations in a bipartite system. After the Page time, we find that δ S ∼ e − S , up to a prefactor that depends logarithmically on the width of the microcanonical energy window. This is not symmetric under exchange of subsystem sizes and so does not agree with the Haar average for a subsystem of fixed Hilbert space dimension. The discrepancy can be attributed to the fact that the black hole Hilbert space dimension is not fixed by the state preparation: even in a microcanonical ensemble with a top-hat smearing function, the GPI yields an additive fluctuation in the number of black hole states. This result, and the fact that the Page curve computed by the GPI is smooth, all point towards an ensemble interpretation of the GPI. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Observation of the p η ' Cusp in the New Precise Beam Asymmetry Σ Data for γ p → p η

Data on the beam asymmetry Σ in the photoproduction of η mesons off protons are reported for tagged photon energies from 1130 to 1790 MeV (mass range from W = 1748 MeV to W = 2045 MeV). The data cover the full solid angle that allows for a precise moment analysis. For the first time, a strong cusp effect in a polarization observable has been observed that is an effect of a branch-point singularity at the pη' threshold [E γ = 1447 MeV (W = 1896 MeV)]. Here, the latest BnGa partial wave analysis includes the new beam asymmetry data and yields a strong indication for the N(1895)1/2 – nucleon resonance, demonstrating the importance of including all singularities for a correct determination of partial waves and resonance parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New theory on the reverberation of rooms

The inadequacy of the various theories which have been proposed for finding the reverberation time of rooms can be explained by an attempt to examine what might occur at a listening point when image sources of determined acoustic power are added to the actual source. The number and locations of the image sources are stipulated. The intensity of sound at the listening point can be calculated by means of approximations whose conditions for validity are given. This leads to the proposal of a new expression for the reverberation time, yielding results which fall between those obtained through use of the Eyring and Millington formulae; these results are made to depend on the shape of the room by means of a new definition of the mean free path.

Pujolle, J.↗

SAR - An instrument for planetary geodesy and navigation

Analysis to define an optimal data plan and to define achievable accuracy levels in determination of the physical parameters, global topography of the planet, and refined orbital element estimates of a spacecraft borne synthetic aperture radar (SAR) placed in a near polar circular orbit of 300 km altitude around the planet Venus is presented. It is shown that radar surface images can be used to improve knowledge of physical parameters of Venus, and the improvement in orbit accuracy can reduce navigational uncertainties derivable from conventional Doppler ratio tracking data, yielding a more precise history of the orbits for sensing the low order gravity field of the planet. Data plan strategies in terms of selection of ground points and their spatial distribution are related to achievable accuracy of the solution parameters, and the influence of spacecraft orbit errors on the solution accuracy was discussed.

Mohan, S. N.↗

Simultaneous elastic and photoelastic calibration of birefringent orthotropic model materials

Transmission photoelastic analysis of composite models has been shown in recent years to be a viable stress analysis method for composite structures. However, difficulties in the fabrication of the model materials require the development of efficient mechanical and optical calibration procedures. In this paper, the methods for measuring elastic and photoelastic constants of composites are briefly reviewed. Then a new method, utilizing a relatively small calibration specimen, is described. In this method, electrical resistance strain gauges are mounted at selected points of a half-plane model and photoelastic measurements and strain readings are simultaneously taken. The data are processed by a least-squares procedure to yield the elastic and photoelastic constants. Comparison of results obtained by the proposed method with the results from conventional tests shows good agreement.

Prabhakaran, R.↗

Slew maneuvers of Spacecraft Control Laboratory Experiment (SCOLE)

This is the final report on the dynamics and control of slew maneuvers of the Spacecraft Control Laboratory Experiment (SCOLE) test facility. The report documents the basic dynamical equation derivations for an arbitrary large angle slew maneuver as well as the basic decentralized slew maneuver control algorithm. The set of dynamical equations incorporate rigid body slew maneuver and three dimensional vibrations of the complete assembly comprising the rigid shuttle, the flexible beam, and the reflector with an offset mass. The analysis also includes kinematic nonlinearities of the entire assembly during the maneuver and the dynamics of the interactions between the rigid shuttle and the flexible appendage. The equations are simplified and evaluated numerically to include the first ten flexible modes to yield a model for designing control systems to perform slew maneuvers. The control problem incorporates the nonlinear dynamical equations and is expressed in terms of a two point boundary value problem.

Kakad, Yogendra P.↗

An upper limit to coronal X-rays from single, magnetic white dwarfs

Pointed ROSAT Position Sensitive Proportional Counter (PSPC) exposures of 9277 and 6992 sec, directed toward the nearby, single, cool, magnetic white dwarfs GR 290 and EG 250 yielded no counts significantly above the expected background rate. The corresponding flux limits (for an assumed source temperature of 1 keV) are 1.0 and 1.7 x 10(exp -14) erg/sq cm/s, within the 0.1-2.5 keV bandpass of the instrument (99% confidence limits). This is more than an order of magnitude below the tentative detection level (for GR 290) and limits (for four other similar stars) obtained from archival Einstein data in 1991. The corresponding limits on coronal electron density are comparable with those implied if cyclotron emission is not responsible for any of the features observed in the optical spectra of magnetic white dwarfs. X-ray data currently provide no evidence for the existence of coronae around these stars. A final long observation (25,000 sec of GD 356) is scheduled for later this year on ROSAT, along with coordinated Extreme Ultraviolet Explorer (EUVE) observations.

Cavallo, Rob↗

Model-Based Engineering Design for Trade Space Exploration throughout the Design Cycle

This paper presents ongoing work to standardize model-based system engineering as a complement to point design development in the conceptual design phase of deep space missions. It summarizes two first steps towards practical application of this capability within the framework of concurrent engineering design teams and their customers. The first step is standard generation of system sensitivities models as the output of concurrent engineering design sessions, representing the local trade space around a point design. A review of the chosen model development process, and the results of three case study examples, demonstrate that a simple update to the concurrent engineering design process can easily capture sensitivities to key requirements. It can serve as a valuable tool to analyze design drivers and uncover breakpoints in the design. The second step is development of rough-order- of-magnitude, broad-range-of-validity design models for rapid exploration of the trade space, before selection of a point design. At least one case study demonstrated the feasibility to generate such models in a concurrent engineering session. The experiment indicated that such a capability could yield valid system-level conclusions for a trade space composed of understood elements. Ongoing efforts are assessing the practicality of developing end-to-end system-level design models for use before even convening the first concurrent engineering session, starting with modeling an end-to-end Mars architecture.

models↗

A Theoretical Investigation of the Plausibility of Reactions Between Ammonia and Carbonyl Species (Formaldehyde, Acetaldehyde, and Acetone) in Interstellar Ice Analogs at Ultracold Temperatures

We have reexamined the reaction between formaldehyde and ammonia, which was previously studied by us and other workers in modestly sized cluster calculations. Larger model systems with up to 12H2O were employed, and reactions of two more carbonyl species, acetaldehyde and acetone, were also carried out. Calculations were performed at the B3LYP/6-31+G** level with bulk solvent effects treated with a polarizable continuum model; limited MP2/6-31+G** calculations were also performed. We found that while the barrier for the concerted proton relay mechanism described in previous work remains modest, it is still prohibitively high for the reaction to occur under the ultracold conditions that prevail in dense interstellar clouds. However, a new pathway emerged in more realistic clusters that involves at least one barrierless step for two of the carbonyl species considered here: ammonia reacts with formaldehyde and acetaldehyde to form a partial charge transfer species in small clusters (4H2O) and a protonated hydroxyamino intermediate species in large clusters (9H2O, 12H2O); modest barriers that decrease sharply with cluster size are found for the analogous processes for the acetone-NH3 reaction. Furthermore, if a second ammonia replaces one of the water molecules in calculations in the 9H2O clusters, deprotonation can occur to yield the same neutral hydroxyamino species that is formed via the original concerted proton relay mechanism. In at least one position, deprotonation is barrierless when zero-point energy is included. In addition to describing the structures and energetics of the reactions between formaldehyde, acetaldehyde, and acetone with ammonia, we report spectroscopic predictions of the observable vibrational features that are expected to be present in ice mixtures of different composition.

Chen, Lina↗

Stereo and IMU-Assisted Visual Odometry for Small Robots

This software performs two functions: (1) taking stereo image pairs as input, it computes stereo disparity maps from them by cross-correlation to achieve 3D (three-dimensional) perception; (2) taking a sequence of stereo image pairs as input, it tracks features in the image sequence to estimate the motion of the cameras between successive image pairs. A real-time stereo vision system with IMU (inertial measurement unit)-assisted visual odometry was implemented on a single 750 MHz/520 MHz OMAP3530 SoC (system on chip) from TI (Texas Instruments). Frame rates of 46 fps (frames per second) were achieved at QVGA (Quarter Video Graphics Array i.e. 320 240), or 8 fps at VGA (Video Graphics Array 640 480) resolutions, while simultaneously tracking up to 200 features, taking full advantage of the OMAP3530's integer DSP (digital signal processor) and floating point ARM processors. This is a substantial advancement over previous work as the stereo implementation produces 146 Mde/s (millions of disparities evaluated per second) in 2.5W, yielding a stereo energy efficiency of 58.8 Mde/J, which is 3.75 better than prior DSP stereo while providing more functionality.

Source record↗

Zoledronate Prevents Simulated Weightlessness-Induced Bone Loss in the Cancellous Compartment While Blunting the Efficacy of a Mechanical Loading Countermeasure

Astronauts using high-force resistance training while weightless show a high-turnover remodeling state within the skeletal system, with resorption and formation biomarkers being elevated. One countermeasure for the skeletal health of astronauts includes an antiresorptive of the bisphosphonate (BP) drug class. We asked, does the combination of an anti-resorptive and high-force exercise during weightlessness have negative effects on bone remodeling and strength? In this study, we developed an integrated model to mimic the mechanical strain of exercise via cyclical loading (CL) in mice treated with the BP Zoledronate (ZOL) combined with hind limb unloading (HU) to simulate weightlessness. We hypothesized that ZOL prevents structural degradation from simulated weightlessness and that CL and ZOL interact to render CL less effective. Thirty-two C57BL/6 mice (male, 16 weeks old, n=8/group) were exposed to 3 weeks of either HU or normal ambulation (NA). Cohorts of mice received one subcutaneous injection of ZOL (45μg/kg), or saline vehicle (VEH), prior to the start of HU. The right tibia was axially compressed in vivo 60x/day to 9N (+1200μstrain on the periosteal surface) and repeated 3x/week during HU. Left tibiae served as a within subject, non-compressed control. Ex vivo μCT was performed on all subjects to determine cancellous and cortical architectural parameters. Static and dynamic histomorphometry were carried out for the left and right tibiae to determine osteoclast- and osteoblast relevant surfaces. Further, micro damage was assessed in select groups by basic-fuchsin staining to test whether CL had an effect. For all assays, a multivariate (2x2x2) ANCOVA model was used to account for body weight changes. Additionally, for the tibiae, we incorporated a random effect for the subject (hence, a mixed model) to account for observations of both left and right tibiae within each subject. P < 0.05 was considered significant. In the cancellous compartment of the proximal tibial metaphysis, we observed a main effect from each independent variable, as determined by structural and histomorphometric assays. Specifically, as expected, ZOL showed an increase in the cancellous bone volume to total volume fraction (BV/TV, +32%) and trabecular number (+18%) compared to the VEH. As expected, ZOL decreased osteoclast surface (OC/BS) by -45% compared to VEH. Surprisingly, ZOL reduced mineralizing surface (MS/BS) and bone formation rate (BFR), indicators of osteoblast activity, by -40% and -54%, respectively, compared to VEH. Altogether, ZOL-treated mice displayed a low turnover state of remodeling in the metaphysis. In the context of skeletal aging, we speculate that ZOL prevented age-related cancellous strut loss during the experiment. As a main effect, as expected, HU decreased BV/TV by - 31% via reductions in both trabecular thickness (-11%) and number (-22%) compared to NA controls. Additionally, HU decreased MS/BS by -38% and bone formation rate (BFR) by -50% compared to NA controls. Altogether, these data are consistent with structural degradation resulting from imbalanced remodeling that favors resorption. As a main effect, CL increased BV/TV by +15% via increased trabecular thickness (+12%) compared to the noncompressed limb. As expected, CL increased MS/BS (+20%) and BFR (+24%), indicating osteoblast mineralization contributed to bone gains. These data show that CL provided an anabolic stimulus to the cancellous tissue. We observed unique interactions in ZOL*CL and HU*CL. First, ZOL prevented CL-induced increases in BV/TV and trabecular number, as compared to VEH. In the context of skeletal aging, these data suggest no added benefit from CL in the ZOL-treated mice. Interestingly, no microdamage was observed in mice that were unloaded and treated with ZOL (independent of CL). Secondly, HU prevented CL-induced increases in BFR, as compared to NA controls. These data suggest that either exercise is less effective or the kinetics of formation are slower during simulated weightlessness. Osteoclast surface was unchanged by either treatment. Thus, in contrast to exercising astronauts, these data do not suggest a high-turnover state in the metaphysis. To assess mechanical properties as a function of HU or ZOL, we tested the left femur in three-point bending ex vivo. As expected, HU decreased stiffness (-30%) compared to NA, and ZOL increased stiffness compared to VEH (+28%). Interestingly, HU increased the post-yield displacement, related to collagenous tensile loading, compared to NA (+20%). ZOL increased yield force (+11%) and ultimate force (+17%), which seems to explain the significant effect of ZOL increasing total energy (work-to-fracture, +15%), while not affecting the post yield displacement. Taken together, ZOL did not have detrimental affect on mechanical properties. Our integrated model simulates the combination of weightlessness, exercise-induced mechanical strain, and anti-resorptive treatment that astronauts experience during space missions. We conclude that Zoledronate was an effective countermeasure against weightlessness-induced bone loss, though zoledronate, as well as weightlessness, rendered exercise-related mechanical loading less effective.

bone↗

An Obscured, Seyfert 2-like State of the Stellar-mass Black Hole GRS 1915+105 Caused by Failed Disk Winds

We report on Chandra grating spectra of the stellar-mass black hole GRS 1915+105 obtained during a novel, highly obscured state. As the source entered this state, a dense, massive accretion disk wind was detected through strong absorption lines. Photoionization modeling indicates that it must originate close to the central engine, orders of magnitude from the outer accretion disk. Strong, nearly sinusoidal flux variability in this phase yielded a key insight: the wind is blueshifted when its column density is relatively low, but redshifted as it approaches the Compton-thick threshold. At no point does the wind appear to achieve the local escape velocity; in this sense, it is a “failed wind.” Later observations suggest that the disk ultimately fails to keep even the central engine clear of gas, leading to heavily obscured and Compton-thick states characterized by very strong Fe K emission lines. Indeed, these later spectra are successfully described using models developed for obscured active galactic nuclei (AGNs). We discuss our results in terms of the remarkable similarity of GRS 1915+105 deep in its “obscured state” to Seyfert 2 and Compton-thick AGNs, and we explore how our understanding of accretion and obscuration in massive black holes is impacted by our observations.

Black holes↗

Engineering specification and system design for CAD/CAM of custom shoes. Phase 5: UMC involvement (January 1, 1989 - June 30, 1989)

The CAD/CAM of custom shoes is discussed. The solid object for machining is represented by a wireframe model with its nodes or vertices specified systematically in a grid pattern covering its entire length (point-to-point configuration). Two sets of data from CENCIT and CYBERWARE were used for machining purposes. It was found that the indexing technique (turning the stock by a small angle then moving the tool on a longitudinal path along the foot) yields the best result in terms of ease of programming, savings in wear and tear of the machine and cutting tools, and resolution of fine surface details. The work done using the LASTMOD last design system results in a shoe last specified by a number of congruent surface patches of different sizes. This data format was converted into a form amenable to the machine tool. It involves a series of sorting algorithms and interpolation algorithms to provide the grid pattern that the machine tool needs as was the case in the point to point configuration discussed above. This report also contains an in-depth treatment of the design and production technique of an integrated sole to complement the task of design and manufacture of the shoe last. Clinical data and essential production parameters are discussed. Examples of soles made through this process are given.

Bao, Han P.↗

Mixtures of CO 2 and poly(fluoroacrylate) based on monomers containing only six or four fluorinated carbons: Phase behavior and solution viscosity

In this study, homopolymerization of fluoroacrylate monomers containing a segment with eight fluorinated carbons, (CH 2 CHCOO(CH 2 ) 2 (CF 2 ) 7 CF 3 ), yield poly(fluoroacrylate) (PFA) with remarkably high solubility in CO 2 , but the corresponding ultimate PFA degradation product perfluorooctanoic acid (PFOA) is bio-accumulative. Based on cloud point loci in the 1–4 wt% PFA in CO 2 concentration range at temperatures of 25, 50, 75, 100 and 125°C, it is shown that C 6 F 13 -based and C 4 F 9 -based PFA, with relatively benign degradation products perfluorohexanoic acid (PFHxA) and perfluorobutanoic acid (PFBA), respectively, retain the same level of CO 2 -solubility as that of C 8 F 17 -based PFA. Further, both C 6 F 13 -based and C 4 F 9 -based PFA can increase the viscosity of single-phase CO 2 -PFA solutions (i.e. thicken CO 2 ) as much as C 8 F 17 -based PFA in the 25–125°C range. Therefore, the design of CO 2 -soluble PFA need not be constrained to monomers containing the C 8 F 17 moiety; fluoroacrylate monomers containing shorter fluoroalkyl segments with only four or six fluorocarbons can be utilized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗