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NASA NTRS1992

LDV measurements on a rectangular wing with a simulated glaze ice accretion

LDV measurement results are presented for the upper surface of a rectangular semispan wing with and without simulated glaze ice accretion. Inspection of the model centerline flow field indicates that a large region of reverse flow exists aft of the ice horn on the iced model. At alpha = 0 deg, this region extends to 7 percent chord, while at alpha = 4 deg the bubble grows to more than 12 percent chord. At alpha = 8 deg, the time-averaged separation bubble is measured well beyond 50 percent chord. Experimental and computational flow visualization support these findings. The flow in the vicinity of the ice shape contains many of the features of flow over a backward-facing step.

Khodadoust, A.↗

DOE OSTI2021

Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF

Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break symmetry in order to lower the overall energy, just as unrestricted Hartree-Fock breaks spin symmetry. Overall, we demonstrate that time reversal symmetry is roughly maintained when using Hartree-Fock, but less so when using Kohn-Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Structural insights into the mechanism of oxidative activation of heme-free H-NOX from Vibrio cholerae

Bacterial heme nitric oxide/oxygen (H-NOX) domains are nitric oxide (NO) or oxygen sensors. This activity is mediated through binding of the ligand to a heme cofactor. However, H-NOX from Vibrio cholerae (Vc H-NOX) can be easily purified in a heme-free state that is capable of reversibly responding to oxidation, suggesting a heme-independent function as a redox sensor. This occurs by oxidation of Cys residues at a zinc-binding site conserved in a subset of H-NOX homologs. Remarkably, zinc is not lost from the protein upon oxidation, although its ligation environment is significantly altered. Using a combination of computational and experimental approaches, we have characterized localized structural changes that accompany the formation of specific disulfide bonds between Cys residues upon oxidation. Furthermore, the larger-scale structural changes accompanying oxidation appear to mimic those changes observed upon NO binding to the heme-bound form. Thus, Vc H-NOX and its homologs may act as both redox and NO sensors by completely separate mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1982

Molecular processes in comets

Potential energy curves for the two lowest 2 sigma- states of OH are computed at the configuration-interaction level using four different basis sets. Electronic transition dipole moments connecting the excited 1 2 sigma- and 2(D) 2 sigma- states with each other and with he ground X2pi state are presented as functions of internuclear distance. The theoretical absorption oscillator strengths for the D 2 sigma-(v prime=0) reverser to X 2pi (v prime prime=0) transition are in good agreement with the empirical value derived from astronomical measurements. The photodissociation cross sections for absorption rom the v prime prime=0,1, and levels of the ground state into the continuum of the 1 2 sigma- state are calculated, and the interstellar and cometary photodissociation rates are derived.

Dalgarno, A.↗

NASA NTRS2013

Calculating Conductance of Ion Channels

We have simulated two small ion channels in a water/membrane system, which consists of 71,000-72,000 atoms, and have estimated the conductance by way of counting ions crossing these channels in applied field. The calculated values of conductance have been compared with predictions of the electrodiffusion model. In a recently developed theoretical framework, all commonly used assumptions of the model can be tested. If they are satisfied, which is often the case, the approach provides a rigorous way to extrapolate conductance calculated at one voltage to other voltages. This, in turn, allows for efficient estimations of current-voltage dependence, examining rectifying behavior of channels and calculating the reversal potential. Furthermore, the consistency of the results can be precisely tested. Simulations at microsecond time scales are required to sufficiently reduce statistical errors and separate them from possible systematic errors. Only then the accuracy of the proposed approach can be properly tested. Linking simulations with electrophysiology provides a stringent, highly relevant test for the correctness of computer simulations of ion channels. Considering biological, medical and pharmaceutical importance of these proteins, results of the proposed study might motivate the development of improved hardware and software that would enable applying a similar strategy to more complex channels at longer times.

Ion↗

DOE OSTI2024

High-resolution source imaging and moment tensor estimation of acoustic emissions during brittle creep of basalt undergoing carbonation

SUMMARY As the high-frequency analogue to field-scale earthquakes, acoustic emissions (AEs) provide a valuable complement to study rock deformation mechanisms. During the load-stepping creep experiments with CO2-saturated water injection into a basaltic sample from Carbfix site in Iceland, 8791 AE events are detected by at least one of the seven piezoelectric sensors. Here, we apply a cross-correlation-based source imaging method, called geometric-mean reverse-time migration (GmRTM) to locate those AE events. Besides the attractive picking-free feature shared with other waveform-based methods (e.g. time-reversal imaging), GmRTM is advantageous in generating high-resolution source images with reduced imaging artefacts, especially for experiments with relatively sparse receivers. In general, the imaged AE locations are found to be scattered across the sample, suggesting a complicated fracture network rather than a well-defined major shear fracture plane, in agreement with X-ray computed tomography imaging results after retrieval of samples from the deformation apparatus. Clustering the events in space and time using the nearest-neighbour approach revealed a group of ‘repeaters’, which are spatially co-located over an elongated period of time and likely indicate crack, or shear band growth. Furthermore, we select 2196 AE events with high signal-to-noise-ratio (SNR) and conduct moment tensor estimation using the adjoint (backpropagated) strain tensor fields at the locations of AE sources. The resulting AE locations and focal mechanisms support our previously assertion that creep of basalt at the experimental conditions is accommodated dominantly by distributed microcracking.

58 GEOSCIENCES↗

DOE OSTI2021

Imaging of Electrothermal Filament Formation in a Mott Insulator

Resistive switching—the current- and voltage-induced change of electrical resistance—is at the core of memristive devices, which play an essential role in the emerging field of neuromorphic computing. This study is about resistive switching in a Mott insulator, which undergoes a thermally driven metal-to-insulator transition. Two distinct switching mechanisms are reported for such a system: electric-field-driven resistive switching and electrothermal resistive switching. The latter results from an instability caused by Joule heating. Here, we present the visualization of the reversible resistive switching in a planar V 2 O 3 thin-film device using high-resolution wide-field microscopy in combination with electric transport measurements. We investigate the interaction of the electrothermal instability with the strain-induced spontaneous phase separation in the V 2 O 3 thin film at the Mott transition. The photomicrographs show the formation of a narrow metallic filament with a minimum width ≲500 nm. Although the filament formation and the overall shape of the current-voltage characteristics (IVCs) are typical of an electrothermal breakdown, we also observe atypical effects such as oblique filaments, filament splitting, and hysteretic IVCs with sawtoothlike jumps at high currents in the low-resistance regime. We are able to reproduce the experimental results in a numerical model based on a two-dimensional resistor network. This model demonstrates that resistive switching in this case is indeed electrothermal and that the intrinsic heterogeneity is responsible for the atypical effects. This heterogeneity is strongly influenced by strain, thereby establishing a link between switching dynamics and structural properties.

42 ENGINEERING↗

DOE OSTI2021

Skyrme pseudopotentials at next-to-next-to-leading order: Construction of local densities and first symmetry-breaking calculations

There is an ongoing quest to improve on the spectroscopic quality of nuclear energy density functionals (EDFs) of the Skyrme type through extensions of its traditional form. One direction for such activities is the inclusion of terms of higher order in gradients in the EDF. We report on exploratory symmetry-breaking calculations performed for an extension of the Skyrme EDF that includes central terms with four gradients at next-to-next-to-leading order (N2LO) and for which the high-quality parametrization SN2LO1 has been constructed recently. Up to now, the investigation of such functionals with higher-order terms was limited to infinite matter and spherically symmetric configurations of singly and doubly magic nuclei. We address here nuclei and phenomena that require us to consider axial and nonaxial deformation, both for reflection-symmetric and also reflection-asymmetric shapes, as well as the breaking of time-reversal invariance. Achieving these calculations demanded a number of formal developments. These all resulted from the formulation of the N2LO EDF requiring the introduction of new local densities with additional gradients that are not present in the EDF at NLO. Their choice is not unique, but can differ in the way the gradients are coupled. While designing a numerical implementation of N2LO EDFs in Cartesian three-dimensional coordinate-space representation, we have developed a novel definition and a new unifying notation for normal and pair densities that contain gradients at arbitrary order. Besides having mnemonic advantages, the new notation allows for the easy identification of redundancies and reducibilities in a given set of local densities, and the new definition makes it straightforward to construct densities that automatically adopt the symmetries of the many-body state they are constructed from. The resulting scheme resolves several issues with some of the choices that have been made for local densities in the past, in particular when breaking time-reversal symmetry. Guided by general practical considerations, we propose an alternative form of the N2LO contribution to the Skyrme EDF that is built from a different set of densities. It has exactly the same physics content, but is much more efficient to handle in formal discussions and, compared to the original formulation, leads to a substantial reduction of computational cost and memory requirements in deformed codes. As representative examples for the performance of SN2LO1, we have chosen the ground states of even-even Kr and Nd isotopes, the fission barrier of 240 Pu as well as the superdeformed rotational band of 194 Hg. Overall, for the nuclei and phenomena studied here, the SN2LO1 parametrization does not yet present a systematic improvement over standard NLO parametrizations. This finding calls for improved fit protocols that better discriminate between NLO and N2LO terms and better exploit the unique features of the additional degrees of freedom offered by the latter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2023

Partition Thickness Considerations for Additively Manufactured Acoustic Liners

Three types of uniform-depth liners are evaluated to explore the effects of partition thickness on the surface impedance achieved with additively manufactured liners. A transmission line code is used to predict the effects of sound transmission through empty chambers and wire mesh facesheets, and is combined with the Motsinger and Kraft model to account for sound transmission through perforated facesheets. The inclusion of partitions causes a blockage effect, i.e., a portion of the surface is ‘blocked’ (nonactive surface). For liners with no facesheet, these blockage effects are incorporated simply by accounting for the change in cross sectional area between the individual chamber and the unit cell that includes half of a partition thickness around the perimeter of this chamber. Comparison of impedances predicted in this manner with data acquired in the NASA Langley Normal Incidence Tube (NIT) confirms the efficacy of this modeling approach. Two approaches are considered to account for the inclusion of a wiremesh or perforated plate facesheet on these same cores. The first accounts for the effects of partition thickness before including the transfer impedance across the facesheet, while the second reverses these steps. A comparison of data acquired in the NASA NIT with modeled impedances suggests the first approach is best when the facesheet is a wire mesh, but the second approach is preferred when a perforated plate facesheet is used. It is hypothesized that this is due to the fact that a lumped element model is used to compute the transfer impedance across a wire mesh, while the corresponding transfer impedance across a perforated sheet explicitly incorporates the efffects of the liner core. However, comparisons of data acquired in the NASA Langley Grazing Flow Impedance Tube with modeled impedances seem slightly better when the first approach is employed with a perforated plate facesheet. Thus, the effects of partition thickness on liners with perforated sheets subjected to grazing incidence sound require further review

acoustic↗

DOE OSTI2021

Robust Molecular Predictive Methods for Novel Polymer Discovery and Applications

Polymeric materials are ubiquitous in modern society and they play an instrumental role in almost all industries, undoubtedly including the energy and environment sectors. Increased demand of energy and awareness to sustainability both necessitates the development of novel polymers with enhanced properties. Unfortunately, their structural and behavioral complexity render such discovery challenging and impeded. To address this problem, scientists are developing various computational modeling techniques and leveraging their power to depict the relationship between structural characteristics of polymers and their properties (such as rheological behaviors), and use such prediction to guide the design and syntheses of novel polymeric materials with enhanced performances. Unfortunately, predicting the relationships between polymer structure and composition with rheological properties via atomistic modeling is still a major challenge because of the extended time and length scales involved. Studying dynamic shear viscosity and linear viscoelasticity using molecular models requires capabilities that have been elusive, including representation of large molecular weight chains with an effective internal scale capable of describing entanglement, shear-rates that are in the s-1 scale with accurate quantitative stresses, and chemically-realistic combinations of both homogeneous and heterogeneous systems. Motivated by these unmet challenges, the overall technical objective of this DOE-STTR Phase II project is to develop robust molecular predictive methods for advanced polymer discovery and applications and especially for designing and demonstrating the “smart” polymer-based waterflooding enhanced oil recovery (EOR) process. In particular, we apply state-of-the-art molecular modeling methods developed by our academic partner, Materials Stimulation Center (MSC) at California Institute of Technology (Caltech), to facilitate and accelerate the experimental discovery processes. During the Phase I of this project, we had focused on development and demonstration of the molecular modeling methods to describe rheological properties of non-Newtonian polymer fluids, and to improve our fundamental understandings of shear-thickening mechanism and kinetics. In Phase II, we further apply the theoretical models to guide our experimental programs to improve our design of smart rheology modifier (SRM) polymers and their optimization for EOR. Specifically, we have three objectives in the Phase II study: (1) to further improve out computational modeling methods, coupling with the advanced machine learning algorithms; (2) to develop cost-effective and efficient SRM-flooding process suitable for EOR applications under typical reservoir conditions; and (3) to further explore the application of our molecular predictive models for innovative material discovery in other industrial applications. The recent development of our multiscale predictive framework allows the successful prediction of rheological properties from the chemical structure for polymers of experimentally relevant molecular weights, and provides an in-silico machine learning engine for screening novel compositions and structures with optimized non-Newtonian response, required for both shear-thinning and shear-thickening applications. Our framework provides: (1) procedures and tools for systematic coarsening from atomistic models and reverse mapping of coarse-grain models to atomistic, (2) unique ab initio methods to characterize the atomistic origin of colloidal and interfacial interactions and phenomena, (3) systematic structure and composition builders based on practical descriptors that drive rheological changes in polymer melts and diluted polymer mixtures, (4) a rheological properties engine capable of predicting viscosity in the zero-shear limit and under realistic dynamic conditions (for shear-rates commensurate with experiments) for large heterogeneous systems, (5) coarse-grain force fields with improved non-bond descriptions based on accurate quantum mechanics, (6) an in-silico screening machine learning engine that feeds from the systematic model builders to cover the descriptors search space, computes the rheological properties from converged trajectories spanning sub-milliseconds and ranks them for each structure/composition using an automated viscosity-vs-shear rate fitness function that can be tuned for shear-thickening, shear-thinning and other rheological responses.

02 PETROLEUM↗

DOE OSTI2025

Olefin Coupling Catalyzed by (Pybox)Os Complexes via Osmacyclopentane Intermediates: Comparison with Isoelectronic (Phebox)Ir

(Pybox)Os is found to catalyze alkene hydrovinylation, effecting the dimerization of ethylene, tail-to-tail coupling of propene and 1-butene, and cross-coupling of ethylene with higher α-olefins. This reactivity contrasts with the previously reported dehydrogenative coupling of ethylene to give butadiene catalyzed by the isoelectronic fragment (Phebox)Ir. The reaction mechanism was investigated through computational and experimental means. Both the Os- and Ir-catalyzed reactions proceed through a [2 + 2 + 1] cyclization of the corresponding bis-olefin complex to yield an experimentally observed metallacyclopentane intermediate. In both cases, the metallacyclopentane undergoes β- H elimination, via a dechelated κ 2 -pincer-ligated intermediate, to yield a σ−π-but-3-enyl hydride complex or derivative. Both the greater reactivity and the distinct chemoselectivity of the Os system relative to the Ir system are attributable to C−H reductive elimination by the σ−π-but-3-enyl hydride having a barrier for Os much lower than that for Ir. This lower barrier to C−H elimination for Os is unexpected given that the thermodynamic driving force for elimination is much less for Os than for Ir. Computational studies of model complexes were conducted, comparing (Pybox)Os(L)(CH 3 )(H) with the isoelectronic (Phebox)Ir(L)(CH 3 )(H). The results indicate that the more facile kinetics with Os relative to Ir may be general for C−H elimination from six-coordinate d 6 complexes of the two metals, as well as for the microscopic reverse, i.e., C−H addition to the corresponding four-coordinate d 8 species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Pressure, temperature, and orientation dependent thermal conductivity of pentaerythritol tetranitrate (PETN)

We use reverse non-equilibrium molecular dynamics to determine the thermal conductivity tensor, κ, of tetragonal pentaerythritol tetranitrate (PETN). The most stable form under standard ambient conditions (PETN I, with space group P4¯2 1 c) is considered in the temperature and pressure intervals 200–500 K and 0–8 GPa, which covers approximately the stability range for this polymorph. We compute κ along the [100] and [001] directions, which is enough to construct the full thermal conductivity tensor for a system with tetragonal symmetry. In addition, we also determine κ along the [010] direction and confirm that κ 100 ~ κ 010 , with less than 4% average absolute error between the two quantities. We observe an anisotropic response for κ, with κ 100 > κ 001 across the whole (T,P) interval, and 37% difference at 300 K, 0 GPa. Furthermore, we provide analytical functions to interpolate κ(P,T) within the fitting interval and serve as input for continuum-scale simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Thermodynamically consistent semi-compressible fluids: a variational perspective

This paper presents (Lagrangian) variational formulations for single and multicomponent semi-compressible fluids with both reversible (entropy-conserving) and irreversible (entropy-generating) processes. Semi-compressible fluids are useful in describing low-Mach dynamics, since they are soundproof. These models find wide use in many areas of fluid dynamics, including both geophysical and astrophysical fluid dynamics. Specifically, the Boussinesq, anelastic and pseudoincompressible equations are developed through a unified treatment valid for arbitrary Riemannian manifolds, thermodynamic potentials and geopotentials. By design, these formulations obey the 1st and 2nd laws of thermodynamics, ensuring their thermodynamic consistency. This general approach extends and unifies existing work, and helps clarify the thermodynamics of semi-compressible fluids. To further this goal, evolution equations are presented for a wide range of thermodynamic variables: entropy density s, specific entropy η, buoyancy b, temperature T, potential temperature θ and a generic entropic variable χ; along with a general definition of buoyancy valid for all three semicompressible models and arbitrary geopotentials. Finally, the elliptic equation for the pressure perturbation (the Lagrange multiplier that enforces semi-compressibility) is developed for all three equation sets in the case of reversible dynamics, and for the Boussinesq/anelastic equations in the case of irreversible dynamics; and some discussion is given of the difficulty in formulating it for the pseudoincompressible equations with irreversible dynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The Architectural Dynamics of the Bacterial Flagellar Motor Switch

The rotary bacterial flagellar motor is remarkable in biochemistry for its highly synchronized operation and amplification during switching of rotation sense. The motor is part of the flagellar basal body, a complex multi-protein assembly. Sensory and energy transduction depends on a core of six proteins that are adapted in different species to adjust torque and produce diverse switches. Motor response to chemotactic and environmental stimuli is driven by interactions of the core with small signal proteins. The initial protein interactions are propagated across a multi-subunit cytoplasmic ring to switch torque. Torque reversal triggers structural transitions in the flagellar filament to change motile behavior. Subtle variations in the core components invert or block switch operation. The mechanics of the flagellar switch have been studied with multiple approaches, from protein dynamics to single molecule and cell biophysics. The architecture, driven by recent advances in electron cryo-microscopy, is available for several species. Computational methods have correlated structure with genetic and biochemical databases. The design principles underlying the basis of switch ultra-sensitivity and its dependence on motor torque remain elusive, but tantalizing clues have emerged. This review aims to consolidate recent knowledge into a unified platform that can inspire new research strategies.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1986

Electromagnetic instabilities driven by cool heavy ion beams

The effects of the mass and density of cool, heavy ion beams on the linear and nonlinear characteristics of right-hand resonant and nonresonant electromagnetic ion beam instabilities are analyzed. The magnetic helicity and Alfven speed for a computer simulated complete linear dispersion equation for electromagnetic instabilities are examined. The data reveal that the maximum growth rate of the resonant mode and the threshold velocity of the nonresonant mode decrease with beam mass; however, the maximum growth rate of the nonresonant mode and the threshold velocity of the resonant mode are independent of the beam mass. The role reversal of the instabilities which occur when a heavy ion beam is the more dense component is studied. The nonlinear behavior of the instabilities is described; variations in the magnetic field fluctuation levels and the beam mass dependence are investigated. It is observed that at low beam density the magnetic field fluctuation level increases with beam mass and at higher beam density the fluctuation level correlates with the core mass. The instability data are applied to observations of Venus and the Comet Giacobini-Zinner.

Winske, D.↗

NASA NTRS2005

Online fault adaptive control for efficient resource management in Advanced Life Support Systems

This article presents the design and implementation of a controller scheme for efficient resource management in Advanced Life Support Systems. In the proposed approach, a switching hybrid system model is used to represent the dynamics of the system components and their interactions. The operational specifications for the controller are represented by utility functions, and the corresponding resource management problem is formulated as a safety control problem. The controller is designed as a limited-horizon online supervisory controller that performs a limited forward search on the state-space of the system at each time step, and uses the utility functions to decide on the best action. The feasibility and accuracy of the online algorithm can be assessed at design time. We demonstrate the effectiveness of the scheme by running a set of experiments on the Reverse Osmosis (RO) subsystem of the Water Recovery System (WRS).

NASA Discipline Life Support Systems↗

NASA NTRS2007

Calibration Test Set for a Phase-Comparison Digital Tracker

An apparatus that generates four signals at a frequency of 7.1 GHz having precisely controlled relative phases and equal amplitudes has been designed and built. This apparatus is intended mainly for use in computer-controlled automated calibration and testing of a phase-comparison digital tracker (PCDT) that measures the relative phases of replicas of the same X-band signal received by four antenna elements in an array. (The relative direction of incidence of the signal on the array is then computed from the relative phases.) The present apparatus can also be used to generate precisely phased signals for steering a beam transmitted from a phased antenna array. The apparatus (see figure) includes a 7.1-GHz signal generator, the output of which is fed to a four-way splitter. Each of the four splitter outputs is attenuated by 10 dB and fed as input to a vector modulator, wherein DC bias voltages are used to control the in-phase (I) and quadrature (Q) signal components. The bias voltages are generated by digital-to-analog- converter circuits on a control board that receives its digital control input from a computer running a LabVIEW program. The outputs of the vector modulators are further attenuated by 10 dB, then presented at high-grade radio-frequency connectors. The attenuation reduces the effects of changing mismatch and reflections. The apparatus was calibrated in a process in which the bias voltages were first stepped through all possible IQ settings. Then in a reverse interpolation performed by use of MATLAB software, a lookup table containing 3,600 IQ settings, representing equal amplitude and phase increments of 0.1 , was created for each vector modulator. During operation of the apparatus, these lookup tables are used in calibrating the PCDT.

Boas, Amy↗

DOE OSTI2023

Computational Predictions of the Stability of Fluorinated Calcium Aluminate and Borate Salts

Energy storage concepts based on multivalent ions, such as calcium, have great potential to become next-generation batteries due to their low cost and comparable cell voltage and energy density to Li-ion batteries. However, the development of Ca batteries is still hindered by the lack of suitable materials that grant a long cycle life. Specific to electrolyte materials, developing a calcium salt that is chemically stable under ambient conditions and enables reversible electrodeposition of Ca is critical. In this work, we use first-principles calculations to study the intrinsic and reductive stability of twelve Ca salts with fluorinated aluminate and borate anions and analyze the decomposition products formed on the metal anode surface that are critical to early-stage solid electrolyte interphase formation. Here we found anions with significant steric hindrance and a high degree of fluorination are intrinsically less stable and deemed unviable designs for Ca salt. Aluminate salts are generally less reactive with the Ca anode than their borate counterparts, and a high degree of fluorination leads to weaker reductive stability. Calcium fluoride is the most prominent decomposition product on the anode surface, and carbide-like motifs were also found from the decomposition of the designed salts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗