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

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Effects of irradiation damage on the hardness and elastic properties of quaternary and high entropy transition metal diborides

Multi-principal component transition metal (TM) diborides represent a class of high-entropy ceramics (HECs) that have received considerable interest in recent years owing to their promising properties for extreme environment applications that include thermal/ environmental barriers, hypersonic vehicles, turbine engines, and next-generation nuclear reactors. While the addition of chemical disorder through the random distribution of TM elements on the cation sublattice has offered opportunities to tailor elastic stiffness and hardness, the effects of irradiation-induced structural damage on the physical properties of these complex materials have remained largely unexplored. To this end, changes in the hardness and elastic moduli of a high-entropy TM diboride (Hf 0.2 Nb 0.2 Ta 0.2 Ti 0.2 Zr 0.2 )B 2 and three of its quaternary subsets following irradiation with 10 MeV gold (Au) ions to fluences of up to 6 × 10 15 Au cm -2 are investigated at the micrometer and sub-micrometer length-scales via the dispersion of laser-generated surface acoustic waves (SAW) and nanoindentation, respectively. The nanoindentation measurements show that the TM diborides exhibit an initial increase in hardness following irradiation with energetic Au ions, with a subsequent decrease in hardness following further irradiation. One quaternary composition, (Hf 1/3 Ta 1/3 Ti 1/3 )B 2 , exhibits a notable exception to the trend and continues to exhibit an increase in hardness with ion irradiation fluence. Although differences in the absolute values of the effective elastic moduli obtained from the measured SAW dispersion and nanoindentation are observed (and attributed to microstructural variations at the measurement length-scale), both techniques yield similar trends in the form of an initial reduction and subsequent saturation in the elastic modulus with increasing ion irradiation fluence. The quaternary TM diboride (Hf 1/3 Ta 1/3 Ti 1/3 )B 2 again exhibits a departure from this trend. The high-entropy TM diboride (Hf 0.2 Nb 0.2 Ta 0.2 Ti 0.2 Zr 0.2 )B 2 exhibits the greatest recovery in hardness and modulus when irradiated to high ion fluences following initial changes at low fluence, indicating superior resistance to radiation-induced damage over its quaternary counterparts. Opportunities for designing HECs with superior hardness and modulus for enhanced radiation resistance (compared to their single constituent counterparts) by tailoring chemical disorder and bond character in the lattice are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Virtualized Logical Qubits: A 2.5D Architecture for Error-Corrected Quantum Computing

Current, near-term quantum devices have shown great progress in the last several years culminating recently with a demonstration of quantum supremacy. In the medium-term, however, quantum machines will need to transition to greater reliability through error correction, likely through promising techniques like surface codes which are well suited for near-term devices with limited qubit connectivity. We discover quantum memory, particularly resonant cavities with transmon qubits arranged in a 2.5D architecture, can efficiently implement surface codes with substantial hardware savings and performance/fidelity gains. Specifically, we virtualize logical qubits by storing them in layers of qubit memories connected to each transmon. Surprisingly, distributing each logical qubit across many memories has a minimal impact on fault tolerance and results in substantially more efficient operations. Our design permits fast transversal application of CNOT operations between logical qubits sharing the same physical address (same set of cavities) which are 6x faster than standard lattice surgery CNOTs. We develop a novel embedding which saves approximately 10x in transmons with another 2x savings from an additional optimization for compactness. Although qubit virtualization pays a 10x penalty in serialization, advantages in the transversal CNOT and in area efficiency result in fault-tolerance and performance comparable to conventional 2D transmon-only architectures. Our simulations show our system can achieve fault tolerance comparable to conventional two-dimensional grids while saving substantial hardware. Furthermore, our architecture can produce magic states at 1.22x the baseline rate given a fixed number of transmon qubits. Here, this is a critical benchmark for future fault-tolerant quantum computers as magic states are essential and machines will spend the majority of their resources continuously producing them. This architecture substantially reduces the hardware requirements for fault-tolerant quantum computing and puts within reach a proof-of-concept experimental demonstration of around 10 logical qubits, requiring only 11 transmons and 9 attached cavities in total.

quantum computing↗
DOE OSTI2025

Revealing atomic-scale switching pathways in van der Waals ferroelectrics

Two-dimensional (2D) van der Waals (vdW) materials hold the potential for ultrascaled ferroelectric (FE) devices due to their silicon compatibility and robust polarization down to atomic scale. However, the inherently weak vdW interactions enable facile sliding between layers, introducing complexities beyond those encountered in conventional ferroelectric materials and presenting substantial challenges in uncovering intricate switching pathways. Here, we combine atomic-resolution imaging under in situ electrical biasing conditions with first-principles calculations to unravel the atomic-scale switching mechanisms in SnSe, a vdW group IV monochalcogenide. Our results uncover the coexistence of a consecutive 90° switching pathway and a direct 180° switching pathway from antiferroelectric (AFE) to FE order in this vdW system. Atomic-scale investigations and strain analysis reveal that the switching processes simultaneously induce interlayer sliding and compressive strain, while the lattice remains coherent despite the presence of multidomain structures. These findings elucidate vdW ferroelectric switching dynamics at atomic scale and lay the foundation for the rational design of 2D ferroelectric nanodevices.

Li, Xinyan [Rice University, Houston, TX (United S↗
DOE OSTI2024

Effects of irradiation damage on the elastic properties and hardness of complex transition metal diborides

Multi-principal component transition metal (TM) diborides represent a class of high-entropy ceramics (HECs) that have received considerable interest in recent years owing to their promising properties for extreme environment applications that include thermal/ environmental barriers, hypersonic vehicles, turbine engines, and next-generation nuclear reactors. While the addition of chemical disorder through the random distribution of TM elements on the cation sublattice has offered opportunities to tailor elastic stiffness and hardness, the effects of irradiationinduced structural damage on the physical properties of these complex materials have remained largely unexplored. To this end, changes in the hardness and elastic moduli of a high-entropy TM diboride (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)B2 and three of its quaternary subsets following irradiation with 10 MeV gold (Au) ions to fluences of up to 6 × 10^15 Au cm-2 are investigated at the micrometer and sub-micrometer length-scales via the dispersion of laser-generated surface acoustic waves (SAW) and nanoindentation, respectively. The nanoindentation measurements show that the TM diborides exhibit an initial increase in hardness following irradiation with energetic Au ions, with a subsequent decrease in hardness following further irradiation. One quaternary composition, (Hf1/3Ta1/3Ti1/3)B2, exhibits a notable exception to the trend and continues to exhibit an increase in hardness with ion irradiation fluence. Although differences in the absolute values of the effective elastic moduli obtained from the measured SAW dispersion and nanoindentation are observed (and attributed to microstructural variations at the measurement length-scale), both techniques yield similar trends in the form of an initial reduction and subsequent saturation in the elastic modulus with increasing ion irradiation fluence. The quaternary TM diboride (Hf1/3Ta1/3Ti1/3)B2 again exhibits a departure from this trend. The high-entropy TM diboride (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)B2 exhibits the greatest recovery in hardness and modulus when irradiated to high ion fluences following initial changes at low fluence, indicating superior resistance to radiation-induced damage over its quaternary counterparts. Opportunities for designing HECs with superior hardness and modulus for enhanced radiation resistance (compared to their single constituent counterparts) by tailoring chemical disorder and bond character in the lattice are discussed.

36 - MATERIALS SCIENCE↗
DOE OSTI2022

Machine learning changes the rules for flux limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock capturing methods. Focusing on flux limiters provides a specific plug-and-play component for existing numerical methods. Since their introduction, an array of flux limiters has been designed. Using the coarse-grained Burgers' equation, we show that flux-limiters may be rank-ordered in terms of their log-error relative to high-resolution data. We then develop a theory to find an optimal flux-limiter and present flux-limiters that outperform others tested for integrating Burgers' equation on lattices with [Formula: see text], and 2x, 3x, 4x, and 8x coarse-grainings. We train a continuous piecewise linear limiter by minimizing the mean-squared misfit to six-grid point segments of high-resolution data, averaged over all segments. While flux limiters are generally designed to have an output of φ(r) = 1 at a flux ratio of r = 1, our limiters are not bound by this rule and yet produce a smaller error than standard limiters. Here we find that our machine learned limiters have distinctive features that may provide new rules-of-thumb for the development of improved limiters. Additionally, we use our theory to learn flux-limiters that outperform standard limiters across a range of values (as opposed to at a specific fixed value) of coarse-graining, number of discretized bins, and diffusion parameter. This demonstrates the ability to produce flux limiters that should be more broadly useful than standard limiters for general applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Freestanding Ammonium Vanadate Composite Cathodes with Lattice Self-Regulation and Ion Exchange for Long-Lasting Ca-Ion Batteries

Calcium-ion batteries (CIBs) have emerged as a promising alternative for electrochemical energy storage. The lack of high-performance cathode materials severely limits the development of CIBs. Vanadium oxides are particularly attractive as cathode materials for CIBs, and preinsertion chemistry is often used to improve their calcium storage performance. However, the room temperature cycling lifespan of vanadium oxides in organic electrolytes still falls short of 1000 cycles. Here, based on preinsertion chemistry, the cycling life of vanadium oxides is further improved by integrated electrode and electrolyte engineering. Utilizing a tailored Ca electrolyte, the constructed freestanding (NH 4 ) 2 V 6 O 16 ·1.35H 2 O@graphene oxide@carbon nanotube (NHVO-H@GO@CNT) composite cathode achieves a 305 mAh g -1 high capacity and 10 000 cycles record-long life. Additionally, for the first time, a Ca-ion hybrid capacitor full cell is assembled and delivers a capacity of 62.8 mAh g -1 . The calcium storage mechanism of NHVO-H@GO@CNT based on a two-phase reaction and the exchange of NH 4 + and Ca 2+ during cycling are revealed. The lattice self-regulation of V—O layers is observed and the layered vanadium oxides with Ca 2+ pillars formed by ion exchange exhibit higher capacity. This work provides novel strategies to enhance the calcium storage performance of vanadium oxides via integrated structural design of electrodes and electrolyte modification.

25 ENERGY STORAGE↗
DOE OSTI2021

Programmable Matter: The Nanoparticle Atom and DNA Bond

Colloidal crystal engineering with DNA has led to significant advances in bottom-up materials synthesis and a new way of thinking about fundamental concepts in chemistry. Here, programmable atom equivalents (PAEs), comprised of nanoparticles (the “atoms”) functionalized with DNA (the “bonding elements”), are assembled through DNA hybridization into crystalline lattices. Unlike atomic systems, the “atom” (e.g., the nanoparticle shape, size, and composition) and the “bond” (e.g., the DNA length and sequence) can be tuned independently, yielding designer materials with unique catalytic, optical, and biological properties. Here in this review, nearly three decades of work that have contributed to the evolution of this class of programmable matter is chronicled, starting from the earliest examples based on gold-core PAEs, and then delineating how advances in synthetic capabilities, DNA design, and fundamental understanding of PAE-PAE interactions have led to new classes of functional materials that, in several cases, have no natural equivalent.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Enhancing Mechanical Properties of Carbon–Silicon Steel through Two–Stage Quenching and Partitioning with Bainitic Transformation: Ultimate Tensile Strength of 1875 MPa and Total Elongation of 8.03%

To achieve the desired microstructural properties, the ongoing development and innovation in new structural steels require novel thermal processing. This study aims to improve the mechanical properties of a commercial spring carbon–silicon steel by tailoring its microstructure through a process involving quenching and partitioning (Q&P) followed by bainitic transformation. A two–stage Q&P process is proposed to generate a nanoscale dispersion of stable retained austenite and carbides within the tempered martensite and bainite microstructure. The resulting tensile properties demonstrate a yield strength of 1280 MPa, an ultimate tensile strength of 1875 MPa, and a total elongation of 8.03%. These values surpass those of conventional spring 9254 steel, highlighting the effectiveness of the thermal treatment design. Microstructure analysis reveals the presence of tempered martensite, bainite sheaves, nanoscale carbides, and aggregates of retained austenite. Moreover, the resulting body–centered cubic matrix exhibits minimal lattice tetragonality of ≈1.0051, coupled with stable retained austenite featuring a carbon concentration of ≈3.42 ± 0.5 wt%, resulting in outstanding strength–ductility properties. In conclusion, these findings indicate that the proposed two–stage Q&P process, followed by bainitic transformation, significantly enhances the mechanical properties of carbon–silicon steels, making it a promising candidate for high–performance spring applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

In-Situ Synchrotron X-Ray Diffraction of Ultrasonic Microstructural Refinement During Solidification in a Commercial Al–Si–Mg Alloy

This study reports the first use of in-situ synchrotron X-ray diffraction (SXRD) to study the effects of ultrasonic melt processing (USMP) on phase and grain size evolution during solidification in a commercial Al–Si–Mg casting alloy. USMP is a technique that, when applied to aluminum as it solidifies, can be used to refine the local microstructure of large-scale castings. Analysis of the in-situ SXRD data to estimate the average grain size of primary α-Al grains during USMP demonstrates that USMP slows the growth rate of α-Al grains and reduces grain size by 36 pct. Furthermore, there is also evidence that USMP causes the primary α-Al grains to move relative to the X-ray beam; such motion increases the probability of primary α-Al grains colliding and fragmenting. This movement becomes constrained at the onset of the Al–Si binary eutectic, suggesting that USMP ceases to effectively refine the microstructure once the Al–Si binary eutectic begins to form. Complementary laboratory-scale X-ray diffraction (XRD) data were used to correlate the lattice parameters of the α-Al and Si (D-A4) phases with temperature to estimate cooling rate during solidification. Thus, this study can guide the design of novel castings with spatially distributed fine-grained regions produced using local ultrasonic processing.

Aluminum Alloys↗
DOE OSTI2025

DONUT: physics-aware machine learning for real-time X-ray nanodiffraction analysis

Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a significant bottleneck, often hindered by artifacts and computational demands. In scanning X-ray nanodiffraction microscopy, which is widely used to spatially resolve structural heterogeneities, this challenge is compounded by the convolution of the divergent beam with the sample’s local structure. To address this, we introduce DONUT (Diffraction with Optics for Nanobeam by Unsupervised Training), a physics-aware neural network designed for the rapid and automated analysis of nanobeam diffraction data. By incorporating a differentiable geometric diffraction model directly into its architecture, DONUT learns to predict crystal lattice strain and orientation in real-time. Crucially, this is achieved without reliance on labeled datasets or pre-training, overcoming a fundamental limitation for supervised machine learning in X-ray science. We demonstrate experimentally that DONUT accurately extracts all features within the data over 200 times more efficiently than conventional fitting methods.

Materials science↗
DOE OSTI2025

DONUT: Physics-aware Machine Learning for Real-time X-ray Nanodiffraction Analysis

SF-25-088 Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a significant bottleneck, often hindered by artifacts and computational demands. In scanning X-ray nanodiffraction microscopy, which is widely used to spatially resolve structural heterogeneities, this challenge is compounded by the convolution of the divergent beam with the sample’s local structure. To address this, we introduce DONUT (Diffraction with Optics for Nanobeam by Unsupervised Training), a physics-aware neural network designed for the rapid and automated analysis of nanobeam diffraction data. By incorporating a differentiable geometric diffraction model directly into its architecture, DONUT learns to predict crystal lattice strain and orientation in real-time. Crucially, this is achieved without reliance on labeled datasets or pre-training, overcoming a fundamental limitation for supervised machine learning in X-ray science. We demonstrate experimentally that DONUT accurately extracts all features within the data over 200 times more efficiently than conventional fitting methods.

Zhou, Tao [Argonne National Laboratory (ANL), Argo↗
DOE OSTI2025

Efficient CO2 and Natural Gas Refinery for Ethylene Production - Catalyst Development for Oxidative Coupling of Methane (OCM)

We designed a new electro-catalyst for oxidative coupling of methane (OCM) reaction, the structure of the Sc doped La0.3Sr0.7TiO3-d (LaSrTi) Sc doping to LaSrTi leading to lattice expansion and more distorted lattice, Investigated the effect of doping on the oxygen vacancy formation energy DFT calculations shows that Sc doping facilitate oxygen vacancy formation. Quantifying the surface basicity of the sample before and after Sc doping Sc doped sample exhibits high surface basicity.

catalysis↗
DOE OSTI2022

Entropy-driven order in an array of nanomagnets

Long-range ordering is typically associated with a decrease in entropy. Yet, it can also be driven by increasing entropy in certain special cases. Here we demonstrate that artificial spin-ice arrays of single-domain nanomagnets can be designed to produce such entropy-driven order. We focus on the tetris artificial spin-ice structure, a highly frustrated array geometry with a zero-point Pauling entropy, which is formed by selectively creating regular vacancies on the canonical square ice lattice. We probe thermally active tetris artificial spin ice both experimentally and through simulations, measuring the magnetic moments of the individual nanomagnets. Furthermore, we find two-dimensional magnetic ordering in one subset of these moments, which we demonstrate to be induced by disorder (that is, increased entropy) in another subset of the moments. In contrast with other entropy-driven systems, the discrete degrees of freedom in tetris artificial spin ice are binary and are both designable and directly observable at the microscale, and the entropy of the system is precisely calculable in simulations. This example, in which the system’s interactions and ground-state entropy are well defined, expands the experimental landscape for the study of entropy-driven ordering.

36 MATERIALS SCIENCE↗
DOE OSTI2026

DASSH-F: Subchannel Based Thermal Analysis

The DASSH thermal analysis code is designed to rapidly allow a reactor design engineer to obtain flow rates requirements that satisfy peak temperature constraints in the domain. The advantage of using DASSH over a hand calculation is that it has a more rigorous treatment of the pin power distribution and coolant heat transfer within an assembly and between assemblies. The advantage of using DASSH over a conventional 3D subchannel code or a computational fluid dynamics code (CFD) is that it can obtain the desired solution in a matter of minutes in serial with minor computer memory needs. The DASSH methodology for pin lattice models is virtually identical to SUPERENERGY-2 with additional functionalities taken from follow on work to SUPERENERGY-2 done at ANL in the 1980s. DASSH today is an integral component of the Argonne Fast Reactor analysis suite for reactor design work. DASSH obtains the power distribution from a coupled neutron-gamma heating calculation in GAMSOR (including DIF3D) at each time point of a companion fuel cycle analysis calculation with REBUS. The domain in DASSH assumes a hexagonal grid typical for fast reactors with much of the geometry information taken from the DIF3D model. DASSH assumes the assemblies that are loaded into each grid position are ducted to control the coolant flow. The user can alternatively provide their own geometry and power profile instead of inheriting it from DIF3D. Considerable detail is given on the subchannel formulation of DASSH in this document. Much of the formulation and design of the code builds upon research done by previous authors with little new investigation. Thus the decisions made in developing the subchannel model used in DASSH have their origins over 50 years ago. Much of the heat transfer methodology in DASSH is built upon correlations for both the coolant mixing and heat transfer coefficients for pins and ducts. DASSH is thus not a rigorous treatment of a given problem, but a rapid assessment of the temperature field that has known limitations with respect to an experimental measurement or CFD calculation. The DASSH input and output are detailed along with usage of the software. The DASSH output provides tables of evaluated material properties and key coolant and pin temperature results. DASSH can create Python scripts that generate domain summary pictures. DASSH can also generate assembly temperature maps and VTK output files which allow the DASSH solution to be visualized. As the primary purpose of the DASSH software is to compute the coolant and fuel pin temperature distribution for a given model of a reactor, much of the output focus is giving the user quick summary tables needed to assess the performance of a given orifice flow specification. The present version of DASSH has a crude orifice search capability and a sufficient orifice flow search capability. The flow search tries to meet user specified constraints for 1) peak 2-sigma clad temperature, 2) peak coolant temperature, and 3) desired bulk outlet temperature. This document serves as the manual for the Fortran based DASSH software that was developed to replace the Python version of DASSH developed as part of the VTR program.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Perfectly Matched Layers and Characteristic Boundaries in Lattice Boltzmann: Accuracy vs Cost

Artificial boundary conditions (BCs) play a ubiquitous role in numerical simulations of transport phenomena in several diverse fields, such as fluid dynamics, electromagnetism, acoustics, geophysics, and many more. They are essential for accurately capturing the behavior of physical systems whenever the simulation domain is truncated for computational efficiency purposes. Ideally, an artificial BC would allow relevant information to enter or leave the computational domain without introducing artifacts or unphysical effects. Boundary conditions designed to control spurious wave reflections are referred to as nonreflective boundary conditions (NRBCs). Another approach is given by the perfectly matched layers (PMLs), in which the computational domain is extended with multiple dampening layers, where outgoing waves are absorbed exponentially in time. Here, in this work, the definition of PML is revised in the context of the lattice Boltzmann method. The impact of adopting different types of BCs at the edge of the dampening zone is evaluated and compared, in terms of both accuracy and computational costs. It is shown that for sufficiently large buffer zones, PMLs allow stable and accurate simulations even when using a simple zeroth-order extrapolation BC. Moreover, employing PMLs in combination with NRBCs potentially offers significant gains in accuracy at a modest computational overhead, provided the parameters of the BC are properly tuned to match the properties of the underlying fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Lattice Boltzmann Method for Predicting Porous Transport Layer Performance During Electrolysis

Electrolysis, the splitting of water into oxygen and hydrogen using electricity, is a sustainable way to produce green hydrogen for energy storage. In polymer electrolyte membrane (PEM) water electrolysis, water is brought into contact with charged catalyst layers and electrochemically separated into oxygen and hydrogen. The hydrogen product formed at the cathode is carried through the catalyst layer for eventual collection, while the oxygen by-product formed at the anode is removed from the surface via a multiphase interaction with circulating water and a solid porous transport layer (PTL). The design of this PTL aids in the detachment and advection of the oxygen by-product and thereby plays a role in the overall efficacy of the catalyst. In this presentation, we present our initial results modeling this multiphase system using a single-component, multiphase lattice Boltzmann method. We use the Shan-Chen model describing inter-particle forces to capture both the cohesion of the water (liquid) and oxygen (gas) phases and their interaction with the PTL (solid) (Shan and Chen, 1993). We use a Carnahan-Starling equation of state to model the effective density governing these inter-particle interactions which allows us to model this relatively high density ratio system (Carnahan and Starling, 1969). With these simulations, we show that the geometry and heterogeneity of the PTL geometry plays a large role in its ability to move oxygen away from the catalyst layer and the resulting bubble structures that are formed within the PTL. The current work demonstrates these effects using synthesized PTL geometries and 2D physics, which will be extended to experimentally-imaged PTL sections and 3D algorithms in the near future.

Boltzmann↗
DOE OSTI2022

Direct strain correlations at the single-atom level in three-dimensional core-shell interface structures

Abstract Nanomaterials with core-shell architectures are prominent examples of strain-engineered materials. The lattice mismatch between the core and shell materials can cause strong interface strain, which affects the surface structures. Therefore, surface functional properties such as catalytic activities can be designed by fine-tuning the misfit strain at the interface. To precisely control the core-shell effect, it is essential to understand how the surface and interface strains are related at the atomic scale. Here, we elucidate the surface-interface strain relations by determining the full 3D atomic structure of Pd@Pt core-shell nanoparticles at the single-atom level via atomic electron tomography. Full 3D displacement fields and strain profiles of core-shell nanoparticles were obtained, which revealed a direct correlation between the surface and interface strain. The strain distributions show a strong shape-dependent anisotropy, whose nature was further corroborated by molecular statics simulations. From the observed surface strains, the surface oxygen reduction reaction activities were predicted. These findings give a deep understanding of structure-property relationships in strain-engineerable core-shell systems, which can lead to direct control over the resulting catalytic properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗