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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Revealing the Correlation between the Solvation Structures and the Transport Properties of Water-in-Salt Electrolytes

Water-in-salt (WIS) electrolytes containing 21 m lithium bis(trifluoromethane sulfonyl)imide (LiTFSI) have been considered as a safe and environment-friendly alternative to common organic electrolytes used in lithium-ion batteries. However, the relation between the solvation structures and transport properties of these materials remains elusive. Here, for this paper, we performed small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), and X-ray pair distribution function (PDF) measurements of LiTFSI aqueous solutions at a wide range of concentrations. Combined with molecular dynamics simulations, the detailed solvation structures from long to short length scale were resolved. We found that the TFSI– solvation structures consist of TFSI– solvated structures and TFSI– networks; the former corresponds to solvent separated ion pairs, while the latter corresponds to contact ion pairs and cation–anion aggregates. In addition, we found that the relaxation time in the q range associated with the anion network structure exhibits the same concentration dependence as the viscosity. By combining the results from the experiments and simulations, this study revealed a correlation between the solvation structures of LiTFSI and the transport properties of the solutions, which is critical to understand the relation between the transport properties and the dynamics of the ions for imide-based lithium-ion salt aqueous electrolytes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Studies on the structure and the magnetic properties of high-entropy spinel oxide (MgMnFeCoNi)Al 2 O 4

The study of high-entropy materials has attracted enormous interest since they could show new functional properties that are not observed in their related parent phases. Here, we report single crystal growth, structure, thermal transport, and magnetic property studies on a novel high-entropy oxide with the spinel structure (MgMnFeCoNi)Al 2 O 4 . We have successfully grown high-quality single crystals of this high-entropy oxide using the optical floating zone growth technique for the first time. The sample was confirmed to be a phase pure high-entropy oxide using x-ray diffraction and energy-dispersive spectroscopy. Through magnetization measurements, we found (MgMnFeCoNi)Al 2 O 4 exhibits a cluster spin glass state, though the parent phases show either antiferromagnetic ordering or spin glass states. Furthermore, we also found that (MgMnFeCoNi)Al 2 O 4 has much greater thermal expansion than its CoAl 2 O 4 parent compound using high resolution neutron Larmor diffraction. We further investigated the structure of this high-entropy material via Raman spectroscopy and extended x-ray absorption fine structure spectroscopy (EXAFS) measurements. From Raman spectroscopy measurements, we observed (MgMnFeCoNi)Al 2 O 4 to display a combination of the active Raman modes in its parent compounds with the modes shifted and significantly broadened. This result, together with the varying bond lengths probed by EXAFS, reveals severe local lattice distortions in this high-entropy phase. Additionally, we found a substantial decrease in thermal conductivity and suppression of the low temperature thermal conductivity peak in (MgMnFeCoNi)Al 2 O 4 , consistent with the increased lattice defects and strain. These findings advance the understanding of the dependence of thermal expansion and transport on the lattice distortions in high-entropy materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Interpretation of wide-angle x-ray diffraction patterns from mesophase pitch-based carbon fibers – a simulation and experimental study

Carbon fiber is a critical material in a wide range of industries, where it is highly valued for its high specific strength/stiffness, excellent wear resistance, efficient electrical and thermal transport properties, chemical resistance, and low coefficient of thermal expansion. The properties of a specific carbon fiber are closely tied to its structural characteristics at all length scales. Here, in this work, we applied wide-angle x-ray diffraction to a set of heat-treated mesophase pitch-based carbon fibers, with the goal of elucidating the crystalline structures as a function of fiber orientation. To assist with analysis and interpretation of the experimental data, we employed diffraction pattern simulations using the scalar and vector forms of the Debye scattering equation to determine the influence of basal plane orientation, crystalline ordering (turbostratic-graphitic), and basal plane asymmetry on the diffraction patterns. The results presented here suggest that growth of the transverse crystallites in mesophase pitch-based carbon fiber is fixed until graphitization temperatures are reached. The work completed here provides a framework for the analysis of carbon fiber and other oriented carbon-based materials via diffraction.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Reification of latent microstructures: On supervised unsupervised and semi-supervised deep learning applications for microstructures in materials informatics

Machine learning (ML), including deep learning (DL), has become increasingly popular in the last few years due to its continually outstanding performance. In this context, we apply machine learning techniques to "learn" the microstructure using both supervised and unsupervised DL techniques. In particular, we focus (1) on the localization problem bridging (micro)structure (localized) property using supervised DL and (2) on the microstructure reconstruction problem in latent space using unsupervised DL. The goal of supervised and semi-supervised DL is to replace crystal plasticity finite element model (CPFEM) that maps from (micro)structure (localized) property, and implicitly the (micro)structure (homogenized) property relationships, while the goal of unsupervised DL is (1) to represent high-dimensional microstructure images in a non-linear low-dimensional manifold, and (2) to discover a way to interpolate microstructures via latent space associating with latent microstructure variables. At the heart of this report is the applications of several common DL architectures, including convolutional neural networks (CNN), autoencoder (AE), and generative adversarial network (GAN), to multiple microstructure datasets, and the quest of neural architecture search for optimal DL architectures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Connecting radiation-driven changes in structural, thermal, and mechanical properties in several medical device polymers

Stemming from security threats and shortages in supply, a recent push has emerged to develop alternatives to radioisotope Cobalt-60 gamma radiation for sterilization of polymeric medical products, including electron beam (e-beam) and X-ray machine-based sources. However, before large-scale implementation, the effects of these non-isotope-based methods must be thoroughly investigated from several perspectives, involving their potential detrimental effects on the structural, thermal, and mechanical properties of polymers in medical devices. This paper investigates such effects in commonly used medical device polymers, including polypropylene homopolymer (PPH), polyolefin elastomer (POE), low-density polyethylene (LDPE), acrylonitrile butadiene styrene (ABS), and chlorobutyl rubber (CIIR). To connect radiation-driven changes in polymer structural and thermal properties and corresponding changes in mechanical properties, several characterization techniques were utilized, including gel permeation chromatography (GPC), Fourier transform infrared spectroscopy (FTIR), dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). We found that the tensile strength of X-ray irradiated PPH, as well as X-ray, e-beam, and gamma irradiated CIIR decreases due to chain scission, which is corroborated by GPC and DMA. The GPC results of LDPE suggest chain scission, but interestingly without a corresponding decline in tensile strength. By comparison, POE and ABS appear to undergo further crosslinking with increasing irradiation dose, which generally strengthens them. Importantly, in the vast majority of the cases, there were small to no changes in properties upon changing radiation technologies (at a given dose), i.e., no radiation source dependence. However, in a few specific cases, radiation method dependencies did arise, for instance, in terms of the molecular weight of PPH being significantly increased upon X-ray irradiation, while the melting temperature, glass transition temperature, and elongation at break reduced compared to gamma. Overall, this study provides valuable insight into radiation-driven chemical and structural changes in polymers that produce changes in physical and functional properties.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Structural, electronic, and magnetic properties of nearly ideal J eff = 1/2 iridium halides

Heavy transition metal magnets with J e f f = 1 2 electronic ground states have attracted recent interest due to their penchant for hosting new classes of quantum spin liquids and superconductors. Unfortunately, model systems with ideal J e f f = 1 2 states are scarce due to the importance of noncubic local distortions in most candidate materials. In this work, we identify a family of iridium halide systems [i.e., K 2 Ir Cl 6 , K 2 Ir Br 6 , ( NH 4 ) 2 Ir Cl 6 , and Na 2 Ir Cl 6 · 6 ( H 2 O ) ] with Ir 4 + electronic ground states exhibiting extremely small deviations from the ideal J e f f = 1 2 limit. We also find ordered magnetic ground states for the three anhydrous systems, with single-crystal neutron diffraction on K 2 Ir Br 6 revealing type-I antiferromagnetism. This spin configuration is consistent with expectations for significant Kitaev exchange in a face-centered-cubic magnet. This work establishes that incorporating isolated Ir X 6 octahedra in materials, where X is a halogen ion with a low electronegativity, is an effective design principle for realizing unprecedented proximity to the pure J e f f = 1 2 state. However, at the same time, we highlight undeniable deviations from this ideal state, even in clean materials with ideal Ir X 6 octahedra as inferred from the global cubic crystal structures.

36 MATERIALS SCIENCE↗
DOE OSTI2026

GBOpt: Grain boundary structure optimization using Monte Carlo and evolutionary algorithms

Polycrystalline materials are made of many small crystals separated by grain boundaries (GBs), whose atomic structure strongly influences material properties. Because the structure of a GB determines its properties, the optimal structure must be known in order to determine those impacts. There are many ways of placing atoms in the GB region, but the optimal structure is defined as the one that gives the lowest value of a target property (typically energy). GB structure optimization has been successfully demonstrated using stochastic and evolutionary methods, but no reusable, community-maintained open-source workflow has been developed. GBOpt (Grain Boundary Optimization) is an open-source Python package that creates that workflow, where we have presently implemented two approaches: Markov Chain Monte Carlo, and genetic algorithm based on elite selection. We demonstrate this capability by successfully reproducing the known optimal structures of a specific GB in two materials, and point interested readers to the GitHub repository for additional examples, including optimization for different properties. Both of the implemented approaches recovered the known structures, with the genetic algorithm approach finding the optimal structure faster on average.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Defects and anomalies in powder bed fusion metal additive manufacturing

Metal additive manufacturing is a disruptive technology that is revolutionizing the manufacturing industry. Despite its unrivaled capability for directly fabricating metal parts with complex geometries, the wide realization of the technology is currently limited by microstructural defects and anomalies, which could significantly degrade the structural integrity and service performance of the product. Accurate detection, characterization, and prediction of these defects and anomalies have an important and immediate impact in manufacturing fully-dense and defect-free builds. As such, this review seeks to elucidate common defects/anomalies and their formation mechanisms in powder bed fusion additive manufacturing processes. They could arise from raw materials, processing conditions, and post-processing. While defects/anomalies in laser welding have been studied extensively, their formation and evolution remain unclear. Additionally, the existence of powder in powder bed fusion techniques may generate new types of defects, e.g., porosity transferring from powder to builds. Practical strategies to mitigate defects are also addressed through fundamental understanding of their formation. Such explorations enable the validation and calibration of models and ease the process qualification without costly trial-and-error experimentation.

42 ENGINEERING↗
DOE OSTI2023

First Principles Modeling of Cluster-Based Solid Electrolytes (Final Technical Report)

Given the trend of global warming and the urgent need to transition from fossil fuels to green energy, lithium-ion batteries continue to be an integral part of our lives. Design, development, and understanding of novel solid-state electrolyte materials play the key role for achieving next-generation all-solid-state batteries with high energy and great safety. The current modeling schemes to develop advanced solid electrolytes are focusing on materials in which the building blocks are individual atoms. Our theoretical approach is a paradigm shift in solid-state electrolyte design. Instead of atoms, we focus on clusters as the building blocks and model these solid electrolytes and their interfaces with electrodes, especially Li-metal anode, for their successful implementation in solid-state batteries. The advantage of using the cluster ions to replace elemental ions is that the size, composition, and shape of the former can be tailored to achieve higher ionic conductivity at room temperature, electrochemical stability, and charge transfer across solid-solid interfaces than conventional materials. Specifically, the project includes: (1) Developing cluster-based solid electrolytes, where the halogen components are replaced by cluster ions that mimic the chemistry of halogens but are characterized by additional degrees of freedom, including the size, shape, composition, and motional dynamics under excitation. (2) Providing a fundamental understanding of the ion conduction mechanism in the developed cluster-based solid electrolytes; (3) Modeling the interfacial properties (i.e., structural, chemical, and transport properties) between the cluster-based solid electrolytes and electrodes at the atomic level. For the cluster-based solid electrolytes incompatible with the Li-metal anode or cathode materials, potential candidates for interfacial coatings are identified and studied. (4) Providing a theoretical framework towards optimizing critical parameters of the solid-state electrolytes that guides experimentalists to attain desired cathode-electrode interface for cluster-based solid-state electrolytes.

25 ENERGY STORAGE↗
DOE OSTI2022

Compressive properties of silicone Bouligand structures

Abstract This article presents an examination of silicone, Bouligand lattices in compression. Appearing frequently in biological organisms and manufacturing design, Bouligand structures comprise layers of parallel strands or fibers oriented in a helical fashion. They can exhibit exceptional fracture resistance when composed of rigid or composite materials. The behavior of elastomeric Bouligand structures, however, is less well understood. Additively manufactured (AM) elastomeric lattices have applications in stress mitigation, medical devices, and soft robotics. This article demonstrates that Bouligand structures are a useful addition to the design space of AM elastomers. By adjusting the layer-rotation parameters, lattice stress can increase by more than 300% without altering the porosity. Additionally, we introduce path length metrics that help explain the observed relationship between layer rotation and compression response. Impact statement Additive manufacturing (AM) continues to push the boundary of manufacturable structures and enhance the ability to robustly design for specific properties and behaviors. The more we understand the design space of a novel AM microstructure, the greater its application range. In this article, we describe the mechanical behavior of helicoidal, elastomeric lattices and introduce path length metrics to help explain their stress response. We show that these structures can exhibit a large range of mechanical behaviors in compression, making them well suited for applications such as stress mitigation and impact absorption. Additionally, the path length metrics could become useful design tools and may be applicable to a larger set of cellular structures. These findings expand our ability to rapidly design materials with highly specific and customizable properties to meet the needs of modern engineering challenges. Graphical abstract

Van Meerbeek, I. M. (ORCID:000000021258132X)↗
DOE OSTI2020

Correlating structural, electronic, and magnetic properties of epitaxial VSe 2 thin films

The electronic and magnetic properties of transition metal dichalcogenides are known to be extremely sensitive to their structure. In this paper we study the effect of structure on the electronic and magnetic properties of mono- and bilayer VSe 2 films grown using molecular beam epitaxy. VSe 2 has recently attracted much attention due to reports of emergent ferromagnetism in the two-dimensional (2D) limit. To understand this compound, high-quality 1$\textit{T}$ and distorted 1$\textit{T}$ films were grown at temperatures of 200 °C and 450 °C, respectively, and studied using 4 K scanning tunneling microscopy and spectroscopy. The measured density of states and the charge density wave (CDW) patterns were compared to band structure and phonon dispersion calculations. Films in the 1$\textit{T}$ phase reveal different CDW patterns in the first layer compared to the second. Interestingly, we find the second layer of the 1$\textit{T}$ film shows a CDW pattern with 4$\textit{a}$ × 4$\textit{a}$ periodicity which is the 2D version of the bulk CDW observed in this compound. We report our phonon dispersion calculations confirm the presence of a soft phonon at the correct wave vector that leads to this CDW. In contrast, the first layer of distorted 1$\textit{T}$ phase films shows a strong stripe feature with varying periodicities, while the second layer displays no observable CDW pattern. Finally, we find that the monolayer 1$\textit{T}$ VSe 2 film is weakly ferromagnetic, with ~3.5 $μ_B$ per unit similar to previous reports.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Mirostructure Characterization of Friction Consolidated Copper-Nickel using a Machine Learning Approach: Developing Process to Microstructure Associations

Friction consolidation (FC) is a solid phase processing approach where discrete material forms such as powders, chips, nuggets, etc. are densified via shear deformation. The precursors are placed in a billet container and brought in contact with a rotating tool that applying the desirable amount of normal force. Under the combined action of the rotation and normal pressure, the discrete precursor is consolidated through porosity reduction and shear deformation. FC is increasingly being studied as an attractive approach to manufacturing fully dense parts from powder forms owing to its ability to mix, alloy and consolidate difficult-to-process precursors in minimal number of process steps. Material consolidation and deformation in shear consolidation processes have been studied extensively previously for different material combinations previously. However, despite the extensive research in this area, understanding of the mechanistic processes in pore consolidation, deformation-induced mixing and material solubility during FC is still evolving. Material development using solid phase processing approaches such as FC is often performed based on research experience/education, which can be biased. Conventional analysis and simulation tools in this area tend to be successful only when material thermodynamic pathways and microstructural evolution sequences resulting from processing are clearly defined or known. They are not as effective for emerging advanced manufacturing technologies where material evolution pathways are not well established. The ability to predict optimal process parameters based on material chemistry and bulk properties is essential to accelerate materials design and processing, as are an understanding of the relevant structure-processing-property relationships. These structure-processing-property-performance relationships are at the core of materials science research. Microstructure characterization provides the link to these four core areas, often through visualizing material microstructure using imaging techniques. However, linking microstructure image data (i.e., micrographs) to variables of interest (e.g., processing parameters, material chemistry) in a reproducible, generalizable, and quantitative manner is a significant challenge. Typically, quantitatively linking image data to processing history relies on significant domain knowledge and manual or subject matter expert (SME)-heuristic based image analysis. Such an approach to image analysis has the potential to be biased, inefficient, and difficult to replicate.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe 2

Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe 2 , with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe 2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. Here, in this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.

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

Role of Fe Doping on Local Structure and Electrical and Magnetic Properties of PbTiO 3

In this work, the local structure and multiferroic properties of iron-doped lead titanate (PbTi 1-x Fe x O 3-δ ) samples was investigated over the entire composition range (x = 0-1). Inherent polarization in PbTiO 3 decreases due to Fe 3+ incorporation up to the solubility limit (x similar to 0.3), although homogeneous doping persists only up to x = 0.1. Ti prefers highly distorted oxygen octahedra for any x value, while Fe prefers more symmetric O-deficient polyhedra (Fe-O n ). The charge compensating oxygen vacancies induce local tilting of the Fe-O n polyhedra beyond a critical x value (x ≥ 0.2), promoting magnetic interaction between two adjacent Fe atoms. The strain induced by local heterogeneity could act as a coupling force between magnetic and ferroelectric properties. Fe-rich clusters evolve into ferromagnetic PbFe 12 O 19 with increased Fe doping. PbTi 1-x Fe x O 3-δ (x ≥ 0.3) samples therefore have separate origins for the ferroelectric (PbTi 1-x Fe x O 3-δ ) and magnetic (PbFe 12 O 19 ) phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Structural, optical, and thermal properties of BN thin films grown on diamond via pulsed laser deposition

Heterostructures based on ultrawide-bandgap (UWBG) semiconductors (bandgap > 4.0 eV), such as BN and diamond, hold significant importance for the development of high-power electronics in the next generation. However, achieving in situ heteroepitaxy of BN/diamond or vice versa remains exceptionally challenging due to the complex growth kinetics involved. In this work, we grew BN thin film on (100) single-crystal diamonds using pulsed laser deposition and investigated its structural, magnetic, optical, and thermal properties. Throughout this study, the structural analyses confirmed the growth of BN films, which exhibited diamagnetic behavior at room temperature. Notably, the film demonstrated anisotropic refractive index characteristics within the visible-to-near-infrared wavelength range. The room-temperature cross-plane thermal conductivity of BN is 1.53 ± 0.77 W/mK, while the thermal conductance of the BN/diamond interface is 20 ± 2 MW/m 2 ⁢K. These findings have significant implications for a range of device applications based on UWBG BN/diamond heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Ab initio investigation of elastic properties of dilute Cu alloys for high-gradient accelerating structures

The elastic properties and solid solution strengthening of several Cu alloys that may be promising for high gradient applications were studied using ab initio calculations based on density functional theory. Specifically, the temperature and solute concentration dependence of elastic properties including bulk and shear moduli, thermal expansion coefficient, and heat capacity of these alloys were calculated. We found that the bulk and shear moduli are linearly dependent on the solute concentration in the dilute regime and change significantly for different Cu alloys. The thermal expansion coefficient and heat capacity are comparatively less sensitive to solute concentrations. Solid solution strengthening is observed to be linearly correlated with the change of lattice parameter of Cu. This work provides an in-depth understanding of the elastic properties of Cu alloys, which is key for predicting their performance at high gradient in normal conducting accelerating structures.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Structural Diversity and Magnetic Properties of Hybrid Ruthenium Halide Perovskites and Related Compounds

Abstract There has been a great deal of recent interest in extended compounds containing Ru 3+ and Ru 4+ in light of their range of unusual physical properties. Many of these properties are displayed in compounds with the perovskite and related structures. Here we report an array of structurally diverse hybrid ruthenium halide perovskites and related compounds: MA 2 Ru X 6 ( X =Cl or Br), MA 2 M RuX 6 ( M =Na, K or Ag; X =Cl or Br) and MA 3 Ru 2 X 9 ( X =Br) based upon the use of methylammonium (MA=CH 3 NH 3 + ) on the perovskite A site. The compounds MA 2 Ru X 6 with Ru 4+ crystallize in the trigonal space group and can be described as vacancy‐ordered double‐perovskites. The ordered compounds MA 2 M Ru X 6 with M + and Ru 3+ crystallize in a structure related to BaNiO 3 with alternating MX 6 and Ru X 6 face‐shared octahedra forming linear chains in the trigonal space group. The compound MA 3 Ru 2 Br 9 crystallizes in the orthorhombic Cmcm space group and displays pairs of face‐sharing octahedra forming isolated Ru 2 Br 9 moieties with very short Ru–Ru contacts of 2.789 Å. The structural details, including the role of hydrogen bonding and dimensionality, as well as the optical and magnetic properties of these compounds are described. The magnetic behavior of all three classes of compounds is influenced by spin–orbit coupling and their temperature‐dependent behavior has been compared with the predictions of the appropriate Kotani models.

Vishnoi, Pratap↗
DOE OSTI2020

Structural Diversity and Magnetic Properties of Hybrid Ruthenium Halide Perovskites and Related Compounds

There has been a great deal of recent interest in extended compounds containing Ru 3+ and Ru 4+ in light of their range of unusual physical properties. Many of these properties are displayed in compounds with the perovskite and related structures. Here we report an array of structurally diverse hybrid ruthenium halide perovskites and related compounds: MA 2 RuX 6 (X=Cl or Br), MA 2 MRuX 6 (M=Na, K or Ag; X=Cl or Br) and MA 3 Ru 2 X 9 (X=Br) based upon the use of methylammonium (MA=CH 3 NH 3 + ) on the perovskite A site. The compounds MA 2 RuX 6 with Ru 4+ crystallize in the trigonal space group R3¯m and can be described as vacancy-ordered double-perovskites. The ordered compounds MA 2 MRuX 6 with M + and Ru 3+ crystallize in a structure related to BaNiO 3 with alternating MX 6 and RuX 6 face-shared octahedra forming linear chains in the trigonal P3¯m space group. The compound MA 3 Ru 2 Br 9 crystallizes in the orthorhombic Cmcm space group and displays pairs of face-sharing octahedra forming isolated Ru 2 Br 9 moieties with very short Ru–Ru contacts of 2.789 Å. The structural details, including the role of hydrogen bonding and dimensionality, as well as the optical and magnetic properties of these compounds are described. The magnetic behavior of all three classes of compounds is influenced by spin–orbit coupling and their temperature-dependent behavior has been compared with the predictions of the appropriate Kotani models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗