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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Improving Ductility of Hydride Embrittled Zirconium (Final Report)

One of the main limiting factors on the lifetimes of nuclear fuel rod claddings is the formation of hydrides and associated detrimental effects on mechanical properties. In this study, we examined the behavior of hydrides in zirconium and zircaloy-4 after tensile stress is applied to determine whether the more ductile γ-ZrH phase was stabilized by the mechanical stress. We did not find a significant increase in the ratio of γ-ZrH phase to δ-ZrH1.5 phases after tensile stress is applied in previously hydrided metals. Previous reports indicate that this stabilization does occur when zircaloy is stressed and hydrided simultaneously, indicating that the formation of the γ-ZrH phase may reverse upon relaxation or may require the stress in-situ during the hydriding process to form in significant quantities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Uptake and Binding of At‐211 Into K‐ and Cs‐Derivatives of Alpha‐Zirconium Phosphate Nanoplatelets for Use as a Targeted Alpha Therapy Delivery Platform

The ion exchange behavior of K- and Cs-derivatives of α-zirconium phosphate, A-ZrP, with the targeted alpha therapy (TAT) radionuclide 211 At, as At + and AtO + , has been investigated. The K-ZrP shows strong affinity for both At+ and AtO + , ≥99% uptake. The affinity to Cs-ZrP was less pronounced, 87%–94% uptake, favoring At + . The binding strength was tested against several leaching solutions, including carbonate, phosphate buffered saline (PBS), 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) buffers, and ethylenediaminetetraacetic acid (EDTA) solutions at various concentrations (0.1–10 mM). K-ZrP retained 211 At in all buffer and EDTA solutions up to 1 mM (<0.5% leaching). The Cs-ZrP showed no leaching of At + , while AtO + leached (1%–3%) in the carbonate and HEPES buffers, along with all of the EDTA solutions, with complete retention only in the PBS buffer. In all cases, when the EDTA concentration reached 10 mM, 211 At leaching was observed. Once incorporated into the ZrP nanoplatelets, significant shielding of the α-particles was observed, not only attenuating the intensity of the emission but also reducing the energy of the α-particles themselves exiting the nanoplatelets. These properties provide the basis for K-ZrP, and to a lesser extent, Cs-ZrP to be further considered as potentially promising candidates for a delivery mechanism of 211 At for application in TAT.

astatine-211↗
DOE OSTI2017

Nuclear Fuel Based on Uranium-Zirconium Carbonitride

The results of Investigations of the nitrogen and uranium pressure in the system U–Zr–C–N in the temperature range 1873–2073 K and the constructed section of the U–Zr–C–N phase diagram at 1873 K are presented. The behavior of the solid fission products in carbonitride fuel, the interaction of the fuel with a pyrolytic carbon coating, and the behavior of micro fuel elements based on such fuel during high temperature firing and in the presence of a temperature gradient are examined. The conditions for the preparation of fuel compositions of the type uranium carbonitride in a carbide-silicon matrix and some of its physicochemical and mechanical properties are determined. It is noted that there is promise in using fuel compositions and micro fuel elements based on uranium-zirconium carbonitride for high-temperature applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Behavior of Modified Zirconium-Alloy Fuel-Element Cladding Under Irradiation

The first reactor tests and post-reactor studies of fuel elements with cladding made from the zirconium alloys E-636M, E-635opt, and E-635M1, developed at VNIINM, have been conducted. The purpose of the studies was to search for alloys of the type E-635 that surpass the base alloy in terms of resistance to corrosion and hydration. The studies make it possible to recommend the alloys E-635M and E-635opt for use as cladding of the fuel elements in extended-life cores.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Microwave Absorption Properties of Cobalt-Zirconium Doped Strontium Hexaferrites in Ku-Frequency Band

In this article, microwave electromagnetic properties of doped strontium hexaferrites have been investigated in Ku microwave frequency band (12.4–18 GHz), along with their performance as microwave absorbing materials. Vector network analyzer has been used for characterization of cobalt-zirconium substituted strontium hexaferrites Sr(CoZr){sub x}Fe{sub (12−2x)}O{sub 19} (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0), synthesized using sol-gel method. Real parts of permittivity and permeability have shown very small variations up to 16 GHz. There has been a dip in spectrum of real part of permittivity and a peak in spectrum of real part of permeability at the same frequency in 16–18 GHz range for every composition. Regarding the electromagnetic wave absorption, all the six prepared compositions have potential (≥90% absorption) for usage in suppressing electromagnetic pollution. The composition with x = 1.0 has achieved the highest −10 dB absorption bandwidth from 15 to 18 GHz frequency. The realization of absorbing materials with maximum absorption is related to the phenomenon of impedance matching and high electromagnetic losses. The correlation of absorption peaks with attenuation constant, wave impedance and complex thickness has also been studied.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Alpha – omega and omega – alpha phase transformations in zirconium under hydrostatic pressure: A 3D mesoscale study

Here, a three dimensional (3D) elastoplastic phase-field model is developed for modeling the hydrostatic pressure-induced alpha – omega phase transformation and the reverse phase transformation, i.e. omega – alpha, in zirconium (Zr). Plastic deformation and strain hardening of the material are also considered in the model. The microstructure evolution during both phase transformations is studied. The transformation start pressures at different temperatures are predicted and are plotted as a phase diagram. The effect of phase transformations on the mechanical properties of the material is also studied. The input data corresponding to pure Zr are acquired from experimental studies as well as by using the CALPHAD method. Our simulations show that three different omega variants form as laths. On release of pressure, reverse phase transformation initiates at lath boundaries. We observe that both phase transformations are martensitic in nature and also occur at the same pressure, i.e. little hysteresis. The transformation start pressures and the kinetics of the transformation predicted by our model are in good agreement with experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2019

A phase-field model for hydride formation in polycrystalline metals: Application to δ-hydride in zirconium alloys

We report a phase-field model for simulating metal hydride formation involving large volume expansion in single- and polycrystals. As an example, we consider δ-hydride formation in α-zirconium (Zr), which involves both displacive crystallographic structural change and hydrogen diffusion process. Thermodynamic Gibbs energy functions are extracted from the available thermodynamic database based on the sublattice model for the interstitial solid solutions. Solute-grain boundary interactions and inhomogeneous elasticity of polycrystals are taken into consideration within the context of diffuse-interface description. The stress-free transformation strains of multiple variants for hcp -Zr (α) to fcc -hydride (δ) transformation are derived based on the well-established orientation relationship between the α and δ phases as well as the corresponding temperature-dependent lattice parameters. In particular, to account for the large volume expansion, we introduced the mixed interfacial coherency concept between those phases—basal planes are coherent and prismatic planes are semi-coherent in computing the strain energy contribution to the thermodynamics. We analyzed the morphological characteristics of hydrides involving multiple structural variants and their interactions with grain boundaries. Moreover, our simulation study allows for the exploration of the possible hydride re-orientation mechanisms when precipitating under applied tensile load, taking into account the variation in the interfacial coherency between hydrides and matrix, their elastic interactions with the applied stress, as well as their morphology-dependent interactions with grain boundaries. Here, the phase-field model presented here is generally applicable to hydride formation in any binary metal–hydrogen systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

On the efficacy of post-build thermomechanical treatments to improve properties of Zirconium fabricated using ultrasonic additive manufacturing

Here, hot-isostatic pressing has been applied to Zirconium plate fabricated using the ultrasonic additive manufacturing (UAM) technique to enhance interfacial bond quality. Specimens heated to 800 C for 1 h at 100 MPa pressure showed grain growth across many prior foil-to-foil interfaces, thereby increasing foil adhesion. In addition to the material softening induced by a loss of Hall-Petch strengthening, premature failure of specimens loaded parallel to the build direction was observed. Premature specimen failure was attributed to the local delamination at prior foil-to-foil boundaries where grain growth was pinned by Ti impurities introduced during the UAM process via the interaction between a Ti-alloy buffer foil and the welded Zr-foils underneath. In addition, the presence of Ti along select foil interfaces resulted in the nucleation and growth of secondary (Zr,Ti)(Fe,Cr) laves phases during higher-temperature thermomechanical processing. Using a combination of micro-scale X-ray computed tomography, fractography, and in-situ digital image correlation, the effect of defects along prior foil-to-foil boundaries was revealed as delamination-assisted plasticity accelerated specimen failure in preferred tensile orientations. These findings underscore the importance of impurity control when optimizing weld quality of higher-strength material systems using ultrasonic welding.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Zirconium-diboride silicon-carbide composites: A review

Zirconium diboride (ZrB 2 ) and silicon carbide (SiC) composites have long been of interest since it was observed that ZrB 2 improved the thermal shock resistance of SiC. However, processing of these materials can be difficult due to high and different sintering temperatures and differences in the thermodynamic stability of each material. ZrB 2 –SiC composites have been processed in a variety of ways including hot-pressing, spark-plasma sintering, reactive melt infiltration, pack cementation, chemical vapor deposition, chemical vapor infiltration, stereolithography, direct ink writing, selective laser sintering, electron beam melting, and binder jet additive manufacturing. Each manufacturing method has its own pros and cons. This review serves to summarize more than 60 years of research and provide a coherent resource for the variety of methods and advancements in development of ZrB 2 –SiC composites.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Exploring laser-material interactions of zirconium carbide under additive manufacturing conditions

Zirconium carbide (ZrC) is an ultra-high temperature ceramic with a melting temperature above 3000°C and a broad range of high temperature applications. Given the high melting and sintering temperatures of pure ZrC, producing near-net shape and fully dense parts remains challenging with conventional techniques. In this study, we investigate the fundamental laser-material interactions of ZrC under laser powder bed fusion (LPBF) additive manufacturing (AM) conditions. Normalized enthalpy, a scaling law term that is used in welding and AM literature for detailing laser-material interactions in metallic alloys, was calculated to determine the predictive capabilities of melt pool features in ZrC. Further, the melt pool quality of laser irradiated ZrC was used to compare LPBF relevant laser parameter combinations of laser power, scan speed, and beam diameter. Laser build parameters that resulted in desirable melt pool morphologies were applied to the fabrication of ZrC coupons using LPBF AM. A custom LPBF system was used to determine hatch spacing and layer height parameters that resulted in a fabricated sample with a density of 85% as measured by Archimedes and a Vicker's microhardness of 20.9 ± 1.9 GPa. This investigation reveals the laser-material interactions of ZrC under AM relevant conditions and is the first step towards LPBF fabrication of ZrC parts.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Combustion in the ZrF 4 -Mg-Si and ZrF 4 -Al-Si systems for preparation of zirconium silicides

The exothermic reactions in the ZrF 4 –Mg-Si and ZrF 4 -Al-Si systems are investigated by a fast temperature recording (thermocouple) technique, differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). A quenching method is used to arrest the combustion process and conduct a layer-by-layer analysis of the products by x-ray diffraction (XRD) and electron microscopy. Two seemingly similar reactive systems exhibited considerably different combustion characteristics, composition, and morphology. Based on these investigations, we propose and discuss phase formation mechanisms at the early stages for each system. Three different pathways involving the reaction of ZrF 4 with other reagents and the Mg 2 Si intermediate are identified to occur in the ZrF 4 –Mg-Si system. Contrary to the complex mechanism in the ZrF 4 –Mg-Si system, the early stage of the combustion process for the ZrF 4 -Al-Si system involves the interaction of ZrF 4 with Al-Si eutectic melt. The exothermic reaction between reduced solid Zr and Si melt is the primary heat-generating step for both systems in spite of substantial differences in the early stages of the reactions. The silicon content in the reactive mixtures governs the phase composition of products. The ZrSi 2 phase, with a high growth rate, forms first on the Zr particle surfaces and then grows by a reactive diffusion mechanism. The ZrSi 2+ Zr reaction produces silicon-lean phases (e.g., ZrSi) when the silicon supply is limited. The combustion temperature also has a considerable influence on the phase compositions of the products. High combustion temperature in the ZrF 4 +2Mg+Si mixture enables the formation of multiphase products (α-ZrSi and β-ZrSi), whereas the relatively lower temperatures in the 3ZrF 4 +4Al+3Si mixture yields a single-phase α-ZrSi. As a result, lower combustion temperatures also make the ZrF 4 -Al-Si system more advantageous for the preparation of zirconium silicides.

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

First-principles studies of the concentration-dependent tritium diffusion in the zirconium hydrides with and without Sn impurity

We performed first-principles calculations to study the 3 H diffusion in the zirconium hydrides with or without Sn impurity. Our results show that the formation of Zr 3 H x becomes preferable as the 3 H concentration increases. Based on the most stable configurations of Zr 3 H x (x = 0.5, 1.0, 1.5, 2.0), we studied the interstitial 3 H diffusion with or without Sn impurity. The results show that the interstitial 3 H diffusion becomes less probable in the hydrides with a higher 3 H concentration. When introducing a substitutional Sn impurity, the diffusion barriers increase. Therefore, the substitutional Sn in the diffusion pathway hampers the 3 H diffusion in Zr hydrides.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Modeling of High-Temperature Corrosion of Zirconium Alloys Using the eXtended Finite Element Method (X-FEM)

Oxidation modeling in modern nuclear fuel performance codes is currently limited by the lack of coupling with mechanics, thus preventing proper description of how high-temperature oxidation impacts mechanical properties. This is mostly due to the fact that the finite difference formalism adopted in corrosion models is incompatible with the direct coupling with mechanics in the finite element modeling employed in modern nuclear fuel performance codes. In this study, a physically based zirconium alloy corrosion model called the Coupled-Current Charge Compensation (C4) model, which was initially developed for operating temperature conditions, has been updated to include high-temperature corrosion in order to provide additional critical information (e.g., oxygen concentration profile) under loss-of-coolant accident (LOCA) conditions—information lacking in existing empirical models. The C4 model was implemented in the MOOSE finite-element framework developed at Idaho National Laboratory, enabling it to be used in the BISON nuclear fuel performance code based on the MOOSE framework. To precisely track the different interfaces at a relatively low computational cost, the eXtended Finite Element Method (X-FEM) was applied in MOOSE. The model’s results were compared to those of existing empirical models as well as metallographic analysis of high-temperature oxidized Zircaloy-4 coupons. Oxygen diffusivities in the a and ß phases resulting from this comparison closely agree with those found in the literature. The C4 model implemented with X-FEM in MOOSE now has the capability to accurately predict oxide, oxygen-stabilized a, and prior ß phase layer growth kinetics under isothermal exposure at high temperature (1000–1500°C). Furthermore, in contrast with the empirical models, the C4 model accounts for the finite thickness of the fuel cladding. It can predict the oxygen concentration profile evolution through the whole cladding, enabling evaluation of the remaining ductile thickness—a crucial variable for modeling the mechanical behavior of the fuel cladding under LOCA. Furthermore, this implementation allows direct coupling with mechanics, at a low computing cost, using finite-element-based nuclear fuel performance codes such as BISON.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Microbeam synchrotron radiation diffraction and fluorescence of oxide layers formed on zirconium alloys at different corrosion temperatures

Autoclave corrosion tests of Zircaloy-4 were performed at temperatures ranging from 274°C to 427 °C to determine how the characteristics of the oxide layer changed with corrosion temperature. Corroded samples were prepared in cross-section and examined at the Advanced Photon Source using x-ray diffraction and fluorescence with sub-micron spatial resolution. These measurements provide high fidelity data for characterization of the oxide layer grown on zirconium alloys over a range of temperatures to better understand the fundamental mechanisms of corrosion. It was found that the size of the monoclinic oxide grains increases with distance from the metal-oxide interface, while the average grain size of the tetragonal oxide phase decreases. This is consistent with the continuous nucleation of a mixture of equiaxed tetragonal and monoclinic grains at the metal-oxide interface, of which only the monoclinic oxide grains that are properly aligned to minimize stresses grow into long columnar oxide grains. The tetragonal phase oxide grains transform to monoclinic oxide once a critical size is reached. While the monoclinic oxide grain size increases with corrosion temperature, the tetragonal phase grain size remains below a maximum value. Evolution of the tetragonal fraction, calculated with the Garvie-Nicholson formula, was observed, with local maxima seen just before transition and local minima seen at oxide locations corresponding to the oxide kinetic transition. No difference was observed in the tetragonal phase fraction in the oxide layers formed at different corrosion temperatures. Detailed fluorescence and diffraction mapping of one sample showed the evolution of the diffraction intensity over a short range in the oxide. In conclusion, this work provides a systematic study revealing fundamental characteristics of the microstructure of Zircaloy-4 oxide layers to further understanding of corrosion resistance of these materials.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Influence of boron isotope ratio on the thermal conductivity of uranium diboride (UB 2 ) and zirconium diboride (ZrB 2 )

Uranium diboride is being proposed as an accident tolerant fuel (either as a part of a composite or an 11 B enriched monolithic fuel pellet), while zirconium diboride is often selected as a burnable absorber in conjunction with uranium dioxide fuel pellets. It is therefore important to understand the thermal properties of these materials and examine methods in which they may be improved. The thermal conductivity of UB 2 and ZrB 2 is calculated through atomic scale modelling methods. Lastly, it was found that the boron-isotope ratio has a significant impact on the thermal conductivity of ZrB 2 , but is negligible for UB 2 due to the large electron-phonon scattering.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

In situ monitoring of microstructure evolution during thermal processing of uranium-zirconium alloys using laser-generated ultrasound

In this study, laser-generated ultrasound was used to monitor microstructure evolution during thermal processing of as-cast, polycrystalline binary uranium-zirconium metallic fuel alloys with compositions of U-20wt.%Zr (U-20Zr), U-50wt.%Zr (U-50Zr) and U-80wt.%Zr (U-80Zr). Ultrasonic waveforms were recorded during heating and cooling the samples from room temperature to >973 K and back. A phase transition temperature for all three compositions was estimated from the temperature at which an abrupt and rapid reduction in ultrasonic velocities was observed. Microstructural features on the length scale of tens of micrometers were inferred from the observation of scattering of ultrasonic waves by elastic heterogeneities above ~823 K in U-20Zr, while a hysteresis in the ultrasonic velocities of U-80Zr upon cooling was attributed to a partial retention of the high temperature phase following thermal annealing. The U-50Zr alloy exhibited a reversible viscoelastic response above 933 K, as evidenced by the observation of high frequency attenuation of the shear component of the waveforms at high temperature. Ultrasonic measurements were supplemented by in situ transmission electron microscopy (TEM). The TEM images revealed that the δ-U-Zr matrix in the three compositions underwent a spinodal decomposition above ~823 K into nanoscale regions. The ultrasonic measurements revealed larger, micron-scale structure evolution in the U-20Zr alloy at the same temperature. This large-scale structure is associated with heterogeneous regions having different Zr content. Our findings show the potential heating rate dependence of microstructural evolution in U-Zr alloys and highlight differences in the thermomechanical response and associated length scales during thermal annealing between single- and dual-phase compositions. These results demonstrate the utility of laser ultrasonics to rapidly and efficiently scan phase boundaries and monitor micrometer-scale structure evolution in metallic fuel alloys.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2012

Mild hydrothermal synthesis, crystal structure, photoluminescence properties and emission quantum yield of a new zirconium germanate with garnet-type structure

The mild hydrothermal synthesis, crystal structure, photoluminescence properties and emission quantum yield of a new sodium zirconium germanate are reported. This material and the method for its preparation represent for the first time a germanium garnet-type material synthesized at autogenous pressure and temperature at 230 Degree-Sign C. The crystal structure was determined by starting from the crystallographic parameters of a common garnet structure and it represents not only a new chemical combination of atoms but also combination of oxidation states in garnet structure. The framework consists of interconnected corner sharing GeO{sub 4} tetrahedra and ZrO{sub 6} octahedra which form small cavities that accommodate charge compensation Na{sup +} cations. In the course of synthesis the structure can be functionalized by in situ doping with different percentage of Eu{sup 3+} ions. This structural flexibility is used to explore the photoluminescent behavior of the active centers embedded in garnet-type host. The materials display the Eu{sup 3+5}D{sub 0}{yields}{sup 7}F{sub 0-4} transitions under excitation via intra-{sup 4}f{sub 6} excitation levels and through the O{sup 2-}{yields}Eu{sup 3+} ligand-to-metal charge transfer. A maximum {sup 5}D{sub 0} quantum efficiency and emission quantum yield values (ca. 0.28 and 0.04{+-}0.01, respectively) were found for the low Eu{sup 3+}-containing sample, suggesting the presence of concentration quenching effects at higher Eu{sup 3+}-content (5%). - Graphical abstract: Na{sub 3}Zr{sub 1.8}Ge{sub 3}O{sub 10}(OH){sub 2} prepared at mild hydrothermal conditions. Highlights: Black-Right-Pointing-Pointer New zirconogermanate with garnet-type structure. Black-Right-Pointing-Pointer Hydrothermal synthesis. Black-Right-Pointing-Pointer Crystal structure. Black-Right-Pointing-Pointer Photoluminescent properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Sulfuric acid functional zirconium (or aluminum) incorporated mesoporous MCM-48 solid acid catalysts for alkylation of phenol with tert-butyl alcohol

Several zirconium (or aluminum) incorporated mesoporous MCM-48 solid acid catalysts (SO{sub 4}{sup 2−}/Zr-MCM-48 and SO{sub 4}{sup 2−}/Al-MCM-48) were prepared by the impregnation method and their physicochemical properties were characterized by means of XRD, FT-IR, TEM, NH{sub 3}-TPD and N{sub 2} physical adsorption. Also, the catalytic activities of these solid acid catalysts were evaluated by the alkylation of phenol with tert-butyl alcohol. The effect of weight hour space velocity (WHSV), reaction time and reaction temperature on catalytic properties was also studied. The results show that the SO{sub 4}{sup 2−}/Zr-MCM-48 and SO{sub 4}{sup 2−}/Al-MCM-48 still have good mesoporous structure and long range ordering. Compared with the Zr (or Al)–MCM-48 samples, SO{sub 4}{sup 2−}/Zr-MCM-48 and SO{sub 4}{sup 2−}/Al-MCM-48 solid acid catalysts have strong acidity and exhibit high activities in alkylation reaction of phenol with tert-butyl alcohol. The SO{sub 4}{sup 2−}/Zr-MCM-48-25 (molar ratio of Si/Zr=0.04) catalyst was found to be the most promising and gave the highest phenol conversion among all catalysts. A maximum phenol conversion of 91.6% with 4-tert-butyl phenol (4-TBP) selectivity of 81.8% was achieved when the molar ratio of tert-butyl alcohol:phenol is 2:1, reaction time is 2 h, the WHSV is 2 h{sup −1} and the reaction temperature is 140 °C. - Highlights: • Sulfuric acid functional mesoporous solid acid catalysts were prepared via impregnation method. • The alkylation of phenol with tert-butyl alcohol was carried out over these solid acid catalysts. • The catalytic activity of SO{sub 4}{sup 2−}/Zr-MCM-48-25 catalyst is much higher than that of the others. • A maximum phenol conversion of 91.6% was achieved under optimum reaction conditions for SO{sub 4}{sup 2−}/Zr-MCM-48-25.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗