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DOE OSTI2022

AI-Enabled Robots for Automated Nondestructive Evaluation and Repair of Power Plant Boilers. Final Report

Boiler failure could cause loss of life and safety issues, cost hundreds of thousands of dollars in equipment repairs, property damage and production losses, and drive up the cost of electric power. Boiler maintenance is challenging and risky for inspectors working on scaffolding in confined hazardous spaces inside of a boiler and sometimes the space is hard to access. The operation is also time-consuming due to the large area of vertical structures for inspection and the tremendous effort needed for scaffolding. Recently, the use of robotics (e.g., drones and crawlers) in power plants for maintenance is growing rapidly. However, the existing robotics solutions show two notable technological gaps: no live repair capability, and no Artificial Intelligence (AI) for smart autonomy. The objective of this project is to develop an integrated autonomous robotic platform that is equipped with compact non-destructive evaluation (NDE) sensors to perform live inspection, operates onboard repair devices to perform live repair, and uses AI for intelligent data fusion and predictive analysis for automated and smart spatiotemporal inspection, analysis and repair of the furnace walls in coal-fired boilers. The approach to achieve the objective includes developing NDE sensors with signal processing techniques, designing and evaluating repair devices for robots based on fusion and solid-state technologies, and an autonomous robotic platform that can attach to and navigate on boiler furnace walls using magnetic drive tracks. The robot is also powered by AI to automate data gathering (e.g., 3D mapping and damage localization) and predictive analysis. This project has advanced the state-of-the-art by providing technological breakthroughs including compact NDE and repair tools for robots, AI capabilities for smart autonomy, and a robotic platform for automated boiler maintenance. This project has great potential to result in significant benefits including limiting or eliminating the need to send operators to assess difficult-to-access or hazardous areas, enabling automated live inspection and repair, avoiding time consuming scaffolding (especially for partial maintenance during unplanned outage), collecting comprehensive and well-organized data smartly, and avoiding or limiting the need for onsite or remote piloting technicians. The impacts can be tremendous in terms of the time and cost savings, reducing the risk for human operators, and increasing boiler reliability, usability, and efficiency. In addition, by developing the new technologies on the autonomous inspection and repair robot, by involving multiple undergraduate and graduate students working together with the faculty members on this project, and by generating knowledge and building up collaborations with industrial partners, this effort will significantly update the education capabilities, support long-term fundamental research, and maintain the leadership of Colorado School of Mines and Michigan State University in energy fields.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2022

Wide bandgap optical switch circuit breaker

A high-voltage switch is adapted for use as a medium-voltage direct current circuit breaker, which provides a low-cost, small-footprint device to mitigate system faults. In one example, a method for operating a wideband optical device includes illuminating the wide bandgap optical device with a light within a first range of wavelengths and a first average intensity, allowing a current to propagate therethrough without substantial absorption of the current, illuminating the wide bandgap optical device with light within the first range of wavelengths and a second average intensity that is lower than the first average intensity to allow a sustained current flow though the wide bandgap optical device, and illuminating the wide bandgap optical device with light within a second range of wavelengths to stop or substantially restrict propagation of the current through the wide gap material.

Voss, Lars F.↗

DOE OSTI2024

Wide bandgap optical switch circuit breaker for controlling propagation of current therethrough a wide bandgap optical device

Voss, Lars F.↗

DOE OSTI2021

Colloidal quantum dot lasers

We report semiconductor nanocrystals represent a promising class of solution-processable optical-gain media that can be manipulated via inexpensive, easily scalable colloidal techniques. Due to their extremely small sizes (typically <10 nm), their properties can be directly controlled via effects of quantum confinement; therefore, they are often termed colloidal quantum dots (CQDs). In addition to size-tunable emission wavelengths, CQDs offer other benefits for lasing applications, including low optical-gain thresholds and high temperature stability of lasing characteristics. Recent progress in understanding and practical control of processes impeding light amplification in CQDs has resulted in several breakthroughs, including the demonstration of optically pumped continuous-wave lasing, the realization of optical gain with direct current electrical injection and the development of dual-function electroluminescent devices that also operate as optically pumped lasers. The purpose of this Review is to assess the status of the field of CQD lasing and discuss the existing challenges and opportunities. A particular focus is on approaches for suppressing nonradiative Auger recombination, novel optical-gain concepts enabled by strong exciton-exciton interactions and controlled CQD charging, effects of nanocrystal form factors on light amplification and practical architectures for realizing electrically pumped CQD lasers. This overview suggests that the accumulated knowledge, along with the approaches developed for manipulating the optical-gain properties of colloidal nanostructures, perfectly position the CQD field for successfully addressing a long-standing challenge: the realization of CQD-based laser diodes. Colloidal quantum dots are promising materials for realizing versatile, wavelength-tunable, solution-processed lasers. This Review surveys recent advances in colloidal quantum dot lasing, provides an in-depth analysis of outstanding challenges and discusses a path forward to implementing technologically viable lasing devices.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Final Report on Aerosol Pretreatment Technology Performance and Benchmarking

Solvent-based post-combustion CO 2 capture (PCC) technology remains one of the leading methods to combat global CO 2 emissions produced from large-scale coal-fired power production. Advanced solventbased PCC technology has made significant improvements in design and performance that reduce capital and operating costs to enable its commercial use. Key to low cost, manageable logistics, and environmentally safe operation of solvent-based PCC technology are minimal solvent losses from the process through the treated gas stream exiting PCC plant absorbers. High flue gas aerosol particle concentrations (>10 5 particles/cm 3 ) for particles in the range of 70-200 nm have been shown to cause significant amine solvent losses for solvent-based PCC processes through several mechanisms including absorption of solvent and water into growing aerosol particles. Flue gas aerosol pretreatment technology is the only realistic and economically attractive method to reduce very high aerosol particle concentrations (>10 7 particles/cm 3 ) to enable solvent-based PCC for existing power plants lacking sufficient particle removal systems, such as baghouses. The overall goal of this project was to design, construct, independently test, and evaluate three flue gas aerosol pretreatment technologies identified to significantly reduce high aerosol particle concentrations (>10 7 particles/cm 3 ) in the 70-200 nm particle size range: (1) a novel, high-velocity water injection spray concept developed by RWE and tested by Linde, (2) an innovative electrostatic precipitator (ESP) device with optimized operating conditions developed by Washington University in St. Louis (WUSTL), and (3) a non-regenerative sorbent-based filter technology developed by InnoSepra for SO x and NO x removal from coal-fired power plant flue gas. Each technology has been validated with tests on 500-1000 scfm of actual coal-fired flue gas and evaluated in terms of particle removal efficiency (%), cost competitiveness, and environmental impact. Aerosol measurements were performed upstream and downstream of each aerosol reduction unit during independent testing of each technology using advanced instrumentation and analytical methods provided by WUSTL. To perform aerosol measurements, isokinetic probes were inserted into flanged pipes attached to the flue gas piping, and a small suction pump was used to sample gas containing aerosol particles. Aerosol particle number concentrations (# particles/cm 3 ) and size distributions were then measured using a scanning mobility particle sizer (SMPS, TSI Inc.) for very fine particles (<1,000 nm) and a particle counter manufactured by GRIMM for particles larger than 1,000 nm. This report summarizes the aerosol removal performance results from pilot scale testing of each technology. Performance results have been benchmarked against pre-defined targets and other flue gas aerosol pretreatment technologies with documented performance. Linde Gas North America LLC has been the prime contractor to DOE responsible for overall project management and provided the design for the high-velocity water spray-based aerosol removal technology based on a design concept developed by the German utility company RWE.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2020

A Quantum Analog Coprocessor for Correlated Electron Systems Simulation

Analog quantum simulation is an approach for studying physical systems that might otherwise be computationally intractable to simulate on classical high-performance computing (HPC) systems. The key idea behind analog quantum simulation is the realization of a physical system with a low-energy effective Hamiltonian that is the same as the low-energy effective Hamiltonian of some target system to be studied. Purpose-built nanoelectronic devices are a natural candidate for implementing the analog quantum simulation of strongly correlated materials that are otherwise challenging to study using classical HPC systems. However, realizing devices that are sufficiently large to study the properties of a non-trivial material system (e.g., those described by a Fermi-Hubbard model) will eventually require the fabrication, control, and measurement of at least 0(10) quantum dots, or other engineered quantum impurities. As a step toward large-scale analog or digital quantum simulation platforms based on nanoelectronic devices, we propose a new approach to analog quantum simulation that makes use of the large Hilbert space dimension of the electronic baths that are used to adjust the occupancy of one or a few engineered quantum impurities. This approach to analog quantum simulation allows us to study a wide array of quantum impurity models. We can further augment the computational power of such an approach by combining it with a classical computer to facilitate dynamical mean-field theory (DMFT) calculations. DMFT replaces the solution of a lattice impurity problem with the solution of a family of localized impurity problems with bath couplings that are adjusted to satisfy a self-consistency condition between the two models. In DMFT, the computationally challenging task is the high-accuracy solution of an instance of a quantum impurity model that is determined self-consistently in coordination with a mean-field calculation. We propose using one or a few engineered quantum impurities with adjustable couplings to baths to realize an analog quantum coprocessor that effects the solution of such a model through measurements of a physical quantum impurity, operating in coordination with a classical computer to achieve a self-consistent solution to a DMFT calculation. We focus on implementation details relevant to a number of technologies for which Sandia has design, fabrication, and measurement expertise. The primary technical advances outlined in this report concern the development of a supporting modeling capability. As with all analog quantum simulation platforms, the successful design and operation of individual devices depends critically on one's ability to predict the effective low-energy Hamiltonian governing its dynamics Our project has made this possible and lays the foundation for future experimental implementations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Self-Security for Grid-Interactive Smart Inverters Using Steady-State Reference Model

Smart inverters exchange information with other devices through a shared communication link, making the inverters more prone to receive harmful commands from external parties. This erroneous data can be received due to an anomaly in the system, such as a device fault, unintentional utility operator action, or a cyber-attack. In this paper, a device-level self-security strategy is implemented using reference models for a grid-interactive inverter to examine the incoming power setpoints, detect the anomalies, and protect the system accordingly. The PQ setpoints received from the utility supervisory controller are autonomously examined using the inverter’s normal and stable operating regions before engaging the setpoints to the inverter’s local controller. Grid parameters are estimated in real-time during the examination process. The efficacy of the self-security algorithm is tested using a three-phase 3-kVA SiC-MOSFET inverter and a 12-kW NHR 9410 regenerative grid emulator. The results verify that the proposed method can detect harmful PQ setpoints that can cause abnormal or unstable inverter operation.

Gursoy, Mehmetcan↗

DOE OSTI2026

Physical Modeling and Design of a Nonvolatile Optically Gated High‐Power Diamond Transistor

In this work, we present the theory and modeling framework of a diamond optically gated junction field‐effect transistor (DOGFET). The device utilizes nitrogen substitutional centers in type‐1b diamond to optically modulate a p‐ boron doped diamond channel. Using sub‐gap lasers with intensities as low as 100 W/cm 2 , electrons are optically excited from substitutional nitrogen sites to the conduction band of the diamond substrate, thus enabling the optical gate to exercise control on modulating the space‐charge region at the junction and therefore the channel conductivity. We show that the device can deliver a current of 7 μA/μm, or equivalently 1750 A/cm 2 , while switching at a frequency greater than 100 kHz, in a form factor of 5 μm 2 . The breakdown voltage is found to be greater than 1850 V, with a breakdown field strength of ~13 MV/cm. Moreover, the device supports nonvolatile operation with a “memory effect” enabling single transistor state retention. The presented simulation framework provides a physically grounded insight into the limits and opportunities of optoelectronic diamond systems.

Engineering - Electronic and electrical engineerin↗

DOE OSTI2021

Switching Device-Cognizant Sequential Distribution System Restoration

This paper presents an optimization framework for sequential reconfiguration using an assortment of switching devices and repair process in distribution system restoration. Compared to existing studies, this paper considers types, capabilities and operational limits of different switching devices, making it applicable in practice. We develop a novel multi-phase method to find the optimal sequential operation of various switching devices and repair faulted areas. We consider circuit breakers, reclosers, sectionalizers, load breaker switches, and fuses. The switching operation problem is decomposed into two mixed-integer linear programming (MILP) subproblems. The first subproblem determines the optimal network topology and estimates the number of steps to reach that topology, while the second subproblem generates a sequence of switching operations to coordinate the switches. For repairing the faults, we design an MILP model that dispatches repair crews to clear faults and replace melted fuses. After clearing a fault, we update the topology of the network by generating a new sequence of switching operations, and the process continues until all faults are cleared. To improve the computational efficiency, a network reduction algorithm is developed to group line sections, such that only switchable sections are present in the reduced network. The proposed method is validated on the IEEE 123-bus and 8500-bus systems.

distribution system↗

DOE OSTI2024

Advanced Laboratory and Field Arrays (ALFA)/Lab Collaboration Project (LCP) for Marine Energy (Final Scientific/Technical Report)

The objective of the Advanced Laboratory and Field Arrays (ALFA) project was to reduce the Levelized Cost of Energy (LCOE) of Marine and Hydrokinetic (MHK) energy by leveraging research, development, and testing capabilities at Oregon State University, University of Washington, and the University of Alaska, Fairbanks. ALFA is a project within the Pacific Marine Energy Center (PMEC; formerly NNMREC), a multi-institution entity with a diverse funding base that focuses on research and development for marine renewables. The ALFA project aimed to accelerate the development of next-generation arrays of wave energy conversion (WEC) and tidal energy conversion (TEC) devices through a suite of field-focused R&D activities spanning a broad range of strategic opportunity areas identified in the Funding Opportunity Announcement: • Device and/or array operation and maintenance (O&M) logistics development; • High-fidelity resource characterization and/or modeling technique development and validation; • Array-specific component technology development (e.g. moorings and foundations, transmission, and other offshore grid components); • Array performance testing and evaluation; and • Novel cost-effective environmental monitoring techniques and instrumentation testing and evaluation. The objective of the Lab Collaboration Project (LCP) was to accelerate the development of next-generation marine energy conversion systems. The LCP aimed to achieve these project objectives in collaboration with the national laboratories by: • Developing concept generation and assessment tools; • Improving access to existing testing resources; • Validating collision risk models between fish and turbines; and • Advancing analysis and simulation capabilities for wave-WEC interactions and PTO analysis in nonlinear ocean waves. The ALFA portion of the project was comprised of six overarching technical tasks: • Task 1: Debris Modeling, Detection and Mitigation; • Task 2: Autonomous Monitoring & Intervention; • Task 3: Resource Characterization for Extreme Conditions; • Task 4: Robust Models for Design of Offshore Anchoring and Mooring Systems; • Task 5: Performance Enhancement for Marine Energy Converter (MEC) Arrays; and • Task 6: Evaluating Sampling Techniques for MHK Biological Monitoring. The LCP was divided into four overarching technical tasks: • Task 7: Project Management and Reporting • Task 8: Novel Design and Assessment Methodologies for Wave Energy Converter Design (Wave- SPARC) • Task 9: Testing Access for Commercial Marine Renewable Energy Technology Developers • Task 10: Quantifying Collision Risk for Fish and Turbines • Task 11: Nonlinear Ocean Waves and PTO Control Strategy Each ALFA/LCP task listed above functioned as a separate and discreet project. A final Technical Report was written for each individual task and these reports were uploaded to OSTI, after receiving DOE approval. The following document is a compilation of each of these final, approved reports arranged as individual chapters.

13 HYDRO ENERGY↗

DOE OSTI2022

Structure/Interface Coupling Effect for High-Voltage LiCoO 2 Cathodes

LiCoO 2 (LCO) is widely applied in today's rechargeable battery markets for consumer electronic devices. However, LCO operations at high voltage are hindered by accelerated structure degradation and electrode/electrolyte interface decomposition. To overcome these challenges, co-modified LCO (defined as CB-Mg-LCO) that couples pillar structures with interface shielding are successfully synthesized for achieving high-energy-density and structurally stable cathode material. Benefitting from the "Mg-pillar" effect, irreversible phase transitions are significantly suppressed and highly reversible Li + shuttling is enabled. Interestingly, bonding effects between the interfacial lattice oxygen of CB-Mg-LCO and amorphous Co x B y coating layer are found to elevate the formation energy of oxygen vacancies, thereby considerably mitigating lattice oxygen loss and inhibiting irreversible phase transformation. Meanwhile, interface shielding effects are also beneficial for mitigating parasitic electrode/electrolyte reactions, subsequent Co dissolution, and ultimately enable a robust electrode/electrolyte interface. As a result, the as-designed CB-Mg-LCO cathode achieves a high capacity and excellent cycle stability with 94.6% capacity retention at an extremely high cut-off voltage of 4.6 V. We report these findings provide new insights for cathode material modification methods, which serves to guide future cathode material design.

25 ENERGY STORAGE↗

DOE OSTI2023

Imaging Light‐Induced Migration of Dislocations in Halide Perovskites with 3D Nanoscale Strain Mapping

Abstract In recent years, halide perovskite materials have been used to make high‐performance solar cells and light‐emitting devices. However, material defects still limit device performance and stability. Here, synchrotron‐based Bragg coherent diffraction imaging is used to visualize nanoscale strain fields, such as those local to defects, in halide perovskite microcrystals. Significant strain heterogeneity within MAPbBr 3 (MA = CH 3 NH 3 + ) crystals is found in spite of their high optoelectronic quality, and both 〈100〉 and 〈110〉 edge dislocations are identified through analysis of their local strain fields. By imaging these defects and strain fields in situ under continuous illumination, dramatic light‐induced dislocation migration across hundreds of nanometers is uncovered. Further, by selectively studying crystals that are damaged by the X‐ray beam, large dislocation densities and increased nanoscale strains are correlated with material degradation and substantially altered optoelectronic properties assessed using photoluminescence microscopy measurements. These results demonstrate the dynamic nature of extended defects and strain in halide perovskites, which will have important consequences for device performance and operational stability.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Infrared-Transparent Semiconductor Membranes for Electromagnetic Interference Shielding of Millimeter Waves

Here, it is demonstrated that single-crystalline and highly doped GaAs membranes are excellent candidates for realizing infrared-transparent shields of electromagnetic interference at millimeter frequencies. Measured optical transmittance spectra for the semiconductor membranes show resonant features between 750 and 2500 nm, with a 100% maximum transmittance. The shielding effectiveness of the membranes is extracted from measured scattering parameters between 65 and 85 GHz. Selected GaAs membranes and membranes/polyamide films exhibit shielding effectiveness ranging from 22 to 40 dB, which are suitable values to ensure the safe operation of infrared devices for commercial applications. Theoretical calculations based on a plane wave model show that the interplay of primary reflection and multiple internal reflections of the radio-frequency waves results in broadband shielding capabilities of the membrane between 10 and 300 GHz.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2024

Advancing Insights into Electrochemical Pre‐Treatments of Supported Nanoparticle Electrocatalysts by Combining a Design of Experiments Strategy with In Situ Characterization

Activation, break-in, and/or pre-treatment protocols are generally applied to energy conversion devices before regular operation to reach stable performance. There remains much to understand about the relationships among physical properties, performance, and electrochemical pre-treatments. Here, a design-of-experiments (DoE) strategy is employed to address this gap by demonstrating the influence of five pre-treatment parameters for carbon-supported Pt-nanoparticle catalysts on the electrocatalytic oxygen reduction reaction (ORR). A subset of pre-treatments, developed using a central composite design, are tested in a flow cell combined with an inductively-coupled plasma mass spectrometer (on-line ICP-MS). The DoE-based approach facilitates comprehensive insights from two orders of magnitude fewer experiments than a conventional grid search. The coupled on-line ICP-MS setup enables effective catalysis and real-time catalyst dissolution data. Leveraging insights from DoE for on-line ICP-MS and additional characterization, a model is built between the degradation of a multi-dimensional supported Pt surface, its performance, and applied electrochemical parameters. These investigations identify surface modifications, such as oxidation, and subsequent restructuring of Pt during pre-treatment as a primary cause of performance deterioration during ORR. By combining DoE with advanced characterization techniques, a powerful approach is demonstrated to gain a mechanistic understanding of pre-treatment protocols that can be broadly adapted to various reaction chemistries.

Platinum↗

DOE OSTI2023

Vanadium and Niobium MXenes—Bilayered V 2 O 5 Asymmetric Supercapacitors

MXenes offer high metallic conductivity and redox capacitance that are attractive for high-power, high-energy storage devices. However, they operate limitedly under high anodic potentials due to irreversible oxidation. Pairing them with oxides to design asymmetric supercapacitors may expand the voltage window and increase the energy storage capabilities. Hydrated lithium preintercalated bilayered V 2 O 5 ( δ-Li x V 2 O 5 ·nH 2 O) is attractive for aqueous energy storage due to its high Li capacity at high potentials; however, its poor cyclability remains a challenge. To overcome its limitations and achieve a wide voltage window and excellent cyclability, it is combined with V 2 C and Nb 4 C 3 MXenes. Asymmetric supercapacitors employing lithium intercalated V 2 C (Li-V 2 C) or tetramethylammonium intercalated Nb 4 C 3 (TMA-Nb 4 C 3 ) MXenes as the negative electrode, and a δ-Li x V 2 O 5 ·nH 2 O composite with carbon nanotubes as the positive electrode in 5 m LiCl electrolyte operate over wide voltage windows of 2 and 1.6 V, respectively. The latter shows remarkably high cyclability—capacitance retention of ≈95% after 10 000 cycles. Here, this work highlights the importance of selecting appropriate MXenes to achieve a wide voltage window and a long cycle life in combination with oxide anodes to demonstrate the potential of MXenes beyond Ti 3 C 2 in energy storage.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Organic photodetector with built-in amplification for the detection of visible light with low optical power

We report on an organic-based photodetector that integrates a dual-gate organic thin-film transistor (DG-OTFT) with an organic photodiode (OPD) to produce a device with a high effective responsivity at low optical power and video-rate compatible response. In this device, the OPD operates in photovoltaic mode, instead of the commonly used photoconductive mode, to modulate one of the gate voltages of the DG-OTFT. Effective responsivity values of 10 A W –1 are measured at optical power values lower than 10 nW at 635 nm. Here, modeling of the operation of this new photodetector suggests that effective responsivity values up to 10 5 A W –1 can be achieved at optical powers of 1 nW using current printing technology and state-of-the-art organic semiconductors.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Orientational Order in Spin-Cast Lead-Iodide Perovskite Nanocrystal Solids

Combined synthetic control over size and composition renders colloidal lead-halide perovskite nanocrystals a tunable platform for high-efficiency optoelectronic applications. However, the properties and operational stability of devices based on nanocrystal solids are often dictated by the method of the evaporation-induced assembly. Ubiquitous slow evaporation techniques can produce highly ordered nanocrystal domains but limit the prospects for scalable fabrication of continuous device layers, calling for investigation of approaches to more rapidly form ordered perovskite nanocrystal solids. Here, we study orientationally ordered lead-iodide perovskite nanocrystal solids prepared by conventional spin coating with molecular additives (excess ligand) to enhance ordering within the arrays. In situ X-ray scattering measurements reveal that orientational ordering occurs rapidly upon solvent removal during spin coating and can be further enhanced by manipulating the spin speed. We vary the additive ligand length and explore trade-offs between ordering and layered perovskite impurity formation. Arrays treated with the intermediate-length octylamine ligand exhibit increased in-plane electronic conductivity, suggesting orientational ordering and internanocrystal electronic coupling can be enhanced by the treatment. In conclusion, these results highlight the prospects of establishing long-range order in lead-halide perovskite nanocrystal solids by using simple and fast coating methods.

14 SOLAR ENERGY↗

DOE OSTI2021

Strain in Metal Halide Perovskites: The Critical Role of A-Site Cation

In this work, we investigate the role of the A-site cation in the lattice strain of metal halide perovskites (MHPs) upon light illumination and heating—two inevitable factors during the operation of photovoltaic devices. We reveal that the A-site cation plays an important role in light-induced strain in MHPs. Density functional theory calculations indicate that hydrogen-bonding interactions and ionization energy of the A-site cation are potential reasons responsible for the light-induced lattice strain in MHPs. These findings offer an approach to modulate the light-induced strain in MHPs, which is critical for further improving the efficiency and stability of MHP photovoltaics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗