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At least 1,333 records · Page 74

Manipulating topological properties in Bi 2 Se 3 / BiSe /transition metal dichalcogenide heterostructures with interface charge transfer

Heterostructures of topological insulator Bi 2 Se 3 on transition metal dichalcogenides (TMDCs) offer a new materials platform for studying novel quantum states by exploiting the interplay among topological orders, charge orders and magnetic orders. Here, the diverse interface attributes, such as material combination, charge re-arrangement, defect and strain, can be utilized to manipulate the quantum properties of this class of materials. Recent experiments of Bi 2 Se 3 /NbSe 2 heterostructures show signatures of strong Rashba band splitting due to the presence of a BiSe buffer layer, but the atomic level mechanism is not fully understood. We conduct first-principles studies of the Bi 2 Se3/BiSe/TMDC heterostructures with five different TMDC substrates (1T phase VSe 2 , MoSe 2 , TiSe 2 , and 2H phase NbSe 2 , MoSe 2 ). We find significant charge transfer at both BiSe/TMDC and Bi 2 Se 3 /BiSe interfaces driven by the work function difference, which stabilizes the BiSe layer as an electron donor and creates interface dipole. The electric field of the interface dipole breaks the inversion symmetry in the Bi 2 Se 3 layer, leading to the giant Rashba band splitting in two quintuple layers and the recovery of the Dirac point in three quintuple layers, with the latter otherwise only occurring in thicker samples with at least six Bi 2 Se 3 quintuple layers. Besides, we find that strain can significantly affect the charge transfer at the interfaces. Our study presents a promising avenue for tuning topological properties in heterostructures of two-dimensional materials, with potential applications in quantum devices.

36 MATERIALS SCIENCE↗

Understanding Hydrogenation Chemistry at MgB 2 Reactive Edges from Ab Initio Molecular Dynamics

Solid-state hydrogen storage materials often operate via transient, multistep chemical reactions at complex interfaces that are difficult to capture. Here, we use direct ab initio molecular dynamics simulations at accelerated temperatures and hydrogen pressures to probe the hydrogenation chemistry of the candidate material MgB 2 without a priori assumption of reaction pathways. Focusing on highly reactive ($10\overline{1}0$) edge planes where initial hydrogen attack is likely to occur, we track mechanistic steps toward the formation of hydrogen-saturated BH 4 – units and key chemical intermediates, involving H 2 dissociation, generation of functionalities and molecular complexes containing BH 2 and BH 3 motifs, and B–B bond breaking. Further, the genesis of higher-order boron clustering is also observed. Different charge states and chemical environments at the B-rich and Mg-rich edge planes are found to produce different chemical pathways and preferred speciation, with implications for overall hydrogenation kinetics. The reaction processes rely on B–H bond polarization and fluctuations between ionic and covalent character, which are critically enabled by the presence of Mg 2+ cations in the nearby interphase region. Our results provide guidance for devising kinetic improvement strategies for MgB 2 -based hydrogen storage materials, while also providing a template for exploring chemical pathways in other solid-state energy storage reactions.

08 HYDROGEN↗

Fundamental Understanding of “Fresh” Lithium Nucleation and Growth in Sulfide-Based Anode-Free Solid-State Batteries: Effects of Substrate, Current Density, and Li + Supply

Understanding the electrochemical extraction and deposition of lithium (Li) from cathode is crucial for advancing anode-free solid-state batteries (AFSSBs). Herein, cryo-transmission electron microscopy (cryo-TEM) and electrochemical studies are employed to investigate how current collector surface properties, current densities, and cathode loadings influence the morphology of fresh electrochemically deposited Li and the electrochemical performance in sulfide-based AFSSBs. Cryo-TEM reveals that Cu current collectors induce irregular, dendritic Li deposits due to their lithiophobic nature and reactivity with Li 5.4 PS 4.4 Cl 1.6 (LPSC), while Ni and Au facilitate more uniform, planar-like Li growth. The morphology of the deposited Li also depends on current density: higher rates produce smaller, porous particles versus larger, denser deposits at lower rates. Importantly, for the first time, we discovered that low cathode loadings lead to poor cycling stability due to insufficient Li + supply for complete anode coverage, contrary to conventional solid-state batteries with preloaded Li metal anodes. This finding establishes a design principle where adequate cathode Li + reservoirs are essential for anode interface stability in AFSSBs. Overall, this work elucidates the interplayed effect of current collectors, current densities, and cathode loadings on Li morphology and cycle stability, offering fundamental insights into cathode-derived Li behavior and practical guidelines for optimizing AFSSBs performance through nucleation control and interface engineering.

25 ENERGY STORAGE↗

Unified computational model of transport in metal-insulating oxide-metal systems

In this paper, a unified physics-based model of electron transport in metal-insulator-metal (MIM) systems is presented. In this model, transport through metal-oxide interfaces occurs by electron tunneling between the metal electrodes and oxide defect states. Transport in the oxide bulk is dominated by hopping, modeled as a series of tunneling events that alter the electron occupancy of defect states. Electron transport in the oxide conduction band is treated by the drift–diffusion formalism and defect chemistry reactions link all the various transport mechanisms. It is shown that the current-limiting effect of the interface band offsets is a function of the defect vacancy concentration. These results provide insight into the underlying physical mechanisms of leakage currents in oxide-based capacitors and steady-state electron transport in resistive random access memory (ReRAM) MIM devices. An explanation of ReRAM bipolar switching behavior based on these results is proposed.

36 MATERIALS SCIENCE↗

Converter-Interfaced CHP Plant for Improved Grid-Integration, Flexibility and Resiliency

GE Research and its partner GE Renewables have proposed the use of an interface converter solution to increase the penetration of small to medium-sized CHP (1MWe to 20MWe) into distribution grids and improve their flexibility and grid support capability. Indeed, the proposed interface converter solution thanks to presence of the grid-ready inverter, allows to streamline the compliance to grid codes requirements, reduce the interconnection delays and costs and ultimately one of the main barriers for CHP adoption by commercial and industrial facilities. An additional benefit provided by the interface converter is the use of the grid-ready inverter for reactive power which eliminates the need of sizing the generator for that capability. These two benefits highly favor the economic feasibility of converter-interfaced CHP. Five user cases, each in one of the leading U.S states for CHP potential reported by the DOE in its estimation of the U.S Technical Potential of CHP, were selected to compare the economic performances of converter-interfaced CHP as compared with directly-coupled. They include a college campus in California, a hospital in New York, a water reclamation plant in Texas, a hotel in Minnesota, and a large office building in Pennsylvania. Results showed that, the presence of the interface converter allows to increase the return on investment (ROI) by 0.5 to 2 percentage points in most of the cases (4 of 5). Indeed, the interface converter by shortening the interconnection process allows to accelerate revenues while reducing interconnection costs. Added to the reduced cost of the required generator these savings trade favorably the capital cost of the converter. The analysis also showed that the profitability of the converter-interfaced CHP is highly sensitive to the energy price, interconnection delay, and converter cost. However, it appears that if the interface converter can shorten the interconnection process by at least 6 months, adopting this solution will be more economically viable than directly-coupled configuration in almost all the +23,000 sites of the U.S Technical Potential CHP. The evaluation of the benefits of a converter-interfaced CHP also showed that it enables higher ROI when coupled with other distributed energy resources (DER) such as battery energy systems (BESS) or solar photovoltaic (PV). Indeed, in those scenario, the grid-ready inverter included in the interface converter eliminates the need of separate inverters if DC-coupling is used. On the technical performance, it has been verified that the presence of the interface converter allows to reduce by 70% to 80% the CHP short-circuit contribution to grid faults. This not only reduces the mechanical and thermal stresses exposed to the CHP electrical components but also increases the grid hosting capacity which ultimately enables higher penetrations CHP. Another key benefit of the interface converter validated with hardware-in-the-loop simulations and testing is its superior capability for reactive power support. Indeed, using a power hardware testbed with two +700kW inverters configured in back-to-back, a microgrid controller and actual facilities loads it was demonstrated that the presence of the interface converter can help maintain a power factor near ~1 or regulate the voltage to ~1.0pu at the point of common coupling. This benefit can be highly valuable if in the future, due to higher penetration of renewable distributed energy resources (DER), utilities start billing demand charge based on kVA instead of kW as currently. It was also validated that converter-interfaced CHP can dispatch heat and power commands and seamlessly switch between the two modes while consistently controlling the power factor or voltage at PCC. Indeed, the power hardware testing showed that grid-connected converter-interfaced CHP can follow either the power or heat demand while maintaining a unity power factor at converter output. This research proved that the adoption of an interface converter as the solution for interconnection of CHP system into the distribution grid can greatly improve the economic feasibility of small to medium-sized CHP as well as the plant power quality, flexibility and resiliency. Additionally, it allows increased penetrations of CHP into the distribution grid, extends their grid support capability, and facilitates the integration of BESS and PV DER by streamlining their collocation within the same facilities. This ultimately provides an opportunity for commercial and small industrial facilities in the U.S to accelerate their energy transition thanks to the high energy efficiency of CHP systems and its reliable, flexible, and resilient microgrid operation when interconnected with an interface converter.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Study on the Correlation Between Dynamical Behavior and Friction/Wear Mechanism Under the Effect of Grooves

In this work, the interfacial friction and wear and vibration characteristics are studied by sliding a chromium bearing steel ball (AISI 52100) over both multi-grooved and single-grooved forged steel disks (20CrMnMo) at low and high rotating speeds in order to reveal the effect mechanism of groove-textured surface on tribological behaviors. The results show that the grooves modify the contact state of the ball and the disk at the contact interface. This consequently causes variations in the normal displacement, normal force, and friction force signals. The changes in these three signals become more pronounced with increasing groove width at a low speed. The collision behavior between the ball and the groove increase the amplitude of vibration acceleration at a high speed. The test results suggest that grooves with appropriate widths could trap wear debris on the ball surface while avoiding a strong collision between the disk and the ball, resulting in an improvement in the wear states.

36 MATERIALS SCIENCE↗

Electrochemical-acoustic time of flight: in operando correlation of physical dynamics with battery charge and health

We demonstrate that a simple acoustic time-of-flight experiment can measure the state of charge and state of health of almost any closed battery. An acoustic conservation law model describing the state of charge of a standard battery is proposed, and experimental acoustic results verify the simulated trends; furthermore, a framework relating changes in sound speed, via density and modulus changes, to state of charge and state of health within a battery is discussed. Regardless of the chemistry, the distribution of density within a battery must change as a function of state of charge and, along with density, the bulk moduli of the anode and cathode changes as well. The shifts in density and modulus also change the acoustic attenuation in a battery. Experimental results indicating both state-of-charge determination and irreversible physical changes are presented for two of the most ubiquitous batteries in the world, the lithium-ion 18650 and the alkaline LR6 (AA). Overall, a one-or two-point acoustic measurement can be related to the interaction of a pressure wave at multiple discrete interfaces within a battery, which in turn provides insights into state of charge, state of health, and mechanical evolution/degradation.

Hsieh, AG↗

Enhanced interfacial thermal transport in pnictogen tellurides metallized with a lead-free solder alloy

Controlling thermal transport across metal–thermoelectric interfaces is essential for realizing high efficiency solid-state refrigeration and waste-heat harvesting power generation devices. Here, the authors report that pnictogen chalcogenides metallized with bilayers of Sn{sub 96.5}Ag{sub 3}Cu{sub 0.5} solder and Ni barrier exhibit tenfold higher interfacial thermal conductance Γ{sub c} than that obtained with In/Ni bilayer metallization. X-ray diffraction and x-ray spectroscopy indicate that reduced interdiffusion and diminution of interfacial SnTe formation due to Ni layer correlates with the higher Γ{sub c}. Finite element modeling of thermoelectric coolers metallized with Sn{sub 96.5}Ag{sub 3}Cu{sub 0.5}/Ni bilayers presages a temperature drop ΔT ∼ 22 K that is 40% higher than that obtained with In/Ni metallization. Our results underscore the importance of controlling chemical intermixing at solder–metal–thermoelectric interfaces to increase the effective figure of merit, and hence, the thermoelectric cooling efficiency. These findings should facilitate the design and development of lead-free metallization for pnictogen chalcogenide-based thermoelectrics.

42 ENGINEERING↗

Atomic-scale determination of spontaneous magnetic reversal in oxide heterostructures

Interfaces between transition metal oxides are known to exhibit emerging electronic and magnetic properties. Here we report intriguing magnetic phenomena for La 2/3 Sr 1/3 MnO 3 films on an SrTiO 3 (001) substrate (LSMO/STO), where the interface governs the macroscopic properties of the entire monolithic thin film. The interface is characterized on the atomic level utilizing scanning transmission electron microscopy and electron energy loss spectroscopy (STEM-EELS), and density functional theory (DFT) is employed to elucidate the physics. STEM-EELS reveals mixed interfacial stoichiometry, subtle lattice distortions, and oxidation-state changes. Magnetic measurements combined with DFT calculations demonstrate that a unique form of antiferromagnetic exchange coupling appears at the interface, generating a novel exchange spring-type interaction that results in a remarkable spontaneous magnetic reversal of the entire ferromagnetic film, and an inverted magnetic hysteresis, persisting above room temperature. Formal oxidation states derived from electron spectroscopy data expose the fact that interfacial oxidation states are not consistent with nominal charge counting. The present work demonstrates the necessity of atomically resolved electron microscopy and spectroscopy for interface studies. Theory demonstrates that interfacial nonstoichiometry is an essential ingredient, responsible for the observed physical properties. The DFT-calculated electrostatic potential is flat in both the LSMO and STO sides (no internal electric field) for both Sr-rich and stoichiometric interfaces, while the DFT-calculated charge density reveals no charge transfer/accumulation at the interface, indicating that oxidation-state changes do not necessarily reflect charge transfer and that the concept of polar mismatch is not applicable in metal−insulator polar−nonpolar interfaces.

36 MATERIALS SCIENCE↗

Study of Void Formation at the Lithium|Solid Electrolyte Interface

There is growing recognition of the critical role of void formation in lithium metal anodes in solid-state batteries and its impact on electrochemical performance. While experimental studies have demonstrated the challenges ensuing from void formation at the lithium metal interface with the solid electrolyte, there is a need to understand and quantify the role of intrinsic transport properties in lithium metal and the impact of external stimuli, such as temperature, pressure, and current density. Here, we develop this understanding by constructing a phase field-based model that captures the evolution of void domains at the lithium-solid electrolyte interface. Growth of the pores is driven by the fast removal of lithium from the interface during stripping at high current densities. Relative magnitudes of the bulk and surface lithium diffusivities, along with the applied current density, dictate the final pore morphology. Increasing the temperature results in faster diffusion, while external applied pressure causes creep flow of lithium, both of which help to mitigate the evolution of voids by quickly transporting metal from the bulk to the interface. Finally, a phase map as a function of temperature and pressure is developed as a guide to determine the regions that can lead to the stable cycling of lithium metal.

25 ENERGY STORAGE↗

Interface-Driven Plasticity: The Presence of an Interface Affected Zone in Metallic Lamellar Composites: The Presence of an Interface Affected Zone…

Large strain deformation is used to make fine nanolayered two-phase composites from stacks of conventional polycrystalline sheets. The final materials made by this technique possess a crystallographically highly oriented structure containing nearly atomically perfect interfaces prevailing ubiquitously throughout the material. How this ordered structure evolves with strain from the coarser, more disordered state is not known. Here, using microstructural analysis and computational modeling, we discover a local interface-affected zone (IAZ) possessing the same crystallographically sharp structure in coarse layered composites as the final nanolayered composites. This means that this strongly oriented interface “zone” survives the mechanical work and overtakes the structure as it refines to the nanoscale. In essence, through the formation of this interface zone, the crossover to a highly oriented nanostructure occurs. Using microstructural analysis and crystal plasticity simulations, we show that the IAZ is a consequence of slip accommodation at the interface. This insight is valuable for developing processing strategies for superior interface-dominated materials.

36 MATERIALS SCIENCE↗

Topological current divider in a Chern insulator junction

A Chern insulator is a two-dimensional material that hosts chiral edge states produced by the combination of topology with time reversal symmetry breaking. Such edge states are perfect one-dimensional conductors, which may exist not only on sample edges, but on any boundary between two materials with distinct topological invariants (or Chern numbers). Engineering of such interfaces is highly desirable due to emerging opportunities of using topological edge states for energy-efficient information transmission. Here, we report a chiral edge-current divider based on Chern insulator junctions formed within the layered topological magnet MnBi 2 Te 4 . We find that in a device containing a boundary between regions of different thickness, topological domains with different Chern numbers can coexist. At the domain boundary, a Chern insulator junction forms, where we identify a chiral edge mode along the junction interface. We use this to construct topological circuits in which the chiral edge current can be split, rerouted, or switched off by controlling the Chern numbers of the individual domains. Our results demonstrate MnBi 2 Te 4 as an emerging platform for topological circuits design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Configurable antiferromagnetic domains and lateral exchange bias in atomically thin CrPS 4

Interfacial exchange coupling between antiferromagnets (AFMs) and ferromagnets (FMs) crucially makes it possible to shift the FM hysteresis, known as exchange bias, and to switch AFM states. Two-dimensional magnets unlock opportunities to combine AFM and FM materials; however, the buried AFM–FM interfaces obtained by stacking remains challenging to understand. Here, in this work, we demonstrate interfacial control via intralayer exchange coupling in the layered AFM CrPS 4 , where connected even and odd layers realize pristine lateral interfaces between AFM-like and FM-like regions. We distinguish antiphase even-layer states by scanning nitrogen-vacancy centre magnetometry due to a weak surface magnetization. This surface magnetization enables control over the even-layer state, with different regions switching at distinct fields due to their own lateral couplings. We toggle three AFM domains adjacent to a FM-like region and demonstrate a tunable multilevel exchange bias. Our nanoscale visualization unveils the microscopic origins of exchange bias and advances single two-dimensional crystals for hybrid AFM–FM technologies.

magnetic devices↗

Resistive switching and synaptic properties of fully atomic layer deposition grown TiN/HfO{sub 2}/TiN devices

Recently proposed novel neural network hardware designs imply the use of memristors as electronic synapses in 3D cross-bar architecture. Atomic layer deposition (ALD) is the most feasible technique to fabricate such arrays. In this work, we present the results of the detailed investigation of the gradual resistive switching (memristive) effect in nanometer thick fully ALD grown TiN/HfO{sub 2}/TiN stacks. The modelling of the I-V curves confirms interface limited trap-assisted-tunneling mechanism along the oxygen vacancies in HfO{sub 2} in all conduction states. The resistivity of the stack is found to critically depend upon the distance from the interface to the first trap in HfO{sub 2}. The memristive properties of ALD grown TiN/HfO{sub 2}/TiN devices are correlated with the demonstrated neuromorphic functionalities, such as long-term potentiation/depression and spike-timing dependent plasticity, thus indicating their potential as electronic synapses in neuromorphic hardware.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Development and Validation of a High-Vacuum Thermal Conductivity Testbed for Aerospace Interface Materials

Thermal Interface Materials (TIMs) are critical components in spacecraft thermal management systems, where thermal performance is strongly influenced by vacuum conditions, interface contact resistance, and layered metallic joint behavior. However, manufacturer-reported thermal conductivity values are often derived under idealized conditions and may not accurately represent performance within operational aerospace applications. To address this limitation, the Testbed for Advanced Interface Materials in Vacuum (TAIMV) was developed as a modular vacuum-compatible thermal conductivity characterization platform capable of evaluating aerospace-relevant TIM configurations under both ambient and high-vacuum environments. The testbed was derived from the ASTM C1044-16 guarded hot plate methodology and incorporates interchangeable layers of stainless steel coupon geometries, independently controlled main and guard heaters, embedded resistance temperature detectors (RTDs), thermocouples, multi-layer insulation (MLI), and a temperature-controlled cold plate to characterize through-thickness thermal gradients across layered interfaces. In the current configuration, interface compression is limited to the nominal contact pressure generated by the experimental stack assembly. Initial experimental campaigns were conducted at ambient pressure and below 1×10-5 torr for vacuum cases using multiple interface materials including Braycote 601EF and Krytox-based greases across a range of thermal operating conditions. In parallel, a coupled numerical Python thermal model was developed to predict temperature distribution throughout the stack while accounting for conduction, radiation, and parasitic heat transfer pathways and effective interface resistance effects. Experimental measurements and numerical predictions showed consistent thermal trends across multiple operating conditions and environmental states. Results also revealed measurable differences between ambient and vacuum thermal behavior, demonstrating the importance of interface resistance, parasitic heat transfer mechanisms, and stack geometry in determining effective thermal performance within layered thermal interfaces. The presented work establishes a foundation for future thermal model correlation efforts and expanded characterization of aerospace thermal interface materials under representative environmental conditions. Future work will focus on the integration of a load cell system to enable controlled pressure-dependent characterization of thermal interface materials under compressive loading. This capability will allow investigation of the influence of contact pressure on effective thermal conductivity, interface resistance, and thermal performance within layered aerospace thermal interfaces under representative operational conditions.

Thermal Development Testing↗

Fiber-Coupled Diamond Quantum Nanophotonic Interface

Color centers in diamond provide a promising platform for quantum optics in the solid state, with coherent optical transitions and long-lived electron and nuclear spins. Building upon recent demonstrations of nanophotonic waveguides and optical cavities in single-crystal diamond, we now demonstrate on-chip diamond nanophotonics with a high-efficiency fiber-optical interface achieving > 90 % power coupling at visible wavelengths. Here, we use this approach to demonstrate a bright source of narrow-band single photons based on a silicon-vacancy color center embedded within a waveguide-coupled diamond photonic crystal cavity. Our fiber-coupled diamond quantum nanophotonic interface results in a high flux (approximately 38 kHz) of coherent single photons (near Fourier limited at < 1 - GHz bandwidth) into a single-mode fiber, enabling possibilities for realizing quantum networks that interface multiple emitters, both on chip and separated by long distances.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Semiconductor-electrocatalyst contacts: theory, experiment, and applications to solar water photoelectrolysis

Semiconductor photoelectrodes coated with electrocatalysts are key components of photoelectrochemical (PEC) energy conversion and storage systems. Such systems could provide a way to convert the energy in sunlight directly into energy stored in a fuel like hydrogen gas to power our modern society without using fossil fuels. Despite an intense effort aimed at optimizing these materials, there has been little systematic work focused on the semiconductor-electrocatalyst (SC|EC) interface. The SC|EC interface is important because it is responsible for collecting the photoexcited electron-hole pairs generated in the semiconductor. During the performance period we initiated a fundamental effort to understand interfacial electron transfer between electrocatalysts and bulk semiconductors. We developed an experimental technique, dual-working-electrode (DWE) photoelectrochemistry, allowing for direct electrical measurement of the SC-EC interface in situ. We also developed the first theory of the SC|EC interface and applied the theory through numerical simulation to explain the measured interfacial charge transfer properties of the SC|EC junction. We discovered that porous, ion-permeable, redox-active catalysts such as Ni-(Fe) oxyhydroxides form so-called “adaptive” junctions where the effective interfacial barrier height for electron transfer depends on the charge state of the catalyst. This is in sharp contrast to interface properties of dense ion-impermeable catalysts, which we found form buried junctions that could be described by simple equivalent electrical circuits. These results elucidated a design principle for catalyzed photoelectrodes - high-performance photoelectrodes with direct SC|EC junctions use soft deposition techniques that yield ion-permeable catalysts. This work thus provides a foundation for the development of improved photoelectrodes that are practically relevant because they provide a mechanism to directly convert and store solar energy in the form of hydrogen gas, a renewable chemical fuel.

08 HYDROGEN↗

Intelligent user interface concept for space station

The space station computing system must interface with a wide variety of users, from highly skilled operations personnel to payload specialists from all over the world. The interface must accommodate a wide variety of operations from the space platform, ground control centers and from remote sites. As a result, there is a need for a robust, highly configurable and portable user interface that can accommodate the various space station missions. The concept of an intelligent user interface executive, written in Ada, that would support a number of advanced human interaction techniques, such as windowing, icons, color graphics, animation, and natural language processing is presented. The user interface would provide intelligent interaction by understanding the various user roles, the operations and mission, the current state of the environment and the current working context of the users. In addition, the intelligent user interface executive must be supported by a set of tools that would allow the executive to be easily configured and to allow rapid prototyping of proposed user dialogs. This capability would allow human engineering specialists acting in the role of dialog authors to define and validate various user scenarios. The set of tools required to support development of this intelligent human interface capability is discussed and the prototyping and validation efforts required for development of the Space Station's user interface are outlined.

Comer, Edward↗