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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Gaussian Process Optimization of Sensitivity-Based Similarity Metrics between New Nuclear Applications and New/Existing Benchmarks [Slides]

This presentation discusses Nuclear Criticality Safety (NCS) and how designing safe, new nuclear criticality experiments requires expert judgement, which could take years of experience. Sensitivity/uncertainty (S/U) analysis can be utilized by less experienced individuals to conservatively estimate uncertainties in important parameters, such as k eff , in newly proposed nuclear experiments. The presentation poses the question of how this analysis can be performed and states that the answer lies in matching new nuclear experiments with existing benchmark experiments using similarity metrics. By increasing the criticality safety of the application in this work, higher mass limits could be used in PF-4 operations. Additionally, the presentation discusses MCNP6.2®, Whisper-1.1, the software that can be used in this analysis. Also discussed is the fact that International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmarks rarely match new nuclear applications and that there are significant differences in given set of materials and/or geometry. If there are no benchmarks that match the application, the presentation discusses the possibility of creating new benchmarks. In conclusion, this work presents a Gaussian process (GP) optimization scheme that was used to generate new benchmarks with the highest sensitivity-based similarity metrics to user-defined nuclear applications. The Gaussian process optimization successfully designed 3 new experimental benchmarks that were highly correlated to the application of interest and had k eff values near critical. Optimization over c k,i-r has shown that investigating specific isotope reactions for different applications is crucial to designing benchmark experiments. Partial contribution from Pu dominates c k similarity metric. Future work includes testing new stand-alone similarity metrics or new combinations of similarity metrics as the design criterion of this optimization – design criterion is application dependent.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Validation of MCNP Critical Benchmark Models of PU-MET-FAST-016 [Slides]

The validation of PU-MET-FAST-016 contributed to the centralized LANL benchmark repository currently under development. The revisions made the MCNP models statistically, significantly more similar to the benchmark models. The overall impact on the USL is negligible. The revisions to the PU-MET-FAST-016 models provide value to the Los Alamos Benchmark Suite without invalidating past Whisper results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Validation and Independent Uncertainty Analysis of the MIX-SOL-THERM-003 ICSBEP Benchmark

The International Criticality Safety Benchmark Evaluation Project (ICSBEP) was started in 1992 by the United States Department of Energy and later in 1995 became an international project with contributions from 22 countries. The project is now organized by the OECD (Organisation for Economic Co-operation and Development) Nuclear Energy Agency (NEA). In its most recent iteration, the ICSBEP handbook contains over five thousand evaluations of critical, near-critical, and subcritical experiments conducted in facilities all around the world. These benchmarks serve as valuable information for criticality safety engineers who can use them to validate calculation techniques and establish minimum subcritical margins for operations with fissionable materials. The benchmarks in the handbook are categorized by their fissile material composition, material form (oxide, solution, or metal), and fission energy spectra. This is especially useful for those looking for benchmarks similar to a system they are working on to compare methods and identify trends. The ICSBEP Handbook Uncertainty Guide is document outlining recommended practices and methods for determining uncertainties in these benchmarks. Quantifying these uncertainties thoroughly is crucial as it allows a higher degree of confidence that data used from them is valid and relevant. The guide stresses the importance of a thorough and well documented uncertainty analysis when evaluating an experiment. All measured values of a system, whether they be dimensions or material compositions, have a certain amount of uncertainty associated with them and can be analyzed one by one to determine their effects on the system. Many evaluated benchmarks in the handbook present this in detail, however some do not, mostly earlier evaluations performed in the 1990’s and early 2000’s. Recently at Los Alamos National Laboratory (LANL), the Nuclear Criticality Safety Division (NCSD) of LANL has been validating MCNP6.2 ® input files of criticality benchmarks for use by Whisper, a criticality safety code developed at LANL. This effort is also part of the OECD NEA Working Party on International Nuclear Data Evaluation Co-operation (WPEC) Subgroup 45, also known as Validation of Nuclear Data Libraries (VaNDaL). The goal of VaNDaL is to compile a set of validated simulation inputs for use in validating nuclear data and simulation codes. As part of these efforts, one of the benchmarks reviewed was the MIX SOL-THERM-003 ICSBEP benchmark. This paper provides an independent uncertainty analysis of this benchmark experiment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Kinetic stability of Chapman–Enskog plasmas

In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$ , and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$ , the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma ( viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$ , the electron inertial scale $d_e$ and the plasma $\beta$ . This work is of general consequence in emphasising the fact that high- $\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$ . In this situation, the determination of transport coefficients via the standard CE approach is not valid.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Aerosol Optical Tweezers Elucidate the Chemistry, Acidity, Phase Separations, and Morphology of Atmospheric Microdroplets

Aerosol particles represent unique chemical environments because of their high surface area-to-volume ratio that promotes the effects of interfacial chemistry in confined environments. Properties such as viscosity, diffusivity, water content, pH, and morphology—following liquid–liquid phase separation—can strongly alter how a particle interacts with condensable vapors and reactive trace gases, thus modifying its continual evolution and environmental effects. Our understanding of this chemical evolution of atmospheric particulate matter and its environmental impacts is largely limited by our ability to directly observe how these critical particle properties respond to the addition or reactive uptake of new chemical components. Aerosol optical tweezers (AOT) stably trap particles in focused laser beams, providing positional control and the retrieval of many of these critical properties required to understand and predict the chemistry of aerosolized microdroplets. The analytical power of the AOT stems from the retrieval of the cavity-enhanced Raman spectrum induced by the trapping laser. Analysis of the whispering gallery modes (WGMs) that resonate as a standing wave around the droplet’s interface, provide high accuracy measurements of the droplet’s size, refractive index (and thus a measurement of composition), and can distinguish between core–shell, partially engulfed, and homogeneous morphologies. In this study, we have advanced the ability to determine the properties of the core and shell phases in biphasic droplets, including obtaining high-accuracy pH measurements. These capabilities were applied to perform AOT physical chemistry experiments on authentic secondary organic aerosol (SOA) produced directly in the AOT chamber by ozonolysis of terpene vapors. The propensity of the SOA to phase separate as a shell from a wide range of nonpolar to polar core phases was observed, along with the discovery of a stable emulsified state of SOA particles in an aqueous salt droplet. Micron-thick SOA shells did not impede the gain or loss of water or squalane from the core to the surrounding air, indicating no significant diffusional limitations to condensational growth or partitioning even under dry conditions. These experiments formed the foundation of a new framework that predicts how the phase-separated morphology of complex aerosols containing organic carbon evolves during continual atmospheric oxidation processes. Increases in oxidation state will quickly drive conversion from a partially engulfed to core–shell morphology that has dramatically different chemical reactivity since the core phase is completely concealed by the shell. The recent advances in the experimental capabilities of the AOT technique such as presented here enable novel experimental methodologies that provide insights into the chemistry and multidimensional properties of aerosol microdroplets, and how these coevolve and respond to continual chemical reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Controlled Assembly of Upconverting Nanoparticles for Low-Threshold Microlasers and Their Imaging in Scattering Media

Micron-sized lasers fabricated from upconverting nanoparticles (UCNP) coupled to whispering gallery mode (WGM) microresonators can exhibit continuous-wave anti-Stokes lasing useful for tracking cells, environmental sensing, and coherent stimulation of biological activity. The integration of these microlasers into organisms and microelectronics requires even smaller diameters, however, which raises threshold pump powers beyond practical limits for biological applications. To meet the need for low lasing thresholds and high fidelity fabrication methods, we use correlative optical and electron microscopy to uncover the nanoparticle assembly process and structural factors that determine efficient upconverted lasing. We show that 5 μm microspheres with controlled submonolayer UCNP coatings exhibit, on average, 25-fold lower laser thresholds (1.7 ± 0.7 kW/cm 2 ) compared to the mean values of the lowest threshold UCNP lasers, and variability is reduced 30-fold. WGMs are observed in the upconversion spectra for TiO 2 -coated microspheres as small as 3 μm, a size at which optical losses had previously prevented such observations. Finally, we demonstrate that the WGM signatures of these upconverting microlasers can be imaged and distinguished through tissue-mimicking phantoms. These advances will enable the fabrication of more efficient upconverting lasers for imaging, sensing, and actuation in optically complex environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Frequency comb generation in WGM microsphere based generators for telecommunication applications

We review the frequency comb generation process, main microresonator parameters such as free spectral range (FSR) and Q-factor, previously used optical frequency comb (OFC) generator parameters and resulting frequency combs, as well as the implementation of OFC for optical data transmission. An optical frequency comb is produced in a setup based on a tapered fibre and a SiO{sub 2} microsphere. The generated frequency comb has a frequency spacing of 2 nm or 257 GHz. During the fabrication of a tapered fibre from SMF28, use is made of the transmission signal to control the taper pulling process. The final measured tapered fibre transmission is ∼96%. A microsphere whispering gallery-mode resonator (WGMR), exhibiting a Q-factor of at least 2 × 10{sup 7}, is fabricated from an optical fibre with a thicker core than SSMF. Moreover, for future experiments, a frequency comb generator based on a free-space setup consisting of lenses, a prism, and a microsphere is developed, and the Q-factor dependence on different distances between the prism and the microsphere is investigated. (optical components of fibre-optic communication lines)

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bistable random momentum transfer in a linear on-chip resonator

Optical switches and bifurcation rely on the nonlinear response of materials. Here, we demonstrate linear temporal bifurcation responses in a passive multimode microresonator, with strongly coupled chaotic and whispering gallery modes (WGMs). In microdisks, the chaotic modes exhibit broadband transfer within the deformed cavities, but their transient response is less explored and yields a random output of the analog signal distributed uniformly from “0” to “1.” Here, we build chaotic states by perturbing the multimode microring resonators with densely packed silicon nanocrystals on the waveguide surface. In vivo measurements reveal random and “digitized” output that ONLY populates around 0 and 1 intensity levels. The bus waveguide mode couples first to chaotic modes, then either dissipates or tunnels into stable WGMs. This binary pathway generates high-contrast, digitized outputs. In conclusion, the fully passive device enables real-time conversion of periodic clock signals into binary outputs with contrasts exceeding 12.3 dB, data rates of up to 10 7 · bits per second, and 20 dB dynamic range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Comparative Analysis of Standard and Advanced USL Methodologies for Nuclear Criticality Safety

The American National Standards Institute/American Nuclear Society national standards 8.1 and 8.24 provide guidance on the requirements and recommendations for establishing confidence in the results of the computerized models used to support operation with fissionable materials. By design, the guidance is not prescriptive, leaving freedom to the analysts to determine how the various sources of uncertainties are to be statistically aggregated. Due to the involved use of statistics entangled with heuristic recipes, the resulting safety margins are often difficult to interpret. Also, these technical margins are augmented by additional administrative margins, which are required to ensure compliance with safety standards or regulations, eliminating the incentive to understand their differences. With the new resurgent wave of advanced nuclear systems, e.g., advanced reactors, fuel cycles, and fuel concepts, focused on economizing operation, there is a strong need to develop a clear understanding of the uncertainties and their consolidation methods to reduce them in manners that can be scientifically defended. In response, the current studies compare the analyses behind four notable methodologies for upper subcriticality limit estimation that have been documented in the nuclear criticality safety literature: the parametric, nonparametric, Whisper, and TSURFER methodologies. Specifically, the work offers a deep dive into the various assumptions of the noted methodologies, their adequacies, and their limitations to provide guidance on developing confidence for the emergent nuclear systems that are expected to be challenged by the scarcity of experimental data. Here, to limit the scope, the current work focuses on the application of these methodologies to criticality safety experiments, where the goal is to calculate a bias, a bias uncertainty, and a tolerance limit for k eff in support of determining an upper subcriticality limit for nuclear criticality safety.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2025

Design Optimization of a Criticality Experiment for the Molten Chloride Reactor Experiment Facility

Neutronics simulations of Molten Chloride Fast Reactors have quantifiable biases that arise from nuclear data, modeling choices, or numerical methods. The multiphysics nature of molten salt reactors makes it challenging to disentangle neutronics modeling biases from biases originating from other physical phenomena. In comparison to a mock-up reactor, criticality experiments can specifically assess the neutronics modeling bias while limiting multiphysics effects. The criticality experiment must be neutronically representative of the full-scale reactor to be valuable. Here, in this paper, we describe the design of a criticality experiment to validate only the neutronics of TerraPower’s Molten Chloride Reactor Experiment (MCRE) and its criticality safety upset scenarios. The proposed experiment uses different chlorine-containing materials to maximize its similarity to the MCRE. The design process uses a constrained Bayesian optimization algorithm to investigate different objective functions that use covariance information for 35 Cl nuclear data. The experiments could reduce the nuclear data–induced uncertainty in k eff of the MCRE from 2161 to 886 pcm. They would also increase the upper subcritical limit of the MCRE criticality safety upset scenario from 0.94101 to 0.94476 when using the WHISPER analysis framework.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Expanded Intercomparison of Nuclear Data Libraries Using Jupiter and Jupiter High-240 Experiments

There is a limited availability of plutonium experiments with sensitivity to lead in the ICSBEP (International Handbook of Evaluated Criticality Safety Benchmark Experiments) Handbook. The Jupiter and Jupiter High-240 experiments were performed at the National Criticality Experiments Research Center as a collaborative effort between Los Alamos National Laboratory and the Japan Atomic Energy Agency to assess lead void coefficients in a plutonium-lead system containing weapons- and reactor-grade plutonium, respectively. Concurrent with benchmark development, an intercomparison of calculations using different nuclear data libraries has been performed to assess the usability of the experimental data for nuclear data adjustment in a “softer-that-fast” neutron energy spectrum. Eigenvalue calculations using MCNP with the ENDF/B-VIII.0 and TENDL-2021 nuclear data libraries calculate closest to the benchmark values for Jupiter. Calculations using JENDL-5 and ENDF/B-VIII.1 match best with the Jupiter High-240 values. Lead void worth calculations using the various nuclear data libraries are all within 3σ of their respective measured values. Perturbation studies between ENDF/B-VIII.0 and ENDF/B-VIII.1 demonstrate an approximate increase in calculated eigenvalues for the Jupiter series experiments by ~240 pcm for plutonium (mostly 239 Pu) and ~120 pcm for lead accompanied by a decrease contributed by ~113 pcm for copper and ~13 pcm for stainless steel. Nuclear data sensitivities and uncertainties investigated using Whisper show slightly lower sensitivity to scatter than a lead-reflected plutonium sphere but greater sensitivity to neutron capture. The sensitivities between Jupiter and Jupiter High-240 for lead are very similar for both ENDF/B-VIII.0 and ENDF/B-VIII.1 nuclear data. These benchmarks are more sensitive to neutron capture in lead than other plutonium benchmark experiments and would be useful for both lead and 240 Pu validation. In conclusion, with the high degree of compensating effects between copper, lead, and plutonium cross sections, additional isolated Pb-Pu and Cu-Pu benchmarks would be beneficial in improving these nuclear data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Characterization of Microwave Loss Using Multimode Superconducting Resonators

Measuring the losses arising from different materials and interfaces is crucial to improving the coherence of superconducting quantum circuits. Although this has been of interest for a long time, current studies can either only provide bounds to those losses, or require several devices for a complete characterization. In this work, we introduce a method to measure the microwave losses of materials and interfaces with a single multi-mode superconducting resonator. We demonstrate a formalism for analyzing the loss sensitivity of multi-mode systems and discuss the design strategies of multi-mode resonators for material loss studies. We present two types of multi-mode superconducting resonators for the study of bulk superconductors: the forky whispering-gallery-mode resonator (FWGMR) and the ellipsoidal cavity. We use these resonators to measure the surface dielectric, conductor, and seam losses of high-purity (5N5) aluminum and aluminum alloy (6061), as well as how they are affected by chemical etching, diamond turning, and thin-film coating. Here, we find that chemical etching and diamond turning reduce both the surface dielectric and conductive losses of high-purity aluminum, but provide no appreciable improvement to the seam. Coating the surfaces of diamond-turned aluminum alloys with e-beam evaporated or sputtered aluminum thinfilms significantly reduces all three losses under study. In addition, we study the effect of chemical etching on the surface of high-purity aluminum using transmission electron microscopy (TEM) and find that the chemical etching process creates a thinner and more uniform oxide layer, consistent with the observed improvement in the surface dielectric loss.

25 ENERGY STORAGE↗
DOE OSTI2022

Topology-empowered membrane devices for terahertz photonics

Control of terahertz waves offers a profound platform for next-generation sensing, imaging, and information communications. However, all conventional terahertz components and systems suffer from bulky design, sensitivity to imperfections, and transmission loss. We propose and experimentally demonstrate on-chip integration and miniaturization of topological devices, which may address many existing drawbacks of the terahertz technology. We design and fabricate topological devices based on valley-Hall photonic structures that can be employed for various integrated components of on-chip terahertz systems. We demonstrate valley-locked asymmetric energy flow and mode conversion with topological waveguide, multiport couplers, wave division, and whispering gallery mode resonators. Our devices are based on topological membrane metasurfaces, which are of great importance for developing on-chip photonics and bring many features into terahertz technology.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Real-Time Tracking of Carbon Dioxide Concentration Using an Optical Microsphere Resonator Sensor

Whispering gallery mode resonator sensors are nondisruptive optical sensors that can detect and monitor perturbations in a gaseous environment. Through its resonant properties of peak wavelength, amplitude, and quality factor (Q factor), changes in concentration can be quantified within seconds and monitored over days with great stability. In addition, the small footprint, low cost, and high sensitivity are ideal properties for a disposable sensor that can be utilized in extreme environments. Further, the large Q factor of the resonant cavity enables long interaction lengths and amplifies the effect of small changes in the background refractive index, which is detectable in picometer shifts of the resonance wavelength. However, this measurement is susceptible to changes in other environmental factors such as temperature, pressure, and humidity, which manifest on the picometer wavelength scale, reinforcing the need to decouple the variables. In this work, we compare the spectral response of different diameter resonators to carbon dioxide, nitrogen, and its mixtures, observing the spectral shifting and broadening of the cavity resonance near 1550 nm. In addition, the effect of environmental temperature on spectral shifting due to the thermo-optic effect is characterized and quantified. Lastly, the gas concentrations are changed in real time to showcase the tracking and recovery capabilities of the resonator sensor.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Validation of MCNP Critical Benchmark Models of Moderated Highly Enriched Uranium Slabs

A new centralized repository of high-quality MCNP models of critical benchmark experiments is currently under development at Los Alamos National Laboratory (LANL). The benchmark experiments are described in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook, and the initial set of benchmark models are derived from the Whisper Suite provided with MCNP6.2. This effort is a collaboration among the Nuclear Criticality Safety, Nuclear Data, and Monte Carlo code development/application organizations at LANL. The goal is to build a single LANL benchmark collection that is up to date with the latest ICSBEP revision, has a formal review and revision process, is contained in an open-source repository, and utilizes new Python tools for improved input and output file review. This paper describes the validation of the models associated with HEU-MET-FAST-007, “Uranium Metal Slabs Moderated with Polyethylene, Plexiglas, and Teflon”. The Monte Carlo n-Particle (MCNP) models were compared to the second revision of HEU-MET-FAST-007. The experiment considered critical configurations of highly enriched uranium (HEU) metal slabs and various moderators in 43 unique cases. The slabs of uranium were separated by layers of moderating material, forming an assembly. The assembly was separated in two halves with one half placed on a stationary table and the other attached to a moveable table that could be raised and lowered via pulleys connected to the ceiling of the shielded room. To reach criticality, the two halves were brought together with a negligible gap between the assemblies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Integrated reference cavity with dual-mode optical thermometry for frequency correction

Photonic integrated resonators have advantages over traditional benchtop cavities in terms of size, weight, and cost with the potential to enable applications that require spectrally pure light. However, integrated resonators suffer from temperature-dependent frequency variations and are sensitive to external environmental perturbations, which hinders their usage in precision frequency applications. One solution is to use interrogation of the cavity temperature through dual-mode optical thermometry (DMOT) by measuring the shift of the resonance frequency difference between two polarization or optical frequency modes. Yet this approach has only been demonstrated in bulk-optic whispering gallery mode and fiber resonators. In this paper, we implement dual-mode optical thermometry in an ultra-high Q integrated silicon nitride resonator. A dual-mode resonance frequency difference temperature sensitivity of 188 ± <#comment/> 15 M H z / K is measured. We demonstrate feedforward DMOT frequency correction that, under an applied external temperature ramp, is able to reduce the optical frequency change to 0.31 kHz/s as compared to an uncorrected 10.03 kHz/s, a factor of 30 × <#comment/> reduction. These results show promise for on-chip frequency correction solutions for quantum, metrology, atomic, and coherent optical communications applications.

Zhao, Qiancheng (ORCID:0000000206968667)↗
DOE OSTI2021

MicroResonators for Compacts Optical Sensors (μRCOS)

As the demand for continuous, in-situ surveillance of health of systems and environments rapidly increases, miniaturized sensors with fast responses are sought. Optical dielectric resonators supporting Whispering Gallery Modes (WGMs) have exceptional properties, like very high-power density, very narrow spectral linewidth, and extremely small mode volume. As the footprint of these sensors is drastically reduced, measurements of microvolumes samples with dramatic reduction in analysis time are possible, enabling large numbers of parallel analyses using microarrays. The high sensitivity and speed of WGM resonators combined with the ability to detect molecules in their native state have great future potential for basic and applied research such as reliable single molecule, trace-gas detection, environmental monitoring, chemical threat sensing, and biodefense Such appealing peculiarities motivated us developing WMG resonators (WGMRs) for Cavity Enhanced Absorption Spectroscopy (CEAS) for chem-bio detection. Specifically, we designed and batch-fabricated microspheres and fiber tapers for resonances excitation. We successfully detected gases (N 2 and CO 2 ) in customized environmental chambers, and bio-organisms (Inf. A and E. Coli) with integrated microfluidic systems. Background calibration and environmental isolation were always accounted for in proving the performances.

36 MATERIALS SCIENCE↗