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At least 631 records · Page 35

3D Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred‐Nanometer Thickness

Magnetic topological states refer to a class of exotic phases in magnetic materials with the non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10 nm. Here, molecular beam epitaxy (MBE) is employed to synthesize magnetic TI trilayers with a thickness of up to ≈106 nm. It is found that these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying the magnetic dopants, gate voltages, temperature, and external magnetic fields, the properties of these thick QAH insulators are examined and the robustness of the 3D QAH effect is demonstrated. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of the thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law.

36 MATERIALS SCIENCE↗

Effect of insulator end cap thickness on time-dependent Hartmann flow in a rotating mirror

We present a framework for analysing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device CMFX (centrifugal magnetic fusion experiment), which will employ more sophisticated physics and realistic magnetic field geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SciDAC ISEP: Integrated Simulation of Energetic Particles in Burning Plasmas

The objective of the SciDAC Center for Integrated Simulation of Energetic Particles in Burning Plasmas (ISEP) is to improve physics understanding of energetic particle (EP) confinement and EP interactions with burning thermal plasmas through large-scale simulations. The ISEP center will develop a multiscale and multiphysics ISEP framework for a predictive capability of EP physics and deliver an EP module incorporating both first-principles simulations and high fidelity reduced transport models to the fusion whole device modeling (WDM) project. The ISEP framework will enable us to perform long time, global kinetic simulations of EP physics in burning plasmas, by utilizing the full power of the next generation supercomputers. Our research and development activities will build on fruitful collaborations with computer scientists and applied mathematicians to offer enabling technologies for performance scalability, portability, solvers, coupling for integration with the fusion WDM project, and long-term preservation of data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

TiN‐Au/HfO 2 ‐Au Multilayer Thin Films with Tunable Hyperbolic Optical Response

Abstract Hyperbolic metamaterials (HMM) possess significant anisotropic physical properties and tunability and thus find many applications in integrated photonic devices. HMMs consisting of metal and dielectric phases in either multilayer or vertically aligned nanocomposites (VAN) form are demonstrated with different hyperbolic properties. Herein, self‐assembled HfO 2 ‐Au/TiN‐Au multilayer thin films, combining both the multilayer and VAN designs, are demonstrated. Specifically, Au nanopillars embedded in HfO 2 and TiN layers forming the alternative layers of HfO 2 ‐Au VAN and TiN‐Au VAN. The HfO 2 and TiN layer thickness is carefully controlled by varying laser pulses during pulsed laser deposition (PLD). Interestingly, tunable anisotropic physical properties can be achieved by adjusting the bi‐layer thickness and the number of the bi‐layers. Type II optical hyperbolic dispersion can be obtained from high layer thickness structure (e.g., 20 nm), while it can be transformed into Type I optical hyperbolic dispersion by reducing the thickness to a proper value (e.g., 4 nm). This new nanoscale hybrid metamaterial structure with the three‐phase VAN design shows great potential for tailorable optical components in future integrated devices.

Chemistry↗

Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH2 and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H2 molecule.

Jouzdani, Pejman (ORCID:0000000256470381)↗

Pedestal magnetic turbulence measurements in ELMy H-mode DIII-D plasmas by Faraday-effect polarimetry

Internal magnetic fluctuation measurements are utilized to identify turbulence associated with micro-tearing modes (MTM) in the DIII-D Edge-Localized-Mode (ELM)-y H-mode pedestal. Using a Faraday-effect polarimeter, magnetic turbulence (150–500 kHz) is directly observed with a typical line-averaged fluctuation amplitude of ~0.8 G at peak frequency (250 kHz) and ~15 G integrated over the spectrum from 150 to 500 kHz. Frequency, poloidal wavenumber, and propagation direction of the magnetic turbulence all serve to identify as MTM. Magnetic turbulence amplitude non-monotonically correlates with collision frequency, peaks off mid-plane, and correlates with electron temperature gradient evolution between ELMs, consistent with MTM features identified from theory and gyro-kinetic simulation. The magnetic turbulence growth correlates with confinement degradation in ELMy H-mode plasmas during a slow density ramp. In conclusion, these internal measurements provide unique constraints toward developing physics understanding and validating models of the H-mode pedestal for future devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modelling a Heaving Point-Absorber with a Closed-Loop Control System Using the DualSPHysics Code

The present work addresses the need for an efficient, versatile, accurate and open-source numerical tool to be used during the design stage of wave energy converters (WECs). The device considered here is the heaving point-absorber developed and tested by Sandia National Laboratories. The smoothed particle hydrodynamics (SPH) method, as implemented in DualSPHysics, is proposed since its meshless approach presents some important advantages when simulating floating devices. The dynamics of the power take-off system are also modelled by coupling DualSPHysics with the multi-physics library Project Chrono. A satisfactory matching between experimental and numerical results is obtained for: (i) the heave response of the device when forced via its actuator; (ii) the vertical forces acting on the fixed device under regular waves and; (iii) the heave response of the WEC under the action of both regular waves and the actuator force. This proves the ability of the numerical approach proposed to simulate accurately the fluid–structure interaction along with the WEC’s closed-loop control system. In addition, radiation models built from the experimental and WAMIT results are compared with DualSPHysics by plotting the intrinsic impedance in the frequency domain, showing that the SPH method can be also employed for system identification.

42 ENGINEERING↗

High‐Efficiency Solar Cells Grown on Spalled Germanium for Substrate Reuse without Polishing

Abstract Radical reduction of III–V device costs requires a multifaceted approach attacking both growth and substrate costs. Implementing device removal and substrate reuse provides an opportunity for substrate cost reduction. Controlled spalling allows removal of thin devices from the expensive substrate; however, the fracture‐based process currently generates surfaces with significant morphological changes compared to polished wafers. 49 single junction devices are fabricated across the spalled surface of full 50 mm germanium wafers without chemo‐mechanical polishing before epitaxial growth. Device defects are identified and related to morphological spalling defects—arrest lines, gull wings, and river lines—and their impact on cell performance using physical and functional characterization techniques. River line defects have the most consistent and detrimental effect on cell performance. Devices achieve a single junction efficiency above 23% and open‐circuit voltage of 1.01 V, demonstrating that spalled germanium does not need to be returned to a pristine, polished state to achieve high‐quality device performance.

14 SOLAR ENERGY↗

InAs sidewall tunnel diodes enabled by surface states

Negative differential resistance (NDR), where the device current decreases with increasing bias voltage, is a representative phenomenon where quantum mechanics induces counterintuitive physical behavior and offers promising applications such as high-frequency oscillators, amplifiers, and multilevel logic circuits. While the NDR behavior has been extensively studied in various materials and devices, the role of surface properties in NDR, particularly in InAs-based diodes, remains underexplored. In this work, we report the observation of NDR in vertically structured InAs p + n diodes that exhibit a peak-valley current ratio of ∼6, which is suitably high for applications. Circumference-normalized current–voltage characterization revealed that the NDR originates from band-to-band tunneling between the valence band of p + -InAs and the conduction band of an n + -InAs surface, where the n + surface is due to surface states on otherwise n − -InAs. In addition, by comparing devices with various surface passivation methods (without intentional passivation, benzocyclobutene polymer, and silicon nitride), we found that the surface termination significantly affects the NDR characteristics. We present an equivalent circuit model to explain the observed device behavior. These findings offer insights into surface-enabled NDR phenomena and present new knobs for engineering NDR devices.

Circuit theorems↗

Towards Predictive Plasma Science and Engineering through Revolutionary Multi-Scale Algorithms and Models (Final Report)

This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.

42 ENGINEERING↗

Numerical Modeling & Optimization of the iProTech Pitching Inertial Pump (PIP) Wave Energy Converter (WEC) (CRADA Final Report)

This project represents a continuation of the collaboration between iProTech and NLR to simulate, optimize and design the iProTech Pitching Inertial Pump (PIP) device. The objectives of this TEAMER project are twofold: 1. Refining the physical characteristics of the existing iProTech PIP WEC-Sim model to enhance the model’s fidelity and include controllable components. Key model enhancements target the inclusion of Coulomb friction, the introduction of a controllable bypass valve, and the replacement of traditional check valves with advanced motorized ones. 2. Exploring traditional and advanced control algorithms. From traditional methods like latching control to cutting-edge reinforcement learning (RL) algorithms, the goal is to ensure the PIP device's adaptability and optimal performance across a range of ocean conditions. NLR is tasked with augmenting the WEC-Sim model and implementing the control algorithms, culminating in performance comparison analyses. iProTech will update their existing 3D models, advise on model improvements, and determine crucial system metrics. WEC-Sim, developed in MATLAB/SIMULINK with Simscape Multibody, is the main piece of software that will be used in this project. Coupled with the MATLAB RL Toolbox, it offers a robust platform for in-depth simulation and optimization of the iProTech PIP device. Building on previous work to explore the PIP design space and optimize its geometry, mass distribution, center of gravity and other key parameters, this project aims to refine iProTech’s existing numerical models and develop effective control algorithms that can seamlessly integrate into their future hardware testing campaigns.

16 TIDAL AND WAVE POWER↗

A spin-wave magnetometer with a positive feedback

In this work, we demonstrate experimentally the operation of a spin-wave magnetometer integrated into a circuit with a positive feedback. The circuit consists of the passive magnetic and active electric parts. The magnetic part includes a sensing element, which is a magnetic cross junction made of Y 3 Fe 2 (FeO 4 ) 3 . The electric part includes a non-linear amplifier and a phase shifter. The electric and magnetic parts are connected via micrometer size antennae. Spin waves are excited by two of these antennae while the output inductive voltage produced by the interfering spin waves is detected by the third antenna. Spin waves propagating in the orthogonal arms of the cross can accumulate significantly different phase shifts, depending on the direction and the strength of the external magnetic field. The output inductive voltage reaches its maximum in the case of constructive spin wave interference. The positive feedback provides further signal amplification. It appears possible to enhance the response function, compared to the passive circuits without a feedback, by a factor of ×100 without an increase in the noise level. The experimental data show a prominent response to the external magnetic field variation, exceeding 5 x 10 3 V/T. The intrinsic noise spectral density of the device can be as low as 10 -16 V 2 /Hz. The estimated sensitivity of the prototype device is 2 x 10 -12 T/√Hz at room temperature. We argue that spin-wave magnetometers can potentially be as sensitive as SQUIDs while operating at room temperature.

36 MATERIALS SCIENCE↗

Enhancement of the spin–orbit torque efficiency in W/Cu/CoFeB heterostructures via interface engineering

Here, the spin-torque ferromagnetic resonance signal and the spin Hall magnetoresistance induced by the spin Hall effect of W/Cu/CoFeB heterostructures with different Cu layer thicknesses (t Cu ) have been systemically studied. The effective spin mixing conductance $g^{↑↓}_{eff}$, the interfacial spin transparency T, and the real spin–orbit torque efficiency ( J s J c ) real show a significant increase compared to the W/CoFeB heterostructure. ( J s J c ) real reaches its maximum of ~0.54, increased up to ~50% at the optimized tCu ~ 0.52 nm according to our theoretical prediction. More importantly, the intrinsic spin Hall angle of W, $θ^{int}_{SH}$ ~ 0.79 ± 0.20, has also been obtained after the correction of the inverse spin Hall effect and T. This suggests that the Cu insertion improves the interface quality and, therefore, assists the spin transport in the heterostructures, which potentially improves the performance of next-generation spintronic devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

UNH TDP - Concurrent Measurements of Inflow, Power Performance, and Loads for a Grid-Synchronized Vertical Axis Cross-Flow Turbine Operating in a Tidal Estuary

This data was collected between October 12 and December 15 of 2021 at the University of New Hampshire (UNH) and Atlantic Marine Energy Center (AMEC) turbine deployment platform (TDP). This data set includes over 29 days of grid connected turbine operation during this 65 day time frame. The priority for this measurement campaign was to collect data while the turbine was electrically connected to the grid by means of a rectifier and inverter. The Fall_2021_UNH_Measurement_Timeline.png highlights when each instrument was functioning and the Fall_2021_UNH_Test_Log.jpg indicates the four main regions for analysis available from this measurement campaign. The TDP is a floating structure moored on the Portsmouth facing side of Memorial Bridge pier #2, which spans the Piscataqua River between Portsmouth, NH and Kittery, ME. The Piscataqua River connects the Great Bay Estuary to the Gulf of Maine and the river currents are dominated by tidal forcing with water velocities exceeding 2.5 m/s during spring ebb tides at this site which were previously characterized by Kaelin Chancey (Assessment Of The Localized Flow And Tidal Energy Conversion System At An Estuarine Bridge - UNH MS Thesis 2019). The turbine under test was a modified New Energy Corporation (Calgary, CA) model EVG-025 4-blade H-Darrius type vertical axis cross flow turbine that rotates in the clockwise direction with a rotor diameter of 3.2m and blade length of 1.7m. The hydro-foil profile was a NACA 0021 with a 10 inch chord length and a blade preset pitch angle of +4deg with a positive angle corresponding with the toe in direction. The standard EVG-025 has a rotor diameter of 3.4m and its rated power output is 25kW at 3 m/s. The rotor diameter was reduced to accommodate the size of the existing TDP moon-pool. This project was pursued to quantify device performance for cross flow turbines operating in a marine environment. Accurate physical models, to characterize cross flow turbine performance, require real operational data sets due to the complexity of blade fluid interactions. This data can help support model development which will help predict turbine performance when analyzing perspective project locations in the future. Instrumentation was deployed to measure; water speed/direction, electrical power output, turbine shaft speed, turbine thrust force, and platform motion. Concurrent measurements of these parameters allow for correlations (cause and affect) to be inferred, allowing for characterization of device performance over a range of operating conditions. Water currents were measured using Acoustic Doppler Current Profilers (ADCP's) and Acoustic Doppler Velocimeters (ADV's) directly upstream and downstream of the turbine for inflow, wake and turbulence measurements. Electrical power output was measured using the Voltsys rectifier and the Shark power meter. Shaft speed was calculated based on the Voltsys measurements of the permanent magnet three phase generator AC generation frequency, coupled directly to the cross flow turbine under test (i.e., no gear box). Platform motions were captured using a Yost IMU (inertial measurement unit). Turbine thrust loading was measured using a reaction arm about the turbine deployment platform spanning beam, where two bi-directional load cells were connected to the system via a pinned connection. This submission includes zipped folders for each instrument containing quality controlled (QC'd) data in daily .csv files for the relevant duration specific to each instrument, along with separate .csv file that contains the units for each variable. Some instrument daily files are quite large and can pose a challenge for a visual spreadsheet editor to open. A processing software like MATLAB or Python is recommended. Note the degree of QC varied between each instrument due to time constraints. Particular time and attention was given to perform quality control tests on the acoustic based instruments that are particularly suscep...

16 TIDAL AND WAVE POWER↗

Understanding the Structure and Dynamics of Conjugated Polymers by Advancing Deuteration Chemistry and Neutron Scattering (Final Report)

The overarching goal of the proposed work was to set up a partnership between the University of Southern Mississippi (USM) and Oak Ridge National Laboratory (ORNL) to develop novel approaches to measure the backbone rigidity of conjugated polymers (CPs) and understand the critical role of sidechains on the backbone conformation and the materials macroscopic property. The backbone rigidity greatly influences the electronic properties of CPs, which ultimately determines the functionality and performance of these materials. Improvements in the electronic properties of CPs would allow for enhanced charge transport in semiconductor devices, improved photovoltaic performance, recycling of waste heat in thermoelectrics, and discovery of new phenomena that will enable the next generation of energy technologies. Although significant progress has been made to optimize the optical and electronic properties of CPs, largely through Edisonian methodologies, it remains a challenge to experimentally characterize conjugated backbone conformation (chain rigidity, torsion, planarity, and short-range order) and relate these to the fundamental optical and electronic properties (electronic coupling, charge transport, etc.). This has left fundamental gaps in our knowledge of the most basic structure/property relationships within these systems, precluded the study of fundamental physical phenomena, and constrained the design and realization of new electronic and device functionalities. Thus, the major goal of this work is to use novel deuteration methodologies via systematic synthetic approaches, and neutron scattering techniques to comprehensively characterize the structural and dynamic properties of CPs in contrast-matching solvents. Our work would, for the first time, elucidate the relationship between backbone rigidity and macroscopic properties. They will also allow a rational formulation of design principles for next-generation CPs that are resilient to disorder through precise control of the delocalized electrons along the polymer backbone. Overall, this project will advance our understanding of the structure, dynamics, and fundamental physics of these materials, which is crucial for enabling the prediction, design, control, and manipulation of current and emerging material electronic properties.

36 MATERIALS SCIENCE↗

Gain characterization of LGAD sensors with beta particles and 28-MeV protons

Low Gain Avalanche Diodes, also known as LGADs, are widely considered for fast-timing applications in high energy physics, nuclear physics, space science, medical imaging, and precision measurements of rare processes. Such devices are silicon-based and feature an intrinsic gain due to a p + -doped layer that allows the production of a controlled avalanche of carriers, with multiplication on the order of 10–100. This technology can provide time resolution on the order of 20–30 ps, and variants of this technology can provide precision tracking too. The characterization of LGAD performance has so far primarily been focused on the interaction of minimum ionizing particles for high energy and nuclear physics applications. This article expands the study of LGAD performance to highly-ionizing particles, such as 28-MeV protons, which are relevant for several future scientific applications, e.g. in biology and medical physics, among others. These studies were performed with a beam of 28-MeV protons from a tandem Van de Graaff accelerator at Brookhaven National Laboratory and beta particles from a ^90Sr source; these were used to characterize the response and the gain of an LGAD as a function of bias voltage and collected charge. Here, the experimental results are also compared to TCAD simulations.

47 OTHER INSTRUMENTATION↗

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↗

Specifying Calibration of Environmental Sensors

The emergence of the Internet of Things is resulting in an increased ability of devices and systems to share data and is generating increasing interest in integrating sensors into a variety of devices deployed in the built environment. The value of such data is a function of how the data can be used. Data-producing devices and systems that enable valuable use-cases in turn can be seen as more valuable. Lighting systems are particularly interesting platforms for integrated sensors. Both indoor and outdoor lighting devices are becoming more connected, and their location is often ideally suited for hosting environmental sensors that can characterize the properties of indoor or outdoor spaces in ways that support a wide variety of use cases, from improving air quality to supporting fault diagnostics and prediction. The value of environmental-sensor-driven use-cases and the lighting systems that house them is dependent to some degree on sensor accuracy. Environmental sensors utilize a wide variety of sensing techniques or technologies and have varying accuracy. More-accurate, laboratory-grade products or reference standards are often used to characterize, refine, calibrate, adjust, and monitor devices that are deployed, or are intended to be deployed, in physical spaces of interest. Sensors or reference standards need to be calibrated periodically to ensure that their use yields accurate measurements. Calibration needs, however, vary in sophistication, based on user and use-case requirements. This paper provides guidance for evaluating the performance of environmental sensors so as to ensure that they meet user or use-case needs. It describes best practices that have been developed for a) calibrating sensors to ensure some known level of accuracy, and b) determining whether calibration-laboratory accreditation meets user or use-case needs. Excerpts from laboratory scopes of accreditation are shared to reveal the diversity of terminology and format among them. In an effort to aid those who currently have sensors calibrated or who have new or changing needs for sensor calibration, rationale is provided for why a specification might be used to request calibration services that meet specific needs. Commercially available calibration-service providers that are accredited for environmental-sensor calibration are compared and contrasted, and a specification template that might be used for requesting this calibration is presented. The specification template should be tailored to meet each user’s needs. To illustrate, an example set of environmental-sensor test conditions (reflecting the planned usage of the device to be calibrated) is used to develop a customized calibration specification, and commercially available service providers are assessed in terms of their qualifications for calibration to that particular implementation of the specification template.

42 ENGINEERING↗