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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Preliminary Design of Reactor Cavity Cooling System for a Horizontal Compact HTGR

The Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed MIGHTR in 3 years and support its commercialization as a safe and low-cost HTGR. Argonne National Laboratory (Argonne) is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept. This report documents the preliminary design study of the RCCS for the HC-HTGR. It includes the establishment of the design requirements, a high-level design study by initial scoping calculations, and preliminary performance calculations of the HC-HTGR RCCS design. Design requirements for the HC-HTGR RCCS have been established to guide preliminary design activities and scoping performance calculations. Initial scoping calculations including estimation of the water inventory, estimation of HVAC thermal capability, and a parametric study on loop dimensions by standalone RCCS analysis. Based on scoping calculation results, a set of baseline dimensions of the HC-HTGR RCCS was derived. A water panel modeling approach was investigated to explore various potential design options for the water panel under consideration for the HC-HTGR RCCS using RELAP5-3D. A test case study was performed to assess the prediction capability of two modeling approaches. The results were compared with CFD simulations conducted in constant RPV temperature and heat flux boundary conditions. It confirms the capability of the RELAP5-3D modeling approach to include all important heat transfer mechanisms expected in the HC-HTGR RCCS operation conditions. Then, a reference RELAP5-3D model for the 1/8 th of a compartment of the preliminary design of the HC-HTGR RCCS was developed. A preliminary performance analysis was conducted to evaluate single-phase natural circulation performance with different top tank temperature values and panel conduction performance in various operation conditions. From single-phase natural circulation performance analysis, the system operation mode was investigated in normal operating and limiting design conditions. It showed operation mode in a subcooled state with a proper top tank water cooling system. Parasitic heat loss by both internal air flow and RCCS was estimated, showing it satisfies maintaining below target maximum heat loss of the HC-HTGR RCCS. From the panel conduction performance analysis, two candidate materials for the riser tube such as carbon steel and stainless steel were compared in the thermal performance of HC-HTGR RCCS. From a single water panel test compared with CFD simulation results, it was confirmed that the current capability of the RELAP5-3D modeling approach for the water panel predicts the thermal conduction of two different materials of the water panel. Then, system-level thermal performance analysis was performed for 1/8 th of the compartment of the preliminary HC-HTGR RCCS design. It was first observed that the current preliminary HC-HTGR RCCS design had minimal impact on the overall thermal performance of the water panel by changing pipe material from carbon steel to stainless steel. From Argonne’s effort on the ongoing water-based NSTF testing program, several considerations other than the thermal performance point of view were addressed to be considered in selecting pipe materials.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Synthesis and Crystal and Electronic Structures of the Zintl Phase Sr21Cd4Sb18

Reported herein are the synthesis and crystal chemistry analysis of the Zintl phase Sr21Cd4Sb18. Single crystals of this compound were grown using the Sn-flux method, and structural characterization was carried out using single-crystal X-ray diffraction. Crystal data: Monoclinic space group C2/m (No. 12, Z = 4); a = 18.2536(6) Å, b = 17.4018(5) Å, and c = 17.8979(6) Å, β = 92.024(1)°. The structure is based on edge- and corner-shared CdSb4 tetrahedra, which ultimately form octameric [Cd8Sb22] fragments, where two symmetry-equivalent subunits are connected via a homoatomic Sb–Sb interaction. The electronic band structure calculations contained herein reveal the emergence of a direct gap between the valence and the conduction bands.

Ghosh, Kowsik (ORCID:0000000326227046)↗
DOE OSTI2023

Evaluation of LPBF Steels for Nuclear Applications

This report provides an update on the prioritization of existing reactor materials for advanced manufacturing. This report is a Milestone 3 deliverable in FY2023, under work package CT-23AN130401 to support research and qualification activities supported by the Advanced Materials and Manufacturing Technologies (AMMT) program here at Argonne National Laboratory (ANL). The focus of FY23 for ANL included the determination of a decision criteria matrix for the prioritization of existing materials, the literature review of a select few Fe-based alloys, and working with vendors to obtain customized powders. The work package also includes fabricating test samples in a Renishaw AM400 Laser Powder Bed Fusion (LPBF) system and optimizing the process parameters. The major outcomes of this work package are: With collaborations from PNNL, ORNL, and INL, we were able to establish a decision criteria matrix containing a total of 6 categories and 31 different criteria. These will be used to downselect alloys for further evaluation; As part of that, 6 different Fe-based alloys were selected, 3 austenitic stainless steels (A709, D9, AFA) and 3 ferritic/martensitic steels (HT9, Grade 91, Grade 92). Customized powders were obtained from vendors in small quantities to fabricate initial prints to check printability of these specific alloys; A total of 72 single track experiments were performed on two alloy systems, 1 austenitic stainless steel (A709) and 1 ferritic/martensitic steel (Grade 91) in order to optimize the process parameters for the full 3d prints. The optimization led to the selection of 20 different processing conditions, 10 for each class of alloys; D9 and AFA alloys showed extensive cracking and porosity in the samples. This was due to less-than-ideal conditions present in the chamber during the deposition. A709 printed using the same process parameters showed almost fully dense samples with no noticeable porosity or any other defects. SEM and EBSD analysis revealed single phase FCC microstructure with cellular structure within the grains; HT9, Grade 91, Grade 92 alloys also showed no noticeable signs of cracking and ImageJ analysis showed porosity <0.5% in all conditions. While Grade 91 and Grade 92 showed single phase BCC microstructures, the presence of martensite laths was noted in HT9 alloy; Future work will include further characterization of these alloys to better understand the microstructural evolution during the 3d printing process.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

An Analysis of Published DAS Studies for Application to SPE Phase III

Distributed Acoustic Sensing (DAS) is an emerging technology capable of recording the acoustic wavefield at unprecedented spatial resolution. However, this new tool requires significant refinements before it becomes operational for explosion monitoring objectives. Recent studies have shown significant development of array processing with DAS data. In this report we explore three such array processing methods including DAS strain-rate data versus geophone measured ground motion, beamforming for event parameters, and machine learning based denoising. Prior to applying these algorithms to the Source Physics Experiment Phase II and Phase III data, we validate these methods through replication analysis.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

On-Line Monitoring of Gas-Phase Molecular Iodine Using Raman and Fluorescence Spectroscopy Paired with Chemometric Analysis

Molten salt reactors (MSRs) have the potential to safely support green energy goals. However, licensing and deployment of these systems will be aided through development of new technology. This includes on-line monitoring tools for real-time compositional analysis. Of particular interest is quantifying iodine within reactor off-gas streams to support design and operational control of reactor off-gas treatment systems. Here we discuss the development of advanced Raman spectroscopy systems for the on-line analysis of I 2(g) within the gas phase. Signal response is explored with two Raman instruments utilizing a 532 nm and a 671 nm excitation source, as a function of I 2(g) pressure and temperature. Furthermore, the applicability of chemometric modeling for advanced analysis of data is explored. Raman spectroscopy paired with chemometric analysis is demonstrated to be a powerful route to analyzing I 2(g) composition within the gas phase, which lays the foundation for applications within molten salt reactor off-gas analysis and other significant chemical processes producing iodine species.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Intentional Uranium Tagging for Material Provenance and Pathway Forensics (LA19-Intentional-Forensics-NDD3Bb) (Annual Report for FY21)

This report describes the outcomes of the third and final year of a project to research the feasibility of tagging uranium materials, especially nuclear fuels. The experimental focus remained on metallic uranium forms under prospective surface and bulk tagging scenarios. Overall, the results showed that the tags could be successfully imparted and characterized in both as-built and degraded conditions. This was in line with expectations coming into this project, indicating promise for both surface and bulk tagging of metallic forms of uranium. Multiple surface tagging techniques and detection strategies were explored in FY21, with an emphasis on improving tag quality, readability, and detection in the field. Non-radioactive materials were used as a testbed. Selective deposition via laser beam was determined to be successful in imparting a readable titanium deposit on a stainless steel base plate, and can be read with high resolution characterization techniques (e.g., scanning electron microscopy) and field capable tools (e.g., eddy current testing). Other deposition techniques, such as selective deposition via electron beam and photoluminescent tags, were explored in FY21, and while success for these techniques would be dependent on additional work, these techniques showed potential for surface tagging applications. To survey bulk taggant elements for bulk uranium metal, 16 tagging elements were spread among 18 depleted uranium castings (4 baseline, 3 mix, 1 dilution, and 10 recycle). Most of these were made and characterized in FY21. Taggant acceptability was based upon manufacturability, detectability, and persistence from the standpoint of two detection options: bulk chemical analysis (for “chemical taggants”) and microstructural analysis (for “second phase taggants”). Taggant detection in both up-front manufacturing and in the face of “degradations” such as dilution, mixing, and recycling was generally good. Two independent laboratories carried out chemical analysis on most of the castings, and often at several locations within a casting, and the results are discussed. Scanning electron microscopy+EDS microanalysis revealed the second phases mostly contained the expected tagging elements. The shapes and 2 spatial distributions of these micron-sized carbides, oxides, and intermetallic particles offers opportunities for further science-based investigation and tagging optimization. Overall, V and Co currently appear as the best choices for chemical taggants while Al, Ti, Mn, Co, Pd, and Tb all look good as second phase taggants. The other elements considered here – Sc, Ni, Ge, Nb, Ce, Ta, W, Ir, and Au – while not being ruled out, require more study to become viable options. It is of special note that in the recycling study only one of the 12 elements fell out of detection even after 10 meltings, demonstrating their persistence. An Appendix tabulates all chemical analysis results to enable more quantitative and statistical studies of detection opportunities and limitations, as a part of a related project.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Controlling topology through targeted composite symmetry manipulation in magnetic systems

The possibility of selecting magnetic space groups by orienting the magnetization direction or tuning magnetic orders offers a vast playground for engineering symmetry-protected topological phases in magnetic materials. In this work, we study how selective tuning of symmetry and magnetism can influence and control the resulting topology in a two-dimensional magnetic system, and we illustrate such a procedure in the ferromagnetic monolayer MnPSe 3 . Density functional theory calculations reveal a symmetry-protected accidental semimetallic (SM) phase for out-of-plane magnetization, which becomes an insulator when the magnetization is tilted in-plane, reaching band-gap values close to 100 meV. We identify an order-2 composite antiunitary symmetry and threefold rotational symmetry that induce the band crossing, and we classify the possible topological phases using symmetry analysis, which we support with tight-binding and k · p models. Breaking of inversion symmetry opens a gap in the SM phase, giving rise to a Chern insulator. We demonstrate this explicitly in the isostructural Janus compound Mn 2 ⁢P 2 ⁢S 3 ⁢Se 3 , which naturally exhibits Rashba spin-orbit coupling that breaks inversion symmetry. Our results map out the phase space of topological properties of ferromagnetic transition-metal phosphorus trichalcogenides, and they demonstrate the potential of the magnetization-dependent metal-to-insulator transition as a spin switch in integrated two-dimensional electronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Spinodal electronic phase separation during insulator-metal transitions

Electronic phase transitions such as insulator-metal transitions are common in strongly correlated systems. Here, using a combination of thermodynamic linear-stability analysis and phase-field simulations and employing VO 2 as a prototypical example, we predict that an insulator-metal transition driven by photoexcitation may involve an intermediate, modulated charge density state with a temperature-dependent characteristic wavelength. It is shown that such an intermediate two-phase electronic state is formed through a spinodal mechanism and that its formation can be generic for insulator-metal transitions driven by fast stimuli. This transient electronic phase separation is expected to stimulate future experimental and computational efforts.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Root Cause Analysis of AC Overcurrent in July 2020 San Fernando Disturbance

On July 7 2020, approximately 1,000 MW reduction in solar photovoltaic (PV) output was experienced by the bulk power system in Southern California after a three-phase fault. Disturbance analysis indicates that instantaneous AC current caused inverter tripping. The projection of the root cause of AC overcurrent from the NERC report is that inverter current control is not tight. This letter provides a quantitative analysis on ac overcurrent and addresses the following questions: (i) what type of current controls may lead to ac overcurrent; and (ii) how controller parameters and grid strength influence ac overcurrent. Here, the letter provides frequency-domain analysis and time-domain simulation results of a grid-integrated inverter to illustrate the effect of control parameters and grid strength on ac overcurrent.

14 SOLAR ENERGY↗
DOE OSTI2024

Ensuring Solution Uniqueness in Three-Phase Power System State Estimation

This paper is concerned with the issue of potential non-unique solutions in three-phase state estimation. Theory of observability analysis for positive sequence power system state estimation is based on certain assumptions that avoid possibility of multiple solutions. Also, it is shown that observability of a positive sequence network remains independent of the network parameters or the operating state. When extending single-phase observability analysis directly to the three-phase case, this paper considers the possibility of converging to multiple solutions, i.e. solution non-uniqueness, even for cases where state estimator successfully converges. The study illustrates via numerical examples the likelihood of converging to entirely different solutions for certain network parameters. It also examines how the operating state, particularly under unbalanced loading, leads to solution non-uniqueness. The paper then describes an alternative approach to ensure a unique solution in three-phase state estimation. This method aims to accurately and uniquely estimate the state of any unbalanced three-phase system, irrespective of load imbalance, network configuration, existence of synchronous generators or transformers.

Power System State Estimation, Three-Phase, Distri↗
DOE OSTI2022

Synthesis and structure of high-purity BaCe 0.25 Mn 0.75 O 3 : an improved material for thermochemical water splitting

Solar thermochemical hydrogen production (STCH) via redox-active metal oxides is an approach for direct solar-driven hydrogen generation typically using a high-temperature redox cycle involving refractory oxides and steam. Typical cycles involve high-temperature reduction of oxides to form oxygen vacancies, followed by lower temperature reaction between oxygen vacancies and steam where the oxide is re-oxidized and the steam is reduced to hydrogen. Only a few materials have demonstrated reversible cycling under the typically harsh STCH conditions (e.g. 1500°C reduction, 900°C re-oxidation) and critical questions remain on the true reversibility of non-stoichiometric multi-cation oxide systems, significantly hampered by the lack of single-phase samples for these material systems. To date, most STCH processes have relied on CeO 2 as a benchmark active material, but more recently, the 12R phase of BaCe 0.25 Mn 0.75 O 3 (BCM) has demonstrated greater hydrogen-generation potential at lower peak temperatures. However, previous reports of 12R-BCM have included large fractions, > 10 wt%, of secondary phases, which complicate analysis of the stability and performance. A comprehensive understanding of the redox mechanism and reversibility of the process in BCM can only be achieved with nearly single-phase samples which, to date, have been difficult to produce. Here two approaches to BCM synthesis are reported: solid state and sol–gel-based routes. It is demonstrated that both routes can be tuned to produce the 12R structure with > 97 wt% yield when annealed ≥1450°C. Herein synchrotron-based diffraction measurements of rhombohedral 12R-BCM enabled characterization of the anisotropy between thermal expansion along the c-axis and within the ab plane. The impact of high-temperature redox cycling on the stability and phase fraction of the 12R-BCM polytype was also investigated. Our results offer two viable routes for synthesis of high-purity 12R-BCM critically needed for evaluating the efficacy of BCM as a STCH material and validate its ability to split water at lower temperatures over extended numbers of redox cycles.

08 HYDROGEN↗
DOE OSTI2020

High-speed x-ray phase contrast imaging and digital image correlation analysis of microscale shock response of an additively manufactured energetic material simulant

The performance of energetic materials subjected to dynamic loading significantly depends on their micro- and meso-scale structural morphology. The geometric versatility offered by additive manufacturing opens new pathways to tailor the performance of these materials. Additively manufactured energetic materials (AMEMs) have a wide range of structural characteristics with a hierarchy of length scales and process-inherent heterogeneities, which are hitherto difficult to precisely control. It is important to understand how these features affect AMEMs’ response under dynamic/shock loading. Therefore, temporally and spatially resolved measurements of both macroscopic behavior and micro- and meso-level processes influencing macroscopic behavior are required. In this paper, we analyze the shock compression response of an AMEM simulant loaded under several impact conditions and orientations. Furthermore, x-ray phase contrast imaging (PCI) is used to track features across the observed shock front and determine the linear shock velocity vs particle velocity equation of state, as well as to quantify the interior deformation fields via digital image correlation (DIC) analyses. Photon Doppler velocimetry is simultaneously used to measure the particle velocities of the specimens, which are consistent with those obtained from x-ray PCI. The DIC analyses provide an assessment of the average strain fields inside the material, showing that the average axial strain depends on the loading intensity and reaches as high as 0.23 for impact velocities up to 1.5 km/s. The overall results demonstrate the utility of x-ray PCI for probing “in-material” equation of state and interior strains associated with dynamic shock compression behavior of the AMEM simulant.

3D printing↗
DOE OSTI2024

An Investigation of Oxides of Tantalum Produced by Pulsed Laser Ablation and Continuous Wave Laser Heating

Recent progress has seen multiple Ta 2 O 5 polymorphs generated by different synthesis techniques. However, discrepancies arise when these polymorphs are produced in widely varying thermodynamic conditions and characterized using different techniques. This work aimed to characterize and compare Ta 2 O 5 particles formed at high and low temperatures using nanosecond pulsed laser ablation (PLA) and continuous wave (CW) laser heating of a local area of tantalum in either air or an 18 O 2 atmosphere. Scanning electron microscopy (SEM) and Raman spectroscopy of the micrometer-sized particles generated by PLA were consistent with either a localized amorphous Ta 2 O 5 phase or a similar, but not identical, crystalline β-Ta 2 O 5 phase. The Raman spectrum of the material formed at the point of CW laser impingement was in good agreement with the previously established ceramic “H-Ta 2 O 5 ” phase. TEM and electron diffraction analysis of these particles indicated the phase structure matched an oxygen-vacated superstructure of monoclinic H-Ta 2 O 5 . Further from the point of laser impingement, CW heating produced particles with a Raman spectrum that matched β-Ta 2 O 5 . We confirmed that the high-temperature ceramic phase characterized in previous work by Raman spectroscopy was the same monoclinic phase characterized in different work by TEM and could be produced by direct laser heating of metal in air.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

2D gravity↗
DOE OSTI2026

Raman spectroscopic investigation of ianthinite [U$_2^{4+}$(UO$_2$)$_4$O$_6$(OH)$_4$(H$_2$O)$_4$]·$5$H$_2$O, a rare mixed-valence uranium oxide hydrate

Ianthinite ([[U$_2^{4+}$(UO$_2$)$_4$O$_6$(OH)$_4$(H$_2$O)$_4$]·$5$H$_2$O) is an exotic mineral that possesses U in both tetravalent and hexavalent oxidation states and is structurally related to the U 3 O 8 polymorphs, which are commonly encountered technogenic materials in the nuclear fuel cycle. Despite the similarities between U 3 O 8 and ianthinite, and the importance of ianthinite in U paragenesis, no Raman spectra have been reported for this mineral. Here, to gain a more complete understanding of how structural attributes of ianthinite give rise to observable spectroscopic features and how these may relate to important materials in the nuclear fuel cycle, we provide, for the first time, Raman spectra of ianthinite. Ianthinite readily oxidizes at ambient conditions, complicating analysis of phase-pure material. Several analytical methods are employed herein to decouple the Raman features of ianthinite from its alteration product(s). First, a simple difference spectrum is presented, then results of Raman spectroscopic mapping are employed, and finally, we use a novel processing and analysis method. Each analysis method provides different insight into structural features that are unique to ianthinite, in particular, features that are attributable to U(IV) in distorted octahedral coordination in both ianthinite and U 3 O 8 phases.

Spano, Tyler L. [Oak Ridge National Laboratory (OR↗
DOE OSTI2025

Linking the Spin Transition of Ferric Iron in δ‐(Al,Fe)OOH to Water Storage in the Lower Mantle

As the most massive geochemical reservoir, the lower mantle affects the Earth's budget of volatile elements, including hydrogen or H 2 O. The properties of minerals in the lower mantle are further affected by changes in the electronic configurations of iron cations, that is, by spin transitions. The feedback between spin transitions and potential storage of H 2 O in solid hydrous phases in the lower mantle, however, remains unexplored. By combining high‐pressure nuclear resonant inelastic X‐ray scattering and high‐pressure high‐temperature X‐ray diffraction experiments, we constrained the thermal equation of state of δ‐(Al,Fe)OOH, a member of the phase H solid solution. Based on the derived thermal equation of state of δ‐(Al,Fe)OOH and the underlying thermodynamic model, we calculate the excess Gibbs free energy that arises from the spin transition of ferric iron in this compound and evaluate the effect on phase equilibria. The results of our analysis show that the spin transition of ferric iron in phase H may significantly reduce the thermodynamic activity and hence the concentration of H 2 O in a coexisting hydrous melt. As a consequence, nominally anhydrous minerals of the lower mantle may become dehydrated in the presence of phase H. Our analysis further suggests that, under certain conditions, the spin transition may expand the thermal stability of Fe 3+ ‐bearing phase H and create a geochemical link between the storage of H 2 O in phase H and ferric iron in the lower mantle.

Buchen, Johannes [Univ. of Bayreuth (Germany); Cal↗
DOE OSTI2022

Isolating intermediate Mg 11 Cu 6 Al 12 phase in ternary Mg-Cu-Al alloy by electrolytic dealloying

While dealloying is widely used to create nanoporous materials, it has rarely been employed to isolate difficult-to-synthesize intermediate phases. Here, in this work, we show how air-free, electrolytic dealloying at room temperature can be used to isolate the ternary intermetallic Mg 11 Cu 6 Al 12 phase. We create a ternary Mg-Cu-Al parent alloy containing the Mg 11 Cu 6 Al 12 compound and other phases, then subsequently remove these other phases via electrolytic dealloying to isolate the Mg 11 Cu 6 Al 12 phase. Isolated Mg 11 Cu 6 Al 12 phase exhibits ≈1 μm diameter rod-shaped microstructure. Phase and chemical analysis conducted using various techniques, including inductively coupled plasma and lab and synchrotron-based X-ray diffraction, show minimal impurities. This new approach to isolate the Mg 11 Cu 6 Al 12 phase can unlock its use in fundamental research and can be applied to other difficult-to-synthesize intermetallic compounds.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap Δ$^α_k$, for all momenta k on the Fermi surface of every band α. While there are a variety of techniques for determining |Δ$^α_k$|, no general method existed to measure the signed values of Δ$^α_k$. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where Δ$^α_k$ has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the Δ$^α_k$ it generates to the Δ$^α_k$ determined from single-atom scattering in FeSe where s ± energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for Δ$^α_k$ of opposite sign.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗