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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2026

An Analysis of Energy Needs and Seawater Extraction Approaches for the Integration of Primary Magnesium Production with Nuclear Power

The cost of primary magnesium production is highly dominated by the energy required to produce the metal. This, along with the current geographical concentration of its production, makes the magnesium price vulnerable as energy-production paradigms begin to rapidly change. In this work, four nuclear-integration pathways for the efficient supply of heat and electricity to magnesium production from a nuclear power plant are considered. A production route using electrified metallothermic reduction is compared to a nuclear-heat-integrated electrolytic pathway. It is shown that the latter can achieve significantly lower primary energy consumption, 261 MJ/kg Mg compared with 416 MJ/kg Mg. The electrolytic pathway can also reduce emissions down to around 2.1 kgCO2/kg Mg, compared to around 34 kgCO2/kg Mg in the Pidgeon process. Beyond energy and emissions, the four pathways considered are also compared to their ability to reduce locational dependence of the production plant and reduce process complexity. This work also highlights future advances in magnesium production with a potential scheme for the efficient extraction of magnesium from seawater with coproduction of desalinated water and the potential of demand-side response from magnesium electrolysis. This is the first work to consider the full integration of primary magnesium production using nuclear cogeneration, and it is hoped the study paves the way for the analysis of economic nuclear integration within metal extraction and manufacturing.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Draft ASME Code Case to qualify L-PBF 316H material for Section III, Division 5 applications

This report documents the AMMT program’s development and submission of a draft ASME Code Case to qualify Laser Powder Bed Fusion (L PBF) Type 316H stainless steel for Section III, Divi-sion 5 Class A and SM high temperature nuclear applications. It summarizes the technical basis, the comprehensive high temperature mechanical test database assembled between 2023–2026, and the proposed code language and qualification framework submitted to ASME. The work was co-ordinated across multiple national laboratories and leverages prior ASME efforts to integrate additive manufacturing into the Boiler & Pressure Vessel Code. The body of the report describes the experimental database and analysis supporting the Code Case: tensile, creep, fatigue, creep fatigue, and thermal aging tests collected from multiple additive manufacturing sites, machine types, and powder lots, with material processed by a solution anneal heat treatment. The dataset — including both full size and subsized specimens and tests oriented parallel and perpendicular to build direction — shows limited tensile anisotropy, tensile properties comparable to wrought 316H, creep strength within the scatter of wrought material, but markedly reduced creep ductility above about 650 °C associated with rapid σ phase formation in L PBF microstructures. The draft Code Case itself prescribes a staged qualification model (manufacturing process qualification, component qualification, and per build witness testing), treats L PBF components as equivalent to Type 316 weld metal for design and inspection, and requires mechanical, chemical, and metallographic controls tied to ASTM/ISO 52946. Key acceptance criteria include tensile tests within a 90% prediction interval of the AMMT dataset, a creep fatigue screening test adapted from ASME Section III, Division 5, Subsection HB, HBB 2800 but with the cycle acceptance reduced to 100 for L PBF material, and double volumetric inspection of production components. The report concludes that the present data support treating L PBF 316H as analogous to conventional fusion weld metal for Division 5 design and inspection, while highlighting important caveats: the σ phase driven loss of creep ductility above ~650 °C, preliminary indications of enhanced creep fatigue sensitivity in some lots, and remaining gaps in long term aging and additional cyclic testing. Recommended next actions include completing outstanding cyclic and long duration creep/aging tests on the solution annealed condition, supporting inclusion of the 316H chemistry and heat treatment in ASTM/ISO 52946, and continuing engagement with ASME and NRC during balloting and review to enable industry adoption.

Messner, Mark C. (ORCID:0000000200404385)↗
DOE OSTI2026

Optimal binning of correlated measurements

Experimental measurements are commonly represented on a discrete grid, requiring a balance between granularity and statistical noise. Two strategies have traditionally been used to improve such representations: selecting an appropriate bin width to control discretization error and applying kernel-based smoothing to suppress fluctuations. Despite their shared goal, these approaches have largely developed independently, without a unified statistical description of how discretization and correlation jointly determine measurement precision. Here, we extend the discussion of optimal interval averaging to a correlation-aware setting by Gaussian process regression, which explicitly accounts for correlations among neighboring bins. Starting from first principles, we derive the mean-squared error of discretized measurements and obtain closed-form asymptotic expressions for the optimal bin width and correlation length. When recast in reduced variables, the theory reveals distinct universal scaling laws governing the error in the correlation-free and correlation-controlled regimes. Characterized by intrinsically smooth intensity profiles and counting-based statistics, neutron scattering measurements are well suited for demonstrating the enhanced error contraction enabled by inter-bin correlations. We show that such improvement is achievable over the experimentally accessible Q-range and across multiple instruments and material systems. These results show that explicitly accounting for correlations systematically reshapes the limits of precision in discretized, noise-limited measurements. More broadly, the framework provides a transferable statistical foundation for optimizing data representation, inference, and experimental design across the physical and data sciences.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2026

Nuclear Security Risks for HALEU Fuels

There is growing interest in high-assay low-enriched uranium (HALEU) for use in advanced nuclear reactors as a high-energy fuel source. The primary objectives of this report are to identify the security risks that directly result from HALEU and to identify the gaps and challenges it presents from a theft and sabotage perspective. This study focuses on HALEU security risks for the front end of the fuel cycle and includes a review of the supply chain, fuel fabrication, and transport for terrestrial reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI1989

Nuclear Safety [Vol. 30, No. 1, January-March 1989]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 1 International Conference on Thermal Reactor Safety: NUCSAFE 88 by A. P. Malinauskas and J. G. Pruett; ACCIDENT ANALYSIS: 18 Chernobyl Today: State of Research by A. Yu. Gagarinskii; CONTROL AND INSTRUMENTATION: 23 Problems Associated with Routine In-Plant Radioactive Effluent Monitoring Systems at U.S. Light-Water Reactors by Barry G. Wahlig, David M. Walker, Mahmoud R. Ghavi, and John M. Palms; DESIGN FEATURES: 34 Twentieth DOE/NRC Nuclear Air-Cleaning Conference by R. R. Bellamy, D. W. Moeller, and M. W. First, 46 Design Options for the Core Support Structure for Liquid-Metal-Cooled Reactor Plants by J. P. Burelbach, W. J. Kann, J. G. Saiveau, and R. W. Seidensticker; ENVIRONMENTAL EFFECTS: 53 The Radiological Consequences of the Chernobyl Accident by L. V. Konstantinov and A. J. González; WASTE AND SPENT FUEL MANAGEMENT: 70 Activities Related to Waste Management Compiled by E. G. Silver; OPERATING EXPERIENCES: 80 Fuel Performance Annual Report for 1986 by W. J. Bailey, 103 Safety Considerations Related to 12-Hour Shift Schedules by S. Gould, 105 Reactor Shutdown Experience Compiled by J. W. Cletcher, 108 Operating U.S. Power Reactors Compiled by E. G. Silver; RECENT DEVELOPMENTS: 130 General Administrative Activities Compiled by E. G. Silver, 140 Reports, Standards, and Safety Guides by D. S. Queener, 145 Status of Power-Reactor Licensing Activities Compiled by E. G. Silver, 153 Proposed Rule Changes as of Sept. 30, 1988; ANNOUNCEMENTS: 69 Northwestern University Short Course on Radiation Safety, 79 International Seminar on Fission Product Transport Processes in Reactor Accidents, 129 Harvard School of Public Health Offers Short Courses, 152 MIT Offers Summer Short Courses on Reactor Safety and Nodal Analysis, 152 Seminar on Use of PCs in Probabilistic Safety Analysis, 157 The Authors, 160 Indexes to Nuclear Safety, Volume 29.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

From the Great Wave of Translation to the Force between Quarks

Here, the chance observation of a novel traveling wave in a canal led over time to the formulation of a nonlinear wave equation—the Korteweg–de Vries equation—that describes strikingly robust disturbances now called solitons. The figure of an isolated soliton corresponds to a reflectionless potential that supports a single bound state in the one-dimensional Schrödinger equation. An appropriate combination of individual solitons yields a symmetric reflectionless potential that supports multiple bound states. Thus, the KdV equation opens the path to solving the inverse scattering problem for a collection of bound states. Applied to the quarkonium spectra, this formalism allows the construction of reflectionless approximations to the confining potentials that account for the force between quarks, and to tests of the flavor-independence of the interquark interaction.

Inverse Scattering↗
DOE OSTI2023

Host galaxies of ultra-strong Mg ii absorbers at z ∼ 0.7

ABSTRACT We report spectroscopic identification of the host galaxies of 18 ultra-strong Mg ii systems (USMg ii) at 0.6 ≤ z ≤ 0.8. We created the largest sample by merging these with 20 host galaxies from our previous survey within 0.4 ≤ z ≤ 0.6. Using this sample, we confirm that the measured impact parameters ($\rm 6.3\leqslant D[kpc] \leqslant 120$ with a median of 19 kpc) are much larger than expected, and the USMg ii host galaxies do not follow the canonical $\rm {\it W}_{2796}-{\it D}$ anticorrelation. We show that the presence and significance of this anticorrelation may depend on the sample selection. The $\rm {\it W}_{2796}-{\it D}$ anticorrelation seen for the general Mg ii absorbers show a mild evolution at low $\rm W_{2796}$ end over the redshift range 0.4 ≤ z ≤ 1.5 with an increase of the impact parameters. Compared to the host galaxies of normal Mg ii absorbers, USMg ii host galaxies are brighter and more massive for a given impact parameter. While the USMg ii systems preferentially pick star-forming galaxies, they exhibit slightly lower ongoing star-forming rates compared to main sequence galaxies with the same stellar mass, suggesting a transition from star-forming to quiescent states. For a limiting magnitude of mr < 23.6, at least 29 per cent of the USMg ii host galaxies are isolated, and the width of the Mg ii absorption in these cases may originate from gas flows (infall/outflow) in isolated haloes of massive star forming but not starbursting galaxies. We associate more than one galaxy with the absorber in $\ge 21~{{\ \rm per\ cent}}$ cases, where interactions may cause wide velocity spread.

Astronomy & Astrophysics↗
DOE OSTI2025

Manganese‐Based Spinel Cathodes: A Promising Frontier for Solid‐State Lithium‐Ion Batteries

Recently, all-solid-state lithium-ion batteries (ASSLIBs), which exhibit improved safety and enhanced energy density compared to conventional commercialized lithium-ion batteries (LIBs), thereby have garnered extensive research interest. Among the promising cathode candidates, Mn-based spinel cathodes LiMn 2 O 4 (LMO) and LiNi 0.5 Mn 1.5 O 4 (LNMO), with the unique characteristics of low cost, structural stability, and 3D Li-ion diffusion channels, have demonstrated excellent performance in LIBs and presented great potential in ASSLIBs applications. However, several challenges, including structural degradations, poor interfacial contact, large interfacial resistance, and Mn-dissolution/diffusion during the electrochemical cycling, hinder their practical applications and commercialization in the ASSLIBs. Particularly, the high-voltage LNMO cathodes suffer from the challenge of electrochemical incompatibility with most of the solid-state electrolytes (SSEs). Herein, the spinel structure, the electrochemical behavior, and the structural degradation of the LMO/LNMO are explored. The characteristics and recent progress of the mitigating strategies to the challenges of various SSEs, including polymer-, oxide-, composite-, sulfide-, halide-, and LiPON-based SSEs, are introduced when paired with LMO/LNMO. Finally, the directions for future research to advance Mn-based spinel cathodes and fulfill the requirements of the next-generation ASSLIBs are also discussed.

Dou, Yu [Concordia University, Montreal, QC (Canad↗
DOE OSTI2026

The impact of metastability on the high-pressure behavior of cerium

The structures adopted by solids under pressure are often assumed to reflect thermodynamic equilibrium, yet in many materials phase selection is strongly influenced by kinetic pathways and microstructural inheritance. Elemental cerium (Ce) exemplifies this challenge, with decades of conflicting reports describing different high-pressure crystal structures emerging under nominally identical conditions. Here we use neutron diffraction from large ( ~ 60 mm 3 ) sample volumes to follow the structural evolution in ultra-high-purity Ce during controlled pressure-temperature cycling between 85 and 295 K and up to 8 GPa. We find that the crystal structure formed at high pressure depends on the compression pathway: slow compression ( ~ 0.25 GPa hr −1 ) at room temperature favors an orthorhombic phase (α'), whereas slow ( ~ 0.25 GPa hr −1 ) and also moderately faster ( ~ 0.5 GPa hr −1 ) compression at low temperature stabilizes a pure monoclinic phase (α"). The low-temperature phase persists metastably over a wide temperature range but transforms irreversibly upon heating above ~ 280 K, or modest pressure cycling. Remarkably, the lower-pressure γ phase remains trapped far beyond the expected stability field, persisting to the highest pressures studied. These observations show that phase selection in Ce is governed by kinetics and microstructural memory rather than equilibrium thermodynamics or sample morphology alone, establishing path dependence as a defining feature of its high-pressure behavior.

Ridley, Christopher J. [Oak Ridge National Laborat↗
DOE OSTI2025

Evaluation of Howard A. Hanson Dam Juvenile Fish Passage and Survival Study: Downstream Passage and Survival (Acoustic Telemetry) (Task Final Report)

The Downstream Passage and Survival (Acoustic Telemetry) task was one of several tasks for the Evaluation of Howard A. Hanson Dam (HAHD) Juvenile Fish Passage and Survival study. For this task, a juvenile fish passage and survival study was conducted at HAHD from March 10, 2024 through June 27, 2024 for arrays in the HAHD Reservoir and Green River, and through July 9, 2024 for the arrays in the Duwamish River. Fish releases occurred over four times from March through May. Active tag (acoustic telemetry) technology was used to provide biological baseline information for the passage and survival of juvenile Puget Sound (PS) Chinook salmon (Oncorhynchus tshawytscha). Results will be used by biologists, engineers, resource managers, and regional decision-makers to inform the engineering design of the new fish passage facility (FPF) at HAHD. However, hatchery sub-yearling PS Chinook salmon of the appropriate size for tag implantation during the study period (> 95 mm in fork length, Geist et al. 2018) were unavailable. Therefore, yearling Coho salmon (O. kisutch) were used as a surrogate species for this acoustic telemetry study.

13 HYDRO ENERGY↗
DOE OSTI2026

15.3% AM1.5G Efficiency GaAs Solar Cells Fabricated via an Epitaxy-Free Process

Here, we report simple and potentially low-cost techniques for creating high-quality n-type gallium arsenide (GaAs) and GaAs p/n junctions and fabricate GaAs p/n junction solar cells. Detailed-balance modeling suggests that 20% AM1.5G efficiency p/n homojunction devices may be possible if the surface doping concentration can be limited to values less than ∼ 5 × 10 19 cm −3 . Our process exploits an open-tube, vapor-phase, deposition-free, zinc diffusion technique for forming p-type layers in melt-grown n-GaAs substrates that results in sheet resistances less than 1 kΩ/$\square$. In addition, we have improved the minority carrier diffusion lengths of melt-grown GaAs from less than one micron to over five microns using an open-tube, vacuum-free, annealing process which reduces the density of EL2 midgap defects. Finally, we have combined these advances to fabricate epitaxy-free, GaAs solar cells with a validated AM1.5G efficiency of 15.3%.

14 SOLAR ENERGY↗
DOE OSTI1988

Nuclear Safety [Vol. 29, No. 1, January-March 1988]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. THE CHERNOBYL ACCIDENT: 1 Core History and Nuclide Inventory of the Chernobyl Core at the Time of Accident by Gerald Kirchner and Cornelius C. Noack; GENERAL SAFETY CONSIDERATIONS: 6 Nonprescriptive Nuclear Safety Regulation: The Example of Loss of Offsite Power by M. W. Golay, V. P. Manno, and C. Vlahoplus, Jr., 20 Nuclear Power Safety Goals in Light of the Chernobyl Accident by C. Whipple and C. Starr; ACCIDENT ANALYSIS: 29 Containment Loads from Severe Accidents—U.S. Program by W. Kerr and M. K. Dey; PLANT SAFETY FEATURES: 36 Safety Characteristics of Modern High-Temperature Reactors: Focus on German Designs by W. Kröger, H. Nickel, and R. Schulten; ENVIRONMENTAL EFFECTS: 49 Radiation Hormesis and Nuclear Safety by C. C. Congdon; OPERATING EXPERIENCES: 58 Evaluation of Nonradiological Water Chemistry at Power Reactors by Harvey Zibulsky, James J. Kottan, Walter J. Pasciak, Mary Ann Castrogivanni, and Sujit Banerjee, 64 Reactor Shutdown Experience Compiled by J. W. Cletcher, 67 Operating U.S. Power Reactors Compiled by E. G. Silver; RECENT DEVELOPMENTS: 85 General Administrative Activities Compiled by E. G. Silver, 94 Reports, Standards, and Safety Guides by D. S. Queener, 100 Status of Power-Reactor Projects Undergoing Licensing Review Compiled by E. G. Silver, 103 Proposed Rule Changes as of Sept. 30, 1987; ANNOUNCEMENTS: 5 Northwestern University Short Course on Radiation Safety, 28 International Approach to Nuclear Safety (After Three-Mile Island and Chernobyl), 57 RPI Short Course on Modern Developments in Boiling Heat Transfer and Two-Phase Flow, 107 20th DOE/NRC Nuclear Air Cleaning Conference, 110 Third International Topical Meeting on Nuclear Power Plant Thermal Hydraulics and Operations, 108 The Authors, 111 Indexes to Nuclear Safety, Volume 28.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Catalytic disproportionation on carbon superstructures enables long-life, high-loading Li–S batteries

Electrocatalysis has been widely explored as an effective strategy to accelerate polysulfide (PS) conversion and suppress the shuttle effect in lithium–sulfur (Li–S) batteries. However, the underlying mechanisms remain elusive, and electrocatalytic reactions are inactive during cell resting. In this work, we reveal and quantitatively analyze a previously unrecognized sulfur reduction route (SRR) driven by catalytic disproportionation at the carbon cathode surface—fundamentally distinct from conventional electrocatalysis. Unlike conventional stepwise pathways, this SRR enables high-order polysulfides (Sₓ²⁻, x = 5–8) to directly convert into S₈ and Li₂S₂, bypassing low-order intermediates. This sulfur-reduction shortcut is systematically elucidated through high-performance liquid chromatography, revealing the intrinsic catalytic contribution of carbon frameworks and the dynamic evolution of PS species. We demonstrate that carbon superstructures (CSS-0.5), assembled from nanosheet subunits with abundant N/O functionalities and interconnected charge-migration channels, synergistically promote this catalytic process. Benefiting from these features, CSS-0.5 delivers superior electrochemical performance under practical conditions, enabling high sulfur loading (6.0 mg cm⁻²) pouch cells with 80.5% capacity retention over 210 cycles. This study provides the first quantitative evidence of electrocatalytic disproportionation in Li–S batteries, offering mechanistic insights and design principles for advanced sulfur cathodes.

25 ENERGY STORAGE↗
DOE OSTI2024

Molecules to Masterpieces: Bridging Materials Science and the Arts

Art and materials innovation have always been intertwined, dating back to the earliest human creations. In modern times, however, the increasing specialization of materials science often restricts artists' access to cutting-edge materials. Here, the materials science aspects of an art-science collaboration between artist Kimsooja and the Wiesner Lab at Cornell University, are detailed. The project involves the development of a custom-made iridescent block copolymer coating by means of self-assembly, originally applied to transparent window panels of a façade for the ≈14 m tall art installation: A Needle Woman: Galaxy Is a Memory, Earth is a Souvenir by artist Kimsooja. After several exhibitions in the US and Europe, the installation is now part of the permanent museum collection at Yorkshire Sculpture Park in Wakefield, UK. Full characterization of the solution blade-cast coatings show shear aligned, standing up lamellar morphologies that behave as volume-phase gratings with periodicities between 300 and 400 nm. Coatings are also applied to foldable (origami) paper and converted into iridescent porous ceramic materials. Furthermore, it is hoped this work inspires and informs communities across materials science, the arts, and architecture.

Architectural nanomaterials↗
DOE OSTI2026

Anode-less Solid-State Li–S Batteries Enabled by Fe-Stabilized Polysulfides

Anode-less solid-state lithium-sulfur batteries (SSLSBs) with lithium sulfide (Li 2 S) as the cathode promise a high energy density and ease of manufacturing. However, Li 2 S is plagued by poor conductivity, sluggish activation kinetics, and a poor cycle life. Here, in this study, we report an FeCl 3 -activated Li 2 S (FLS) cathode with solid-state polysulfide intermediates generated through a redox reaction between FeCl 3 and Li 2 S. This strategy is shown to boost the electrical conductivity of Li 2 S by 7 orders of magnitude and lower the activation barrier. During cycling, Fe plays a significant role in stabilizing the highly active polysulfide species, contributing to the exceptional electrochemical performance. The FLS cathode achieves 80% capacity retention over 500 cycles with >99% Li 2 S utilization. Furthermore, a Li-metal-free (anode-less) full cell retained over 80% of its initial capacity after 240 cycles. This work underscores the promise of leveraging Fe-stabilized polysulfides in enabling high-energy, long-lasting, solid-state Li-S batteries.

25 ENERGY STORAGE↗
DOE OSTI2021

DEPRECATED AI-Batt-OS (Autonomous Identification of Battery Life Models - Open Source) [SWR 21-17]

DEPRECATED. This repository was archived by the owner on Jun 30, 2026. It is now read-only. Open source implementation of some of the methods utilized by AI-Batt, a battery lifetime modeling and analysis toolkit provided by the National Laboratory of the Rockies (NLR). This software demonstrates the use of bi-level optimization and symbolic regression techniques to semi-autonomously identify algebraic models predicting the capacity fade of lithium-ion batteries during calendar aging. Modeling the degradation of batteries is a complex task, due to the difficulty in separating the time-dependent and time-independent factors impacting cell level degradation, across multiple data series with different numbers of measurements and/or data quality. Bi-level optimization enables model parameters to be optimized to either the entire data set or to individual data series, allowing statistical disambiguation of global behaviors (data series independent) and local behaviors (data series dependent). Symbolic regression is used to automatically search for optimal low-dimesional models predicting the variation of locally optimized parameters versus time-independent experimental variables from millions of possible models, resulting in a more accurate and repeatable model identification process than is possible by a manual search. The provided tools also implement cross-validation and bootstrap resampling schemes, empowering statistical model comparison/selection and quantification of model uncertainties. An example script replicates the results from the manuscript "Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning", submitted to ECS. All code is written in MATLAB. Requires the Statistics and Machine Learning Toolbox. Contact Dr. Paul Gasper at Paul.Gasper@nlr.gov for any questions.

Gasper, Paul [National Renewable Energy Lab. (NREL↗
DOE OSTI2024

The cluster decomposition of the configurational energy of multicomponent alloys

Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.

Chemistry↗