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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 OSTI2025

A Cross‐Linked Flexible Metaferroelectrolyte Regulated by 2D/2D Perovskite Heterostructures for High‐Performance Compact Solid‐State Sodium Batteries

Abstract To address the issues of limited ionic conductivity and poor interface stability at room and low temperatures in solid‐state electrolytes, a robust intrinsic ferroelectrolyte or nanoferroelectrolyte strategy for engineering solid‐state flexible ferroelectric composite electrolytes utilizing strongly coupled intrinsic ion conducting 2D/2D sodium‐rich anti‐perovskite (NaRAP)/ferroelectric perovskite heterostructures is introduced. Herein, highly scalable PVDF‐based metaferroelectrolytes with Na 2.99 Ba 0.005 OCl/Ca 2 Na 2 Nb 5 O 16 − (CNNO − ) nanosheets into a ferroelectric poly(vinylidene fluoride‐co‐hexafluoropropylene) (PVDF‐HFP) matrix, through an in situ cross‐linking and spontaneous bridging method, for compact solid‐state sodium batteries (SSBs), are reported. Benefiting from unique well‐dispersed 3D ferroelectric coupled network and the Na 2.99 Ba 0.005 OCl/CNNO − ‐induced PVDF‐HFP ferroelectric β phase, the Na + flux is regulated, thereby inhibiting Na dendrite growth at the interface. Notably, the optimized PH‐5% NC metaferroelectrolyte exhibits rapid ion transport (1.11 × 10 −4 S cm −1 at 25 °C), a wide electrochemical window (> 4.8V), superior conformal mechanical compatibility, improved flexibility, good elasticity and flame retardancy. The solid‐state Na 3 V 2 (PO 4 ) 3 /PH‐5% NC/Na batteries present a stable cycling performance (remaining 56.4 mAh g −1 after 500 cycles at 1 C) even at 0 °C, potential for cost‐effective, safe, stable and compact SSB energy storage over 600 Wh L −1 , vastly surpassing 365 Wh L −1 of the current commercial sodium‐ion liquid‐electrolyte batteries.

Chemistry↗

NASA NTRS2000

Nonintrusive Diagnostic Strategies for Arcjet Stream Characterization

In the previous lecture, the issues related to arcjet flow modeling were introduced, and the limitations of conventional instrumentation in addressing these issues were discussed. The general level of understanding of the arcjet flows was seen to preclude the use of arcjets as aerothermodynamic test facilities beyond the current role in aerothermal material testing, despite their long test duration capability. In this section, the focus will be on new developments in spectroscopic instrumentation and techniques that can be brought to bear on the fundamental problem of arcjet stream characterization. Although a wide selection of arcjet facilities were introduced in the previous section, the discussion of nonintrusive diagnostic instrumentation will be restricted to the large-scale, segmented, constricted-arc heater facilities that are most widely used in thermal protection material testing for aerospace applications. After a brief review of the important features of arcjet flows, the topic of nonintrusive, optical diagnostics is introduced with a discussion of some of the basic aspects of radiative transitions. The lecture is then organized into two sections covering emission measurements and laser-induced fluorescence measurements. Emission measurements are presented next for different regions of arcjet flows, while the fluorescence measurements are presented for the free stream region only. Summaries are given for each of the two main sections, and observations on arcjet characterization by optical diagnostics in general are given at the end.

Douglas G Fletcher↗

NASA NTRS2026

A Review of Superconducting Electric Machines with On-Board Cryocoolers

This paper reviews the evolution and emerging direction of superconducting electric machines that employ onboard cryocoolers integrated directly into the rotor, eliminating the need for cryogenic fluid coupling and, in some cases, rotary seals. Traditional low-temperature superconducting (LTS) machines relied on external cryogenic systems and liquid helium transfer couplers, which introduced excessive complexity, poor reliability, and significant parasitic energy losses. The advent of high-temperature superconductors (HTS) has enabled compact, closed-cycle cryocoolers that support self-contained, fluid-free refrigeration architectures suitable for rotating applications. This paper examines the key technological challenges associated with on-board cryocooler integration and reviews three representative efforts by KAIST, NASA, and Hinetics, each illustrating distinct strategies and milestones toward practical implementation. KAIST demonstrated early proof-of-concept for rotating machines with on-board cryocoolers, NASA developed a shaft-integrated Stirling-type pulse tube cryocooler for a 1.4 MW hybrid-electric motor, and Hinetics achieved full-scale validation of a self-contained HTS rotor incorporating a commercial Stirling cryocooler and spoke-suspension torque tube. Collectively, these achievements confirm the technical feasibility of on-board cryogenic refrigeration and highlight steady progress toward compact and efficient superconducting rotating systems across various applications. Embedding cryocoolers directly within the rotor enables practical, efficient, and commercially viable superconducting propulsion technologies.

Cryogenics↗

NASA NTRS2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λc, that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λc-based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

Amanda Stricklan↗

DOE OSTI2025

Optoelectronic polymer memristors with dynamic control for power-efficient in-sensor edge computing

Abstract As the demand for edge platforms in artificial intelligence increases, including mobile devices and security applications, the surge in data influx into edge devices often triggers interference and suboptimal decision-making. There is a pressing need for solutions emphasizing low power consumption and cost-effectiveness. In-sensor computing systems employing memristors face challenges in optimizing energy efficiency and streamlining manufacturing due to the necessity for multiple physical processing components. Here, we introduce low-power organic optoelectronic memristors with synergistic optical and mV-level electrical tunable operation for a dynamic “control-on-demand” architecture. Integrating signal sensing, featuring, and processing within the same memristors enables the realization of each in-sensor analogue reservoir computing module, and minimizes circuit integration complexity. The system achieves 97.15% fingerprint recognition accuracy while maintaining a minimal reservoir size and ultra-low energy consumption. Furthermore, we leverage wafer-scale solution techniques and flexible substrates for optimal memristor fabrication. By centralizing core functionalities on the same in-sensor platform, we propose a resilient and adaptable framework for energy-efficient and economical edge computing.

Optics↗

DOE OSTI2025

Amphiphilic nanopores that condense undersaturated water vapor and exude water droplets

Condensation of water vapor in confined geometries, known as capillary condensation, is a fundamental phenomenon with far-reaching implications. While hydrophilic pores enable liquid formation from undersaturated vapor without energy input, the condensate typically remains confined, limiting practical utility. Here, we explore the use of amphiphilic nanoporous polymer-infiltrated nanoparticle films that condense and release liquid water under isothermal and undersaturated conditions. By tuning the polymer fraction and nanoparticle size, we optimize condensation and droplet formation. As vapor pressure increases, voids fill with condensate, which subsequently exudes onto the surface as microscopic droplets. This behavior, enabled by a balance of polymer hydrophobicity and capillarity, reveals how amphiphilic nanostructures can drive accessible water collection. Our findings provide design insights for materials supporting energy-efficient water harvesting and heat management without external input.

Science & Technology - Other Topics↗

NASA NTRSDate not supplied

Enabling Reliable, Fault-Tolerant Autonomous Lunar Habitats with High-Performance Spaceflight Computing

The lunar surface presents unfavorable constraints and harsh living conditions. To address these challenges, autonomous habitats will require complex integrated systems that combine advanced software, high-performance hardware, and cutting-edge sensors to ensure sustainability, safety, and operational efficiency. Consequently, maintaining a sustainable presence on the Moon requires reliable infrastructure and efficient development, precise monitoring, and utilization of resources within a lunar installation. These elements are essential not only to ensure that lunar settlement can be long-term, self-sustaining, and resource-efficient, but also to serve as a foundation for future missions and eventual human habitation on Mars. Humans are not native to the Moon; therefore, our survival and ability to thrive will depend on autonomous systems that can foster safety and resilience through high-availability architectures, graceful degradation, and highly fault-tolerant spaceflight hardware capable of continuing operation during failures. This requires advanced human-rated distributed systems architectures with specialized electronics, scalable capabilities, and an integrated design approach. Unlike current practices focused on short-term missions and regularly maintained components, permanent lunar compute systems must be designed for extended operations beyond mission durations. This paper explores the necessity of transitioning toward fault- tolerant, highly autonomous hardware systems designed for multi-year missions. It also identifies critical subsystems that require high levels of autonomy, supported by radiation-hardened processors and extreme thermal loads, which are essential to mitigate long-term degradation and ensure sustainable lunar habitation. Finally, the paper aligns with NASA’s identified Civil Space Shortfalls, particularly in high-performance onboard computing, advanced data acquisition, extreme-environment avionics, radiation monitoring and countermeasures, and autonomous health management. It proposes NASA’s new High-Performance Spaceflight Computing (HPSC) processor as a turnkey solution, delivering 100 times the performance-per-watt of legacy rad-hard CPUs and enabling onboard AI, edge computing, and fault-tolerant features essential for sustained lunar autonomy and beyond.

Sarkis S Mikaelian↗

DOE OSTI2025

Self-generated electrokinetic flows from active-charged boundary patterns

We develop a hydrodynamic description of self-generated electrolyte flow in capillaries whose bounding walls feature nonuniform distributions of charge nonuniform active ionic fluxes. The hydrodynamic velocity arising in such a system has components that are forbidden by symmetry in the absence of charge and fluxes. However, when these two boundary mechanisms are simultaneously present, they can lead to a symmetry broken state where steady flows with both unidirectional and circulatory components emerge. We show that these flow states arise when modulated boundary patterns of charge and fluxes are offset by a flux-charge phase difference, which is associated with the separation between sites of their peak densities on the wall. Mismatch in diffusivity of cationic and anionic species can modify the flow states and becomes an enhancing factor when fluxes of both ion species are being produced together at the same site. We demonstrate that this mechanism can be realized with a microfluidic generator that is powered by enzyme-coated patches that catalyze reactants in the solution to produce fluxes of ions. The local ionic elevation or depletion, which disrupts a nonuniform double layer, promotes self-induced gradients yielding persistent body forces to generate bulk fluid motion. Our work quantifies a boundary-driven mechanism behind self-sustained electrolyte flow in confined environments that exists without any external bulk-imposed fields or gradients. It provides a theoretical framework for understanding the combined effect of active and charged boundaries that are relevant in biological or soft matter systems, and can be utilized in electrofluidic and iontronic applications.

active matter↗

NASA NTRSDate not supplied

Fire-Resistant Textile Development for Exploration Vehicles With Enriched-Oxygen Cabin Environments

Material selection is a key part of the National Aeronautics and Space Administration (NASA) spacecraft fire safety management plan. Non-flammable textiles are necessary to ensure large-scale flame propagation events do not occur inside a spacecraft. An increased use of textiles and other softgood material is crucial to the pursuit of exploration spaceflight to reduce mass and volume. Exploration spaceflight missions benefit from enriched oxygen cabin environments (>21% O2) by allowing a reduced prebreathe protocol before Extravehicular Activity (EVA). However, materials become exponentially more flammable the higher the O2 levels become. Recent testing within the agency has revealed the lack of commercial-off-the-shelf (COTS) materials that can meet safety requirements in oxygen-enriched environments. Most of the fibers and textiles developed during Apollo (100% O2 cabin environment) and Skylab (>70% O2 cabin environment) are no longer commercially available due to those Programs ending and the discontinuation of raw materials or closure of the original manufacturers. As NASA returns to higher oxygen concentrations inside spacecraft, non-flammable textile development efforts have begun to meet the agency’s needs. This paper discusses those efforts including overall fire safety approach, state-of-the-art textile review and testing, an agency-wide assessment of textile needs performed by the NASA Engineering and Safety Center (NESC), the textile development strategy and expected challenges.

Mary Walker↗

DOE OSTI2026

Getting Warmer: IceCube Nears Freeze Out

IceCube has recently detected a diffuse population of high-energy neutrinos arising from the Milky Way. We use this high-significance detection to place new limits on dark matter (DM) annihilation to neutrinos with two complementary approaches. The first method uses the background-subtracted Galactic longitude distribution of shower events to place a conservative bound on the DM annihilation cross section that does not rely on any assumed Galactic cosmic ray emission model; the resulting limits on the velocity-averaged annihilation cross section improve upon existing bounds by factors of a few. The second method uses the template-dependent neutrino energy spectra from the Inner Galaxy, inferred under different Galactic cosmic ray emission models. This complementary approach shows that the inferred Galactic neutrino intensities are already sensitive to DM contributions near the thermal-relic benchmark for a range of TeV-scale DM masses, though this comparison is more model-dependent. Our results demonstrate that measurements of diffuse Galactic neutrino emission can be used as a powerful probe of DM annihilation into neutrinos. Future observations with IceCube-Gen2 and KM3NeT will substantially extend this sensitivity, potentially allowing a decisive test of the thermal freeze-out mechanism with Galactic neutrino observations.

Mukhopadhyay, Mainak [Fermilab; Chicago U., KICP; ↗

DOE OSTI2024

Derivation of low-energy Hamiltonians for heavy-fermion materials

Here, by utilizing a multiorbital periodic Anderson model with parameters obtained from ab initio band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both nonmagnetic 4⁢𝑓 0 and magnetic 4⁢𝑓 2 virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn 3 . The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of 4⁢𝑓 materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

SPT clusters with DES and HST weak lensing. II. Cosmological constraints from the abundance of massive halos

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel’dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range 0.25–1.78 over a total sky area of 5200 deg 2 . We use DES Year 3 weak-lensing data for 688 clusters with redshifts 𝑧 < 0.95 and HST weak-lensing data for 39 clusters with 0.6 < 𝑧 < 1.7. The weak-lensing measurements enable robust mass measurements of sample clusters and allow us to empirically constrain the SZ observable-mass relation without having to make strong assumptions about, e.g., the hydrodynamical state of the clusters. For a flat Λ⁢ CDM cosmology, and marginalizing over the sum of massive neutrinos, we measure Ω m = 0.286 ± 0.032, 𝜎 8 = 0.817 ± 0.026, and the parameter combination 𝜎 8 ⁢(Ω m /0.3) 0.25 = 0.805 ± 0.016. Our measurement of 𝑆 8 ≡ 𝜎 8 ⁢$\sqrt{Ω_{m}/0.3}$ = 0.795 ± 0.029 and the constraint from Planck CMB anisotropies (2018 TT, TE, EE+lowE) differ by 1.1⁢𝜎. In combination with that Planck dataset, we place a 95% upper limit on the sum of neutrino masses ∑𝑚 𝜈 < 0.18 eV. When additionally allowing the dark energy equation of state parameter 𝑤 to vary, we obtain 𝑤 = −1.45 ± 0.31 from our cluster-based analysis. In combination with Planck data, we measure 𝑤 =−1.3⁢4$^{+0.22}_{−0.15}$, or a 2.2⁢𝜎 difference with a cosmological constant. We use the cluster abundance to measure 𝜎8 in five redshift bins between 0.25 and 1.8, and we find the results to be consistent with structure growth as predicted by the Λ⁢ CDM model fit to Planck primary CMB data.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2026

Highly Porous Polyimide Gel for Use as Battery Separator with Room Temperature Ionic Liquid Electrolytes

Advanced aerospace vehicular concepts require advances in many existing technologies, including space power and energy storage systems. Batteries represent one of the major areas in need of improvement, both in terms of energy density and safety, with growing concerns over the fire safety of commercial lithium-ion batteries. This has prompted efforts to develop nonflammable battery components, namely the electrolyte and separator. Existing commercial lithium-ion batteries utilize polyolefin microporous membranes as separators with an electrolyte consisting of a lithium salt dissolved in a mixture of cyclic carbonate solvents. This separator/electrolyte combination has ionic conductivities in the range of 10 −2 to 10 −3 S/cm. However, the cyclic carbonate solvents are inherently flammable. Room-temperature ionic liquids (RTILs) appear to be a safer alternative. They offer good ionic conductivities and are inherently nonvolatile and nonflammable, giving them a safety advantage. However, many promising RTILs for battery electrolytes are not compatible with commercial polyolefin separator materials. Alternative separator materials, such as polyimides, are non-flammable and are capable of accepting RTILs into their structure. Polyimide gels, with a composition of 4,4′-oxydianiline, 3,3′,4,4′-tetracarboxylic dianhydride and cross-linked with Desmodur N3300A, possess an open-porous, fibrillar network architecture which offers a high degree of porosity (typically greater than 85% porosity) for lithium-ion transport and conduction, as well as good mechanical properties. Furthermore, these polyimide gels are compatible with selected imidazolium-based RTILs. Nonflammable separator/electrolyte systems with room-temperature conductivities in the range of 10 −3 S/cm have been evaluated. It has been demonstrated that 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide was the most promising among six RTILs screened, in terms of both ionic conductivity and constant current cycling.

Polyimide↗

NASA NTRSDate not supplied

AstroDOME: Standardized, Mass-Produceable, Small NASA Astrophysics Observatories for Big Missions

NASA’s Goddard Space Flight Center is investigating the use of small, commercial off the shelf (COTS) spacecraft to enable breakthrough astrophysics research at radically reduced cost over previous generations of missions. This paper will focus on the Mission Systems perspective of this investigation. It will cover the spacecraft to instrument interface, and lessons learned in early concept payload development. Low-cost COTS spacecraft have proliferated in the last ~5 years. They represent an order of magnitude reduction in the cost of spacecraft bus development and acquisition. They are enabled by the advent of low-cost smallsat launch options in the immediately preceding years, and are seeded by recent distributed and disaggregated missions in other sectors such as telecommunications megaconstellations (e.g. Starlink, OneWeb, Project Kuiper) and ongoing Space Development Agency (SDA) developments. Our study was tasked with developing a standardized, mass-produceable, astrophysics payload which is reconfigurable to different wavelength bands while maintaining a single optics bench design, and a standardized mechanical, electrical, data, and thermal interface to the spacecraft bus, and which may be reconfigured to multiple COTS spacecraft offerings. In this paper we will discuss lessons learned from our case study. We will also present identified keys to mission success for performing cutting edge astrophysics observations while taking advantage of economies of scale with a disaggregated, standardized architecture.

Matthew Marcus↗

DOE OSTI2026

Trajectory-independent speed limits for controlled open quantum systems

Existing quantum speed limits for controlled open quantum systems depend on the specified trajectory. For example, lower bounds on quantum annealing times in the presence of dissipation depend explicitly on the chosen annealing schedule. Recently, schedule-independent speed limits have been derived for annealing in the closed quantum system setting [L. P. García-Pintos et al ., SciPost Phys. 18 , 159 (2025)]. In this work, we generalize these results to open quantum systems, deriving schedule-independent lower bounds for quantum annealing times in systems described by a Lindblad master equation. We analyze the interplay between coherent control and dissipation in single- and two-qubit examples, demonstrating that the derived lower bounds capture key scaling behavior with respect to the strength of the dissipator. Finally, we apply the bound to thermal state preparation and show that the bound matches the expected asymptotic behavior for an Ising model in the high-temperature limit.

open quantum systems & decoherence↗

NASA NTRSDate not supplied

Physics-Guided Deep Learning for Complex System Health Management and Decision Making

The landscape of complex engineered systems is rapidly evolving, from smart manufacturing facilities to next-generation transportation vehicles. As these systems become increasingly sophisticated and interconnected, the need for advanced health management systems grows ever more critical. These systems must go beyond simple monitoring, actively predicting potential failures before they occur. This paradigm shift from fixed maintenance schedules to condition-based predictions is key to optimizing system performance, enhancing safety, and paving the way for autonomous decision-making across various industries. Whether in industrial processes, energy systems, or advanced transportation, the ability to anticipate and prevent failures is becoming a cornerstone of operational excellence. To accurately predict the future health of any complex system, knowledge of its current health state and future operational conditions is essential. Recent advancements in data-driven algorithms have generated growing interest in artificial intelligence for industrial applications. However, the limitations of pure data-driven methods, particularly in industries where data acquisition is costly and limited, have become apparent. This has led to a focus on blending physics with data-driven algorithms, mitigating the drawbacks of both approaches while emphasizing their respective advantages. This research proposes a novel framework for integrating physics-based performance models with deep learning algorithms for the prognostics of complex safety-critical systems. In this approach, physics-based models serve as a blueprint, capturing fundamental system behaviors, while deep learning algorithms, leveraging real-world sensor data, fill in gaps and identify subtle patterns indicative of potential problems. This hybrid methodology, utilizing techniques such as Physics-Informed Neural Networks (PINNs), offers a powerful solution for predicting system health. By fusing domain knowledge with data-driven insights, this approach promises more accurate, adaptable, and reliable models for health prediction. The resulting framework is versatile, applicable across various sectors including aerospace, manufacturing, and energy systems, ultimately contributing to safer, more efficient operations in our increasingly complex technological landscape.

Diagnostics↗

DOE OSTI2024

Analytical Model for Atomic Relaxation in Twisted Moiré Materials

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe 2 bilayers using large-scale molecular dynamics simulations. Our single-parameter theory is valid in graphene bilayers for twist angles 𝜃 ≳ 0.7°, and in twisted WSe 2 for 𝜃 ≳ 1.6°. Furthermore, we also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

36 MATERIALS SCIENCE↗