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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Structural and Reactivity Effects of Secondary Metal Doping into Iron-Nitrogen-Carbon Catalysts for Oxygen Electroreduction

While improved activity was recently reported for bimetallic iron-metal-nitrogen-carbon (FeMNC) catalysts for the oxygen reduction reaction (ORR) in acid medium, the nature of active sites and interactions between the two metals are poorly understood. Here, FeSnNC and FeCoNC catalysts were structurally and catalytically compared to their parent FeNC and SnNC catalysts. While CO cryo-chemisorption revealed a twice lower site density of M-N x sites for FeSnNC and FeCoNC relative to FeNC and SnNC, the mass activity of both bimetallic catalysts is 50–100% higher than that of FeNC due to a larger turnover frequency in the bimetallic catalysts. Electron microscopy and X-ray absorption spectroscopy identified the coexistence of Fe-N x and Sn-N x or Co-N x sites, while no evidence was found for binuclear Fe-M-N x sites. 57 Fe Mössbauer spectroscopy revealed that the bimetallic catalysts feature a higher D 1 /D 2 ratio of the spectral signatures assigned to two distinct Fe-N x sites, relative to the FeNC parent catalyst. Furthermore, the addition of the secondary metal favored the formation of D 1 sites, associated with the higher turnover frequency.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Shubnikov–de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe 2 and RbV 3 Sb 5 , by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe 2 and RbV 3 Sb 5 , respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe 2 , the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV 3 Sb 5 , two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

2D materials↗
DOE OSTI2024

Shubnikov-de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe 2 and RbV 3 Sb 5 , by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe 2 and RbV 3 Sb 5 , respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe 2 , the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV 3 Sb 5 , two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

SISGR: Chemomechanics of Far-From-Equilibrium Interfaces (COFFEI)

Portable, reliable, and deployable devices for energy storage and conversion require fundamental changes in design of solid-state composites comprising ceramics and metals. These materials comprise the electrodes and electrolytes of next-generation solid-oxide fuel cells and all solid-state batteries, forming solid-state functional composites. The advent of solid-state batteries – which replace liquid electrolytes with solid electrolytes capable of lithium ion transport for reliable energy storage in portable batteries – and the increased demand space for all solid-state fuel cells capable of oxygen reduction at intermediate temperatures remain important challenges for improved material stability and decreased system cost. However, little is understood about three fundamental facets of materials that enable such solid-state energy applications. First, how do such materials deform, fracture, or delaminate under operando conditions? Second, how does such mechanical deformation limit or facilitate electronic and ionic transport within and across such material interfaces? Third, how we can predictably design interface-rich composites to engineer both structural and electrochemical stability? This COFFEI Group comprised expertise from Materials Science & Engineering and Nuclear Science & Engineering to integrate unique in situ experiments, simulations, and fabricated interfaces that address these fundamental questions in solid-state interfaces of nanoscale composites that will guide solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric materials that enable such applications. In particular, we built on COFFEI’s understanding of chemomechanical coupling among defect concentrations, ionic transport, electron transport, and stored elastic energy that is particularly acute in the far-from-equilibrium conditions typical of energy device applications. By tailoring our focus to solid-state interfaces, we addressed these important issues by (a) developing and applying advanced in situ and ex situ characterization tools to characterize model materials and interfaces synthesized with molecular-level control, under both laboratory-controlled and extreme environments representative of energy device operation; and (b) employing computational modeling and simulation frameworks to predict transport mechanisms, reactivity and stability of these model materials and interfaces under significant chemical strains typical of energy device operation. Recent progress provided insights to additional materials systems and electrochemomechanical fatigue and fracture that were not fully envisioned when the program was initiated. Specifically, in the final three years of COFFEI we pursued two integrated thrusts, with complementary focus. Thrust I focused on failure-resistant electrochemomechanical composites, while Thrust II focused on strain-modulated conductivity and reactivity across interfaces. In contrast to our initial COFFEI focus, these thrusts concentrated wholly on solid-state material interfacial interactions and included greater integration of multiscale visualization including in situ electron microscopy of strained structures/interactions and mesoscale simulations. Successful development of functionally superior and long-lived battery and fuel cell systems and stress adaptable oxides requires a deeper, fundamental understanding of the coupling among the historically important subfields of solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric metal oxide electrodes. In this program, the understanding and the application of chemomechanical coupling of defect concentrations, ionic transport, electro-catalytic activity and stored elastic energy, particularly acute in the far-from-equilibrium conditions typical of energy device applications, are being refined and implications for device operation clarified, including for miniaturized solid-state batteries and fuel cells.

36 MATERIALS SCIENCE↗
DOE OSTI2021

High-Speed Ionic Synaptic Memory Based on 2D Titanium Carbide MXene

Synaptic devices with linear high-speed switching can accelerate learning in artificial neural networks (ANNs) embodied in hardware. Conventional resistive memories however suffer from high write noise and asymmetric conductance tuning, preventing parallel programming of ANN arrays. Electrochemical random-access memories (ECRAMs), where resistive switching occurs by ion insertion into a redox-active channel, aim to address these challenges due to their linear switching and low noise. ECRAMs using 2D materials and metal oxides however suffer from slow ion kinetics, whereas organic ECRAMs enable high-speed operation but face challenges toward on-chip integration due to poor temperature stability of polymers. Here, ECRAMs using 2D titanium carbide (Ti 3 C 2 T x ) MXene that combine the high speed of organics and the integration compatibility of inorganic materials in a single high-performance device are demonstrated. These ECRAMs combine the speed, linearity, write noise, switching energy, and endurance metrics essential for parallel acceleration of ANNs, and importantly, they are stable after heat treatment needed for back-end-of-line integration with Si electronics. The high speed and performance of these ECRAMs introduces MXenes, a large family of 2D carbides and nitrides with more than 30 stoichiometric compositions synthesized to date, as promising candidates for devices operating at the nexus of electrochemistry and electronics.

2D materials↗
DOE OSTI2022

Toward Metal-free Photocatalysis: Photochemical Regeneration of Organic Hydride Donors Using Phenazine-Based Photosensitizers

Earth-abundant chromophores and catalysts are important molecular building blocks for artificial photosynthesis applications. Our team previously reported that metal-free hydride donors, such as biomimetic benzoimidazole-based motifs, can reduce CO 2 selectively to the formate ion and that they can be electrochemically regenerated using the proton-coupled mechanism. To enable direct utilization of solar energy, we report here the photochemical regeneration of a benzoimidazole-based hydride donor using a phenazine-based metal-free chromophore. The photochemical regeneration was investigated under different experimental conditions involving varying sacrificial donors, proton donors, solvents, and component concentrations. The best hydride regeneration yield of 50% was obtained with phenol as a proton source and thiophenolate as a sacrificial electron donor. The mechanism of photochemical regeneration was studied using steady-state and time-resolved UV/Vis spectroscopies. Based on the results of these studies, we hypothesize that the initial photoinduced electron transfer from photoexcited phenazine chromophores involves the benzoimidazole cation and that this process is likely coupled with proton transfer to generate protonated benzoimidazole-based radical cation. The second photoinduced electron transfer is hypothesized to generate the hydride form. Furthermore, our findings provide the requisite information for the future development of reductive photocatalysts for solar energy and light-harvesting applications utilizing earth-abundant metal-free materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Goals and Progress for Mil Handbook 17, Vol. 5 on Ceramic Matrix Composites: Testing and Characterization

The initial edition of the Mil Handbook 17, Vol. 5 on ceramic matrix composites (CMCs) was recently published. Part C of this CMC volume describes procedures for characterization of the thermal, physical, and mechanical properties of CMCs and subsequent data analysis procedures. As is the case for entire CMC volume, this chapter is a "work in progress" with sections on recommended test plans and matrices, data reduction, and test methods. This presentation will describe the current status in development of this section of the CMC volume and will highlight examples of critical issues that will be addressed in this volume. CMC systems are a different class of material than metals or polymer matrix composite with different mechanical response and failure modes, design rules, test methods, and characterization techniques. The CMC test protocols need to include guidance on how to generate enough reliable data in order to estimate, with reasonable confidence, the lower bounds of performance properties, such as strength and life. Strength data sets on two material systems, C/SiC and Nicalon/SiNC, and a creep rupture data set on C/SiC, will be presented to highlight this issue. The structural properties of CMC parts can sometimes be significantly different than those obtained from flat panels because of changes in fiber architecture often required to make shapes and spatial and lot-to-lot variations in processing conditions. To illustrate an example, the hoop tensile properties of SiC/SiC cylinders will be compared to properties obtained from flat panels fabricated from the same composites. These CMC testing-design issues are being defined and documented in the Mil Handbook 17 CMC volume.

Verrilli, Michael J.↗
NASA NTRS2000

Probabilistic Multi-Scale, Multi-Level, Multi-Disciplinary Analysis and Optimization of Engine Structures

Aircraft engines are assemblies of dynamically interacting components. Engine updates to keep present aircraft flying safely and engines for new aircraft are progressively required to operate in more demanding technological and environmental requirements. Designs to effectively meet those requirements are necessarily collections of multi-scale, multi-level, multi-disciplinary analysis and optimization methods and probabilistic methods are necessary to quantify respective uncertainties. These types of methods are the only ones that can formally evaluate advanced composite designs which satisfy those progressively demanding requirements while assuring minimum cost, maximum reliability and maximum durability. Recent research activities at NASA Glenn Research Center have focused on developing multi-scale, multi-level, multidisciplinary analysis and optimization methods. Multi-scale refers to formal methods which describe complex material behavior metal or composite; multi-level refers to integration of participating disciplines to describe a structural response at the scale of interest; multidisciplinary refers to open-ended for various existing and yet to be developed discipline constructs required to formally predict/describe a structural response in engine operating environments. For example, these include but are not limited to: multi-factor models for material behavior, multi-scale composite mechanics, general purpose structural analysis, progressive structural fracture for evaluating durability and integrity, noise and acoustic fatigue, emission requirements, hot fluid mechanics, heat-transfer and probabilistic simulations. Many of these, as well as others, are encompassed in an integrated computer code identified as Engine Structures Technology Benefits Estimator (EST/BEST) or Multi-faceted/Engine Structures Optimization (MP/ESTOP). The discipline modules integrated in MP/ESTOP include: engine cycle (thermodynamics), engine weights, internal fluid mechanics, cost, mission and coupled structural/thermal, various composite property simulators and probabilistic methods to evaluate uncertainty effects (scatter ranges) in all the design parameters. The objective of the proposed paper is to briefly describe a multi-faceted design analysis and optimization capability for coupled multi-discipline engine structures optimization. Results are presented for engine and aircraft type metrics to illustrate the versatility of that capability. Results are also presented for reliability, noise and fatigue to illustrate its inclusiveness. For example, replacing metal rotors with composites reduces the engine weight by 20 percent, 15 percent noise reduction, and an order of magnitude improvement in reliability. Composite designs exist to increase fatigue life by at least two orders of magnitude compared to state-of-the-art metals.

Chamis, Christos C.↗
DOE OSTI2020

Carbon Fiber Prepreg Recycling- Automated Perform Manufacturing Equipment (Final Technical Report)

Discontinuous fiber composites have a compelling business case as related to light metals such as aluminum and magnesium machined or die cast components. DFC’s have been in commercial production using carbon fiber/epoxy prepreg for both commercial aircraft and for military applications for a number of years and their usage is expanding into automotive and consumer goods components. Reasons for this include significantly lower cost as compared to continuous fiber composites easier design and understanding of the material by metal traditionalists, higher degree of part complexity with relatively simple and low cost molds when compared to high-pressure die casting, and potential for near zero waste. IACMI’s 10-year goals of reduction in carbon fiber reinforced plastics manufacturing cost by 25%, reduction in their embodied energy by 50%, and recyclability of 95% can all be advanced through robust recycling. With recycling We have shown that a 15% contribution in manufacturing cost reduction is feasible, that a significant reduction in embodied energy (over 90% for the recycled fraction) is achievable, and that when combined with primary pyrolysis recycling, the 95% target can be met. Large-scale application of advanced composites began with the aerospace industry, and CRTC’s location in Washington State provided access to a waste stream of nearly 900 tonnes/year that was going to landfill. As the aerospace industry has automated parts production, their material forms have become significantly easier to recycle, and some evidence of this exists for the future automotive and wind turbine components as well. CRTC decided to focus on re-purposing the carbon fiber/epoxy aerospace scrap streams through materials reformatting and reuse, and not on primary recycling (pyrolysis mainly) as this technology is commercially available. The main reasons for this were that it offers a route to effective use of the most widely available and consistent feedstock called edge-trim, as well as allows creation of complex and low-cost parts using rapid and cost-effective compression molding technologies. The reasons also include leading the way for potential automotive pre-preg recycling as the combination of roughly 85% virgin pre-preg and 15% recycled pre-preg directly supports IACMI’s goals and enables significant part cost reduction and a path to zero-waste composite manufacturing at the OEMs or Tier 1’s. The purpose of the project was to develop equipment and technology to transform continuous fiber pre-preg in roll forms into smaller chip-format DFC feedstock, and to determine impacts on moldability and performance based on lessons learned along the path. The availability of scrap from pre-preg manufacturers was a significant value to the program even though the aerospace pre-preg is designed to be autoclave molded thus has handling, tackiness, and processing factors that are not ideal for DFCs. The scope of the project was to develop a Phase 1 system that could identify and resolve some of the major hurdles, determine where to focus effort on building a commercial-scale Phase 2 system, and develop technology for handling a wide variety of incoming scrap materials to produce the most usable product. A chopping system was developed and reduced to practice via an experimental approach that enabled all forms of scrap coming from the pre-preg manufacturers and some forms of the scrap coming from OEM production lines to be very effectively re-purposed. The systems that were developed were not considered to be production robust but rather identified and resolved some of the major technical hurdles, and demonstrated the path towards effective full-scale commercialization.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Evaluation of Composite Structural Materials for Heliostat Cost Reduction

Structures manufactured from steel comprise up to 40% of a CSP heliostat's cost. Composite structures represent a potential opportunity to reduce this cost. A reference heliostat structural model has been created with a reflector area of 25m 2 . The design, constructed of low-carbon steel, pro-vides baseline deflection and stiffness under a 21 m/s operating wind speeds. Wind loads on the tracker structure are determined for both operating and stow conditions. An established roster of suitable metal alternative materials is considered including: glass, basalt, and carbon reinforced polymer (GFRP, BFRP, and CFRP respectively). Three heliostat components are investigated: the pylon, torque tube, and the purlin-strut assembly. Composite material properties are substituted for those of steel, and the beams are re-sized to match the original steel components' deflection under given wind loads. Weight and cost changes resulting from this resizing are evaluated. It is found that GFRP and BFRP represent a 3X–6X cost premium for the same operating deflection character-istics as steel across all three investigated component classes; with weight reduction only achieved for the purlin-strut assembly. While CFRP components can achieve approximately 25–75% weight savings depending on the application, this comes with a 9X–14X cost increase over the steel base-line for tube-type structures and roughly 5X cost increase when replacing c-channel structures. This work does not rule out the possibility of cost savings when the heliostat design and kinematics to take advantage of composites' specific properties.

14 SOLAR ENERGY↗
DOE OSTI2023

Liquid-type room-temperature fluoride ion batteries

The present disclosure relates to fluoride ion batteries and structures of metal based electrode materials for various fluoride ion batteries. The structures of the metal based electrode materials comprise one or more shells or interfaces, enabling the electrodes to operate at room temperature with a liquid electrolyte.

Xu, Qingmin↗
DOE OSTI2020

Equilibrium shapes of facetted 3D metal nanoclusters intercalated near the surface of layered materials

Experimental studies indicate that 3D crystalline metal nanoclusters (NCs) intercalated under the surface of graphite have flat-topped equilibrated shapes. In this work, we characterize the shapes of these facetted NCs sandwiched between a blanketing graphene layer and the underlying graphite substrate. Specifically, we focus on the cases of fcc Cu and hcp Fe NCs. Furthermore, the analysis involves numerical minimization of the system energy for a specified NC volume and NC height, the latter corresponding to the separation between parallel top and bottom facets. Our numerical analysis quantifies how the distance of the side facet planes from center of the nanocluster varies linearly with a natural characteristic linear dimension of the nanocluster. Calculated shapes of fcc Cu and hcp Fe NCs are consistent with the hexagonal footprints observed in scanning tunneling microscopy studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Controlled Demolition and Reconstruction of Imidazolate and Carboxylate Metal–Organic Frameworks by Acid Gas Exposure and Linker Treatment

The metal-linker coordination bond in metal–organic frameworks (MOFs) can be unstable in humid and acid gas environments, leading to loss of crystallinity and porosity. This degradation is not necessarily irreversible; solvent-assisted crystal redemption (“SACRed”) has been shown to recover the physical and chemical properties of ZIF-8 exposed to humid SO 2 . This approach can also be useful in creating mixed-linker materials that might be challenging to produce via de novo synthesis. Here, we expand more generally the concept of controlled degradation of a MOF with acid gas, followed by treatment with a fresh linker solution, to the use of different template MOFs (ZIFs, UiO-66, and UiO-67) and acid gases (SO 2 and NO 2 in dry and humid conditions). Significant losses in porosity and crystallinity along with structural changes (acid gas-linker complexes and linker functionalizations) are observed in the acid gas-exposed MOF templates, and SACRed is shown to reconstruct these partially demolished MOFs with a high degree of structural recovery. Detailed structural and spectroscopic characterizations of the controlled degradation and subsequent recovery are presented and analyzed. Furthermore, these findings indicate the generality of controlled degradation and reconstruction as a means for linker replacement in a wider variety of MOFs and also create the potential for linker substitutions (with non-native linkers) to obtain new hybrid MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Studies toward the Use of Ionic Liquids and Supercritical CO 2 for the Recovery and Separation of Praseodymium from Waste Streams

Waste streams from the incineration of metal-containing materials like such as computer processor boards and batteries may contain critical rare earth elements like praseodymium. Data on the solubility of Pr compounds and on their distribution coefficients in supercritical CO 2 /ionic liquid two-phase systems are important to determine if an ionic liquid/supercritical CO 2 two-phase approach is feasible toward the recovery of a particular metal. This work provides data on the solubility of various praseodymium compounds in butyl-methyl-pyrrolidinium bis(trifluoromethylsulfonyl)imide (BMPyTf2N) ionic liquid and on the distribution coefficients of these praseodymium compounds in the supercritical CO 2 phase of the two-phase BMPyTf2N ionic liquid/supercritical CO 2 system, with and without a tributyl phosphate additive.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1985

Metallic and metalloceramic coating by thermal decomposition

Metallic and metalloceramic coatings were prepared by thermal decomposition of a number of inorganic and metallo-organic compounds. The compounds were applied by spraying and by immersion, especially on ceramic fibers and fiber forms, which are easily coated by this procedure. Penetration of low-density ceramics is examined, and procedures are described that were used for converting the deposited materials to metals, oxides, or metal oxide films. Multiple-component films were also prepared. Photomicrographs illustrate the structure of these films.

Hendricks, R. C.↗
NASA NTRS2006

Polarization Phase-Compensating Coats for Metallic Mirrors

A method of compensating for or minimizing phase differences between orthogonal polarizations of light reflected from metallic mirrors at oblique incidence, as, for example, from weakly curved mirrors, is undergoing development. The method is intended to satisfy a need to maintain precise polarization phase relationships or minimum polarization differences needed for proper operation of telescopes and other scientific instruments that include single or multiple mirrors. The basic idea of the method is to optimally coat mirrors with thin engineered layers of materials that introduce phase differences that, as nearly precisely as possible, are opposite of the undesired phase differences arising in reflection with non-optimum coatings. Depending on the specific optical system, the method could involve any or all of the following elements: a) Optimization of a single coat on all the mirrors in the system. b) Optimization of a unique coat for each mirror such that the polarization phase effects of the coat on one mirror compensate, to an acceptably high degree over an acceptably wide wavelength range, for those of the coat on another mirror. c) Tapering the coat on each mirror. Optimization could involve the choice of a single dielectric coating material and its thickness, or design of a more complex coat consisting of multiple layers of different dielectric materials and possibly some metallic materials. Such designs and coatings are particularly significant and needed for obtaining very high quality of wavefront required in high-contrast imaging instruments such as the NASA Terrestrial Planet Finder Coronagraph.

Balasubramanian, Kunjithapatham↗
DOE OSTI2021

Emergent anomalies and generalized Luttinger theorems in metals and semimetals

Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy. In this paper, we present a unified framework which allows one to discuss Luttinger theorems for ordinary metals as well as closely analogous exact statements for topological (semi)metals, whose low-energy description contains either discrete points or continuous line nodes. This framework is based on the 't Hooft anomaly of the emergent charge conservation symmetry at each point on the Fermi surface, a concept recently proposed by Else et al. Here we find that the Fermi surface codimension p plays a crucial role for the emergent anomaly. For odd p, such as ordinary metals (p = 1) and magnetic Weyl semimetals (p = 3), the emergent symmetry has a generalized chiral anomaly. For even p, such as graphene and nodal line semimetals (both with p = 2), the emergent symmetry has a generalized parity anomaly. When restricted to microscopic symmetries, such as U(1) and lattice symmetries, the emergent anomalies imply (generalized) Luttinger theorems, relating Fermi surface volume to various topological responses. The corresponding topological responses are the charge density for p = 1, Hall conductivity for p = 3, and polarization for p = 2. As a by-product of our results, we clarify exactly what is anomalous about the surface states of nodal line semimetals.

36 MATERIALS SCIENCE↗