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At least 1,441 records · Page 80

Expansion-driven Weibel instability in magnetohydrodynamics: Linear theory for static systems

The Weibel dispersion relation is obtained in the magnetohydrodynamic (MHD) approximation by including a tensor expression for temperature. MHD gives an upper cutoff wavenumber for Weibel growth identical to kinetic theory if the electron drift velocity is included in the evolution of the electron temperature. MHD overestimates growth rates compared to kinetic theory and gives maximum growth at larger wavenumbers, but it only leads to divergent results as temperature anisotropy tends to infinity. Thermal conduction in MHD lowers the growth rates and shifts maximum growth to smaller wavenumbers, but flux-limited or nonlocal thermal conduction is found to significantly limit these effects. The results are used as a first step in evaluating the potential of MHD to simulate expansion-driven Weibel instability, which occurs due to the temperature tensor only cooling in the direction of expansion. Finally, the small temperature anisotropy found in expansion-driven Weibel instability means that MHD could be an adequate model because growth rates are much less than the electron plasma frequency, and wavelengths are much greater than the Debye length.

Davies, J. R. [Univ. of Rochester, NY (United Stat↗

Strain-modulated helimagnetism and emergent magnetic phase diagrams in highly crystalline MnP nanorod films

Here, we explore strain-modulated helimagnetism in highly crystalline MnP nanorod films grown on Si(100) substrates using molecular beam epitaxy. The strained MnP film exhibits a paramagnetic to ferromagnetic (FM) phase transition at $T_C$ ~ 279 K, and the FM to helical phase transition at $T_N$ ~ 110 K. The value of $T_N$ is greater than $T_N$ ~ 47K for the MnP single crystal, indicating strong strain-modulated helimagnetic states in the MnP nanorod film. The presence of significant thermal hysteresis in the helical phase indicates the coexistence of competing magnetic interactions, leading to the first-order metamagnetic transition. Similar to its single-crystal counterpart, an anisotropic magnetic effect is observed in the MnP film, which is independently confirmed by magnetic hysteresis loop and radio-frequency transverse susceptibility (TS) measurements. The evolution of the screw to the cone and fan phases is precisely tracked from magnetization vs magnetic field/temperature measurements. The temperature dependence of the anisotropy fields, extracted from the TS spectra, yields further insight into the competing nature of the magnetic phases. Unfolding of the different helical phases at $\textit{T}$ < 120 K (~$T_N$) is analyzed by the temperature- and field-dependent magnetic entropy change. Based on these findings, the comprehensive magnetic phase diagrams of the MnP nanorod film are constructed for both the in-plane and out of plane magnetic field directions, revealing emergent strain/dimensionality-driven helical magnetic features that are absent in the magnetic phase diagram of the MnP single crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dilution impacts on smoke aging: evidence in Biomass Burning Observation Project (BBOP) data

Abstract. Biomass burning emits vapors and aerosols into the atmosphere that can rapidly evolve as smoke plumes travel downwind and dilute, affecting climate- and health-relevant properties of the smoke. To date, theory has been unable to explain observed variability in smoke evolution. Here, we use observational data from the Biomass Burning Observation Project (BBOP) field campaign and show that initial smoke organic aerosol mass concentrations can help predict changes in smoke aerosol aging markers, number concentration, and number mean diameter between 40–262 nm. Because initial field measurements of plumes are generally >10 min downwind, smaller plumes will have already undergone substantial dilution relative to larger plumes and have lower concentrations of smoke species at these observations closest to the fire. The extent to which dilution has occurred prior to the first observation is not a directly measurable quantity. We show that initial observed plume concentrations can serve as a rough indicator of the extent of dilution prior to the first measurement, which impacts photochemistry, aerosol evaporation, and coagulation. Cores of plumes have higher concentrations than edges. By segregating the observed plumes into cores and edges, we find evidence that particle aging, evaporation, and coagulation occurred before the first measurement. We further find that on the plume edges, the organic aerosol is more oxygenated, while a marker for primary biomass burning aerosol emissions has decreased in relative abundance compared to the plume cores. Finally, we attempt to decouple the roles of the initial concentrations and physical age since emission by performing multivariate linear regression of various aerosol properties (composition, size) on these two factors.

54 ENVIRONMENTAL SCIENCES↗

Consumable development to tailor residual stress in parts fabricated using directed energy deposition processes

Distortion and residual stresses are major challenges that limit the ability to fabricate large scale structures using Additive Manufacturing (AM). Researchers worldwide are evaluating techniques to induce compressive residual stress in the parts via intermittent rolling. While reasonable success has been documented, the idea of lowering the martensite start temperature to induce compressive stresses has not been evaluated in the context of AM, despite demonstrated success by the welding community. This study validates the hypothesis that, by a proper selection of materials and process parameters, one may effectively reduce distortion and induce a compressive residual stress in AM parts. Using neutron diffraction to measure residual stresses in parts, we demonstrate that, in addition to selection of the correct materials, the inter pass temperature plays a major role in controlling the residual stress evolution. The observations relating to the residual stresses are rationalized based on a microstructural evolution in these samples. Based on this preliminary study, a strategy to fabricate large structures with minimal distortion and residual stress is outlined.

36 MATERIALS SCIENCE↗

Ultrahigh Oxygen Evolution Reaction Activity Achieved Using Ir Single Atoms on Amorphous CoO x Nanosheets

Developing efficient electrocatalysts for an oxygen evolution reaction (OER) is important for renewable energy storage. Here, we design high-density Ir single-atom catalysts supported by CoO x amorphous nanosheets (ANSs) for the OER. Experimental results show that Ir single atoms are anchored by abundant surface-absorbed O in CoO x ANSs. Ir single-atom catalysts possess ultrahigh mass activity that is 160-fold of commercial IrO 2 . The OER of IrCoO x ANSs reached a record low onset overpotential of less than 30 mV. In situ X-ray absorption spectroscopy reveals that Ir-O-Co pairs directly boosted the OER efficiency and enhanced the Ir stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-Gradient Wien Spin Rotators at Jefferson Lab

Nuclear physics experiments performed in the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Laboratory (JLab) require spin manipulation of electron beams. Two Wien spin rotators in the injector keV region are essential at CEBAF to establish longitudinal polarization at the end station target, and to flip the polarization direction by ? rad to rule out false asymmetries. In a Wien filter, the homogeneous and independent electric and magnetic fields, along with the velocity vectors of the electrons that traverse it, form a mutually orthogonal system. The magnitude of the electrostatic field, established by biasing two highly-polished electrodes, defines the desired spin angle at the target yet deviates the beam trajectory due to the Lorentz force. The beam trajectory in the Wien is then re-established by adjusting the magnetic field, induced by an electromagnet encasing the device vacuum chamber. This contribution describes the evolution design and high voltage testing of Wien filters for spin manipulation at increased beam energies in the keV injector region, required by high precision parity violation experiments like MOLLER.

Palacios Serrano, G. G.↗

3D printed Ni-Mn-Fe Bi-Functional Catalyst for Metal Air Batteries

Oxygen evolution catalyst with porous structures on the submillimeter and millimeter ranges have been shown to have high catalytic activity. Often, a limiting factor in the performance of a catalyst can be its specific surface area as this can limit the availability of active sites which encourage the desired reaction. As such, the inclusion of a hierarchical structure that include both meso-scale and nano-scale porosity can offer a means to greatly increase the performance of electrochemical catalysts. We have developed a method for manufacturing samples with such a hierarchical structure by combining techniques of direct ink writing (DIW), thermal sintering and free corrosion based dealloying. This allows us to prepare three-dimensionally structured samples with open-cell porosity at the macro-, micro- and nano-scales. Each level of porosity offers a different advantage to the overall functionality and applicability of this technology.

25 ENERGY STORAGE↗

Platinum group metal-free (PGM-free) integrated tandem junction photoelectrochemical (PEC) water splitting devices (Final Technical Report)

This project involves using solar light, a photoabsorber, and a catalyst to split water and produce hydrogen. The Department of Energy (DOE) targets for integrated photoelectrochemical (PEC) cells emphasize cost (electrode cost < $200/m 2 ), performance (> 15% solar to hydrogen (STH) efficiency), and stability (> 6 months electrode lifetime), but most approaches skew toward one specific metric. This project exploited interfacial integration of platinum group metal-free (PGM-free) catalysts on the high performance and high value tandem solar cells to attain or exceed the DOE benchmark STH energy conversion efficiency and durability. This was investigated in two thrusts by developing two PEC devices for direct comparison: the first is a high-performance monolithic device based on state-of-the-art GaInP 2 /GaAs tandem solar cells developed at National Renewable Energy Laboratory (NREL), and the second is a high-value device based on earth-abundant wide band gap photoabsorber materials including oxynitride and hybrid organic-inorganic perovskite (HOIP) coupled with commercial narrow band gap silicon (Si). Both these devices were paired with electrocatalysts developed for this purpose at Rutgers University by adapting them to thin films on the photoabsorbers. These catalysts are based on the hydrogen evolution reaction (HER) catalysts (Ni 5 P 4 ), oxygen evolution reaction (OER) catalysts (LiCo 2 O 4 ) previously developed at Rutgers for high-efficiency electrolyzers. For using the high-performance tandem solar cell and Ni 5 P 4 catalysts, we achieved a durability of > 200 h at a STH efficiency of > 10%. For using the high-value wide band gap single junction solar cells on n + Si, we achieved 0.73 mA/cm 2 at 1.23V vs reversible hydrogen electrode (RHE) and -15.9 mA/cm 2 at 0V vs RHE using the oxynitride- and HOIP-based photoelectrodes, respectively. After comparing their photocurrent densities, we down selected the HOIP photoabsorber to couple Si for fabrication of a tandem photocathode. However, due to the COVID-19 pandemic, both the laboratories at Rutgers and NREL were locked down for three months and reopened only partially in 2020. The HOIP/Si tandem photocathode using robust nickel phosphide thin film catalysts cannot be developed within the project period, which is expected to achieve a STH efficiency of > 20%. Also, the low-cost LiCo 2 O 4 OER catalysts need to replace the benchmark IrO 2 for evaluation. Finally, techonomic analysis of full high-performance and high-value integrated PEC devices needs to be carried out for comparison in terms of cost.

08 HYDROGEN↗

High-Gradient Wien Spin Rotators at Jefferson Lab

Nuclear physics experiments performed in the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Laboratory (JLab) require spin manipulation of electron beams. Two Wien spin rotators in the injector keV region are essential at CEBAF to establish longitudinal polarization at the end station target, and to flip the polarization direction by ? rad to rule out false asymmetries. In a Wien filter, the homogeneous and independent electric and magnetic fields, along with the velocity vectors of the electrons that traverse it, form a mutually orthogonal system. The magnitude of the electrostatic field, established by biasing two highly-polished electrodes, defines the desired spin angle at the target yet deviates the beam trajectory due to the Lorentz force. The beam trajectory in the Wien is then re-established by adjusting the magnetic field, induced by an electromagnet encasing the device vacuum chamber. This contribution describes the evolution design and high voltage testing of Wien filters for spin manipulation at increased beam energies in the keV injector region, required by high precision parity violation experiments like MOLLER.

Palacios Serrano, G. G.↗

Catalysts by pyrolysis: Direct observation of chemical and morphological transformations leading to transition metal-nitrogen-carbon materials

Transition metal-nitrogen-carbon materials (M-N-C catalysts) are promising electrocatalysts in polymer electrolyte fuel cells (PEFCs) and electrolyzer applications. High temperature treatment in inert atmosphere (pyrolysis) is the essential, most common method for the synthesis of M-N-C catalysts and critical to achieve high electrocatalytic activity and electronic conductivity. To this day, despite many uses and successful implementations in materials manufacturing, pyrolysis has been an entirely empirical technology, with process control and optimization relying exclusively on “Edisonian” approach. The knowledge gap in the mechanism about how the precursor is being transformed into catalysts hinders further development of the M-N-C catalysts regardless of the precursor class and processing protocols. In this work, we probed the morphological evolution and chemical transformation of a nitrogen-containing charge transfer organic salt, mixed with transition metal (iron) salt and amorphous silica powder (precursor) during the pyrolysis process via a combination of in situ synchrotron and laboratory-based diagnostic techniques. The pyrolysis process is found to be divided into three stages. During a controlled temperature ramp, the selected organic N-C precursor (nicarbazin) began melting and decomposing just below 400 °C, forming a certain number of micrometer-scale pores and pathways. With increase in temperature from 400 °C to 900 °C, amorphous carbon domains started forming, and reduced (metallic) iron nanoclusters appeared, being dispersed uniformly throughout the carbonaceous matrix. When temperature advanced above 900 °C, graphitization of carbon commenced, associated with appearance and evolution of atomically dispersed metal-nitrogen moieties in the carbonaceous matrix. As the graphitization advanced further, a secondary process of agglomeration of metal nanoparticles occurred. Multi-analytical technique observations conducted here provide a base for rational design and optimization of M-N-C electrocatalysts via pyrolysis.

36 MATERIALS SCIENCE↗

Domain fluctuations in a ferroelectric low-strain BaTiO 3 thin film

In this work, a ferroelectric BaTiO 3 thin film grown on a NdScO 3 substrate was studied using x-ray photon correlation spectroscopy (XPCS) to characterize thermal fluctuations near the a/b to a/c domain structure transformation present in this low-strain material, which is absent in the bulk. XPCS studies provide a direct comparison of the role of domain fluctuations in first- and second-order phase transformations. The a/b to a/c domain transformation is accompanied by a decrease in fluctuation timescales, and an increase in intensity and correlation length. Surprisingly, domain fluctuations are observed up to 25 °C above the transformation, concomitant with the growth of a/c domains and coexistence of both domain types. After a small window of stability, as the Curie temperature is approached, a/c domain fluctuations are observed, albeit slower, potentially due to the structural transformation associated with the ferroelectric to paraelectric transformation. The observed time evolution and reconfiguration of domain patterns highlight the role played by phase coexistence and elastic boundary conditions in altering fluctuation timescales in ferroelectric thin films.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Gene expression of functionally-related genes coevolves across fungal species: detecting coevolution of gene expression using phylogenetic comparative methods

Researchers often measure changes in gene expression across conditions to better understand the shared functional roles and regulatory mechanisms of different genes. Analogous to this is comparing gene expression across species, which can improve our understanding of the evolutionary processes shaping the evolution of both individual genes and functional pathways. One area of interest is determining genes showing signals of coevolution, which can also indicate potential functional similarity, analogous to co-expression analysis often performed across conditions for a single species. However, as with any trait, comparing gene expression across species can be confounded by the non-independence of species due to shared ancestry, making standard hypothesis testing inappropriate. We compared RNA-Seq data across 18 fungal species using a multivariate Brownian Motion phylogenetic comparative method (PCM), which allowed us to quantify coevolution between protein pairs while directly accounting for the shared ancestry of the species. Our work indicates proteins which physically-interact show stronger signals of coevolution than randomly-generated pairs. Interactions with stronger empirical and computational evidence also showing stronger signals of coevolution. We examined the effects of number of protein interactions and gene expression levels on coevolution, finding both factors are overall poor predictors of the strength of coevolution between a protein pair. Simulations further demonstrate the potential issues of analyzing gene expression coevolution without accounting for shared ancestry in a standard hypothesis testing framework. Furthermore, our simulations indicate the use of a randomly-generated null distribution as a means of determining statistical significance for detecting coevolving genes with phylogenetically-uncorrected correlations, as has previously been done, is less accurate than PCMs, although is a significant improvement over standard hypothesis testing. These methods are further improved by using a phylogenetically-corrected correlation metric. Our work highlights potential benefits of using PCMs to detect gene expression coevolution from high-throughput omics scale data. This framework can be built upon to investigate other evolutionary hypotheses, such as changes in transcription regulatory mechanisms across species.

59 BASIC BIOLOGICAL SCIENCES↗

Air quality impact of the Northern California Camp Fire of November 2018

The Northern California Camp Fire that took place in November 2018 was one of the most damaging environmental events in California history. Here, we analyze ground-based station observations of airborne particulate matter that has a diameter <2.5 µm (PM 2.5 ) across Northern California and conduct numerical simulations of the Camp Fire using the Weather Research and Forecasting model online coupled with chemistry (WRF-Chem). Simulations are evaluated against ground-based observations of PM 2.5 , black carbon, and meteorology, as well as satellite measurements, such as Tropospheric Monitoring Instrument (TROPOMI) aerosol layer height and aerosol index. The Camp Fire led to an increase in Bay Area PM 2.5 to over 50 µg m –3 for nearly 2 weeks, with localized peaks exceeding 300 µg m –3 . Using the Visible Infrared Imaging Radiometer Suite (VIIRS) high-resolution fire detection products, the simulations reproduce the magnitude and evolution of surface PM 2.5 concentrations, especially downwind of the wildfire. The overall spatial patterns of simulated aerosol plumes and their heights are comparable with the latest satellite products from TROPOMI. WRF-Chem sensitivity simulations are carried out to analyze uncertainties that arise from fire emissions, meteorological conditions, feedback of aerosol radiative effects on meteorology, and various physical parameterizations, including the planetary boundary layer model and the plume rise model. Downwind PM 2.5 concentrations are sensitive to both flaming and smoldering emissions over the fire, so the uncertainty in the satellite-derived fire emission products can directly affect the air pollution simulations downwind. Our analysis also shows the importance of land surface and boundary layer parameterization in the fire simulation, which can result in large variations in magnitude and trend of surface PM 2.5 . Inclusion of aerosol radiative feedback moderately improves PM 2.5 simulations, especially over the most polluted days. Results of this study can assist in the development of data assimilation systems as well as air quality forecasting of health exposures and economic impact studies.

54 ENVIRONMENTAL SCIENCES↗

Dihadron correlations in small- x DIS at NLO: transverse momentum dependent fragmentation

We compute the inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small x in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is –$\frac{αs}{2π}$ [C F + $\frac{Nc}{2}$] instead of –$\frac{αsNc}{4π}$ when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizsäcker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small x at the future Electron-Ion Collider with full NLO accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A direct numerical simulation study of the dilution tolerance of propane combustion under spark-ignition engine conditions

Modern spark ignition internal combustion (IC) engines rely on highly diluted fuel-air mixtures to achieve high brake thermal efficiencies. To support this, new engine designs have introduced high stroke-to-bore ratios and cylinder head designs that promote high tumble flow and turbulence intensities. However, mixture dilution through exhaust gas recirculation (EGR) is limited by combustion instabilities manifested in the form of cycle-to-cycle variability. Propane has been observed to have superior EGR dilution tolerance than gasoline, which makes it a very competitive low-carbon fuel for the new IC engines without sacrificing efficiency. Two-dimensional direct numerical simulations (DNS) are performed with detailed chemistry to study and contrast the effect of turbulence intensity and dilution on propane and iso-octane premixed flames at high pressure conditions similar to those in-cylinder. A new reduced mechanism for propane consisting of 53 transported species and 17 quasi-steady state species is developed based on a previously published mechanism and used in these simulations. Three levels of turbulence intensity and two levels of exhaust gas dilution are chosen based on conditions relevant to IC engine operation. The DNS results are analyzed based on the evolution of the flame surface area and the statistics of its driving terms, which are found to be similar for both fuels when there is no dilution but considerably different under high dilution. The analysis of the DNS data provides fundamental insights into the underlying mechanisms for improved stability under dilution.

42 ENGINEERING↗

Upcycling waste PET into functional multiblock copolymers through controlled macromolecular design

Poly(ethylene terephthalate) (PET) oligomers derived from glycolysis depolymerization were converted into multiblock copolymers through diisocyanate-mediated coupling with dihydroxy-terminated oligomers, enabling precise control over copolymer sequence distribution, connectivity, and mechanical performance. Here, we demonstrate that telechelic PET oligomers isolated directly from depolymerized consumer waste can serve as reactive building blocks for the formation of segmented multiblock copolymers, eliminating the need to revert to monomeric feedstocks. Dihydroxy-terminated PET oligomers (Mw ≈ 8 kg mol−1) were coupled with poly(ethylene oxide) (PEO, Mw ≈ 4 kg mol−1) to form PET-PEO multiblock copolymers with high molar mass (Mw ≈ 160 kg mol−1). We further show that the timing of end-capping reactions provides a key control parameter that governs the competition between chain extension and termination, thereby dictating the resulting multiblock architecture and molecular-weight evolution. Evaluation of their mechanical properties reveals that virgin PET exhibits high modulus (∼3 GPa) and strength (43 MPa) but limited ductility (<10% elongation). In contrast, PET–PEO multiblock copolymers retain comparable tensile strength (44 MPa), albeit while exhibiting dramatically enhanced ductility (>90% elongation), forming tougher materials with efficient stress transfer between the rigid PET domains and the flexible PEO segments. When incorporated into PET/PEO blends at low loadings, the multiblock copolymers serve as effective compatibilizers, yielding materials with an intermediate modulus (1.1–1.2 GPa) and improved elongation compared to uncompatibilized blends. Furthermore, the presence of PEO blocks increases water uptake and gas permeability relative to virgin PET, reflecting the tunability of molecular transport through the copolymeric blocks. To our knowledge, this represents the first report of PET–PEO multiblock copolymers derived from post-consumer PET for gas transport applications. These results demonstrate that multiblock copolymer formation from telechelic PET oligomers provides a versatile platform for tailoring the mechanical and transport behavior of polyester-based materials through controlled macromolecular design and establishes a generalizable strategy for transforming consumer plastic waste into functional segmented polymers without requiring complete depolymerization to monomers.

Watson-Sanders, Shelby [Department of Chemistry, U↗

Out-of-time-order correlators bridge classical transport and quantum dynamics

The out-of-time-order correlator (OTOC) has emerged as a central tool for quantifying decoherence across wide-ranging physical platforms. Here, we demonstrate its direct measurement in a classical ensemble using nuclear magnetic resonance with a modulated gradient spin echo sequence and extend the method into a multidimensional correlation to track exchange phenomena. Position is encoded through magnetic field gradients and momentum through the velocity autocorrelation function, enabling experimental access to OTOCs for proton motion confined within the self-similar lattice of the metal–organic framework MOF-808. Here, water confined to specified geometries within the MOF pores gives rise to spatially distinct diffusive eigenmodes with characteristic relative entropies. We demonstrate that periodic radio frequency driving combined with gradient modulation yields entropy evolution through the selection of distinct diffusion modes. Frequency-resolved diffusion spectra connect these entropy dynamics to classical heat exchange laws, revealing how operational features of quantum systems are mirrored in confined, macroscopic spin ensembles.

Fricke, Sophia N. [University of California, Berke↗

Analytical modeling of the evolution of the nonlinearity parameter of sensitized stainless steel

Austenitic stainless steels are subject to the precipitation of chromium carbides (M 23 C 6 ) during exposure to high temperatures, causing these alloys to be susceptible to intergranular corrosion due to chromium depletion along grain boundaries. The acoustic nonlinearity parameter, β, shows sensitivity to the formation of carbides in these alloys. The Thermo-Calc TC-PRISMA module was used to model the nucleation and growth of grain boundary M 23 C 6 carbides. The model was verified with scanning transmission electron microscopy analysis that allowed measurements of the grain boundary precipitates. The paper introduces a reduced-order model of the acoustic nonlinearity based on the formation of misfit dislocations at the interface of the grain boundary precipitate and matrix to explain the change in β during isothermal aging. Furthermore, a direct relationship between the radius of the M 23 C 6 grain boundary carbides and β was observed and verified with nonlinear ultrasound measurements on 304L and 316L stainless steels.

36 MATERIALS SCIENCE↗