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At least 19 records

Reverse phonon thermal flux from an applied electric field

In the phenomenon known as electron drag, a phonon thermal flux is established in a conducting crystal by an electric field applied under isothermal conditions through directed transfer of quasimomentum from the electronic charge current to the phonon subsystem. Prior understanding of this phenomenon involves a thermal current composed of low-frequency acoustic phonons that is in the same direction as the charge current. This results in an increase of the Peltier thermopower. Here, we show that it is also possible to establish a phonon thermal current that is in the opposite direction to the charge current, which we refer to as a reverse phonon thermal flux. We demonstrate this behavior both through a simple qualitative model and through first-principles calculations performed for three materials: p-type 𝜃-TaN, n-type BAs, and n-type Si. The reverse phonon flux is shown to arise through intervalley electron-phonon scattering processes involving high-frequency acoustic phonons. Unlike n-BAs and n-Si, the combined features in the band structure and phonon dispersions of p-type 𝜃-TaN promote a particularly large reverse phonon thermal flux comparable in magnitude to the oppositely directed thermal flux from low-frequency phonons. Finally, this work highlights a previously unrecognized behavior in the coupled electron-phonon system and advances our understanding of the rich physics of transport in solids.

lattice dynamics↗

Multi-sensor Observations of a High-velocity Fireball over the South Atlantic on 2026 April 1

A high-velocity fireball was detected over the South Atlantic (41.9°S, 54.7°W) on 2026 April 1 at 02:13:14 UTC by U.S. Government (USG) sensors, with peak brightness at 90.5 km altitude. The event was well-observed from geostationary orbit by two civilian lightning imagers with near-orthogonal geometry, the Geostationary Operational Environmental Satellite-East Geostationary Lightning Mapper (GLM) and the Exploitation of Meteorological Satellites Meteosat Third Generation Imager 1 Lightning Imager, and it produced low-frequency acoustic signatures. The GLM measured a total radiated energy of 2.4 × 10 10 J, corresponding to a calculated impact energy of 0.086 kt TNT equivalent. Stereoscopic triangulation of the imager tracks yields an independent pre-atmospheric velocity of ~57 km s −1 , some 18% below the USG-reported value. Because orbital provenance is acutely sensitive to the entry velocity, whose reported uncertainty could be substantial, this discrepancy is notable. We document the multi-sensor record and identify the analysis required to assess provenance, which a subsequent study will present.

Silber, Elizabeth Allaryce [Sandia National Lab. (↗

Measurement of the thermal effects in the dispersion relation of the dust acoustic wave in the presence of a magnetic field

This award supported an experimental study of the properties of the dust acoustic wave, low-frequency, l ongitudinal wave mode that propagates through the dust component of a dusty plasma system and is self-excited by the free energy from the ion streaming p ast the dust, in the presence of a high magnetic fiel d. In particular, this project measured the thermal state of dusty plasma system by measuring the dispersi on relation of the dust acoustic wave while varying (1) the strength and direction of the magnetic field relative to the propagation direction of the wave and (2) the neutral gas pressure. By exploiting the unique ability of the MDPX facility to generate a dusty plasma in a high magnetic field environment, it is possible to create a preferential ion flow along the magnetic field lines as the ions become magnetized. In this way, the magnetic field strength can be used to control t he strength of the ion flow through the dust cloud an d provide insight into the contribution that one of the physical mechanisms, a two-stream ion-dust instability, thought to be responsible for high temperatures that have been previously observed might have. This work was completed over two, one-week long runs o n the Magnetized Dusty Plasma eXperiment (MDPX) in the Magnetized Plasma Research Laboratory at Auburn University and supported by work at Wittenberg University (development of an electrode system that would allow for the wave mode to propagate in th e direction of gravity as the orientation of the magnetic field is changed by rotating the magnets on the M DPX device, analysis of data acquired during the experimental campaigns, testing alternative strategies to form a dust cloud based on what was learned the first experimental campaign, etc.).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Distributed Fiber Optic Sensing for in-well hydraulic fracture monitoring

This study presents the results from in-well hydraulic fracture monitoring within a horizontal well in an unconventional reservoir utilizing Distributed Fiber Optic Sensing (DFOS). An in-house-developed Brillouin-based Distributed Strain Sensing (DSS) interrogator was deployed to obtain strain measurements, complemented by a commercial Raman-based Distributed Temperature Sensing (DTS) interrogator for temperature measurements and a commercial Rayleigh-based Low-Frequency Distributed Acoustic Sensing (LF-DAS) interrogator for strain-rate measurements. Examined over a ten-day period, the spatio-temporal distribution of temperature-compensated strain obtained from DSS and DTS revealed distinct signatures of the multi-stage hydraulic fracturing process. These signatures were analyzed with respect to fracture width growth and closure, residual strain effects, and fracture conductivity near the wellbore. Fracture widths within the fracture zone were estimated for individual stages. The findings were assessed with LF-DAS measurements for further evaluation. This work integrates DFOS-measured strain, temperature, and strain-rate data for monitoring in-well hydraulic fracturing, with the goal of supporting future studies in interpreting DFOS measurements for improved understanding of hydraulic fracturing in unconventional reservoirs.

58 GEOSCIENCES↗

Integration of the Biot–Gassmann Fluid Substitution Method and Machine Learning-Based Velocity–Stress Relationship for Estimating In Situ Stresses

Recent advancements have shown that in situ stresses can be reliably estimated through an integrated machine/deep learning (ML/DL)-based framework, which relies on models trained and validated using true triaxial ultrasonic velocity (TUV) experimental data that involve measurements of ultrasonic velocity in saturated rocks under varying stress configurations. However, when the goal is to interpret lower frequency measurements, it may be more appropriate to run experiments on dry rocks and then obtain Biot–Gassmann-derived equivalent saturated velocities (low-frequency approximation) and employ these quantities for training ML/DL models to predict in situ stress. Whether the dispersion effect of frequency on the velocity–stress relationship substantially impacts in situ stress prediction is an important and unresolved question. This work presents an enhancement of ML/DL-based workflow by training and implementing ML/DL models using equivalent saturated acoustic velocities (low-frequency) obtained by applying Biot–Gassmann fluid substitution on the ultrasonic velocities of dry cores. The models were trained on TUV data sets derived from three subsurface cores extracted from the geothermal well 16B(78)-32 at the Utah FORGE site. Each core was subjected to 75 unique stress configurations for velocity measurement in the dry state. The ML/DL trained on the TUV data set with equivalent saturated velocities demonstrated promising performance to predict in situ stress in subsurface geological rocks using velocity–stress relationships with R 2 of 0.86, 0.971, and 0.975 and root mean squared error (RMSE) of 2.59, 1.92, and 1.80 for validation/testing phases of vertical, minimum horizontal, and maximum horizontal stress models, respectively. Additionally, interpretation and explanation by Shapley additive explanations (SHAP) analysis further improved scientific validation and model reliability for estimating in situ stresses.

colloids↗

Quantitative Assessment of Parent Well Effect on Hydraulic Fracture Propagation at HFTS2: Insights from Cross-Well Strain Measurements and Microseismic Data

Understanding fracture propagation behavior is essential for optimizing hydraulic fracturing in unconventional reservoirs. This study demonstrates the value of integrating Low-Frequency Distributed Acoustic Sensing (LF-DAS) and microseismic data, which together provide a more complete picture of fracture growth. Using data from Hydraulic Fracturing Test Site 2 (HFTS2), we identify stress changes in depletion zones induced by parent wells as a key factor influencing fracture propagation. This result is shown by new measurements of in-situ fracture propagation velocity and fracture-hit volume (fluid volume at fracture hit?) from LF-DAS and event density from microseismic. These findings highlight the importance of considering parent well effects, well spacing, and stimulation sequencing in completion design to improve reservoir development and production efficiency.

depletion zones↗

Particle Size gradients in Modeled Vibrated beds of continuously sized powders

Ensuring powder mixture homogeneity is paramount for modern powder processing techniques. A promising recent development in the field of powder processing, resonant acoustic mixing (RAM), proposes to use low-frequency vertical vibration to deliver well-mixed powders without relying on mechanical agitators. However, an undesirable outcome of vibrations applied to granular materials comprised of non-uniform particle sizes is the tendency towards size segregation. In this work, we experimentally ex

Renfroe, Steven Emad [Sandia National Laboratories↗

Audible enclaves crafted by nonlinear self-bending ultrasonic beams

Delivering audible content to a targeted listener without disturbing others is paramount in audio engineering. However, achieving this goal has long been challenging due to the diffraction of low-frequency (long-wavelength) audio waves in linear acoustics. Here, we introduce an approach for creating remote audio spots, dubbed audible enclaves, by harnessing the local nonlinear interaction of two self-bending ultrasonic beams with distinct spectra. The self-bending ultrasonic beams created by acoustic metasurfaces, though inaudible, can bypass obstacles such as human heads. At their intersection behind obstacles, highly localized audible enclaves are formed due to the local nonlinear interactions. Additionally, we demonstrate the ultrabroadband capabilities of our metasurface-based implementation both numerically and experimentally, spanning from 125 Hz to 4 kHz (6 octave bands), covering the majority of the audible frequency range. The practicality of our proposed technique is underscored by its compact implementation size (0.16 m, equivalent to 0.06 wavelengths at 125 Hz), as well as its robust performance under wideband transient audio signal excitation and in a common room with reverberations. Our proposed audible enclaves hold significant potential for various applications in advanced audio engineering, including private speech communications, immersive spatial audio reproduction, and high-resolution sound/quiet zone control.

Science & Technology - Other Topics↗

Acoustic waves from the 2023 April 20 SpaceX Starship rocket explosion travelling in the elevated ‘AtmoSOFAR’ channel

SUMMARY The ability to detect low-frequency sounds from distant energetic events depends on the temperature and wind structure of the atmosphere. Thus, from time to time surface-based acoustic detectors may not be able to capture sounds arriving from certain directions. However, the temperature minimum at the tropopause may create an acoustic duct called the ‘AtmoSOFAR’ channel that could transmit acoustic waves laterally—but perhaps not to the ground. If true, then elevated sensors such as those borne aloft by balloons would record the signatures even in regions where ground-based sensors cannot. This has been difficult to prove because high altitude acoustic sources are rare and balloon deployments are sporadic. This work describes the detection and characterization of powerful acoustic waves generated during the launch and terminal explosion of the SpaceX Starship rocket on 2023 April 20 using a pair of microbarometers on a stratospheric balloon. The signals travelled through the AtmoSOFAR channel, carrying information about the size and nature of their source. This channel also appears to leak some acoustic energy to the ground, in agreement with previous studies. The acoustic yield of the Starship terminal explosion was on the order of $10^3$ tons trinitrotoluene equivalent, which agrees with the estimated fuel load of the vehicle to about a factor of 2, but is two orders of magnitude larger than optical estimates. These results support an earlier study that claimed lateral transmission of sound from a smaller rocket through the AtmoSOFAR channel. The transmission of source information through the AtmoSOFAR channel motivates its use for monitoring other natural and anthropogenic events using balloon-borne sensors. This may become increasingly important as more and more private and government entities conduct spacecraft launches and reentries. It may also provide a means of monitoring clear air turbulence and other sound-generating atmospheric phenomena at a distance.

58 GEOSCIENCES↗

Retrospective on decadal progress of the NOAA/NPS ocean noise reference station network

The National Oceanic and Atmospheric Administration (NOAA), in partnership with the U.S. National Park Service (NPS), established the Ocean Noise Reference Station Network (NRS) in 2014 as a foundational component of NOAA’s Ocean Noise Strategy. This long-term effort aims to characterize baseline ocean ambient sound conditions across diverse marine environments and to inform management of noise impacts on protected species and habitats within U.S. waters. The NRS is now composed of 13 autonomous passive acoustic monitoring stations strategically positioned across the U.S. Exclusive Economic Zone (EEZ), extending from Arctic regions to tropical waters in depths ranging from 33 to 4,790 m. These locations include several National Marine Sanctuaries and National Parks, such as the recently designated Chumash Heritage National Marine Sanctuary off the coast of California. Each station is equipped to continuously sample low-frequency underwater sound at five kHz, enabling the detection of anthropogenic, geophysical, and biological acoustic signals. To date the network has sampled over 72 years of calibrated acoustic data. The spatial breadth and consistent methodology of the NRS allow for comparative acoustic assessments across diverse marine ecosystems. In addition to applied research functions, the NRS has served as a platform for education and training, offering opportunities for students to develop skills for marine science and data analysis. Looking forward, the NRS project team is focused on network expansion, improved data delivery, and broader integration with collaborative scientific initiatives. NRS recordings are being archived in partnership with NOAA’s National Centers for Environmental Information to enhance accessibility and long-term utility. Efforts are underway to develop standardized metadata and summary products to accompany raw audio files, making the data more usable for a wide range of stakeholders in the ocean science community. The NRS is evolving into a fully integrated national framework for ocean sound monitoring that supports scientific inquiry, management decision-making, national security interests, and public engagement with ocean acoustic environments.

Long-term monitoring↗

Phonon lifetimes and mode softening in cubic Cs 2 AgBiBr 6

Metal halide perovskites (MHPs) have emerged as noteworthy candidates for photovoltaic applications in recent years. Their high power-conversion efficiency is largely attributed to the structure-function relationship, which is not well understood. In this study, we examine the low-frequency phonons of the double perovskite Cs 2 AgBiBr 6 using neutron inelastic scattering. We find that the acoustic phonon lifetimes decrease from 16 to 3 ps along Γ to X, which is indicative of significant anharmonicity that contributes to the ultralow thermal conductivity. Additionally, we observe a linear temperature dependence of the square of the zone-center soft optical phonon energy, which is consistent with a weakly first-order displacive cubic-tetragonal structural phase transition. These results provide a deeper understanding of the lattice dynamics and phase transitions in MHPs as well as the effects of anharmonicity by comparison with prototypical hybrid organic-inorganic MHPs, (CH 3 NH 3 ) PbX 3 (X = Br, I).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ultrasonic deterrents provide no additional benefit over curtailment in reducing bat fatalities at an Ohio wind energy facility

Wind energy is important for achieving net-zero greenhouse gas emissions but also contributes to global bat mortality. Current strategies to minimize bat mortality due to collision with wind-turbine blades fall broadly into two categories: curtailment (limiting turbine operation during high-risk periods) and deterrence (discouraging bat activity near turbines). Recently, there has been interest in combining these strategies to achieve greater reductions in bat fatalities than either strategy might achieve in isolation. To investigate the effectiveness of combining curtailment with ultrasonic deterrent minimization strategies, we deployed six ultrasonic deterrents at nacelle height on 16 experimental turbines at Avangrid Renewables’ Blue Creek Wind Energy Facility. We rotated between four conditions (normal operations, curtailment only, deterrent only, curtailment and deterrent) randomly assigned to four wind turbines each night between 15 June and 3 October 2017. We found that bat mortality at wind turbines was independent of wind speed. The effectiveness of ultrasonic acoustic deterrents varied between high-frequency-calling species (eastern red bats) and low-frequency-calling species (hoary bats, silver-haired bats, and big brown bats). When deterrents were active, mortality was twice as high for eastern red bats compared to the control. Conversely, deterrents had a weak dampening effect on bat mortality for low-frequency species. We found no additive effects on mortality reduction for turbines operating both curtailment and deterrents compared to either approach in isolation. Our findings suggest that ultrasonic acoustic deterrents may not be effective for both high and low frequency echolocating bats. The increase in fatalities of eastern red bats is alarming and underscores the importance of considering site- and species-specific effects of minimization solutions.

60 APPLIED LIFE SCIENCES↗

Observations and seismoacoustic simulations of earthquake-generated infrasound waves in non-epicentral regions

We analysed infrasound waves associated with the Gyeongju earthquake (ML 5.8) that occurred on 2016 September 12, in the southeastern Korean Peninsula. For infrasound wave detection, the Progressive Multichannel Correlation method was applied to the infrasound data set recorded at seven arrays operating in South Korea at epicentral distances ranging from 178 to 472 km. Based on the back-projection method constrained by array-dependent celerity and azimuth deviation models, the source regions were identified in both the epicentral and non-epicentral regions. Remarkably, the non-epicentral secondary sources of this earthquake were located in regions with shallow water depths: (i) the western coastal area in the Yellow Sea and (ii) the shallow ocean basin and bank in the East Sea. The location results obtained from the earthquake could be corroborated through its foreshock (ML 5.1), yielding location results consistent with those of the main shock. The generation of infrasound waves over shallow water depths was fortuitously validated by direct recordings of dominant single-frequency (~0.3 Hz) infrasound waves at close range via temporary sensors near the ocean basin and bank. We interpreted that low-frequency infrasound signals could be generated from interactions among the ocean floor, shallow seawater and atmosphere. We performed numerical simulations of seismoacoustic fields to predict ground motions on the seafloor and acoustic transmission efficiency between the water and air interface. The simulations quantified the energy transfer through different media and clarified our observational results. We found that because this solid Earth‒water‒atmosphere coupled air wave has a relatively low frequency (~0.3 Hz), it can survive propagation over long distances compared with high-frequency infrasound waves generated in inland and mountain regions. In this study, we extend our understanding of water‒atmosphere coupling and the monitoring framework for earthquake-associated non-epicentral infrasound waves, encompassing not only inland ground shaking but also shallow sea regions located far from the epicentre.

Earthquake monitoring and test-ban treaty verifica↗

Coherent and Dynamic Small Polaron Delocalization in CuFeO 2

Small polarons remain a bottleneck in realizing efficient transition metal oxide devices. Routes to engineer small polaron coupling to electronic states and lattice modes to control carrier localization remain unclear. Here, we measure small polaron formation in CuFeO 2 using transient extreme ultraviolet reflection spectroscopy and compare to theoretical predictions in realistically parametrized Holstein models, demonstrating that polaron localization depends on coupling to high-frequency versus low-frequency phonon bath components. We measure small polaron formation on a comparable ∼100 fs timescale to other Fe(III) compounds. Dynamic delocalization of the polaron follows formation through a coherent lattice expansion between Fe–O layers and charge-sharing with surrounding Fe(IV) states. Simulations reveal two major factors dictate polaron formation timescales: phonon density and reorganization energy distributions between acoustic and optical modes, matching experimental findings. Our work shows how electronic-structural coupling in a polaron-host material can be leveraged to suppress polaronic effects for various applications.

Hematite↗

Detection of a Space Capsule Entering Earth’s Atmosphere with Distributed Acoustic Sensing (DAS)

On 24 September 2023, the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer sample return capsule (SRC) entered Earth’s atmosphere after successfully collecting samples from an asteroid. The known trajectory and timing of this return provided a rare opportunity to strategically instrument sites to record geophysical signals produced by the capsule because it travelled at hypersonic speeds through the atmosphere. For this work, we deployed two distributed acoustic sensing (DAS) interrogators to sample over 12 km of surface-draped fiber-optic cables, as well as six collocated seismometer-infrasound sensor pairs, spread across two sites near Eureka, Nevada. This campaign-style rapid deployment is the first reported recording of an SRC re-entry with any distributed fiber-optic sensing technology. The DAS interrogators recorded an impulsive arrival with an extended coda which had features that were similar to recordings from both the seismometers and infrasound sensors. While the signal-to-noise ratio of the DAS data was lower than the seismic-infrasound data, the extremely dense spacing of fiber-optic sensors allowed for more phases to be clearly distinguished and the visualization of the continuous transformation of the wavefront as it impacted the ground. Unexpectedly, the DAS recordings contain less low-frequency content than is present in both the seismic and infrasound data. The deployment conditions strongly affected the recorded DAS data; in particular, we observed that fiber selection and placement exert strong controls on data quality.

58 GEOSCIENCES↗

Continuous surface-to-distributed acoustic sensor snapshots explain reactivation of individual natural fractures during an unconventional reservoir stimulation

ABSTRACT Fiber-optic sensing technologies allow petroleum engineering teams to detect hydraulic fracture interaction with boreholes during unconventional reservoir stimulation. In combination with high-repeatability seismic sources, the same distributed acoustic sensors (DASs) enable vertical seismic profiling (VSP) of the fracture evolution away from the boreholes. We discovered clear signatures of seismic scattering on activated fractures during nine days of continuous seismic monitoring of the fracturing stages at the Austin Chalk/Eagle Ford Field Laboratory. The present study applies a novel approach for quantitative analysis of the scattering events in terms of the evolution of the geometry and elastic stiffness of individual fractures. Our characterization strategy sequentially refines the fracture models: from a stack of 1D soft layers to 3D rectangular inclusions. First, we estimate the number of fracture locations and reflectivity using a modified sparse-spike deconvolution of the stacked VSP traces. The fracture set consists of five fractures spaced by 15–30 m with a reflectivity of approximately 1%. Then, we develop a scattering integral method to refine these estimates along with an inversion of the fracture top and bottom for each monitoring vintage. We find that, initially, some of the fractures are located above the monitoring fiber with the height of approximately 100 m. Then we integrate the seismic interpretation with the low-frequency DAS and pressure and microseismic monitoring to reconstruct the activation process of the fractures. Most likely, some of the natural fractures slowly grew downward to the monitoring fiber as a result of fluid injections in the stimulated well. This led to bright strain anomalies but did not trigger seismicity. The top of the fractures remained almost constant and were limited by a lithologic boundary/stress barrier. To our knowledge, this is the first time VSP data enabled tracking of the fracture evolution with such high spatial and temporal resolution, which was previously only available for crosswell surveys and at a much smaller scale.

Glubokovskikh, Stanislav↗

Room‐Temperature Mid‐Infrared Detection Using Metasurface‐Absorber‐Integrated Phononic Crystal Oscillator

Mid-infrared (MIR) detectors find extensive applications in chemical sensing, spectroscopy, communications, biomedical diagnosis, and space exploration. Alternative to semiconductor MIR photodiodes and bolometers, mechanical-resonator-based MIR detectors show advantages in higher sensitivity and lower noise at room temperature, especially toward longer wavelength infrared. Here, uncooled room-temperature MIR detectors based on lithium niobate surface acoustic wave phononic crystal (PnC) resonators integrated with wavelength-and-polarization-selective metasurface absorber arrays are demonstrated. The detection is based on the resonant frequency shift induced by the local temperature change due to MIR absorptions. The PnC resonator is configured in an oscillating mode, enabling active readout and low-frequency noise. The 1-GHz oscillator-based MIR detector shows a relative frequency deviation of 5.24 × 10 −10 Hz −1/2 at an integration time of 50 µs, leading to an incident noise equivalent power of 197 pW Hz −1/2 when input 6-µm MIR light is modulated at 1.8 kHz, and a large dynamic range of 10 7 in incident MIR power. The device architecture is compatible with the scalable manufacturing process and can be readily extended to a broader spectral range by tailoring the absorbing wavelengths of metasurface absorbers.

Xi, Zichen [Virginia Polytechnic Inst. and State U↗

Crystalline Order Yet Glass-Like Heat Transport Driven by Hidden Local Distortions as the Structural Origin of Ultralow Thermal Conductivity in AgErTe 2

Given their rich chemical diversity and the interplay among the p-, d-, and f-orbitals of chalcogens, transition metals, and lanthanides, respectively, rare-earth transition-metal chalcogenides exhibit a wide variety of structural, magnetic, and transport phenomena. As a result, they form a particularly appealing platform for investigating structure–property relationships, emergent electronic and magnetic behaviors, and thermal transport. Here we investigate AgErTe 2 as a model system to understand phonon-glass behavior in ordered crystalline solids, which establishes the design principles for thermal barrier coatings and next-generation thermoelectrics. The local bonding asymmetry and lattice softness suppress the inherently low lattice thermal conductivity, resembling the characteristics of amorphous materials. This suppression is significantly influenced by local off-centering of Ag atoms, which breaks lattice periodicity while maintaining global crystallinity. The presence of antibonding states just below the Fermi level, arising from Ag 4d and Te 5p orbital interactions, leads to lattice softening and destabilizes ideal tetrahedral coordination, resulting in a pseudo Jahn–Teller distortion. Furthermore, the coexistence of weaker, more polarizable Ag–Te bonds and stronger Er–Te bonds creates a complex vibrational landscape enriched with low-frequency modes and enhanced phonon scattering. A pronounced disparity in interatomic force constants gives rise to highly localized, low-energy optical phonons linked to Ag rattling. These flat vibrational modes exhibit strong coupling with transverse acoustic phonons, resulting in ultrashort phonon lifetimes and mean free paths approaching interatomic distances. These features collectively enhance phonon scattering across a broad range of length and energy scales. This work offers a framework for engineering suppressed thermal conductivity in crystalline systems without the introduction of alloying elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗