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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Dual phase patterning during a congruent grain boundary phase transition in elemental copper

The phase behavior of grain boundaries can have a strong influence on interfacial properties. Little is known about the emergence of grain boundary phases in elemental metal systems and how they transform. Here, we observe the nanoscale patterning of a grain boundary by two alternating grain boundary phases with distinct atomic structures in elemental copper by atomic resolution imaging. The same grain boundary phases are found by computational grain boundary structure search indicating a first-order transformation. Finite temperature atomistic simulations reveal a congruent, diffusionless transition between these phases under ambient pressure. The patterning of the grain boundary at room temperature is dominated by the grain boundary phase junctions separating the phase segments. Our analysis suggests that the reduced mobility of the phase junctions at low temperatures kinetically limits the transformation, but repulsive elastic interactions between them and disconnections could additionally stabilize the pattern formation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Phase Transitions of Cu and Fe at Multiscales in an Additively Manufactured Cu–Fe Alloy under High-Pressure

A state of the art, custom-built direct-metal deposition (DMD)-based additive manufacturing (AM) system at the University of Michigan was used to manufacture 50Cu–50Fe alloy with tailored properties for use in high strain/deformation environments. Subsequently, we performed preliminary high-pressure compression experiments to investigate the structural stability and deformation of this material. Our work shows that the alpha (BCC) phase of Fe is stable up to ~16 GPa before reversibly transforming to HCP, which is at least a few GPa higher than pure bulk Fe material. Furthermore, we observed evidence of a transition of Cu nano-precipitates in Fe from the well-known FCC structure to a metastable BCC phase, which has only been predicted via density functional calculations. Finally, the metastable FCC Fe nano-precipitates within the Cu grains show a modulated nano-twinned structure induced by high-pressure deformation. The results from this work demonstrate the opportunity in AM application for tailored functional materials and extreme stress/deformation applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Direct Observation of Electron Beam-Induced Phase Transition in MgCrMnO 4

Irreversible structural transformation in intercalation-type cathode materials, which has been frequently observed, has been perceived as a principal cause of capacity fading and voltage decay in (uni) multivalent batteries. Herein, we explored the electron beam-induced spinel to defective rocksalt phase transitions in MgCrMnO 4 , a potential multivalent cation intercalation cathode, using atomic-resolution imaging and spectroscopy in an aberration-corrected scanning transmission electron microscope. This dynamic electron beam irradiation study of specific structural transformations provides an atomistic understanding of the structural evolution observed in transition-metal oxide spinels during electrochemical cycling using multivalent cations, such as Mg 2+ . By combining an imaging study with first-principles modeling, we demonstrate that the mechanism of the spinel to defective rocksalt transformation in MgCrMnO 4 nanostructures is enabled by the presence of oxygen vacancies and is, therefore, very similar to that observed in transition-metal oxide spinels upon Li intercalation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Accelerating the Electrochemical Formation of the δ Phase in Manganese-Rich Rocksalt Cathodes

Mn-rich disordered rocksalt materials with Li-excess (DRX) materials have emerged as a promising class of earth-abundant and energy-dense next-generation cathode materials for lithium-ion batteries. Recently, an electrochemical transformation to a spinel-like “δ” phase has been reported in Mn-rich DRX materials, with improved capacity, rate capability, and cycling stability compared with previous DRX compositions. However, this transformation unfolds slowly over the course of cycling, complicating the development and understanding of these materials. In this work, it is reported that the transformation of Mn-rich DRX materials to the promising δ phase can be promoted to occur much more rapidly by electrochemical pulsing at elevated temperature, rate, and voltage. To extend this concept, micron-sized single-crystal DRX particles are also transformed to the δ phase by the same method, possessing greatly improved cycling stability in the first demonstration of cycling for large, single-crystal DRX particles. To shed light on the formation and specific structure of the δ phase, X-ray diffraction, scanning electron nanodiffraction (SEND) and atomic resolution STEM-HAADF are used to reveal a nanodomain spinel structure with minimal remnant disorder.

25 ENERGY STORAGE↗
DOE OSTI2022

Thermodynamics of high-pressure ice phases explored with atomistic simulations

Most experimentally known high-pressure ice phases have a body-centred cubic (bcc) oxygen lattice. Our large-scale molecular-dynamics simulations with a machine-learning potential indicate that, amongst these bcc ice phases, ices VII, VII' and X are the same thermodynamic phase under different conditions, whereas superionic ice VII" has a first-order phase boundary with ice VII'. Moreover, at about 300 GPa, the transformation between ice X and the Pbcm phase has a sharp structural change but no apparent activation barrier, whilst at higher pressures the barrier gradually increases. Our study thus clarifies the phase behaviour of the high-pressure ices and reveals peculiar solid–solid transition mechanisms not known in other systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Primary and secondary ice production: interactions and their relative importance

A discrepancy of up to 5 orders of magnitude between ice crystal and ice nucleating particle (INP) number concentrations was found in the measurements, indicating the potentially important role of secondary ice production (SIP) in the clouds. However, the interactions between primary and SIP processes and their relative importance remain unexplored. In this study, we implemented five different ice nucleation schemes as well as physical representations of SIP processes (i.e., droplet shattering during rain freezing, ice-ice collisional break-up, and rime splintering) in the Community Earth System Model version 2 (CESM2). We ran CESM2 in the single column mode for model comparisons with the DOE Atmospheric Radiation Measurement (ARM) Mixed-Phase Arctic Cloud Experiment (M-PACE) observations. We found that the model experiments with aerosol-aware ice nucleation schemes and SIP processes yield the best simulation results for the M-PACE single-layer mixed-phase clouds. We further investigated the relative importance of ice nucleation and SIP to ice number and cloud phase as well as interactions between ice nucleation and SIP in the M-PACE single-layer mixed-phase clouds. Our results show that SIP contributes 80 % to the total ice formation and transforms ~30 % of pure liquid-phase clouds simulated in the model experiments without considering SIP into mixed-phase clouds. The SIP is not only a result of ice crystals produced from ice nucleation, but also competes with the ice nucleation by reducing the number concentrations of cloud droplets and cloud-borne dust INPs. Conversely, strong ice nucleation also suppresses SIP by glaciating mixed-phase clouds and thereby reducing the amount of precipitation particles (rain and graupel).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Elucidating the temperature dependence of TRIP in Q&P steels using synchrotron X-Ray diffraction, constituent phase properties, and strain-based kinetics models

Understanding the deformation-induced martensitic transformation (DIMT) is critical for interpreting the structure-property relationships that govern the performance of transformation-induced plasticity (TRIP) assisted steels. However, modern TRIP-assisted steels often exhibit DIMT kinetics that are not easily captured by existing empirical models based on bulk tensile strain. We address this challenge by combined bulk uniaxial tensile tests and in-situ high energy synchrotron X-ray diffraction, which resolved the phase volume fractions, stress-strain response, and microstructure evolution of each constituent phase. A modification of the Olson-Cohen model is implemented, which describes the martensitic transformation kinetics as a function of the estimated partitioned strain in austenite, rather than the bulk tensile strain. This DIMT kinetic model is used as a framework to clarify the root cause of an insufficiently understood toughness trough reported for TRIP-assisted steels during deformation at elevated temperatures. Here, the importance of the temperature-dependent toughness is discussed, based on the opportunity to modify deformation processes to tailor the DIMT kinetics and mechanical properties during forming and in service.

36 MATERIALS SCIENCE↗
DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Measurement of Thermal Conductivity in a Supercooled Hydrogel-Salt Complex Near Its Phase Transition

Solid-liquid phase transitions, i.e. solidification processes, have applications in data storage, development of novel thermoelectric materials, cooling of microelectronic substrates and air conditioning condensers. Standard analyses of solidification (Stefan problem) assume constant thermal properties of the solid and liquid sides. It is not known how these properties change across the spatial transition interface, though most studies report a discontinuity in the solid and liquid properties through the transition temperature [1]. When the phase transition releases enthalpy, recent research has shown if the phonon or electron transport time is of the same order of magnitude as the time scale of the atomic transformation, this increases the heat capacity of the solid material at temperatures near the phase transition temperature [2]. A fundamental understanding of the phase transition may help shed light on the molecular origins of supercooling and spontaneous nucleation, which will help with applications involving them. We report studies of supercooling and nucleation of sodium sulfate decahydrate, a salt hydrate which is of recent interest in thermal storage, and of a hydrogel-sodium sulfate complex which shows limited supercooling. We will also report the measurement of their thermal properties during the phase transition process. This will be done with a hot-wire setup which produces small temperature changes of the order of ~1 C.

crystallization, phase transformation, thermal con↗
DOE OSTI2025

Decoupled few-femtosecond phase transitions in vanadium dioxide

Abstract The nature of the insulator-to-metal phase transition in vanadium dioxide (VO 2 ) is one of the longest-standing problems in condensed-matter physics. Ultrafast spectroscopy has long promised to determine whether the transition is primarily driven by the electronic or structural degree of freedom, but measurements to date have been stymied by their sensitivity to only one of these components and/or their limited temporal resolution. Here we use ultra-broadband few-femtosecond pump-probe spectroscopy to resolve the electronic and structural phase transitions in VO 2 at their fundamental time scales. Our experiments show that the system transforms into a bad-metallic phase within 10 fs after photoexcitation, but requires another 100 fs to complete the transition, during which we observe electronic oscillations and a partial re-opening of the bandgap, signalling a transient semi-metallic state. Comparisons with tensor-network simulations and density-functional theory calculations show these features result from an unexpectedly fast structural transition, in which the vanadium dimers separate and untwist with two different timescales. Our results resolve the structural and electronic nature of the light-induced phase transition in VO 2 and establish ultra-broadband few-femtosecond spectroscopy as a powerful tool for studying quantum materials out of equilibrium.

Science & Technology - Other Topics↗
DOE OSTI2024

Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. Validation on simulations

Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulationbased analysis of a set of Gaussian and non-Gaussian weak lensing statistics using detailed mock catalogs of the Dark Energy Survey (DES). Here, we implement: 1) second and third moments; 2) wavelet phase harmonics (WPH); 3) the scattering transform (ST). Our analysis is fully based on simulations, it spans a space of seven $νw$CDM cosmological parameters, and it forward models the most relevant sources of systematics of the data (masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration). We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a likelihood-free-inference approach. We validate the pipeline extensively, and we find that WPH exhibits the strongest performance when combined with second moments, followed by ST, and then by third moments. The combination of all the different statistics further enhances constraints with respect to second moments, up to 25 percent, 15 percent, and 90 percent for S 8 , Ω m , and the figure-of-merit FoM S8;Ωm , respectively. We further find that non-Gaussian statistics improve constraints on w and on the amplitude of intrinsic alignment with respect to second moments constraints. The methodological advances presented here are suitable for application to Stage IV surveys from Euclid, Rubin-LSST, and Roman with additional validation on mock catalogs for each survey. In a companion paper we present an application to DES Year 3 data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The transformation of diamond to graphite: Experiments reveal the presence of an intermediate linear carbon phase

Natural diamonds that have been partially replaced by graphite have been observed to occur in natural rocks. While the graphite-to-diamond phase transition has been extensively studied the opposite of this (diamond to graphite) remains poorly understood. We performed high-pressure and temperature hydrous and anhydrous experiments up to 1.0 GPa and 1300 °C using Amplex premium virgin synthetic diamonds (20–40 μm size) as the starting material mixed with Mg(OH) 2 as a source of H 2 O for the hydrous experiments. The experiments revealed that the diamond-to-graphite transformation at P = 1.0 GPa and T = 1300 °C was triggered by the presence of H 2 O and was accomplished through a three-stage process. Stage 1: diamond reacts with a supercritical H 2 O producing an intermediate 200–500 nm size “globular carbon” phase. This phase is a linear carbon chain; i.e. a polyyne or carbyne. Stage 2: the linear carbon chains are unstable and highly reactive, and they decompose by zigzagging and cross-linking to form sp 2 -hybridized structures. Stage 3: normal, disordered, and onion-like graphite is produced by the decomposition of the sp-hybridized carbon chains which are re-organized into sp 2 bonds. Our experiments show that there is no direct transformation from sp 3 C-bonds into sp 2 C-bonds. Our hydrous high-pressure and high-temperature experiments show that the diamond-to-graphite transformation requires an intermediate metastable phase of a linear hydrocarbon. This process also provides a simple mechanism for the substitution of other elements into the graphite structure (e.g. H, S, O).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Tuning the Radius Ratio to Enhance Thermoelectric Properties in the Zintl Compounds AM 2 Sb 2 (A = Ba, Sr; M = Zn, Cd)

Five novel Zintl phase solid solutions in the Ba 1–x Sr x Zn 2–y Cd y Sb 2 (0 ≤ x ≤ 0.13(1); 0 ≤ y ≤ 0.32(2)) system were successfully synthesized by the molten Pb metal-flux method, and the powder X-ray diffraction and single-crystal X-ray diffraction analyses proved that all five title compounds adopted the BaCu 2 S 2 -type phase having the orthorhombic Pnma space group (Z = 4, Pearson code oP20) with five crystallographically independent atomic sites. The previously studied BaCu 2 S 2 -type antimonides demonstrated a limited tolerance for doping in contrast to the CaAl 2 Si 2 -type antimonides. To understand the relatively narrower phase width and limited dopability of the title BaCu 2 S 2 -type phase than the CaAl 2 Si 2 -type phase in the overall Ba 1–x Sr x Zn 2–y Cd y Sb 2 system, the radius ratio of cations and anionic elements r + /r – for two structure types were thoroughly investigated. For the first time, the r + /r – ratio was identified as a critical factor for the phase selectivity: (1) r + /r – > 1 favored the BaCu 2 S 2 -type phase, and (2) r + /r – < 1 favored the CaAl 2 Si 2 -type phase. Further, we also revealed the structural transformation mechanism from the more widely observed CaAl 2 Si 2 -type phase to the title BaCu 2 S 2 -type phase as the relatively larger cationic elements were introduced to the system. A series of DFT calculations using the three hypothetical models indicated that a resonance peak near EF in the density of states curves was descended from the relatively flat band structure at several special symmetry points rationalizing the enhanced Seebeck coefficients of Ba 0.94(1) Sr 0.06 Zn 1.86(3) Cd 0.14 Sb 2 and Ba 0.96(1) Sr 0.04 Zn 1.68(2) Cd 0.32 Sb 2 . Electron localization function analysis rationalized the correlation between the polarity change of anionic Zn/Cd–Sb bonds and the charge carrier mobility on the anionic frameworks. Temperature-dependent thermoelectric properties were studied for the four title compounds, and the results proved that the Sr and Cd doping in the title Ba 1–x Sr x Zn 2–y Cd y Sb 2 system successfully enhanced the ZT values through the increased Seebeck coefficients and the reduced total thermal conductivities.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Nucleation and growth of α phase in a metastable β-Titanium Ti-5Al-5Mo-5V-3Cr alloy: Influence from the nano-scale, ordered-orthorhombic O" phase and α compositional evolution

We investigated the nucleation and growth of α precipitates in the presence of nano-scale, titanium-rich, ordered-orthorhombic O" precipitates formed during heating at 5 °C/min to 400 °C in a metastable β-Ti alloy, Ti-5Al-5Mo-5V-3Cr. The O" precipitates are found to assist α nucleation by serving as preferential nucleation sites. In the very initial stages of its precipitation, the α phase is found to have formed via a coupled diffusional-displacive mode as titanium-rich plates. At this stage, aluminum partitions equally between the β matrix and the growing α precipitates, but slowly diffuses up-hill into the α phase during isothermal aging at 400 °C for 15 h. The interplay between such pre-formed metastable phases and α can be exploited to tailor the microstructure, by refining the α distribution, and consequently improve the mechanical properties of β-Ti alloys. Finally, our work paves the way for exploiting this cascade of metastable phases for further microstructural engineering of β-Ti alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Multiplicity of Th(IV) and U(VI) HEH[EHP] Chelates at Low Temperatures from Concentrated Nitric Acid Extractions

Organophosphorus extractants have been widely investigated for lanthanide recovery from ore and for application in the reprocessing of spent nuclear fuel, such as in Advanced TALSPEAK schemes. Determining the speciation of the extracted metal complex in the organic phase remains a significant challenge. A better understanding of the variability of HEH[EHP]–actinide complexes and the speciation of chelates for tetra- and hexavalent actinides can improve the predictability of actinide phase transfer in such biphasic systems. Here, the extraction of Th(IV) and U(VI) from nitric acid media using HEH[EHP] in heptane is examined. The distribution ratio as a function of nitric acid concentration was quantified using UV–vis spectroscopy, and then the speciation of HEH[EHP]–metal complexes in the organic phase was investigated using Fourier transform infrared (FTIR) spectroscopy and low-temperature 31 P nuclear magnetic resonance (NMR) spectroscopy. In addition to perturbation of the vibrational modes proximal to the phosphonic moiety in HEH[EHP] in the FTIR spectra, the appearance of a nitrate signal was found in the organic phase following extraction from the highest acidity conditions for U(VI). The 31 P NMR spectra of the organic phase at a low temperature (-70 °C) exhibited a surprising number (n) of resonances (n ≥ 7 for Th(IV) and n ≥ 11 for U(VI)), with the distribution between these resonances changing with the initial concentration of nitric acid in the aqueous phase. These results indicate that the compositions of the inner and outer spheres of the extracted actinides in the organic phase are more diverse than initially thought.

31P NMR↗
DOE OSTI2022

Deformation Mechanism Transition in Additively Manufactured Compositionally Graded Fe-Base Alloys

Microstructure-dependent deformation and fracture behavior was investigated for an additively manufactured compositionally graded alloy (CGA) printed using the laser-directed energy deposition (L-DED) method to explore an alternative approach for dissimilar metal joints in nuclear energy systems. The electron backscatter diffraction (EBSD) maps from scanning electron microscopy (SEM) display a clear microstructural transition with decreasing austenite-forming elements (Ni and Mn), from an austenite (γ) dominant structure, to a complex composite structure containing ferrite (α), martensite (α') and retained austenite, and then to a fully ferritic structure. EBSD data were recorded in situ during tensile testing in SEM, and the evolution of the deformation mechanism and microstructure was characterized using Kikuchi diffraction pattern analysis. Complementary analysis for high-resolution features was also performed using scanning transmission electron microscopy (STEM). The Ni/Mn-rich austenite-dominant microstructures showed a complex deformation mechanism of two-step martensitic transformation (γ→ε→α'), whereas the minor austenite phase retained in the ferrite and/or martensite matrix showed a single transformation route (γ→α'). Ordinary dislocation glide and twinning via partial dislocation glide were observed in the austenite deformation. Meanwhile, the ferrite and martensite grains deformed mainly by ordinary dislocation slips and grain rotation. Furthermore, static tensile fracture was also highly dependent on local composition and phase constituents.

36 MATERIALS SCIENCE↗
DOE OSTI2024

High Pressure–Temperature Study of MgF 2 , CaF 2 , and BaF 2 by Raman Spectroscopy: Phase Transitions and Vibrational Properties of AF 2 Difluorides

The phase transition of AF 2 difluorides strongly depends on pressure, temperature, and cationic radius. Here, we have investigated the phase transition of three difluorides, including MgF 2 , CaF 2 , and BaF 2 , at simultaneously high pressures and temperatures using Raman spectroscopy and X-ray diffraction in externally heated diamond anvil cells up to 55 GPa at 300–700 K. Rutile-type difluoride MgF 2 with a small cationic radius undergoes a transition to the CaCl 2 -type phase at 9.9(1) GPa and 300 K, to the HP-PdF 2 -type phase at 21.0(2) GPa, and to the cotunnite-type phase at 44.2(2) GPa. The phase transition pressure to the HP-PdF 2 and cotunnite structure at 300 K for our single crystal was found to be higher than that in previous studies using polycrystalline samples. Elevating the temperature increases the transition pressure from rutile- to the CaCl 2 -type phase but has a negative influence on the transition pressure when MgF 2 transforms from the HP-PdF 2 - to cotunnite-type phase. Meanwhile, the transition pressure from the CaCl 2 - to HP-PdF 2 -type phase for MgF 2 was identified to be independent of the temperature. Raman peaks suspected to belong to the α-PbO 2 -type phase were observed at 14.6–21.0(1) GPa and 400–700 K. At 300 K, difluorides CaF 2 and BaF 2 in the fluorite structure with larger cationic radii transform to the cotunnite-type phase at 9.6(3) and 3.0(3) GPa at 300 K, respectively, and BaF 2 further undergoes a transition to the Ni 2 In-type phase at 15.5(4) GPa. For both CaF 2 and BaF 2 , elevating the temperature leads to a lower transition pressure from fluorite- to the cotunnite-type phase but has little influence on the transition to the Ni 2 In structure. Raman data provide valuable insights for mode Grüneisen parameters. We note that the mode Grüneisen parameters for both difluorides and dioxides vary linearly with the cation radius. Further calculations for the mode Grüneisen parameters at high pressures for MgF 2 , CaF 2 , and BaF 2 yield a deeper understanding of the thermodynamic properties of the difluorides.

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

Design Methodologies for Integrated Quantum Frequency Processors

We report frequency-encoded quantum information offers intriguing opportunities for quantum communications and networking, with the quantum frequency processor paradigm—based on electro-optic phase modulators and Fourier-transform pulse shapers—providing a path for scalable construction of quantum gates. Yet all experimental demonstrations to date have relied on discrete fiber-optic components that occupy significant physical space and impart appreciable loss. In this article, we introduce a model for the design of quantum frequency processors comprising microring resonator-based pulse shapers and integrated phase modulators. We estimate the performance of single and parallel frequency-bin Hadamard gates, finding high fidelity values that extend to frequency bins with relatively wide bandwidths. By incorporating multi-order filter designs as well, we explore the limits of tight frequency spacings, a regime extremely difficult to obtain in bulk optics. Overall, our model is general, simple to use, and extendable to other material platforms, providing a much-needed design tool for future frequency processors in integrated photonics.

97 MATHEMATICS AND COMPUTING↗