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At least 73 records · Page 4

Stabilization of the Polar Structure and Giant Second-Order Nonlinear Response of Single Crystal γ-NaAs 0.95 Sb 0.05 Se 2

The dearth of suitable materials significantly restricts the practical development of infrared (IR) laser systems with highly efficient and broadband tuning. Recently, γ-NaAsSe 2 is reported, and it exhibits a large nonlinear second-harmonic generation (SHG) coefficient of 590 pm V —1 at 2 µm. However, the crystal growth of γ-NaAsSe 2 is challenging because it undergoes a phase transition to centrosymmetric δ-NaAsSe 2 . Herein, the stabilization of non-centrosymmetric γ-NaAsSe 2 by doping the As site with Sb, which results in γ-NaAs 0.95 Sb 0.05 Se 2 is reported. The congruent melting behavior is confirmed by differential thermal analysis with a melting temperature of 450 °C and crystallization temperature of 415 °C. Single crystals with dimensions of 3 mm × 2 mm are successfully obtained via zone refining and the Bridgman method. The purification of the material plays a significant role in crystal growth and results in a bandgap of 1.78 eV and thermal conductivity of 0.79 Wm —1 K —1 . The single-crystal SHG coefficient of γ-NaAs 0.95 Sb 0.05 Se 2 exhibits an enormous value of |d 11 | = 648 ± 74 pm V —1 , which is comparable to that of γ-NaAsSe 2 and ≈20× larger than that of AgGaSe 2 . Importantly, the bandgap of γ-NaAs 0.95 Sb 0.05 Se 2 (1.78 eV) is similar to that of AgGaSe 2 , thus rendering it highly attractive as a high-performing nonlinear optical material.

36 MATERIALS SCIENCE↗

Synthesis and characterization of the novel breathing pyrochlore compound Ba 3 ⁢Tm 2⁢ Zn 5⁢ O 11

In this study, a novel material from the rare-earth based breathing pyrochlore family, Ba 3 ⁢Tm 2 ⁢Zn 5 ⁢O 11 , was successfully synthesized. Powder x-ray diffraction and high-resolution powder neutron diffraction confirmed phase purity and the $F\bar4$3⁢𝑚 breathing pyrochlore crystal structure, while thermogravimetric analysis revealed incongruent melting behavior compared to its counterpart, Ba 3 ⁢Yb 2⁢ Zn 5⁢ O 11 . High-quality single crystals of Ba 3 ⁢Tm 2 ⁢Zn 5 ⁢O 11 were grown using the traveling solvent floating zone technique and assessed using Laue x-ray diffraction and single crystal x-ray diffraction. Further, thermodynamic characterization indicated paramagnetic behavior down to 0.05 K, and inelastic neutron scattering measurements identified distinct dispersionless crystal electric field energy bands, with the fitted crystal electric field model predicting a single-ion singlet ground state and an energy gap of ∼9 meV separating it from the first excited (singlet) state. Additional low-energy excitation studies on single crystals revealed dispersionless bands at 0.8 and 1 meV. Computed phonon dispersions from first-principles calculations ruled out phonons as the origin of these modes, further illustrating the puzzling and unique properties of Ba 3 ⁢Tm⁢ 2 Zn 5 ⁢O 11 .

36 MATERIALS SCIENCE↗

Noninteracting electrons in a prototypical one-dimensional sinusoidal potential

A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied, where the argument of the cosine potential energy, periodic with the lattice, contains the first reciprocal lattice vector G 1 =2π/a, where a is the lattice constant. The time-independent Schrödinger equation can be written in reduced variables as a Mathieu equation for which numerically exact solutions for the band structure and wave functions are obtained. The band structure has band gaps that increase with increasing amplitude q of the cosine potential. In the extended-zone scheme, the energy gaps decrease with increasing index n of the Brillouin-zone boundary ka=nπ, where k is the crystal momentum of the electron. The wave functions of the band electron are derived for various combinations of k and q as complex combinations of the real Mathieu functions with even and odd parity, and the normalization factor is discussed. The wave functions at the bottoms and tops of the bands are found to be real or imaginary, respectively, corresponding to standing waves at these energies. Irrespective of the wave vector k within the first Brillouin zone, the electron probability density is found to be periodic with the lattice. The Fourier components of the wave functions are derived versus q, which reveal multiple reciprocal-lattice-vector components with variable amplitudes in the wave functions unless q = 0. The magnitudes of the Fourier components are found to decrease exponentially as a power of n for n~3 to 45 for ka = π/2 and q = 2, and a precise fit is obtained to the data. The probability densities and probability currents obtained from the wave functions are also discussed. The probability currents are found to be zero for crystal momenta at the tops and bottoms of the energy bands, because the wave functions for these crystal momenta are standing waves. To conlcude, the band structure is calculated from the central equation and compared to the numerically exact band structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bent Crystal Channeling for Optimized Beam Shadowing and Proton Extraction at Mu2e

The Mu2e experiment is designed to investigate the CLFV through the observation of a neutrinoless muon-to-electron conversion in the field of an Al nucleus. The observation of such a process would be clear evidence of physics beyond the standard model. Due to the rarity of this process, a cutting-edge, intense muon beam is required to achieve an improvement of the current single-event sensitivity by 4 orders of magnitude. To achieve this goal, a primary proton beam with 8 GeV is extracted from the Fermilab Delivery Ring using the slow resonant extraction technique. Mu2e requires ~3.6x10$^{20}$ protons-on-target to meet its goal; hence, it is crucial to minimize the extraction losses. An important source of such losses are the particles impacting on the electrostatic septum blade. A very promising solution to the problem lies in the beam shadowing scheme tested at CERN SPS. In this approach, a bent crystal is strategically placed upstream of the septum, deflecting particles from the blade at a precise angle via the phenomenon of channeling. As a result, a zone with reduced particle flux is created downstream of the crystal, safeguarding the septum anode by minimizing interactions with the beam. This work explores the optimization of beam shadowing design and the process in the manufacturing and characterization of the bent crystal sample. It emphasizes the promising role of channeling in bent crystals, and it underscores the significant potential of channeling in bent crystals to assist the Mu2e experiment.

Fedeli, Pierluigi [Ferrara U.; INFN, Ferrara] (ORC↗

Electronic transport, thermal transport, thermal expansion, and magnetization in the strongly correlated metal LaNi⁢O 3

Perovskite structured LaNiO 3 is a strongly correlated metal with intriguing thermal and magnetic properties. The volume dependence of calculated and measured physical properties can add additional critical information to develop a more in-depth understanding of this strongly correlated phenomenon. Taking advantage of recent single crystal LaNiO 3 growth using the floating-zone method, we have measured the thermal expansion, the magnetostriction, and the pressure dependence of the magnetic susceptibility, which then allows derivation of the Grüneisen parameters γ e = $\frac{dlnN(E_F)}{d lnV}$, γ χ = $\frac{dlnχ}{d lnV}$, as well as of electric and thermal transport properties. We simulate the volume dependence of structural and magnetic properties using Density Functional Theory calculations at the Generalized Gradient Approximation level. A large discrepancy between experimental values and calculated ones suggests that strong correlations are likely to be dynamic in nature. This study also provides a side-by-side comparison of measurements in single crystal and polycrystalline samples of LaNiO 3 to elucidate intrinsic materials properties. A broad hump at high temperatures in the temperature dependence of magnetization found in the single crystal sample of LaNiO 3 has been rationalized by a model that includes the influence of electron correlations on the Landau diamagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Oxygen Inhomogeneity and Reversibility in Single Crystal LaNiO{sub 3-{delta}}.

LaNiO 3− δ single crystals have been obtained via high pressure floating zone growth under 149 bar of oxygen pressure. We find a radial gradient in the magnetic properties of specimens extracted from the as-grown boule, which we correlate with the appearance of ordered oxygen vacancy structures. This radial oxygen inhomogeneity has been characterized systematically using a combination of magnetization and X-ray scattering measurements. We establish the presence of rhombohedral ( R 3 ¯ c ), oxygen stoichiometric specimens at the periphery of the boule and the presence of a dilute concentration of ordered oxygen-deficient orthorhombic La 2 Ni 2 O 5 in the center. Furthermore, we demonstrate that the as-grown, oxygen-deficient central regions of the crystal can be annealed under high oxygen pressure, without loss of crystallinity, into fully oxygenated LaNiO 3 , recovering magnetic properties that are characteristic of stoichiometric specimens from the exterior region of the crystal. Thus, single crystals of LaNiO 3− δ possess oxygen content that can be reversibly modified under oxidizing and reducing conditions.

crystal growth↗

Modeling the evolution of slip localization: Realization of link to material strength

Slip localization formation is the chief mechanism underlying the deformation of almost all metals, from pure elements to high-performance superalloys. The intensity of individual slip localizations is often related to the ultimate strain level for failure but not to the strength of the metal. Here we show that across 15 distinct metals, the intensity of slip in individual slip localizations and slip localization spacings are strongly related to material yield strength. Using a three-dimensional crystal plasticity-based micromechanical model that explicitly simulates the growth of discrete slip localizations, we reveal that the stronger the metal, the faster and earlier slip localizations intensify. The relationship is attributed to the formation of a zone that surrounds the slip localization where the driving force for slip is absent. We find that the zone size is controlled by the strength of the neighboring crystal. Consequently, as strength increases, slip becomes increasingly preferred within the slip localization itself and formation of other slip localizations becomes more likely further away.

36 MATERIALS SCIENCE↗

Evaluating the effects of structural disorder on the magnetic properties of Nd 2 Zr 2 O 7

Motivated by the variation in reported lattice parameters of floating-zone-grown Nd 2 Zr 2 O 7 crystals, we have performed a detailed study of the relationship between synthesis environment, structural disorder, and magnetic properties. Using a combination of polycrystalline standards, electron-probe microanalysis, and scattering techniques, we show that crystals grown under atmospheric conditions have a reduced lattice parameter relative to pristine polycrystalline powders due to occupation of the Nd site by excess Zr (i.e., negative stuffing). In contrast, crystals grown under high-pressure Ar are nearly stoichiometric with an average lattice parameter approaching the polycrystalline value. While minimal disorder of the oxygen sublattices is observed on the scale of the average structure, neutron pair-distribution function analysis indicates a highly local disorder of the oxygen coordination, which is only weakly dependent on growth environment. Most importantly, our magnetization, heat capacity, and single-crystal neutron scattering data show that the magnetic properties of crystals grown under high-pressure Ar match closely with those of stoichiometric powders. Neutron scattering measurements reveal that the signature of magnetic moment fragmentation—the coexistence of all-in-all-out (AIAO) magnetic Bragg peaks and diffuse pinch-point scattering due to spin-ice correlations–persists in these nearly stoichiometric crystals. However, in addition to an increased AIAO transition temperature, the diffuse signal is seemingly stabilized and remains nearly unchanged upon warming to 800 mK. This behavior indicates that both the AIAO magnetic order and spin-ice correlations are sensitive to deviations of the Nd stoichiometry.

36 MATERIALS SCIENCE↗

Observation of bound states in the continuum embedded in symmetry bandgaps

In the past decade, symmetry-protected bound states in the continuum (BICs) have proven to be an important design principle for creating and enhancing devices reliant upon states with high-quality (Q) factors, such as sensors, lasers, and those for harmonic generation. However, as we show, current implementations of symmetry-protected BICs in photonic crystal slabs can only be found at the center of the Brillouin zone and below the Bragg diffraction limit, which fundamentally restricts their use to single-frequency applications. By microprinting a three-dimensional (3D) photonic crystal structure using two-photon polymerization, we demonstrate that this limitation can be overcome by altering the radiative environment surrounding the slab to be a 3D photonic crystal. This allows for the protection of a line of BICs by embedding it in a symmetry bandgap of the crystal. This concept substantially expands the design freedom available for developing next-generation devices with high-Q states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lattice anharmonicity effects in fluorite oxide single crystals and anomalous increase in phonon lifetime in ceria at elevated temperature

Here, we investigate the temperature dependence of the frequency and linewidth of the triply degenerate T 2g zone-centered optical phonon in flux-grown ceria and hydrothermally synthesized thoria single crystals from room temperature to 1273 K using Raman spectroscopy. Both crystals exhibit an expected increase in the phonon linewidth with temperature due to enhanced phonon–phonon scattering. However, ceria displays an anomalous linewidth reduction in the temperature range of 1023–1123 K. First-principles phonon linewidth calculations considering cubic and quartic phonon interactions within temperature-independent phonon dispersion fail to describe this anomaly. A parameterization of the temperature-dependent second-order interatomic force constants based on previously reported phonon dispersion measured at room and high temperatures predicts a deviation from the monotonic linewidth increase, albeit at temperatures lower than those observed experimentally for ceria. The qualitative agreement in the trend of temperature-dependent linewidth suggests that lattice anharmonicity-induced phonon renormalization plays a role in phonon lifetime. Specifically, a change in the overlap between softened acoustic and optical branches in the dispersion curve reduces the available phonon scattering phase space of the Raman-active mode at the zone center, leading to an increased phonon lifetime within a narrow temperature interval. These findings provide insights into higher-order anharmonic interactions in ceria and thoria, motivating further investigations into the role of anharmonicity-induced phonon renormalization on phonon lifetimes at high temperatures.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Mineralogical transformations in polymetallic nodules and the change of Ni, Cu and Co crystal-chemistry upon burial in sediments

Polymetallic nodules from the Clarion and Clipperton Zone of the equatorial Pacific Ocean were studied using X-ray diffraction, X-ray absorption, Fourier-transformed infrared spectroscopy and transmission electron microscopy. Here, this study includes nodules found at the sediment surface as well as subsurface (14–16 cm sediment depth) and deeply buried (530–985 cm sediment depth) nodules. The surface and subsurface nodules are currently under oxic conditions whereas the deeply buried nodules are under suboxic conditions. Surface nodules consist mainly of turbostratic phyllomanganates (7 Å and 10 Å vernadite and Fe-vernadite); todorokite is a minor phase, if present at all. In contrast, subsurface and especially deeply buried nodules predominantly consist of todorokite, which increases in abundance with depth in the sediment. Thus, upon burial of nodules within the shallow sediment, phyllomanganates transform to todorokite, probably through the combined action of time and change in the ambient chemical conditions. Nodules from deeper sediment depth (>500 cm) consist primarily of todorokite and additionally show signs of dissolution. The transformation of phyllomanganates to todorokite and their further dissolution upon nodule burial under suboxic conditions induces modifications in the crystal-chemistry of Ni, Co, and Cu. In surface nodules, Ni and Co are incorporated in the octahedral sheets of phyllomanganates, whereas Cu mainly is located at the edges of those phyllomanganate sheets. In buried nodules Cu and to a lesser extent Ni are incorporated in todorokite by forming outer-sphere complexes within the tunnels. However, Ni is predominantly incorporated within the octahedra of the newly formed todorokite structure. Co is also enriched in the octahedra of todorokite as a result of dissolution of hydrogenetic vernadite and re-incorporation in the more stable Mn-phase formed during the diagenetic transformation. Co enrichment under suboxic conditions after burial within the sediments is noteworthy since Co in surface nodules is characteristic for oxic conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum paramagnetism in a non-Kramers rare-earth oxide: Monoclinic Pr 2 Ti 2 O 7

Little is so far known about the magnetism of the A 2 B 2 O 7 monoclinic layered perovskites that replace the spin-ice supporting pyrochlore structure for r A /r B > 1.78. We show that high quality monoclinic Pr 2 Ti 2 O 7 single crystals with a three-dimensional network of non-Kramers Pr 3+ ions that interact through edge-sharing superexchange interactions, form a singlet ground-state quantum paramagnet that does not undergo any magnetic phase transitions down to, at least, 1.8 K. The chemical phase stability, structure, and magnetic properties of the layered perovskite Pr 2 Ti 2 O 7 were investigated using x-ray diffraction, transmission electron microscopy, and magnetization measurements. Synthesis of polycrystalline samples with the nominal compositions of Pr 2 Ti 2+x O 7 (–0.16 ≤ x ≤ 0.16 ) showed that deviations from the Pr 2 Ti 2 O 7 stoichiometry lead to secondary phases of related structures including the perovskite phase Pr 2/3 TiO 3 and the orthorhombic phases Pr 4 Ti 9 O 24 and Pr 2 TiO 5 . No indications of site disordering (stuffing and antistuffing) or vacancy defects were observed in the Pr 2 Ti 2 O 7 majority phase. A procedure for growth of high-structural-quality stoichiometric single crystals of Pr 2 Ti 2 O 7 by the traveling solvent floating zone method is reported. Thermomagnetic measurements of single-crystalline Pr 2 Ti 2 O 7 reveal an isolated singlet ground state that we associate with the low-symmetry crystal electric-field environments that split the (2J + 1 = 9)-fold degenerate spin-orbital multiplets of the four differently coordinated Pr 3+ ions into 36 isolated singlets resulting in an anisotropic temperature-independent van Vleck susceptibility at low T. Here, a small isotropic Curie term is associated with 0.96(2)% noninteracting Pr 4+ impurities.

36 MATERIALS SCIENCE↗

Modified Dirac Fermions in the Crystalline Xenon and Graphene Moiré Heterostructure

Abstract The interface between two‐dimensional (2D) crystals often forms a Moiré superstructure that imposes a new periodicity, which is a key element in realizing complex electronic phases as evidenced in twisted bilayer graphene. Acombined angle‐resolved photoemission spectroscopy measurements and first‐principles calculations reveal the formation of a Moiré superstructure between a 2D Dirac semi‐metallic crystal, graphene, and a 2D insulating crystal of noble gas, xenon. Incommensurate diffraction pattern and folded Dirac cones around the Brillouin zone center imply the formation of hexagonal crystalline array of xenon atoms. The velocity of Dirac fermions increases upon the formation of the 2D xenon crystal on top of graphene due to the enhanced dielectric screening by the xenon over‐layer. These findings not only provide a novel method to produce a Moiré superstructure from the adsorption of noble gas on 2D materials, but also to control the physical properties of graphene by the formation of a graphene‐noble gas interface.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

pathSQE : an automated workflow for single-crystal inelastic neutron scattering data processing and analysis

Inelastic neutron scattering (INS) experiments utilizing modern time-of-flight spectrometers enable the comprehensive mapping of the energy (E)- and momentum (Q)-resolved dynamical structure factor of single crystals, probing both the lattice and magnetic excitations. Yet, the large size and complexity of four-dimensional INS data are challenging current analysis workflows, often resulting in an underutilization of the measured information. To help address this issue, this paper introduces new software interfaced with the Mantid framework, pathSQE, designed to streamline the processing, analysis and interpretation of 4D single-crystal INS data. By automating key tasks such as 1D/2D slicing, symmetrization, Brillouin zone folding, data visualization, prioritization and filtering, and comparisons with simulations, pathSQE facilitates and accelerates INS data analysis workflows. Here, this paper outlines the features and implementation and provides several illustrations of the use of pathSQE on data collected on single crystals using direct-geometry time-of-flight spectrometers at the Spallation Neutron Source, including Ge, FeSi, MnO and SnS single-crystal measurements on the ARCS, HYSPEC and CNCS neutron spectrometers. Beyond streamlining post-experiment data processing, pathSQE establishes an automated and modular processing pipeline that could support future real-time experiment steering.

36 MATERIALS SCIENCE↗

A deep insight on the coal ash-to-slag transformation behavior during the entrained flow gasification process

Recent research provided deep insight on the coal ash-to-slag transformation characterization during the entrained flow gasification process, with experimentation on a 40 kg/hr (dry basis) coal-fed opposed multi-burner (OMB) entrained flow gasifier and simulation via FactSage™ software. A general mechanism is presented to relate the gasifier design temperature, ash fluid temperature, and operating temperature with the degree of the slag polymerization. The change of the high temperature zone, the corresponding particle residence time in the high temperature zone, and syngas composition have obvious effects on the slag mineral transformation behavior. Mineral types formed on the wall of the gasifier chamber were mainly anorthite (CaAl 2 Si 2 O 8 ), aluminum oxide (Al 2 O 3 ), and calcium sulfide (CaS). These minerals transformed to anorthite and diopside (CaMgSi 2 O 6 ) at the slag hole zone, while the minerals at the lock hopper were anorthite, orthoclase (KAlSi 3 O 8 ), quartz (SiO 2 ), gypsum (CaSO 4 ), calcite (CaCO 3 ), and halite (NaCl). FactSage™ predicted minerals as anorthite, diopside, orthoclase, and albite (NaAlSi 3 O 8 ), etc., where the slag temperature was below the ash fluid temperature and when the ratios of CO/CO 2 and (CO + H 2 )/CO 2 were lower than 1.0 and 2.0, respectively. By simulation, residual carbon was found to be the dominant factor over syngas composition to cause mineral transformation, and this was verified experimentally. The Ca-based crystals, typically anorthite, was shifted to diopside, near the slag hole zone, and a linear relationship was found between the content ratios of diopside/(anorthite + diopside), CaO/SiO 2 , and (CaO + MgO)/SiO 2 . A dimensionless number, θ, was defined to characterize the changing chemical composition and the degree of slag polymerization, with temperature deviation from the design condition. Three zones of θ were identified and related to the deviation between the actual gasification condition from the design condition. Finally, a low slag polymerization degree corresponded with a higher temperature deviation between the actual condition and design condition, and this proved that increased residual carbon content and changing iron valence state increased the mineral types when the slag temperature was below the ash fluid temperature.

01 COAL, LIGNITE, AND PEAT↗

Fuel-cladding chemical interaction of a prototype annular U-10Zr fuel with Fe-12Cr ferritic/martensitic HT-9 cladding

As an alternative fuel form, the annular metallic fuel design eliminates the liquid sodium bond between the fuel and the cladding, providing back-end fuel cycle and other benefits. The fuel-cladding chemical interaction (FCCI) of annular fuel also presents new features. In this work, state-of-the-art electron microscopy and spectroscopy techniques were used to study the FCCI of a prototype annular U-10wt%Zr (U-10Zr) fuel with ferritic/martensitic HT-9 cladding irradiated to 3.3% fission per initial heavy atom. Compared with sodium-bonded solid fuels, negligible amounts of lanthanides were found in the FCCI layer in the investigated helium-bonded annular fuel. Instead, most lanthanides were retained in the newly formed UZr 2 phase in the fuel center region. The interdiffusion of iron and uranium resulted in tetragonal ( U ,Zr) 6 Fe phase (space group I4/mcm) and cubic ( U ,Zr)( Fe ,Cr) 2 phase (space group Fd 3 ¯ m). The ( U ,Zr)( Fe ,Cr) 2 phase contains a high density of voids and intergranular uranium monocarbides of NaCl-type crystal structure (space group Fm 3 ¯ m). At the interdiffusion zone and inner cladding interface, a porous lamellar structure composed of alternating Cr-rich layers and U-rich layers was observed. Next to the lamellar region, the unexpected phase transformation from body-centered cubic ferrite (α-Fe) to tetragonal binary Fe-Cr σ phase (space group P4 2 /mnm) occurred, and tetragonal Fe-Cr-U-Si phase (space group I4/mmm) was identified. Due to the diffusion of carbon into the interdiffusion zone, carbon depletion inside the HT-9 led to the disappearance of the martensite lath structure, and intergranular U-rich carbides formed as a result of the diffusion of uranium into the cladding. These detailed new findings reveal the unique features of the FCCI behavior of annular U-Zr fuels, which could be a promising alternative fuel form for high burnup fast reactor applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Development of improved higher-order correction for the NIF opacity spectrometer

X-ray opacity measurements on the National Ignition Facility (NIF) are in the process of reproducing earlier measurements from the Sandia Z Facility, in particular for oxygen and iron plasmas. These measurements have the potential to revise our understanding of the “solar problem” and of the hot degenerate Q class white dwarf structure by probing plasma conditions near the base of their convection zones. Accurate opacity measurements using soft x-ray Bragg crystal spectrometers require correction for higher-order diffraction effects. Extending prior work in this area [Dutra et al., Review of Scientific Instruments 93, 113527 (2022)], we have developed a new method to remove higher-order spectral components from NIF opacity spectrometer data. Furthermore, by modeling absorption and backlighting continuum spectra and subtracting the second- and third-order components from the measured data, we are able to perform this correction while avoiding imprinting first-order model line features onto the data.

79 ASTRONOMY AND ASTROPHYSICS↗