Search NASA⌕ Search

SEARCH · Search NASA

Results for “Crystal field theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Structural, electronic, and magnetic properties of CoFeVGe-based compounds: Experiment and theory

We have carried out a combined theoretical and experimental investigation of both stoichiometric and nonstoichiometric CoFeVGe alloys. In particular, we have investigated CoFeVGe, Co 1.25 Fe 0.75 VGe, Co 0.75 Fe 1.25 VGe, and CoFe 0.75 VGe bulk alloys. Our first principles calculations suggest that all four alloys show ferromagnetic order, where CoFeVGe, Co 1.25 Fe 0.75 VGe, and Co 0.75 Fe 1.25 VGe are highly spin polarized with spin polarization values of over 80%. However, the spin polarization value of CoFe 0.75 VGe is only about 60%. We have synthesized all four samples using arc melting and high-vacuum annealing at 600 °C for 48 hours. The room temperature x-ray diffraction of these samples exhibits a cubic crystal structure with disorder. All the samples show single magnetic transitions at their Curie temperatures, where the Curie temperature and high field (3T) magnetization are 288 K and 42 emu/g; 305 K and 1.5 emu/g; 238 K and 39 emu/g; and 306 K and 35 emu/g for CoFeVGe, Co 1.25 Fe 0.75 VGe, Co 0.75 Fe 1.25 VGe, and CoFe 0.75 VGe, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Needle-Like Ferroelastic Domains in Individual Ferroelectric Nanoparticles

Superior structural, physical and electronic properties make ferroelectric nanocrystals essential in enabling a range of next-generation devices. Ferroelectric responses are determined by crystal structure and domain morphology. The ability to reversibly displace, create and annihilate elastic domains is critical to device applications. Whereas electric-field control has been demonstrated for ferroelectric 180° surface domain walls and vortices, similar control of ferroelastic domains and domain boundaries within individual nanocrystals remains challenging. Using controlled external compressive and tensile axial stress, deterministic and reversible control of highly mobile ferroelastic domains and axial polarization in three dimensions is demonstrated in this study. While many studies exist on ferroelastic domains in thin films and bulk, little is known about ferroelastic interactions at the single nanoparticle level, especially involving domain boundaries. Through combining Bragg coherent X-ray diffractive imaging and Landau theory, strain gradients in individual BaTiO3 nanocrystals are shown to stabilize needle-like ferroelastic twin domains. These domains are highly labile under applied axial stress, producing a locally enhanced electric polarization mediated by a ferroelectric phase transition. The efficacy of Bragg coherent X-ray diffractive imaging in studying in operando domains in three-dimensions is demonstrated, while synergy with theory provides a paradigm for domain boundary engineering and potential for nanoscale functional devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A theory for colors of strongly correlated electronic systems

Many strongly correlated transition metal insulators are colored, even though they have band gaps much larger than the highest energy photons from the visible light. An adequate explanation for the color requires a theoretical approach able to compute subgap excitons in periodic crystals, reliably and without free parameters—a formidable challenge. The literature often fails to disentangle two important factors: what makes excitons form and what makes them optically bright. We pick two archetypal cases as examples: NiO with green color and MnF 2 with pink color, and employ two kinds of ab initio many body Green’s function theories; the first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, while the same theory is unable to explain why MnF 2 is pink. We show its color originates from higher order spin-flip transitions that modify the optical response, which is contained in dynamical mean-field theory (DMFT). We show that symmetry lowering mechanisms may determine how ‘bright’ these excitons are, but they are not fundamental to their existence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Modeling Framework to Predict Melting Dynamics at Microstructural Defects in TNT-HMX High Explosive Composites

Many high explosive (HE) formulations are composite materials whose microstructure is understood to impact functional characteristics. Interfaces are known to mediate the formation of hot spots that control their safety and initiation. Here, to study such processes at molecular scales, we developed all-atom force fields (FFs) for Octol, a prototypical HE formulation comprised of TNT (2,4,6-trinitrotoluene) and HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). We extended a FF for TNT and recasted it in a form that can be readily combined with a well-established FF for HMX. The resulting FF was extensively validated against experimental results and density functional theory calculations. We applied the new combined TNT-HMX FF to predict and rank surface and interface energies, which indicate that there is an energetic driver for coarsening of microstructural grains in TNT-HMX composites. Finally, we assess the impact of several microstructural environments on the dynamic melting of TNT crystal under ultrafast thermal loading. We find that both free surfaces and planar material interfaces are effective nucleation points for TNT melting. However, MD simulations show that TNT crystal is prone to superheating by at least 50 K on subnanosecond time scales and that the degree of superheating is inversely correlated with surface and interface energy. The modeling framework presented here will enable future studies on hot spot formation processes in accident scenarios that are governed by strong coupling between microstructural interfaces, material mechanics, momentum and energy transport, phase transitions, and chemistry.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Modeling the Environment-Dependent Kinetics of Oxygen Reduction Reaction – a Continuum Model for Electric Double Layer

Here, for proton-exchange-membrane fuel cells (PEMFCs) to achieve broad commercialization, improved energy-conversion efficiency with minimal Pt-based electrocatalyst is required. Because the sluggish rate of oxygen reduction reaction (ORR) limits the efficiency of PEMFCs, the efficiency improvement requires a better understanding of ORR kinetics and mechanism to design better catalyst. To understand the ORR mechanism, theoretical and experimental analyses have been conducted. While previous studies reasonably explained the catalyst-dependent activity on single crystal catalysts in 0.1 M perchloric acid solution, the explicit effect of electrolyte and related microenvironments is not thoroughly understood. The change in the electrolyte alters the electric-double-layer (EDL) structure and thus the local microenvironment at the electrode/electrolyte interface. Thus, the structure of the EDL should be carefully analyzed to uncover the electrolyte-dependent reaction kinetics. In this talk, we propose a multiscale continuum model to predict the EDL structure and examine the effect of perchloric acid concentration on ORR activity on Pt (111). The model includes Density Potential Functional Theory (DPFT) for electron density and Modified Poisson Boltzmann equation for species’ density and electric potential. Also, the interaction between adsorbents and electric field is taken into account by minimizing the grand potential. After model validation with experimentally measured double-layer capacity data as a function of applied potential and concentration, the effect of the perchloric acid concentration (0.02 M – 0.2 M) on ORR activity is analyzed and discussed. It is shown that the model reproduces the specific activity obtained in the experiments when assuming the oxygen adsorption is limiting the rate, which can be attributed to the large energetic barrier for solvent reorganization. Then, extension of the model to PEMFC ionomer electrolytes will be introduced. Overall, the model framework and findings provide insights into the ORR mechanism and guidance on how to tailor catalyst materials for increased PEMFC performance.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2022

First-Principles Calculations of the Structural, Electronic, Optical, and Mechanical Properties of 21 Pyrophosphate Crystals

Pyrophosphate crystals have a wide array of applications in industrial and biomedical fields. However, fundamental understanding of their electronic structure, optical, and mechanical properties is still scattered and incomplete. In the present research, we report a comprehensive theoretical investigation of 21 pyrophosphates A 2 M (H 2 P 2 O 7 ) 2 •2H 2 O with either triclinic or orthorhombic crystal structure. The molecule H 2 P 2 O 7 is the dominant molecular unit, whereas A = (K, Rb, NH 4 , Tl), M = (Zn, Cu, Mg, Ni, Co, Mn), and H 2 O stand for the cation elements, transition metals, and the water molecules, respectively. The electronic structure, interatomic bonding, partial charge distribution, optical properties, and mechanical properties are investigated by first-principles calculations based on density functional theory (DFT). Most of these 21 crystals are theoretically investigated for the first time. The calculated results show a complex interplay between A, M, H 2 P 2 O 7 , and H 2 O, resulting in either metallic, half-metallic, or semi-conducting characteristics. The novel concept of total bond order density (TBOD) is used as a single quantum mechanical metric to characterize the internal cohesion of these crystals to correlate with the calculated properties, especially the mechanical properties. This work provides a large database for pyrophosphate crystals and a road map for potential applications of a wider variety of phosphates.

36 MATERIALS SCIENCE↗
NASA NTRS1976

Waves in active and passive periodic structures - A review

The theory and recent applications of waves in periodic structures are reviewed. Both the Floquet and coupled waves approach are analyzed in some detail. The theoretical part of the paper includes wave propagation in unbounded and bounded active or passive periodic media, wave scattering from periodic boundaries, source radiation (dipole, Cerenkov, transition, and Smith-Purcell) in periodic media, and pulse transmission through a periodic slab. The applications part covers the recent development in a variety of fields: distributed feedback oscillators, filters, mode converters, couplers, second-harmonic generators, deflectors, modulators, and transducers in the fields of integrated optics and integrated surface acoustics. Work on insect compound eyes, mechanical structures, ocean waves, pulse compressions, temperature waves, and cholesteric liquid crystals, and particles interaction with crystals is briefly reviewed, especially in the case of zeolite crystals and superlattices. Recent advances in fabrication techniques for very fine gratings are also covered.

Elachi, C.↗
DOE OSTI2025

Softening of dd excitation in the resonant inelastic x-ray scattering spectra as a signature of Hund's coupling in nickelates

We investigate the effects of Hund's coupling on the resonant x-ray absorption spectra of the recently discovered family of layered nickelate superconductors. We contrast two scenarios depending on the relative strength of the ratio of the effective Hund's coupling ( J H ) to the crystal fields ( Δ ) in these systems. We carry out the cluster and DFT + DMFT simulations of the RIXS signal at the Ni L edge for different values of Hund's coupling. We find the latter dominates for the parent compound while the former becomes important for sufficiently large doping. Our results are consistent with the observations of a softening of a RIXS peak as a function of doping by Rossi [], only when the Hund coupling is sizable. To interpret the results, we separate the theoretical RIXS signal into spin conserving and nonspin conserving channels and conclude that the infinite layer nickelates are in a regime where Δ and J compete effectively and suggest further experimental tests of the theory. Published by the American Physical Society 2025

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Physical properties of YbFe 5 P 3 with a quasi-one-dimensional crystal structure

We report basic physical properties of the quasi-one-dimensional heavy-fermion compound Yb Fe 5 P 3 . Its magnetic susceptibility follows a modified Curie-Weiss behavior at high temperatures with a Weiss temperature between - 5 and - 21 K depending on the direction of the applied magnetic field. Our single crystals of Yb Fe 5 P 3 are good metals with a room-temperature resistivity of ~ 140 μ Ω cm and a residual resistivity of less than 2 μ Ω cm. Below ~ 2 K the resistivity reflects the presence of strong quantum fluctuations, which is supported by specific heat measurements that show a similar strong enhancement in C / T at low temperatures reaching 1.5 J/mol K 2 below T = 0.5 K. No magnetic ordering is observed down to 80 mK. Magnetic fields up to 8 T rapidly suppress the magnetic fluctuations, while resistivity measurements under pressures up to 2.54 GPa indicate the enhancement of quantum fluctuations, although still no order is observed down to 0.3 K. Density functional theory calculations suggest the presence of electronically quasi-one-dimensional (1D) Fermi surface sheets together with three-dimensional electronic pockets. We suggest that the quasi-1D nature of this compound leads to an extended regime of large quantum fluctuations within the paramagnetic state prior to reaching a magnetic instability.

36 MATERIALS SCIENCE↗
NASA NTRS1986

A study of the applicability of nucleation theory to quasi-thermodynamic transitions of second and higher Ehrenfest-order, supplement 3

The work includes an investigation of the applicability of the nucleation theory to second and higher order thermodynamic transitions in the Ehrenfest sense, and a number of significant conclusions relevant to first order transitions, as well. The underlying theoretical method consisted of expanding the Gibbs' free energy in a Maclarin or Taylor series and then using fundamental thermodynamic determinable quantities, and interpreting the results. Work was performed on the existence and interpretation of an interfacial energy between phases in a second order transition in addition to an investigation of the solid-liquid interfacial energy for various polymers. Extensive considerations were devoted to various aspects of a particular polymer, polyvinylidene fluoride (PVDF or PVF2), including an experimetal investigation of the effects of an applied electric field on the morphology of melt crystallization and on the nucleation and growth of polarized domains.

Barker, R. E., Jr.↗
DOE OSTI2025

Layer-dependent spin-resolved electronic structure of ferromagnetic triple-layered ruthenate Sr4Ru3O10

High-resolution angle- and spin-resolved photoemission spectroscopy (ARPES) of the triple-layered ruthenate Sr4Ru3O10 reveals features of the electronic structure that extend our understanding of the layered strontium ruthenates. The spectra near the Fermi energy are very different from the nonmagnetic analogues Sr2RuO4 and Sr3Ru2O7 with distinct Fermi surfaces for wide electronlike minority spin bands around the zone center and narrow holelike majority spin Fermi surface contours around the zone corners. The most dramatic results are two narrow spectral peaks ∼30 meV below the Fermi level, a spin-minority holelike band at the Brillouin zone center, and a spin-majority saddle-band van Hove singularity at the zone edge, which exhibits almost 100% spin polarization at low temperature, and a strong temperature dependent coherence-incoherence crossover attributed to Hund metal correlations. Quantitative comparison of the ARPES to spin-polarized density functional theory (DFT) calculations identify the specific antibonding and nonbonding orbital origins of the narrow bands, with a prediction of different spatial localization in the central and outer layers. This is shown to be consistent with experimental ARPES multizone matrix element intensity variations, and implicates outer-layer-specific control of the in-plane metamagnetism. The renormalization of the bands relative to the mean-field DFT, the demonstration of spin-polarized oxygen bands, and of spin-minority and spin-majority band-crossing hybridization provide a more complete picture of the magnetism which displays aspects of both delocalized and local moment behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Intense infrared lasers for strong-field science

The advent of chirped-pulse amplification in the 1980s and femtosecond Ti:sapphire lasers in the 1990s enabled transformative advances in intense laser–matter interaction physics. Whereas most of experiments have been conducted in the limited near-infrared range of 0.8–1 μm, theories predict that many physical phenomena such as high harmonic generation in gases favor long laser wavelengths in terms of extending the high-energy cutoff. Significant progress has been made in developing few-cycle, carrier-envelope phase-stabilized, high-peak-power lasers in the 1.6–2 μm range that has laid the foundation for attosecond X ray sources in the water window. Even longer wavelength lasers are becoming available that are suitable to study light filamentation, high harmonic generation, and laser–plasma interaction in the relativistic regime. Long-wavelength lasers are suitable for sub-bandgap strong-field excitation of a wide range of solid materials, including semiconductors. In the strong-field limit, bulk crystals also produce high-order harmonics. In this review, we first introduce several important wavelength scaling laws in strong-field physics, then describe recent breakthroughs in short- (1.4–3 μm), mid- (3–8 μm), and long-wave (8–15 μm) infrared laser technology, and finally provide examples of strong-field applications of these novel lasers. Furthermore, some of the broadband ultrafast infrared lasers will have profound effects on medicine, environmental protection, and national defense, because their wavelengths cover the water absorption band, the molecular fingerprint region, as well as the atmospheric infrared transparent window.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3

Here, we report a detailed study of the specific heat and magnetic susceptibility of single crystals of a spin-liquid candidate: the hyperhoneycomb Cu oxalate framework compound [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3 . The specific heat shows no anomaly associated with a magnetic transition at low temperatures down to T ~ 180 mK in zero magnetic field. We observe a large linear-in-T contribution to the specific heat γT, γ = 98 (1) mJ / mol K 2 , at low temperatures, indicative of the presence of fermionic excitations despite the Mott insulating state. The low-T specific heat is strongly suppressed by applied magnetic fields H, which induce an energy gap, Δ(H), in the spin-excitation spectrum. We use the four-component relativistic density-functional theory (DFT) to calculate the magnetic interactions, including the Dzyaloshinskii-Moriya antisymmetric exchange, which causes an effective staggered field acting on one copper sublattice. The magnitude and field dependence of the field-induced gap, Δ (H) ∝ H 2/3 , are accurately predicted by the soliton mass calculated from the sine-Gordon model of weakly coupled antiferromagnetic Heisenberg chains with all parameters determined by our DFT calculations. Thus our experiment and calculations are entirely consistent with a model of [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3 in which anisotropic magnetic exchange interactions due to Jahn-Teller distortion cause one copper sublattice to dimerize, leaving a second sublattice of weakly coupled antiferromagnetic chains. We also show that this model quantitatively accounts for the measured temperature-dependent magnetic susceptibility. Thus [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3 is a canonical example of a one-dimensional spin-1/2 Heisenberg antiferromagnet and not a resonating-valence-bond quantum spin liquid, as previously proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1983

Gravitational effects in dendritic growth

The theories of diffusion-controlled dendritic crystallization will be reviewed briefly, along with recently published critical experiments on the kinetics and morphology of dendritic growth in pure substances. The influence of the gravitational body force on dendrite growth kinetics will be shown to be highly dependent on the growth orientation with respect to the gravity vector and on the level of the thermal supercooling. In fact, an abrupt transition occurs at a critical supercooling, above which diffusional transport dominates the growth process and below which convective transport dominates. Our most recent work on binary mixtures shows that dilute solute additions influence the crystallization process indirectly, by altering the interfacial stability, rather than by directly affecting the transport mode. Directions for future studies in this field will also be discussed.

Glicksman, M. E.↗
DOE OSTI2023

Tetragonal Kondo Insulator EuCd 2 Sb 2 Discovered via High Pressure High Temperature Synthesis

Abstract Magnetic and electronic properties of quantum materials heavily rely on the crystal structure even in the same chemical compositions. In this study, it is demonstrated that a layered tetragonal EuCd 2 Sb 2 structure can be obtained by treating bulk trigonal EuCd 2 Sb 2 under high pressure (6 GPa) and high temperature (600 °C). Magnetization measurements of the newly formed layered tetragonal EuCd 2 Sb 2 confirm an antiferromagnetic ordering with Neel temperature ( T N ) around 16 K, which is significantly higher than that ( T N ≈ 7 K) of trigonal EuCd 2 Sb 2 , consistent with heat capacity measurements. Moreover, bad metal behavior is observed in the temperature dependence of the electrical resistivity and the resistivity shows a dramatic increase around the Neel temperature. Electronic structure calculations with local density approximation dynamic mean–field theory (LDA+DMFT) show that this material is strongly correlated with well‐formed large magnetic moments, due to Hund's coupling, which is known to dramatically suppress the Kondo scale.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Enhanced superconductivity and ferroelectric quantum criticality in plastically deformed strontium titanate

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach using irreversible, plastic deformation of single crystals. We show that compressive plastic deformation induces low-dimensional superconductivity well above the superconducting transition temperature (Tc) of undeformed SrTiO3, with evidence of possible superconducting correlations at temperatures two orders of magnitude above the bulk Tc. The enhanced superconductivity is correlated with the appearance of self-organized dislocation structures, as revealed by diffuse neutron and X-ray scattering. We also observe deformation-induced signatures of quantum-critical ferroelectric fluctuations and inhomogeneous ferroelectric order using Raman scattering. Our results suggest that strain surrounding the self-organized dislocation structures induces local ferroelectricity and quantum-critical dynamics that strongly influence Tc, consistent with a theory of superconductivity enhanced by soft polar fluctuations. Our results demonstrate the potential of plastic deformation and dislocation engineering for the manipulation of electronic properties of quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Chemical and architectural intricacy from nanoscale tetrahedra and their analogues

The tetrahedron, as the simplest platonic shape, is a profound building block with the potential to create intricate superstructures. Noteworthy designs utilizing tetrahedral building blocks include the Sierpiński tetrahedron (the most fundamental three-dimensional fractal), a one-dimensional helical structure known as the tetrahelix, and various crystalline and quasicrystalline packings. Historically, the practicality of tetrahedral superstructures has been evident, providing stable, well-defined frameworks for various constructions, including truss bridges, tower cranes, and electricity transmission line pylons. In the field of self-assembled nanocrystal superlattices, tetrahedral nanocrystals, as building blocks, occupy a unique place among all the possible nanoscale particles. Mathematical models, simulation work, and experimental studies using nanocrystals in the laboratory have suggested that self-assembled structures derived from nanoscale tetrahedral building blocks are notably intricate, giving rise to new horizons of high-entropy nanocrystal superlattices. An important implication from previous works is that such tetrahedral nanocrystal superlattices form through highly delicate interparticle interactions, emphasizing the importance of the fine features of these nanocrystals. In this article, we summarize the advances in superlattices assembled from tetrahedral nanocrystals. Here, we first define the tetrahedron and tetrahedron analogues based on Conway’s transformation and graph theory, underscoring their relevance to the crystallization process producing tetrahedral nanocrystals. Then, we showcase previous reports on the synthesis of tetrahedral nanocrystals and the resulting nanocrystal superstructures. Finally, we conclude by offering insights and perspective into the chemical and architectural intricacy that could emerge from tetrahedral nanocrystals.

Nanostructure↗
NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗