Average Absorption Coefficient Research Articles

Preparation of natural bio-based Eucommia ulmoides gum/styrene-butadiene rubber composites and the evaluation of their damping and sound absorption properties

To achieve effective sound absorption in wide frequency bands under high pressures, Eucommia ulmoides gum (EUG) as one of the natural biopolymers was incorporated into styrene-butadiene rubber (SBR) to prepare sound absorption materials. The morphology, crystalline structure, and macro-performance (damping, sound absorption, and mechanical properties) of the as-produced composites were systemically investigated. When the EUG content was less than 30 phr, the EUG was dispersed in the SBR matrix as nanocrystallites primarily existed in the β-crystal form, which is demonstrated by wide-angle X-ray diffraction (WAXD) and polarizing microscope (POM). The dynamic mechanical thermal analyzer (DMA) results expressed that EUG had two dynamic mechanical loss peaks, i.e. the glass transition peak (Peak 1, -60–40°C) and melting transition peak (Peak 2, 30–60°C). Thus, the addition of EUG improved the damping performance of the composites in high-temperature areas to some extent. Moreover, in comparison to the neat SBR, the average sound absorption coefficient of SBR/EUG (70/30) composite increased by 24.23% in the frequency range of 3–8 kHz under 2.5 MPa, which show the excellent sound absorption properties. And since the EUG nanocrystallites played the role of physical crosslingking points, the SBR/EUG (70/30) composite also had outstanding comprehensive mechanical properties. The SBR/EUG composites may be applied to underwater sound absorption materials.

Development and validation of the HPLC method for quality control of radiolabelled DOTA-TATE and DOTA-TOC preparations

IntroductionThe information on the presence of cold metal complexes in radiolabeled DOTA-TATE or DOTA-TOC is important in assessing the cause of the radiolabeling failure, poor radiolabeling yield and/or low effective molar activity. DOTA-peptide complexes are detectable using UV–Vis detector. The main limitation in the quantitative analysis is the limited availability of standard substances and the lack of data on their molar absorption coefficients. The aim of our study was development and validation of HPLC method enabling RCP analysis and identification and quantification of metal complexes impurities in the radiopharmaceutical preparations of DOTA-chelated peptides. MethodsComplexes of DOTA-TATE and DOTA-TOC with several metals, were prepared. Their molar absorption coefficients at 220 nm were determined. The developed HPLC method has been validated in terms of quantitative determination of non-complexed DOTA-TATE and DOTA-TOC and their respective complexes with metallic individuals. ResultsGood chromatographic separation of the individual metal-DOTA-peptide complexes was achieved. The resolution between peaks of interest in radioactive preparations (complexes with: yttrium-90, lutetium-177, gallium-68) and metallic impurities was well above 1.5 (except gallium-68 DOTA-TOC preparations). Limits of detection and quantification were determined based on the parameters of the calibration curves. Based on the spectrophotometric and HPLC-DAD studies and statistical analysis of the results obtained, the average molar absorption coefficient was determined for studied DOTA-TATE and DOTA-TOC complexes, εHPLC-DAD = 48 × 103M−1 cm−1. With the use of the determined molar absorption coefficient the method enabled quantitative determination of non-labelled peptide in the radioactive preparation in the linearity range of 0.5–100 μg/mL for DOTA-TATE(net) and 0.5–100 μg/mL for DOTA-TOC(net). ConclusionThe developed HPLC method is suitable for RCP determination of radiolabelled DOTA-TATE and DOTA-TOC preparations. Determination of the average molar absorption coefficient for DOTA-TATE and DOTA-TOC complexes allows assessment of the total content of the peptide in radiopharmaceutical preparation regardless of its chemical form (free ligand, associated with radionuclide, in the form of a complex with metal ions being the impurity) using the HPLC method with UV detection.

A compact low-frequency sound-absorbing metasurface constructed by resonator with embedded spiral neck

This Letter reports an acoustic metasurface for low-frequency sound absorption with a compact size in both vertical and lateral directions, which is constructed by a series of Helmholtz resonators with spiral extended necks. Analytical, numerical, and experimental results show that the metasurface with a thickness of 13.5 mm possesses total sound absorption at 320 Hz under normal incidence. The thickness of the prototype is only about 1/80th of the operating wavelength (λ). What is more, the side length of the basic unit (25 mm) is also on the deep-subwavelength scale (λ/43). To widen the narrow effective absorption bandwidth of the uniform absorber, the strategy of parallel arrangement of different elements is employed. A wideband absorber consisting of four inhomogeneous units is optimally designed to maximize the averaged absorption coefficient in a prescribed frequency range of [360, 410] Hz. The experimental results show that the absorber with a thickness of 13.5 mm exhibits high absorption (the averaged absorption coefficient is about 0.9) in the desired frequency range. The features of effective low-frequency sound absorption, compact dimension, and high absorption with a tunable bandwidth make the proposed acoustic metasurface promising for various applications in noise control engineering.

A DFT study on optoelectronic properties of near-infrared In0.53Ga0.47As (001), (011) and (111) surfaces

The III-V In x Ga 1- x As photocathodes have important application prospects in the fields of marine submarine exploration, marine communication, and undersea imaging. Different semiconductor surfaces show different atomic arrangements, leading to different properties. In this paper, the optoelectronic properties of three representative In 0.53 Ga 0.47 As surfaces have been studied and analyzed at the atomic levels by using the first-principles calculation method. Results show that the (001), (011) and (111) In 0.53 Ga 0.47 As surfaces are all chemically stable, and the lowest work function is obtained at (001) surface. The band diagram shows that the conduction bands of the three surfaces are all shifted down to the Fermi level. At the same time, the valence bands on the (001) and (111) surfaces move up, crossing the Fermi level, indicating the enhancement of metallic property. The narrowing of the conduction band leads to the weakening of electron locality. Among the three representative surfaces, the average absorption coefficient and reflectance of In 0.53 Ga 0.47 As (001) surface are decreased most significantly, reflecting higher photoelectrons emitting performance. • The photons are most likely to escape into the vacuum from the In 0.53 Ga 0.47 As (001) surface. • The conduction bands of all three surfaces move downward, leading to the weakening of electron locality. • The (001) In 0.53 Ga 0.47 As surface owns the strongest photo-emitting performance.

Low-Frequency Broadband Acoustic Metasurface Absorbing Panels

A broadband sound absorption attained by a deep-subwavelength structure is of great interest to the noise control community especially for extremely low frequencies (20-100 Hz) in room acoustics. In this paper, we report on an analytical, numerical and experimental study of a low-frequency broadband (50-63 Hz, one third octave band), high absorption (average absorption coefficient ≈93%), near-omnidirectional (0° - 75°) acoustic metasurface absorber at a thickness of 15.4 cm (1/45 of the wavelength at 50 Hz). To further broaden the bandwidth (50-100 Hz, one octave band), another design is analytically studied to achieve an average absorption coefficient of 85% for a wide angle range (0°-75°) at a thickness of 20 cm (1/34 of wavelength at 50 Hz). The proposed design methodology may solve the long-standing issue for low frequency absorption in room acoustics.

Elucidating the Sound Absorption Characteristics of Foxtail Millet (Setariaitalica) Husk.

The current study deals with the analysis of sound absorption characteristics of foxtail millet husk powder. Noise is one the most persistent pollutants which has to be dealt seriously. Foxtail millet is a small seeded cereal cultivated across the world and its husk is less explored for its utilization in polymer composites. The husk is the outer protective covering of the seed, rich in silica and lingo-cellulose content making it suitable for sound insulation. The acoustic characterization is done for treated foxtail millet husk powder and polypropylene composite panels. The physical parameters like fiber mass content, density, and thickness of the composite panel were varied and their influence over sound absorption was mapped. The influence of porosity, airflow resistance, and tortuosity was also studied. The experimental result shows that 30-mm thick foxtail millet husk powder composite panel with 40% fiber mass content, 320 kg/m3 density showed promising sound absorption for sound frequency range above 1000 Hz. We achieved noise reduction coefficient (NRC) value of 0.54. In view to improve the performance of the panel in low-frequency range, we studied the efficiency of incorporating air gap and rigid backing material to the designed panel. We used foxtail millet husk powder panel of density 850 kg/m3 as rigid backing material with varying air gap thickness. Thus the composite of 320 kg/m3 density, 30-mm thick when provided with 35-mm air gap and backing material improved the composite’s performance in sound frequency range 250 Hz to 1000 Hz. The overall sound absorption performance was improved and the NRC value and average sound absorption coefficient (SAC) were increased to 0.7 and 0.63 respectively comparable with the commercial acoustic panels made out of the synthetic fibers. We have calculated the sound absorption coefficient values using Delany and Bezlay model (D&B model) and Johnson–Champoux–Allard model (JCA model) and compared them with the measured sound absorption values.

Simulation studies to understand sensitivity and timing characteristics of an optical property modulation-based radiation detection concept for PET

The concept of using the modulation mechanisms of a material’s optical properties for annihilation photon detection has been proposed as a potential method to significantly improve the coincidence time resolution (CTR) of positron emission tomography detectors. However, the possibility of detecting individual 511 keV photons with largely improved CTR using the proposed detection method has not yet been demonstrated, either experimentally or theoretically. In addition, the underlying physical picture of the optical modulation effects induced by annihilation photons has not been fully understood. In this work, we perform simulation studies including generation of the annihilation photon-induced ionization energy deposition trajectory, estimation of the charge carrier cascade time and temporal variance, simulation of the distribution of ionization-induced charge carrier density, and calculation of the strength of the modulation of two optical parameters: the absorption coefficient and the refractive index, as well as evaluation of the resulting optical intensity and phase change experienced by a probe laser beam. Our simulation results show that the average absorption coefficient modulation induced by individual 511 keV photon interactions is around 0.04 cm−1, and the average refractive index change is 3.6 × 10−5, leading to modulations in the probe laser intensity of around 0.1% and phase modulation of around 0.05 radians. We have also found that the ionization process induced by a single 511 keV photon interaction occurs within 2.3 ps with a temporal variance of 0.4 ps. The fundamental limit on CTR using the optical property modulation-based detection mechanism is estimated to be around 1.2 ps full width at half maximum. Our simulation results indicate that with proper experiment design, it is possible to detect the ionization produced by an individual 511 keV photon with significantly improved CTR using the optical property modulation-based detection concept.

A method based on ejector technology to suppress the infrared radiation of the special vehicle exhaust gas

In this study, a method based on ejector technology is proposed to effectively suppress the infrared radiation associated with the exhaust gas of special vehicles such as tanks, armored vehicles, and missile carriers. These vehicles emit exhaust gases at very high temperatures. First, a mathematical model of the exhaust pipe was established for the exhaust system of a certain type of special vehicle. Then, the 3-D flow field outside the exhaust pipe was numerically simulated using FLUENT 6.3 software. Thus, the temperature, pressure, and density of the exhaust-gas-flow field before and after adopting the proposed ejector technique were obtained. Second, the statistical narrowband model based on the Lorentzian profile was used to determine the average absorption coefficient of a narrow band. Then, the finite volume method was used to solve the radiation transfer equation in the gaseous medium. Finally, the spectral radiation brightness and mid-infrared radiation intensity distribution of the exhaust gas before and after adopting the ejector technique were obtained. Results show that the proposed method considerably decreased the infrared radiation intensity of the exhaust gas by approximately 70%. Thus, using the proposed ejector technology, the infrared radiation associated with the exhaust system of special vehicles can be effectively suppressed.

Graded and Anisotropic Porous Materials for Broadband and Angular Maximal Acoustic Absorption.

The design of graded and anisotropic materials has been of significant interest, especially for sound absorption purposes. Together with the rise of additive manufacturing techniques, new possibilities are emerging from engineered porous micro-structures. In this work, we present a theoretical and numerical study of graded and anisotropic porous materials, for optimal broadband and angular absorption. Through a parametric study, the effective acoustic and geometric parameters of homogenized anisotropic unit cells constitute a database in which the optimal anisotropic and graded material will be searched for. We develop an optimization technique based on the simplex method that is relying on this database. The concepts of average absorption and diffuse field absorption coefficients are introduced and used to maximize angular acoustic absorption. Numerical results present the optimized absorption of the designed anisotropic and graded porous materials for different acoustic targets. The designed materials have anisotropic and graded effective properties, which enhance its sound absorption capabilities. While the anisotropy largely enhances the diffuse field absorbing when optimized at a single frequency, graded properties appear to be crucial for optimal broadband diffuse field absorption.

Experimental investigation of underwater locally multi-resonant metamaterials under high hydrostatic pressure for low frequency sound absorption

This research develops an underwater acoustic metamaterial, which can serve to absorb broadband low-frequency underwater sound under high hydrostatic pressure ranging from 200 to 2000 Hz. Every unit cell includes 12 harmonic oscillators as multi-scatterers in the proposed acoustic metamaterial, which induces lots of local resonance modes for absorbing sound energy in the investigated frequency range. The sound absorption band can be greatly widened in the low frequency range due to strong coupling and multiple scattering effects among harmonic oscillators. The effectiveness of the prototype is experimentally demonstrated in a standing wave tube under different hydrostatic pressure conditions. The effects of high hydrostatic pressure on local multi-resonance mechanism are investigated experimentally. Experimental results show that the average sound absorption coefficient of the proposed acoustic metamaterial achieves 0.78 in the frequency range [600 Hz, 2000 Hz] under 0.5 MPa. Furthermore, the proposed acoustic metamaterial can achieve better sound absorption performance than the pure viscoelastic polymer under high hydrostatic pressure.

Vertical profiles of light absorption and scattering associated with black carbon particle fractions in the springtime Arctic above 79° N

Abstract. Despite the potential importance of black carbon (BC) for radiative forcing of the Arctic atmosphere, vertically resolved measurements of the particle light scattering coefficient (σsp) and light absorption coefficient (σap) in the springtime Arctic atmosphere are infrequent, especially measurements at latitudes at or above 80∘ N. Here, relationships among vertically distributed aerosol optical properties (σap, σsp and single scattering albedo or SSA), particle microphysics and particle chemistry are examined for a region of the Canadian archipelago between 79.9 and 83.4∘ N from near the surface to 500 hPa. Airborne data collected during April 2015 are combined with ground-based observations from the observatory at Alert, Nunavut and simulations from the Goddard Earth Observing System (GEOS) model, GEOS-Chem, coupled with the TwO-Moment Aerosol Sectional (TOMAS) model (collectively GEOS-Chem–TOMAS; Kodros et al., 2018) to further our knowledge of the effects of BC on light absorption in the Arctic troposphere. The results are constrained for σsp less than 15 Mm−1, which represent 98 % of the observed σsp, because the single scattering albedo (SSA) has a tendency to be lower at lower σsp, resulting in a larger relative contribution to Arctic warming. At 18.4 m2 g−1, the average BC mass absorption coefficient (MAC) from the combined airborne and Alert observations is substantially higher than the two averaged modelled MAC values (13.6 and 9.1 m2 g−1) for two different internal mixing assumptions, the latter of which is based on previous observations. The higher observed MAC value may be explained by an underestimation of BC, the presence of small amounts of dust and/or possible differences in BC microphysics and morphologies between the observations and model. In comparing the observations and simulations, we present σap and SSA, as measured, and σap∕2 and the corresponding SSA to encompass the lower modelled MAC that is more consistent with accepted MAC values. Median values of the measured σap, rBC and the organic component of particles all increase by a factor of 1.8±0.1, going from near-surface to 750 hPa, and values higher than the surface persist to 600 hPa. Modelled BC, organics and σap agree with the near-surface measurements but do not reproduce the higher values observed between 900 and 600 hPa. The differences between modelled and observed optical properties follow the same trend as the differences between the modelled and observed concentrations of the carbonaceous components (black and organic). Model-observation discrepancies may be mostly due to the modelled ejection of biomass burning particles only into the boundary layer at the sources. For the assumption of the observed MAC value, the SSA range between 0.88 and 0.94, which is significantly lower than other recent estimates for the Arctic, in part reflecting the constraint of σsp<15 Mm−1. The large uncertainties in measuring optical properties and BC, and the large differences between measured and modelled values here and in the literature, argue for improved measurements of BC and light absorption by BC and more vertical profiles of aerosol chemistry, microphysics and other optical properties in the Arctic.

Research on Effect of Equivalent Diameter of Voids on Sound Absorption Performance of Porous Asphalt Concrete Based on Grey Entropy Method

The sound absorption performance of porous asphalt concrete (PAC) is inseparable from the sizes of voids, as different sizes of voids have different absorption effects on noise in different frequency bands. However, the relationship between the two is not clear. In this study, the equivalent diameter of voids was obtained by the proposed image segmentation algorithm based on the square area, then grey entropy method was used to analyze the effect of different equivalent diameter of voids on the sound absorption performance of PAC in the frequency range of traffic noise. The results show that with the increase of air voids, the peak and average sound absorption coefficient of PAC increase, the sound absorption performance of PAC is improved; and the sound absorption performance of PAC is mainly affected by the equivalent diameter of voids of 3-4mm.

Teaching-learning-based optimization of a composite metastructure in the 0-10 kHz broadband sound absorption range.

This paper proposes a strategy to broaden the sound absorption region of porous materials by embedding ribs. The theoretical solution and the numerical simulations of the optimization model show that the composite metastructure exhibits ultra-wide high absorption characteristics and an average sound absorption coefficient of 0.937 in the 0-10 kHz range upon its teaching-learning-based optimization. High sound pressures are present only among the embedded ribs. A significant slowing down of the sound takes place inside the metastructure. The impedance tube test confirms the design of the broadband sound absorption region in agreement with the teaching-learning-based optimization method.

A Highly Selective and Simple Spectrophotometric Method for the Determination of Zinc at Nano-trace Levels in Some Environmental, Biological, Food, and Pharmaceutical Samples Using 2-hydroxynaphthaldehydebenzoylhydrazone

A simple, ultra-sensitive, and highly selective spectrophotometric method has been established for the trace quantification of zinc (Zn), using 2-hydroxynaphthaldehyde benzoylhydrazone (HNABH). Zn forms a pale yellowish-green complex (maximum absorption at 426 nm) with HNABH (1:1, v:v) in a marginally acidic solution (0.00005-0.00023 M H2SO4). The average molar absorption coefficient and Sandell’s sensitivity were found: 2.87×105 L/mol.cm and 12 ng/cm2 of Zn, respectively. The observed linearity range for Zn was 0.01-50 mg/Lwith a detection limit of 1 µg/L. The analysis of biological, food, and vegetable samples using the suggested method were found to be in tremendous accord with those acquired by Atomic Absorption Spectroscopy (AAS) and Inductively Coupled Plasma-Optical Emission Spectroscopy (ICP-OES). The method has high precision and accuracy (s = ±0.01 for 0.5 mg/L). The limit of quantification of the proposed method was 10 µg/L.

Flame-Retardant and Sound-Absorption Properties of Composites Based on Kapok Fiber.

In order to improve the utilization rate of kapok fiber, flame-retardant and sound-absorption composites were prepared by the hot pressing method with kapok fiber as the reinforced material, polyε-caprolactone as the matrix material, and magnesium hydroxide as the flame retardant. Then, the effects of hot pressing temperature, hot pressing time, density of composites, mass fraction of kapok fiber, thickness of composites, and air layer thickness on the sound-absorption properties of composites were analyzed, with the average sound absorption coefficient as the index. Under the optimal process parameters, the maximum sound absorption coefficient reached 0.830, the average sound absorption coefficient was 0.520, and the sound-absorption band was wide. Thus, the composites belonged to high-efficiency sound-absorbing material. The flame-retardant effect of magnesium hydroxide on the composites was investigated, and the limiting oxygen index could reach 31.5%. Finally, multifunctional composites based on kapok fiber with flame retardant properties, and sound-absorption properties were obtained.

Sound absorption performance of a lightweight ceramic foam

Porous materials can be effective for sound absorption and noise reduction. A kind of lightweight cellular ceramic foam with bulk density of 0.38–0.56 g cm-3 was successfully prepared by conventional molding with pore forming agent. The porosity is from 76.4% to 83.7% for the sample with relatively large pores (the average pore size: 5.3–5.6 mm), and from 74.1% to 81.1% for the sample with relatively small pores (the average pore size: 1.5–1.7 mm). The effects were investigated for processing parameters on the structure of samples, and for the pore size, sample thickness and porosity on the sound absorption performance of samples. The results show that the absorption performance of the ceramic foam product with relatively large pores may be superior to that with relatively small pores in the case of the approximately same porosity. The first absorption peak moves from a higher frequency to a lower frequency with the increase of sample thickness. When the porosity increases, the average sound absorption coefficient increases for all of the samples, and the first absorption peak moves from a higher frequency to a lower frequency for the sample with relatively large pores but does not change for that with relatively small pores.

Carbon substitution enhanced electronic and optical properties of MgSiP2 chalcopyrite through TB-mBJ approximation

In this work, we used the first-principles calculation based on density functional theory to investigate the effect of carbon substitution on structural, electronic, and optical properties of the MgSiP2 compound. Our calculations for the lattice constants show that both a and c decrease when the C atoms increasingly replace Si atoms in MgSiP2, however, the bulk modulus is found to be increasing. The calculated negative values of the formation energy (Ef) reveal that all MgSi1-xCxP2 alloys are thermodynamically stables. In addition, the substitution of the C atoms leads to a reduction of the value of the band-gap to 1.51 eV, 1.47 eV, and 1.30 eV for x = 0.25, 0.5 and, 0.75 respectively, these values have been calculated using the TB-mBJ approximation. We have calculated also the optical properties and the results show that the average absorption coefficient of MgSi1-xCxP2 alloys is improved in the visible light region (α ∼ 105 cm−1). Therefore, the band-gap values and the high absorption coefficient (α ∼ 105 cm−1) make MgSi1-xCxP2 alloys a promising candidate for photovoltaic applications.

The Optical Properties of Aerosols at the Summit of Mount Tai in May and June and the Retrieval of the Complex Refractive Index

To study the optical properties of background atmospheric aerosols in East China, we carried out observations of the physical, chemical and optical properties of atmospheric aerosols at the summit of Mount Tai (Mt. Tai, 1533.7 m above sea level) from 13 May to 25 June 2017. The results show that the average scattering coefficient ( σ sca , 550 ) at 550 nm of the aerosols at the summit of Mt. Tai is 40.3 Mm−1, and the average absorption coefficient ( σ abs , 550 ) at 550 nm is 16.0 Mm−1. The complex refractive index of aerosols is a key parameter for aerosol retrieval and modeling. There are few studies on the equivalent complex refractive index of aerosol in the Taishan area. We calculated the aerosol equivalent complex refractive index using the observed aerosol scattering coefficients, absorption coefficients and particle size distribution data, providing more data support for future modeling in this region. The real part (n) of the complex refractive index at 550 nm of aerosol ranges from 1.31 to 1.98 (mostly under 1.50), with an average value of 1.38, while the imaginary part (k) ranges from 0.014 to 0.251 (less than 0.10 for over 95% samples), with an average value of 0.040. The analysis of the n and k of the aerosol average complex refractive index shows that the scattering properties of the aerosols at the summit of Mt. Tai are relatively weak and the absorption properties are relatively strong when compared with those of other kinds of aerosols. The k of the aerosol complex refractive index at the summit of Mt. Tai has strong correlations with the wind speed, temperature, as revealed by the correlation analysis.

Unique carbon nanofiber@ Co/C aerogel derived bacterial cellulose embedded zeolitic imidazolate frameworks for high-performance electromagnetic interference shielding

Recently, lightweight and highly efficient electromagnetic interference (EMI) shielding composites are crucial but changing for the development of modern electronics and telecommunication. Here, a novel polyhedral Co/C particle embedded carbon nanofiber (CNF@Co/C) aerogels were synthesized via pyrolysis of bacterial cellulose wired zeolitic imidazolate frameworks-67 (ZIF-67) aerogel under argon. The flexible CNF@Co/C aerogels exhibit a high EMI shielding effectiveness (SE) is approaching 56.07 dB at a density of only 0.023 g cm−3 in the X band, and the average absorption coefficient is as high as 0.79, indicating 79% of electromagnetic (EM) waves are absorbed in shielding process. The remarkable performance results from the three-dimensional (3D) CNF-threaded porous structure with interconnected network and the magnetic Co/C particle strung by CNF, which contribute to a conduction loss and optimal impedance matching along with multiple polarization and strong magnetic loss. This work paves a promising way for the new generation of electronic device with lightweight and efficient EMI shielding.

A New k-Distribution Scheme for Clear-Sky Radiative Transfer Calculations in Earth’s Atmosphere. Part I: Thermal Infrared (Longwave) Radiation

Abstract A new k-distribution scheme of longwave radiation without the correlated-k-distribution assumption is developed. Grouping of spectral points is based on the line-by-line (LBL)-calculated absorption coefficient k at a few sets of reference pressure pr and temperature θr, where the cooling rate is substantial in a spectral band. In this new scheme, the range of k(pr, θr) of a band is divided into a number of equal intervals, or g groups, in log10(kr). A spectral point at the wavenumber ν is identified with one of the g groups according to its kν(pr, θr). For each g group, a Planck-weighted k-distribution function Hg and a nonlinearly averaged absorption coefficient k¯g⁡(p,θ) are derived. The function Hg and the absorption coefficient k¯g⁡(p,θ) constitute the new k-distribution scheme. In this k-distribution scheme, a spectral point can only be identified with a g group regardless of pressure and temperature, which is different from the correlated-k distribution scheme. The k-distribution scheme is applied to the H2O, CO2, O3, N2O, and CH4 absorption bands, and results are compared with LBL calculations. To balance between the accuracy and the computational economy, the number of g groups in a band of a given gas is chosen such that 1) the difference in cooling rate is <0.1 K day−1 in the troposphere and <1.0 K day−1 in the stratosphere and 2) the difference in fluxes is <0.5 W m−2 at both the top of the atmosphere and the surface. These differences are attained with 130 g groups, which is the sum of the g groups of all five gases.