Optical modeling of mineral dust particles: A review

Dust particles are uniquely and irregularly shaped, they can be inhomogeneous, form agglomerates, be composed of anisotropic materials, and have a preferred orientation. As such, modeling their light scattering is very challenging. This review takes a look at the advances in dust optical modeling over the last decade. It is obvious that our ability to model the single-scattering properties of dust particles accurately depends on the size parameter. Unfortunately, our ability to account realistically for all the relevant physical properties in light-scattering modeling is the best for small particles; whereas, the realistic treatment of the particles would be most important for large size parameters. When particles are not much larger than the wavelength, even simple model shapes such as homogeneous spheroids appear to perform well; practically any reasonable shape distribution of non-spherical model particles seems superior compared to the Mie theory. Our ability to model scattering by dust particles much larger than the wavelength is very limited: no method presently exists to predict reliably and accurately the single-scattering properties of such particles, although there are models that can be tuned to agree well with the laboratory-measured reference scattering matrices. The intermediate size parameters between the resonance domain and the geometric-optics domain appear to be almost uncharted territory and, consequently, very little can be said about the impact of different physical properties on scattering in this region. Despite the challenges, the use of Mie theory should be avoided: contrary to the popular belief, the use of Mie spheres is a major source of error even in radiation-budget considerations.     

Study of the sensitivity of size-averaged scattering matrix elements of nonspherical particles to changes in shape, porosity and refractive index

Studies of the physical parameters that influence the single scattering properties of a size distribution of small particles in random orientation are fundamental in understanding the origin of the observed dependence of the scattering matrix elements on the scattering angle. We present results of extensive calculations of the single scattering matrices of small nonspherical particles performed by a computational model based on the Discrete-Dipole Approximation. We have particularly studied the sensitivity of the size-averaged scattering properties at visible wavelengths of nonspherical, randomly oriented absorbing particles considering changes in shape, porosity and refractive index. These studies have importance regarding the inversion of physical properties of small particles as measured in the laboratory and the dust properties in various astrophysical and atmospherical environments. We have found that size distributions of randomly oriented irregular particles of different shape, including large aspect ratio particles, show similar scattering matrix elements as a function of the scattering angle, in contrast with the pattern found for regularly shaped particles of varying axis ratios, for which the scattering matrix elements as a function of the scattering angle show much larger differences among them. Regarding porosity, we have found a very different pattern in the scattering matrix elements for an ensemble of compact and porous particles. In particular, the linear polarization for incident unpolarized light produced by compact and absorbing particles of large size parameter tend to mimic the pattern found for large absorbing spheres. For porous particles, however, the linear polarization for incident unpolarized light tends to decrease as the size of the particle grows, with the maximum being displaced towards smaller and smaller scattering angles.     

Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200

The applicability, efficiency, and accuracy of the pseudo-spectral time domain (PSTD) method are investigated with specific emphasis on the computation of the single-scattering properties of homogeneous dielectric particles. By truncating the high spectral terms, the Gibbs phenomenon is eliminated, and, consequently, the applicability of the PSTD is enhanced. The PSTD simulations for ice spheres, with moderate refractive indices and size parameters up to 200, are compared with the exact Lorenz–Mie solutions at three wavelengths. In addition, the comparison is extended to a case with an extremely large refractive index (7.150+i2.914) and size parameters up to 40. Furthermore, the single-scattering properties of randomly oriented spheroids and circular cylinders for size parameters up to 150 and 75, respectively, are calculated with the PSTD in comparison with those computed from the T-matrix method. The aspect ratio of the spheroid and the diameter-to-length ratio of the circular cylinder are 0.5 and 1, respectively. The relative errors, given by the PSTD for these randomly oriented non-spherical particles, are smaller than 2% for the extinction efficiencies and asymmetry factors and less than 30% for the phase function. The PSTD is also employed to compute the phase matrices of randomly oriented hexagonal columns with size parameters of 50 and 100. The simulations show the PSTD to be a robust method for simulating the single-scattering properties of particles with small-to-medium size parameters and for a wide range of refractive indices.     

Modeling single-scattering properties of small cirrus particles by use of a size-shape distribution of ice spheroids and cylinders

In this study, we model single-scattering properties of small cirrus crystals using mixtures of polydisperse, randomly oriented spheroids and cylinders with varying aspect ratios and with a refractive index representative of water ice at a wavelength of 1.88 μm. The Stokes scattering matrix elements averaged over wide shape distributions of spheroids and cylinders are compared with those computed for polydisperse surface-equivalent spheres. The shape-averaged phase function for a mixture of oblate and prolate spheroids is smooth, featureless, and nearly flat at side-scattering angles and closely resembles those typically measured for cirrus. Compared with the ensemble-averaged phase function for spheroids, that for a shape distribution of cylinders shows a relatively deeper minimum at side-scattering angles. This may indicate that light scattering from realistic cirrus crystals can be better represented by a shape mixture of ice spheroids. Interestingly, the single-scattering properties of shape-averaged oblate and prolate cylinders are very similar to those of compact cylinders with a diameter-to-length ratio of unity. The differences in the optical cross sections, single-scattering albedo, and asymmetry parameter between the spherical and the nonspherical particles studied appear to be relatively small. This may suggest that for a given optical thickness, the influence of particle shape on the radiative forcing caused by a cloud composed of small ice crystals can be negligible.     

基于组合拟合法的冰晶粒子的光散射计算

利用组合拟合法计算了冰晶粒子的单次散射特性。给出了消光效率因子、单次散射反照度及非对称因子的拟合公式,利用拟合公式对有效粒子尺度为20μm和120μm的六种冰晶粒子的消光效率因子、单次散射反照度及非对称因子进行了计算。结果表明,粒子的消光效率因子、单次散射反照率和非对称因子随着入射波长的增加有着较大的起伏,后两者随着波长的增加而变化趋势基本一致;对于单次散射反照率来说,在可见光波段,反照率非常接近于1;在短波段,粒子的非对称因子变化较小,并且随着波长的增加,非对称因子会逐渐增大。     

The scattering matrix for size distributions of irregular particles: An application to an olivine sample

We have compared simulated and measured scattering matrices of a size distribution of olivine particles at wavelengths of 633 and 442 nm. The computations were carried out for size distributions of irregularly-shaped compact particles with different average projected areas using the discrete-dipole approximation (DDA). The results of the comparison show that the model of irregularly-shaped particles mimic the observations far better than the results given by spheres, spheroids or rectangular prisms having a wide range in aspect ratios. The computed scattering matrices for size distributions of irregularly-shaped particles do not depend very strongly on the precise particle shape assumed, providing a method to infer certain physical properties of an ensemble of natural dust particles, such as the refractive index, when some information on the sample, as the size distribution, is known a priori.     

Effect of ice crystal shape and effective size on snow bidirectional reflectance

We tested the applicability of three rigorous radiative transfer computational approaches, namely, the discrete ordinates radiative transfer (DISORT) method, the adding–doubling approach, and an efficient computational technique based on Ambartsumian's nonlinear integral equation for computing the bidirectional reflectance of a semi-infinite layer. It was found that each of these three models, in a combination with the truncation of the forward peak of the bulk scattering phase functions of ice particles, can be used to simulate the bidirectional reflectance of a semi-infinite snow layer with appropriate accuracy. Furthermore, we investigate the sensitivity of the bidirectional reflectance of a homogeneous and optically infinite snow layer to ice crystal habit and effective particle size. It is shown that the bidirectional reflectance is not sensitive to the particle effective size in the visible spectrum. The sensitivity of the bidirectional reflectance in the near-infrared spectrum to the particle effective size increases with the increase of the incident wavelength. The sensitivity of the bidirectional reflectance to the effective particle size and shape is attributed fundamentally to the sensitivity of the single-scattering properties to particle size and shape. For a specific ice crystal habit, the truncated phase function used in the radiative transfer computations is not sensitive to particle effective size. Thus, the single-scattering albedo is primarily responsible for the sensitivity of the bidirectional reflectance to particle size, particularly, at a near-infrared wavelength.     

Light scattering by large Saharan dust particles: Comparison of modeling and experimental data for two samples

Light scattering by large mineral-dust particles with small-scale surface roughness is investigated by comparing model simulations with laboratory-measured scattering matrices of two distinct dust samples collected from the Sahara desert. The samples have been chosen on the basis of their large effective radii, and the simulations are based on their measured size distributions. Size parameters larger than about 30 are modeled using a modified ray-optics model RODS (Ray optics with diffuse and specular interactions), while smaller particles are simulated with a T-matrix model. RODS allows us to mimic the surface roughness of large dust particles by covering the particle surface by a thin layer of external scatterers with specific single-scattering properties. The Gaussian-random-sphere geometry is used for the shapes of large dust particles. Small particles are modeled as an axial-ratio distribution of spheroids with smooth surfaces. One of the samples consists wholly of large particles and its scattering matrix can be reproduced very well by the RODS model, except for the phase function. The incorporation of wavelength-scale roughness is, however, necessary for good fits. The other sample, consisting of both small and large particles, proves more challenging to match with simulations. The analysis indicates, however, that the difficulties arise at least partially from the small-particle contribution, while RODS results are consistent with the measurements. Further, the results imply that the agreement with measurements would improve if roughness could also be accounted for in the small-particle simulations. Overall, the RODS method seems promising for modeling the optical properties of mineral-dust particles much larger than the wavelength.     

Microwave scattering properties of sand particles: Application to the simulation of microwave radiances over sandstorms

The single-scattering properties of sand/dust particles assumed to be ellipsoids are computed from the discrete dipole approximation (DDA) method at microwave frequencies 6.9-89.0 GHz in comparison with the corresponding Lorenz-Mie solutions. It is found that the single-scattering properties of sand particles are strongly sensitive to the shapes of the particles. The bulk scattering properties of sandstorms composed of spherical or nonspherical particles are investigated by averaging the single-scattering properties of these particles over log-normal particle size distributions. Furthermore, a vector radiative transfer model is used to simulate microwave radiances. The microwave brightness temperatures in the vertical polarization model are essentially not sensitive to sand particle habit, whereas microwave brightness temperature polarization differences are influenced by particle habit. It is shown that microwave brightness temperatures and brightness temperature polarization differences may be useful for estimating the effective particle sizes and mass loading of sandstorms.     

Effect of the orientation of the optic axis on simulated scattering matrix elements of small birefringent particles

We study how the orientation of the optic axis affects single-scattering properties for small, birefringent calcite particles simulated using DDSCAT 7.1.1. We consider two irregular model particles, a flake and a rhomboid, in either a (i)?fixed or (ii)?random orientation. Simulations are performed for three volume-equivalent radii of 0.1, 0.45, and 1.0?μm. For each target, we repeat the computations for three sets of orientations of the optic axis. When a fixed spatial orientation of the target is considered, the simulations are significantly affected by the orientation of the optic axis. However, the effect is considerably weaker when assuming the same targets in random spatial orientation.     

Numerical accuracy of “equivalent” spherical approximations for computing ensemble-averaged scattering properties of fractal soot aggregates

Numerical accuracy is quantitatively assessed in conjunction with the application of four “equivalent” spherical approximations in the computation of the optical properties of small aggregate soot particles. The approximations are based on equal volume, equal surface area, the radius of gyration, and a collection of independent spheres with the same volume and the same volume-to-projected area ratio as the original nonspherical particle. A diffusion-limited cluster-cluster aggregation algorithm is used to specify the geometries of soot particles. Furthermore, the Generalized Multi-particle Mie (GMM) method is utilized to compute the single-scattering properties of individual soot aggregate particles assumed to be randomly oriented in space. The ensemble-averaged single-scattering properties of the particles are obtained by accounting for the probability distribution functions (PDF) of the number of monomers per aggregate at two wavelengths, 0.628 and 1.1 μm. It is shown that all of the aforementioned equivalent-spherical approximations lead to large errors in the computation of the phase function.     

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.     

T2 relaxation induced by clusters of superparamagnetic nanoparticles: Monte Carlo simulations

Clustering strongly affects the transverse (T2) relaxation induced by superparamagnetic nanoparticles in magnetic resonance experiments. In this study, we used Monte Carlo simulations to investigate systematically the relationship between T2 values and the geometric parameters of nanoparticle clusters. We computed relaxation as a function of particle size, number of particles per cluster, interparticle distance, and cluster shape (compact vs. linear). We found that compact clusters induced relaxation equivalent to similarly sized single particles. For small particles, the shape and density of clusters had a significant effect on T2. In contrast, for larger particles, T2 relaxation was relatively independent of cluster geometry until interparticle distances within a cluster exceeded ten times the particle diameter. Results from our simulations suggest principles for the design of nanoparticle aggregation-based sensors for MRI.     

椭球模型下通过雾场的多重光散射谱

由于雾滴的非球形、多重散射特性以及几何光学效应,光通过实际雾场的散射问题成为一个研究难点. 建立了近于实际的椭球雾滴模型,考虑光的衍射、透射及反射特性后,利用辐射传播方程得到了在不同的雾滴大小分布 及不同的雾滴形状分布下通过雾场的多重散射光强公式.在两种特例下与已有的结果较为相符,说明了方法的可靠性. 计算表明:与随机取向的非球形颗粒场的散射谱呈圆形特征不同,通过椭球形雾滴场的散射谱呈椭圆特征, 不同方位角的散射光强角分布有所差异,雾滴的形状因子越接近于1,差异越小;与单散射不同, 散射谱中的条纹随光学厚度增大逐步消失;对于不同大小分布及不同形状分布的雾滴场, 在不同方位角及不同观察角的散射光强随光学厚度τ的增加总是先增大再减小,光强的极大值位置在τ = 1.0---3.0 范围内.计算同时还表明,由于多数情况下实际雾场的雾滴大小偏差较大, 因而通过雾场的散射谱将呈现以中央亮斑为中心向四周弥散的图样.     

Evidence for particle size–shape correlations in the optical properties of silicate clay aerosol

Accurate modeling of the optical properties of atmospheric mineral dust is important for climate modeling calculations and remote sensing data retrievals. Atmospheric mineral dust in the accumulation mode size range is often rich in silicate clays including kaolinite and illite. This is important because dust optical properties depend on particle shape, and fundamental clay particles are known to consist of very thin flakes.In this combined laboratory and modeling study, we investigate the optical properties (IR extinction and visible light scattering) of two samples of silicate clay dust aerosol, kaolinite and illite. Particle size distributions are measured simultaneously with the optical properties. T-Matrix theory based simulations using a spheroidal particle approximation are compared with experimental data. We find that the full range of visible scattering and polarimetry data, and IR extinction profiles are not well fit by assuming a single size–shape distribution for the aerosol. In contrast, a simple bimodal distribution model that treats small particles (fundamental clay flakes) in the distribution as highly eccentric oblate spheroids with axial ratio parameters ≥5, but approximates larger particles by a more moderate shape distribution with axial ratio parameters <3, gives better agreement with the full range of experimental data. These conclusions are consistent with mineralogical data on the dimensions of fundamental clay particles.     

Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers

We analyze ground-based radar polarimetric observations of Saturn's rings at a wavelength of 12.6 cm by employing the model of a vertically and horizontally plane-parallel homogeneous slab composed of clumpy particles in the form of fractal aggregates of small ice monomers. Our model takes full account of the effects of polarization, multiple scattering, and coherent backscattering. Using efficient superposition T-matrix and vector radiative transfer codes, we perform computations of the backscattering circular polarization ratio for fractal aggregates generated with a cluster–cluster aggregation model and having the following characteristics: monomer refractive index m=1.78+i0.003; monomer packing density p=0.2; fractal dimensions D_f=2.5 and 3; and overall fractal radii R in the range 4?R?10 cm. In order to obtain physically realistic values of single-scattering properties of the aggregates we perform averaging over an ensemble of clusters generated for the same values of fractal parameters but having different geometrical configurations of the monomers. We conclude that in the framework of the above morphological model of Saturn's rings and the specific cluster–cluster aggregation procedure, it may be problematic to obtain a satisfactory and realistic agreement between theoretical computations and the observed values of the radar circular polarization ratio.     

Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry

The single-scattering properties of Gaussian random spheres are calculated using the discrete dipole approximation. The ensemble of model particles is assumed to be representative for a feldspar dust sample that is characteristic for weakly absorbing irregularly shaped mineral aerosol. The morphology of Gaussian random spheres is modeled based on a statistical shape analysis using microscope images of the dust sample. The size distribution of the dust sample is based on a particle sizing experiment. The refractive index of feldspar is estimated using literature values. All input parameters used in the light scattering simulations are thus obtained in an objective way based on the true properties of the mineral sample. The orientation-averaged and ensemble-averaged scattering matrices and cross sections of the Gaussian random spheres are compared with light scattering simulations using spheroidal shape models which have been shown to be applicable to the feldspar sample. The Gaussian random sphere model and the spheroidal shape model are assessed using the measured scattering matrix of the feldspar dust sample as a reference. Generally, the spheroidal model with strongly elongated prolate and strongly flattened oblate shapes agrees better with the measurement than the Gaussian random sphere model. In contrast, some features that are characteristic for light scattering by truly irregular mineral dust particles are rendered best by the Gaussian random sphere model; these features include the flat shape of the phase function and a minimum in the scattering matrix element F₂₂/F₁₁ as a function of the scattering angle.     

Prediction of particle sticking efficiency for fly ash deposition at high temperatures

The tendency of ash particles to stick under high temperatures is dictated by the ash chemistry, particle physical properties, deposit surface properties and furnace operation conditions. A model has been developed in order to predict the particle sticking efficiency for fly ash deposition at high temperatures. The model incorporates the particle properties relevant to the ash chemistry, particle kinetic energy and furnace operation conditions and takes into consideration the partial sticking behaviour and the deposit layer. To test the model, the sticking behaviours of synthetic ash in a drop tube furnace are evaluated and the slagging formation from coal combustion in a down-fired furnace is modelled. Compared with the measurements, the proposed model presents reasonable prediction performance on the particle sticking behaviour and the ash deposition formation. Through a sensitivity analysis, furnace operation conditions (velocity and temperature), contact angle and particle size have been found to be the significant factors in controlling the sticking behaviours for the synthetic ash particles. The ash chemistry and furnace temperature dictate the wetting potential of the ash particles and the melting ability of the deposit surface; particle size and density not only control the particle kinetic energy, but also affect the particle temperature. The furnace velocity condition has been identified as being able to influence the selective deposition behaviour, where the maximum deposition efficiency moves to smaller particles when increasing the gas velocity. In addition, the thermophoresis effect on the arrival rate of the particles reduces with increasing the gas velocity. Further, increasing the melting degree of the deposit layer could greatly enhance the predicted deposition formation, in particular for the high furnace velocity condition.     

Laser Simulations of the Destructive Impact of Nuclear Explosions on Hazardous Asteroids

We present the results of preliminary experiments at laser facilities in which the processes of the undeniable destruction of stony asteroids (chondrites) in space by nuclear explosions on the asteroid surface are simulated based on the principle of physical similarity. We present the results of comparative gasdynamic computations of a model nuclear explosion on the surface of a large asteroid and computations of the impact of a laser pulse on a miniature asteroid simulator confirming the similarity of the key processes in the fullscale and model cases. The technology of fabricating miniature mockups with mechanical properties close to those of stony asteroids is described. For mini-mockups 4–10 mm in size differing by the shape and impact conditions, we have made an experimental estimate of the energy threshold for the undeniable destruction of a mockup and investigated the parameters of its fragmentation at a laser energy up to 500 J. The results obtained confirm the possibility of an experimental determination of the criteria for the destruction of asteroids of various types by a nuclear explosion in laser experiments. We show that the undeniable destruction of a large asteroid is possible at attainable nuclear explosion energies on its surface.     

The effect of shape and size on the electronic properties of ultrafine metallic particles

The subject of ultrafine metallic particles is treated with emphasis on energy level statistics. The energy level statistics so far proposed are reviewed based on the effect of shape of particles. The deviation of the nature of the chemical bond and that of magnetic properties in small size systems from those of bulk is described. The relevant electronic properties are expressed by formulae that incorporate the effect of shape in addition to size. New and old experiments including NMR Knight shift and static magnetic susceptibility are analyzed by means of the proposed formulae. The shape of particles is discussed in connection with the preparation methods. A concept of “the degree of metallicity” is introduced to characterize the statistics of level spacing fluctuation of small metal particles. A number of electronic properties of small size materials are also explained in terms of their sizes. The systems examined are small particles and conjugated chain compounds. The concept of zero-dimensionality is proposed and it is correlated with certain conservation laws such as topological invariance (conservation of shape) and as a conservation of the number of spins (parity of electrons).