Hexagonal Columns Research Articles

Establishment and Preliminary Application of the Forward Modeling Method for Doppler Spectral Density of Ice Particles

Owing to the various shapes of ice particles, the relationships between fall velocity, backscattering cross-section, mass, and particle size are complicated. This affects the application of cloud radar Doppler spectral density data in the retrieval of the microphysical properties of ice crystals. In this study, under the assumption of six particle shape types, the relationships between particle mass, fall velocity, backscattering cross-section, and particle size were established based on existing research. Variations of Doppler spectral density with the same particle size distribution (PSD) of different ice particle types are discussed. The radar-retrieved liquid and ice PSDs, water content, and mean volume-weighted particle diameter were compared with airborne in situ observations in the Xingtai, Hebei Province, China, in 2018. The results showed the following. (1) For the particles with the same equivalent diameter (De), the fall velocity of the aggregates was the largest, followed by hexagonal columns, hexagonal plates, sector plates, and stellar crystals, with the ice spheres falling two to three times faster than ice crystals with the same De. Hexagonal columns had the largest backscattering cross-section, followed by stellar crystals and sector plates, and the backscattering cross-sections of hexagonal plates and the two types of aggregates were very close to those of ice spheres. (2) The width of the simulated radar Doppler spectral density generated by various ice crystal types with the same PSD was mainly affected by the particle’s falling velocity, which increased with the particle size. Turbulence had different degrees of influence on the Doppler spectrum of different ice crystals, and it also brought large errors to the PSD retrieval. (3) PSD comparisons showed that each ice crystal type retrieved from the cloud radar corresponded well to aircraft observations within a certain scale range, when assuming that only a certain type of ice crystals existed in the cloud, which could fully prove the feasibility of retrieving ice PSDs from the reflectivity spectral density.

Experimental Study on Hydro-mechanical Behaviour of Anisotropic Columnar Jointed Rock-Like Specimens

Columnar jointed rock masses (CJRM), characterized by regular arrays of polygonal prisms or columns, are exposed in the dam foundation of the Baihetan hydropower station and pose a challenge to the stability of the project. To understand the hydro-mechanical behaviour of Baihetan CJRM, triaxial compression experiments are carried out on artificial CJRM specimens with regular arrays of hexagonal columns, which are similar to the actual CJRM. Based on the experimental results, mechanical and hydraulic behaviour of CJRM is studied. It is found that the compressive strength of CJRM varies in a typical U-shape with the joint inclination angle. Three failure modes associated with the angle of joint inclination are observed. The evolution of permeability with stress exhibits distinct phased characteristics: initial compression stage, linear elastic stage, yield stage, and strain-softening stage. The results of this study provide helpful information for the design and construction of the Baihetan project involving CJRM.

Morphology evolution of acetic acid-modulated MIL-53(Fe) for efficient selective oxidation of H2S

MIL-53(Fe) was synthesized using a “modulator approach” that utilizes acetic acid (HAc) as an additive to control the size and morphology of the resulting crystals. We demonstrate that after activation under vaccum at 100 °C, the MIL-53(Fe) functions well for H2S selective oxidation. The introduction of acetic acid in the presence of benzene-1,4-dicarboxylic acid (H2BDC) would result in a series of MIL-53(Fe) nanocrystals (denoted as MIL-53(Fe)-xH, x stands for the volume of added HAc with morphology evoluting from irregular particles to short hexagonal columns. The vacuum treatment facilitates the removal of acetate groups, thus generating Fe3+ Lewis acid sites. Consequently, the resulted MIL-53(Fe)-xH exhibits good catalytic activity (98% H2S conversion and 92% sulfur selectivity) at moderate reaction temperatures (100–190 °C). The MIL-53(Fe)-5H is superior to the traditional iron-based catalysts, showing stable performance in a test period of 55 h.

Implementation of an ice crystal single-scattering property database in the radiative transfer model SCIATRAN

Ice crystal single-scattering properties (single-scattering albedo, extinction cross section, scattering matrix) determine the radiative transfer through ice clouds and snow layers. In the radiative transfer model SCIATRAN, only a limited range of particle sizes and shapes were available. Consequentially, and to achieve a much more realistic representation, a new database of nine ice crystals (droxtals, solid and hollow columns, aggregates of eight hexagonal solid columns, hexagonal plates, aggregates of five or 10 hexagonal plates, and solid and hollow bullet rosettes) with maximum dimensions from 2 to 10 000 µm has been implemented and tested. SCIATRAN now includes the relevant single-scattering albedo, extinction cross section, and scattering matrix. Additionally, the scattering matrix is expanded in generalized spherical functions based on a combination of trapezoidal and Gaussian quadrature. This implemented database in conjunction with a built in user-defined particle size distribution and an arbitrary habit ratio enable the radiative transfer through a variety of layers, composed of polydisperse ice particles having particular habit mixtures. A comparison of satellite measured snow surface reflectances with respective simulations demonstrates that assuming ice crystal habit mixtures rather than single-habits as snow crystals reduces significantly the differences between the model and satellite data from 8.5 % to 2 %.

Study on the growth morphology and induction mechanism of strontium hydroxyapatite controlled by anionic and cationic surfactants

Abstract Using Sr(NO3)2, NaH2PO4 and urea as the raw starting materials, under the induction of anionic/cationic surfactants (sodium dodecyl benzene sulfonate (SDBS) and dodecy dimethyl benzyl ammonium bromide (DDBAB)), strontium hydroxyapatite (SrHAp) crystals with different morphology were successfully synthesized at low temperature (85 °C). The XRD patterns analysis showed that both surfactants could induce the growth of pure SrHAp crystals. The SEM images showed that the SrHAp crystals grew under DDBAB induction was one-dimensional hexagonal column along c-axis. The SEM and HRTEM images provided that the growth of SrHAp crystal induced by SDBS generated two-dimensional plate-like structure, along both a- and b-axis. It is indicated that the ionic structures of DDBAB and SDBS affect the crystal growth and development of the SrHAp hexagonal system. According to the crystal plane formation energy (Gibbs-Thomson formula) and the crystal plane normal growth rate formula, the crystal-induced directional growth model was obtained and its formation mechanism was analyzed. Our results revealed that the surface active fragment C21H38N+ of DDBAB and the fragment C18H29SO3− of SDBS could change the interfacial energy (γ(hkl)) of the crystal plane, affect the normal growth rate of the crystal plane (І(hkl)), and finally control the crystal morphology of SrHAp. Therefore, under the induction of C21H38N+, γc{001} Іm{100} enable the crystal grow along the c-axis resulting in the hexagonal column morphology of SrHAp crystal. However, the induction of C18H29SO3− gives γc{001} > γm{100}, Іm{100} > Іc{001}, which drives the crystals grow along both a- and b-axis generating plate-like morphology of SrHAp crystal.

Experimental characterization of the influence of dispersant addition on rising oil droplets in water column

The accident of the Deepwater Horizon platform in the Gulf of Mexico in April 2010 clearly shows the importance of fully understanding the oil and gas leaks phenomena in the water column and their consequences at the sea surface. While the modelling of the rise of oil droplets in the water column is widely documented, in particular through analytical model using slip velocity concept, there is a lack of information on the effect of dispersants addition on rising oil droplet. Yet dispersants, given their surfactant capacity, will necessarily modify the oil droplets behavior in the water column in terms of buoyancy due to the oil shape variations. This paper contributes to the characterization of dispersant effect on accidental oil release especially in term of physical modification for oil droplets. To investigate the study, experimental tests were performed in the Cedre Experimental Column (CEC) which is a five meter high hexagonal column with internal diameter of 1 m and total capacity of 4.50 m3 (Le Floch, 2009). This experimental device is equipped with an injection system, equipable with different nozzles diameters, and two high speed video recording systems based on shadowgraphy. It is designed to observe the shape of the droplets, including rise trail, and the dissolution rate during the ascension to the surface. This paper presents the physical modifications undergone by an oil droplet when surface active molecules are positioned at its interface with seawater. The oil droplets observation shows the addition of dispersant decreases the average droplet volume and conversely increases the number of droplets observed in the water column. Thus, the water-oil contact surface area is increased, enhancing the exchanges between these two phases, in particular in terms of the dissolution of the lightest hydrocarbon molecules. In terms of physical appearance, oil droplets showing spherical shape modify to elliptical shape from which filaments of varying sizes are fluttering. Changing shape implies a variation in the oil droplets slip velocity throughout the seawater column as well as the definition of a more complex trajectory. These two changes tend to decrease the buoyancy of oil droplets in the water column. The formation of a plume instead of surface oil slick occurs and is carried by marine currents.

A new look at the environmental conditions favorable to secondary ice production

Abstract. This study attempts a new identification of mechanisms of secondary ice production (SIP) based on the observation of small faceted ice crystals (hexagonal plates or columns) with typical sizes smaller than 100 µm. Due to their young age, such small ice crystals can be used as tracers for identifying the conditions for SIP. Observations reported here were conducted in oceanic tropical mesoscale convective systems (MCSs) and midlatitude frontal clouds in the temperature range from 0 to −15 ∘C and heavily seeded by aged ice particles. It was found that in both MCSs and frontal clouds, SIP was observed right above the melting layer and extended to higher altitudes with colder temperatures. The roles of six possible mechanisms to generate the SIP particles are assessed using additional observations. In most observed SIP cases, small secondary ice particles spatially correlated with liquid-phase, vertical updrafts and aged rimed ice particles. However, in many cases, neither graupel nor liquid drops were observed in the SIP regions, and therefore, the conditions for an active Hallett–Mossop process were not met. In many cases, large concentrations of small pristine ice particles were observed right above the melting layer, starting at temperatures as warm as −0.5 ∘C. It is proposed that the initiation of SIP above the melting layer is stimulated by the recirculation of large liquid drops through the melting layer with convective turbulent updrafts. After re-entering a supercooled environment above the melting layer, they impact with aged ice, freeze, and shatter. The size of the splinters generated during SIP was estimated as 10 µm or less. A principal conclusion of this work is that only the freezing-drop-shattering mechanism could be clearly supported by the airborne in situ observations.

Algorithm for Solving the Light Scattering Problem for Arbitrary Shaped Ice Particles with Absorption

The work presents the estimation of the absorption influence effect on the light scattering problem for atmospheric ice particles. The calculation of light scattering matrices was performed for two types of particles: the solid hexagonal columns and the arbitrary shaped particles. The range of the size for both types of particles varies from 10 μm to 1000 μm. The results of the research show an insignificant decrease of the value of the M11 element of the light scattering matrix for small-sized particles for all chosen wavelengths (0.355 μm, 0.532 μm, 1.064 μm и 1.6 μm), and a significant decrease for big-sized particles for a 1.6 μm wavelength.

Improvements in the computational efficiency and convergence of the Invariant Imbedding T-matrix method for spheroids and hexagonal prisms.

The invariant-imbedding T-matrix (II-TM) method is a numerical method for accurately computing the single-scattering properties of dielectric particles. Because of the linearity of Maxwell's equations, the incident electric field and the scattered electric field can be related through a transition matrix (T-Matrix). The II-TM method computes the T-matrix through a matrix recurrence formula which stems from an electromagnetic volume integral equation. The recurrence starts with an inscribed sphere within the particle and ends with the circumscribed sphere of the particle. For each iteration, a matrix known as the U-matrix is computed with the Gauss Legendre (GL) quadrature, and matrix inversion is subsequently performed to obtain the T-matrix corresponding to the portion of the particle enclosed by the spherical shell. We modify a commonly used scheme to avoid applying the quadrature scheme to discontinuities. Moreover, we apply a new scheme to generate nodes and weights in conjunction with the GL quadrature. This leads to a considerable improvement on convergence and computational efficiency in the cases of hexagonal prisms and spheroids. The basic shapes of ice crystals in the atmosphere are hexagonal columns and plates. The single-scattering properties of hexagonal ice prisms are important to atmospheric optics, radiative transfer, and remote sensing. We demonstrate that the present approach can significantly accelerate the convergence in simulating light scattering by hexagonal ice crystals.

Oriented Ice Crystals: A Single-Scattering Property Database for Applications to Lidar and Optical Phenomenon Simulations

Abstract A database (TAMUoic2019) of the scattering, absorption, and polarization properties of horizontally oriented hexagonal plates (HOPs) and horizontally oriented hexagonal columns (HOCs) at three wavelengths (355, 532, and 1064 nm) is developed for applications to radiative transfer simulations and remote sensing implementations involving oriented ice crystals. The maximum dimension of oriented ice crystals ranges from 50 to 10 000 μm in 165 discrete size bins. The database accounts for 94 incident directions. The single-scattering properties of oriented ice crystals are computed with the physical-geometric optics method (PGOM), which is consistent with the invariant-imbedding T-matrix method for particles with size parameters larger than approximately 100–150. Note that the accuracy of PGOM increases as the size parameter increases. PGOM computes the two-dimensional phase matrix as a function of scattering polar and azimuth angles, and the phase matrix significantly varies with the incident direction. To derive the bulk optical properties of ice clouds for practical radiative transfer applications, the optical properties of individual HOPs and HOCs are averaged over the probability distribution of the tilting angle of oriented ice crystals based on the use of the TAMUoic2019 database. Simulations of lidar signals associated with ice clouds based on the bulk optical properties indicate the importance of the fraction of oriented ice crystals and the probability distribution of the tilting angle. Simulations of optical phenomena caused by oriented ice crystals demonstrate that the computed single-scattering properties of oriented ice crystals are physically rational.

Extinction Matrix of Atmospheric Ice Crystals with Their Preferred Spatial Orientation for the Visible and IR Regions

The extinction matrix for an ensemble of hexagonal ice plates and columns is presented. The extinction matrix for droxtal and bullet crystals has been estimated. The calculations have been carried out for particles with characteristic dimensions from 10 to 100 μm and wavelengths from 0.3 to 10 μm assuming a gamma distribution of particle size with a width parameter μ < 4. It has been found that the extinction matrix of an ensemble of atmospheric ice crystals in the visible wavelength region is a unit matrix with a coefficient equal to the doubled area of the particle projection. The error of this representation does not exceed tenths of a percent and does not depend on the type of crystals and their spatial orientation. It has also been found that such a representation of the extinction matrix in the IR region is possible only for hexagonal columns, bullets, and similar crystals with a characteristic size greater than 20 μm for wavelengths less than 8 μm.

Constraints on Mars Aphelion Cloud Belt phase function and ice crystal geometries

This study constrains the lower bound of the scattering phase function of Martian water ice clouds (WICs) through the implementation of a new observation aboard the Mars Science Laboratory (MSL). The Phase Function Sky Survey (PFSS) was a multiple pointing all-sky observation taken with the navigation cameras (Navcam) aboard MSL. The PFSS was executed 35 times during the Aphelion Cloud Belt (ACB) season of Mars Year 34 over a solar longitude range of Ls=61.4°−156.5°. Twenty observations occurred in the morning hours between 06:00 and 09:30 LTST, and 15 runs occurred in the evening hours between 14:30 and 18:00 LTST, with an operationally required 2.5 h gap on either side of local noon due the sun being located near zenith. The resultant WIC phase function was derived over an observed scattering angle range of 18.3°–152.61°, normalized, and compared with 9 modeled phase functions: seven ice crystal habits and two Martian WIC phase functions currently being implemented in models. Through statistical chi-squared probability tests, the five most probable ice crystal geometries observed in the ACB WICs were aggregates, hexagonal solid columns, hollow columns, plates, and bullet rosettes with p-values greater than or equal to 0.60, 0.57,0.56,0.56, and 0.55, respectively. Droxtals and spheres had p-values of 0.35, and 0.2, making them less probable components of Martian WICs, but still statistically possible ones. Having a better understanding of the ice crystal habit and phase function of Martian water ice clouds directly benefits Martian climate models which currently assume spherical and cylindrical particles.

Photo-Enhanced Acid Chemical Etching of High-Quality Aluminum Nitride Grown by Metal-Organic Chemical Vapor Deposition

Photo-enhanced chemical (PEC) etch of wurtzite aluminum nitride (AlN) was investigated to overcome its low etch rate. Epitaxial AlN grown on Al2O3 substrate by metal-organic chemical vapor deposition method was immersed in phosphoric acid at different temperatures under 185 nm deep-UV excitation. An inverted pyramid structure with {10-1-1} faces initially appeared, after chemical etching, evolving into hexagonal columns with {1-100} m-planes. The PEC etch rate of m-plane AlN was six-fold higher than that of non-PEC one because the reaction was enhanced by the electron-hole pairs photo-generated by 185 nm wavelength. The decrease of the activation energy from 68.5 kJ/mol (non-PEC etch) to 48.1 kJ/mol (PEC etch) was extracted, implying a reaction-limited etching process. The PEC etch mechanism of wurtzite AlN in phosphoric acid was proposed, including the initiation and growth of the etch pit and the agglomeration of the hexagonal columns. Our results propose a facile method to control the surface morphology of AlN-based electronic and optoelectronic devices.

ON THE CONVERGENCE OF NUMERICAL COMPUTATIONS FOR BOTH EXACT AND APPROXIMATE SOLUTIONS FOR ELECTROMAGNETIC SCATTERING BY NONSPHERICAL DIELECTRIC PARTICLES (INVITED REVIEW)

We summarize the size parameter range of the applicability of four light-scattering computational methods for nonspherical dielectric particles. These methods include two exact methods - the extended boundary condition method (EBCM) and the invariant imbedding T-matrix method (II-TM) and two approximate approaches - the physical-geometric optics method (PGOM) and the improved geometric optics method (IGOM). For spheroids, the single-scattering properties computed by EBCM and II-TM agree for size parameters up to 150, and the comparison gives us confidence in using IITM as a benchmark for size parameters up to 150 for other geometries (e.g., hexagonal columns) because the applicability of II-TM with respect to particle shape is generic, as demonstrated in our previous studies involving a complex aggregate. This study demonstrates the convergence of the exact II-TM and approximate PGOM solutions for the complete set of single-scattering properties of a nonspherical shape other than spheroids and circular cylinders with particle sizes of ~ 48λ(size parameter ~150), specifically a hexagonal column with a length size parameter of kL = 300 where k = 2π/λ and L is the column length. IGOM is also quite accurate except near the exact 180°backscattering direction. This study demonstrates that a synergetic combination of the numerically-exact II-TM and the approximate PGOM can seamlessly cover the entire size parameter range of practical interest. To demonstrate the applicability of the approach, we compute the optical properties of dust particles and demonstrate a downstream application to the retrieval of dust aerosol optical thickness and effective particle size from satellite polarimetric observations.

Experimental Investigation on the Axially Loaded Performance of Notched Hexagonal Concrete‐Filled Steel Tube (CFST) Column

This study aimed to investigate the static performance of notched hexagonal concrete‐filled steel tube (CFST) stub columns through axial loading. Notch length, notch location, and notch direction in 14 CFST stub columns were experimentally studied. Stress process, failure mechanism, and ultimate strength in the notched CFST columns were analyzed. Results show that notches in steel tubes can weaken the restraining effect of steel pipes on core concrete and induce a decrease in the ultimate strength of specimens. The failure mode of components is greatly affected by notch orientation. The notch is closed under axial compression in the horizontally notched specimen, and the slotting indicates outward buckling in the vertically notched specimen. Based on the test results, a method for calculating the ultimate strength of notched hexagonal CFST columns was established. This research encourages the extensive application of these structures in civil engineering.

Square and Hexagonal Columnar Liquid Crystals Confined in Square and Triangular Pores

AbstractColumnar liquid crystals confined in cylindrical pores are known to orient perpendicular to the pore axis, although for potential nanoelectronic applications they would need to be aligned axially. The X‐ray diffraction study reveals that while in all three compounds examined, the columns arrange in concentric circles in circular pores, axial alignment is indeed achieved for the hexagonal phase of a discotic hexa‐peri‐hexabenzocoronene in “triangular pores,” and for the square phase of a T‐shaped amphiphile in “square pores.” For the third compound, a carbazole dendron with very soft hexagonal columns, a new three‐circle configuration is observed by atomic force microscopy (AFM) in triangular pores. The complex structure of domain walls in columnar liquid crystals is thus seen for the first time on the level of individual columns. A simple estimation of free energies confirms that it is the distortion of polygonal columnar lattice that prevents axial orientation in circular pores. The model also explains the appearance of the three‐circle arrangement of soft columns.

Subwavelength acoustic topological edge states realized by zone folding and the role of boundaries selection

This article reports a realization of subwavelength acoustic topological edge states realized by a triangular array of hexagonal columns with Helmholtz resonators. Using the strategy of zone folding, Dirac cones can be folded into double Dirac cones to construct pseudo-spin states. By adjusting the length of both the center and corner units, topological phase transition as well as the common bulk bandgap can be achieved. The calculated results show that the acoustic metamaterials with different boundaries exhibit different bulk transmission properties. Topological acoustic metamaterials can be combined with different boundaries to construct nine different interfaces, and the simulation results show that nine different interfaces can exhibit robust, weak, and even disappearing topological edge states. We manufacture the samples and carry out experiments to test the transmission spectra of nine different interfaces. Experimental results demonstrate that a sound wave can transmit well along the topological interface 1 path compared with the other eight interface paths. This study provides a simple approach to create acoustic topological edge states at the subwavelength scale and experimentally confirms the influence of boundaries selection on acoustic topological insulators.

Modified Beam-Splitting 1 (MBS-1) Algorithm for Solving the Problem of Light Scattering by Nonconvex Atmospheric Ice Particles

A new algorithm for solving the problem of light scattering by nonconvex crystals typical for cirrus clouds is presented. It is based on the beam tracing algorithm for convex particles (Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences). The new algorithm is applied for solving the problem of light scattering by hollow-column particles and aggregates of hexagonal ice columns. It is an opensource freely available algorithm.

Mechanical performance of hexagonal multi-cell concrete-filled steel tubular (CFST) stub columns under axial compression

Multi-cell concrete-filled steel tubular (CFST) column is a type of composite members developing from conventional CFST columns. Featuring greater cross-sectional dimensions and the use of internal webs to separate inner concrete into smaller isolated cells, multi-cell CFST columns have been used in super high-rise buildings recently as the main vertical load bearing members. However, existing research on CFST members is mainly focused on conventional single-cell CFST members. To fill this research gap, this paper numerically investigates the mechanical performance of hexagonal multi-cell CFST stub columns under axial compression. A finite element analysis (FEA) model was initially established to simulate the mechanical performance of hexagonal multi-cell CFST columns. The FEA model was validated against existing experimental data. The mechanical performance of the multi-cell CFST columns were analysed, including the full-range load versus deformation relationships, the stress distributions of the main components and the distribution of contact stress on each concrete cell. A parametric study was then conducted to investigate the sensitivity of various geometric and material parameters on the compressive behaviour of multi-cell CFST columns. Finally, analytical formulae were derived to predict the axial compressive ultimate strength of hexagonal multi-cell CFST columns. The methods were found to be acceptable with reasonably good accuracy.

Optical properties of ZnO nanorod films prepared by CBD method

ZnO nanorods were grown on ITO substrate by CBD method. The XRD and SEM show that nanorods with hexagonal column structure were uniformly distributed. Then the optical properties of NRs were investigated. The transmittance spectrum shows a sharp absorption edge in the UV region. The reflection spectrum has a certain oscillation frequency, so the thickness of film can be obtained by the principle of light interference. The PL spectrum shows a UV emission peak at about 380 nm and a broad green emission centered at around 550 nm. By readily adjusting the preparation parameters, the green emission was very weak.