Shells Of Constant Thickness Research Articles

Growth per cycle of alumina atomic layer deposition on nano- and micro-powders

Core–shell powders consisting of a tungsten particle core and thin alumina shell have been synthesized using atomic layer deposition in a rotary reactor. Standard atomic layer deposition of trimethylaluminum/water at 150 °C utilizing a microdosing technique was performed on four different batches of powder with different average particle sizes. The particle size of the powders studied ranges from ∼25 to 1500 nm. The high mass-thickness contrast between alumina and tungsten in transmission electron microscopy images demonstrates that the particle core/shell interface is abrupt. This allows for the uncomplicated measurement of alumina thickness and therefore the accurate determination of growth per cycle. In agreement with prior works, the highest growth per cycle of ∼2 Å/cycle occurred on the batch of powder with the smallest average particle size and the growth per cycle decreased with increasing average particle size of a powder batch. However, the growth per cycle of the alumina film on an individual particle in a batch is shown to be independent of the size of an individual particle, and therefore, a powder batch which consists of particles size spanning orders of magnitude has constant shell thickness on all particles. This uniformity of thickness on different particle sizes in a particular batch is determined to be due to the difficulty of removing residual water molecules from the powder during the purging cycle of the atomic layer deposition (ALD) process. Therefore, rotary ALD on a single batch of powder with wide particle size distribution provides the same shell thickness regardless of individual particle size, which may have positive implications for particle ALD applications where the shell thickness determines critical parameters, such as particle passivation and manipulation of optical properties.

Determination of the Natural Frequencies of an Elliptic Shell of Constant Thickness by the Finite-Element Method

We study natural vibrations of a thin isotropic elliptic shell of constant thickness by the finite-element method realized with the use of the high-performance FEMAR software developed for the engineering analyses. The comparative analysis of the numerical results and experimental data is carried out.

Effect of in-situ formed core–shell inclusions on the mechanical properties and impact fracture of polypropylene

To obviate the reduction of stiffness in rubber toughened and yield strength in rigid particle toughened iPP, various strategies were adopted. Here, we report on the static and impact properties of isotactic polypropylene (iPP) with in situ formed (rigid thermotropic liquid crystalline core)–(soft copolymer shell) inclusions (RCSS inclusions). We found that, at constant soft shell thickness (ts) and stiffness (Es), the elastic modulus of iPP/RCSS (Ec) increased with the total RCSS volume fraction (vRCSS), and, at constant vRCSS, the Ec increased with Es. At constant ts and Es, the yield strength of iPP/RCSS (σyc) decreased with the vRCSS and, at constant vRCSS and ts, the σyc decreased with Es in an agreement with the simple micromechanics models of Matonis and Small. At small vRCSS, the changes in Ec and σyc with vRCSS contributed simultaneously to the significant enlargement of the crack tip plastic zone size, enhancing the impact fracture toughness in terms of the apparent critical strain energy release rate (Gc′), substantially, without significantly reducing stiffness and yield strength. The SEM fractography revealed extension of the RCSS inclusions into fibrous shape providing an additional means for dissipation of mechanical energy stored in the fracturing solid. Experimental data agreed reasonably well with the prediction based on a simple mixed mode fracture model proposed earlier.

Finite Element Study of Human Pelvis Model in Side Impact for Chinese Adult Occupants

Objective: The occupant's pelvis is very vulnerable to side collision in road accidents. Finite element (FE) studies on pelvic injury help to design occupant protection devices to improve vehicle safety. This study was aimed to develop a highly biofidelic pelvis model of Chinese adults and assess its sensitivity to variations in pelvis cortical bone thickness, bone material properties, and loading conditions.Methods: In this study, 4 different FE models of the pelvis were developed from the computed tomography (CT) data of a volunteer representing the 50th percentile Chinese male. Two of them were meshed using entirely hexahedral elements with variable and constant cortical thickness distribution (the V-Hex and C-Hex models), and the others were modeled with hexahedral elements for cancellous bone and variable or constant thickness shell elements for cortical bone (the V-HS and C-HS models). In model developments, the semi-automatic multiblock meshing approach was employed to maintain the pelvis geometric curvature and generate a high-quality hexahedral mesh. Then, several simulations with postmortem human subjects (PMHS) tests were performed to obtain the most accurate model in predicting pelvic injury. Based on the most accurate model, sensitivity studies were conducted to analyze the effects of the cortex thickness, Young's modulus of the cortical and cancellous bone, impactor velocity, and impactor with or without padding on the biomechanical responses and injuries of pelvis.Results: The results indicate that the models with variable cortical bone thickness can give more accurate predictions than those with constant cortical thickness. Both the V-Hex and V-HS models are favorable for simulating pelvic response and injury, but the simulation results of the V-Hex model agree with the tests better. The sensitivity study shows that pelvic response is more sensitive to alterations in the Young's modulus of cortical bone than cancellous bone. Compared to failure displacement, peak force is more sensitive to the cortical bone thickness. However, displacement is more sensitive to the Young's modulus of cancellous bone than peak force. The padding attached on the impactor plays a significant role in absorbing the impact energy and alleviating pelvic injury.Conclusions: The all-hex meshing method with variable cortical bone thickness has the highest accuracy but is time-consuming. The cortical bone plays a determining role in resisting pelvic fracture. Peak impact force appears to be a reasonable injury predictor for pelvic injury assessment. Some appropriate energy absorbers installed in the car door can significantly reduce pelvic injury and will be beneficial for occupant protection.

Testing of the Kriging-based Finite Element to Shell Structures with Varying Thickness

A variant of the finite element method with Kriging basis functions has been recently developed and applied to plane, plate bending, and shell elastostatic problems. The main advantage of this novel method is that high degree of basis functions can be easily constructed without additional finite element nodes (such as mid-side and inner nodes). This paper revisits the formulation of the Kriging-based finite element method for analysis of curved shell structures, referred to as K-Shell, and presents new numerical tests to shell structures with varying thickness. The K-Shell was formulated based on degenerated 3D elasticity theory. The basis functions were constructed using a set of nodes covering several layers of triangular elements and were employed to approximate both the displacement and geometry. The quartic polynomial basis was chosen to alleviate shear and membrane locking. The K-Shell has been tested using a series of shell benchmark problems with constant shell thickness. The tests showed that K-Shell performed very well in analyzing moderately thick smooth shells. In this paper the K-Shell is tested using two modified shell benchmark problems with varying thickness, i.e. the modified pinched cylinder and the modified hemispherical shell with 18 degrees cut-off. The converged results of three-dimensional finite element model using commercial software Abaqus were used to assess the convergence of the results. The tests show that the performance of K-Shell in analyzing shells with varying thickness is satisfactory.

Study of oscillator strengths of hydrogenic impurity in a inhomogeneous finite and infinite spherical quantum dots

In this study, using the effective mass approximation and continuum dielectric media, the Schrödinger equation of nano systems is solved in terms of Whittaker functions. The oscillator strengths of both finite and infinite confining potentials from ground to the first and second allowed excited states are calculated with hydrogenic impurity. Regarding this, the oscillator strengths of system with hydrogenic impurity are studied by means of dipole approximation. The results show that in the case of constant shell thickness, when the inner radius of shell thickness is small, the value of oscillator strengths of both transitions (from ground to the first and second allowed excited states) is strongly affected by changes in shell thickness. In the large enough inner radius of shell thickness, the corresponding oscillator strength curves coincide for two transitions. Generally, these two transitions behave differently, i.e. by increasing the value of inner radius of shell, the first two transitions decrease and decrease respectively (due to conservation of probability).

Holographic Interferometry Study of the Free Vibrations of Cylindrical Shells of Constant and Variable Thickness

A holographic interferometry technique is used to determine the natural frequencies of isotropic circular cylindrical shells of constant and variable thickness and equivalent mass. It is established that the resonant frequencies of the cylindrical shell of variable thickness exceed those of the cylindrical shell of constant thickness of the same mass if circumferential halfwaves are few

Test example of calculation of thin-walled structures with truncated conical shell

Problems related to axisymmetric deformation of a truncated conical shell of constant thickness under the effect of a constant pressure are encountered when calculating the linear stress-deformed state of shell structures used in the nuclear fuel cycle within the framework of a model of the Kirchhoff–Love parameters. In practice, an analytic solution of such boundary-value problems leads to certain mathematical difficulties related to integration of one of the two differential decision equations, which is of fourth order, reduced to second order by means of a complex transformation. The differential decision equations for a truncated conical shell obtained following Meisner were transformed without any reduction in order to a new form more convenient for practical integration by means of infinite power series. The solution found in terms of power series was tested in compiling a test example of a calculation of the parameters of a deformed annular apparatus one of whose platforms is in the form of a truncated conical shell. The test example contains the results of an analytic solution of the above boundary-value problem and finite-element modeling using the CAN program. The error of the calculated stresses is estimated for an analytic solution, making it possible to consider the solution as a standard for comparison.

Nonylphenol polyethoxylate coated body-center-cubic iron nanocrystals for ferrofluids with technical applications

An approach to the design of a suitable system for technological applications, such as magneto-rheological fluids with controllable performance, showing high saturation magnetization and low coercivity and remanence, is presented. This approach is based on the synthesis of stable iron nanoparticles with a relatively thick polymeric coating—the non-ionic surfactant nonylphenol polyethoxylate—by a microemulsion method with NaBH4 as a reducing agent. X-ray diffractometry, Mössbauer spectroscopy, and high resolution electron microscopy reveal a body-center-cubic structure in the iron cores. The resulting nanoparticles are predominantly spherical, having an average core size of 7 nm and a constant shell thickness of 3 nm. Magnetic measurements reveal a higher saturation magnetization (127.4 Am2 kg−1 at 300 K and 153.2 Am2 kg−1 at 5 K) than in other approaches and a small coercive field of 12 mT. X-ray diffractometry results account for the presence of iron borate traces as a secondary phase, formed at the initial stages of the synthesis during the reduction process of precursors. Preliminary studies under oxidant conditions show a reduction in saturation magnetization lower than 9% over a six months period.

Oscillator strengths of the intersubband electronic transitions in the multi-layered nano-antidots with hydrogenic impurity

In this study, we have obtained the exact solutions of the Schr\"{o}dinger equation for a multi-layered quantum antidot (MLQAD) within the effective mass approximation and dielectric continuum model for the spherical symmetry. The MLQAD is nano-structured semiconductor system that consists of a spherical core (e.g. $Ga_{1-x}Al_{x}As $) and a coated spherical shell (e.g. $Ga_{1-y}Al_{y}As $) as the whole anti-dot is embedded inside a bulk material (e.g. $GaAs $). The dependence of the electron energy spectrum and its radial probability density on nano-system radius are studied. The numeric calculations and analysis of oscillator strength of intersubband quantum transition from the ground state into two first allowed excited states at the varying radius, for both the finite and infinite confining potential (CP) as well as constant shell thickness, are performed. It is shown that, in particular, the binding energy and the oscillator strength of the hydrogenic impurity of a MLQAD behave differently from that of a single-layered quantum antidot (SLQAD). For a MLQAD with finite core and shell CPs, the state energies and the oscillator strengths of the impurity are found to be dependent on the shell thickness. At the large core radius and very small shell thickness, our results are closer to respective values for a SLQAD that previously reported.

Investigation of free vibrations of noncircular cylindrical shells by the spline-collocation method

We consider free vibrations of thin isotropic elliptic shells of constant thickness on the basis of the spline-collocation method. It is established that, in the case of conservation of mass of elliptic and circular cylindrical shells, the frequencies of free vibrations of noncircular cylindrical shells decrease with increase in eccentricity of the cross section of the shell.

Correcting for a Density Distribution: Particle Size Analysis of Core–Shell Nanocomposite Particles Using Disk Centrifuge Photosedimentometry

Many types of colloidal particles possess a core-shell morphology. In this Article, we show that, if the core and shell densities differ, this morphology leads to an inherent density distribution for particles of finite polydispersity. If the shell is denser than the core, this density distribution implies an artificial narrowing of the particle size distribution as determined by disk centrifuge photosedimentometry (DCP). In the specific case of polystyrene/silica nanocomposite particles, which consist of a polystyrene core coated with a monolayer shell of silica nanoparticles, we demonstrate that the particle density distribution can be determined by analytical ultracentrifugation and introduce a mathematical method to account for this density distribution by reanalyzing the raw DCP data. Using the mean silica packing density calculated from small-angle X-ray scattering, the real particle density can be calculated for each data point. The corrected DCP particle size distribution is both broader and more consistent with particle size distributions reported for the same polystyrene/silica nanocomposite sample using other sizing techniques, such as electron microscopy, laser light diffraction, and dynamic light scattering. Artifactual narrowing of the size distribution is also likely to occur for many other polymer/inorganic nanocomposite particles comprising a low-density core of variable dimensions coated with a high-density shell of constant thickness, or for core-shell latexes where the shell is continuous rather than particulate in nature.

Geometrical Modeling of Concrete Microstructure for the Assessment of ITZ Percolation

Percolation is considered to be a critical factor affecting the transport properties of multiphase materials. In the case of concrete, the transport properties are strongly dependent on the interfacial transition zone (ITZ), which is a thin layer of cement paste next to aggregate particles. It is not computationally simple to assess ITZ percolation in concrete, as the geometry and topology of this phase is complex. While there are many advanced models that analyze the behavior of concrete, they are mostly based on the use of spherical or ellipsoidal shapes for the geometry of the aggregate inclusions. These simplified shapes may become unsatisfactory in many simulations, including the assessment of ITZ percolation. This paper deals with geometrical modeling of the concrete microstructure using realistic shapes of aggregate particles, the geometry of which is represented in terms of spherical harmonic expansion. The percolation is assessed using the hard core – soft shell model, in which each randomly-placed aggregate particle is surrounded by a shell of constant thickness representing ITZ.

Theoretical investigation of diffusion along columns packed with fully and superficially porous particles

Abstract Chromatographic columns packed with shell particles are now nearly twice more efficient than columns packed with conventional, fully porous particles. Shell particles are made of a solid core surrounded by a porous shell of constant thickness. Diffusion through the bed of packed columns is complex due to their heterogeneity. It involves diffusion through the external and the internal fluid, and surface diffusion. Six diffusion models are compared that combine these diffusion mechanisms. They involve the external porosity of the bed ( ϵ e ), the ratio of the core to the particle diameters ( ρ), and the ratio of the shell diffusivity to the bulk diffusion coefficient ( Ω). Four different theoretical approaches were considered. They are based on (1) the additivity of the mass flux densities modulated by the obstruction factors caused by non-porous spherical inclusions; (2) the effective medium theory of Landauer; (3) the effective medium theory of Garnett for spherical inclusions; and (4) the probabilistic theory of Torquato (for binary composite materials only). The two Landauer models fail because they cannot account for the obstruction factor imposed by the presence of non-porous spherical inclusions. The ternary Garnett model (3) provides an excellent approximation of the actual diffusion mechanism but the most physically relevant model seems to be the one derived from a combination of the Garnett model for a binary core–shell particle and of the Torquato model for random dispersion of contacting spheres in a matrix. Accurate measurements of axial dispersion coefficients are needed to validate or reject the semi-empirical parallel diffusion models and to select the most appropriate one. The results of such measurements made with the peak parking method for various compounds are reported in the companion paper.

Immobilized Polymer Fraction in Hyperbranched Polymer/Silica Nanocomposite Suspensions

The glass transition behavior of hyperbranched polymer (HBP) molecules with suspensions of silica and glass particles up to the concentrated regime (25 vol %) was analyzed by modulated differential scanning calorimetry (MDSC). The reversing and nonreversing components of the MDSC signal were measured on suspensions of untreated and silylated particle of size in the nanometer and micrometer ranges. The heat capacity step (ΔCp) at the glass transition of the HBP was found to be independent of silica loading for microparticles, whereas it decreased with increasing particle amount in the case of nanoparticles. A similar behavior was observed for the enthalpy relaxation. These changes in chain dynamics and the progressive suppression of aging were attributed to immobilization effects of the HBP at the surface of the particles, which became detectable only in the case of a very high specific surface. The immobilized HBP fraction was assumed to form a shell of constant thickness around individual particles and was calculated from the ΔCp at the transition. In the case of untreated particles with a silanol surface, the immobilized shell was formed by HBP molecules H-bonded to the particles. The thickness of the shell was found to be equal to 1.9 nm, which corresponded to half the size of the HBP. In the case of methacrylsilane-treated silica, the immobilized shell thickness was found to be equal to 1.3 nm, which corresponded to a monolayer of covalently bound silane. © 2010 American Chemical Society.

Local temperature pattern in plasmonic gold nanoshell: tuning the heat generation

Under quasi-steady-state conditions, we investigated the photo-heat conversion in a gold nanoshell by calculating the local equilibrium temperature distribution. In a thinner gold shell, the hot spots take place near the poles of both shell-surrounding and core-shell interface, perpendicularly to the incident field. In a thicker gold shell, the hot spots only take place near the core-shell interface. The maximum local temperature also depends greatly on the core media and shell thickness. Optimal heat generation can be obtained with small core dielectric constant and thin shell thickness. The mechanism of this local heating distribution is explained by the local field enhancement that is induced by the plasmon coupling.

Vibration of elliptic cylindrical shells: Higher order shell theory

The equations for the free vibration of an elliptic cylindrical shell of constant thickness were derived using a Ritz approach. A higher order shell theory is employed that includes the effects of shear deformation, rotary inertia, and symmetric and antisymmetric thickness stretch deformations. The frequency-wavenumber spectrum has seven branches: flexural, extensional, torsional, two thickness shear, and two thickness stretch. The resulting seven coupled algebraic equations are symmetric and positive definite. The shell has a constant thickness, h, finite length, L, and is "simply supported" at its ends, (z=0,L), where z is the axial coordinate. The elliptic cross-section is defined by the shape parameter, a, and the half-length of the major axis, l. The modal solutions are expanded in a doubly infinite series of comparison functions in terms of circular functions in the angular and axial coordinates. Numerical results for the natural frequencies were obtained for two values of h/l and L/l, and various shape parameters, including the limiting case of a simply supported cylindrical shell (a approximately 100).

Preparation of Core–Shell‐Structured Nanoparticles (with a Noble‐Metal or Metal Oxide Core and a Chromia Shell) and Their Application in Water Splitting by Means of Visible Light

Core-shell-structured nanoparticles, consisting of a noble metal or metal oxide core and a chromia (Cr(2)O(3)) shell, were studied as promoters for photocatalytic water splitting under visible light. Core nanoparticles were loaded by impregnation, adsorption or photodeposition onto a solid solution of gallium nitride and zinc oxide (abbreviated GaN:ZnO), which is a particulate semiconductor photocatalyst with a band gap of approximately 2.7 eV, and a Cr(2)O(3) shell was formed by photodeposition using a K(2)CrO(4) precursor. Photodeposition of Cr(2)O(3) on GaN:ZnO modified with a noble metal (Rh, Pd and Pt) or metal oxide (NiO(x), RuO(2) and Rh(2)O(3)) co-catalyst resulted in enhanced photocatalytic activity for overall water splitting under visible light (lambda>400 nm). This enhancement in activity was primarily due to the suppression of undesirable reverse reactions (H(2)-O(2) recombination and/or O(2) photoreduction) and/or protection of the core component from chemical corrosion, depending on the core type. Among the core materials examined, Rh species exhibited relatively high performance for this application. The activity for visible-light water splitting on GaN:ZnO modified with an Rh/Cr(2)O(3) core-shell configuration was dependent on both the dispersion of Rh nanoparticles and the valence state. In addition, the morphology of the Cr(2)O(3) photodeposits was significantly affected by the valence state of Rh and the pH at which the photoreduction of K(2)CrO(4) was conducted. When a sufficient amount of K(2)CrO(4) was used as the precursor and the solution pH ranged from 3 to 7.5, Cr(2)O(3) was successfully formed with a constant shell thickness (approximately 2 nm) on metallic Rh nanoparticles, which resulted in an effective promoter for overall water splitting.

Anionic surfactants templating route for synthesizing silica hollow spheres with different shell porosity

Silica hollow spheres with different shell porosity were simply synthesized with micelle and emulsion dual templating route. Various anionic surfactants, such as palmitic acid (C 16AA), N-acyl- l-phenylalanine (C 18Phe), N-palmitoyl- l-alanine (C 16AlaA) and oleic acid (OA) have been used as templates, and 3-aminopropyl-triethoxysilane (APES) and tetraethyl orthosilicate (TEOS) have been used as co-structure directing agent (CSDA) and silica source, respectively. The circle lamellar layer structure and mesopores vertical to the silica hollow spheres surface are believed to originate from the initial formation of amphiphilic carboxylic acid oil drop, which afterwards self-assemble to form the shell of hollow spheres and its mesostructure upon addition of CSDA and silica source. The mesoporous silica hollow spheres with high porosity could be achieved by adding a moderate amount of ethanol in the OA synthesis system, depending on the co-surfactant effect of ethanol that changes the curvature of micelles. The particle diameter and the hollow structure have been controlled by choosing different templates and by manipulating synthesis gel composition. The average particle diameter of the mesoporous silica hollow spheres were controlled in the range of 80–220 nm with constant shell thickness of ∼20 nm and constant mesopore size of ∼4 nm. Besides, the formation of the silica hollow spheres has been investigated in detail with reaction time. These mesoporous silica hollow spheres would have potential applications on catalysis, bimolecular encapsulation, adsorption, drug release, etc.

East–west faults due to planetary contraction

Contraction, expansion and despinning have been common in the past evolution of Solar System bodies. These processes deform the lithosphere until it breaks along faults. Their characteristic tectonic patterns have thus been sought for on all planets and large satellites with an ancient surface. While the search for despinning tectonics has not been conclusive, there is good observational evidence on several bodies for the global faulting pattern associated with contraction or expansion, though the pattern is seldom isotropic as predicted. The cause of the non-random orientation of the faults has been attributed either to regional stresses or to the combined action of contraction/expansion with another deformation (despinning, tidal deformation, reorientation). Another cause of the mismatch may be the neglect of the lithospheric thinning at the equator or at the poles due either to latitudinal variation in solar insolation or to localized tidal dissipation. Using thin elastic shells with variable thickness, I show that the equatorial thinning of the lithosphere transforms the homogeneous and isotropic fault pattern caused by contraction/expansion into a pattern of faults striking east–west, preferably formed in the equatorial region. By contrast, lithospheric thickness variations only weakly affect the despinning faulting pattern consisting of equatorial strike-slip faults and polar normal faults. If contraction is added to despinning, the despinning pattern first shifts to thrust faults striking north–south and then to thrust faults striking east–west. If the lithosphere is thinner at the poles, the tectonic pattern caused by contraction/expansion consists of faults striking north/south. I start by predicting the main characteristics of the stress pattern with symmetry arguments. I further prove that the solutions for contraction and despinning are dual if the inverse elastic thickness is limited to harmonic degree two, making it easy to determine fault orientation for combined contraction and despinning. I give two methods for solving the equations of elasticity, one numerical and the other semi-analytical. The latter method yields explicit formulas for stresses as expansions in Legendre polynomials about the solution for constant shell thickness. Though I only discuss the cases of a lithosphere thinner at the equator or at the poles, the method is applicable for any latitudinal variation of the lithospheric thickness. On Iapetus, contraction or expansion on a lithosphere thinner at the equator explains the location and orientation of the equatorial ridge. On Mercury, the combination of contraction and despinning makes possible the existence of zonal provinces of thrust faults differing in orientation (north–south or east–west), which may be relevant to the orientation of lobate scarps.