A Displacement-Based Finite-Element Formulation for General Polyhedra using Harmonic Shape Functions
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Cu 2 BaGe 1–x Sn x Se 4 (CBGTSe) represents an exemplary system within the I 2 –II–IV–X 4 (I = Ag, Cu; II = Sr, Ba; IV = Ge, Sn; X = S, Se) family, which has been introduced to target suppressing the formation of anti-site defects and associated defect clusters within the analogous kesterite Cu 2 ZnSn(S,Se) 4 . Previous studies on CBGTSe films showed relatively low hole carrier densities (<10 13 cm –3 ), which may limit their corresponding application as active layers within photovoltaic, thermoelectric, and optoelectronic devices. In the current study, we explore the incorporation of alkali elements (Li, Na, K, and Rb) into CBGTSe films as prospective dopants to address the low hole carrier density and to allow for property tunability. First, incorporation of Na-, K-, and Rb-dopants noticeably increases the average grain sizes for CBGTSe films, while the Li-dopant has relatively limited impact. In addition, the alkali-dopants lead to a 1 to 3 orders of magnitude increase in hole carrier density (up to 10 15 cm –3 is achieved using K doping, corresponding to the alkali element yielding the highest doping efficiency). Here, the alkali-doped films show slightly lower minority carrier lifetimes and carrier mobility values than the non-doped samples, and these values are found to follow an approximate universal dependence with carrier density (also considering data derived from other previously explored vacuum-deposited I 2 –II–IV–X 4 chalcogenide films). As alkali-doping can significantly increase carrier densities, alkali elements can be considered useful p-type dopants for CBGTSe, as well as prospectively for other analogous I 2 –II–IV–X 4 systems.
Here, we use a nanofabricated scanning tunneling microscope tip as a detector to investigate local X-ray induced tunneling and electron emission from a single cobalt nanocluster on a Au(111) surface. The tip-detector is positioned a few angstroms above the nanocluster, and ramping the incident X-ray energy across the Co photoabsorption K-edge enables the detection of element specific electrons. Atomic-scale spatial dependent changes in the X-ray absorption cross section are directly measured by taking the X-ray induced current as a function of X-ray energy. From the measured sample and tip currents, element specific X-ray induced current components can be separated and thereby the corresponding yields for the X-ray induced processes of the single cobalt nanocluster can be determined. The detection of element specific synchrotron X-ray induced electrons of a single nanocluster opens a new avenue for materials characterization on a one particle at-a-time basis.
The family of 17 elements known as the “rare earth elements” are difficult to produce economically. Despite this, they are described as “critical raw materials” because of their unique properties and their various technological applications. This means their use is accelerating globally. Separation of these elements is a fundamental challenge, but this does not daunt Dr Santa Jansone-Popova and her team at Oak Ridge National Laboratory. In recovering praseodymium from neodymium using a variety of ligands known as diglycolamides, she has been demonstrating potentially game-changing advances in liquid-liquid separations that could realise more of these in-demand materials.
The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method (FEM) for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. We numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular and square meshes where the method coincides with the P 1 - P 0 Scott-Vogelius scheme, which is well-known to be unstable.
The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.
Coal combustion ash and pre-combustion coal refuse are currently under consideration as potential sources of rare earth elements. One of the early steps in recovering REEs from coal by-products is often acid leaching, which can result in low pH leachates with complex aqueous chemistry. The aim of this work was to understand the connection between REE solubility, pH, and major elemental components of leachates for coal by-products. To accomplish this, we investigated the effects of solids concentration (i.e., pulp density) and pH adjustment on REE solubility in acid leachates of coal fly ashes from the Powder River Basin (PRB) and Appalachian Basin in the United States, and a coal processing refuse from the Southwestern U.S. For PRB ashes, the concentrations of soluble REEs generally increased with increasing pulp density; however, at pulp density values above 80–100 g/L, the soluble REE concentrations in the leachates were markedly lower. Similarly, the soluble concentrations of other major solutes (Fe, Al, Si) that leached from PRB fly ashes were also non-linear with pulp density. These major elements tended to reach maximum concentration values at 60–70 g/L pulp density. In contrast, for the Appalachian fly ashes and the coal by-product, soluble concentrations of REE and major elements in leachates increased linearly with pulp density. Chemical equilibria calculations of mineral saturation indices indicated that trends in soluble REE concentrations could be explained by saturation conditions for Fe and Al-(hydr)oxides and possibly sulfate minerals, but not lanthanide hydroxides. Furthermore, pH adjustment of the acid leachates showed that REEs and many major solutes were removed from solution at pH values above 4.5, also consistent with Fe- and Al-(hydr)oxide precipitation. These results highlight the importance of understanding the chemical composition of leachates when designing REE recovery processes for low-grade geologic feedstocks and that precipitation of hydr(oxide) or sulfate minerals of major elements rather than discreet formation of REE mineral phases could be used for process optimization.
Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.
Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.
Despite the numerous studies on changes within the reservoir following CO2 injection and the effects of CO2 release into overlying aquifers, little or no literature is available on the effect of CO2 release on rock between the storage reservoirs and subsurface. To address this knowledge gap, relevant rock materials, temperatures and pressures were used to study mineralogical and elemental changes in this intermediate zone. After rocks reacted with CO2, liquid analysis showed an increase of major elements (e.g., Ca, and Mg) and variable concentrations of potential contaminants (e.g., Sr and Ba); lower concentrations were observed in N2 controls. In experiments with As/Cd and/or organic spikes, representing potential contaminants in the CO2 plume originating in the storage reservoir, most or all of these contaminants were removed from the aqueous phase. SEM and Mössbauer spectroscopy results showed the formation of new minerals and Fe oxides in some CO2-reacted samples, indicating potential for contaminant removal through mineral incorporation or adsorption onto Fe oxides. These experiments show the interactions between the CO2-laden plume and the rock between storage reservoirs and overlying aquifers have the potential to affect the level of risk to overlying groundwater, and should be considered during site selection and risk evaluation.
Abstract The mantle source beneath the Southwest Indian Ridge (SWIR) reflects a complex history of contamination. Magmatic volatile contents are vital tracers of these kinds of heterogeneities, which may fractionate otherwise constant volatile/non‐volatile elemental ratios, such as the H 2 O/Ce ratio. Although several studies have recently used trace element and isotopic data to address mantle source heterogeneity and magmatic processes at SWIR 48°–51°E region, volatile element constraints provide a valuable test of models for the origins of mantle heterogeneities in this region. Here, we present new data for nine rare basaltic glass samples from the 48°–51°E region, which enable careful assessment of the effects of primary versus secondary processes on the glass volatile contents. These samples are strongly affected by variable extents of carbon degassing, and shallow assimilation of Cl‐rich fluid, but also reveal consistently high H 2 O/Ce ratios (458.8 ± 14.9), among the highest in MORBs, that cannot be explained by late‐stage secondary processes, crustal assimilation, or simple melting of peridotite mantle at variable depths. Instead, the high H 2 O/Ce ratios are features of the mantle source composition. The 48°–51°E region is notably more depleted in highly incompatible trace elements relative to other regions of the SWIR, although this depletion is not apparent in H 2 O, which is similarly abundant throughout the SWIR. We link the high H 2 O/Ce ratios in these glasses with other trace element characteristics diagnostic of subduction and fluid addition, suggesting that the mantle source reflects signatures of a refractory mantle residue that previously melted within a subduction zone.
The solvent-picking procedure in phenix.refine has been extended and combined with Phaser anomalous substructure completion and analysis of coordination geometry to identify and place elemental ions. Many macromolecular model-building and refinement programs can automatically place solvent atoms in electron density at moderate-to-high resolution. This process frequently builds water molecules in place of elemental ions, the identification of which must be performed manually. The solvent-picking algorithms in phenix.refine have been extended to build common ions based on an analysis of the chemical environment as well as physical properties such as occupancy, B factor and anomalous scattering. The method is most effective for heavier elements such as calcium and zinc, for which a majority of sites can be placed with few false positives in a diverse test set of structures. At atomic resolution, it is observed that it can also be possible to identify tightly bound sodium and magnesium ions. A number of challenges that contribute to the difficulty of completely automating the process of structure completion are discussed.
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