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DOE OSTI2011

Interlocked optimization and fast gradient algorithm for a seismic inverse problem

Highlights: {yields} A 2D extension of the 1D nonlinear inversion of well-seismic data is given. {yields} Appropriate regularization yields a well-determined large scale inverse problem. {yields} An interlocked optimization loop acts as an efficient preconditioner. {yields} The adjoint state method is used to compute the misfit function gradient. {yields} Domain decomposition method yields an efficient parallel implementation. - Abstract: We give a nonlinear inverse method for seismic data recorded in a well from sources at several offsets from the borehole in a 2D acoustic framework. Given the velocity field, approximate values of the impedance are recovered. This is a 2D extension of the 1D inversion of vertical seismic profiles . The inverse problem generates a large scale undetermined ill-conditioned problem. Appropriate regularization terms render the problem well-determined. An interlocked optimization algorithm yields an efficient preconditioning. A gradient algorithm based on the adjoint state method and domain decomposition gives a fast parallel numerical method. For a realistic test case, convergence is attained in an acceptable time with 128 processors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

A 2.5D boundary element formulation for modeling damped waves in arbitrary cross-section waveguides and cavities

Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- Abstract: A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of Rayleigh waves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Noiseless Vlasov–Poisson simulations with linearly transformed particles

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Discontinuous Galerkin methods for plasma physics in the scrape-off layer of tokamaks

A new parallel discontinuous Galerkin solver, called ArcOn, is developed to describe the intermittent turbulent transport of filamentary blobs in the scrape-off layer (SOL) of fusion plasma. The model is comprised of an elliptic subsystem coupled to two convection-dominated reaction–diffusion–convection equations. Upwinding is used for a class of numerical fluxes developed to accommodate cross product driven convection, and the elliptic solver uses SIPG, NIPG, IIPG, Brezzi, and Bassi–Rebay fluxes to formulate the stiffness matrix. A novel entropy sensor is developed for this system, designed for a space–time varying artificial diffusion/viscosity regularization algorithm. Some numerical experiments are performed to show convergence order on manufactured solutions, regularization of blob/streamer dynamics in the SOL given unstable parameterizations, long-time stability of modon (or dipole drift vortex) solutions arising in simulations of drift-wave turbulence, and finally the formation of edge mode turbulence in the scrape-off layer under turbulent saturation conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics

The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The method of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗

DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Effects of the microalgae Chlamydomonas on gastrointestinal health

The effects of consuming whole-cell biomass of the green algae Chlamydomonas reinhardtii on gastrointestinal health in mice and humans was examined. A 14-day murine model of acute colitis revealed significantly less weight loss in mice that received C. reinhardtii biomass by oral gavage. Based on this result, human volunteers with varying gastrointestinal symptoms were asked to consume 1 or 3 g of C. reinhardtii daily for 30 days. Participants reported changes in their gastrointestinal health through a questionnaire and provided stool samples to analyze the composition of their gut microbiome. Those who typically experience frequent gastrointestinal symptoms reported significantly less bowel discomfort or diarrhea, significantly less gas or bloating, more regular bowel movements, and better stool consistency when regularly consuming C. reinhardtii. Analysis of participant stool samples suggested the gut microbiome composition in all groups remained complex, and no signs of dysbiosis or adverse effect on microbial composition were observed.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗

DOE OSTI2011

Design of highly ordered Ag-SrTiO{sub 3} nanotube arrays for photocatalytic degradation of methyl orange

Ag-SrTiO{sub 3} nanotube arrays were successfully prepared for the degradation of methyl orange (MO) under ultraviolet irradiation. In order to form highly ordered SrTiO{sub 3} nanotube arrays, the preparation of TiO{sub 2} nanotube arrays by anodic oxidation of titanium foil in different electrolytes was investigated. The selected organic solvents in electrolytes include glycerol, dimethyl sulfoxide and glycol. The results indicate that the morphology of TiO{sub 2} nanotube arrays prepared in glycol containing ammonium fluoride electrolyte is more regular. Then SrTiO{sub 3} nanotube arrays were synthesized by a hydrothermal method using TiO{sub 2} nanotube arrays as the precursor. In order to further improve the photocatalytic activity of SrTiO{sub 3} nanotube arrays, Ag nanoparticles were loaded on SrTiO{sub 3} nanotube arrays by two sets of experiments. The loaded Ag results in an enhancement of photocatalytic activity of SrTiO{sub 3} nanotube arrays. Moreover, the effect of pH on the photocatalytic degradation of MO was also studied. - Graphical abstract: Ag-SrTiO{sub 3} nanotube arrays were successfully prepared. The photocatalytic activity was evaluated by degradation of methyl orange under ultraviolet irradiation. Highlights: > TiO{sub 2} nanotube arrays prepared in glycol+NH{sub 4}F electrolyte are more regular. > Highly ordered Ag-SrTiO{sub 3} nanotube arrays were successfully synthesized. > Ag loading could enhance the photocatalytic activity of SrTiO{sub 3} nanotube arrays. > Ag-SrTiO{sub 3} nanotube arrays show excellent catalytic activity at a low pH value.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2011

The influence of diffusion temperature on the structural, optical and magnetic properties of manganese-doped zinc oxysulfide thin films

We investigated the structural, optical and magnetic properties of Mn-doped zinc oxysulfide films. Zn(O,S) films were deposited by a spray pyrolysis method on glass substrate. A thin Mn layer evaporated on these films served as the source for the diffusion doping. The XRD pattern of undoped films revealed the presence of two wurtzite phases corresponding to ZnS and ZnO with a strong preferred orientation along the ZnS (0 0 2) hexagonal plane direction. SEM showed a similar surface morphology for the undoped and Mn-doped films, displaying regular arrays of hexagonal micro-rods perpendicular to the substrate. The optical transmission measurements showed that both undoped and Mn diffusion-doped films had a low average transmittance less than about 10%. The gap energy is decreased from 3.42 to 3.33 eV upon annealing at 400 deg. C. Photoluminescence studies at 300 K show that the incorporation of manganese leads to a decrease of deep level band intensity compared to undoped sample. Clear ferromagnetic loops were observed for the Mn-doped Zn(O,S) films, which might be due to the presence of point defects. - Graphical abstract: M-H variation of Mn diffusion-doped Zn(O,S) thin films measured at 300 K. Highlights: > Zinc oxysulfide thin films fabricated by spray pyrolysis and doped with Mn. > Regular arrays of hexagonal micro-rods perpendicular to the substrate. > Optical transmission measurements showed that both undoped and Mn diffusion-doped films had a low average transmittance less than about 10%. > Magnetic measurements show that Mn-doped zinc oxysulfide thin films exhibit a ferromagnetism behavior at room temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Influence of structural distortions upon photoluminescence properties of Eu{sup 3+} and Tb{sup 3+} activated Na{sub 3}Ln(BO{sub 3}){sub 2} (Ln=Y, Gd) borates

The comparative study of the structure and photoluminescence (PL) properties of the Eu{sup 3+} and Tb{sup 3+} activated Na{sub 3}Ln(BO{sub 3}){sub 2}, with Ln=Y, Gd, showed the important role of the host lattice structure upon PL. Higher emission intensities of Eu{sup 3+} and Tb{sup 3+} are observed for Na{sub 3}Gd(BO{sub 3}){sub 2} than for Na{sub 3}Y(BO{sub 3}){sub 2}, through direct Eu{sup 3+} excitation at 395 nm for Eu{sup 3+} doped borates, and through Gd{sup 3+} excitation around 280 nm for Tb{sup 3+} doped borates. This higher performance for Na{sub 3}Gd(BO{sub 3}){sub 2} is due to the less regular environment of Eu{sup 3+} (Tb{sup 3+}) in the Gd sites than in the Y sites and to energy transfer from Gd{sup 3+} to Eu{sup 3+}(Tb{sup 3+}). The smaller critical concentration in Na{sub 3}Ln{sub 1-x}Tb{sub x}(BO{sub 3}){sub 2} observed for Ln=Gd, x=0.5, compared to x=0.6 for Ln=Y, is explained by shorter Ln-Ln distances (4.11 A for Gd-Gd vs. 4.59 A for Y-Y). Both Na{sub 3}Y{sub 0.4}Tb{sub 0.6}(BO{sub 3}){sub 2} and Na{sub 3}Gd{sub 0.5}Tb{sub 0.5}(BO{sub 3}){sub 2} show intense green emission under UV excitation. - Graphical abstract: The PL properties of Eu{sup 3+} and Tb{sup 3+} are studied in Na{sub 3}Ln(BO{sub 3}){sub 2} (Ln=Y, Gd) borates. Eu{sup 3+} and Tb{sup 3+}exhibits higher emission intensity in Na{sub 3}Gd(BO{sub 3}){sub 2} compared to Na{sub 3}Y(BO{sub 3}){sub 2} due to the less regular environment of the Gd{sup 3+} ion. Energy transfer from Gd{sup 3+} to Tb{sup 3+} is observed. Highlights: Black-Right-Pointing-Pointer Crystal structure of Na{sub 3}Gd(BO{sub 3}){sub 2} by X-ray powder diffraction. Black-Right-Pointing-Pointer Photoluminescence properties of Eu{sup 3+} and Tb{sup 3+} doped Na{sub 3}Ln(BO{sub 3}){sub 2} (Ln=Y, Gd). Black-Right-Pointing-Pointer Higher Eu{sup 3+} and Tb{sup 3+} emission for Na{sub 3}Gd(BO{sub 3}){sub 2} due to an irregular environment of Gd{sup 3+}. Black-Right-Pointing-Pointer Higher Eu{sup 3+} and Tb{sup 3+} emission for Na{sub 3}Gd(BO{sub 3}){sub 2} due to energy transfer from Gd{sup 3+}. Black-Right-Pointing-Pointer Lower Tb{sup 3+} critical concentration for Na{sub 3}Gd(BO{sub 3}){sub 2} due to short Gd{sup 3+}-Gd{sup 3+} distances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Crystal structure analysis of tungsten bronzes {beta}-SrTa{sub 2}O{sub 6} and {beta} Prime -SrTa{sub 2}O{sub 6} by synchrotron X-ray and neutron powder diffraction

Strontium ditantalum oxide SrTa{sub 2}O{sub 6} exists in {alpha}-, {beta}-, and {beta} Prime -polymorphs. Herein the crystal structures of the latter two were studied using synchrotron X-ray and constant-wavelength neutron powder diffraction. While {beta} Prime -SrTa{sub 2}O{sub 6} [space group P4/mbm, a=12.47099(1) A, c=3.898210(5) A, V=606.271(2) Angstrom-Sign {sup 3}, Z=5] belongs to the regular tetragonal tungsten bronze (TTB) family, it contains locally disordered strontium atoms within the pentagonal channel. {beta}-SrTa{sub 2}O{sub 6} [space group Pnam, a=12.36603(2) Angstrom-Sign , b=12.43467(2) A, c=7.72403(1) A, V=1187.705(4) Angstrom-Sign {sup 3}, Z=10] can be described as an orthorhombic modification of the TTB, where the octahedral tilting distortion effectively alleviates the bonding strains around TaO{sub 6} and SrO{sub 13} polyhedra. For comparison, rynersonite type {alpha}-SrTa{sub 2}O{sub 6} [space group Pnma, a=11.00610(6) Angstrom-Sign , b=7.63397(3) Angstrom-Sign , c=5.62634(3) Angstrom-Sign , V=472.727(5) Angstrom-Sign {sup 3}, and Z=4] is built from edge-shared dimer units of TaO{sub 6} octahedra. As measured by diffuse-reflection absorption spectroscopy, {alpha}-, {beta}-, and {beta} Prime -SrTa{sub 2}O{sub 6} have indirect band gap energies of 4.4, 4.0, and 3.8 eV, respectively. - Graphical Abstract: Difference Fourier map for {beta} Prime -SrTa{sub 2}O{sub 6} at z=0. Highlights: Black-Right-Pointing-Pointer Structure refinements of {beta}-SrTa{sub 2}O{sub 6} and {beta} Prime -SrTa{sub 2}O{sub 6}. Black-Right-Pointing-Pointer Strontium disorder in tetragonal tungsten bronze {beta} Prime -SrTa{sub 2}O{sub 6}. Black-Right-Pointing-Pointer Orthorhombic distortion and cell doubling in {beta}-SrTa{sub 2}O{sub 6}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗