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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

The Pursuit of K: Reflections on the Current State-of-the-Art in Stress Intensity Factor Solutions for Practical Aerospace Applications

The elastic stress intensity factor (SIF, commonly denoted as K) is the foundation of practical fracture mechanics (FM) analysis for aircraft structures. This single parameter describes the first-order effects of stress magnitude and distribution as well as the geometry of both structure/component and crack. Hence, the calculation of K is often the most significant step in fatigue analysis based on FM. This presentation will provide several reflections on the current state-of-the-art in SIF solution methods used for practical aerospace applications, including a brief historical perspective, descriptions of some recent and ongoing advances, and comments on some remaining challenges. Newman and Raju made significant early contributions to practical structural analysis by developing closed-form SIF equations for surface and corner cracks in simplified geometries, often based on empirical fits of finite element (FE) solutions. Those solutions (and others like them) were sometimes revised as new analyses were conducted or limitations discovered. The foundational solutions have exhibited striking longevity, despite the relatively "coarse" FE models employed many decades ago. However, in recent years, the accumulation of different generations of solutions for the same nominal geometry has led to some confusion (which solution is correct?), and steady increases in computational capabilities have facilitated the discovery of inaccuracies in some (not all!) of the legacy solutions. Some examples of problems and solutions are presented and discussed, including the challenge of maintaining consistency with legacy design applications. As computational power has increased, the prospect of calculating large numbers of SIF solutions for specific complex geometries with advanced numerical methods has grown more attractive. Fawaz and Andersson, for example, have been generating literally millions of new SIF solutions for different combinations of multiple cracks under simplified loading schemes using p-version FE methods. These data are invaluable, but questions remain about their practical use, because the tabular databases of key results needed to support practical life analysis can occupy gigabytes of storage for only a few classes of geometries. The prospect of using such advanced numerical methods to calculate in real time only those K solutions actually needed to support a specific crack growth analysis is also tempting, but the stark reality is that the computational cost is still so high that the approach is not practical except for specific, critical application problems. Some thoughts are offered about alternative paradigms. Compounding approaches are some of the earliest building blocks of SIF development for more complex geometries. These approaches are especially attractive because of their very low computational cost and their conceptual robustness; they are, in some ways, an intriguing contrast and complement to the brute-force numerical methods. In recent years, researchers at NRC-Canada have published remarkable results showing how compounding approaches can be used to generate accurate solutions for very difficult problems. Examples are provided of some successes--and some limitations--using this approach. These closed-form, tabulated numerical, and compounding approaches have typically been used for simple remote loading with simple load paths to the crack. However, many significant cracks occur in complex stress gradient fields. This is a job for weight function (WF) methods, where the arbitrary stress distribution on the crack plane in the corresponding uncracked body (typically determined using FE methods) is used to determine K. Several significant recent advances in WF methods and solutions are highlighted here. Fueled by advanced 3D numerical methods, many new solutions have been generated for classic geometries such as surface and corner cracks with wide ranges of geometrical validity. A new WF formulation has also be developed for part-through cracks considering the arbitrary stress gradients in all directions in the crack plane (so-called bivariant solutions). Basic WF methods have recently been combined with analytical expressions for crack plane stresses to develop a large family of accurate SIF solutions for corner, surface, and through cracks at internal or external notches with very wide ranges of shapes, sizes, acuities, and offsets. Finally, WF solutions are much faster than FE or boundary element solutions, but can still be much slower than simple closed-form solutions, especially for bivariant solutions that can require 2D numerical integration. Novel pre-integration and dynamic tabular methods have been developed that substantially increase the speed of these advanced WF solutions. The practical utility of advanced SIF methods, including both WF and direct numerical methods, is greatly enhanced if the FM life analysis can be directly and efficiently linked with digital models of the actual structure or component (e.g., FE models for stress analysis). Two recent advances of this type will be described. One approach directly interfaces the FM life analysis with the FE model of the uncracked component (including stress results). Through a powerful graphical user interface, simplified FM life models can be constructed (and visualized) directly on the component model, with the computer collecting the geometry and stress gradient information needed for the life calculation. An even more powerful paradigm uses expert logic to automatically build an optimum simple fracture model at any and every desired location in the component model, perform the life calculation, and even generate fatigue crack growth life contour maps, all with minimal user intervention. This paradigm has also been extended to the automatic calculation of fracture risk, considering uncertainty or variability in key input parameters such as initial crack size or location. Another new integrated approach links the engineering life analysis, the component model, and a 3D numerical fracture analysis built with the same component model to generate a table of SIF values at a specific location that can then be employed efficiently to perform the life calculation. Some attention must be given to verification and validation (V&V) issues and challenges: how good are these SIF solutions, how good is good enough, and does anyone believe the life answer? It is important to think critically about the different sources of error or uncertainty and to perform V&V in a hierarchal, building-block manner. Some accuracy issues for SIF solutions, for example, may actually involve independent material behavior issues, such as constraint loss effects for crack fronts near component surfaces, and can be a source of confusion. Recommendations are proposed for improved V&V approaches. This presentation will briefly but critically survey the range of issues and advances mentioned above, with a particular view towards assembling an integrated approach that combines different methods to create practical tools for real-world design and analysis problems. Examples will be selectively drawn from the recent literature, from recent enhancements in the NASGRO and DARWIN computer codes, and from previously unpublished research

CraigMcClung, R.↗
NASA NTRS1996

Gravity Induced Formation of Concentration Gradients in Supersaturated Binary Solutions

Experimental and theoretical studies of the formation of solute concentration gradient in supersaturated binary solutions in a gravitational field were carried out. The formation of solute concentration gradient was associated with the gravity induced redistribution of subcritical solute clusters. The birth-death process of the new solute-rich phase domains (subcritical solute clusters) was described in terms of the time-dependent Ginzburg Landau model developed for metastable state relaxation in binary (solute + solvent) non-critical solutions in the presence of a gravitational field. A new mathematical Ansatz was developed for solution of the model equations. This Ansatz has allowed to approach for the first time the following important problems: (1) Microstructure of solute distribution inside of the subcritical solute clusters. The analytical results obtained demonstrate that solute inside of the subcritical solute clusters is heterogeneously distributed with a spatially periodic structure. (2) Macrostructure of the solute subcritical clusters distribution in a gravitational field. The subcritical solute clusters are found to be distributed heterogeneously in a gravitational field. This heterogeneity, which is due to the heterogeneous birth-death process of the subcritical solute clusters in a gravitational field, initiates a noticeable solute concentration gradient in vertical columns of supersaturated binary solutions. An analysis and comparison of theoretical results and experimental data related to the solute concentration gradient formation in a gravitational field are presented. It is also demonstrated that the critical radius of solute clusters (radius of nucleation) and induction time are gravity-dependent.

Izmailov, Alexander F.↗
DOE OSTI2020

Solute-vacancy clustering in aluminum

In this study, we present an extensive first-principles database of solute-vacancy, homoatomic, heteroatomic solute-solute, and solute-solute-vacancy binding energies of relevant alloying elements in aluminum. We particularly focus on the systems with major alloying elements in aluminum, i.e., Cu, Mg, and Si. The computed binding energies of solute-vacancy, solute-solute pairs, and solute-solute-vacancy triplets agree with available experiments and theoretical results in literature. We consider physical factors such as solute size and formation energies of intermetallic compounds to correlate with binding energies. Systematic studies of the homoatomic solute-solute-vacancy and heteroatomic (Cu, Mg, or Si)-solute-vacancy complexes reveal the overarching effect of the vacancy in stabilizing solute-solute pairs. The binding energy database presented here elucidates the interaction between solute cluster and vacancy in aluminum, and it is expected to provide insight into the design of advanced Al alloys with tailored properties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Solutes that reduce yield strength anisotropies in magnesium from first principles

Using Labusch-type solid solution strengthening models parameterized with DFT-computed solute-dislocation interaction energies, we perform a computational search for 63 solutes across the periodic table to find those that lower anisotropy ratios (non-basal to basal CRSS) of magnesium potentially increasing its ductility per the von Mises criterion. For this purpose, we compute changes in strength for solutes as a function of composition and temperature, and compute anisotropy ratios for solutes that include both rare earth and non-rare earth elements. Here we specifically focus on solute-dislocation interaction energies in the following DFT-optimized dislocations as representative of three non-basal plastic deformation modes: $\langle c + a \rangle$ edge, (10$\bar1$2) tension twinning edge, and the (10$\bar{1}$1) compression twinning edge. We find that solute-induced changes in non-basal deformation modes can be approximated using a second-order polynomial in the size misfit of the solutes, which permits rapid screening of solutes. Our approach to identify solutes known to improve strengthening incorporates solute solubility, and suggests other solutes that not have been previously explored for strengthening. The 8 rare-earth solutes that our method suggests as the best, ordered by increasing anisotropy ratios at their optimal concentrations, are: Gd, Tb, Dy, Nd, Ho, Er, Tm, and Yb. The 12 non-rare-earth solutes that our method suggests as the best, ordered by increasing anisotropy ratios, are: Y, Mn, Sc, Pb, Ca, Ag, Bi, Tl, Zn, Li, Ga, and Al. Of these, Gd, Nd, Er, Yb, Y, Mn, Ca, Zn, Li, and Al are used in commercial Mg alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Signatures of Thermoreversible Associations in X-ray and Neutron Scattering from Dilute Polyzwitterion Solutions

In aqueous solutions of polyzwitterions (PZs), an interplay between dipole–dipole interactions and hydration of zwitterionic groups can lead to thermoreversible associations, which have been difficult to detect in experiments. Here, in this study, we investigated dilute aqueous solutions of poly(1-(3-sulphonatopropyl)-2-vinylpyridinium) (P2VPPS) using small-angle X-ray and neutron scattering (SAXS and SANS) to probe the structure and neutron spin-echo (NSE) spectroscopy to probe dynamics. The SAXS and SANS data show that the correlation length increases with an increase in the concentration of P2VPPS for three different molecular weights. The addition of 0.1 M NaCl to one of the solutions led to almost no dependence of the correlation length on the concentration. Such a concentration dependence of the correlation length suggests the formation of clusters driven by thermoreversible associations in the solutions. The NSE measurements show that the solutions with a larger correlation length display slower relaxation, reflecting the reduced mobility of larger clusters. These results should be considered as signatures of thermoreversible associations in the solutions of P2VPPS. To establish a quantitative link between local structure (clusters) and dynamics in dilute solutions of P2VPPS, we combined a thermoreversible gelation theory for the structure of PZ solutions (Li, S.-F.; Muthukumar, M. Theory of Thermoreversible Gelation and Anomalous Concentration Fluctuations in Polyzwitterion Solutions. J. Chem. Phys. 2024, 161, 024903) with a model for the dynamics of the clusters (generalized Zimm model), developed in this work. Using such a theoretical framework, we have predicted the distribution of clusters in the solutions probed with SANS and SAXS. With the distributions, the generalized Zimm model has been used to extract the diffusion constant of the clusters and their characteristic size from the NSE data, where the latter agrees with the values estimated from the SAXS/SANS data. These findings confirm the presence of thermoreversible associations and establish a quantitative link between local structure (clusters) and dynamics in dilute solutions of P2VPPS. Furthermore, with growing interest in technological applications, this work can provide useful insights into the structural and dynamical properties of other PZ solutions.

field theory↗
DOE OSTI2023

Exact solution of burst pressure for thick-walled pipes using the flow theory of plasticity

This paper develops an exact solution of burst pressure for defect-free, thick-walled pipes using the flow theory of plasticity in terms of the average shear stress yield criterion (or Zhu-Leis yield criterion). The pipe steel is assumed to obey the power-law strain hardening rule, and large plastic deformation is described by the finite strain theory. On this basis, internal pressure is obtained as a power series function of the effective strains on the inside and outside surfaces of the thick-walled pipe with use of the second Bernoulli numbers. At burst failure, the Zhu-Leis flow solution of burst pressure is determined as a power series solution, and the burst effective strains, the burst effective stresses, and the burst pressure are functions of the diameter ratio (D o / D i ), strain hardening exponent (n), and ultimate tensile strength (UTS). Similarly, the Tresca and von Mises flow solutions of burst pressure are also determined as a power series solution in terms of the Tresca and von Mises yield criteria. A general closed-from exact solution of burst pressure is then proposed for the three yield criteria, and the results showed that the proposed exact solution matches well with the power series solution for each yield criterion. Moreover, the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction that agrees well with the finite element analysis results of burst pressure for thick-walled pipes. Furthermore, two datasets of full-scale burst tests are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin and thick-walled pipes.

42 ENGINEERING↗
NASA NTRS1994

Improved solution accuracy for TDRSS-based TOPEX/Poseidon orbit determination

Orbit determination results are obtained by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) using a batch-least-squares estimator available in the Goddard Trajectory Determination System (GTDS) and an extended Kalman filter estimation system to process Tracking and Data Relay Satellite (TDRS) System (TDRSS) measurements. GTDS is the operational orbit determination system used by the FDD in support of the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft navigation and health and safety operations. The extended Kalman filter was implemented in an orbit determination analysis prototype system, closely related to the Real-Time Orbit Determination System/Enhanced (RTOD/E) system. In addition, the Precision Orbit Determination (POD) team within the GSFC Space Geodesy Branch generated an independent set of high-accuracy trajectories to support the TOPEX/Poseidon scientific data. These latter solutions use the geodynamics (GEODYN) orbit determination system with laser ranging and Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) tracking measurements. The TOPEX/Poseidon trajectories were estimated for November 7 through November 11, 1992, the timeframe under study. Independent assessments were made of the consistencies of solutions produced by the batch and sequential methods. The batch-least-squares solutions were assessed based on the solution residuals, while the sequential solutions were assessed based on primarily the estimated covariances. The batch-least-squares and sequential orbit solutions were compared with the definitive POD orbit solutions. The solution differences were generally less than 2 meters for the batch-least-squares and less than 13 meters for the sequential estimation solutions. After the sequential estimation solutions were processed with a smoother algorithm, position differences with POD orbit solutions of less than 7 meters were obtained. The differences among the POD, GTDS, and filter/smoother solutions can be traced to differences in modeling and tracking data types, which are being analyzed in detail.

Doll, C. E.↗
NASA NTRS2004

Comparisons of the Solutions for the Category 3--Problem 2: Cascade-Gust Interaction

Six different solutions were submitted for this benchmark problem. These were obtained using a variety of methods that can be conveniently categorized in two main groups, a nonlinear time-domain group and a linearized frequency-domain group. The first includes solutions submitted by (1) Hixon, (2) Nallasamy et. al, (3) Shieh et. al, and (4) Wang et. al, and the second includes solutions submitted by (5) Coupland and (6) Serrano et. al. Methods (1) and (2) use sixth order compact differencing schemes and the rest are essentially second order in space. With the exception of the solution submitted by Shieh et. al, all are individually discussed in great detail in the workshop proceedings. Comparisons of the submitted solutions with the benchmark solution are presented below. Due to differences in the level of solution detail provided to the author by the participants, the comparisons do not always include results from all submissions. It should be noted at the outset that, since the benchmark solution itself was numerically computed, the comparisons are somewhat subjective. In order to provide maximum latitude for the participants of the workshop, no restrictions were placed on the type of method that could be used to solve the problem. Neither was there were any stipulations to use a particular grid topology or grid density. Therefore, without a detailed study of the critical features of the computed solutions, it is not possible to make concrete statements about the relative merits of one method over another. Such a study is beyond the scope of the current exercise, especially since complete flowfield details were not provided to the author by all participants. Instead a package, containing the information about the benchmark solution (both the steady and unsteady parts of it), is included on the proceedings CD should the authors who submitted solutions for this problem wish to examine in detail the benchmark solution and compare their results to it.

Envia, Edmane↗
DOE OSTI2021

Dissolution kinetics of a sodium borosilicate glass in Tris buffer solutions: impact of Tris concentration and acid (HCl/HNO 3 ) identity

Here, understanding the corrosion behavior of glasses in near-neutral environments is crucial for many technologies including glasses for regenerative medicine and nuclear waste immobilization. To maintain consistent pH values throughout experiments in the pH = 7 to 9 regime, buffer solutions containing tris(hydroxymethyl)aminomethane (“Tris”, or sometimes called THAM) are recommended in ISO standards 10993-14 and 23317 for evaluating biomaterial degradation and utilized throughout glass dissolution behavior literature—a key advantage being the absence of dissolved alkali/alkaline earth cations (i.e. Na + or Ca 2+ ) that can convolute experimental results due to solution feedback effects. Although Tris is effective at maintaining the solution pH, it has presented concerns due to the adverse artificial effects it produces while studying glass corrosion, especially in borosilicate glasses. Therefore, many open questions still remain on the topic of borosilicate glass interaction with Tris-based solutions. We have approached this topic by studying the dissolution behavior of a sodium borosilicate glass in a wide range of Tris-based solutions at 65 °C with varied acid identity (Tris–HCl vs. Tris–HNO 3 ), buffer concentration (0.01 M to 0.5 M), and pH (7–9). The results have been discussed in reference to previous studies on this topic and the following conclusions have been made: (i) acid identity in Tris-based solutions does not exhibit a significant impact on the dissolution behavior of borosilicate glasses, (ii) ~0.1 M Tris-based solutions are ideal for maintaining solution pH in the absence of obvious undesirable solution chemistry effects, and (iii) Tris–boron complexes can form in solution as a result of glass dissolution processes. The complex formation, however, exhibits a distinct temperature-dependence, and requires further study to uncover the precise mechanisms by which Tris-based solutions impact borosilicate glass dissolution behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evaluation of the Potential for Precipitation of Solids during Storage of Non-Aluminum SNF Solutions

Non-aluminum clad spent nuclear fuels (NASNF) stored in the L-Area basin will be dissolved in H-Canyon using the 6.3D electrolytic dissolver. The solutions will be stored in either the hot or warm canyon until the preparation of a sludge batch for the Defense Waste Processing Facility. Spent nuclear fuel solutions could be stored for 1-2 years before transfer to the H-Area Tank Farm depending on the interval between sludge batches. The solution level in the storage tanks will be maintained; therefore, precipitation of solids due to evaporation is not an issue. However, the precipitation of solids from completely dissolved SNF due to solution instabilities has been observed during intermediate storage of solutions generating hydrated oxides.The presence of fissile material in these solids is generally associated with zirconium molybdate, which is known to act as a host lattice for Pu and can carry the actinides upon precipitation. The formation of zirconium molybdate solids which carry fissile material is a potential concern for the storage of NASNF solutions. To address this concern, the Savannah River National Laboratory performed a literature review to identify knowledge gaps which may require experimental work to determine if the formation of solids is a concern during storage of these solutions. Based on the literature review, the precipitation of zirconium molybdate solids from the Campaign 1 NASNF solutions during intermediatestorage is expected. This conclusion is supported by the identification of zirconium molybdate solids found on the H-Canyon 6.1D Dissolver MK-12 insert spacer. The formation of the zirconium molybdate solids is attributed to hydrolysis and radiolytic processes in the nitric acid solution. As the molybdate solids form, U and Pu can substitute for Zr in the crystal lattice resulting in co-precipitation. Generally, the Pu substitutes directly into the crystal lattice during precipitation while the U associated with the molybdate solids more likely absorbs from the solution. The U in the NASNF solutions is present as uranyl nitrate, a 2+ cation which will not substitute as easily into the molybdate crystal lattice for the Zr 4+ ion.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Mass action model of solution activity via speciation by solvation and ion pairing equilibria

Abstract Solutes and their concentrations influence many natural and anthropogenic solution processes. Electrolyte and solution models are used to quantify and predict such behavior. Here we present a mechanistic solution model based on mass action equilibria. Solvation and ion pairing are used to model speciated solute and solvent concentrations such that they correlate to a solution’s vapor pressure (solvent activity) according to Raoult’s law from dilute conditions to saturation. This model introduces a hydration equilibrium constant ( K ha ) that is used with either an ion dissociation constant ( K id ) or a hydration modifier ( m ) with an experimentally determined ion dissociation constant, as adjustable parameters to fit vapor–liquid equilibrium data. The modeled solvation equilibria are accompanied by molecular dynamics (MD) studies that support a decline in the observed degree of solvation with increased concentration. MD calculations indicate this finding is a combination of a solvent that solvates multiple solutes, and changes in a solute’s solvation sphere, with the dominant factor changing with concentration. This speciation-based solution model is lateral to established electrostatics-based electrolyte theories. With its basis in mass action, the model can directly relate experimental data to the modeled solute and solvent speciated concentrations and structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Supersaturated Electrolyte Solutions: Theory and Experiment

Highly supersaturated electrolyte solutions can be prepared and studied employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the conserved order parameter omega(r,t) associated with fluctuations of the mean solute concentration n(sub 0). Parameters of the corresponding Ginzburg-Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured quantities. A correspondence of 96-99 % between theory and experiment for all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin), and its calculation for various electrolyte solutions at 298 K. The assumption that subcritical solute clusters consist of the electrically neutral Bjerrum pairs has allowed both analytical and numerical investigation of the number-size N(sub c) of nucleation monomers (aggregates of the Bjerrum pairs) which are elementary units of the solute critical clusters. This has also allowed estimations for the surface tension Alpha, and equilibrium bulk energy Beta per solute molecule in the nucleation monomers. The dependence of these properties on the temperature T and on the solute concentration n(sub 0) through the entire metastable zone (from saturation concentration n(sub sat) to spinodal n(sub spin) is examined. It has been demonstrated that there are the following asymptotics: N(sub c), = I at spinodal concentration and N(sub c) = infinity at saturation.

Izmailov, Alexander F.↗
NASA NTRS1999

Gravitational Effects on the Morphology and Kinetics of Photodeposition of Polydiacetylene Thin Films From Monomer Solutions

The goal of this proposed work is to study gravitational effects on the photodeposition of polydiacetylene thin films from monomer solutions onto transparent substrates. Polydiacetylenes have been an extensively studied class of organic polymers because they exhibit many unusual and interesting properties, including electrical conductivity and optical nonlinearity. Their long polymeric chains render polydiacetylenes readily conducive to thin film formation, which is necessary for many applications. These applications require thin polydiacetylene films possessing uniform thicknesses, high purity, minimal inhomogeneities and defects (such as scattering centers), etc. Also, understanding and controlling the microstructure and morphology of the films is important for optimizing their electronic and optical properties. The lack of techniques for processing polydiacetylenes into such films has been the primary limitation to their commercial use. We have recently discovered a novel method for the formation of polydiacetylene thin films using photo-deposition from monomer solutions onto transparent substrates with UV light. This technique is very simple to carry out, and can yield films with superior quality to those produced by conventional methods. Furthermore, these films exhibit good third-order properties and are capable of waveguiding. We have been actively studying the chemistry of diacetylene polymerization in solution and the photo-deposition of polydiacetylene thin films from solution. It is well-known that gravitational factors such as buoyancy-driven convection and sedimentation can affect chemical and mass transport processes in solution. One important aspect of polydiacetylene thin film photodeposition in solution, relevant to microgravity science, is that heat generated by absorption of UV radiation induces thermal density gradients that under the influence of gravity, can cause fluid flows (buoyancy-driven convection). Additionally, changes in the chemical composition of the solution during polymerization may cause solutal convection. These fluid flows affect transport of material to and from the film surface and thereby affect the kinetics of the growth process. This manifests itself in the morphology of the resulting films; films grown under the influence of convection tend to have less uniform thicknesses, and can possess greater inhomogeneities and defects. Specifically, polydiacetylene films photodeposited from solution, when viewed under a microscope, exhibit very small particles of solid polymer which get transported by convection from the bulk solution to the surface of the growing film and become embedded. Even when carried out under conditions designed to minimize unstable density gradients (i.e., irradiating the solution from the top), some fluid flow still takes place (particles remain present in the films). It is also possible that defect nucleation may be occurring within the films or on the surface of the substrate; this, too, can be affected by convection (as is the case with crystal growth). Hence films grown in 1-g will, at best, still possess some defects. The objective of this proposal is to investigate, both in 1-g and in low-g, the effects of gravitational factors (primarily convection) on the dynamics of these processes, and on the quality, morphology, and properties of the films obtained.

Paley, Mark S.↗
DOE OSTI2022

Methods and systems for treating an aqueous solution

A method of treating an aqueous solution comprises forming a treatment stream comprising a condensable material. The treatment stream is introduced to an aqueous solution comprising water and a solute to fractionally precipitate the solute out of the aqueous solution and form a solids stream comprising the solute and an aqueous liquid stream comprising at least one solute-depleted solution of the water and the condensable material. The condensable material of at least a portion of the aqueous liquid stream is separated from the water of the at least a portion of the aqueous liquid stream to at least partially reform the treatment stream and form an aqueous liquid product stream depleted in the solute. Aqueous solution treatment systems and additional methods of treating an aqueous solution are also described.

Wilson, Aaron D.↗
DOE OSTI2020

Equilibrium solute segregation to matrix- θ' precipitate interfaces in Al-Cu alloys from first principles

Particular combinations of solute atoms segregated to the interface of the Al and θ ' - Al 2 Cu in Al-Cu alloys can help stabilize θ ' precipitates at high temperatures. Stabilization of such precipitates is determined by a combination of thermodynamics (including driving forces for coarsening and transformation and solute segregation tendencies) and kinetic effects (including solute diffusion and interfacial mobility in the presence of interfacial solute segregation). For some alloys such as recent Al-Cu-based alloys, multiple solutes segregate in significant quantities to interfaces, and solute-solute interactions at the interface are important, with multiple types of solutes competing for similar interfacial sites. To treat this situation, we develop and apply a statistical mechanics approach to calculate the temperature-dependent equilibrium solute atoms distribution near the coherent and semicoherent interfaces between the Al matrix and the θ ' - Al 2 Cu precipitates. The developed approach is applied to the investigation of Si, Mn, and Zr segregation at the interface, as particular combinations of these elements affect the thermal stability of the θ ' precipitates. We demonstrate that because Si and Mn atoms segregate on the same semicoherent interface, the presence of Si reduces the concentration of Mn solutes at the interface. Si atoms preferably occupy the first layer of the interface and compete with Mn atoms for one type of particular sites in the layer. Mn atoms preferably occupy the second layer of the semicoherent interface, and the Mn-Mn interaction plays an important role in their distribution. Zr atoms mostly segregate on one of the two nonequivalent sites of the second layer of the coherent interface. Due to symmetry properties of the coherent interface, the calculations show that the segregation Zr of atoms to this interface will likely lead to the formation of L 1 2 ordered Al 3 Zr layer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Removal of High Specific Activity Fission Products from Uranyl Sulfate Waste Solutions

The Savannah River National Laboratory (SRNL) is currently providing support to SHINE Medical Technologies (SHINE) which plans to deploy a low energy, accelerator-based neutron source to fission low enriched U in a uranyl sulfate target solution for 99 Mo production. The 99 Mo is initially separated from the fission products and target solution by an extraction column. Subsequent washing of the column will generate waste solutions containing residual U and fission product activity. A small number of high specific activity fission products (e.g., 90 Sr, 137 Cs, and 144 Ce) in these streams will likely control the classification of the low level waste (LLW). If a sufficient amount of the high specific activity isotopes are separated from the SHINE waste streams and concentrated into a waste form, it would be possible to treat a majority of the wash solutions from the column operations as a lower class of LLW (Class A versus Class B or C or Class B versus Class C). The high specific activity fission product elements could then be dispositioned as a much smaller volume of waste rather than requiring the disposal of the entire waste stream at the higher waste classification. The Savannah River Site (SRS) has experience with using monosodium titanate (MST) and crystalline silicotitanate (CST) to remove Cs and Sr from high salt content waste solutions generated during the reprocessing of nuclear fuels and targets. Both of these materials have worked very well for their intended purposes at the SRS where the fission product elements are removed from highly alkaline waste. On the other hand, SHINE waste streams from the extraction column contain H 2 SO 4 which makes the solution acidic. Additionally, the SRS waste streams do not contain other fission product elements such as transition metals or lanthanides because they precipitate upon neutralization of the SRS waste and are not present in the supernate which is dispositioned as LLW following treatment. As such, there are inherent differences between SHINE and SRS waste treatment strategies. Savannah River National Laboratory was tasked with performing scoping studies to see if MST and CST would remove Sr, Cs, and Ce from an acidic mixed metal simulant solution. Batch contact experiments were performed using MST and two CST type materials. The MST material is a 15 wt % powder in 0.15 M NaOH slurry. The MST showed low adsorption for elements of interest from acidic solution. Furthermore, the powder size makes MST non-ideal for column operations. A CST IE-911 ion exchange material had high Cs adsorption, moderate Sr, and marginal Ce adsorption. Based on adsorption of all species, the ion exchange capacity was found to be 0.032 meq/mL. A bench-top column experiment to measure elemental breakthrough curves was performed using CST IE-911 where chromatographic separations of the mixed simulant were expected to occur. While most elements behaved as expected, the lanthanide series, containing Ce, broke though the column earlier than expected. The second CST material, CST R9120, displayed high adsorption for all elements in the acidic mixed simulant solutions in a batch contact study, and had a calculated loading capacity of 0.091 meq/mL. Future studies to develop a waste treatment flowsheet should focus on CST R9120 to treat SHINE waste solutions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗