Phase and defect diagrams based on spectral grain boundary segregation: A regular solution approach
Not provided.
Materials Science↗
SEARCH · Engineering Papers
Results for “solution regularity”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN 2 :ZnO system
We present a new solid-state material phase which is a disordered solid solution but offers many ordered line-compound features. The emergent physical phenomena are rooted in the perfect short-range order which conserves the local octet rule. We model the dual-sublattice-mixed semiconductor alloy (ZnSnN 2 ) 1-x (ZnO) 2x using first-principles calculations, Monte-Carlo simulations with a model Hamiltonian, and an extension of the regular solution model by incorporating short-range order. We demonstrate that this unique solid solution, occurring at a “magic” composition, can provide an electronically pristine character without disorder-induced charge localization and, therefore, a superior carrier transport similar to ordered phases. Interestingly, this phase shows singularities that are absent in the conventional solid-solution models, such as the regular solution and band-gap bowing model. Thermodynamically, this alloy phase has a sharply reduced enthalpy at its composition (like a line compound), but it still requires the entropy from long-range disorder to be stabilized at experimentally accessible temperatures.
36 MATERIALS SCIENCE↗
Energetics of hydroxylbastnäsite solid solutions, La 1-$\chi$ Nd $\chi$ CO 3 OH
Bastnäsites (LnCO 3 (F,OH)) are a group of common rare earth elements (REE)-bearing minerals and are one of the primary global sources of REE. Due to the chemical similarities among REE, bastnӓsites tend to occur as solid solutions instead of end members in REE containing ores. To better understand the processes and the mechanisms of formation of such deposits, it is essential to determine the thermodynamic properties of bastnӓsites, including hydroxylbastnӓsite (LnCO 3 OH) solid solutions. In this work, we performed detailed structural and calorimetric investigations on synthetic hexagonal La–Nd hydroxylbastnӓsite (La 1-$\chi$ NdCO 3 OH, $\chi$ = 0, 0.25, 0.5, 0.75, 1) solid solutions. X-ray diffraction confirms the crystal structure of the solid solution series in the $\ P$6 space group, and pair distribution function (PDF) analysis reveals local bonding environments characterized by three different types of 9-coordinated metal-oxygen polyhedra. Unit cell parameters of La1–xNdxCO3OH exhibit a nearly linear relation with the Nd content x, suggesting a random distribution of La and Nd in the structure. Their standard enthalpies of formation (Δ$\ H$° f ) were determined by high temperature oxide melt drop solution calorimetry, from which the enthalpies of mixing (Δ$\ H$ mix ) were derived. The Δ$\ H$ mix can be fitted by a regular solution model with an interaction parameter of 12.58 ± 0.16 kJ/mol, suggesting enthalpic metastability of La1–xNdxCO3OH relative to the two endmembers. Combining entropy and enthalpy, we further estimated the Gibbs free energies of mixing (Δ$\ G$ mix ) at relevant temperatures, revealing favorable temperatures under which the intermediate La 1-$\chi$ NdCO 3 OH phases can be stabilized. Such entropy-driven stabilization, as is consistent with our geochemical modeling results, may explain the enhancement of thermal stability of the solid solutions in nature. Additionally, the temperature range constrained from this study may be used to estimate the thermal history of REE bastnӓsite deposit.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Effective pair potential for random fcc CoCrFeMnNi alloys
The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C 12 - C 44 , which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.
Materials Science↗
Recent developments in mathematical aspects of relativistic fluids
Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.
Disconzi, Marcelo (ORCID:0000000234497778)↗
Synthesis and Characterization of Macrocyclic Ionic Liquids for CO 2 Separation
In this work, a series of ionic liquids with symmetric, macrocyclic cations composed of N-heterocycles connected by alkyl or ether linkages coupled with bis(trifluoromethylsulfonyl)imide or bis(pentafluoroethanesulfonyl)amide anions were synthesized to explore their application in CO 2 separation. These novel ionic liquids showed selective physical absorption of CO 2 compared to N 2 making them potential candidates for carbon capture. We examined the effect of cation structure on the physicochemical and separations properties of the ionic liquid and showed that these ionic liquids exhibit an inverse relationship between molar volume and CO 2 sorption capacity following the trend predicted by models based on regular solution theory. The fractional free volumes of the ionic liquids were lower than typical alkyl-imidazolium ionic liquids despite the cyclic structure of the cations which could be related to the flexibility of the alkyl and ether linkages. These results provide added insight into our understanding of structure–property relationships in CO 2 solubility in ionic liquids and afford a path toward enhancing the separations properties based on structure.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Risk-averse optimal control of semilinear elliptic PDEs
In this paper, we consider the optimal control of semilinear elliptic PDEs with random inputs. These problems are often nonconvex, infinite-dimensional stochastic optimization problems for which we employ risk measures to quantify the implicit uncertainty in the objective function. In contrast to previous works in uncertainty quantification and stochastic optimization, we provide a rigorous mathematical analysis demonstrating higher solution regularity (in stochastic state space), continuity and differentiability of the control-to-state map, and existence, regularity and continuity properties of the control-to-adjoint map. Our proofs make use of existing techniques from PDE-constrained optimization as well as concepts from the theory of measurable multifunctions. We illustrate our theoretical results with two numerical examples motivated by the optimal doping of semiconductor devices.
97 MATHEMATICS AND COMPUTING↗
Overcoming time and complexity limitations in molecular dynamics investigations of equilibrium melting
Abstract A hybrid Monte-Carlo molecular-dynamics method for determining solidus and liquidus compositions in multicomponent systems is presented that overcomes both the time limitations in conventional molecular dynamics that prevent the evolution of distinct solid and liquid compositions via diffusion and the complexity challenge that prevents use of thermodynamic assessment in systems of many components. This hybrid method is validated in the Cu–Ni system against an independent assessment of solidus and liquidus compositions based on the regular solution model. Strategies for efficient mapping of different phase diagrams, based on the thermodynamic parameter T 0 , the temperature at which two phases of the composition X 0 have equal free energies, are presented and then demonstrated for the copper-nickel fully miscible system and the gold–silicon eutectic system. A calculation of the solidus and liquidus sampled during the equilibrium melting of equiatomic CrMnFeCoNi is performed, indicating that this method has potential to be extended to the study of many component alloys.
Au-Si↗
Ladder symmetries of black holes. Implications for love numbers and no-hair theorems
It is well known that asymptotically flat black holes in general relativity have a vanishing static, conservative tidal response. Here, we show that this is a result of linearly realized symmetries governing static (spin 0,1,2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties: (1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon; (2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.
79 ASTRONOMY AND ASTROPHYSICS↗
Heterostructural Alloy Phase Diagram for (Cd 1-x Zn x ) 3 As 2
Alloying the topological semimetal Cd 3 As 2 with Zn 3 As 2 provides a potential route for controlling the electronic properties. We predict the alloy phase diagram from first-principles calculations, considering that both end members have a crystal structure derived from the antifluorite lattice, but with different arrangements of the unoccupied cation sites. To overcome the limitations of the regular solution approximation and to include short-range order effects, we perform Monte Carlo simulations, parameterize the temperature dependence of the mixing enthalpy ΔH m , and perform thermodynamic integration of the free energy. The resulting phase diagram exhibits features that are unique to heterostructural alloy systems and provides computational predictions of solubility limits and composition ranges that are stable against spinodal decomposition.
36 MATERIALS SCIENCE↗
A correction procedure for self-induced velocity of a finite-sized particle in two-way coupled Euler–Lagrange simulations
The importance of incorporating a correction to undo the self-induced perturbation velocity of a particle, when its size becomes comparable to the Eulerian grid, in a two-way coupled Euler–Lagrange (EL) simulation is now well appreciated. The present work improves upon the prior correction procedures in a few important ways. First, the past correction procedures have been scalar-based with the assumption that the quasi-steady force is the source of self-induced velocity perturbation. Here we generalize to a vector correction procedure and thereby the directions of feedback force and relative velocity can be different. This allows the correction procedure to be used even in the presence of added-mass, history, and lift forces. Second, the effect of a nearby wall has been systematically included in the correction procedure. The correction procedure depends on fundamental Oseen solutions of streamwise and transverse regularized feedback forces. We present a Fourier transform-based analytical approach to obtaining these regularized Oseen solutions. We also present a step-by-step numerical procedure for obtaining the Oseen solutions in any EL code. With the analytical or numerical Oseen functions, the correction procedure can be easily implemented in any EL code. Iterations are required in solving the implicit correction equations and it is demonstrated that the correction procedure converges rapidly within three or four iterations. In conclusion, a simple empirical approach is also presented to account for unsteady effects in the correction procedure.
97 MATHEMATICS AND COMPUTING↗
Online State Estimation for Time-Varying Systems
The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares (LS) approach well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix the paper proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized LS cost augmented with a proximal-point-type regularization. With the solution of the regularized LS problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.
24 POWER TRANSMISSION AND DISTRIBUTION↗
3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers
With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Apparently superluminal superfluids
We consider the superfluid phase of a specific renormalizable relativistic quantum field theory. We prove that, within the regime of validity of perturbation theory and of the superfluid effective theory, there are consistent and regular vortex solutions where the superfluid’s velocity field as traditionally defined smoothly interpolates between zero and arbitrarily large superluminal values. We show that this solution is free of instabilities and of superluminal excitations. We show that, in contrast, a generic vortex solution for an ordinary fluid does develop an instability if the velocity field becomes superluminal. All this questions the characterization of a superfluid velocity field as the actual velocity of “something”.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Thermodynamic stabilization of nanocrystalline aluminum
Nanocrystalline metals are generally unstable due to a large volume fraction of high-energy grain boundaries associated with a small grain size. Preferential dopant segregation to the high-energy grain boundaries is observed to enhance the stability of the material’s microstructure by minimizing its energy. Nanocrystalline aluminum-dopant systems were evaluated for thermodynamic stability against grain growth and phase precipitation via the mechanism of grain boundary segregation according to a modified regular nanocrystalline solution model. Fifty-one potential dopant elements have been evaluated for their efficacy in stabilizing nanostructures with three potential candidates, magnesium, lanthanum, and silicon, identified possessing the characteristics to promote grain boundary segregation and a state of thermodynamic stability in aluminum’s nanocrystalline regime. Here, the minimum dopant content required to achieve nanocrystalline microstructure stability is identified for each of the three candidate elements. Beyond this minimum content, further addition of the dopant elements decreased the final microstructure’s stability with no effects on the existence of a stable nanocrystalline state.
36 MATERIALS SCIENCE↗
Deep Eutectic Solvents: A Review of Fundamentals and Applications
Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These green materials are promising for applications as inexpensive ’designer’ solvents exhibiting a host of tunable physicochemical properties. Here, a detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding behavior is postulated as the root cause of their melt-ing point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework for understanding DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies gainful research thrusts that would advance the field towards predictive models and fundamental understanding of these solvents.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Node Distortion as a Tunable Mechanism for Negative Thermal Expansion in Metal–Organic Frameworks
Chemically functionalized series of metal–organic frameworks (MOFs), with subtle differences in local structure but divergent properties, provide a valuable opportunity to explore how local chemistry can be coupled to long-range structure and functionality. Using in situ synchrotron X-ray total scattering, with powder diffraction and pair distribution function (PDF) analysis, we investigate the temperature dependence of the local- and long-range structure of MOFs based on NU-1000, in which Zr 6 O 8 nodes are coordinated by different capping ligands (H 2 O/OH, Cl – ions, formate, acetylacetonate, and hexafluoroacetylacetonate). We show that the local distortion of the Zr 6 nodes depends on the lability of the ligand and contributes to a negative thermal expansion (NTE) of the extended framework. Using multivariate data analyses, involving non-negative matrix factorization (NMF), we demonstrate a new mechanism for NTE: progressive increase in the population of a smaller, distorted node state with increasing temperature leads to global contraction of the framework. The transformation between discrete node states is noncooperative and not ordered within the lattice, i.e., a solid solution of regular and distorted nodes. Density functional theory calculations show that removal of ligands from the node can lead to distortions consistent with the Zr···Zr distances observed in the experiment PDF data. Control of the node distortion imparted by the nonlinker ligand in turn controls the NTE behavior. Furthermore, these results reveal a mechanism to control the dynamic structure of MOFs based on local chemistry.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗