Phase and defect diagrams based on spectral grain boundary segregation: A regular solution approach
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Materials Science↗
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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↗
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↗
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↗
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↗
Quantification of Dynamic Scattering Effects in Molecular Crystals using Large Angle Rocking Beam Electron Diffraction
Electron crystallography provides a pathway to solve structure of small crystals (< 1um) in size, and thus overcomes difficult synthesis constraints involved in growing large crystals. Generally, electron diffraction data is collected in the form of integrated intensity using continuous rotation or by precession. The measured intensities in 3D are utilized for structure solution. Using this approach, structure solution of difficult crystals, such as small crystals of zeolites, metal-organic frameworks, molecular crystals, and proteins , can be solved by electron diffraction. However, electron structure solutions are regularly reported with higher Rvalues than x-ray or neutron diffraction. While similar structures are found despite the high R-values, the differences in the measure intensity and theory calculated intensity limit information that can be extracted by electron diffraction. Previous work demonstrated that including multiple-scattering effects significantly reduce the R-values . Thus, it is critical to be able to quantify the dynamical diffraction effects in molecular crystals.
Crystallography↗
PolyODENet: Deriving mass-action rate equations from incomplete transient kinetics data
Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space. Here, using simple catalytic reaction models, we demonstrate that PolyODENet can predict reaction profiles of unknown species and doing so even reveal hidden parts of reaction mechanisms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Solution Irregularity Remediation for Spatial Discretization Error Estimation for S N Transport Solutions
The discrete ordinates linear Boltzmann transport equation is typically solved in its spatially discretized form, incurring spatial discretization error. Quantification of this error for purposes such as adaptive mesh refinement or error analysis requires an a posteriori estimator, which utilizes the numerical solution to the spatially discretized equation to compute an estimate. Because the quality of the numerical solution informs the error estimate, irregularities, present in the true solution for any realistic problem configuration, tend to cause the largest deviation in the error estimate vis-a-vis the true error. In this paper, an analytical partial singular characteristic tracking (pSCT) procedure for reducing the estimator’s error is implemented within our novel residual source estimator for a zeroth-order discontinuous Galerkin scheme, at the additional cost of a single inner iteration. Here, a metric-based evaluation of the pSCT scheme versus the standard residual source estimator is performed over the parameter range of a Method of Manufactured Solutions test suite. The pSCT scheme generates near-ideal accuracy in the estimate in problems where the dominant source of the estimator’s error is the solution irregularity, namely, problems where the true solution is discontinuous and problems where the true solution’s first derivative is discontinuous and the scattering ratio is low. In problems where the scattering ratio is high and the true solution is discontinuous in the first derivative, the error in the scattering source, which is not converged by the pSCT scheme, is greater than the error incurred due to the irregularity. Ultimately, a pSCT scheme is judged to be useful for error estimation in problems where the computational cost of the scheme is justified. In the presence of many irregularities, such a scheme may be intractable for general use, but in benchmarks, as an analytical tool, or in problems that have nondissipative discontinuities, the scheme may prove invaluable.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
PolyODENet
Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space.
Wu, Qin [Brookhaven National Lab. (BNL), Upton, NY↗