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At least 523 records · Page 29

Theoretical and experimental constraints for the equation of state of dense and hot matter

Abstract This review aims at providing an extensive discussion of modern constraints relevant for dense and hot strongly interacting matter. It includes theoretical first-principle results from lattice and perturbative QCD, as well as chiral effective field theory results. From the experimental side, it includes heavy-ion collision and low-energy nuclear physics results, as well as observations from neutron stars and their mergers. The validity of different constraints, concerning specific conditions and ranges of applicability, is also provided.

Kumar, Rajesh (ORCID:0000000327463956)↗

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SymbolFit: Automatic Parametric Modeling with Symbolic Regression

We introduce SymbolFit (API: https://github.com/hftsoi/symbolfit), a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run. Traditionally, constructing a parametric model to accurately describe binned data has been a manual and iterative process, requiring an adequate functional form to be determined before the fit can be performed. The main challenge arises when the appropriate functional forms cannot be derived from first principles, especially when there is no underlying true closed-form function for the distribution. In this work, we develop a framework that automates and streamlines the process by utilizing symbolic regression, a machine learning technique that explores a vast space of candidate functions without requiring a predefined functional form because the functional form itself is treated as a trainable parameter, making the process far more efficient and effortless than traditional regression methods. We demonstrate the framework in high-energy physics experiments at the CERN Large Hadron Collider (LHC) using five real proton-proton collision datasets from new physics searches, including background modeling in resonance searches for high-mass dijet, trijet, paired-dijet, diphoton, and dimuon events. We show that our framework can flexibly and efficiently generate a wide range of candidate functions that fit a nontrivial distribution well using a simple fit configuration that varies only by random seed, and that the same fit configuration, which defines a vast function space, can also be applied to distributions of different shapes, whereas achieving a comparable result with traditional methods would have required extensive manual effort.

Tsoi, Ho Fung [Univ. of Pennsylvania, Philadelphia↗

Alloying Effects on the Transport Properties of Refractory High-entropy Alloys

Additive Manufacturing (AM) has opened new frontiers for the design of refractory high-entropy alloys (HEAs) for high-temperature applications. The thermal conductivity of the AM feedstock is among the most important thermo-physical properties that control the melting and solidification process. Despite its significance, there remains a notable gap in both computational and experimental research concerning the thermal conductivity of HEAs. Here, we use density functional theory (DFT) to systematically investigate the alloying effects on the transport properties of Ti-Cr-Mo-W-V-Nb-Ta RHEAs, including electrical and thermal conductivities and Seebeck coefficient. The relaxation time of charge carriers is a key underlying parameter determining thermal conductivity that is exceedingly challenging to predict from first principles alone, and we thus follow the approach by Mukherjee, Satsangi, and Singh [Chem Mater 32, 6507 (2022)] to optimize the relaxation time for RHEAs. Here we validated thermal conductivity predictions on elemental solids, binary and ternary alloys, and RHEAs and compared them against thermodynamic (CALPHAD) predictions and our experiments with good correlations. To understand observed trends in thermal conductivity, we assessed the phase stability, electronic structure, phonon, and intrinsic- and tensile strength of down-selected RHEAs. Our electronic structure and phonon results connect well with the observed compositional trends for thermal transport in RHEAs. Our DFT assessment and CALPHAD predictions provide a unique design guide for RHEAs with tailored thermal conductivity, a critical consideration for AM and thermal-management applications.

36 MATERIALS SCIENCE↗

Destabilizing high-capacity high entropy hydrides via earth abundant substitutions: From predictions to experimental validation

The vast chemical space of high entropy alloys (HEAs) makes trial-and-error experimental approaches for materials discovery intractable and often necessitates data-driven and/or first principles computational insights to successfully target materials with desired properties. In the context of materials discovery for hydrogen storage applications, a theoretical prediction-experimental validation approach can vastly accelerate the search for substitution strategies to destabilize high-capacity hydrides based on benchmark HEAs, e.g. TiVNbCr alloys. Here, in this study, machine learning predictions, corroborated by density functional theory calculations, predict substantial hydride destabilization with increasing substitution of earth-abundant Fe content in the (TiVNb) 75 Cr 25-x Fe x system. The as-prepared alloys crystallize in a single-phase bcc lattice for limited Fe content x < 7, while larger Fe content favors the formation of a secondary C14 Laves phase intermetallic. Short range order for alloys with x < 7 can be well described by a random distribution of atoms within the bcc lattice without lattice distortion. Hydrogen absorption experiments performed on selected alloys validate the predicted thermodynamic destabilization of the corresponding fcc hydrides and demonstrate promising lifecycle performance through reversible absorption/desorption. This demonstrates the potential of computationally expedited hydride discovery and points to further opportunities for optimizing bcc alloy ↔ fcc hydrides for practical hydrogen storage applications.

36 MATERIALS SCIENCE↗

The atomic-level structure and stability of interfaces of Pt nanoparticles in alumina: An experimental and computational evaluation

The atomic-level structure of interfaces between Pt and a transition form of Al2O3 were studied using a combination of electron microscopy and first principles calculations. A model system of Pt nanoprecipitates in Al2O3 were formed in sapphire wafers via high-energy ion implantation of Pt followed by thermal annealing at 1000 °C in air. The Pt nanoparticles took the form of tetrahedra and truncated tetrahedra primarily bound by {111}Pt facets. The high prevalence of these facets motivated the development of density functional theory (DFT) based models of (111)Pt interfaces with six different chemical terminations of ( 2 ¯ 01 ) θ-alumina. The atomic-level structure of the Pt/Al2O3 interfaces was characterized with aberration-corrected scanning transmission electron microscopy (STEM) and the experimental images were compared to STEM image simulations of the DFT models. The model interface with Pt bonded to oxygen-terminated θ-Al2O3, with the Pt located on top of the O and with an underlying layer of octahedral Al, provided the best match to the experimental images. This interfacial termination is also the most stable for the thermal annealing conditions used based on thermodynamic calculations of the interfacial energy as a function of temperature and oxygen partial pressure. This experimentally verified model provides a basis for improving models of Pt/γ-alumina interfaces.

Clauser, A L↗

The many faces of θ' -Al 2 Cu precipitates: Energetics of pristine and solute segregated Al/ θ' semi-coherent interfaces

θ'-Al 2 Cu precipitates in Al-Cu alloys have various distorted octagon shapes, which can be explained by the competition between {100} and {110} type semi-coherent interfaces with the Al matrix. While most prior studies on the semi-coherent Al/θ' interfaces have focused on the {100} orientation, little is known about the {110} interface. We have investigated the energetics of pristine and solute-segregated {110} semi-coherent Al/θ' interfaces with advanced characterization and first-principles studies. We report interfacial, strain, and solute segregation energetics of the {110} Al/θ' semi-coherent interface for 39 elements and compared them with previously reported values of the {100} interface. We discuss the atomic features and atomic local structures to identify similarities and differences between the two types of Al/θ' semi-coherent interfaces. Here, the isotropy in pristine Al/θ' semi-coherent interfacial energy and the anisotropy resulting from solute segregation provide insight into the formation of different types of θ' precipitate “faces” reported in the literature.

36 MATERIALS SCIENCE↗

Influence of isoelectronic mass modulation on phonon decay and transport in layered pnictogen-carbon systems

This study systematically investigates the structural, electronic, and thermal transport properties of layered pnictogen–carbon (Pn 2 C 2 ; Pn = P, As, Sb, Bi) monolayers, revealing a profound influence of isoelectronic mass modulation on phonon dynamics and thermal conductivity. Through first-principles calculations and lattice dynamics analysis, we demonstrate that increasing the atomic mass of pnictogens leads to elongated Pn-C bonds, weakened interatomic interactions, and enhanced phonon-phonon scattering, resulting in a dramatic reduction in lattice thermal conductivity (κ). Specifically, κ decreases exponentially from 65.6 W/m-K in P 2 C 2 to an ultralow 0.37 W/m-K in Bi 2 C 2 , driven by suppressed acoustic-optical phonon gaps Δ$^{Γ}_{A-0}$, increased anharmonicity, and reduced phonon lifetimes and group velocities. The transition from semiconducting to metallic behavior in heavier pnictogen-based systems further enhances phonon-electron scattering, contributing to thermal conductivity suppression. Structural analysis highlights the strengthening of out-of-plane C—C bonds and the contraction of C—Pn—C bond angles, which disrupt in-plane phonon transport. Further, these findings establish a design framework for engineering ultralow-κ materials through chemical substitution and structural tuning, offering significant potential for thermoelectric and thermal management applications. This work provides fundamental insights into phonon decay mechanisms and thermal transport in 2D materials, paving the way for advanced phononic and energy-efficient devices.

2D materials↗

Thermodynamic assessment of the quaternary WTaCrV refractory high entropy alloy as a means to guide experimental approaches

The deployment of fusion energy poses challenges for materials in plasma facing components to withstand high temperatures and thermal gradients, particle implantation and neutron damage. The current material of choice is tungsten, although property degradation limits its consideration in future fusion reactors. Hence, materials with better resistance to harsh environments need to be developed for fusion energy to become a reality. High entropy alloys are being explored as potential candidates with some compositions showing good radiation resistance to defect cluster formation. One of these materials is the WTaCrV system, although only one composition has been tested under ion irradiation. In this work, we study the thermodynamic properties of the entire quaternary alloy composition range. Coupling first principles calculations, cluster expansion approaches, and Monte Carlo methods, we access the free energy functionals, short-range ordering as a function of temperature, and atomic configurations that can be compared to experimental observations. We use this data to inform experiments into compositions with higher propensity to form solid solutions, instead of phase separating. With this formalism we have developed thermodynamic database (TDB) files that can be used to plot quaternary phase diagrams.

Cluster Expansion↗

Tailoring microstructures with mild magnetic-field processing: A case study of CuNiFe alloys

Combined experimental and computational investigations of the CuNiFe spinodal system confirm that application of a mild magnetic field during thermal treatment alters elemental redistribution and the resulting microstructure, relative to that obtained from zero-field annealing. Spinodal decomposition of a Cu 40 Ni 42 Fe 18 alloy was initiated during thermal treatment at 773 K, conducted either under zero field or modest (60 mT) magnetic f ield conditions for up to 200 h. Periodic (~10 nm) chemical modulations into Cu-rich and NiFe-rich regions were observed under both conditions, with the amplitude and wavelength of the segregated regions increasing with treatment time. However, magnetic field annealing resulted in a more than twofold increase in the amplitude of elemental modulations relative to zero-field conditions – consistent with enhanced diffusional f luxes during spinodal decomposition – while the modulation wavelength remained largely unaffected. These microstructural differences are reflected in various extrinsic magnetic properties. In parallel, first-principles DFT calculations indicate that long-range ferromagnetic order, as induced by an applied magnetic field, substantially alters the strength and nature of atomic interactions, enhancing the thermodynamic instability of the CuNiFe solid solution. Collectively, these results suggest that incorporating a mild (millitesla-level) magnetic field – distinct from the strong (tesla-level) fields commonly used in prior studies – during thermal processing has the potential to deliver enhanced control of microstructures for targeted engineering outcomes.

36 MATERIALS SCIENCE↗

Chemical complexity suppresses interstitial solute segregation to screw dislocation cores in the bcc NbTaTiHfZr high-entropy alloy

Recent reports suggest that interstitial solute additions to body-centered cubic (bcc) high-entropy alloys (HEAs) may enhance their mechanical properties. However, details of interactions between interstitial atoms and dislocations in these HEAs remain incompletely understood. Using first-principles calculations, we examine the energetics of C, N, and O interstitial solutes in elemental bcc metals and NbTaTiHfZr, focusing on their segregation in screw dislocation cores. We examine two types of core sites and show that the low-energy configuration and associated segregation energy depend on the transition metal group. In NbTaTiHfZr, we find that chemical complexity substantially suppresses interstitial segregation in dislocation cores, as fluctuations in bulk solute energies induce energetically favorable sites that disfavor segregation to core sites. Local chemical order further enhances this effect by promoting solute clustering away from dislocation cores. These findings reveal fundamental differences between the behavior of interstitial atoms in elemental metals and HEAs, with implications for high-temperature plasticity and dynamic strain aging.

Body-centered cubic transition metals↗

Effect of magneto-mechanical synergism in the process-structure correlation in Fe–C alloys: A phase-field modeling approach

Applied magnetic fields can alter phase equilibria and kinetics in steels; however, quantitatively resolving how magnetic, chemical, and elastic driving forces jointly influence the microstructure remains challenging. We develop a quantitative magneto-mechanically coupled phase-field model for the Fe–C system that couples a CALPHAD-based chemical free energy with demagnetization-field magnetostatics and microelasticity. Here, the model reproduces single- and multi-particle evolution during the α → γ inverse transformation at 1023 K under external fields up to 20 T, including ellipsoidal morphologies observed experimentally at 8 T. Chemically driven growth is isotropic; a magnetic interaction introduces an anisotropic driving force that elongates γ precipitates along the field into ellipsoids, while elastic coherency promotes faceting, yielding elongated cuboidal or “brick-like” particles under combined magneto-elastic coupling. Growth kinetics increase with C content, and decrease with field strength and misfit strain. Multi-particle simulations reveal dipolar interaction-mediated coalescence for field-parallel neighbors and ripening for field-perpendicular neighbors. Incorporating field-dependent diffusivity from experiment slows kinetics as expected; a first-principles-motivated anisotropic diffusivity correction is estimated to be small (<2%). These results establish a process-structure link for magnetically assisted heat treatments of Fe–C alloys and provide guidance for microstructure control via chemo-magneto-mechanical synergism.

Magnetic field↗

Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System

Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Water effects on NH 3 -SCR over Cu-based small-pore zeolite catalysts: A review

The selective catalytic reduction (SCR) of NO x with NH 3 as the reductant over small-pore Cu-zeolite catalysts is a leading strategy for controlling emissions from diesel engines and mobile sources. While the hydrothermal stability of Cu-zeolites such as Cu-SSZ-13, Cu-SAPO-34, and Cu-SSZ-39 has been extensively studied, the multifaceted role of water vapor under operating conditions has only recently received systematic attention. Water impacts multiple aspects of SCR catalysis, including NO x conversion, N 2 O formation, Cu ion speciation, redox kinetics, and surface reactions. This review comprehensively summarizes recent advances in understanding the effect of water on NH 3 -SCR over Cu-based catalysts. For Cu-SSZ-13, water vapor induces both inhibitory and promotive effects depending on temperature, Cu loading, and Si/Al ratio by altering NH 3 adsorption, Cu mobility, and redox half-cycle kinetics. Studies have revealed that water can suppress ammonium nitrate formation at low temperatures and enhance nitrate pathways at higher temperatures. Over Cu-SAPO-34, water promotes NO conversion by improving Cu(II) reducibility and strengthening Brønsted acidity. First-principles calculations confirm that water-coordinated Cu species lower O 2 activation barriers. In Cu-SSZ-39, water was found to facilitate Cu reduction, migration, and O 2 activation, resulting in superior water tolerance and unexpected catalytic promotion. Both experimental and computational studies highlight that water vapor exerts complex, catalyst-dependent effects on NH 3 -SCR performance, underscoring the need for tailored catalyst designs that leverage beneficial water interactions while minimizing inhibitory impacts.

Ammonia selective catalytic reduction↗

Ghost states and surface structures of the charge density wave kagome metal ScV 6 Sn 6

In this work, we investigate the high-temperature phase of the kagome metal ScV 6 Sn 6 using scanning tunneling microscopy/spectroscopy (STM/S) and density functional theory calculations. STM topographic images of the cleaved sample reveal two distinct surface terminations: flat islands with Sn termination and trenches terminated by kagome layers with Sn as the outermost atomic layer. STS measurements on the Sn-terminated and kagome-terminated surfaces show significant differences, in particular the presence of large density of states near the Fermi level in the former case. Our first-principles calculations reveal that the charge density on the kagome-terminated surface gives rise to “ghost states” which show intensity away from surface atoms, arising due to hybridization of orbitals above the surface. These states can obscure the intrinsic properties of the surface, potentially leading to misattribution of the surface termination. This underscores the need for careful interpretation in STM studies, especially when discerning surface states of localized states. Understanding the surface structure of this versatile quantum material provides essential information for interpreting surface-sensitive experiments, tailoring material properties, engineering interfaces, and controlling stability and reactivity. This knowledge paves the way for further exploration and potential applications of kagome lattice materials in various fields, including quantum computing, topological physics, and advanced electronic devices.

36 MATERIALS SCIENCE↗

Rational design of heterogeneous single-site catalysts via surface organometallic chemistry

Single-site heterogeneous catalysts offer an attractive route to unite the molecular precision of homogeneous catalysis with the durability and practical advantages of solids. Surface organometallic chemistry (SOMC) provides a particularly powerful strategy for this purpose by grafting molecular precursors onto tailored surfaces and converting support functionalities into ligand environments for isolated metal centers. As a result, SOMC brings the language and logic of coordination chemistry to heterogeneous catalysis, where the support becomes an integral part of the active site coordination sphere. This Review surveys recent progress in the rational design of SOMC-derived single-site catalysts, with emphasis on synthetic routes, post synthetic transformations, and the deliberate tuning of catalytic behavior through metal-support interactions. Discussions are made on how support identity, hydroxyl topology, acidity, and redox activity shape the geometry, electronic structure, and oxidation state of supported metal sites, as well as how these factors determine activity, selectivity, and stability. We also examine a central limitation of these systems: despite their molecularly informed design, supported single sites often exist as structurally distributed ensembles rather than uniform species, particularly on amorphous supports. This site heterogeneity, along with catalyst dynamics under operating conditions, remains a major barrier to definitive structure-activity relationships. Therefore, emerging approaches that combine advanced characterization, first-principles modeling, ensemble kinetics, and machine learning to resolve active-site structure and guide catalyst development are highlighted. Together, these advances position SOMC as a versatile coordination chemistry framework for the predictive design of heterogeneous catalysts with well-defined molecularly tailored active sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Macroscale properties and atomic-scale mechanisms of ash removal in low-temperature hydrothermal carbonization

Biogenic ash is a significant impediment to the utilization of agricultural residues in biofuel production. Such challenge can be addressed by various treatments, as demonstrated in this study on the experimental and computational mechanisms involved in the hydrothermal treatment (HT) of wheat straw. A combination of classical (all-atom) molecular dynamics simulations of cellulose carrying silica and calcium species, along with first principles quantum chemical calculations, indicates the dissociation of inorganics from the cellulose with increased HT temperature. Here, this observation is confirmed by experimental evidence of effective ash removal by HT, showing at least 50% removal of sulfur, chlorine, potassium, and calcium, and 12.5% of silica, leading to a reduced total ash content (from 6.7% to 4.2%).Changes in structural features upon HT, such as surface cellular structure and porosity, were revealed, accompanied by an increased specific surface area (from 1.17 to 6.34 m 2 /g). Our simulations suggest that silica binds tightly to the hydrophobic face of cellulose at room temperature, but HT significantly reduces the binding free energy of association with both hydrophobic and hydrophilic surfaces. Most significantly, ash removal leads to an increased calorific value, rising from approximately 16 MJ/kg to about 19 MJ/kg, along with improved thermal behavior. The improved integration combustion index parameter S indicates that the combustion properties improve with ash removal efficiency. The proposed atomic-level mechanism for the observed removal of inorganics during mild HT underscores the potential of such treatment in producing energy-dense wheat straw, a widely available agricultural residue.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the applicability of the Redlich-Kister framework for viscosity estimation of molten halide salt mixtures

For molten halide salt mixtures already being utilized or under consideration for carbon-free energy production systems, it is crucial that their viscosity is well understood so that system thermal hydraulics can be reliably assessed. Because of the difficulty in accurately measuring molten halide viscosity and the sheer size of the matrix of possible higher order salt mixtures that may be of interest to the energy industry, there are several gaps in the quantified understanding of molten halide viscosity across this matrix. As such, both first-principles and semi-empirical modeling techniques may be crucial for rapidly assessing this broad, complex compositional domain. Herein, the Redlich-Kister framework is applied to assess the feasibility of broadly interpolating and estimating the viscosity of several pseudobinary and pseudoternary molten halide salt systems that may be of key interest to the energy industry. The framework is based on the assumption that an ideal component and a nonideal component collectively describe the viscosity as a function of composition and temperature for a given molten halide system. Three different ideal models were considered for the ideal component, including Grunburg-Nissan, Katti-Chaudhri, and Gambill methods. Regarding the pseudobinary interpolations, the Redlich-Kister models with either the Grunburg-Nissan or Katti-Chaudhri models as the ideal component resulted in either highly (average error less than 5%) or reasonably (average error less than 15%) accurate interpolations of pseudobinary halide viscosity; BeF 2 - or UF 4 -bearing salts tended to result in reasonably accurate interpolations, whereas other pseudobinary mixtures tended to show high accuracy. Regarding the pseudoternary extrapolations, the Redlich-Kister framework shows reasonable success at estimating the extent to which a pseudoternary system may indicate deviations from ideal Grunburg-Nissan mixing, where discrepancies with comparative experimental data generally stay within 30%. Finally, the primary reasons identified for such discrepancies are (1) inaccuracy in the underlying experimental data, (2) different complexation behavior in the higher order systems compared to the pseudobinary subsystems, and (3) extrapolation into temperatures too far out of the domain, which is valid for the underlying experimental data feeding the Redlich-Kister model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗