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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.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

A Computational and Experimental Investigation of Shear Coaxial Jet Atomization

The instability and subsequent atomization of a viscous liquid jet emanated into a high-pressure gaseous surrounding is studied both computationally and experimentally. Liquid water issued into nitrogen gas at elevated pressures is used to simulate the flow conditions in a coaxial shear injector element relevant to liquid propellant rocket engines. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative form. Numerical solutions of the governing equations subject to appropriate initial and boundary conditions are obtained via a robust finite difference scheme. The computations yield real-time evolution and subsequent breakup characteristics of the liquid jet. The experimental investigation utilizes a digital imaging technique to measure resultant drop sizes. Data were collected for liquid Reynolds number between 2,500 and 25,000, aerodynamic Weber number range of 50-500 and ambient gas pressures from 150 to 1200 psia. Comparison of the model predictions and experimental data for drop sizes at gas pressures of 150 and 300 psia reveal satisfactory agreement particularly for lower values of investigated Weber number. The present model is intended as a component of a practical tool to facilitate design and optimization of coaxial shear atomizers.

Ibrahim, Essam A.↗
DOE OSTI2019

Evolving charge correlations in a hybrid model with both hydrodynamics and hadronic Boltzmann descriptions

Background: Correlations from charge correlation, known as charge balance functions, provide critical tests of the chemical evolution of matter in a heavy-ion collision. Comparisons of experimental balance functions with calculations from parametric descriptions of the final state suggest that the charge production in the earliest stages of a heavy-ion collision are consistent with having generated an amount of light up, down, and strange quarks that are largely consistent with expectations for creating a chemically equilibrate quark-gluon plasma. Purpose: This work describes a full simulation of the evolving correlations superimposed on a state-of-the-art microscopic description of the collision. Methods: The creation and diffusion of balancing charges is modeled on the background of a hybrid description of the evolution based on hydrodynamics, for when the matter’s temperature is above 155 MeV, and a microscopic hadronic simulation, for the breakup stage. The translation of the charge-charge correlation function, indexed by the flavors up, down, and strange, into correlations between specific hadron species is built on the assumption that differential charges enhance differential yields according to statistical equilibrium. Monte Carlo methods are implemented when applicable. Results: The charge balance functions are predicted for pairs indexed by charge alone or by whether the particle pairs are any combination of pions, kaons, or protons. We report comparisons with experiment are remarkably successful except for the proton-kaon balance functions. Conclusions: This demonstrates first that two-particle correlations from charge conservation can be calculated for a state-of-the-art model of the evolution with moderate amounts of computation. Aside from the magnitude of the proton-kaon correlations, the calculations well describe preliminary experimental results from the STAR Collaboration at the Relativistic Heavy Ion Collider. Ignoring the one disagreement, this suggests that the matter in a heavy-ion collision comes close to maintaining chemical equilibrium during the superhadronic stage of a heavy-ion collision.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

The Fundamental Creep Behavior Model of Gr.91 Alloy by ICME Approach (Final Report)

The current project mainly focused on the fundamental creep cracking mechanism of the Grade 91 system during the operation conditions in the advanced technologies FE power plants and build the link among Composition-Processing Parameters-Phase Stability-Microstructure-Creep Resistance. A model based on computational thermodynamics and diffusion kinetics will be developed to provide guidance on how to improve the creep resistance of the alloy system. The PI mainly investigate the Gr.91 base alloy and weldment with the Integrated Computational Materials Engineering (ICME) approach. The long-term goal of the proposed program is to develop a model for creep and fatigue resistant alloys with different elemental systems, compositions, and processing parameters of weldment and heat-treatment. In addition, new creep and fatigue resistant alloys are to be designed based on the predictions from the model. The computational as well as experimental results include three sections: 1) The compositional optimization and secondary phases evaluation regarding the creep resistance in Grade 91 steel through the CALPHAD approach. In this section, the formation of the critical secondary phases, M23C6, MX and Z-phase were well predicted based on many conditions like the temperature as well as compositions. Meanwhile, the role of different alloying elements was also considered as they will directly affect the formation of the secondary phases mentioned above based on the compositional evolution of the alloying elements. 2) An investigation of Creep Resistance in Grade 91 Steel through Computational Thermodynamics. We systematically considered the evolution of the four critical temperatures, Ac3, Ac1, the threshold of M23C6 and Z-phase, on basis of the computational approach. Meanwhile, the equilibrium cooling as well as Scheil simulations were also considered to perform further predictions based on the different cooling rates. 3) Creep lifetime and microstructural evolution of the Grade 91 steel. In this part, mainly experimental approach was performed on the real creep test from the beginning of the commercial Gr.91 alloys. The alloys were normalized, tempered, welded (Gleeble) and PWHT and finally subjected to the creep lifetime analyses. Finally, all the samples after each process were further characterized based on the OM, XRD and SEM technique to draw final conclusions.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2021

Compositionally-Driven Formation Mechanism of Hierarchical Morphologies in Co-Deposited Immiscible Alloy Thin Films

Co-deposited, immiscible alloy systems form hierarchical microstructures under specific deposition conditions that accentuate the difference in constituent element mobility. The mechanism leading to the formation of these unique hierarchical morphologies during the deposition process is difficult to identify, since the characterization of these microstructures is typically carried out post-deposition. We employ phase-field modeling to study the evolution of microstructures during deposition combined with microscopy characterization of experimentally deposited thin films to reveal the origin of the formation mechanism of hierarchical morphologies in co-deposited, immiscible alloy thin films. Our results trace this back to the significant influence of a local compositional driving force that occurs near the surface of the growing thin film. We show that local variations in the concentration of the vapor phase near the surface, resulting in nuclei (i.e., a cluster of atoms) on the film’s surface with an inhomogeneous composition, can trigger the simultaneous evolution of multiple concentration modulations across multiple length scales, leading to hierarchical morphologies. We show that locally, the concentration must be above a certain threshold value in order to generate distinct hierarchical morphologies in a single domain.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Effect of Direct Reduced Iron (DRI) on Dephosphorization of Molten Steel by Electric Arc Furnace Slag

We investigated the effect of direct reduced iron (DRI) addition on dephosphorization of molten steel by electric arc furnace (EAF) slag at 1823 K (1550 °C). Various phenomena such as CO gas evolution and slagmaking by gangue oxides in DRI were experimentally observed at each reaction step. Thermodynamic behaviors of phosphorus, oxygen, and carbon were strongly dependent on DRI content. Basicity, which is the thermodynamic driving force of dephosphorization, decreased with the increasing DRI content because SiO{sub 2} concentration in the slag was proportional to DRI addition. The excess free energy of P{sub 2}O{sub 5} increased with the increasing SiO{sub 2} content in slag. A higher DRI content made dephosphorization difficult by decreasing the basicity and stability of P{sub 2}O{sub 5} in the slag. Therefore, when using DRI in EAF process, it is very important to control the basicity of slag.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Constitutive Model for Hot Deformation of the Cu-Zr-Ce Alloy

Hot compressive deformation behavior of the Cu-Zr-Ce alloy has been investigated according to the hot deformation tests in the 550-900 °C temperature range and 0.001-10 s{sup −1} strain rate range. Based on the true stress–true strain curves, the flow stress behavior of the Cu-Zr-Ce alloy was investigated. Microstructure evolution was observed by optical microscopy. Based on the experimental results, a constitutive equation, which reflects the relationships between the stress, strain, strain rate and temperature, has been established. Material constants n, α, Q and ln A were calculated as functions of strain. The equation predicting the flow stress combined with these materials constants has been proposed. The predicted stress is consistent with experimental stress, indicating that developed constitutive equation can adequately predict the flow stress of the Cu-Zr-Ce alloy. Dynamic recrystallization critical strain was determined using the work hardening rate method. According to the dynamic material model, the processing maps for the Cu-Zr and Cu-Zr-Ce alloy were obtained at 0.4 and 0.5 strain. Based on the processing maps and microstructure observations, the optimal processing parameters for the two alloys were determined, and it was found that the addition of Ce can promote the hot workability of the Cu-Zr alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

An Integrated High-Speed Microstructural Characterization Method Using Simultaneous XRD, Stereo-DIC, and PCI

High-speed characterization of the deformation mechanisms in polycrystalline metals requires the quantification of full strain fields and local microstructural evolutions simultaneously. In this paper, we present a novel experimental method to integrate phase-contrast imaging (PCI), stereographic digital image correlation (stereo-DIC), and full-ring X-ray diffraction (XRD) to allow for the simultaneous characterization of polycrystalline metals at 1MHz or higher. A Kolsky bar was integrated into the synchrotron X-ray source in Sector 32 ID-B at the Advance Photon Source (APS) at Argonne National Laboratory. When the sample is dynamically loaded, the diagnostic methods of full-ring XRD, PCI, and stereo-DIC are properly synchronized to record the deformation behavior at both continuum and microstructural scales as a function of the loading history. An advanced high-strength steel (AHSS) is used as a model material to demonstrate the capabilities of this new experimental method.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction

We study the evolution of a spin-s system described by the long-range zz-type Ising interaction. The Fubini–Study metric of the quantum state manifold defined by this evolution is obtained. We explore the topology of this manifold and show that it corresponds to a sphere. Exploration of the Riemannian curvature allows us to determine the manifold geometry. Also we calculate the speed of evolution of the system and represent the curvature by means of this speed. This is important for an experimental measurement of the curvature. The conditions for achieving the minimal and maximal values of the speed of evolution are obtained. Also we examine the geometry of state manifold and speed of evolution of spin system in the thermodynamic limit. We propose the physical system of methane molecule for application of our considerations. Finally, we study the influence of an external magnetic field on the metric of state manifold and on the speed of evolution. In this case we obtain the conditions for achieving the minimal possible speed of evolution. For some predefined initial states the orientations of magnetic fields to reach the minimal and maximal values of the speed are found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

The development and applications of multidimensional biomolecular spectroscopy illustrated by photosynthetic light harvesting

The parallel and synergistic developments of atomic resolution structural information, new spectroscopic methods, their underpinning formalism, and the application of sophisticated theoretical methods have led to a step function change in our understanding of photosynthetic light harvesting, the process by which photosynthetic organisms collect solar energy and supply it to their reaction centers to initiate the chemistry of photosynthesis. The new spectroscopic methods, in particular multidimensional spectroscopies, have enabled a transition from recording rates of processes to focusing on mechanism. We discuss two ultrafast spectroscopies – two-dimensional electronic spectroscopy and two-dimensional electronic-vibrational spectroscopy – and illustrate their development through the lens of photosynthetic light harvesting. Both spectroscopies provide enhanced spectral resolution and, in different ways, reveal pathways of energy flow and coherent oscillations which relate to the quantum mechanical mixing of, for example, electronic excitations (excitons) and nuclear motions. The new types of information present in these spectra provoked the application of sophisticated quantum dynamical theories to describe the temporal evolution of the spectra and provide new questions for experimental investigation. While multidimensional spectroscopies have applications in many other areas of science, we feel that the investigation of photosynthetic light harvesting has had the largest influence on the development of spectroscopic and theoretical methods for the study of quantum dynamics in biology, hence the focus of this review. We conclude with key questions for the next decade of this review.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Kinetic Monte Carlo Framework for Coupled Degradation and Dehydration of Anion Exchange Membranes

Kinetic Monte Carlo (kMC) simulations, augmented with temporal-acceleration schemes, can efficiently handle stiff reaction-transport networks when fast processes rapidly relax to quasi-equilibrium on a fixed lattice. However, in glassy anion-exchange membranes (AEM), rare and irreversible chemical degradation events continuously reshape the nanoscale morphology, and the associated hydration and transport degrees of freedom remain far from a well-defined local equilibrium. This combination of evolving state space and nonequilibrated fast dynamics lies outside the scope of existing kMC acceleration frameworks. Here, to address this challenge, we introduce an auxiliary-particle kinetic Monte Carlo (AP-kMC) scheme. In AP-kMC, short-lived mobile particles spawned at degradation sites execute hop, water-elimination, and decay moves, enforcing rapid local relaxation of the hydration structure while preserving the stochastic rules of kMC. Parameterized with molecular-dynamics morphologies and experimental solution degradation kinetics, AP-kMC reproduces the evolution of ion-exchange capacity, water uptake, and conductivity, and reveals a feedback loop in which poorly hydrated sites degrade first and each degradation event induces further local dehydration. The resulting thinning and fragmentation of water channels cause loss of hydrophilic percolation and abrupt conductivity collapse well before complete charge loss. AP-kMC thus reframes AEM durability as a coupled degradation–drying–percolation problem and provides a transferable strategy to simulate reactive, out-of-equilibrium polymer electrolytes where local solvation controls reactivity.

organic↗
DOE OSTI2026

Sculpting 2D Crystals via Membrane Contractions before and during Solidification

When phospholipids crystallize within the otherwise fluid membranes of giant unilamellar vesicles, the resulting molecularly thin “2D” solids exhibit great variety in their morphology evolution. For example, within membranes containing moderate amounts of the crystallizing component, crystals grow with a fixed morphology depending on vesicle size. Conversely for membranes containing large amounts of the crystallizing species, we find small compact crystals on vesicles of all sizes. However, on large vesicles, growing crystals sprout flower petals that lengthen progressively. These behaviors result from two combined mechanisms: first, like other 2D solids, the shear rigidity of phospholipid crystals renders them intolerant to morphologies with nonzero Gaussian curvature. As a result and especially at elevated membrane tension, the cost of bending elasticity is reduced at the expense of line energy by the formation of flowers as opposed to compact crystals. Second, the composition-dependent tension rise during cooling relaxes via water permeation of the membrane with a time constant scaling as R2. The amount of crystal formed for a small decrease in temperature determines this composition-dependent increase in stress from thermal contractions versus solidification. Surface Evolver computations were motivated using the predicted tension evolution to develop a processing space that maps to experimental observations for initial and growing crystal morphology. Important variable groups are identified, including a scaled ratio of bending to line energy, a vesicle-size-independent group for membrane contractions, and a time constant for stress relaxation. Though processing stresses ultimately relax, the crystal morphology persists well beyond the processing window.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Hot Hole Collection and Photoelectrochemical CO 2 Reduction with Plasmonic Au/p-GaN Photocathodes

Harvesting nonequilibrium hot carriers from plasmonic- metal nanostructures offers unique opportunities for driving photo- chemical reactions at the nanoscale. Despite numerous examples of hot electron-driven processes, the realization of plasmonic systems capable of harvesting hot holes from metal nanostructures has eluded the nascent field of plasmonic photocatalysis. In this work, we fabricate gold/p-type gallium nitride (Au/p-GaN) Schottky junctions tailored for photoelectrochemical studies of plasmon-induced hot-hole capture and conversion. Despite the presence of an interfacial Schottky barrier to hot-hole injection of more than 1 eV across the Au/p-GaN heterojunction, plasmonic Au/p-GaN photocathodes exhibit photoelectrochemical properties consistent with the injection of hot holes from Au nanoparticles into p- GaN upon plasmon excitation. The photocurrent action spectrum of the plasmonic photocathodes faithfully follows the surface plasmon resonance absorption spectrum of the Au nanoparticles and open-circuit voltage studies demonstrate a sustained photovoltage during plasmon excitation. Comparison with Ohmic Au/p-NiO heterojunctions confirms that the vast majority of hot holes generated via interband transitions in Au are sufficiently hot to inject above the 1.1 eV interfacial Schottky barrier at the Au/p-GaN heterojunction. We further investigated plasmon-driven photoelectrochemical CO 2 reduction with the Au/p-GaN photocathodes and observed improved selectivity for CO production over H 2 evolution in aqueous electrolytes. Taken together, our results offer experimental validation of photoexcited hot holes more than 1 eV below the Au Fermi level and demonstrate a photoelectrochemical platform for harvesting hot carriers to drive solar-to-fuel energy conversion.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Real-Time KMC Simulation of Vacancy-Mediated Intermixing in Au@Ag Octahedral Core–Cubic Shell Nanocrystals with Ab Initio-Guided Kinetics

Utilization of core–shell rather than monometallic nanocrystals (NCs) facilitates fine-tuning of NC properties for applications. However, compositional evolution via intermixing can degrade these properties prompting recent experimental studies. We develop an atomistic-level stochastic model for vacancy-mediated intermixing exploiting a formalism which allows incorporation at an ab initio density functional theory level of not just the thermodynamics of vacancy formation, but also relevant diffusion barriers for a vast number of possible local environments (in the core and in the shell, at the interface, and in the intermixed phase). This facilitates a predictive treatment and comprehensive understanding of intermixing on the relevant time scale (e.g., 10 1 –10 3 s). In contrast, previous modeling at the atomistic level utilized only unrealistic generic prescriptions of barriers or employed simplified continuum treatments. For Au@Ag octahedral core–cubic shell NCs, our modeling not only captures the experimentally observed rate or time scale for intermixing of ~100 s at 450 °C for 60 nm NCs, but also elucidates the underlying rate controlling processes and the effective intermixing barrier.

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

Continuous operation of a coherent 3,000-qubit system

Neutral atoms are a promising platform for quantum science, enabling advances in areas ranging from quantum simulations and computation to metrology, atomic clocks and quantum networking. Although atom losses typically limit these systems to a pulsed mode, continuous operation could substantially enhance cycle rates, remove bottlenecks in metrology and enable deep-circuit quantum evolution through quantum error correction. Here we demonstrate an experimental architecture for high-rate reloading and continuous operation of a large-scale atom-array system while realizing coherent storage and manipulation of quantum information. Our approach utilizes a series of two optical lattice conveyor belts to transport atom reservoirs into the science region, where atoms are repeatedly extracted into optical tweezers without affecting the coherence of qubits stored nearby. Using a reloading rate of 300,000 atoms in tweezers per second, we create over 30,000 initialized qubits per second, which we leverage to assemble and maintain an array of over 3,000 atoms for more than 2 hours. Furthermore, we demonstrate persistent refilling of the array with atomic qubits in either a spin-polarized or a coherent superposition state while preserving the quantum state of stored qubits. Our results pave the way for the realization of large-scale continuously operated atomic clocks, sensors and fault-tolerant quantum computers.

atomic and molecular physics↗
DOE OSTI2021

Revisiting trends in the exchange current for hydrogen evolution

Nørskov and collaborators proposed a simple kinetic model to explain the volcano relation for the hydrogen evolution reaction on transition metal surfaces such that j 0 = k 0 f(ΔG H ) where j 0 is the exchange current density, f(ΔG H ) is a function of the hydrogen adsorption free energy ΔG H as computed from density functional theory, and k 0 is a universal rate constant. Herein, focusing on the hydrogen evolution reaction in acidic medium, we revisit the original experimental data and find that the fidelity of this kinetic model can be significantly improved by invoking metal-dependence on k 0 such that the logarithm of k 0 linearly depends on the absolute value of ΔG H . Here, we further confirm this relationship using additional experimental data points obtained from a critical review of the available literature. Our analyses show that the new model decreases the discrepancy between calculated and experimental exchange current density values by up to four orders of magnitude. Furthermore, we show the model can be further improved using machine learning and statistical inference methods that integrate additional material properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Interpreting inorganic compositional depth profiles to understand the rate-limiting step in vapor phase infiltration processes

Vapor phase infiltration (VPI) is a post-polymerization modification technique that infuses inorganics into polymers to create organic–inorganic hybrid materials with new properties. Much is yet to be understood about the chemical kinetics underlying the VPI process. The aim of this study is to create a greater understanding of the process kinetics that govern the infiltration of trimethyl aluminum (TMA) and TiCl 4 into PMMA to form inorganic-PMMA hybrid materials. To gain insight, this paper initially examines the predicted results for the spatiotemporal concentrations of inorganics computed from a recently posited reaction–diffusion model for VPI. This model provides insight on how the Damköhler number (reaction versus diffusion rates) and non-Fickian diffusional processes (hindering) that result from the material transforming from a polymer to a hybrid can affect the evolution of inorganic concentration depth profiles with time. Subsequently, experimental XPS depth profiles are collected for TMA and TiCl 4 infiltrated PMMA films at 90 °C and 135 °C. The functional behavior of these depth profiles at varying infiltration times are qualitatively compared to various computed predictions and conclusions are drawn about the mechanisms of each of these processes. TMA infiltration into PMMA appears to transition from a diffusion-limited process at low temperatures (90 °C) to a reaction-limited process at high temperatures (135 °C) for the film thicknesses investigated here (200 nm). While TMA appears to fully infiltrate these 200 nm PMMA films within a few hours, TiCl 4 infiltration into PMMA is considerably slower, with full saturation not occurring even after 2 days of precursor exposure. Infiltration at 90 °C is so slow that no clear conclusions about mechanism can be drawn; however, at 135 °C, the TiCl 4 infiltration into PMMA is clearly a reaction-limited process, with TiCl 4 permeating the entire thickness (at low concentrations) within only a few minutes, but inorganic loading continuously increasing in a uniform manner over a course of 2 days. Near-surface deviations from the uniform-loading expected for a reaction-limited process also suggest that diffusional hindering is high for TiCl 4 infiltration into PMMA. In conclusion, these results demonstrate a new, ex situ analysis approach for investigating the rate-limiting process mechanisms for vapor phase infiltration.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Measuring autoionization decay lifetimes of optically forbidden inner valence excited states in neon atoms with attosecond noncollinear four-wave-mixing spectroscopy

Attosecond noncollinear four-wave-mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48-eV XUV photon excites a 2s electron into the 2s2p 6 (np) Rydberg series, broadband NIR pulses couple the 2s2p 6 3p XUV-bright state to neighboring 2s2p 6 3s and 2s2p 6 3d XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or bright states, respectively. Experimental lifetimes for the 3s, 3p, and 3d states are measured to be 7±2, 48±8, and 427±40 fs, respectively, with 95% confidence. Accompanying calculations with two independent ab initio theoretical methods, newstock and astra, verify the findings. The results support the expected trend that the autoionization lifetime should be longer for states that have a smaller penetration in the radial region of the 2s core hole, which in this case is for the higher angular momentum Rydberg orbitals. In conclusion, the underlying theory thus links the lifetime results to electron correlation and provides an assessment of the direct and exchange terms in the autoionization process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Magnetic properties of the honeycomb oxide Na 2 Co 2 TeO 6

We have studied the magnetic properties of Na 2 Co 2 TeO 6 , which features a honeycomb lattice of magnetic Co 2 + ions, through macroscopic characterization and neutron diffraction on a powder sample. We also show that this material orders in a zigzag antiferromagnetic structure. Additionally by allowing a linear magnetoelectric coupling, this magnetic arrangement displays very peculiar spatial magnetic correlations, larger in the honeycomb planes than between the planes, which do not evolve with the temperature. We have investigated this behavior by classical Monte Carlo calculations using the J 1 - J 2 - J 3 model on a honeycomb lattice with a small interplane interaction. Furthermore, our model reproduces the experimental neutron structure factor, although its absence of temperature evolution must be due to additional ingredients, such as chemical disorder or quantum fluctuations enhanced by the proximity to a phase boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗