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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 109 records · Page 6

Entropic Control of HD Exchange Rates over Dilute Pd-in-Au Alloy Nanoparticle Catalysts

Dilute Pd-in-Au alloy catalysts are promising materials for selective hydrogenation catalysis. Extensive surface science studies have contributed mechanistic insight on the energetic aspect of hydrogen dissociation, migration and recombination on dilute alloy systems. Yet, translating these fundamental concepts to the kinetics and free energy of hydrogen dissociation on nanoparticle catalysts operating at ambient pressures and temperatures remains challenging. Here, the effect of the Pd concentration and Pd ensemble size on the catalytic activity, apparent activation energy and rate limiting process is addressed by combining experiment and theory. Experiments in a flow reactor show that a compositional change from 4 to 8 atm% Pd of the Pd-in-Au alloy catalyst leads to strong increase in activity, even exceeding the activity per Pd atom of monometallic Pd under the same conditions, albeit with an increase in apparent activation energy. First-principles calculations show that the rate and apparent activation enthalpy for HD exchange increase when increasing the Pd ensemble size from single Pd atoms to Pd trimers in a Au surface, suggesting that the ensemble size distribution shifts from mainly single Pd atoms on the 4 atm% Pd alloy to larger Pd ensembles of at least three atoms for the 8 atm% Pd/Au catalyst. The DFT studies also indicated that the rate-controlling process is different: H 2 (D 2 ) dissociation determines the rate for single atoms whereas recombination of adsorbed H and D determines the rate on Pd trimers. Both experiment and theory suggest that the increased reaction rate with increasing Pd content and ensemble size stems from an entropic driving force. Lastly, our results support hydrogen migration between Pd sites via Au and indicate that the dilute alloy design prevents the formation of subsurface hydrogen, which is crucial in achieving high selectivity in hydrogenation catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Role of local atomic short-range order distribution in alloys: Why it matters in Si-Ge-Sn alloys

Short-range order (SRO) in alloys refers to deviations from a perfectly random distribution of atoms in lattice sites within a short distance. Conventionally, the degree of the deviations has been quantified using an average SRO parameter, but such a coarse-grained description does not reflect how the deviations occur at a finer level. Here we show the distribution of the local atomic SRO parameter, which describes the occurring frequency of a local structural motif, carries the crucial information for both structures and properties in Si-Ge-Sn alloy system. Here this is demonstrated through the fact that distinct SRO structures can exhibit the same average SRO parameter but very different distributions and disparate electronic structures. By deliberately creating special structures that explicitly match the structural information at different levels, we show the distribution of local atomic SRO parameters contain critical structural features that are missing in the average SRO parameter but can substantially contribute to material’s properties. Our finding thus calls for the need for considering the finer structural details to effectively describe alloys’ structures and properties.

36 MATERIALS SCIENCE↗

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↗

Strengthening model development and effects of low diffusing solutes to coarsening resistance in aluminum alloys

A modified Orowan strengthening model is proposed to account for finite rod-shaped precipitates with hemispherical caps in aluminum alloy systems. A combined computational and experimental approach is used to study the influences of anisotropic Orowan looping and solute-dislocation interaction on temperature-dependent yield strength. Here, the strengthening model is validated with a dataset containing 297 experimental precipitate geometries, chemistries, temperatures, and strength measurements, and achieves a strong predictive correlation of 0.8713 with experimentally measured yield strengths. Under conditions that are applicable to coarsening, constant particle volume fraction and aspect ratio, the model predicts that short rod precipitates provide far superior strengthening effects compared to plate precipitates. A cast Al-Si-Mg-Cu alloy with rod-shaped Q-phase (Al 3 Cu 2 Mg 9 Si 7 ) precipitates was developed with a novel chemistry exploring the use of low-diffusivity elements (Mn, Ni, V, Zr) to limit precipitate coarsening. The thermodynamic behavior of Mn, Ni, V, and Zr across the Q-phase interface is examined using transmission electron microscopy (TEM), first-principles density-functional theory (DFT) calculations. and atom-probe tomography (APT). DFT calculations utilizing TEM identified Q-phase/Al-matrix interfaces show that Mn, Ni, V, and Zr preferentially segregate to the Q-phase precipitate boundaries which suggests inhibition of precipitate coarsening and higher strengths after temperature exposure. Atom-probe tomography confirms solute atom partitioning/segregation at the Q-phase/Al-matrix interface, found in the modified commercial AS7GU alloy (A356 +0.5%Cu), which supports these observations.

36 MATERIALS SCIENCE↗

Disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y alloys

This dataset contains input and output files from density functional theory (DFT) simulations used to study the disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y (0 ≤ x + y ≤ 1) alloys and their binary end members MnTe, MnSb, and MnBi. The alloys adopt the hexagonal NiAs-type (nickeline) structure and span ternary (MnTexSb1-x, MnTexBi1-x, MnBixSb1-x), and quaternary compositions across the full MnTe–MnSb–MnBi composition triangle. For each alloy composition, the dataset provides DFT calculations in three magnetic configurations: A-type antiferromagnetic (AFM), C-type AFM, and ferromagnetic (FM). Every magnetic configuration folder contains the fully relaxed crystal structure (CONTCAR), VASP input parameters (INCAR), and the main VASP output file (OUTCAR), from which total electronic energies, Mn magnetic moments, lattice parameters, and percent volume changes between magnetic states are extracted. These data are used to construct compositional phase diagrams, evaluate thermodynamic stability (formability), and map magnetoelastic responses across the alloy space. For A-type AFM and FM configurations, additional data are provided as follows: (i) FORCE_CONSTANTS and thermal_properties.yaml files at the top level of A-type_AFM/ and FM/ folders — present only for compositions marked with an asterisk (*) in Table I of the main text. These are derived from Phonopy finite-displacement calculations on full disordered 128-atom supercells and provide vibrational free energy, entropy (Svib)contribution from explicit disorder calculations. (Table I of the associated main manuscript) (ii) A VCA/ subfolder within A-type_AFM/ and FM/, containing FORCE_CONSTANTS and thermal_properties.yaml from Virtual Crystal Approximation phonon calculations (without spin-orbit coupling). VCA data are available for all compositions and are used to estimate vibrational contributions to the Gibbs free energy across the full composition space. (iii) A SOC/ subfolder containing CONTCAR, INCAR, and OUTCAR from spin-orbit coupling calculations, providing relativistic corrections to electronic energies and lattice parameters (Tables S2–S3 of the SM, and Table I of the main manuscript). (iv) A SOC/VCA/ subfolder containing FORCE_CONSTANTS and thermal_properties.yaml from VCA phonon calculations performed within the SOC framework, combining relativistic and vibrational thermodynamic corrections. The computed properties are used to map the AFM–FM magnetic crossover near MnTe0.75Sb0.25, demonstrate disorder- and spin-induced phonon broadening, identify a semiconductor-to-metal crossover, and quantify the pronounced magnetoelastic volume response near the magnetic phase boundary.

36 MATERIALS SCIENCE↗

Model for the Softening Factor within Stages of Work Hardening

A formulation for a dimensionless coefficient c b is derived that represents a scale of microstructural softening for alloys which follow Kocks-Mecking (K-M) work hardening behavior. The variation of the true plastic strain ε p between the proportional limit σ y and the strength σ u at the instability is determined using the Considère criterion. Parameterization of the model is limited to variables expressly measured within tensile experiments. Further development is now made for the softening factor c bi through the individual and sequential stages 3 and 4 of plastic deformation during K-M work hardening Q behavior. Application is shown for tensile test results of Ti-6Al-4V made by different additively manufactured (AM) processes. It is found that the variation in plastic strain as a function of c bi produces a continuous curve representative of the alloy system. The results of data analysis indicate that Θ o3 and c b3 increase, while Θ o4 and c b4 decrease, as the total plastic strain ε p increases. Furthermore, formulations derived for K-M stages 3 and 4 enable the evaluation of other material parameters such as the activation volume ν* for the onset of plastic deformation. This activation volume is found to be near constant, at a ν*-value of 0.353±0.036 nm 3 as computed using a strain-rate sensitivity of strength exponent m of 0.014, irrespective of the AM method used to produce the Ti-6Al-4V alloy.

36 MATERIALS SCIENCE↗

Development of interatomic potential and effect of ordering on defect properties in CrMnV

Developing materials that can withstand extreme environments, such as high radiation doses and elevated temperatures, is crucial for next-generation particle accelerators, including the 2.4 MW Long-Baseline Neutrino Facility. High-Entropy Alloys have emerged as promising candidates for beam window materials due to their superior mechanical strength, corrosion resistance, and radiation tolerance. In this study, we focus on the Cr–Mn–V alloy system, developing and employing machine-learning interatomic potentials (MLIPs) to investigate the formation of an ordered phase and its influence on defect properties. Using hybrid Monte Carlo-Molecular Dynamics simulations, we observe the formation of a B2-ordered phase at lower temperatures, consistent with Density Functional Theory (DFT) predictions. Ordered structures display a bimodal distribution of migration energies and reduced mean square displacement values, indicating suppressed vacancy diffusion. Our results also show that the migration energy barrier varies based on the atomic species, with Mn and V exhibiting the highest and lowest average barriers, respectively. These findings suggest that atomic ordering inhibits defect mobility, potentially enhancing the radiation resistance of CrMnV alloys. The validated MLIP provides a reliable framework for simulations that are faster than traditional DFT while maintaining the accuracy required to study defect and ordering properties.

36 MATERIALS SCIENCE↗

High-throughput additive manufacturing and characterization of refractory high entropy alloys

Refractory High Entropy Alloys (RHEAs) and Refractory Complex Concentrated Alloys (RCCAs) are high-temperature structural alloys ideally suited for use in harsh environments. While these alloys have shown promising structural properties at high temperatures that exceed the practical limits of conventional alloys, such as Ni-based superalloys, exploration of the complex phase-space of these materials remains a significant challenge. We report on a high-throughput alloy processing and characterization methodology, leveraging laser-based metal additive manufacturing (AM) and mechanical testing techniques, to enable rapid exploration of RHEAs/RCCAs. We utilized in situ alloying and compositional grading, unique to AM processing, to rapidly-produce RHEAs/RCCAs using readily available and inexpensive commercial elemental powders. We demonstrate this approach with the MoNbTaW alloy system, as a model material known for having exceptionally high strength at elevated temperature when processed using conventional methods (e.g., casting). Microstructure analysis, chemical composition, and strain rate dependent hardness of AM-processed material are presented and discussed in the context of understanding the structure-properties relationships of RHEAs/RCCAs.

36 MATERIALS SCIENCE↗

Theoretical antiferromagnetism of ordered face-centered cubic Cr-Ni alloys

Contrary to prior calculations, the Ni-rich ordered structures of the Cr-Ni alloy system are found to be antiferromagnetic under semilocal density-functional theory. The optimization of local magnetic moments significantly increases the driving force for the formation of CrNi 2 , the only experimentally observed intermetallic phase. This structure's ab initio magnetism appears well described by a Heisenberg Hamiltonian with longitudinal spin fluctuations; itinerant Cr moments are induced only by the strength of exchange interactions. The role of magnetism at temperature is less clear and several scenarios are considered based on a review of experimental literature, specifically a failure of the theory, the existence of an overlooked magnetic phase transition, and the coupling of antiferromagnetism to chemical ordering. In conclusion, implications for related commercial and high-entropy alloys are discussed for each case.

36 MATERIALS SCIENCE↗

Exploring the formation of gold/silver nanoalloys with gas-phase synthesis and machine-learning assisted simulations

While nanoalloys are of paramount scientific and practical interest, the main processes leading to their formation are still poorly understood. Key structural features in the alloy systems, including the crystal phase, chemical ordering, and morphology, are challenging to control at the nanoscale, making it difficult to extend their use to industrial applications. Here, in this contribution, we focus on the gold/silver system that has two of the most prevalent noble metals and combine experiments with simulations to uncover the formation mechanisms at the atomic level. Nanoparticles were produced using a state-of-the-art inert-gas aggregation source and analyzed using transmission electron microscopy and energy-dispersive X-ray spectroscopy. Machine-learning-assisted molecular dynamics simulations were employed to model the crystallization process from liquid droplets to nanocrystals. Our study finds a preponderance of nanoparticles with five-fold symmetric morphology, including icosahedra and decahedra which is consistent with previous results on mono-metallic nanoparticles. However, we observed that gold atoms, rather than silver atoms, segregate at the surface of the obtained nanoparticles for all the considered alloy compositions. These segregation tendencies are in contrast to previous studies and have consequences on the crystallization dynamics and the subsequent crystal ordering. We finally showed that the underpinning of this surprising segregation dynamics is due to charge transfer and electrostatic interactions rather than surface energy considerations.

36 MATERIALS SCIENCE↗

CASM — A software package for first-principles based study of multicomponent crystalline solids

CASM is a software package that enables first-principles based studies of crystalline materials. It has been designed to treat coupled chemical, mechanical, vibrational, and magnetic degrees of freedom to determine ground state and finite temperature properties of crystals. The symmetry of the underlying parent crystal structure is used to enumerate perturbations of the parent crystal structure and generate derivative structures which can be input to first-principles calculations in order to explore the ground state energy landscape. CASM algorithmically constructs cluster expansions that fully couple discrete and continuous degrees of freedom, and generates highly efficient code to evaluate the cluster expansion basis functions. Widely used machine learning methods are integrated for fitting expansion coefficients to first-principle calculations. The fully parameterized cluster expansions can be combined with (kinetic) Monte Carlo methods to calculate finite temperature thermodynamic and kinetic properties. CASM Alloy Manager identifies distinct parent crystal structures in an alloy system, creating individual projects for each, and integrating the results. The integrated infrastructure facilitates the linkage between first-principles statistical mechanics predictions with higher length scale computational methods, such as phase field simulations. In conclusion, CASM projects are designed to be easy to share in repositories, to re-use, and to extend to include additional chemical species or types of degrees of freedom.

36 MATERIALS SCIENCE↗

High-Entropy Alloy R&D for Accelerator Beam Window Applications

High-Entropy Alloys are a class of novel material that can offer improved resistance to beam-induced radiation damage and thermal shock. Development of these new alloys to serve as beam windows in multi-megawatt accelerator target applications is ongoing at Fermilab. Currently we are investigating AlCoCrMnTiV alloy systems of 4-6 components for service as beam windows; these compositions are predicted by CALPHAD simulation to have a low density and single-phase BCC crystal structure. The microstructures of these systems are being studied by electron microscopy techniques such as energy dispersive X-ray spectroscopy (EDS) to determine elemental homogeneity and composition, electron backscatter diffraction (EBSD) to quantify grain structure and orientation, and transmission electron microscopy (TEM) to observe defect structures and precipitate formation; nanoindentation is used to probe microstructural mechanical properties. Initial bulk property characterization utilizes differential scanning calorimetry to quantify specific heat capacity (cp), dilatometry to determine the coefficient of thermal expansion (CTE), and time-domain thermoreflectance (TDTR) to measure thermal conductivity (K). A miniature tensile testing apparatus is also being developed to test tensile properties. Post-irradiation examination is currently ongoing for several of these compositions that have been irradiated by low-energy ions to damage levels and at a temperature relevant to beam window applications at future next-generation accelerator facilities. This talk will briefly describe the alloy design and synthesis before going into more depth covering microstructural pre-characterization, and post-irradiation examination results from low-energy ion irradiated specimens. This will be followed by the plans for alloy down selection and future prototypic proton irradiations.

43 PARTICLE ACCELERATORS↗

Shining light on nanoscale ‘vine-on-stick’ eutectic structures in the Al-Ce-Ni system

Multiphase eutectics often comprise entangled solid phases with nanoscale periodicity, making it difficult to unravel their 3D connectivity using conventional 2D techniques. Among such systems, the three-phase eutectic Al-Al 11 Ce 3 -Al 3 Ni stands out for its ultrafine (∼100 nm) interphase spacing and promising creep resistance, yet its microstructure remains relatively unexplored despite its potential for high-temperature applications. Here, we use scanning hard X-ray microscopy with an unprecedented ∼10 nm pixel size to resolve its 3D morphology. Reconstructions reveal a novel “vine-on-stick” motif, wherein Al 11 Ce 3 wraps around Al 3 Ni pillars. Analysis of phase tortuosities confirms that Al 11 Ce 3 exhibits more convoluted morphologies than Al 3 Ni. No orientation relationship was observed between the two intermetallics, suggesting that growth is controlled by local solute gradients rather than epitaxy. Fragmentation of intermetallics along their longitudinal axis suggests a Rayleigh-type breakup mechanism in solid state. The “vine-on-stick” pattern may generalize to other alloy systems with variable interfacial anisotropies and low mutual solubilities.

36 MATERIALS SCIENCE↗

Splat Quenching as a High Throughput Rapid Solidification Testing Method for Developing Additive Manufacturing Alloys

Splat quenching as a high throughput rapid solidification screening tool is evaluated. Samples were made using known alloys (SS316, IN625, Ti-5553) to evaluate and establish the microstructures for a variety of alloy systems as well as the predicted cooling rates. The samples are inductively heated and levitated prior to being struck between two platens that produce a high contact pressure and a thin sample resulting in cooling rates on the order of 10 6 to 10 7 K/s. Process parameters were evaluated with analytical models in addition to numerical simulations to provide an effect of process variables such as substrate material, melt superheat, and platen velocity on the resulting solidification. The splat thickness was found to be controlled by platen velocity, melt superheat, as well as the feedstock volume. The sample thickness is the key controlling factor for varying the average cooling rate experienced by the splat quenched sample. The splat quenching techniques can reach regions of rapid solidification space that meet and exceed laser and electron beam techniques across the sample. In conclusion, the results of the study provide a useful foundation in understanding the splat quenching technique and its potential as a low effort tool to explore rapid solidification effects on alloys.

Alloy Design↗

Cu–Ni Oxidation Mechanism Unveiled: A Machine Learning-Accelerated First-Principles and in Situ TEM Study

Here, the development of accurate methods for determining how alloy surfaces spontaneously restructure under reactive and corrosive environments is a key, long-standing, grand challenge in materials science. Using machine learning-accelerated density functional theory and rare-event methods, in conjunction with in situ environmental transmission electron microscopy (ETEM), we examine the interplay between surface reconstructions and preferential segregation tendencies of CuNi(100) surfaces under oxidation conditions. Our modeling approach predicts that oxygen-induced Ni segregation in CuNi alloys favors Cu(100)-O c(2 × 2) reconstruction and destabilizes the Cu(100)-O (2√2 × √2)R45° missing row reconstruction (MRR). In situ ETEM experiments validate these predictions and show Ni segregation followed by NiO nucleation and growth in regions without MRR, with secondary nucleation and growth of Cu 2 O in MRR regions. Our approach based on combining disparate computational components and in situ ETEM provides a holistic description of the oxidation mechanism in CuNi, which applies to other alloy systems.

36 MATERIALS SCIENCE↗

Competing Interactions between Mesoscale Length-Scales, Order-Disorder, and Martensitic Transformation in Ferromagnetic Shape Memory Alloys

In the present study, the effects of composition and heat treatments and the resulting microstructural changes on the martensitic transformation and ferromagnetic transition have been investigated in NiCoMnIn metamagnetic shape memory alloys. In this shape memory alloy system, it is observed that upon heat treatments at a wide temperature range, the onset temperature of the martensitic transformation follows a non-monotonic behavior with respect to heat treatment time, and the nature of the non-monotonic behavior is also a function of composition. This behavior cannot be attributed to well-known factors such as precipitation, change in local composition due to the precipitation and/or global degree of order. In this work, a systematic investigation through synthesis, thermal processing and characterization via thermo-physical measurements, transmission electron microscopy and in-situ synchrotron x-ray diffraction experiments has been used to correlate the non-monotonic dependence of the martensitic transformation and ferromagnetic transition temperatures to the evolution of L2 1 domains arising from a order/disorder phase transition. A thermodynamic model for the magneto-structural transition is combined with classical nucleation theory to further ascertain the role of microstructural length-scales on the onset of the martensitic transformation. This work thus provides understanding of the thermodynamic and kinetic factors that can be controlled to tune the coupled magneto-structural transformations in NiCoMnIn metamagnetic shape memory alloys.

36 MATERIALS SCIENCE↗

The effect of Zr on precipitation in oxide dispersion strengthened FeCrAl alloys

Oxide dispersion strengthened (ODS) FeCrAl alloys are promising candidate materials for advanced nuclear reactor applications requiring high-temperature strength, corrosion resistance, and irradiation tolerance. As these alloys have increased in compositional complexity through attempts to use highly reactive elements such as Zr to refine particle sizes and optimize nanoprecipitate dispersion characteristics, much debate has ensued as to the effects of these alloying element additions on alloy properties. In an attempt to reconcile differences in nanoprecipitate distributions reported in the literature over the past decade, a detailed investigation of a recently developed ODS FeCrAl alloy with nominal composition Fe–10Cr-6.1Al-0.3Zr+0.3Y 2 O 3 is presented here using a combination of atom probe tomography (APT), scanning/transmission electron microscopy (S/TEM), and computational thermodynamics modeling. It is illustrated that based on the amount of Zr available in the lattice, Zr competes with Al and Cr to form carbides and nitrides as opposed to oxygen-rich precipitates. This alloy system has a high number density (>10 23 m -3 ) of ~2–4 nm diameter (Y,Al,O)-rich nanoprecipitates, but it is shown that due to the compositional spread and unknown partitioning of Al between the matrix and precipitates, significant challenges still exist for quantifying the exact compositions of these precipitates using APT. However, the noted compositional spread is supported by identified complex oxides yttrium aluminum monoclinic (YAM) and yttrium aluminum garnet (YAG) using S/TEM. As a result of these findings, researchers developing ODS FeCrAl with reactive element additions must pay careful attention to C and N impurities when optimizing reactive element additions.

electron microscopy↗

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗