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DOE OSTI2025

Nucleation rate controlled grain boundary and lattice creep

Nucleation versus diffusion rate-limited bicrystal and single crystal creep exhibit different scaling dependencies that enable the mechanisms to be isolated when measured as a function of sample size. It has recently been suggested that nucleation rate-limited kinetic models generally describe the non-Newtonian portion of the creep response well, but more direct evidence is required. This work analyzes the grain boundary creep response of UO 2 , a pyrochlore high entropy oxide, silver, and palladium, along with the lattice creep of silver using small-scale in situ loading in the transmission electron microscope. At small sizes, each system exhibits scale dependence associated with nucleation rate-limited kinetics. Fits of the data produce activation volumes on the order of a few Burgers vectors cubed with positive temperature coefficients as expected for nucleation kinetics. The activation enthalpies fall in the range of about 0.4 eV to 1.7 eV, being lower for the metals and higher for the oxides.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Effect of stress on Laves phase precipitation in creep ruptured Grade 92 ferritic martensitic steel characterized by a novel accessible method

At high temperature conditions relevant to fossil and nuclear energy plants, Laves phase (Fe 2 X, X=Mo, W) precipitation is observed in common ferritic martensitic (FM) structural steels, with various reported effects on creep behavior. Despite being valuable metrics to correlate with mechanical properties and other precipitate phases, the volume fraction and number density of Laves phase precipitates has been difficult to quantify accurately using common techniques such as transmission electron microscopy (TEM) due to the relatively large size (∼0.25 μm) and low number density (∼10 11 cm −3 ) of Laves precipitates. Here, to address this characterization challenge, we developed and demonstrated a high-throughput and widely accessible method to quantify the volume fraction and number density of the Laves phase based on scanning electron microscope (SEM) images with a backscattered electron signal and the information depth (ID) of backscattered electrons. We applied this new technique in creep ruptured Grade 92 FM steel to study the effect of Laves phase on creep properties and determine the influence of stress on Laves phase precipitation. The quantitative accuracy of the SEM-based volume fraction and number density values was verified using synchrotron high energy X-ray diffraction and serial sectioning tomography. Stress did not significantly affect the Laves phase size or volume fraction during creep testing at 550 – 650°C and stress levels of 90 – 260 MPa (vs. unstressed conditions). Conversely, a moderate but statistically significant stress-enhanced increase in Laves phase number density, corresponding to an increase in nucleation rate, occurred during creep exposure above 110 MPa.

Creep↗

DOE OSTI2025

Nuclear β − -decay with statistical de-excitation

he accurate description of nuclear β − -decay has far-reaching consequences for applications spanning nuclear reactors to the creation of heavy elements in astrophysical environments. We present the nuclear particle spectra associated with the β -decay of neutron-rich nuclei calculated with the well benchmarked coupled Quasi-particle Random Phase Approximation and Hauser–Feshbach (QRPA+HF) model. This approach begins with the population of the daughter nucleus via semi-microscopic Gamow-Teller or First-Forbidden strength distributions (QRPA) and follows the statistical de-excitation (HF) until the initial available excitation energy is exhausted. At each stage of de-excitation the emission by neutrons and $γ$-rays is considered obeying quantum mechanical selection rules. For completeness we also provide parsed Auger and Internal Conversion (IC) electron spectra from Evaluated Nuclear Data Files (ENDF). Our results are tabulated and provided in parsable ASCII formatted tables that are suitable for inclusion in various applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A survey study on arsenic speciation in coal fly ash and insights into the role of coal combustion conditions

Coal fly ashes (CFAs) are the low-density byproducts of the coal combustion process. Improper or uncontrolled CFA disposal poses significant environmental and health concerns due to the potential leaching of toxic heavy metals such as arsenic (As). Previous studies have investigated the content and speciation of As in different CFA samples, yet systematic information on As speciation in CFA with representative coal source and combustion conditions is still missing. Based on a recent survey study on the typical coal sources and combustion conditions across the U.S., this study selected 19 representative CFA samples to systematically investigate As speciation and potential correlations with these parameters. The composition, morphology, mineralogy, and As speciation of these CFA samples were characterized by complementary analytical, microscopic, and spectroscopic techniques. Synchrotron X-ray spectroscopy and microscopy analyses revealed the dominant As oxidation state to be As(V) and with strong associations to Ca, with the exception of 3 samples that had 19–51% As(III), likely due to the use of selective catalytic reduction (SCR) process. Principal component analysis was conducted to identify potential correlations of As concentration and oxidation state with parameters such as major element content, loss on ignition (LOI), average particle size, coal source, and combustion condition. Al 2 O 3 and FeO content were found to capture a majority of the variability. Further, results from this study provide fundamental basis for understanding the correlations between coal source, combustion conditions, CFA characteristics, and As speciation, and providing insights for downstream beneficial utilization or disposal management.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2025

LABQ3: Bayesian method for quantification of mineral compositions and nano-scale elemental mapping of 3D synchrotron XCT data

Quantitative analysis of mineral compositions is essential in understanding geochemical, mineralogical and environmental processes. Fine-resolution 3D imaging is widely done using synchrotron X-ray computed tomography (XCT), but existing analyses are limited to visualization and segmentation. This paper presents a new method, Linear Attenuation Bayesian Quantitative 3D-mapper (LABQ3), based on the linearity of X-ray attenuation with respect to elemental concentrations. To address the random variability in attenuation measurements, LABQ3 employs Bayesian decision theory to minimize classification error, using reference attenuation distributions from scans of pure mineral standards. To demonstrate LABQ3 and test its performance, we studied precipitated carbonate samples. XCT scans were done at multiple energies using the transmission X-ray microscope (TXM) at beamline 32-ID-C of the Advanced Photon Source at Argonne National Laboratory. The reconstructed 3D images have a voxel size of 20 nm. Analyses revealed rich nano-scale compositional heterogeneity within individual particles. A mixture of calcium and cadmium produced an overall stoichiometric composition of (Ca 0.78 ,Cd 0.22 )CO 3 , with some voxels containing nearly pure CdCO 3 . The addition of zinc led to an overall stoichiometric composition of 33% Ca, 28% Cd, 39% Zn, with a nearly pure CaCO 3 core and compositional zonation through the rim. These compositional gradients are related to temporal sequences of carbonate mineral formation where Cd precipitated at the beginning in (Ca,Cd)CO 3 , while Cd and Zn precipitated at the end in (Ca, Cd,Zn)CO 3 . Results differ from bulk analyses using Inductively Coupled Plasma-Mass Spectrometry (ICP-MS), showing that LABQ3 provides particle-specific insights. LABQ3 distinguishes itself by quantifying chemical compositions along a continuum, making it different from XCT analyses based on segmentation. LABQ3 allows simultaneous acquisition of morphology and chemical composition in 3D, facilitating the interpretation of chemical gradients of trace elements, quantification of solid solution compositions, inferences about temporal sequences of mineral precipitation, and addressing other concerns about solid-phase chemistry.

58 GEOSCIENCES↗

DOE OSTI2025

Component Identification of Solid Biomass Fuels Using Reflected Light Microscopy: Interlaboratory Study 2

As nations transition toward sustainable energy systems, biomass has become a vital component of global energy portfolios. Derived from organic materials such as wood, agricultural residues, forestry byproducts, and organic waste, biomass is a renewable energy source with significant environmental and economic benefits. Responsible biomass energy production can improve waste management, reduce emissions of greenhouse gases, and mitigate environmental pollution. However, as the diversity of biomass-derived fuels increases, robust quality assessment methods are essential to ensure their efficiency, safety, and minimal environmental impact. Reflected light microscopy (RLM) is one such technique with the potential to complement conventional physico-chemical analyses by enabling a rapid identification of material constituents and impurities. To refine this methodology and evaluate the reproducibility of solid biomass component identification using RLM, an interlaboratory study (ILS) was conducted. The study involved the recognition of 58 components across 45 photomicrographs, with the participation of 65 scientists and students from 25 countries. The participants faced high difficulty identifying some of the marked components, and as a result, the percentage of correct answers ranged from 19.0 % to 98.3 %, with an average correct identification rate of 62.7 %. The most challenging aspects of the identification process included distinguishing between woody and non-woody (agro) biomass, accurately identifying petroleum-derived materials, and differentiating agro biomass from inorganic matter. The results suggest that while RLM is an important tool for characterizing solid biomass, further development of methodology guidelines and training are necessary to enhance its effectiveness. Future research should prioritize preparing detailed, image-rich, microscopic morphological descriptions of biomass fuel components, which could improve the accuracy and reliability of using RLM in biomass fuel characterization.

09 BIOMASS FUELS↗

DOE OSTI2024

Optical image analysis for graphene layer detection: Enhanced green channel methodology

Graphene, a material of increasing research interest, requires accurate layer identification due to its sensitivity to layer count. Existing methods for graphene layer number identification are either time-consuming or of low accuracy, with high-accuracy methods often requiring expensive processes. This paper aims to address this challenge by proposing a cost-effective and efficient approach. Specifically, the current work highlights only the green channel—one of the three primary color channels (red, green, blue) that make up an optical image—from images of exfoliated graphene flakes for layer count identification. A linear regression is performed between pixel position and substrate green channel value, and this effect is subtracted from the entire optical image to mitigate background effects. By storing the range of green channel values for each type of flake (monolayer, bilayer, or tri-layer) based on a few images, we establish thresholds for identifying different types of layers in a particular setup. Additionally, our methodology allows for flexible threshold tuning using a single reference image, enabling adjustment to changes in detection setup such as illumination level, magnification, or microscope used. Finally, demonstrating high accuracy and flexibility, this methodology presents a suitable technique for graphene layer number identification without the need for large datasets or expensive instruments.

2D materials↗

DOE OSTI2025

Benchmarking image processing techniques for porosity measurement in polymer additive manufacturing: Review and experimental analysis

An image processing workflow is proposed for porosity measurement in polymer additive manufacturing. Various techniques, including global and local thresholding, region growing, and K-means clustering, were applied to microscopic images of carbon fiber reinforced acrylonitrile butadiene styrene (CF-ABS) and benchmarked for their ability to accurately measure porosity. Global methods included Otsu, minimum error, iterative, and entropy-based thresholding, while local methods included Niblack, Bernsen, Sauvola, and Bradley-Roth algorithms. Artificial uneven illumination was introduced to test local adaptive thresholds. Results showed significant differences in porosity values across methods. Otsu, region growing, and K-means clustering excelled under uniform illumination, while Sauvola and Bradley-Roth performed better with uneven illumination. Comparison with X-ray computed tomography (XCT) revealed slightly lower porosity values (2.55 %) than optimized methods (2.73–2.79 %) due to XCT's lower resolution excluding smaller pores. While XCT offers finer pore detection, it limits sample volume and underestimates porosity due to spatial variation. Validation using artificial grayscale images with 5 % porosity confirmed that Otsu, Bradley-Roth, region growing, and Sauvola algorithms produced accurate results. Although tested on a single material system, these methods can be adapted to others with optimization. In conclusion, given XCT's high computational and time costs, this study highlights suitable image processing techniques as cost-effective alternatives for porosity analysis in polymer composites.

Additive manufacturing↗

DOE OSTI2025

Damage progression and failure of SiC/SiC composite tubes under hard-contact radial expansion

The response of silicon carbide (SiC) fiber-reinforced SiC matrix (SiC/SiC) composite cladding to mechanical interaction with fissile fuel is a knowledge gap that must be overcome to design and assess SiC-based cladding systems for advanced nuclear applications. This study developed the relevant mechanical testing capability and identified the failure behavior and the critical microstructural features and processing defects. Sections of SiC composite tube were subjected to a modified expansion-due-to-compression (EDC) test in an X-ray computed tomography microscope: a polyurethane plug pressed surrogate Al 2 O 3 into the inner walls of the SiC/SiC composite tubes to achieve hard contact. A pure EDC test with just a polyurethane plug was also performed as a reference. Through the use of displacement fields, digital volume correlation revealed inhomogeneous deformation fields in the tubes, even for pure EDC, which was related to the inherent defects in the structure. Deep learning–aided segmentation and systematic data analysis revealed that the presence of inhomogeneous deformation applied by the hard contact was exaggerated by the presence of inner surface imperfections left behind from the matrix densification process. In conclusion, the findings provide insights into the applications, highlighting the necessity for improvements in inner surface roughness and the incorporation of localized contacts in pellet–cladding mechanical interaction computational models.

Composites↗

DOE OSTI2025

Delamination-informed lifecycle decisions: A dielectric and machine learning framework for composite sorting and recycling

Composite materials are widely used in aerospace, marine, and automotive sectors due to their high strength-to-weight ratio and durability. However, their long-term reliability can be compromised by damage accumulation. Specifically, delamination initiation serves as a precursor to structural failure, which is often difficult to detect during damage inspection. Identifying and sorting delamination initiation in samples not only increases operational safety while providing critical information for end-of-life decisions, which influences both the service life extension value and the efficiency of fiber extraction during recycling. This research addresses two challenges: (1) developing a nondestructive, ex-situ framework to sort composite materials based on damage severity, particularly delamination, and (2) understanding how damage in composites influences resin removal during pyrolysis. Both experimental work and finite element analysis were performed to predict critical stress levels that are associated with delamination onset. Based on these results, three loading levels 50 %, 75 %, and 90 % of maximum stress, were selected for controlled experiments, generating composite samples with varying extents of damage for machine learning model training. Microscopic imaging of these samples confirmed the damage progression from matrix cracking to delamination, validating the computational predictions. We explored supervised machine learning using dielectric measurements to classify damage states. Preliminary results show an artificial neural network can identify early delamination which is a potential precursor to failure, with 94.44 % accuracy on our dataset. A parallel investigation into the effect of damage severity on pyrolysis recycling showed that heavily delaminated samples required significantly less energy for comparable matrix removal than undamaged samples.

dielectric variables↗

DOE OSTI2025

Cross-scale modeling and experimental integration for advancing cathode electrolyte interphase studies in high energy density lithium-ion batteries

Electrochemical interfaces are critical to the performance and durability of lithium-ion batteries (LIBs). The solid electrode-electrolyte interphase (SEI and CEI) structures that form during cycling can passivate reactive surfaces, ensuring safe operation, but also may contribute to performance degradation. Understanding the microscopic factors influencing interphase formation, growth, and evolution is essential for balanced battery design. While significant research has focused on the anode-electrolyte interphase (SEI), the cathode-electrolyte interphase (CEI) remains less explored, despite its importance in high-voltage and advanced battery technologies. Challenges in conducting in-situ or operando experiments arise from the occluded nature of these interfaces and the long timescales involved, often leading to biased interpretations. A validated multi-scale, multi-physics modeling approach, integrated with advanced characterization techniques, can effectively elucidate the intrinsic stability of electrolyte and cathode surfaces, the impact of chemical heterogeneity, and the role of microstructural features on CEI performance. In conclusion, this article reviews current modeling and simulation strategies for studying CEI in advanced LIBs and highlights opportunities for future methodological advancements and experimental integration.

Cathode-electrolyte interphase↗

DOE OSTI2026

Physics-informed machine learning exploration of Na storage mechanisms in disordered carbon

Sodium-ion batteries are a cost-effective, sustainable alternative to lithium-ion systems for large-scale energy storage. However, optimizing sodium storage in carbon-based anodes with microstructural complexity and atomic disorder remains a major challenge. The intrinsic inhomogeneity of these materials produces diverse local environments, making it difficult for conventional methods to predict and control ion dynamics. Hard carbon (HC) anodes, composed of ranges of ordered-to-disordered graphitic and amorphous nanodomains, offer tunable ion storage and rate capacity, yet rationale design remains a challenge due to poorly understood correlation between local atomic feature and ion transport mechanism. Here, to address this challenge, we introduce a data-driven framework that integrates validated machine-learned interatomic potentials, large-scale molecular dynamics simulations, and machine learning to elucidate sodium transport mechanisms as a function of carbon and sodium loading densities. By computing per-ion structural descriptors and applying unsupervised learning, we identify distinct diffusion modes governed by microscopic features. Supervised analysis and correlation mapping then establish quantitative links between these transport regimes and processing variables such as bulk carbon density and sodium content. This physics-informed approach establishes quantitative structure–transport relationships and offers actionable design principles for engineering high-performance HC anodes.

Data-driven framework↗

DOE OSTI2024

Understanding particle size effect on fast-charging behavior of graphite anode using ultra-thin-layer electrodes

Extreme fast charging (≤ 15 min) of lithium-ion batteries is highly desirable to accelerate mass-market adoption of electric vehicles. However, significant capacity fading, as well as safety issues due to the lithium plating caused by the fast charging rate, limit its implementation. In this study, we investigated the fast-charging capability of graphite materials with various particle sizes. To eliminate the Li + ion concentration gradient effect across the thickness of the electrode, ultra-thin-layer graphite electrodes were developed to investigate the "real" fast-charging capability of graphite at the particle level. Electrochemical assessments as well as microscopic characterizations revealed that smaller particles exhibited superior fast-charging performance, featuring enhanced capacity reversibility, faster charging rate, and less lithium plating under the same fast-charging conditions. It is shown that small-particle graphite (mean radius of 3.3 μm) could withstand a 4C charge (to 80 % state-of-charge) without plating, with minimal plating occurring at 6C. Thicker particles exhibited plating at lower C-rates. Since the experimental data could not directly explain whether intra-particle diffusion limitations or interfacial reaction limitations dominated the plating mechanism, the pseudo-2-dimensional model was used to evaluate the most likely plating mechanism. The model suggested that particle-level diffusion is the dominant mechanism contributing to plating at high rates. Finally, this work provides comprehensive insights into the particle size effects on fast-charging capability, offering a better understanding of fast-charging behavior and valuable guidance for designing optimal electrode architecture for high-rate lithium-ion batteries.

25 ENERGY STORAGE↗

DOE OSTI2025

Evolving physical and mechanical rock properties during exposure at Earth's surface

Rocks at Earth's surface experience progressive damage due to exposure to environmental conditions. Although environmental damage to rocks is recognized as being time-dependent, our quantitative understanding of its effects on physical and mechanical properties remains limited by field and laboratory studies constrained to short timescales. In this study, we aim to rigorously quantify how these properties evolve under longer natural environmental exposure spanning from the Holocene to the late Pleistocene. We conducted a ‘time series’ analysis of key physical and mechanical rock properties using multiple interior samples from 10 cogenetic granitoid boulders exposed for different amounts of time at two sites in Eastern California, USA. We find that over the late Pleistocene (~30 ka), rocks exhibit porosity increases of 40 ± 4 % and seismic velocity decreases of 7 ± 1 % at both sites. Similarly, over the same time period, rock tensile and compressive strengths declined by an average of 11 ± 4 %, and rock permeability increased on average by 104 ± 50 %. Microscopic analysis of thin sections of the same rocks indicates that microfracture density and intensity also progressively increased over the same timescales. These results suggest that time-dependent fracture propagation due to environmental exposure is likely a central contributor to the observed changes in rock properties. This study provides quantitative documentation that pronounced changes in the physical and mechanical properties of rock progressively occur within thousands of years of exposure.

Critical zone↗

DOE OSTI2024

Microwave-assisted ammonia decomposition over metal nitride catalysts at low temperatures

The negative environmental impact of fossil fuel-based energy systems has unveiled the need to develop a CO x -free sustainable hydrogen (H 2 ) economy. Employing a microwave-assisted route, a ternary metal nitride catalyst (i.e., Co 2 Mo 3 N), and a low-temperature-pressure NH 3 decomposition process, this study investigated the possibility of developing a distributed H 2 production process. Here, this study not only explored lower cost-based catalyst systems but also the use of a microwave reactor to increase the energy efficiency of the process. Results from catalytic NH 3 decomposition experiments, performed in microwave reactors on Co 2 Mo 3 N catalyst, demonstrated the peak energy efficiency (of ~0.006 kgH 2 /kWh) at 400 °C in ambient pressure (with an NH 3 conversion >90%) which was around ninety times (~90 x) more efficient than a conventional system. Activation energy calculation also displayed a 20% less energy requirement for the microwave-based process (~31 kJ mol -1 ) than the conventional system (~37 kJ mol -1 ), indicating the advantage of the microwave-based process. Further microwave-assisted catalytic measurements and characterization of the Co 2 Mo 3 N catalyst, using x-ray diffraction (XRD) technique and scanning electron microscopic (SEM) images, revealed the excellent stability of this material at its peak performance (at 400 °C) and illustrated the potential of using this catalyst for a sustainable, economic, and energy-efficient approach for producing CO x -free H 2 .

08 HYDROGEN↗

DOE OSTI2024

A prediction model of failure threshold for shear deformation in a Zr-based bulk metallic glass

The failure of bulk metallic glasses (BMGs) during plastic deformation at room temperature is abrupt and instantaneous, while the analysis of precursor information based on avalanche events helps predict catastrophic failure. An acoustic emission (AE) signal can provide accurate precursor information for material failure, due to its sensitive and high fast calculation ability. In the current study, AE monitoring tests are carried out during uniaxial compression tests of BMGs at different strain rates. The AE experimental failure threshold, E max , is proposed on the basis of AE cumulative energy, which reflects the intensity of damage evolution at different loading conditions. Compared with the critical shear band velocity (CSBV) associated with stick-slip dynamics of serrated flow, E max is a more sensitive failure parameter since it is connected with the local microscopic changes that occur during the material response process. Here, the E max is obtained prior to reaching the CSBV since the calculation of these two avalanches analysis focuses on the different stages of shear band growth. In particular, AE events are related to the “dry” friction process in the first stage, however, the CSBV is responsible for the “viscous” glide in the second stage. Therefore, Emax is not affected by the complex interactions between the shear bands during the stick-slip process. The maximum avalanche of serrated flow, S max , is proposed as the experimental failure threshold, which depends on the applied strain rate as S max ~ $\dot{ε}$ –λ . According to the relationship of E max and S max , the theoretical failure threshold, E max , follows a criterion E max = 2545$\dot{ε}$ –λ - 4468, where λ is equivalent to 0.15 for this work. Finally, combining the different calculations and AE measurements, this model gives new insights to predict the deformation failure behavior of Zr-based BMGs.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Reactive flash sintering and characterization of bulk high entropy nitrides

Over the past decade, numerous high-entropy ceramics have been synthesized, often displaying attractive properties. However, the study on facile preparation of bulk high entropy nitrides (HEN) are limited, despite its broad potential applications. This research demonstrates for the first time rapid fabrication (within ∼6 min) of bulk high-entropy nitrides, especially (Al 0.17 Nb 0.17 Ta 0.17 Ti 0.32 Zr 0.17 )N, from binary nitride powder mixtures using a highly efficient reactive flash sintering (RFS) technique. X-ray diffraction (XRD) shows the HENs from RFS are near single-phase solid solutions with a rock salt crystal structure, while in situ synchrotron study carried out during RFS captured in real time the formation of HEN, which was preserved upon cooling, suggesting thermodynamic stability of the HEN phase, even up to extreme pressure (∼35.6 GPa). Microscopic analyses using SEM, STEM, and EDS reveal decent uniformity for HEN with no obvious segregation of elements, even to submicron scale. Some properties of the obtained bulk HENs are consistent with expectations. For example, their hardness and bulk modulus are close to estimates based on rule-of-mixture (ROM) values from the constituent binary nitrides. Meanwhile, some other measured properties seem to show surprises. For example, the fracture toughness for the HENs (e.g., 7.81 ± 1.40 MPa•m 1/2 or higher) turns out to be more than double of the expected ROM estimates. The significantly improved fracture toughness is attributed to the observed nano-layered structure of the HENs, despite the HEN’s cubic crystal structure and high hardness. In addition, the oxidation resistance shows improvement up till ∼800°C, possibly due to Ta doping that suppress oxygen vacancy formation in the oxide shell, while the 5-metal HEN of (Al 0.17 Nb 0.17 Ta 0.17 Ti 0.32 Zr 0.17 )N displays superconductivity (T c of ∼5–7 K from magnetism and resistivity measurements, slightly lower than ROM estimate), despite insulating property of starting AlN. Furthermore, future study combining experimental investigation using larger samples to confirm the observed increase in fracture toughness and oxidation resistance, theoretical modeling at different length scale, and more detailed structural/chemical characterization, especially at the atomic scale, are all needed to fully understand the inter-relationships between composition, processing, structure, and novel properties for these HENs and the development of related new materials for different applications.

Flash sintering↗

DOE OSTI2024

Solid–liquid transition in a skyrmion matter

We report Monte-Carlo studies of the orientational order and melting of a 2D skyrmion lattice containing more than one million spins. Two models have been investigated, a microscopic model of lattice spins with Dzyaloshinskii–Moryia interaction that possesses skyrmions, and the model in which skyrmions are treated as point particles with repulsive interaction derived from a spin model. They produce similar results. The skyrmion lattice exhibits a sharp one-step transition between solid and liquid phases on temperature and the magnetic field. This solid–liquid transition is characterized by the kink in the magnetization. Here, the field-temperature phase diagram is computed. We show that the application of the field gradient to a 2D system of skyrmions produces a solid–liquid interface that must be possible to observe in experiments.

2D melting↗