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DOE OSTI2020

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\textit{α}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α > \frac{1}{2}$ . A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\textit{α}$, corresponding to a critical behavior with an effective central charge $\textit{c}$ = ln(2), independent of $\textit{α}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\textit{α}$. For a wide range of partition size $\textit{l}$, the EE fits a critical behavior with a central charge close to $\textit{c}$ = 1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\textit{α}$ = 2. Only for small $l \ll L$, in a range which increases with the number of spins N, we find deviations which are rather consistent with the strong disorder fixed point central charge $\textit{c}$ = ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. Finally, we also present results obtained with DMRG and find agreement with ED for sufficiently small $\textit{α}$ < 2, whereas for larger $\textit{α}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Relativistic and correlation effects in the photoionization dynamics of oganesson ( Z = 118): Spin-orbit-interaction-activated interchannel coupling effects

High-Z atoms are excellent laboratories to study the combination of relativistic and many-electron correlation effects in electronic structure and dynamics. In the present work, the relativistic-random-phase approximation at different levels of truncation is employed to explore the final-state correlation effects in the photoelectron dynamics of the heaviest known element in the Periodic Table: oganesson (Og) with Z = 118. Here, the focus of this work is to illustrate the relativistic effects resulting from coupling different photoionization channels arising from spin-orbit split subshells, termed the spin-orbit-interaction-activated interchannel coupling effect. Comparison with the photoelectron dynamics of Rn on a qualitative level is also carried out, since Og is a homologue of Rn. The photoelectron dynamics of 7p, 7s, and 6d subshells are investigated and differences between Og and Rn, due to enhanced relativistic effects, are investigated.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation

Here, we study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of U c ≈5t these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Measurement of Deformation Heterogeneity During Shale Swelling Using Digital Image Correlation

Abstract Rock-fluid interactions in shale formations are one of the main sources of wellbore instability issues and inadequate stimulation performance. For better planning of fracturing operations and optimizing production from these reservoirs, it is important to understand the mechanisms behind these interactions. These issues are especially prevalent in clay-rich shales, such as Tuscaloosa Marine Shale, which is the subject of this study. Conventional techniques to quantify these shale-fluid interactions comprise of measuring swelling in powdered rock grains or measurement of deformation in the whole pieces of the core using a linear variable differential transformer and strain gages. However, the contribution from individual laminae to overall deformation cannot be evaluated using these methods. In this study, we developed an experimental setup to evaluate the spatial deformation in shale during interaction with water using digital image correlation (DIC). Deformation of two shale samples, with 34 wt% to 51 wt% clay content, was studied. White paint was used to generate a random speckle pattern on the specimen and then immersed in deionized water. The deformation process was captured using a digital camera and images were analyzed using DIC to quantify the deformation. The implementation of the DIC technique enables the visualization and quantification of spatial deformation in the specimen during interacting with water. The results show the localization of large strains in select laminations. The results provide a better understanding of shale deformation when interacting with water in comparison to traditional measurements that can provide only an average strain value.

Energy & Fuels↗

DOE OSTI2023

Enhancing Composite Toughness Through Hierarchical Interphase Formation

High strength and ductility are highly desired in fiber-reinforced composites, yet achieving both simultaneously remains elusive. A hierarchical architecture is developed utilizing high aspect ratio chemically transformable thermoplastic nanofibers that form covalent bonding with the matrix to toughen the fiber-matrix interphase. The nanoscale fibers are electrospun on the micrometer-scale reinforcing carbon fiber, creating a physically intertwined, randomly oriented scaffold. Unlike conventional covalent bonding of matrix molecules with reinforcing fibers, here, the nanofiber scaffold is utilized - interacting non-covalently with core fiber but bridging covalently with polymer matrix - to create a high volume fraction of immobilized matrix or interphase around core reinforcing elements. This mechanism enables efficient fiber-matrix stress transfer and enhances composite toughness. Molecular dynamics simulation reveals enhancement of the fiber-matrix adhesion facilitated by nanofiber-aided hierarchical bonding with the matrix. The elastic modulus contours of interphase regions obtained from atomic force microscopy clearly indicate the formation of stiffer interphase. These nanoengineered composites exhibit a ≈60% and ≈100% improved in-plane shear strength and toughness, respectively. This approach opens a new avenue for manufacturing toughened high-performance composites.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Non-Markovian Hole Excess Noise in Avalanche Amorphous Selenium Thin Films

Enhancing the signal-to-noise ratio in avalanche photodiodes by utilizing impact ionization gain requires materials exhibiting low excess noise factors. Amorphous selenium (a-Se) as a wide bandgap at ~2.1 eV, a solid-state avalanche layer, demonstrates single-carrier hole impact ionization gain and manifests ultralow thermal generation rates. A comprehensive study of the history dependent and non-Markovian nature of hot hole transport in a-Se was modeled using a Monte Carlo (MC) random walk of single hole free flights, interrupted by instantaneous phonon, disorder, hole–dipole, and impact-ionization scattering interactions. The hole excess noise factors were simulated for 0.1–15 μm a-Se thin-films as a function of mean avalanche gain. The hole excess noise factors in a-Se decreases with an increase in electric field, impact ionization gain, and device thickness. The history dependent nature of branching of holes is explained using a Gaussian avalanche threshold distance distribution and the dead space distance, which increases determinism in the stochastic impact ionization process. An ultralow non-Markovian excess noise factor of ~1 was simulated for 100 nm a-Se thin films corresponding to avalanche gains of 1000. Future detector designs can utilize the nonlocal/non-Markovian nature of the hole avalanche in a-Se, to enable a true solid-state photomultiplier with noiseless gain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Phenomenology of Spectral Functions in Disordered Spin Chains at Infinite Temperature

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Impact of HF-CRPA CCQE Model on the Latest NOvA Results

NOvA is a long-baseline neutrino experiment based at Fermilab, dedicated to measuring various neutrino oscillation parameters. Recently, the NOvA collaboration presented new results at NEUTRINO 2024. A significant enhancement in the modeling of charged-current quasi elastic (CCQE) interactions has been achieved with the implementation of the Hartree-Fock (HF) mean-field model, incorporating continuum random phase approximation (CRPA) corrections. This HF-CRPA model offers substantial improvements in the low-energy region. In this presentation, I will discuss the impact of the HF-CRPA model on the latest three-flavor oscillation results of the NOvA experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Modeling Lithium Diffusion in Battery Cathodes Considering Chemo-Mechanically Induced Damage

This talk will present a 3D, continuum-level damage model for simulating Lithium diffusion within generated Li_{x}Ni_{0.5}Mn_{0.3}Co_{0.2} (NMC 532) secondary cathode particles. The primary motivation of the particle-level model is to inform cathode-particle design and determine charging profiles that reduce cathode fracture. The model considers NMC 532 secondary particles containing an agglomeration of anisotropic, randomly oriented grains. The model predicts that secondary-particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. The model predicts that small secondary-particles with large grains develop significantly less damage than larger secondary particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first high-rate cycles. This chemo-mechanical “damage saturation” effect indicates that initial secondary-particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Bottlebrush Block Copolymer Thin Films

The self-assembly of block copolymers (BCPs) in thin films is governed by interfacial interactions (enthalpy) between the blocks and interfaces (at both the substrate and the surface). Advantage can also be taken of entropy to control the polymer orientation. Here, we synthesized a series of bottlebrush block copolymers (BBCPs), with deuterated polystyrene (DPS) as the core block and poly(solketal acrylate) (PSA) as the corona block, where the backbone length (N BB) and grafting densities (GDs) were varied. The hydrophobic PSA block was converted to a hydrophilic poly(glyceryl acrylate) (PGA) block by solid-state hydrolysis, bringing the BBCP from a disordered state into an ordered state with a lamellar microdomain morphology. The orientation of the morphology as a function of distance from the interfaces was systematically investigated by atomic force microscopy (AFM), interference microscopy, grazing-incidence small-angle X-ray scattering (GISAXS), and grazing-incidence small angle neutron scattering (GISANS). For N BB = 1 (diblock BCP), a mixed lamellar orientation was found. For N BB = 5 (star-like BBCP), a vertical orientation of the lamellar microdomains was found dominantly at the interfaces that propagated into the bulk of the film due to the entropic penalty associated with constraints on the junction points. Increasing the N BB to 50 (rod-like BBCP) and 100 (worm-like BBCP) yielded a random orientation, as the side chains became overcrowded when aligned in the same direction. By reducing the grafting density (GD) of a N BB = 50 BBCP from 100% to 75% and 50% by the incorporation of spacers into the backbone, the steric hindrance of side chains is reduced markedly, facilitating a vertical orientation of the lamellar microdomains. However, the vertical orientation becomes more random within the bulk of the thin film for different BBCP architectures. By modifying the substrate with a layer of PS, the preferential interactions between the core block of the BBCP and the interfaces induce a reconfiguration of the BBCP, drawing the core block out to contact substrate directly driven by enthalpy. Under these conditions, N BB = 5 showed a predominantly parallel orientation of the lamellar microdomains with the corona block minimizing contact with the substrate. Higher N BB values of 50 and 100 showed a more random orientation of the lamellar microdomains at different depths on the PS-modified substrate. Overall, thin-film morphology was regulated by tuning the configuration of the BBCP, varying the entropic contribution to the microdomain orientation.

Chen, Zhan↗

DOE OSTI2020

Chaos on the hypercube

We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude φ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at φ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at φ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of φ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

1/N expansion↗

DOE OSTI2022

Multiscale spatial analysis of fracture arrangement and pattern reconstruction using Ripley's K-function

This work presents novel multiscale spatial data analytics using Ripley's K-function, as a measure of spatial interaction, to study one-dimensional arrangement of fractures. Fracture spatial arrangements are classified into clustered, anticlustered, or indistinguishable from random by testing statistical significance of the calculated Ripley's K-function. Characterizations of fracture arrangements are performed as a function of length scale and position. Analysis of the K-function along the study interval identifies where fracture clustering and anticlustering occur. Here, a simulation technique is also introduced here to statistically reconstruct spatial arrangements and to generate fracture realizations that are spatially similar to the fractures observed in the field. With this simulation technique, one can also fill spatial gaps in fracture measurements where data are absent, unreliable, or unused. Synthetic as well as field-measured 1D fracture datasets are used for testing and demonstration. Methods introduced in this work can be readily applied to fracture datasets observed in outcrops, borehole image logs, and cores.

58 GEOSCIENCES↗

DOE OSTI2020

Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter

Centroid energies, E CEN , of the isoscalar (T = 0) and isovector (T = 1) giant resonances of multipolarities L = 0 – 3 in 40,48 Ca, 68 Ni, 90 Zr, 116 Sn, 144 Sm and 208 Pb, were calculated within the fully self-consistent spherical Hartree-Fock (HF)-based random phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon-nucleon interactions of the standard form commonly employed in the literature. Here, we also calculate the Pearson linear correlation coefficients between each E CEN and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of E CEN to bulk properties of NM. By comparing the calculated values of E CEN to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, m* / m = 0.70 to 0.90, incompressibility coefficient, K NM = 210 to 240 MeV, and the enhancement coefficient of the energy weighted sum rule of the isovector giant dipole resonance, κ = 0.25 to 0.70, best reproduce the experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

MONACO: accurate biological network alignment through optimal neighborhood matching between focal nodes

Motivation: Alignment of protein–protein interaction networks can be used for the unsupervised prediction of functional modules, such as protein complexes and signaling pathways, that are conserved across different species. To date, various algorithms have been proposed for biological network alignment, many of which attempt to incorporate topological similarity between the networks into the alignment process with the goal of constructing accurate and biologically meaningful alignments. Especially, random walk models have been shown to be effective for quantifying the global topological relatedness between nodes that belong to different networks by diffusing node-level similarity along the interaction edges. However, these schemes are not ideal for capturing the local topological similarity between nodes. Results: Here, we propose MONACO, a novel and versatile network alignment algorithm that finds highly accurate pairwise and multiple network alignments through the iterative optimal matching of ‘local’ neighborhoods around focal nodes. Extensive performance assessment based on real networks as well as synthetic networks, for which the ground truth is known, demonstrates that MONACO clearly and consistently outperforms all other state-of-the-art network alignment algorithms that we have tested, in terms of accuracy, coherence and topological quality of the aligned network regions. Furthermore, despite the sharply enhanced alignment accuracy, MONACO remains computationally efficient and it scales well with increasing size and number of networks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

HfZr_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-zirconium (Hf-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

HfTa_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-tantalum (Hf-Ta). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Ta. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect BCC lattice sites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,040 randomized atomic structures over 31 chemical compositions. Further methodological and structural information is contained in the dataset README.txt file.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Bead–Spring Simulation of Ionomer Melts—Studying the Effects of Chain-Length and Associating Group Fraction on Equilibrium Structure and Extensional Flow Behavior

Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system’s mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters’ size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups’ fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer–Grest type bead–spring model and perform large-scale MD simulations to explore the effect of polymer chain-length (l) and fraction (f s ) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by ‘sticky’ beads) between 5 and 20%, and a fixed sticky–sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S(q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing f s and l. The average cluster size Nc increases with f s . However, the effect of chain-length on Nc appears to be pronounced only at higher values of f s . Under extensional flows, the computed stress (and viscosity) is higher at higher f s and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response.

36 MATERIALS SCIENCE↗

DOE OSTI2026

HfTi_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-titanium (Hf-Ti). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Ti. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions. The calculations have been collected on Air Force HPC11 cluster using the VASP 6.5.1. Additional methodology and file structure information is available in the dataset README.txt file.

36 MATERIALS SCIENCE↗