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DOE OSTI2023

A general non-Fourier Stefan problem formulation that accounts for memory effects

The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. Further, on shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.

42 ENGINEERING↗

DOE OSTI2026

Quadratic magnetoresistance across the insulator–metal transition in V4O7 thin films

We present a comparative magnetotransport study of V4O7 thin films grown simultaneously on single-crystal Al2O3 (r-cut) and amorphous SiO2 substrates, to examine substrate-induced effects on electronic transport across the insulator–metal transition (IMT). Temperature-dependent resistivity reveals a broad electronic ordering regime below the IMT, with both films exhibiting similar transition temperatures but differing by nearly an order of magnitude in absolute resistivity. Despite this strong substrate dependence of the resistivity scale, the magnetoresistance remains predominantly quadratic in magnetic field over wide temperature intervals for both substrates. Analysis of the quadratic magnetoresistance defines an effective mobility scale that evolves systematically across the IMT and exhibits a similar temperature dependence for the two films. Structural characterization, including atomic-resolution scanning transmission electron microscopy of the V4O7/Al2O3 interface and azimuthal X-ray diffraction measurements, reveals a sharp interface and well-defined in-plane crystallographic registry for the r-cut film, in contrast to the rotationally averaged in-plane structure expected for films grown on amorphous SiO2. These results indicate that while substrate-controlled structural registry modifies the resistivity scale, the quadratic magnetotransport response across the IMT remains largely robust, providing a consistent diagnostic of electronic transport in V4O7 thin films.

25 ENERGY STORAGE↗

DOE OSTI2022

A Phase-Field Model for In-Space Manufacturing of Binary Alloys

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Extending Interfaces in 3D to Achieve Superior Nanoscale Strength in Ti/Nb Nanolaminates

Tuning the atomic-level structure of nanolaminates enables high strength, increased deformability, and the ability to absorb and mitigate damage due to varied crystalline defects, including dislocations. Here, we present the enhanced strength of Ti/Nb nanolaminates containing thick 3D interfaces (3DIs), relative to their chemically abrupt 2D counterparts. We examine the effects of crystallographic alignment and compositional gradients on mechanical behavior via experiments and phase-field-dislocation dynamics (PFDD) modeling. Mechanical testing reveals that nanolaminates containing thicker 3DIs demonstrate a 28% hardness enhancement compared with sharp-interface nanolaminates. PFDD modeling shows that the critical resolved shear stress (CRSS) increases with the 3DI thickness. Gradual compositional transitions in 3DIs were confirmed via scanning transmission electron microscopy and high-resolution transmission electron microscopy, showing sharp crystallographic transitions and a heightened interface topography. The findings establish a positive function between the 3DI thickness and mechanical robustness for hexagonal-closest-packed-containing composites, emphasizing the role of defect–interface interactions in tailoring the mechanical performance and providing a foundation for future interfacial engineering.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Simulating hindered grain boundary diffusion using the smoothed boundary method

Abstract Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the smoothed boundary method to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method’s capability.

Materials Science↗

DOE OSTI2022

Ephemeral antibubbles: Spatiotemporal evolution from direct numerical simulations

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions, that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar-order-parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface volume-of-fluid DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as σ 1/2 , where σ is the surface tension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Localized Excitons in NbSe 2 -MoSe 2 Heterostructures

Neutral and charged excitons (trions) in atomically thin materials offer important capabilities for photonics, from ultrafast photodetectors to highly efficient light-emitting diodes and lasers. Recent studies of van der Waals (vdW) heterostructures comprised of dissimilar monolayer materials have uncovered a wealth of optical phenomena that are predominantly governed by interlayer interactions. Here, we examine the optical properties in NbSe 2 -MoSe 2 vdW hetero- structures, which provide an important model system to study metal–semiconductor interfaces, a common element in optoelectronics. Through low-temperature photoluminescence (PL) microscopy, we discover a sharp emission feature, L1, that is localized at the NbSe 2 -capped regions of MoSe 2 . L1 is observed at energies below the commonly studied MoSe 2 excitons and trions and exhibits temperature- and power-dependent PL consistent with exciton localization in a confining potential. This PL feature is robust, observed in a variety of samples fabricated with different stacking geometries and cleaning procedures. Using first-principles calculations, we reveal that the confinement potential required for exciton localization naturally arises from the in-plane band bending due to the changes in the electron affinity between pristine MoSe 2 and NbSe 2 -MoSe 2 heterostructure. Here, we discuss the implications of our studies for atomically thin optoelectronics devices with atomically sharp interfaces and tunable electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Dislocation dynamics in heterogeneous nanostructured materials

Crystalline materials can be strengthened by introducing dissimilar phases that impede dislocation glide. At the same time, the changes in microstructure and chemistry usually make the materials less ductile. One way to circumvent the strength–ductility dilemma is to take advantage of heterogeneous nanophases which simultaneously serve as dislocation barriers and sources. Owing to their superior mechanical properties, heterogeneous nanostructured materials (HNMs) have attracted a lot of attention worldwide. Nevertheless, it has been difficult to characterize dislocation dynamics in HNMs using classical continuum models, mainly due to the challenges in describing the elastic and plastic heterogeneity among the phases. Here, in this work, we advance a phase-field dislocation dynamics (PFDD) model to treat multi-phase materials, consisting of phases differing in composition, structural order, and size in the same system. We then apply the advanced PFDD model to exploring two important but divergent materials design problems in HNMs: dislocation/obstacle interactions and dislocation/interface interactions. Results show that the interactions between a dislocation and distribution of obstacles varying in structure and composition cannot be understood by simply interpolating from their individual interactions with a dislocation. It is also found that materials containing interfaces with nanoscale thicknesses and compositional gradients have a much higher dislocation bypass stress than those with sharp interfaces, providing an explanation for the simultaneous high strength and toughness of thick interface-containing nanolaminates as observed in recent experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Exploring the effects of molecular beam epitaxy growth characteristics on the temperature performance of state-of-the-art terahertz quantum cascade lasers

This study conducts a comparative analysis, using non-equilibrium Green’s functions (NEGF), of two state-of-the-art two-well (TW) Terahertz Quantum Cascade Lasers (THz QCLs) supporting clean 3-level systems. The devices have nearly identical parameters and the NEGF calculations with an abrupt-interface roughness height of 0.12 nm predict a maximum operating temperature (T max ) of ~ 250 K for both devices. However, experimentally, one device reaches a T max of ~ 250 K and the other a T max of only ~ 134 K. Both devices were fabricated and measured under identical conditions in the same laboratory, with high quality processes as verified by reference devices. The main difference between the two devices is that they were grown in different MBE reactors. Our NEGF-based analysis considered all parameters related to MBE growth, including the maximum estimated variation in aluminum content, growth rate, doping density, background doping, and abrupt-interface roughness height. From our NEGF calculations it is evident that the sole parameter to which a drastic drop in T max could be attributed is the abrupt-interface roughness height. We can also learn from the simulations that both devices exhibit high-quality interfaces, with one having an abrupt-interface roughness height of approximately an atomic layer and the other approximately a monolayer. However, these small differences in interface sharpness are the cause of the large performance discrepancy. This underscores the sensitivity of device performance to interface roughness and emphasizes its strategic role in achieving higher operating temperatures for THz QCLs. We suggest Atom Probe Tomography (APT) as a path to analyze and measure the (graded)-interfaces roughness (IFR) parameters for THz QCLs, and subsequently as a design tool for higher performance THz QCLs, as was done for mid-IR QCLs. Our study not only addresses challenges faced by other groups in reproducing the record T max of ~ 250 K and ~ 261 K but also proposes a systematic pathway for further improving the temperature performance of THz QCLs beyond the state-of-the-art.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2024

2-D seismic wave propagation using the distributional finite-difference method: further developments and potential for global seismology

SUMMARY We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth’s internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency.

Geochemistry & Geophysics↗

DOE OSTI2024

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Here, we present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

42 ENGINEERING↗

DOE OSTI2024

A mineral precipitation model based on the volume of fluid method

A novel volume of fluid method is presented for mineral precipitation coupled with fluid flow and reactive transport. The approach describes the fluid-solid interface as a smooth transitional region, which is designed to provide the same precipitation rate and viscous drag force as a sharp interface. Specifically, the governing equation of mineral precipitation is discretized by an upwind scheme, and a rigorous effective viscosity model is derived around the interface. The model is validated against analytical solutions for mineral precipitation in channel and ring-shaped structures. It also compares well with interface tracking simulations of advection-diffusion-reaction problems. Here, the methodology is finally employed to model mineral precipitation in fracture networks, which is challenging due to the low porosity and complex geometry. Compared to other approaches, the proposed model has a concise algorithm and contains no free parameters. In the modeling, only the pore space requires meshing, which improves the computational effciency especially for low-porosity media.

58 GEOSCIENCES↗

DOE OSTI2025

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A Method to Probe the Interfaces in La2−xSrxCuO4-LaSrAlO4-La2−xSrxCuO4 Trilayer Junctions

C-axis trilayer cuprate Josephson junctions are essential for basic science and digital circuit applications of high-temperature superconductors. We present a method for probing the interface perfection in La2−xSrxCuO4 (LSCO)-LaSrAlO4 (LSAO)-La2−xSrxCuO4 trilayer junctions. A series of LSCO-LSAO superlattices with atomically smooth surfaces and sharp interfaces were grown by the atomic-layer-by-layer molecular beam epitaxy (ALL-MBE) technique. We have systematically varied the thickness of LSCO and LSAO layers with monolayer precision. By studying the mutual inductance and electrical transport in these superlattices, we detect the non-superconducting (“dead”) layers at the interfaces and quantify their thicknesses. Our results indicate that two optimally doped LSCO monolayers just above and below the one monolayer LSAO barrier are no longer superconducting, rendering the actual barrier thickness of five monolayers. Next, we have shown that introducing a protective highly-overdoped LSCO layer reduces the thickness of dead layers by one or two monolayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Giant Orbital Anisotropy with Strong Spin–Orbit Coupling Established at the Pseudomorphic Interface of the Co/Pd Superlattice

Orbital anisotropy at interfaces in magnetic heterostructures has been key to pioneering spin–orbit-related phenomena. However, modulating the interface’s electronic structure to make it abnormally asymmetric has been challenging because of lack of appropriate methods. Here, the authors report that low-energy proton irradiation achieves a strong level of inversion asymmetry and unusual strain at interfaces in [Co/Pd] superlattices through nondestructive, selective removal of oxygen from Co3O4/Pd superlattices during irradiation. Structural investigations corroborate that progressive reduction of Co3O4into Co establishes pseudomorphic growth with sharp interfaces and atypically large tensile stress. The normal component of orbital to spin magnetic moment at the interface is the largest among those observed in layered Co systems, which is associated with giant orbital anisotropy theoretically confirmed, and resulting very large interfacial magnetic anisotropy is observed. All results attribute not only to giant orbital anisotropy but to enhanced interfacial spin–orbit coupling owing to the pseudomorphic nature at the interface. They are strongly supported by the observation of reversal of polarity of temperature-dependent Anomalous Hall signal, a signature of Berry phase. This work suggests that establishing both giant orbital anisotropy and strong spin–orbit coupling at the interface is key to exploring spintronic devices with new functionalities.

42 ENGINEERING↗

DOE OSTI2021

Investigating the magnetic and atomic interface configuration for a model Fe/CrN bilayer system

A bilayer of iron on chromium nitride (Fe/CrN) is an interesting system for exchange biasing and sensing applications as the Néel temperature of CrN is 280 K and the Curie temperature of Fe is 1043 K. In this paper, we study the crystal and magnetic structures of the Fe/CrN interface at the atomic level. High quality epitaxial Fe/CrN bilayers prepared by molecular beam epitaxy grow in 001 orientation on MgO(001) substrates with uniform layer thicknesses and sharp interfaces. Our data reveal the epitaxial correlation between Fe and CrN crystals and their magnetic structures at the interface. The magnetic anisotropy directions of Fe and CrN are found parallel to [110] MgO . We studied the electronic and magnetic properties of the interface by performing the first-principles total-energy calculations. Here, we present a model that combines the crystal and magnetic structures of the Fe/CrN bilayer and fully explains all results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

Here, we present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://doi.org/10.1016/j.cma.2024.117135), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors

Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi 2 Sr 2 CaCu 2 O 8+x crystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Furthermore, our results open a path to engineering topological devices at higher temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗