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DOE OSTI2023

Parallel simulation via SPPARKS of on-lattice kinetic and Metropolis Monte Carlo models for materials processing

Abstract SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A multiscale insight into the growth of h-BN: effect of the enclosure

Abstract There is a lack of knowledge on the fundamental growth mechanisms governing the characteristics of 2D materials synthesized by the chemical vapor deposition (CVD) technique and their correlation with experimentally controllable parameters, which hindered their wafer-scale synthesis. Here, we pursued an analytical and computational approach to access the system states that are not experimentally viable to address these critical needs. We developed a multiscale computational framework correlating the macroscale heat and mass flow with the mesoscale morphology of the as-grown 2D materials by solving the coupled system of heat/mass transfer and phase-field equations. We used hexagonal boron nitride (h-BN) as our model material and investigated the effect of substrate enclosure on its growth kinetics and final morphology. We revealed a lower concentration with a more uniform distribution on the substrate in an enclosed-growth than open-growth. It leads to a more uniform size distribution of the h-BN islands, consistent with existing experimental investigations.

Materials Science↗

DOE OSTI2024

Accelerate microstructure evolution simulation using graph neural networks with adaptive spatiotemporal resolution

Abstract Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Magnetism of Nd 2 O 3 single crystals near the Néel temperature

Single crystals of Nd 2 O 3 were grown and characterized using neutron scattering and thermodynamic measurements. Nd 2 O 3 has long-range antiferromagnetic order below T N =0.55 K and specific-heat measurements have demonstrated that a significant amount of the magnetic entropy is released above T N . Inelastic neutron scattering experiments reveal a magnetic mode(s) with little dispersion peaked at ≈0.37meV that is of greatest intensity below T N but persists above 2T N . This persistence of dynamic correlations is likely related to frustrated interactions associated with the nearly ideal stacked triangular lattice geometry of J eff =12 spins on Nd 3+ ions. Furthermore, the magnetization is observed to be strongly anisotropic at all temperatures due to crystal field effects, with easy-plane anisotropy observed. Additionally, a noncompensated magnetic structure is inferred from the temperature dependence of the magnetization when a magnetic field of sufficient strength is applied within the basal plane near T N , and the evolution of the long-range order is summarized in a temperature-field phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Condensation of collective polar vortex modes

The dynamics of extended objects such as domain walls, domain bubbles, vortex structures, etc., can be described by their equations of motion associated with their effective mass and spring constant. Here we analytically derive the equations of motion for the polarization dynamics and elastodynamics for the structural responses of ferroelectric polar vortices, and theoretically extract their effective mass, spring constant, and mode frequencies. We demonstrate two subterahertz phonon modes and predicted their frequencies, both consistent with our recent experimental measurements and phase-field simulations. We show that elastic modulation of the energy function and spring constants leads to a condensation of a collective mode upon a second-order structural transition from symmetric to asymmetric vortices at a critical strain, analogous to the ferroelectric soft phonon mode at a ferroelectric transition. Furthermore, the present work offers a theoretical framework for predicting and manipulating the ultrafast collective dynamics of polar nanostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Coupled magnetostructural continuum model for multiferroic BiFeO 3

Here, a continuum approach to study magnetoelectric multiferroic BiFeO 3 (BFO) is proposed. Our modeling effort marries the ferroelectric (FE) phase field method and micromagnetic simulations to describe the entire multiferroic order parameter sector (polarization, oxygen antiphase tilts, strain, and magnetism) self-consistently on the same time- and length scale. In this paper, we discuss our choice of FE and magnetic energy terms and demonstrate benchmarks against known behavior. We parametrize the lowest order couplings of the structural distortions against previous predictions from density functional theory calculations giving access to simulations of the FE domain wall (DW) topology. This allows us to estimate the energetic hierarchy and thicknesses of the numerous structural DWs. We then extend the model to the canted antiferromagnetic order and demonstrate how the FE domain boundaries influence the resulting magnetic DWs. We also highlight some capabilities of this model by providing two examples relevant for applications. We demonstrate spin-wave transmission through the multiferroic domain boundaries which identify rectification in qualitative agreement with recent experimental observations. As a second example of application, we model fully dynamical magnetoelectric switching, where we find a sensitivity on the Gilbert damping with respect to switching pathways. We envision that this modeling effort will set the basis for further work on properties of arbitrary 3D nanostructures of BFO (and related multiferroics) at the mesoscale.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Mapping the three-dimensional fermiology of the triangular lattice magnet EuAg 4 Sb 2

In this paper, we report the temperature-field phase diagram as well as present a comprehensive study of the electronic structure and three-dimensional fermiology of the triangular-lattice magnet EuAg 4 ⁢Sb 2 , utilizing quantum oscillation measurements, angle-resolved photoemission spectroscopy, and first-principles calculations. The complex magnetic phase diagram of EuAg 4 ⁢Sb 2 highlights many transitions through nontrivial AFM states. Shubnikov-de Haas and de Haas-van Alphen oscillations were observed in the polarized ferromagnetic state of EuAg 4 ⁢Sb 2 , revealing three pairs of distinct spin-split frequency branches with small effective masses. A comparison of the angle-dependent oscillation data with first-principles calculations in the ferromagnetic state and angle-resolved photoemission spectra shows good agreement, identifying tubular hole pockets and hourglass-shaped hole pockets at the Brillouin zone center, as well as diamond-shaped electron pockets at the zone boundary. As the temperature increases, the frequency branches of the tiny hourglass pockets evolve into a more cylindrical shape, while the larger pockets remain unchanged. This highlights that variations in exchange splitting, driven by changes in the magnetic moment, primarily impact the small Fermi pockets without significantly altering the overall band structure. As a result, this is consistent with first-principles calculations, which show minimal changes near the Fermi level across ferromagnetic and simple antiferromagnetic states or under varying on-site Coulomb repulsion.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Structural short-range forces between solid-melt interfaces

We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase field crystal modeling. The solid ordering decays exponentially on the scale of the interface thickness at solid-melt interfaces; the overlap of two such profiles leads to a short-range interaction, which is mainly carried by the longest-range density waves, which can facilitate grain boundary premelting. Here, we calculate the tail of these interactions, depending on the relative translation of the two crystals, fully analytically and predict the interaction potential, and compare it to numerical simulations. For grain boundaries the interaction is predicted to decay twice as fast as for two crystals without misorientation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient

We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid interfaces outside of equilibrium. We use this extension to derive an analytical expression for the kinetic coefficient, which is the proportionality constant μ(nˆ) between the interface velocity along a direction nˆ normal to the interface and the interface undercooling. The kinetic coefficient is expressed as a spatial integral along the normal direction of a sum of gradient square terms corresponding to different nonlinear density wave profiles. Anisotropy arises naturally from the dependence of those profiles on the angles between the principal reciprocal lattice vectors K → i and nˆ. Values of the kinetic coefficient for the (100), (110), and (111) interfaces are compared quantitatively to the prediction of linear Mikheev-Chernov (MC) theory and previous molecular dynamics (MD) simulation studies of crystallization kinetics for a classical model of Fe. Additional MD simulations are carried out here to compute the relaxation time of density waves in the liquid in order to make this comparison free of fit parameters. The GL theory predicts an expression for μ similar to the MC theory but yields a better agreement with MD simulations for both its magnitude and anisotropy due to a fully nonlinear description of density wave profiles across the solid-liquid interface. In particular, the overall magnitude of μ predicted by GL theory is an order of magnitude larger than predicted by the MC theory. GL theory is also used to derive an inverse relation between μ and the solid-liquid interfacial free energy. Here, the general methodology used here to derive an expression for μ(nˆ) also applies to amplitude equations derived from the phase-field-crystal model, which only differ from GL theory by the choice of cubic and higher order nonlinearities in the free-energy density.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Domain pinning near a single-grain boundary in tetragonal and rhombohedral lead zirconate titanate films

The interaction of grain boundaries with ferroelectric domain walls strongly influences the extrinsic contribution to piezoelectric activity in Pb(Zr,Ti)O 3 (PZT), ubiquitous in modern transducers and actuators. However, the fundamental understanding of these phenomena has been limited by complex mechanisms originating from the interplay of atomic-level domain wall pinning, collective domain wall dynamics, and emergent mesoscopic behavior. This contribution utilizes engineered grain boundaries created by depositing epitaxial PZT films with various Zr:Ti ratio onto 24º SrTiO 3 tilt bicrystals. The nonlinear piezoelectric response and surface domain structure across the boundary are investigated using piezoresponse force microscopy whilst cross section domain structure is studied using transmission electron microscopy. The grain boundary reduces domain wall motion over a width of 800±70 nm for PZT 45:55 and 450±30 nm for PZT 52:48. Phase field modeling provides an understanding of the elastic and electric fields associated with the grain boundary and local domain configurations. In conclusion, this study demonstrates that complex mesoscopic behaviors can be explored to complement atomic-level pictures of the material system.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Scaling laws for two-dimensional dendritic crystal growth in a narrow channel

Here, we investigate analytically and computationally the dynamics of two-dimensional needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $\textit{V}$ decreases in time $\textit{t}$ as a power law $V ~t^{–2/3}$, which we validate by phase-field and dendritic-needle-network simulations. Simulations further reveal that, above a critical channel width $Λ ≈ 5l_D$, where $l_D$ is the diffusion length, needle crystals grow with a constant $V < V_s$, where $V_s$ is the free-growth needle crystal velocity, and approaches $V_s$ in the limit $Λ \gg l_D$.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Viscous fingering with partially miscible fluids

Viscous fingering—the fluid-mechanical instability that takes place when a low-viscosity fluid displaces a high-viscosity fluid—has traditionally been studied under either fully miscible or fully immiscible fluid systems. In this work, we study the impact of partial miscibility (a common occurrence in practice) on the fingering dynamics. Through a careful design of the thermodynamic free energy of a binary mixture, we develop a phase-field model of fluid-fluid displacements in a Hele-Shaw cell for the general case in which the two fluids have limited (but nonzero) solubility into one another.We show, bymeans of high-resolution numerical simulations, that partial miscibility exerts a powerful control on the degree of fingering: fluid dissolution hinders fingering while fluid exsolution enhances fingering. Additionally, we show that, as a result of the interplay between compositional exchange and the hydrodynamic pattern-forming process, stronger fingering promotes the system to approach thermodynamic equilibrium more quickly.

42 ENGINEERING↗

DOE OSTI2015

Crack Front Segmentation and Facet Coarsening in Mixed-Mode Fracture

A planar crack generically segments into an array of “daughter cracks” shaped as tilted facets when loaded with both a tensile stress normal to the crack plane (mode I) and a shear stress parallel to the crack front (mode III). We investigate facet propagation and coarsening using in situ microscopy observations of fracture surfaces at different stages of quasistatic mixed-mode crack propagation and phase-field simulations. The results demonstrate that the bifurcation from propagating a planar to segmented crack front is strongly subcritical, reconciling previous theoretical predictions of linear stability analysis with experimental observations. As a result, they further show that facet coarsening is a self-similar process driven by a spatial period-doubling instability of facet arrays.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Facilitation of Ferroelectric Switching via Mechanical Manipulation of Hierarchical Nanoscale Domain Structures

Heterogeneous ferroelastic transition that produces hierarchical 90° tetragonal nanodomains via mechanical loading and its effect on facilitating ferroelectric domain switching in relaxor-based ferroelectrics were explored. Combining in situ electron microscopy characterization and phase-field modeling, we reveal the nature of the transition process and discover that the transition lowers by 40% the electrical loading threshold needed for ferroelectric domain switching. Our results advance the fundamental understanding of ferroelectric domain switching behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Defect-Induced Hedgehog Polarization States in Multiferroics

Continuous developments in nanotechnology require new approaches to materials synthesis that can produce novel functional structures. Here, we show that nanoscale defects, such as nonstoichiometric nanoregions (NSNRs), can act as nano-building blocks for creating complex electrical polarization structures in the prototypical multiferroic BiFeO 3 . An array of charged NSNRs are produced in BiFeO 3 thin films by tuning the substrate temperature during film growth. Atomic-scale scanning transmission electron microscopy imaging reveals exotic polarization rotation patterns around these NSNRs. These polarization patterns resemble hedgehog or vortex topologies and can cause local changes in lattice symmetries leading to mixed-phase structures resembling the morphotropic phase boundary with high piezoelectricity. Phase-field simulations indicate that the observed polarization configurations are mainly induced by charged states at the NSNRs. Engineering defects thus may provide a new route for developing ferroelectric-or multiferroic-based nanodevices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Sign-Reversing Hall Effect in Atomically Thin High-Temperature Bi 2.1 Sr 1.9 CaCu 2.0 O 8 + δ Superconductors

We developed novel techniques to fabricate atomically thin Bi 2.1 Sr 1.9 CaCu 2.0 O 8+δ van der Waals heterostructures down to two unit cells while maintaining a transition temperature T c close to the bulk, and carry out magnetotransport measurements on these van der Waals devices. We find a double sign change of the Hall resistance E-xy as in the bulk system, spanning both below and above T c . Further, we observe a drastic enlargement of the region of sign reversal in the temperature-magnetic field phase diagram with decreasing thickness of the device. We obtain quantitative agreement between experimental R xy ( T, B ) and the predictions of the vortex dynamics-based description of Hall effect in high-temperature superconductors both above and below T c .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Anomalous strain-energy-driven macroscale translation of grains during nonisothermal annealing

We report a mode of grain growth, involving the macroscopic translation of grain centers during nonisothermal annealing. Through synchrotron high-energy x-ray diffraction microscopy, we find dissolution of semicoherent precipitates generates dislocations, thereby raising the stored strain energy within grains. Here, the subsequent evolution of grains shows unexpected grain translations over length scales of 10-100 mu m. Phase-field simulations reveal that such translations are not uncommon in strain-energy-driven grain growth, wherein different regions of a grain may grow and shrink simultaneously.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Parity breaking at faceted crystal growth fronts during ice templating

Directional solidification of water-based solutions has emerged as a versatile technique to template hierarchical porous materials, but this nonequilibrium process remains incompletely understood. Here, in this study, we use phase-field simulations to shed light on the mechanism that selects the growth direction of the lamellar ice structure that templates those materials. Our results show that this selection can be understood within the general framework of spontaneous parity breaking, yielding quantitative predictions for the tilt angle of lamellae with respect to the thermal axis. The results provide a theoretical basis to interpret a wide range of experimental observations.

Materials science↗