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DOE OSTI2020

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Inferring topological transitions in pattern-forming processes with self-supervised learning

Abstract The identification of transitions in pattern-forming processes are critical to understand and fabricate microstructurally precise materials in many application domains. While supervised methods can be useful to identify transition regimes, they need labels, which require prior knowledge of order parameters or relevant microstructures describing these transitions. Instead, we develop a self-supervised, neural-network-based approach that does not require predefined labels about microstructure classes to predict process parameters from observed microstructures. We show that assessing the difficulty of solving this inverse problem can be used to uncover microstructural transitions. We demonstrate our approach by automatically discovering microstructural transitions in two distinct pattern-forming processes: the spinodal decomposition of a two-phase mixture and the formation of binary-alloy microstructures during physical vapor deposition of thin films. This approach opens a path forward for discovering unseen or hard-to-discern transitions and ultimately controlling complex pattern-forming processes.

Abram, Marcin↗

DOE OSTI2022

Rheology and dynamics of a solvent segregation driven gel (SeedGel)

Bicontinuous structures promise applications in a broad range of research fields, such as energy storage, membrane science, and biomaterials. Kinetically arrested spinodal decomposition is found responsible for stabilizing such structures in different types of materials. A recently developed solvent segregation driven gel (SeedGel) is demonstrated to realize bicontinuous channels thermoreversibly with tunable domain sizes by trapping nanoparticles in a particle domain. As the mechanical properties of SeedGel are very important for its future applications, a model system is characterized by temperature-dependent rheology. The storage modulus shows excellent thermo-reproducibility and interesting temperature dependence with the maximum storage modulus observed at an intermediate temperature range (around 28 °C). SANS measurements are conducted at different temperatures to identify the macroscopic solvent phase separation during the gelation transition, and solvent exchange between solvent and particle domains that is responsible for this behavior. Further, the long-time dynamics of the gel is further studied by X-ray Photon Correlation Spectroscopy (XPCS). The results indicate that particles in the particle domain are in a glassy state and their long-time dynamics are strongly correlated with the temperature dependence of the storage modulus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Effects of tensile loading during annealing of alnico melt spun ribbons

Conventional magnetic annealing (MA) of the permanent magnet alloy alnico involves application of an external magnetic field at temperatures within the spinodal decomposition range. This field biases the growth of the Fe-Co rich, ferromagnetic α 1 -phase in an energetically favorable 〈001〉 direction in alignment with the applied field within an Al-Ni rich, paramagnetic α 2 -phase. Utilizing a magnetic field to bias the α 1 -phase may limit alnico from reaching theoretical coercivity due to (1) the field having maximum biasing ability at temperatures near the Curie temperature where large α 1 -phase nanorods form and (2) connectivity of the α 1 -phase occurs unavoidably during MA. Both decrease the effective shape anisotropy of the α 1 -phase, thereby reducing coercivity. Herein, we explore tensile-loading as a biasing mechanism to control and optimize the final alnico nanostructure beyond that achieved by MA. Two samples of melt-spun alnico were heat-treated at 860 °C for 5 minutes: one sample was subjected to 10 MPa tensile stress for comparison with a stress-free control sample. Structural and magnetic characterization revealed that the stress-annealed ribbon sample possessed expected phase assemblages, but was distinguished by a ∼2× larger grain diameter and an elongated anisotropic α 1 -phase within grains that were oriented to a shear stress along 〈001〉 directions at an angle of ∼45° relative to the loading direction. Both types of annealing produced a similar increase in the coercivity and remanence, but a decrease in saturation magnetization.

Rinko, E. A.↗

DOE OSTI2023

Molecular dynamics analysis of particle number fluctuations in the mixed phase of a first-order phase transition

Molecular dynamics simulations are performed for a finite nonrelativistic system of particles with Lennard-Jones potential. We study the effect of liquid-gas mixed phase on particle number fluctuations in coordinate subspace. A metastable region of the mixed phase, the so-called nucleation region, is analyzed in terms of a noninteracting cluster model. Large fluctuations due to spinodal decomposition are observed. They arise due to the interplay between the size of the acceptance region and that of the liquid phase. These effects are studied with a simple geometric model. The model results for the scaled variance of particle number distribution are compared with those obtained from the direct molecular dynamic simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Effect of transport mechanism on the coarsening of bicontinuous structures: A comparison between bulk and surface diffusion

Here, coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to t 1/4 for surface diffusion and t 1/3 for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Microstructural pattern formation during liquid metal dealloying: Phase-field simulations and theoretical analyses

In recent years, liquid metal dealloying has emerged as a promising material processing method to generate micro- and nanoscale bicontinuous or porous structures. Most previous studies focused on the experimental characterization of the dealloying process and on the properties of the dealloyed materials, leaving the theoretical study incomplete to fully understand the fundamental mechanisms of the liquid metal dealloying process. In this paper, we use theoretical models and phase-field simulations to clarify the kinetics and pattern formation during liquid metal dealloying. Our investigation starts from a theoretical analysis of the 1D dissolution of a binary precursor alloy, which reveals that the 1D dissolution process involves two regimes. In the first regime, due to the low solubility of one of the elements in the melt, it accumulates at the solid-liquid interface, which reduces the dissolution kinetics. In the second regime, the interface kinetics reaches a stationary regime where both elements of the precursor alloy dissolve into the melt. Previous works revealed that in the early dealloying stage, the dealloying front is destabilized by an interfacial spinodal decomposition, which triggers the formation of interconnected ligaments. Here we extend this line of work by proposing a linear stability analysis able to predict the initial length scale of the ligaments formed in the initial stage of the dealloying. Combining this analysis with the 1D dissolution model proposed here enables us to better understand the initial conditions (composition of the precursor alloy and the melt) leading to a planar dissolution without interface destabilization. Finally, we report a strong influence of solid-state diffusion on dealloying. Although the solid-state diffusivity is four to five orders of magnitude smaller than in the liquid phase, it is found to affect both dissolution kinetics and ligament morphologies.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Chemomechanics in alloy phase stability

We describe a first-principles statistical mechanics method to calculate the free energies of crystalline alloys that depend on temperature, composition, and strain. The approach relies on an extension of the alloy cluster expansion to include an explicit dependence on homogeneous strain in addition to site occupation variables that track the degree of chemical ordering. The method is applied to the Si-Ge binary alloy and is used to calculate free energies that describe phase stability under arbitrary epitaxial constraints. We find that while the incoherent phase diagram (in which coexisting phases are not affected by coherency constraints) hosts a miscibility gap, coherent phase equilibrium predicts ordering and negative enthalpies of mixing. Instead of chemical instability, the chemomechanical free energy exhibits instabilities along directions that couple the composition of the alloy with a volumetric strain order parameter. Furthermore, this has fundamental implications for phase field models of spinodal decomposition as it indicates the importance of gradient energy coefficients that couple gradients in composition with gradients in strain.

Materials Science↗

DOE OSTI2024

Heterostructural Alloy Phase Diagram for (Cd 1-x Zn x ) 3 As 2

Alloying the topological semimetal Cd 3 As 2 with Zn 3 As 2 provides a potential route for controlling the electronic properties. We predict the alloy phase diagram from first-principles calculations, considering that both end members have a crystal structure derived from the antifluorite lattice, but with different arrangements of the unoccupied cation sites. To overcome the limitations of the regular solution approximation and to include short-range order effects, we perform Monte Carlo simulations, parameterize the temperature dependence of the mixing enthalpy ΔH m , and perform thermodynamic integration of the free energy. The resulting phase diagram exhibits features that are unique to heterostructural alloy systems and provides computational predictions of solubility limits and composition ranges that are stable against spinodal decomposition.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Competing magnetic phases in Cr 3+𝛿 ⁢Te 4 are spatially segregated

Cr 1+𝑥⁢ Te 2 is a self-intercalated van der Waals system that is of current interest for its room-temperature room-temperature ferromagnetic (FM) phases and tunable topological properties. In bulk samples, the strain from the interstitial Cr ions leads to distinct structural phases for different ranges of 𝑥. Early neutron powder diffraction (NPD) measurements on the monoclinic phase Cr 3 ⁢Te 4 (𝑥=0.5) presented evidence for competing FM and antiferromagnetic (AFM) phases. Here we apply neutron diffraction to a single crystal of Cr 3+𝛿 ⁢Te 4 with 𝛿=−0.10 and discover that it consists of two distinct monoclinic phases, one with FM order below 𝑇 C ≈321 K and another that develops AFM order below 𝑇 N ≈86 K. In contrast, we find that a crystal with 𝛿=−0.26 exhibits only FM order below 𝑇 C ≈285 K. The single-crystal analysis is complemented by results obtained with NPD, x-ray powder diffraction, and transmission electron microscopy (TEM) measurements on the 𝛿=−0.10 composition. From observations of spontaneous magnetostriction of opposite sign at 𝑇 C and 𝑇 N , along with the TEM evidence for both monoclinic phases in a single thin ( ≈100 nm) grain, we conclude that the two phases must have a fine-grained ( ≲100 nm) intergrowth character, as might occur from high-temperature spinodal decomposition during the growth process. Calculations of the relaxed lattice structures for the FM and AFM phases with density functional theory provide a rationalization of the observed spontaneous magnetostrictions. Correlations between the magnitude and orientation of the magnetic moments with lattice parameter variation demonstrate that the magnetic orders are sensitive to strain, thus explaining why magnetic ordering temperatures and anisotropies can be different between bulk and thin-film samples, when the latter are subject to epitaxial strain. Our results point to the need to investigate the supposed coexistence FM and AFM phases reported elsewhere in the Cr 1+𝑥 ⁢Te 2 system, such as in the Cr 5 ⁢Te 8 phase (𝑥=0.25).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1984

Separation processes during binary monotectic alloy production

Observation of microgravity solidification processes indicates that outside of sedimentation, at least two other important effects can separate the phases: critical-point wetting and spreading; and thermal migration of second-phase droplets due to interfacial tension gradients. It is difficult to study these surface tension effects while in a unit gravity field. In order to investigate the processes occurring over a temperature range, i.e., between a consolute point and the monotectic temperature, it is necessary to use a low-gravity environment. The MSFC drop tube (and tower), the ballistic trajectory KC-135 airplane, and the Space Shuttle are ideal facilities to aid formation and testing of hypotheses. Much of the early work in this area focuses on transparent materials so that process dynamics may be studied by optical techniques such as photography for viewing macro-processes; holography for studying diffusional growth; spinodal decomposition and coalescence; ellipsometry for surface wetting and spreading effects; and interferometry and spectroscopy for small-scale spatial resolution of concentration profiles.

Frazier, D. O.↗

NASA NTRS1984

Phase stability of weakly crosslinked interpenerating polymer networks

A phenomenological theory is formulated for chemically quenched binary interpenetrating polymer networks (IPNs), considering both simultaneously crosslinked networks and sequentially crosslinked networks, as well as pseudointerpenetrating networks (where only one component is crosslinked and the other is a linear polymer). The construction of free energy functionals for homogeneous weakly crosslinked IPNs and pseudo-IPNs and their spinodal curves and critical points of unmixing is described. These free energy functionals are augmented with gradient energy terms in order to consider effects due to spatially varying small inhomogeneities in the network chain concentration. The dynamic response and the initial spinodal decomposition of IPNs are discussed.

Binder, K.↗

NASA NTRS1987

Growth process of gamma'-particles in a liquid-quenched Ni-15 at percent Al alloy

The growth of gamma-prime particles in a supersaturated Ni-15 at% Al alloy prepared by the liquid-quench method was studied using a magnetic mass balance, transmission electron microscopy, and field ion microscopy. Three stages in the precipitation and growth of these particles are demonstrated. In the first phase, the gamma-prime phase was produced by nucleation of spinodal decomposition of the alloy. In the second stage, spherical gamma-prime particles were arranged at random in the matrix with the size independent of aging time. Then, the Al concentration in the matrix decreased with the -1/3 power of the aging time. These results suggest that the degree of ordering increases with aging time. In the third stage, the particles were coarsened with aging time. They were arranged in the matrix (100) zone and were cubic, with the cube face lying on (100). The interfacial free energy was 28.4 mJ/sq m at 873 K and 22.4 mJ/sq m at 973 K.

Tachikake, A.↗

NASA NTRS1989

Determination of the Fe-Ni phase diagram below 400 C

Analytical EM techniques have been used to obtain a phase diagram for the Fe-Ni system below 400 C in the composition range from 0-52 wt pct Ni. The present diagram is consistent with all the phases observed in the Fe-Ni regions of meteorites. An asymmetric spinodal decomposition results in the expected two-phase isotropic microstructure. The present experimentally-determined miscibility gap below 400 C, located between 11.7 and 51.9 wt pct Ni at 200 C, is shown to be wider than the calculated miscibility gap.

Reuter, K. B.↗

NASA NTRS1988

The critical complex in nucleation is not the nucleus

A theory of nucleation is presented which combines features of classical nucleation. In this theory, the nucleus is a cluster of finite size with a sharp interface and spinodal decomposition, in which a fluctuation in density or composition generates the critical complex and nucleus. Thus, the nucleus is a product of nucleation. Schematic models for the classical and the proposed routes to nucleation are compared, focusing on the relation between pressure and volume in the models. In the proposed model, the critical complex, or critical state, is between the parent state and the nucleus.

Rasmussen, Don H.↗

NASA NTRS1992

Dynamics of phase separation of binary fluids

The results of molecular-dynamics studies of surface-tension-dominated spinodal decomposition of initially well-mixed binary fluids in the absence and presence of gravity are presented. The growth exponent for the domain size and the decay exponent of the potential energy of interaction between the two species with time are found to be 0.6 +/- 0.1, inconsistent with scaling arguments based on dimensional analysis.

Ma, Wen-Jong↗

NASA NTRS1992

FNAS modify matric and transparent experiments

Monotectic alloy materials are created by rapid melt/rapid solidification processing on the NASA KC-135. Separation of the uniform liquid into two liquids may occur by either of two processes; spinodal decomposition or nucleation followed by growth. In the first case, the liquid is unstable to composition waves, which form and grow, giving liquids of two different compositions. In the latter process discrete particles of the second liquid phase form via thermal fluctuations and then grow by diffusion. The two processes are very different, with the determining process being dictated by temperature, composition, and thermodynamic characteristics of the alloy. The first two quantities are process variables, while the third is determined by electronic interactions between the atoms in the alloy. In either case the initial alloy decomposition is followed by coarsening, resulting in growth of the particle size at nearly constant volume fraction. In particular, reduced gravity experiments on monotectic solutions have shown a number of interesting results in the KC-135. Monotectic solutions exhibit a miscibility gap in the liquid state, and consequently, gravity driven forces can dominate the solidification parameters at 1 g. In reduced gravity however, the distribution of the phases is different, resulting in new and interesting microstructures. The Rapid Melt/Rapid Quench Furnace allows one to melt a sample and resolidify it in one parabola of the KC-135's flight path, thus eliminating any accumulative influence of multiple parabolas to affect the microstructure of the material.

Smith, Guy A.↗

NASA NTRS1993

Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition).

Izmailov, Alexander F.↗