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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Ambient-pressure 151-K superconductivity in HgBa 2 Ca 2 Cu 3 O 8+δ via pressure quench

Superconductivity has been a vigorously researched topic since its discovery in 1911. Raising the superconducting transition temperature (T c ) has been the main driving force behind such long-sustained efforts due to its potential for impacting humanity and the fundamental knowledge gained from understanding this macroscopic coherent quantum state at high temperatures. The successful development of high-T c superconductivity will make possible extraordinarily efficient generation, delivery, and utilization of energy and could also enable the development of controlled fusion while impacting other burgeoning fields like quantum computation and quantum electronics. However, progress has been hindered by a longstanding plateau in the record ambient-pressure T c , unchanged since 1993. Subsequent significant advancements in T c have been achieved only under high pressures, preventing the realization of superconductivity’s full potential. To directly address this challenge, we developed a pressure-quench protocol (PQP) to stabilize pressure-induced/-enhanced superconducting states at ambient pressure. Here, we achieve a record ambient-pressure T c of 151 K in the cuprate HgBa 2 Ca 2 Cu 3 O 8+δ via PQP. The experimental results are further supported by synchrotron X-ray diffraction measurements and phonon and electronic structure calculations. This breakthrough opens avenues for stabilizing and exploring ambient-pressure high-T c superconducting states and other quantum states that have been previously only accessible under pressure, paving the way for deeper understanding and practical applications of high-T c superconductivity and beyond.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Electrochemical Switching of a Fluorescent Molecular Rotor Embedded within a Bistable Rotaxane

We report how the nanoconfined environment, introduced by the mechanical bonds within an electrochemically switchable bistable [2]rotaxane, controls the rotation of a fluorescent molecular rotor, namely, an 8-phenyl-substituted boron dipyrromethene (BODIPY). The electrochemical switching of the bistable [2]rotaxane induces changes in the ground-state coconformation and in the corresponding excited-state properties of the BODIPY rotor. In the starting redox state, when no external potential is applied, the cyclobis(paraquat-p-phenylene) (CBPQT4+) ring component encircles the tetrathiafulvalene (TTF) unit on the dumbbell component, leaving the BODIPY rotor unhindered and exhibiting low fluorescence. Upon oxidation of the TTF unit to a TTF2+ dication, the CBPQT4+ ring is forced toward the molecular rotor, leading to an increased energy barrier for the excited state to rotate the rotor into the state with a high nonradiative rate constant, resulting in an overall 3.4-fold fluorescence enhancement. On the other hand, when the solvent polarity is high enough to stabilize the excited charge-transfer state between the BODIPY rotor and the CBPQT4+ ring, movement of the ring toward the BODIPY rotor produces an unexpectedly strong fluorescence signal decrease as the result of photoinduced electron transfer from the BODIPY rotor to the CBPQT4+ ring. The nanoconfinement effect introduced by mechanical bonding can effectively lead to modulation of the physicochemical properties as observed in this bistable [2]rotaxane. On account of the straightforward synthetic strategy and the facile modulation of switchable electrochromic behavior, our approach could pave the way for the development of new stimuli-responsive materials based on mechanically interlocked molecules for future electro-optical applications, such as sensors, molecular memories, and molecular logic gates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Dual-loop Solvent-based CCS for Net Negative CO 2 Emissions with Lower Cost

This final technical report details the successful design, construction, and operational validation of an innovative dual-loop CO 2 capture technology designed to achieve deep decarbonization (>99%) from Natural Gas Combined Cycle (NGCC) power plants that results in the electricity with carbon intensity of approximate 42 kg CO 2 -eq/MWh, less than the electricity produced by solar PV. The integrated process couples a primary aqueous solvent (in this project, a water lean solvent – WLS) absorption loop for bulk CO 2 removal with a secondary potassium hydroxide (KOH) polishing loop featuring electrochemical regeneration. This architecture leverages the higher exergy efficiency of the primary loop while utilizing the fastest kinetic of the secondary loop to capture dilute residual CO 2 , achieving an overall capture rate of 99.9% and co-producing pure hydrogen after moisture being condensed and dehydrated. Technical feasibility was established through a comprehensive 2,000-hour experimental campaign on a bench-scale fully-integrated unit (using 4” absorber and 4” stripper) with the feeding flue gas flowrate in the range of 8-20 cfm, confirming the attainment of Technology Readiness Level (TRL) 4. The project executed extensive parametric testing followed by 1,000 hours of continuous steady-state testing, demonstrating exceptional process stability with the electrochemical regenerator exhibiting less than a 10% reduction in electrical conductivity over the duration of the campaign. Operational characterization gathering on the bench unit revealed distinct energy profiles for the hybrid system: the primary loop required approximately 280 kJ mol -1 for bulk removal, while the polishing loop required approximately 1,600 kJ mol -1 specifically when reducing dilute CO 2 concentrations from ~740 ppm down to <50 ppm. (Please note those energy values/numbers can only be viewed as relative relationship and should not be extrapolated as absolute values required for CO 2 capture). Furthermore, dynamic testing validated the system’s flexibility for utility applications, demonstrating a rapid process response time of <30 minutes to changes in flue gas flowrate. Emission monitoring confirmed that the dual-loop architecture effectively mitigates solvent losses, utilizing a water wash to remove entrained aerosols to <1 ppm. The Techno-Economic Analysis (TEA) indicates a cost of capture of $\$$59.3/tonne and a Levelized Cost of Electricity (LCOE) of 71.7 $\$$/MWh at the overall capture efficiency of 99.8% of total carbon in the flue gas stream, with sensitivity analysis identifying an economic optimum when the primary loop captures 97% of the total CO 2 . A Life Cycle Assessment (LCA) confirms the technology’s potential for net-negative emissions, determining a Global Warming Potential (GWP) of 52 kg CO 2 -eq/MWh—significantly lower than the baseline—which further decreases to 42 kg CO 2 -eq/MWh when crediting the displacement of conventional hydrogen production.

03 NATURAL GAS↗
DOE OSTI2021

Stromataxic Stabilization of a Metastable Layered ScFeO3 Polymorph

Metastable polymorphs--materials with the same stoichiometry as the ground state but a different crystal structure--enable many critical technologies. This work describes the development of a stabilization approach for metastable polymorphs that are difficult to achieve through other stabilization techniques (such as epitaxy or quenching) called stromataxy. Stromataxy is a method based on controlling the precursor structure during the initial stages of material growth to dictate phase formation. To illustrate this approach, we controlled the atomic layering of the precursors of ScFeO3 and stabilized the metastable P63cm phase, under conditions that previously led to the ground-state Ia3¯ bixbyite phase. Ab initio mechanistic calculations highlight the importance of the variable oxidation state of Fe and the layer stability during layer-by-layer growth. The broad applicability of a stromataxy approach was demonstrated by stabilizing this metastable phase on substrates that have previously been shown to stabilize other polymorphs under continuous growth. Stromataxy is shown as a viable option for accessing polymorphs that are close in energy, difficult to differentiate by strain, or that lack a well epitaxially matched substrate.

calculations↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

CFD Simulation of an Inward-Turning Supersonic Inlet Unstart at Flight Mach Number 1.7

Interest in inward-turning supersonic inlets renewed during NASA’s Commercial Supersonic Technology Project, as a means of reducing disturbances caused by propulsion integration. Inward-turning designs have the potential to greatly reduce the strength of shock waves emanating outward from the nacelle, and therefore their contribution to the overall sonic boom signature. For top-mounted, or over-wing installations, disturbances to aircraft aerodynamics are reduced. The nature of the inward-turning geometry results in a boundary-layer thickening effect, opposite that of the familiar thinning of an outward-turning cone boundary-layer. The application of a small amount of boundary-layer bleed at the throat has been shown to alleviate the negative effects of the boundary-layer on subsonic diffuser performance. Boundary-layer bleed, however, comes at the expense of increased complexity, and external disturbances at bleed exits that would partially defeat the purpose of the inward-turning scheme. Vortex generators were proposed as an alternative to bleed, and an initial CFD study of their effectiveness in this application forms the basis of the present work. A source-term model in the Wind-US CFD code was used to model the effects of an array of vortex generators placed at the entrance to the subsonic diffuser. Baseline results with no vortex generators compared favorably to previously reported results with no bleed at back-pressures near the design point, but stability margin in the present case was limited by a curious non-linear phenomena similar to unstart in mixed-compression inlets. While some improvement was noted with vortex generators, their effectiveness was diminished by the limited stability margin. A time-accurate calculation was subsequently performed to better understand this process. Results of this calculation are presented and instantaneous solutions compared with steady-state, subcritical results previously reported. The stability margin limitation is attributed to the use of a constant-pressure outflow boundary condition, which differed from that used in the prior simulations.

Pre-Compressor Cooling, Water Injection, Hypersoni↗
DOE OSTI2021

Computation-guided discovery of coating materials to stabilize the interface between lithium garnet solid electrolyte and high-energy cathodes for all-solid-state lithium batteries

All-solid-state batteries with a lithium metal anode, enabled by lithium garnet solid electrolytes such as Li 7 La 3 Zr 2 O 12 (LLZO), are a promising next-generation energy-storage technology. The further development of all-solid-state battery requires the integration of high-energy cathodes such as LiNi 1-x-y Mn x Co y O 2 (NMC) with the garnet solid electrolyte with stable and low-resistance interfaces, which requires a coating layer to stabilize the interface during high-temperature sintering and electrochemical cycling. In order to guide the future development of interfacial coatings, we perform high-throughput thermodynamic analyses based on first-principles computation to investigate the stability of LLZO garnet and high-energy NMC cathodes with a wide range of materials chemistries. Here our study reveals the factors governing the materials stability with LLZO garnet and NMC cathodes, and identifies the mechanisms of good coating layers stable with LLZO and NMC. In addition to classifying known coating layers, our study provides detailed guiding charts and multiple new materials systems as promising coatings for stabilizing LLZO—NMC interfaces to enable high-energy-density garnet-based all-solid-state batteries. Our demonstrated computation scheme and high-throughput analyses are generally applicable to investigate and screen coating materials for stabilizing interfaces in energy-related applications.

25 ENERGY STORAGE↗
DOE OSTI2023

Mott insulators in moiré transition metal dichalcogenides at fractional fillings: Slave-rotor mean-field theory

In this study, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moiré systems, that captures both the formation of Wigner crystals as well as exotic spin states on top of these charge backgrounds. Phase diagrams are mapped out for different choices of long-range Coulomb repulsion strength, reproducing several experimentally found Wigner crystal states. Assuming unbroken time-reversal symmetry, we find several spin-liquid states as well as dimer states at fractional fillings. While spin dimer states are always found to have the lowest mean-field energy, several spin-liquid states are energetically competitive and may be stabilized by including gauge fluctuations or further interaction terms. We further discuss possible experimental signatures of these states pertinent to two-dimensional moiré heterostructures.

Charge order↗
NASA NTRS1980

Nonlinear state estimation and feedback control of nonlinear and bilinear distributed parameter systems

This paper presents a theory of nonlinear state observers for nonlinear and bilinear distributed parameter systems. Convergence results are proved for these observers. Linear feedback control derived from such state observers is applied to the distributed parameter system and conditions are presented for closed-loop stability. The emphasis is on finite dimensional state observers and controllers (which can be implemented with on-line computers) and conditions for their successful operation with infinite dimensional distributed parameter systems.

Balas, M. J.↗
DOE OSTI2022

Phase Stability of Garnet Solid-Electrolyte Interfacing with Various Cathodes in All Solid-State Batteries

Garnet-structured Li 6.75 La 3 Zr 1.75 Ta 0.25 O 12 (LLZTO) is one of the most promising electrolyte materials for solid-state Li batteries (SS-LiB). The design and fabrication of a good cathode/electrolyte interface is an important criterion for the SS-LiB. In this work, we performed a systematic study on the impact of cathode crystal structure and chemical compositions on their chemical stabilities against the LLZTO at elevated temperatures, which are required for their adhesion during cell fabrication processes. X-ray Diffraction (XRD) and Rietveld refinement analyses revealed the chemical stabilities of various cathode materials in contact with the LLZTO. While layered LiCoO 2 cathode showed good stability in contact with LLZTO to 900 °C, LiNiO 2 or Ni-rich LiNi x Mn y Co 1–x–y O 2 (NMC) cathodes suffered from the formation of La 4 NiLiO 8 due to La-diffusion from LLZTO. Furthermore, Mn-rich LiMn 2 O 4 spinel and layered LiNi 1/3 Mn 1/3 Co 1/3 O 2 cathodes suffered from the formation of La 2 Zr 2 O 7 due to Li-diffusion and production of Li 2 MnO 3 . As a result, LiNi 0.6 Mn 0.2 Co 0.2 O 2 , having an ideal balance of Ni/Mn/Co composition, or Li 2 MnO 3 containing cathodes such as Li 1.2 Ni 0.15 Mn 0.55 Co 0.1 O 2 were found to have excellent phase stability as the cathodes for LLZTO-based SS-LiBs.

25 ENERGY STORAGE↗
DOE OSTI2020

A New Family of Proton‐Conducting Electrolytes for Reversible Solid Oxide Cells: BaHf x Ce 0.8− x Y 0.1 Yb 0.1 O 3− δ

Abstract Reversible solid oxide cells based on ceramic proton conductors have potential to be the most efficient system for large‐scale energy storage. The performance and long‐term durability of these systems, however, are often limited by the ionic conductivity or stability of the proton‐conducting electrolyte. Here new family of solid oxide electrolytes, BaHf x Ce 0.8− x Y 0.1 Yb 0.1 O 3− δ (BHCYYb), which demonstrate a superior ionic conductivity to stability trade‐off than the state‐of‐the‐art proton conductors, BaZr x Ce 0.8− x Y 0.1 Yb 0.1 O 3− δ (BZCYYb), at similar Zr/Hf concentrations, as confirmed by thermogravimetric analysis, Raman, and X‐ray diffraction analysis of samples over 500 h of testing are reported. The increase in performance is revealed through thermodynamic arguments and first‐principle calculations. In addition, lab scale full cells are fabricated, demonstrating high peak power densities of 1.1, 1.4, and 1.6 W cm −2 at 600, 650, and 700 °C, respectively. Round‐trip efficiencies for steam electrolysis at 1 A cm −2 are 78%, 72%, and 62% at 700, 650, and 600 °C, respectively. Finally, CO 2 H 2 O electrolysis is carried out for over 700 h with no degradation.

Murphy, Ryan↗
DOE OSTI2020

The Concept of Negative Capacitance in Ionically Conductive Van der Waals Ferroelectrics

Negative capacitance (NC) provides a path to overcome the Boltzmann limit that dictates operating voltages in transistors and, therefore, may open up a path to the challenging proposition of lowering energy consumption and waste heat in nanoelectronic integrated circuits. Typically, NC effects in ferroelectric materials are based on either stabilizing a zero-polarization state or slowing down ferroelectric switching in order to access NC regimes of the free-energy distribution. Here, a fundamentally different mechanism for NC, based on CuInP 2 S 6 , a van der Waals layered ferrielectric, is demonstrated. Using density functional theory and piezo-response force microscopy, it is shown that an unusual combination of high Cu-ion mobility and its crucial role in determining polarization magnitude and orientation (P) leads to a negative slope of the polarization versus the electric field E, dP/dE < 0, which is a requirement for NC. This mechanism for NC is likely to occur in a wide class of materials, offering new possibilities for NC-based devices. Finally, the nanoscale demonstration of this mechanism can be extended to the device-level by increasing the regions of homogeneous polarization and polarization switching, for example, through strain engineering and carefully selected electric field pulses.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Chemical Bond Covalency in Superionic Halide Solid‐State Electrolytes

Abstract Halide solid‐state electrolytes (SSEs) are promising superionic conductors with high oxidative stability and ionic conductivity, making them attractive for all‐solid‐state lithium‐ion batteries. However, most studies have focused on ion‐stacking structures, overlooking the role of bond characteristics in ionic transport. Here, we investigate bond dynamics and the superionic transition (SIT) in bromide electrolyte, Li 3 InBr 6 , using synchrotron X‐ray techniques and ab initio molecular dynamics (AIMD) simulations. We demonstrate that the SIT in halide SSEs is driven by a thermally induced transition in bonding character (ionic to covalent) rather than a change in crystal phase. AIMD simulations further reveal enhanced Li⁺ diffusion and collective anion motion at elevated temperatures. Expanding our study to Li 3 LnBr 6 (Ln = Gd, Tb, Ho, Tm, and Lu), we confirm the widespread occurrence of SIT in this material class, with Li 3 GdBr 6 exhibiting the highest ionic conductivity (5.2 mS cm −1 at 298 K). More importantly, the ionic‐covalent transition is highly tunable through electrolyte modifications, such as cation/anion substitution and synthesis methods. Our findings provide a new perspective on ionic transport, highlighting the critical role of chemical bond characteristics in halide SSEs.

Chemistry↗
DOE OSTI2026

Variations of Alloying Site Density in Pd 1 Cu Single‐Atom Alloy Catalysts Lead to Shifted Product Yields in Electrochemical CO Reduction

Single-atom alloy (SAA) catalysis research often reports that a SAA catalyst, in the general formulation of a single-atom metal M1 alloyed on the surface of the host metal M2, facilitates a probe reaction. However, for catalytic reactions that present decoupled rate- and selectivity-limiting steps, the alloying site density may significantly manipulate these independent steps, but it has rarely been explicitly examined for any SAA systems. Herein, using the electrocatalytic CO reduction as a probe reaction, we report that the nominal Pd 1 Cu cube SAA catalysts exhibit distinctive high reactivity toward ethylene or ethanol, respectively, depending on whether the Pd atoms are in dilute or crowded forms. Although the presence of single-atom Pd embedded on Cu uniformly promotes CHO* formation and C─C coupling, the dilute-Pd 1 Cu favors ethylene formation by enabling low-barrier C─O cleavage from a flat CH 2 CH 2 OH* intermediate, whereas the crowded-Pd 1 Cu promotes ethanol formation by stabilizing an upright hydrogenation transition state of the same intermediate. Furthermore, we present evidence that the catalytic chemistry of crowded Pd 1 species differs from that of the Pd 2 -dimer; the latter, albeit unstable, steers reaction selectivity to acetate instead. In conclusion, these results uncovered the underappreciated importance of controlling SAA catalytic chemistry from the perspective of single-atom site densities.

Jin, Zehua [Clemson University, SC (United States)↗
DOE OSTI2023

Solution synthesis of two-dimensional zinc oxide (ZnO)/molybdenum disulfide (MoS 2 ) heterostructure through reactive templating for enhanced visible-light degradation of rhodamine B

Numerous inorganic materials have been identified as potential candidates for high-performance photocatalysts. However, their solar-to-energy conversion efficiencies still fail to meet commercial requirements. Here, the main hurdle is the rapid recombination of photoexcited electrons and holes in single-phase materials. A viable predicted approach to suppress charge recombination is coupling two materials to form a two-dimensional (2D) heterostructure that physically separates photoinduced electrons and holes in different layers. In this work, the heterostructure-based paradigm was tested and a scalable solution synthesis of epitaxial ZnO-MoS 2 heterostructure was developed. A 2D ZnO-MoS 2 heterostructure was synthesized under hydrothermal conditions by stabilizing intermediate Zn-hydroxide states on a functionalized MoS 2 surface. Detailed characterization showed the formation of multilayer heterostructure with MoS 2 flakes intercalated between large size ZnO plates. The performance of this heterostructure was evaluated using photocatalytic degradation of rhodamine B. A degradation efficiency of 70% was measured within 90 minutes of visible-light irradiation, almost doubling the efficiency of the corresponding single-phase materials or their physical mixtures.

2D heterostructure↗
DOE OSTI2020

Towards understanding and predicting the hydronium ion catalyzed dehydration of cyclic-primary, secondary and tertiary alcohols

The varying steric environment of zeolites subtly influences the rates of hydronium-ion-catalyzed dehydration of alcohols containing a cyclohexyl group in aqueous phase. Here, the investigated primary, secondary, and tertiary alcohols show an increasing stabilization of an ionic transition state in this sequence, i.e., an increasing tendency to move from a concerted (E2 mechanism) to a stepwise dehydration (E1 mechanism). Hydronium ions confined in the micropores of MFI and BEA zeolites induced much higher catalyzed rates than those in the aqueous phase. Independent of the reaction mechanism and the environment, however, all alcohols investigated follow one compensation correlation between activation enthalpy and entropy for primary, secondary, and tertiary alcohols, respectively. For a given transition enthalpy, the rate of dehydration is the higher the larger the reaction space (translated to the reaction entropy). Surprisingly, all compensation relations intersect in one point. These dependences for the different alcohols are also reflected in the turnover rates, for which all alcohols also intersect in a common point, which appears to mark the highest reaction rate for dehydration catalyzed by hydronium ions at the investigated temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Synthesis, structure and canted antiferromagnetism of layered cobalt hydroxide sorbate

Layered hybrid organic–inorganic compounds of the transition metal hydroxides, in which part of the hydroxide ions are exchanged for organic ligands that act as spacers of the 2-dimensional inorganic layers, elicit new or enhanced properties. The interlayer ligands enable fine-tuning of the physicochemical properties of the metal hydroxide layers, including their magnetism. Specifically, within the Co(OH) 2 family of transition ion hydroxides, this approach has been leveraged to stabilize antiferromagnetic and ferrimagnetic ground states for pillared and layered complexes, respectively. Here, in this work, we further investigate the effects of changing dimensionality, local Co coordination, and interlayer spacing on the magnetic ground state of brucite-like β-Co(OH) layered complexes. We report the hydrothermal synthesis of a new crystalline material, Co(OH)(sorb), where the inorganic layers are spaced by monotopic, doubly unsaturated sorbate ligands (sorb = [C 6 H 7 O 2 ] – ). The material was structurally characterized using powder X-ray and neutron diffraction measurements and the crystal structure was solved ab initio from powder diffraction data and refined using the Rietveld method. The magnetic susceptibility and magnetization measurements reveal canted antiferromagnetic ordering with T N = 41.7 K. This report augments our understanding of tuning magnetism through dimensionality in layered complexes and represents a step forward in the design of new 2D layered hybrid compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Migration of inclusions in a matrix due to a spatially varying interface energy

An interfacial energy can be a function of a bulk field such as temperature or electric field. Here we find that in a system with a gradient in temperature or electric potential, the resulting variation in interfacial energy can induce a particle to migrate by either surface or bulk diffusion. For a circular particle under a constant unidirectional gradient in the bulk field, the field dependence of the interfacial energy induces a circular particle to move as a circle at a constant velocity along the direction from higher to lower interfacial energy. A linear stability analysis of this steady state migration suggests that perturbations will damp out as time evolves, and thus under these conditions a migrating circular particle is morphologically stable. Other spatial distributions of interface energy can lead to the distortion of an initially circular shaped particle during migration. A phase field model is developed that captures these distortions and verifies the theoretical results mentioned above.

36 MATERIALS SCIENCE↗