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At least 523 records · Page 29

Developing solid-surface plasma facing components for pilot plants and reactors with replenishable wall claddings and continuous surface conditioning. Part A: concepts and questions

Abstract It is estimated that pilot plants and reactors may experience rates of net erosion and deposition of solid plasma facing component (PFC) material of 10 3 –10 5 kg yr −1 . Even if the net erosion (wear) problem can be solved, the redeposition of so much material has the potential for major interference with operation, including disruptions due to so-called ‘unidentified flying objects (UFOs)’ and unsafe dust levels. The potential implications appear to be no less serious than for plasma contact with the divertor target: a dust explosion or a major UFO-disruption could be as damaging for an actively-cooled deuterium-tritium (DT) tokamak as target failure. It will therefore be necessary to manage material deposits to prevent their fouling operation. This situation appears to require a fundamental paradigm shift with regard to meeting the challenge of taming the plasma–material interface: it appears that any acceptable solid PFC material will in effect be flow-through , like liquid–metal PFCs, although at far lower mass flow rates. Solid PFC material will have to be treated as a consumable , like brake pads in cars. ITER will use high-Z (tungsten) armor on the divertor targets and low-Z (beryllium) on the main walls. The ARIES-AT reactor design calls for a similar arrangement, but with SiC cladding on the main walls. Non-metallic low-Z refractory materials such as ceramics (graphite, SiC, etc) used as in situ replenishable, relatively thin—of order mm—claddings on a substrate which is resistant to neutron damage could provide a potential solution for the main walls, while reducing the risk of degrading the confined plasma. Separately, wall conditioning has proven essential for achieving high performance. For DT devices, however, standard methods appear to be unworkable, but recently powder droppers injecting low-Z material ∼continuously into discharges have been quite effective and may be usable in DT devices as well. The resulting massive generation of low-Z debris, however, has the same potential to seriously disrupt operation as noted above. Powder droppers provide a unique opportunity to carry out controlled studies on the management of low-Z slag in all current tokamaks, independent of whether their protection tiles use low-Z or high-Z material.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multifidelity validation of digital surrogates using variable-density turbulent mixing models

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged NavierStokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, here the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Rayleigh-Taylor Instability: A Status Review of Experimental Designs and Measurement Diagnostics

The focus of experiments and the sophistication of diagnostics employed in Rayleigh-Taylor instability (RTI) induced mixing studies have evolved considerably over the past seven decades. The first theoretical analysis by Taylor and the two-dimensional experimental results by Lewis on RTI in 1950 examined single-mode RTI using conventional imaging techniques. Over the next 70 years, several experimental designs have been used to creating an RTI unstable interface between two materials of different densities. These early experiments though innovative, were arduous to diagnose and provided little information on the internal, turbulent structure and initial conditions of the RT mixing layer. Coupled with the availability of high-fidelity diagnostics, the experiments designed and developed in the last three decades allow detailed measurements of various turbulence statistics that have allowed broadly to validate and verify late-time nonlinear models and mix-models for buoyancy-driven flows. Besides, they have provided valuable insights to solve several long-standing disagreements in the field. Herein, this review serves as an opportunity to discuss the understanding of the RTI problem and highlight valuable insights gained into the RTI driven mixing process with a focus on low to high Atwood number (> 0.1) experiments.

42 ENGINEERING↗

Enhancing Oxygen Stability in Low-Cobalt Layered Oxide Cathode Materials by Three-Dimensional Targeted Doping

In this project, we propose to develop a new concept and a generic platform that can lead to the greatly enhanced stabilization of all high-energy cathode materials, and in particular high-nickel (Ni) and low-cobalt (Co) oxides. The new concept is a 3D doping technology that hierarchically combines surface and bulk doping. We will use surface doping to stabilize the surface of primary particles and also introduce dopants in the bulk to further enhance oxygen stability, conductivity, and structural stability in low-Co oxides under high voltage and deep discharging operating conditions. This new concept not only will deliver a low-cost, high-energy cathode but also will provide a generic method that can stabilize all high-energy cathodes. The proposed novel 3D doping approach is poised to resolve some longstanding challenges in fundamental doping effects on battery materials as well as to reduce Li-ion batteries’ cost and improve their safety, energy density, and lifetime. To tackle this problem, we have formed a highly complementary multi-university/national labs/industry team to enable a doping-central and systematic investigation of low-Co materials and create a knowledge base for many electrode materials to be used in advanced electric vehicles. The successful execution of the proposed project relies on five components that can be carried out by the complementary team members: (1) a theoretical investigation of the surface and bulk stabilizing dopants (Persson), (2) a precise synthesis of materials with targeted doping (Lin and Xin), (3) development of electrolytes for high-Ni low-Co oxides (Xu), (4) multi-scale characterization of the structures and their interfaces by scanning transmission electron microscopy (SEM) and synchrotron X-ray imaging and spectroscopy tools (Xin and Lin), and (5) pouch cell-level integration (Fan). The UCI-led project will enable a doping-central and systematic investigation of low-Co materials and create a knowledge base for many electrode materials to be used in advanced electric vehicles.

25 ENERGY STORAGE↗

Cryogenic Control Circuitry for Superconducting Qubits

Superconducting qubits have reached the point where system designers are worried about the heat that control wiring brings into the cryostat. To continue scaling cryogenic quantum systems, control solutions that work inside the cold space must be explored. One possibility is to use control electronics that is native to superconductivity, so called single-flux-quantum (SFQ) circuitry, to form an interface between qubits and whatever other electronics is needed to control eventual quantum systems. To begin exploring the utility of SFQ as control circuitry, we performed modeling and experiments on qubit readout using ballistic fluxons which are SFQ in the limit of ballistic fluxon transport. Our modeling results show that a flavor of qubit, the fluxonium, can be read out using ballistic fluxons. We designed test samples to prove some of the key concepts needed for such a readout but were ultimately unable to getting a working demonstration. The lack of testing success was due to challenges in fabrication and running short of time to perform testing rather than a fundamental problem with our analysis.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Melting of spatially modulated phases at domain wall/surface junctions in antiferrodistortive multiferroics

A physical understanding of the nature of spatially modulated phases (SMPs) in rare-earth-doped antiferrodistortive (AFD) multiferroics and how they behave close to surfaces and interfaces is lacking. Here the emergence of the antiferroelectric (AFE), ferroelectric (FE), or ferrielectric (AFE-FE) spatial modulation in the vicinity of the morphotropic phase transition in La x Bi 1 – x Fe O 3 ( x ~ 0.2 ) is explored on the atomic level using high-resolution scanning transmission electron microscopy (HRSTEM). The suppression, or “melting,” of the AFE-type SMP in the vicinity of the AFD twin wall/surface junction is revealed by HRSTEM in La 0.22 Bi 0.78 Fe O 3 films and explained by the hybrid approach combining Landau-Ginzburg-Devonshire (LGD) phenomenology and the semimicroscopic four-sublattice model (FSM). The LGD-FSM approach reduces the problem of AFE (or AFE-FE) SMP emergence and stability to the thermodynamic analysis of the free-energy functional with AFE, FE, and AFD long-range order parameters and two master parameters: the FE-AFE coupling strength between four neighboring A sites and the nonstoichiometry factor, which are proportional to the variations of La concentration in La x Bi 1 – x Fe O 3 films. Finally, we establish that the surface-induced melting of SMPs and the associated broadening of AFE AFD domain walls minimize the film free energy under certain conditions imposed on the master parameters and gradient energy below the critical value. The observed behavior provides insight into the origin of SMPs in AFD multiferroics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electrochemical-mechanical coupling failure mechanism of composite cathode in all-solid-state batteries

Composite cathode composed of active particles and solid electrolytes (SEs) can considerably enlarge the particle-SE contact areas and achieve high areal loadings in all-solid-state batteries (ASSBs). However, the challenging interfacial instability and particle damage problems remain unsolved. Herein, we establish a 3D electrochemical-mechanical coupled model to investigate the underlying failure mechanism by considering the governing electrochemical and physics processes. Micro-scale heterogeneous primary particles with random crystallographic orientation and size inside the LiNi 1/3 Co 1/3 Mn 1/3 O 2 (NCM111) secondary particle of the model result in the anisotropic Li diffusion and volume variation within the secondary particle, leading to significant nonuniformity of the Li concentration, and GPa-level stress distributions at primary particle boundaries, and finally causing the particle internal cracks. The particle volume shrinkage under the constraint of stiff Li 7 La 3 Zr 2 O 12 (LLZO) SE triggers the interface debonding (gap>50 nm) with increased interfacial impedance to degrade cell capacity. Higher C-rates result in larger residual stress (~100 MPa)/strain/debonding gap at dis-charging end, more likely to deteriorate the cell performance. Increasing the interfacial strength between the particle and SE can suppress the interface debonding but induces high stress (up to 10 GPa). In conclusion, results reveal the underlying mechanism of the electrochemical-mechanical coupling failure mechanism for composite cathode and provide promising guidance on the further improvement of a more robust composite cathode for ASSBs.

25 ENERGY STORAGE↗

Composite Solid Ion Conductor with Engineered Lithium Interface

Successful widespread commercialization of electric vehicles is contingent upon development of safe high energy density batteries capable of long cycle life. Lithium metal affords the highest theoretical capacity (3,860 mAh/g) and lowest electrochemical potential (-3.04V vs SHE), which offers the highest specific energy density of anode materials today. While Li-ion batteries are capable of delivering energy densities of 400-600 Wh/kg, the development of lithium metal batteries such as Li-S and Li-air may boost this number up to 650 and 950 Wh/kg, respectively. However, significant progress towards the passivation of lithium metal must occur before the energy density benefit can be realized. Issues with lithium dendrite formation, anode volume expansion, and continuous solid electrolyte interphase (SEI) build-up often result in significant safety concerns, high cell resistance, and poor cycle life. The intrinsic high reactivity between lithium metal with conventional lithium ion electrolytes (organic carbonate-based solvents) makes it extremely difficult to overcome these problems. In this project, Wildcat performed focused, fundamental research and development on composite polymer/ceramic electrolytes and protected lithium metal anodes to develop an all solid state lithium metal battery targeting the DOE requirements to enable commercialization. Wildcat successfully leveraged its high throughput battery platform and explored a broad composite electrolyte compositional space. Additionally, Wildcat screened large numbers of inorganic and organic coatings for lithium metal protection using in situ liquid methods and translated the best results to all solid cells. The proposed composite polymer/ceramic electrolyte and a protected lithium metal anode enabled a solid-state lithium metal battery. The ultimate targets from this effort will deliver a safe all solid-state lithium metal pouch cell with over 350 Wh/kg and over 1,000 cycles (C/3) with the cost estimate below $100/kWh. During the course of the project, we demonstrated stable cycling of 10’s of cycles with the composite SSE and our protected lithium. The work has continued after the conclusion of the DOE funding, demonstrating further improvements in catholyte composition and thinner composite solid electrolytes.

25 ENERGY STORAGE↗

Corrosion behavior of Monofrax K-3 refractory in borosilicate-based model low activity waste glass melts

Owing to its good chemical and thermal durabilities at high temperatures, Monofrax K-3 refractory is widely used in nuclear waste vitrification as a lining material in melting vessels. However, the corrosion of K-3 refractory during the vitrification of nuclear waste is a serious problem because it affects the melter's safety, performance, and lifetime. Therefore, in the present study, we have focused on unearthing the impact of glass network formers, such as SiO 2 , B 2 O 3 , and Al 2 O 3 , in a model nuclear waste glass composition on the corrosion of Monofrax K-3 refractory. The corrosion tests have been performed per ASTM C621 at 1150°C for 5 days. The dimensional measurements on corroded K-3 refractory suggest that Al 2 O 3 and SiO 2 tend to reduce the refractory corrosion (neck loss), with the effect of Al 2 O 3 being significant. A corroded region on the K-3 refractory at the melt–refractory interface is observed. The corrosion occurs via a coupling of the melt infiltration induced by a capillary effect and the dissolution of Al, Mg, and Fe components from K-3 into the melt through chemical reactions. A Cr-rich layer is retained on the glass contact surface of the corroded K-3 refractory.

36 MATERIALS SCIENCE↗

Juqbox.jl

The Juqbox.jl package implements functionality for solving the quantum optimal control problem for realizing logical gates in closed quantum systems. The dynamics of the quantum system is modeled by Schroedinger's equation, which takes to form of a linear system of ordinary differential equations (ODE). Juqbox.jl solves this ODE by numerical time stepping and applies a gradient-based optimization technique to determine control pulses for driving an initial state to a final state, according to the desired logical gate transformation. To evaluate the gradient, Juqbox.jl applies the ``first discretize, then optimize'' approach based on a discrete adjoint time stepping technique. The actual optimization is performed by the open source Ipopt libaray. Juqbox.jl is written in the Julia programming language which, among many other features, provides a convenient interface to the Ipopt library.

PETERSSON, NILSA.↗

Transition Zone Morphology Dynamics of Dissolved Oxygen (DO) in a Salinity-Impacted Hyporheic Zone

Freshwater salinization is a common yet underappreciated environmental problem in rivers, yet how this process impacts the transport of dissolved oxygen (DO) in the hyporheic zone remains unknown. Here, using flume experiments and numerical simulations, we have demonstrated that the morphological dynamics of the DO transition zone are controlled by the dimensionless number Da·Ra –2 , a measure of the rate of aerobic respiration to free convection. At low Da·Ra –2 , the oxic front breaks up into fingers which subsequently grow, and leads to accelerating of DO transport and shrinking of the anaerobic zone in the underlying sediment. As Da·Ra –2 increases, the growth rate of the instability decreases, and the DO plume fingers are suppressed and delayed compared with the saltwater-freshwater interface, the mixing area between saltwater and freshwater. These results indicate that the freshwater salinization syndrome can have significant impacts on the functioning of aquifer ecosystems unless regulated and managed effectively.

54 ENVIRONMENTAL SCIENCES↗

Solidification and grain formation in alloys: a 2D application of the grand-potential-based phase-field approach

Solidification is a significant step in the forming of crystalline structures during various manufacturing and material processing techniques. Solidification characteristics and the microstructures formed during the process dictate the properties and performance of the materials. Hence, understanding how the process conditions relate to various microstructure formations is paramount. In this work, a grand-potential-based multi-phase, multi-component, multi-order-parameter phase-field model is used to demonstrate the solidification of alloys in 2D. This model has several key advantages over other multi-phase models such as it decouples the bulk energy from the interfacial energy, removes the constraints for the phase concentration variable, and prevents spurious third-phase formation at the two phase interfaces. Here, the model is implemented in a finite-element-based phase-field modeling code. The role of various modeling parameters in governing the solidification rate and the shape of the solidified structure is evaluated. It is demonstrated that the process conditions such as temperature gradient, thermal diffusion, cooling rate, etc, influence the solidification characteristics by altering the level of undercooling. Furthermore, the capability of the model to capture directional solidification and polycrystalline structure formation exhibiting various grain shapes is illustrated. In both these cases, the process conditions have been related to the growth rate and associated shape of the dendritic structure. As a result, this work serves as a stepping stone towards resolving the larger problem of understanding the process–structure–property–performance correlation in solidified materials.

36 MATERIALS SCIENCE↗

Scheduling and Performance of Asynchronous Tasks in Fortran 2018 with FEATS

Most parallel scientific programs contain compiler directives (pragmas) such as those from OpenMP (Hermanns in Parallel programming in Fortran 95 using openMP, 2002. School of Aeronautical Engineering, Universidad Politécnica de Madrid, España, 2011), explicit calls to runtime library procedures such as those implementing the Message Passing Interface (MPI) (in A message-passing interface standard version 4.0, 2021. https://www.mpi-forum.org/docs/mpi-4.0/mpi40-report.pdf), or compiler-specific language extensions such as those provided by CUDA (Ruetsch and Fatica in CUDA Fortran for scientists and engineers: best practices for efficient CUDA Fortran programming, Elsevier, 2013). By contrast, the recent Fortran standards empower developers to express parallel algorithms without directly referencing lower-level parallel programming models (Numrich in Parallel programming with co-arrays, CRC Press, 2018, and Curcic in Modern Fortran: building efficient parallel applications, Manning Publications, 2020). Fortran’s parallel features place the language within the Partitioned Global Address Space (PGAS) class of programming models. When writing programs that exploit data parallelism, application developers often find it straightforward to develop custom parallel algorithms. Problems involving complex, heterogeneous, staged calculations, however, pose much greater challenges. Such applications require careful coordination of tasks in a manner that respects dependencies prescribed by a directed acyclic graph. When rolling one’s own solution proves difficult, extending a customizable framework becomes attractive. Further, the paper presents the design, implementation, and use of the Framework for Extensible Asynchronous Task Scheduling (FEATS), which we believe to be the first task scheduling tool written in modern Fortran. We describe the benefits and compromises associated with choosing Fortran as the implementation language, and we propose ways in which future Fortran standards can best support the use case in this paper.

97 MATHEMATICS AND COMPUTING↗

A comparative analysis of numerical approaches for the description of gas flow in clay-based repository systems: From a laboratory to a large-scale gas injection test

There is nowadays a consensus among many countries that geological disposal is a favourable solution for the long-term management. Although different host formations and different barrier systems are under consideration around the world, clay-based materials form an important component for waste isolation in most national programmes. Hence, a good comprehension of the effect of gas flow on the hydro-mechanical behaviour of clay-based soils is essential, both at laboratory and field scale. Task B under the international cooperative project DECOVALEX-2023 has recently shown that, after some enhancement, models can be employed to reproduce laboratory scale tests, even with different sample geometries 37 . However, further work is required to understand whether they can be applied to simulate a large-scale experiment. Up-scaling of models for the advective transport of gas through clay-based low permeable material presents a number of problems related to the difficulty in obtaining consistent hydrogeological parameters and constitutive relationships at both laboratory and field scale. Based on a unique dataset from a large-scale gas injection test (Lasgit) performed at the Äspö Hard Rock Laboratory (Sweden), Task B within DECOVALEX-2023 has explored the refinement of these numerical strategies applied to the simulation of gas flow. Work performed within the task reveals that codes do not need to be substantially modified from the laboratory models to reproduce full-scale tests: indeed, model parameters calibrated and validated at laboratory scale have been applied to predict field scale gas flow at Lasgit, including peak gas pressure and injected cumulative gas volume. By means of (1) the introduction of interfaces between blocks to reflect the experimental configuration and the (2) adjustment of some parameters (e.g., higher permeability), the updated models are able to represent most of the key features observed in the experimental data, even at a large scale.

Tamayo-Mas, E↗

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗

User Manual for the Thermal Hydraulic Code SE2RCT

SE2-ANL is a modified version of SUPERENERGY-2 which interfaces the power distribution in the ANL maintained physics codes for the user. SE2RCT is a special version of SE2-ANL developed for specific use on models of the Experimental Breeder Reactor-II (EBR-II). SE2RCT fulfills a specific role in the calculated results as part of the Fuels Irradiation and Physics Database (FIPD) and is built to connect with the Physics and Analysis DataBase (PADB) for metallic fuel research and development in advanced sodium-cooled fast reactors (SFRs) created for EBR-II. SE2RCT is primarily a thermal analysis code that interfaces with the RCT based pin power details instead of the built-in pin power dehomogenization strategy in SE2-ANL. Beyond the thermal hydraulic calculation, the SE2RCT code provides detailed axial distributions of the RCT calculated results. SE2RCT also calculates the the axial distribution of pin wise DPA for the cladding materials which is part of the FIPD calculated results. This report serves as the user manual for SE2RCT and thus eliminates the QA gap of missing documentation on the SE2RCT software. All of the features and limitations of SE2RCT are documented in this report. The input and output specifications of SE2RCT are discussed in detail, and some unique features of SE2RCT, e.g. accurate pin power and temperature results for problems with non-uniform composition within an assembly, are also demonstrated and tested.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

MOOSE Optimization Module Overview: Application to Residual Stress Inversion in Nuclear Fuel Plates

Manufacturing methods, material selections and unique plate geometries used in low enriched uranium plate fuels for the High Performance Research Reactor (HPRR) have led to concerns about the residual stresses effect on bond strength of the fuel/cladding interfaces and overall fuel performance under irradiation. The current HPRR plate fuel test program performed residual stress calculations using the contour method with experimental displacement data obtained by incrementally cutting the plate fuel. In this work, we use a gradient based inverse optimization module developed within the MOOSE framework to estimate normal and shear residual stresses within the plate fuels using displacement data taken from a cut placed in the HPRR fuel plate. These results are verified against residual stress calculations obtained from the contour method. The inversion protocol used in this work utilizes two meshes to separately discretize the physics and parameter space. This allows a fine mesh to be used to fully resolve the physics and geometry of the forward problem. A coarser mesh is used to resolve the parameter space with spatially varying mesh density determined from a sensitivity analysis. The adaptive resolution of the parameter space essentially has the effect of regularization as it is designed to achieve the bias-variance tradeoff.

42 ENGINEERING↗

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↗