Phase Field Research Articles

Phase field modeling of sub-parabolic oxidation kinetics and in-plane stress in Zircaloy under neutron/proton irradiation

Abstract A detailed study of the sub-parabolic oxidation kinetics in Zircaloy system has been carried out by using phase field modeling under conditions related to oxidation in autoclave and during neutron/proton irradiation. The exploited phase field model is factored in temperature gradient and voltage change between metal and oxide surface. It is shown that the irradiation accelerates oxidation rate and induces development of conjugated in-plane stress. It is found that both in-plane and tensile stresses result in a power-law decrease in a critical time for fragmentation \emph{versus} dose rate. 
It is shown that a critical crystallite size for the related tetragonal to monoclinic phase transformation at the oxide/metal interface decreases with the dose rate. Obtained results correlate well with experimental observations in the reference points and can be exploited to estimate corrosion resistance linked to transformation to monoclinic structure and fragmentation in zirconium-based cladding materials. 
This study provides a deep insight into the details of oxidation kinetics at irradiation in zirconium alloys.

Phase Equilibria and Trace Element Deportments in Fe–O–Al2O3–SiO2 Slags and Molten Copper Matte at 1473 K (1200 °C), Fixed p(O2) and p(SO2), and Silica/Magnetite Saturation

Abstract Understanding the role of major components of electric waste during smelting of these materials to recover valuable trace metals is poorly constrained by experimental data. In this study, phase equilibria and trace element deportments were studied at 1473 K (1200 °C) in conditions of combined sulfide concentrate and electric and electronic equipment waste processing in batchwise submerged lance smelting. In this system, liquid slag domain is limited by silica and magnetite saturation boundaries or primary phase fields at all alumina concentrations from alumina-free slags to silica-spinel double saturation. The impact of alumina concentration in slag at fixed oxygen and sulfur dioxide partial pressures on the distributions of Ag, Cu, In, Pb, and Sn was studied. Elemental concentrations in slag, matte, and solid magnetite (a Fe–Al spinel solid solution) were measured using electron probe microanalysis and laser ablation-ICP-mass spectrometry techniques. The observed impact of alumina on the distribution coefficient of silver, copper, and indium favored the matte phase at silica and magnetite saturation but lead and tin behaved differently within different primary phase fields as a function of alumina concentration.

Physics-informed neural networks for phase-field simulation in designing high energy storage performance polymer nanocomposites

Dielectric polymers for electrostatic energy storage are used in modern electronic and electrical systems, and their performance can be significantly enhanced through doping with ultralow content nanofillers to improve energy storage performance. Understanding the underlying physical mechanisms of polymer nanocomposites is essential for designing high-performance dielectric polymers. This paper presents a conduction model that integrates Richardson–Schottky emission and hopping conduction to describe charge injection and transport in polymer composites. Phase-field simulations, incorporating electrical, thermal, and mechanical breakdown mechanisms, investigate the influence of nanofiller volume fraction, size, and dielectric constant on the dielectric response and breakdown behaviors under high temperature and electric fields. We propose the Physics-Informed Neural Networks for phase-field simulation that integrates the physical rules of charge transport, phase evolution, and boundary conditions. By embedding phase field models within the Physics-Informed Neural Networks' structure, this method demonstrates the ability to predict the breakdown strength and energy density of polymer nanocomposites. This work provides crucial guidelines for designing high-performance dielectric energy storage capacitors under extreme conditions.

Phase field model of tunnel excavation damage zone

Phase field model of tunnel excavation damage zone

Phase Field Simulation and Experimental Study of Carbide Precipitation Process in Submerged Arc Welding on Descaling Roll

The mechanical properties of surfacing layers are significantly affected by the precipitation and evolution of carbides in nickel-based alloys. At present, the study of carbide precipitation in a Ni-Cr-B-Si surfacing layer is described by using the phase field method. In this paper, the true Gibbs free energy of the M23C6 carbide phase in Ni-Cr-C ternary alloy was established by the CALPHAD method and thermodynamic database. The growth and coarsening process of M23C6 carbide was simulated based on phase field method. The microstructure of M23C6 carbide of Ni-Cr-C alloy at 1373 °C isothermal aging time was observed by scanning electron microscope (SEM). The results show that the growth and coarsening of the precipitated M23C6 carbide phase are undergone through multiple processes during isothermal aging. First, a single precipitate core is formed, and then the single precipitate continues to coarsen and grow, forming a lamellar structure. Two precipitates contact to form a single rod-like structure, and multiple precipitates form slender rod-like structures. Finally, the contacting elongated rod-like structures grow, forming a typical layered eutectic carbide. The precipitation behavior, growth, and coarsening process of M23C6-type carbides in Ni-Cr-B-Si series alloys are explored through phase field simulation and experimental research in this paper. A theoretical basis is provided for the rational control and distribution of carbides in surfacing layers. A reference is also offered for optimizing the nickel-based superalloy materials used for surfacing the surface of descaling rolls.

A nonlocal macro-meso-scale damage model based modeling for crack propagation in ferroelectric materials

The accurate simulation of crack growth for ferroelectric materials plays a crucial role in the application of ferroelectric materials in electronic devices. In recent years, a nonlocal macro-meso-scale consistent damage (NMMD) model has been proposed for simulating the crack propagation in brittle materials, which offers the advantage of higher efficiency compared to the phase-field method. Different from the phase field method, this model does not need to solve the phase field equation at the same time. Therefore, the degree of freedom in solving can be reduced, thereby reducing the computational workload. In this paper, the authors proposed a new integration strategy for microscopic damage and devised a simple and efficient implementation of the NMMD model for the modelling of quasi-static fracture in the general purpose commercial software developer, COMSOL Multiphysics based on the finite element method (FEM) and studied the crack propagation for ferroelectric materials under the applied stress and electric fields. Different from the original NMMD model, only the tensile stress induced geometric damage is accounted for crack propagation by using the decomposition of elastic strain energy. The effects of different crack-face conditions, electrical boundary conditions and the electromechanical loading for crack growth of ferroelectric materials have been considered in our FEM simulation are discussed in this work.

Phase field simulation of columnar grain formation induced by pore migration in UO2

Phase field simulation of columnar grain formation induced by pore migration in UO2

Reevaluating feature selection in phase field models for battery performance: A call for robust statistical approaches

Reevaluating feature selection in phase field models for battery performance: A call for robust statistical approaches

Phase field fracture modeling of mechanical degradation and crack propagation in random porous sintered nano-silver with thermal and strain-rate effects

Phase field fracture modeling of mechanical degradation and crack propagation in random porous sintered nano-silver with thermal and strain-rate effects

An adaptive mesh refinement algorithm for stress-based phase field fracture models for heterogeneous media: Application using FEniCS to ice-rock cliff failures

An adaptive mesh refinement algorithm for stress-based phase field fracture models for heterogeneous media: Application using FEniCS to ice-rock cliff failures

Sharp interface limit of a two-time scale phase field model of a binary mixture.

Due to its analytical flexibility and thermodynamic consistency, the phase field model is widely used in the analysis of equilibrium states and transformation between phases. The present review is devoted to one of the classes of kinetic models in the form of the hyperbolic phase field, which is applicable to slow and fast phase transformations. In the example of solidification from metastable liquid, the analysis is presented for the important procedure of reducing of the diffuse interface to the sharp interface. A special asymptotic analysis is discussed for application to solidifying binary mixture with diffuse phase interface under arbitrary concentration of species and under isothermal and isobaric conditions. Asymptotic analysis states that the hyperbolic phase field model arrives at the known hyperbolic Stefan problem within the sharp interface limit. The solution of this problem together with the common tangent construction allows us to analyze ($i$) nonequilibrium effect in the form of solute trapping and ($ii$) the complete transition from the diffusion-limited to the diffusionless (chemically partitionless) solidification at the finite interface velocity. A comparison with other theoretical models is summarized and the discussion on accessible experimental results is given.

Lithium Deposition Mechanism under Different Thermal Conditions Unraveled via an Optimized Phase Field Model.

As one of the most important physical fields for battery operation, the regulatory effect of temperature on the growth of lithium dendrites should be studied. In this paper, we develop an optimized phase field model to explore the effect of temperature on the growth of Li dendrites in Li metal batteries. We incorporated full lithium deposition kinetics, including atom diffusion and solid electrolyte interface restriction on interface kinetics, into the model and revealed their significance in determining the transformation of the lithium deposition morphology from moss-like to dendrite-like. We found that a high temperature or dispersed hot spots are more conducive to stable battery operation than a low temperature or concentrated hot spots due to the enhanced diffusion kinetics at the high temperature and the more uniform temperature distribution of dispersed hot spots. We believe our work can provide a useful tool for further exploring the thermal effect on stable lithium metal battery operation.

Phase Field Simulation of Al-Fe-Mn-Si Quaternary Eutectic Solidification

This study investigates the eutectic equilibrium phases in a multicomponent system through 3-D multi-phase-field simulations. Emphasizing the directional solidification process, the work examines the growth dynamics of intermetallic phase Al13Fe4, a lamellar structure (FCC-A1), and a quaternary phase beta-AlMnSi from the liquid that is solidified at a specific temperature. The eutectic transformation, described by the four phase reaction L→Al13Fe4+FCC-A1+beta-AlMnSi, is analyzed to develop a microstructure selection map. This map correlates stable growth modes with initial system composition and lamellar spacing. The results provide detailed insights into the segregation behaviour of alloying elements and their influence on transformation kinetics, enhancing the understanding of eutectic microstructure evolution in complex alloy systems.

Parametric study on the role of energy and mobility on abnormal grain growth in systems undergoing complexion transition

Abstract Despite many decades of research, the exact mechanism contributing to the persistence of abnormal grain growth (AGG) is poorly understood. In many materials, a structural transition at grain boundary (GB), known as complexion transition, has been suggested as a cause of AGG. However, the precise link between complexion transitions and AGG is still unclear and challenging to study experimentally. Recently, we proposed a thermodynamically consistent complexion transition model and using a phase field study we demonstrated persistent AGG induced by the proposed model. Building on our earlier research, this work aims to clarify the relationship between induced grain growth and the underlying complexion transitions. Complexion transitions can be characterized by their type, which is defined by changes in GB properties such as mobility and energy, and their likelihood of occurrence. By systematically varying the type and likelihood of these transitions, we map the development of microstructure and identified the parameter space for occurrence of AGG through two-dimensional phase-field simulations. Quantitative analysis of relative growth of abnormal grains provides valuable insights into the role of complexion transition parameters on AGG. The findings from this study can contribute to a better understanding of the relationship between processing parameters and microstructure during complexion transitions.

Enhanced brittle fracture modeling in heterogeneous materials: A variational phase field approach integrating XFEM and Level-Set methods

Enhanced brittle fracture modeling in heterogeneous materials: A variational phase field approach integrating XFEM and Level-Set methods

Phase field theoretical study of the electrocaloric effect in porous ferroelectric films

Phase field theoretical study of the electrocaloric effect in porous ferroelectric films

Dynamic Evolution and Effective Tuning of Lithium Dendrites Revealed by Phase Field Model and 2D Numerical Simulation.

Lithium dendrites are widely acknowledged as the main culprit of the degradation of performance in various Li-based batteries. Studying the mechanism of lithium dendrite formation is challenging because of the high reactivity of lithium metal. In this work, a phase field model and in situ observation experiments were used to study the growth kinetics and morphologies of lithium dendrites in terms of anisotropy, temperature, and potential difference. Subsequently, a 2D numerical simulation has been developed to illustrate the impact of microscopic parameters, such as electrolyte potential, current distribution, and anode overpotential, on the growth of lithium dendrites after nucleation. Meanwhile, the influence of electrode interface, charging rate, and charging mode on lithium dendrites was also studied using the 2D model and in situ experiments. This work provides comprehensive insights into the kinetics of dendrite formation and morphologies, offering an important theoretical reference for the safety and long-life applications of batteries.

Integrated Experimental and Thermodynamic Modelling Study of Phase Equilibria in the PbO-AlO1.5-SiO2 System in Air

Abstract The present study focused on phase equilibria in the PbO–AlO1.5 and PbO–AlO1.5–SiO2 systems. The equilibration and quenching technique followed by the electron probe X-ray microanalysis (EPMA) was used in the present study. The liquidus of the PbO–AlO1.5–SiO2 system in air, including corundum (Al2O3), cristobalite/tridymite/quartz (SiO2), feldspar (PbAl2Si2+x O8+2x ), massicot (PbO), mullite (Al6+2x Si2−2x O13−x ), PbAl12O19, PbAl2O4, Pb9Al8O21, Pb6Al2Si6O21, Pb4Al2Si2O11, Pb4Al4Si3O16, Pb3Al10SiO20 and Pb12Al2Si20O55 primary phase fields, has been characterised. New lead aluminosilicate compounds, Pb13Al4Si6O31, Pb12Al6Si10O31, Pb9Al4Si8O31, Pb7Al2Si8O26 and Pb7Al2Si10O30 were found to coexist with oxide liquid. The PbO–AlO1.5 binary and PbO–AlO1.5–SiO2 ternary systems in air were reoptimized based on the obtained experimental data. New experimental results together with phase equilibria and thermodynamic literature data were used to obtain a self-consistent set of parameters of the thermodynamic model for all phases of the PbO–AlO1.5–SiO2 system in air. The predicted liquidus projection of the PbO–AlO1.5–SiO2 system was presented for the first time in the full range of temperatures and compositions. Graphical Abstract

Ultrahigh piezoelectric performances of (K,Na)NbO3 based ceramics enabled by structural flexibility and grain orientation

(K,Na)NbO3-based ceramics are deemed among the most promising lead-free piezoelectric materials, though their overall piezoelectric performance still lags behind the mainstream lead-containing counterparts. Here, we achieve an ultrahigh piezoelectric charge coefficient d33 ∼ 807 pC·N−1, along with a high longitudinal electromechanical coupling factor (k33 ∼ 88%) and Curie temperature (Tc ∼ 245 °C) in the (K,Na)(Nb1-xSbx)O3-Bi0.5Na0.5ZrO3-BiFeO3 (KNN-xSb) system through structural flexibility and grain orientation strategies. Phenomenological models, phase field simulations and high-angle annular dark-field scanning transmission electron microscopy reveal that the structural flexibility originates from the high Coulomb force between K+/Na+ ions and Sb ions in the KNN-xSb system, while the grain orientation promotes the displacement of B-site cations leveraging the engineered domain configuration. As a result of its excellent comprehensive piezoelectric properties, the textured KNN-5Sb/epoxy 1-3 piezoelectric composite is found to possess a broader bandwidth BW = 60% and higher amplitude output voltage than commercial PZT-5 and other KNN counterparts. These findings suggest that the textured KNN-5Sb ceramics could potentially replace current lead-based piezoceramics in transducer applications.

Understanding and control of gas porosity in metal laser powder-bed fusion additive manufacturing

ABSTRACT The presented study discusses mechanism leading to gass porosity formation during additive manufacturing (AM) process. The method employs numerical scheme, which includes fluid dynamics of the melt pool and on-the-fly ray-tracing implemented within a phase field framework where the liquid/vapor interface is captured within volume of fluid approach. The emission of pores in the middle or the stripe happens only for relatively low scan speed (less than 0.6 m/s for IN718). The stripe edges (laser turning points) are identified as potential source of gas pores at scan speeds as high as 1 m/s. Simulations of laser turning, representative of the edge of a stripe, suggest the way the process parameters can be altered to avoid local porosity formation, while still ensuring a deep melt pool suitable for high build rates. The laser power modulation around the edge can lead to over 50% reduction of the pores emission. The proposed numerical framework requires only moderate computational resources, thus providing a holistic tool to decrease defect density and thus further improve quality of additive manufactured components.