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A simulation model of recrystallization and grain growth has been developed to investigate grain structure evolution during deformation and heat treatment in polycrystalline U-10 wt pct Mo (U-10Mo) fuel. Experimentally obtained U-10Mo post-homogenization microstructures were used as input for closed-loop simulations of multiple rolling passes, intermediate heating, and final annealing. Finite element model calculations of deformation and Potts model simulations of recrystallization and grain growth were used to iteratively inform each subsequent stage of simulation. The model was then applied to predict the grain structure evolution during multiple-pass hot rolling and annealing of U-10Mo and benchmarked against experimentally observed U-10Mo recrystallization behavior. The results showed that our model was able to capture the coupling between deformation and recrystallization as a function of microstructure, including particle stimulated nucleation and recrystallization nucleation on grain boundaries. Additionally, we have achieved reasonable quantitative agreement with U-10Mo recrystallization and grain growth behavior.

Using ab initio calculations and the magnetic cluster expansion formula, a model with the magnetic effects on the energetic landscape of Fe–Cu was developed. The (partially) disordered local moment picture and Monte Carlo simulation method were combined to study the magnetically disordering effects on the thermodynamic properties in Fe–Cu alloys. The simulation results show nonlinear enhancements of Fe magnetism with increasing Cu concentration under varying magnetic ordering/disordering states, and the nonlinearity of the enhancement is more significant under the ferromagnetic state. It is also found that magnetism has subtle effects on the clustering of Cu because both the substitutional and binding energies could be affected but in different ways depending on the magnetic states. The results suggest that the alloying-induced enhancement of the Fe magnetism is a fundamental feature of Fe–Cu, which introduces difference on the concentration dependence of mixing, depending on the magnetic ordering/disordering states. In conjunction with the concentration dependence of short-range ordering, the enhancement of Fe magnetism also strongly affects the Curie temperatures in Fe–Cu.

Pre-existing second phase particles can induce particle stimulated nucleation (PSN) and pinning effect on grain boundaries during DRX process of magnesium alloys. The interaction among pinning effect, PSN mechanism and strain-induced grain boundary migration (SIBM) nucleation mechanism imposes challenge in quantitative study of microstructure evolution. A phase field model that describes discontinuous dynamic recrystallization process considering second phase particles (PF-DDRX-SP) which mainly distribute along grain boundaries is developed. The second phase order parameter with diffusion interface is introduced to the free energy function. With considering the pinning effect of second phase particles on grain boundaries, the grain boundary energy couples the interaction between second phase and grains. The effect of second phase on dislocation density evolution is considered in the model, and the PSN and SIBM mechanism are both executed by limiting the nucleation position to the grain boundary and the second phase interface. For the validation, the initial topology consistent with initial microstructure is applied to the simulation of DRX kinetics and flow behavior of AZ80 magnesium alloy, and great reliability and accuracy of developed model is indicated. Furthermore, through the model, the microstructure evolution with different particle size and with different volume fraction of round particle during DRX process were simulated. The results show that particles with higher dispersion reduce the number of DRX nuclei, which indicate that second phase particles suppress the nucleation at grain boundaries because of the pinning effect. More importantly, the proposed model could also quantitatively predict the relationships between the parameters of second phase particles and DRX behaviors, and enable to optimize the initial second phase structure in a uniform grain structure during thermomechanical process.

Chemical dealloying beckons researchers both for scientific interest in corrosion failure of metallic materials and for the fabrication of nanoporous materials that have versatile applications due to their ultra-high surface area. Empirically, nanoporous structure evolves by the corrosion of less noble elements coupled with the rearrangement of more noble elements in the alloys. However, how topologically complex porous structures form and how environmental and material factors affect the dealloying kinetics are still unknown. This work develops a multi-phase-field model to demonstrate that a nucleation-growth mechanism can explain the formation of nanoporous structures under chemical attack. The evolution of nanoporous patterns from a binary alloy is examined as a function of the chemical content of the electrolyte, precursor alloy composition, dimensionality, and bulk and surface diffusion coefficients, which is validated with experimental observations. Two-phase composite dealloying and the effect of defect pre-existed in the precursor are also presented. The comprehensive model developed in this study provides a powerful tool to tailor made nanoporous metallic structures under chemical dealloying.

A three-dimensional phase-field model was developed to study the effects of surface energy and diffusivity anisotropy on void growth behavior in irradiated Zr. The gamma surface energy function used in the phase-field model was developed with the surface energy anisotropy calculated from the molecular dynamics simulations. The model assumes that vacancies have larger mobility in the c-axis than in the a-axis and b-axis, whereas interstitials have larger mobility in the basal plane than in the c-axis. The equilibrium void morphology and the effect of defect concentrations and mobility anisotropy on void growth behavior were simulated using the developed model. The simulations demonstrated that (1) the developed phase-field model correctly reproduces the faceted void morphology predicted by the Wulff construction; (2) with isotropic diffusivity, the void prefers to grow on the basal plane; and (3) when the vacancy has large mobility along the c-axis and interstitial has a large mobility on the basal plane of hexagonal closed-packed Zr alloys, a platelet void grows in the c-direction and shrinks on the basal plane. These findings are in agreement with the observation of void morphology and growth behavior in irradiated Zr, and reveal that the strong mobility anisotropy of defects results in the anisotropic growth of voids in Zr.

Grain growth kinetics are known to deviate from the classical n = 2 behavior when particles in the microstructure impede grain boundary motion, and eventually halt as the driving force of grain boundary curvature approaches the pinning force exerted by the particles. Potts Model simulations were evaluated with respect to the non-physical Monte Carlo simulation temperature and theoretical predictions of grain growth behavior in the presence of second-phase particles. These simulations demonstrate that by modifying the simulation temperature, the pinned grain size will follow a selected inverse-linear relationship with respect to particle volume fraction. From these results, we suggest an approach for selecting Potts Model simulation temperature. Additionally, parameterizations of particle size, volume fraction, and simulation temperature in which the previously observed simulation phenomenon “Particle-Assisted Abnormal Grain Growth” (PA-AGG) occurred were recorded and discussed. The majority of this grain growth behavior occurred for simulation temperatures TS ≥ 1.5, particle diameters of less than six cells, and particle volume fractions smaller than 10%. However, PA-AGG was also observed in simulation for particle diameters of up to ten cells, particle volume fractions of twenty percent, and simulation temperatures as small as TS = 0.5. An analysis of the simulated grain size distributions showed that the occurrence of PA-AGG was not dependent on the abnormal grain reaching a critical relative grain size. The simulation domain size does not appear to have an influence on this effect.

Nonlinear ultrasonic technique is one of several promising nondestructive evaluation methods for monitoring the evolution of nanosized defects such as radiation-induced defects in nuclear materials. In this work, a microstructure-based phase-field model of dynamic deformation in elastically nonlinear materials has been developed for investigating the dynamic interaction between distributed defects and a propagating longitudinal sound wave. With the model, the effect of second phase precipitates’ size and properties on the nonlinearity parameter β that describes the magnitude of the 2nd harmonic wave was simulated. The results showed that (1) the nonlinearity parameter β increases as the elastic inhomogeneity increases regardless of whether the precipitates are softer or harder than the matrix; (2) β linearly increases with the increase of lattice mismatch strain; and (3) for a given volume fraction of second phase precipitates, β strongly depends on the precipitate size. The predicted precipitate size dependence of β agrees with the experimental data. These results demonstrate that the developed model enables one to predict the contributions of different nonlinear sources to β, to explain the signal physics behind the measured nonlinear ultrasonic response, and to guide the development of nonlinear ultrasound nondestructive detection of material defects in nuclear reactor materials.

Early experimental data on void swelling in electron-irradiated materials disagree with the dislocation bias models based on the dislocation-point defect elastic interactions. Later, this became one of the factors that prompted the development of models based on production bias (PBM) as the main driver for swelling, which assumed that the dislocation bias was much lower than that predicted by theoretical analyses of dislocation bias. However, the PBM in its present form fails to account for important and common observations, namely, the indefinite void growth often observed under cascade irradiation and the swelling saturation observed under high-dose irradiation and in void lattices. In this paper, we show that these contradictions can be naturally resolved in the framework of the rate theory that accounts for the radiation-induced vacancy emission from extended defects, such as voids, dislocations and grain boundaries. This modification introduces a new bias type in the theory, namely, the emission bias. This modified rate theory agrees well with the experimental data and demonstrates that the original dislocation bias should be used in rate theory models along with the emission bias in different irradiation environments. The modified theory predictions include, but are not limited to, the radiation-induced annealing of voids, swelling saturation under high-dose irradiation, generally, and in void lattices, in particular.

A multiscale methodology was developed to predict the evolution of thermal conductivity of polycrystalline fuel under irradiation. At the mesoscale level, a phase field model was used to predict the evolution of gas bubble microstructure. Generation of gas atoms and vacancies was taken into consideration. Gas bubbles were predicted to form, grow, and coalesce around grain boundary (GB) areas. On the macroscopic scale, a statistical continuum mechanics model was applied to predict the anisotropic thermal conductivity evolution during irradiation. Microstructures predicted by the phase field model were fed into the statistical continuum mechanics model to predict properties and behavior. A decrease of thermal conductivity during irradiation was demonstrated. The influence of irradiation flux, the exposure time, and the grain microstructure were investigated. If the initial GB microstructure was isotropic, the thermal conductivity under irradiation would be similarly isotropic. If the initial GB configuration was anisotropic, anisotropy of thermal conductivity would intensify under irradiation as gas bubbles coalesce around GB areas. The prediction of microstructure and property evolution of polycrystalline materials under irradiation by bridging two models in different scales were demonstrated successfully. This approach provides a deep understanding from a basic scientific viewpoint.

We propose a phase-field model for modeling microstructure evolution during deformation twinning. The order parameters are proportional to the shear strains defined in terms of twin plane orientations and twinning directions. Using a face-centered cubic Al as an example, the deformation energy as a function of shear strain is obtained using first-principle calculations. The gradient energy coefficients are fitted to the twin boundary energies along the twinning planes and to the dislocation core energies along the directions that are perpendicular to the twinning planes. The elastic strain energy of a twinned structure is included using the Khachaturyan's elastic theory. We simulated the twinning process and microstructure evolution under a number of fixed deformations and predicted the twinning plane orientations and microstructures.

Twinning in certain metals or under certain conditions is a major plastic deformation mode. Here we present a phase field model to describe twin formation and evolution in a polycrystalline fcc metal under loading and unloading. The model assumes that twin nucleation, growth and de-twinning is a process of partial dislocation nucleation and slip on successive habit planes. Stacking fault energies, energy pathways (γ surfaces), critical shear stresses for the formation of stacking faults and dislocation core energies are used to construct the thermodynamic model. The simulation results demonstrate that the model is able to predict the nucleation of twins and partial dislocations, as well as the morphology of the twin nuclei, and to reasonably describe twin growth and interaction. The twin microstructures at grain boundaries are in agreement with experimental observation. It was found that de-twinning occurs during unloading in the simulations, however, a strong dependence of twin structure evolution on loading history was observed.

Interpreting nonlinear ultrasonic signals detected in a nondestructive evaluation of radiation damage requires the knowledge of the correlation between defects and nonlinearity. In this work, molecular dynamics simulations are performed to study the effect of distributed vacancies, voids, Cu atoms, and Cu precipitates on the nonlinear ultrasonic response in body-centered cubic (bcc) Fe. The nonlinearity parameter calculated from the second harmonic amplitude in the perfect lattice is 2.73. Vacancies are found to increase the nonlinearity. However, clusters of vacancies in the form of spherical voids show an opposite effect. This finding can be used to conveniently distinguish vacancies from voids in the material. Unlike vacancies, individual Cu atoms decrease the nonlinearity. Clustering of Cu atoms into Cu precipitates further decreases the nonlinearity. Interestingly, precipitates with a diameter of 2 nm and larger exhibit a similar effect despite their different structure and coherency with the Fe matrix.

We, for the first time, propose a phase-field model to simulate the evolution of void ensembles under irradiation. The model takes into account one-dimensional migration of self-interstitial atoms (1-D SIA), vacancy diffusion, the generation and reaction between SIA and vacancies as well as the nucleation of voids. A one-dimensional random walker model (based on the theory of first-passage processes) is applied to describe the fast 1-D SIA while the Cahn–Hilliard equation is used to describe the slow three dimensional diffusion of vacancies. The coupling of these two methods greatly improves the computational efficiency for a system with strong inhomogeneity and anisotropy of diffusion. The formation of void lattices is simulated with the resultant model. It is found that a void lattice forms when the mobility of the 1-D SIA is four orders of magnitude larger than that of the vacancy mobility. A high generation rate of interstitials during displacement cascades delays the formation of a void lattice.

Te precipitates are one of principal defects that form during cooling of melt-grown CdTe or CZT crystals when grown Te-rich. Many factors such as the kinetic properties of intrinsic point defects (vacancy, interstitial, and antisite defects); stresses associated with the lattice mismatch between precipitate and matrix; temperature gradients and extended defects (dislocations, twin and grain boundaries); non-stoichiometric composition; thermal treatment history all affect the formation and growth/dissolution of Te precipitates in CdTe. A good understanding of these effects on Te precipitate evolution kinetics is technically important in order to optimize material processing and obtain high-quality crystals. This research develops a phase-field model capable of investigating the evolution of coherent Te precipitates in a Te-rich CdTe crystal undergoing cooling from the melt. Cd vacancies and Te interstitials are assumed to be the dominant diffusing species in the system, which is in two-phase equilibrium (matrix CdTe and liquid Te inclusion) at high temperatures and three-phase equilibrium (matrix CdTe, Te precipitate, and void) at low temperatures. Using available thermodynamic and kinetic data from experimental phase diagrams and thermodynamic calculations, the effects of Te interstitial and Cd vacancy mobility, cooling rates and stresses on Te precipitate, and void evolution kinetics are investigated.

A coring structure in which δ (fcc) grains have Ga-rich cores with Ga-poor shells forms during the \(\varepsilon\) (bcc) to δ (fcc) phase transformations in Pu-Ga alloys. There are considerable differences between the diffusivities of Ga in \(\varepsilon\) and δ and a large and anisotropic stress field exists in the coring structure due to the large lattice mismatch between these two phases and strong elastic anisotropy. We developed a phase-field model for simulating the coring structure evolution in three dimensions, taking into account the inhomogeneities of both Ga diffusivity and elastic properties. It is shown that the elastic interactions among different oriented δ grains and diffusive Ga atoms affect Ga diffusion path, the coring structure, and the growth kinetics of the δ phase.

This report compares two approaches for simulating microstructure evolution of plate-like precipitates during artificial ageing of aluminum alloys: the phase field and the cellular automaton methods. Although both methods are based on thermodynamics, they handle the kinetics in quite different ways, each with its own advantages and disadvantages. Both methods were applied to the growth of semi-coherent plate-like h 0 precipitates in Al-4 wt% Cu. Good agreement is found between the results of these two models, as well as experiments. A combination of these two methods would provide a novel approach that is both physically sound and computationally effective for the application of precipitation modeling.

Phase field approach is applied to modeling the spinodal decomposition process in a thin film with periodically distributed arrays of interfacial dislocations. The elastic stress field in the simultaneous presence of interfacial dislocations, substrate constraint, and compositional strains is obtained by solving the mechanical equilibrium equations using an iteration method. It is shown that the periodic stress field associated with the array of interfacial dislocations leads to a directional phase separation and the formation of ordered mesoscale microstructures. It is demonstrated that when the periodicity of the dislocation is small, the wavelength of the ordered microstructure tends to be the same periodicity as the dislocation array. The results have important practical implications that an ordered nanostructures could be produced by controlling the interfacial dislocation distribution.

The morphological evolution during spinodal decomposition of a binary alloy thin film elastically constrained by a substrate is studied. Elastic solutions, derived for elastically anisotropic thin films subject to the mixed stress-free and constraint boundary conditions, are employed in a three-dimensional phase-field model. The Cahn–Hilliard diffusion equation for a thin film boundary condition is solved using a semi-implicit Fourier-spectral method. The effect of composition, coherency strain, film thickness and substrate constraint on the microstructure evolution was studied. Numerical simulations show that in the absence of coherency strain and substrate constraint, the morphology of decomposed phases depends on the film thickness and the composition. For a certain range of compositions, phase separation with coherency strain in an elastically anisotropic film shows the behavior of surface-directed spinodal decomposition driven by the elastic energy effect. Similar to bulk systems, the negative elastic anisotropy in the cubic alloy results in the alignment of phases along 100 elastically soft directions.  2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A phase-field model was developed for predicting the domain structure evolution in a thin film with an arbitrary distribution of dislocations and subject to a substrate constraint. The effect of interfacial dislocations on the formation of tetragonal ferroelectric domains in a cubic paraelectric matrix was studied. It was found that the presence of interfacial dislocations locally modifies the ferroelectric transition temperature and leads to the preferential formation of ferroelectric domains around misfit dislocations. The types of tetragonal variants depend on the directions of the dislocation lines and their Burgers vectors.

The morphological evolution during spinodal decomposition in binary alloy thin films elastically constrained by substrates is studied. Elastic solutions, derived for both elastically isotropic and anisotropic thin films subject to mixed stress-free and constraint boundary conditions, are employed in a three-dimensional phasefield model to investigate the effect of coherency strain and substrate constraint on microstructural evolution. The temporal evolution of the Cahn-Hilliard equation under thin film boundary conditions is solved with a semi-implicit Fourier-spectral method. The phase separation with coherency strain in an elastically anisotropic film shows the behavior of surface-directed spinodal decomposition driven by the elastic energy effect. Negative elastic anisotropy in the cubic alloy causes the alignment of the phases along elastically soft directions.

A diffuse-interface phase field model is described for modeling the interactions between compositional inhomogeneities and structural defects. The spatial distribution of these structural defects is described by the space-dependent eigenstrains. It takes into account the effect of the coherency elastic energy of a compositional inhomogeneity, and the elastic coupling between the coherency strains and defect strains. The temporal evolution of composition is described by the Cahn–Hilliard equation. Particularly, the solute segregation, and nucleation and growth around dislocation slip bands and crack-like condensed interstitial dislocation loops are discussed. The effect of nucleated coherent precipitates on the stress field around these defects is analyzed 2002 Elsevier Science B.V. All rights reserved.

The stability and evolution of ferroelectric domain structures in thin films are studied. Elastic solutions are derived for both elastically anisotropic and isotropic thin films with arbitrary domain structures, subject to the mixed stress-free and constraint boundary conditions. These solutions are employed in a three-dimensional phase-field model to investigate simultaneously the effect of substrate constraint and temperature on the volume fractions of domain variants, domain-wall orientations, surface topology, domain shapes, and their temporal evolution for a cubic-to-tetragonal ferroelectric phase transition. A specific example of a [001] orientated film heteroepitaxially grown on a [001] cubic substrate is considered. It is shown that the shapes of a-domains with tetragonal axes parallel to the film surface are significantly different from those of c-domains with tetragonal axes perpendicular to the film surface. For the substrate constraints and temperatures under which both a- and c-domains coexist, both types of a-domains are present with their tetragonal axes perpendicular to each other, and the domain wall orientations deviate from the 45 orientation generally assumed in thermodynamic analyses. It is demonstrated that a substrate constraint results in sequential nucleation and growth of different tetragonal domains during a ferroelectric phase transition.

A diffuse-interface field model is proposed for describing diffusional processes in coherent systems with arbitrary microstructures and arbitrary spatial distribution of structural defects such as dislocations. It takes into account the effect of both the coherency elastic energy of a microstructure and the elastic coupling between the coherency strains and defect strains. In this model, any arbitrary spatial distribution of defects is described using the micromechanics concept of space-dependent “stress-free” or “eigen” strains. As examples, the solute segregation as well as the nucleation and diffusional growth of a coherent precipitate around an edge dislocation are considered. It is shown that coherent nucleation may become barrierless under the influence of the local elastic field of a dislocation.

In order to better understand the effect of fine Cu precipitates on the mechanical properties of body-centred-cubic (bcc) Fe, atomic simulations of bcc Fe with bcc Cu precipitates under mechanical loading were conducted by using the molecular dynamics (MD) method in conjunction with embedded atom method (EAM) potentials. The atomic configurations showed that all bcc Cu precipitates in bcc Fe matrices have the transformation tendency from bcc to 9R in the absence of external loading. When compressive stresses were loaded and reached a critical value, the transformation from bcc to the 9R variant occurred inside Cu precipitates, and these transformed Cu precipitates resulted in structure changes of matrix Fe. On the other hand, this kind of transformation did not take place under tensile stress. The corresponding internal stress fields around the distorted and transformed Cu precipitates were evaluated. It was found that the resolved shear stresses of the internal stress field on the main slip systems of bcc Fe are of the same order of magnitude as the yield stress of perfect single crystal Fe. This may affect the dislocation slip and contribute to material hardening.

The stress-strain curves of single crystals under uniaxial tensile deformation are obtained for the whole deformation process by atomistic molecular statics simulations. Effects of model sizes, boundary conditions, crystal orientations and displacement increment on the stress-strain curves are investigated. Various deformation evidence such as dislocation movement, dislocation piling up and twinning are clearly observed. The deformation and fracture characteristics of and their dependence on the boundary conditions or the stress states are studied.

Thermal stresses in coated structures were investigated by the boundary element method (BEM). It was found that the singular stress field near the free edge of the interface has a converging distribution with decreasing coating thickness. This converging distribution can be described by an asymptotic expression including one singular term and one constant term. In determining the effective range of the asymptotic expression, some quantities relating to a failure criterion of coated structures are presented.

Singular integral equations are used to formulate the torsion problem of a circular cylinder containing a polygonal opening and a line crack. The formulation is based on degenerating a system of connecting line cracks to that of a polygon, the sides of which coincides with the cracks. Considered, in particular, is the torsion of a circular cylinder with a rectangular hole and a nearby slanted line crack. Mode III stress intensity factors are computed at both ends of the crack to reflect their relative position to the rectangular hole in addition to change in the dimensions of the crack relative to the other geometric variables. Recognizing that the singular behavior of the stresses near a reentrant's corner differs from that of the crack tip, intensification of the local stresses at the corners of the rectangular hole is also examined. The results show the influence of the crack size and position.

A phase-field model for predicting the coherent microstructure evolution in constrained thin films is developed. It employs an analytical elastic solution derived for a constrained film with arbitrary eigenstrain distributions. The domain structure evolution during a cubic→tetragonal proper ferroelectric phase transition is studied. It is shown that the model is able to simultaneously predict the effects of substrate constraint and temperature on the volume fractions of domain variants, domain-wall orientations, domain shapes, and their temporal evolution.

The migration mechanisms and the corresponding activation energies of Cr-vacancy (Cr-V) clusters and Cr interstitials in $\ensuremath{\alpha}\text{-Fe}$ have been investigated using the dimer and the nudged elastic-band methods. Dimer searches are employed to find the possible transition states of these defects and the lowest-energy paths are used to determine the energy barriers for migration. A substitutional Cr atom can migrate to a nearest-neighbor vacancy through an energy barrier of 0.56 eV but this simple mechanism alone is unlikely to lead to the long-distance migration of Cr unless there is a supersaturated concentration of vacancies in the system. The Cr-vacancy clusters can lead to long-distance migration of a Cr atom that is accomplished by Fe and Cr atoms successively jumping to nearest-neighbor vacancy positions, defined as a self-vacancy-assisted migration mechanism, with the migration energies ranging from 0.64 to 0.89 eV. In addition, a mixed Cr-Fe dumbbell interstitial can easily migrate through Fe lattices, with the migration energy barrier of 0.17, which is lower than that of the Fe-Fe interstitial. The on-site rotation of the Cr-Fe interstitial and Cr atom hopping from one site to another are believed to comprise the dominant migration mechanism. The calculated binding energies of Cr-V clusters are strongly dependent on the size of clusters and the concentration of Cr atoms in clusters.

The use of nondestructive magnetic signatures for continuous monitoring of the degradation of structural materials in nuclear reactors is a promising yet challenging application for advanced functional materials behavior modeling and measurement. In this work, a numerical model, which is based on the Landau–Lifshitz–Gilbert equation of magnetization dynamics and the phase field approach, was developed to study the impact of defects such as nonmagnetic precipitates and/or voids, free surfaces and crystal orientation on magnetic domain structures and magnetic responses in magnetic materials, with the goal of exploring the correlation between microstructures and magnetic signatures. To validate the model, single crystal iron thin films (~240 nm thickness) were grown on MgO substrates and a focused ion beam was used to pattern micrometer-scale specimens with different geometries. Magnetic force microscopy (MFM) was used to measure magnetic domain structure and its field-dependence. Numerical simulations were constructed with the same geometry as the patterned specimens and under similar applied magnetic field conditions as tested by MFM. The results from simulations and experiments show that 1) magnetic domain structures strongly depend on the film geometry and the external applied field and 2) the predicted magnetic domain structures from the simulations agree quantitatively with those measured by MFM. The results demonstrate the capability of the developed model, used together with key experiments, for improving the understanding of the signal physics in magnetic sensing, thereby providing guidance to the development of advanced nondestructive magnetic techniques.

The magnetic hysteresis loops and Barkhausen noise of a single α-iron with nonmagnetic particles are simulated to investigate into the magnetic hardening due to Cu-rich precipitates in irradiated reactor pressure vessel (RPV) steels. Phase field method basing Landau-Lifshitz-Gilbert (LLG) equation is used for this simulation. The results show that the presence of the nonmagnetic particle could result in magnetic hardening by making the nucleation of reversed domains difficult. The coercive field is found to increase, while the intensity of Barkhausen noise voltage is decreased when the nonmagnetic particle is introduced. Simulations demonstrate the impact of nucleation field of reversed domains on the magnetization reversal behavior and the magnetic properties.

The magnetization reversal process and hysteresis loops in a single crystal α-iron with nonmagnetic particles are simulated in this work based on the Landau—Lifshitz—Gilbert equation. The evolutions of the magnetic domain morphology are studied, and our analyses show that the magnetization reversal process is affected by the interaction between the moving domain wall and the existing nonmagnetic particles. This interaction strongly depends on the size of the particles, and it is found that particles with a particular size contribute the most to magnetic hardening.

Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the evolution of the phases, composition, microstructure and morphology of such thin films. The phase-field model is quite general, describing compounds and solid solution alloys with sufficient freedom to choose solubilities, grain boundary and interface energies, and heats of segregation to all interfaces. We present analytical results which describe the interface profiles, with and without segregation, and confirm them using numerical simulations. We demonstrate that the present model accurately reproduces the theoretical grain boundary groove angles both at and far from equilibrium. As an example, we apply the phase-field model to the special case of a Ni(Pt)Si (Ni/Pt silicide) thin film on an initially flat silicon substrate., Comment: 12 pages, 5 figures, submitted to Modelling Simulation Mater. Sci. Eng

In this work, we developed a phase field model describing surface evolution dynamics of a strained solid in contact with gas phase. Elastic solutions are solved with an iteration method for the system in which a solid film, strained by the mismatch strain between the film and substrate, has anisotropic elastic constants and the vapor phase has zero elastic constants. Elastic solutions are incorporated into the phase field evolution equation. The model predicts stable morphology at a given mismatch strain and perturbation wavelength.

In this manuscript, we have quantitatively calculated the thermodynamic properties of the critical nuclei of Cr precipitates in FeCr alloys. The concentration profiles of the critical nuclei and nucleation energy barriers were predicted by the constrained shrinking dimer dynamics method. It is found that Cr concentration distribution in the critical nuclei strongly depends on the overall Cr concentration as well as on the temperature. The critical nuclei are non-classical because the concentration in the nuclei is smaller than the thermodynamic equilibrium value. These results are in agreement with atomic probe observation. The growth kinetics of both classical and non-classical nuclei was investigated by the phase-field approach. The simulations of critical nucleus evolution showed a number of interesting phenomena: (1) a critical classical nucleus first shrinks toward its non-classical nucleus and then grows; (2) a non-classical nucleus has much slower growth kinetics at its earlier growth stage compared to the diffusion-controlled growth kinetics and (3) a critical classical nucleus grows faster at the earlier growth stage than does a non-classical nucleus. All of these results demonstrate that it is critical to introduce the correct critical nuclei in order to correctly capture the kinetics of precipitation.

A phase-field model for predicting the domain structure evolution in constrained ferroelectric thin films is developed. It employs an analytical elastic solution derived for a constrained film with arbitrary eigenstrain distributions. In particular, the model is applied to the domain structure evolution during a cubic→tetragonal proper ferro- electric phase transition. The effect of substrate constraint on the volume fractions of domain variants, domain-wall orientations, and domain shapes is studied. It is shown that the predicted results agree very well with existing experimental observations in ferroelectric thin films.

Magnetic domain switching and hysteresis loops in a single crystal α-iron with and without nonmagnetic particles were simulated based on the Landau-Lifshitz-Gilbert equation of magnetization dynamics. Both the nonmagnetic particle and the 360° domain wall are nucleation sites of an antidirection domain during domain switching; however, the 360° Bloch domain wall is the easiest nucleation site. The nucleation occurs by splitting the 360° Bloch domain wall into two 180° Bloch domain walls. The existence of nonmagnetic particles could prevent the formation of 360° Bloch domain walls and cause magnetic hardening. Simulations demonstrate the impact of nonmagnetic particle sizes on magnetic domain switching and coercive field.

Interstitial loops are one of the principal evolving defects in irradiated materials. The evolution of interstitial loops, including spatial and size distributions, affects both vacancy and interstitial accumulations in the matrix, hence, void formation and volumetric swelling. In this work, a phase-field model describing the growth kinetics of interstitial loops in irradiated materials during aging is developed. The diffusion of vacancies and interstitials and the elastic interaction between interstitial loops and point defects are accounted in the model. The effects of interstitial concentration, chemical potential, and elastic interaction on the growth kinetics and stability of interstitial loops are investigated in two and three dimensions. It is found that the elastic interaction enhances the growth kinetics of interstitial loops. The elastic interaction also affects the stability of a small interstitial loop adjacent to a larger loop. The model predicts linear growth rates for interstitial loops that is in agreement with the previous theoretical predictions and experimental observations.

Orientation dependence of the longitudinal piezoelectric coefficients (d33∗) of a KNbO3 single crystal has been investigated as a function of temperature by using the Landau–Ginzburg–Devonshire phenomenological theory. It is shown that the maximum of d33∗ is not always along the polarization direction of the ferroelectric phase. The enhancement of d33∗ along a nonpolar direction is attributed to a ferroelectric phase transition at which a polarization changes its direction. In the tetragonal phase, the maximum of d33t∗ at high temperatures is along the tetragonal polar direction and then changes its direction toward the polar direction of the orthorhombic phase when the temperature is close to the tetragonal-orthorhombic phase transition. The maximum of d33o∗ of the orthorhombic phase depends on both the high-temperature and low temperature ferroelectric phase transitions. In the rhombohedral phase, the maximum of d33r∗ is relatively insensitive to temperature due to the absence of any further phase trans...

The Landau–Ginzburg–Devonshire phenomenological theory is employed to model and predict the ferroelectric phase transitions and properties of single-domain potassium niobate (KNbO3). Based on the LGD theory and the experimental data of KNbO3 single crystal, an eighth-order polynomial of free energy function is proposed. The fitted coefficients are validated by comparing to a set of experimental measured values including phase transition temperatures, spontaneous polarization, dielectric constants, and lattice constants. The effects of hydrostatic pressure and external electric field on phase transition temperatures and piezoelectric coefficients are investigated. The free energy function may be used to predict ferroelectric domain structures and properties of KNbO3 bulk and films by phase-field approach.

We investigated the influence of dislocations, located at the interface of a ferroelectric film and its underlying substrate, on the ferroelectric hysteresis loop including the remanent polarization and coercive field using phase-field simulations. We considered epitaxial ferroelectric BaTiO3 films and found that the hysteresis loop is strongly dependent on the type and density of interfacial dislocations. The dislocations that stabilize multiple ferroelectric variants and domains reduce the coercive field, and consequently, the corresponding remanent polarization also decreases.

A three-dimensional phase-field model was developed for studying domain structures in ferroelectric islands attached onto a substrate. It simultaneously takes into account the long-range electric and elastic interactions, substrate constraint, as well as the stress relaxation caused by the surfaces of an island. The phase-field simulations demonstrated that the domain structures of ferroelectric islands could be dramatically different from those of continuous thin films due to the change of stress state. The stress distribution inside islands is highly dependent on the aspect ratio of the islands. It provides us an effective way for engineering the domain structures of ferroelectric materials.

A phase-field model for investigating the surface morphological evolution of a film is developed, taking into account the surface energies of film and substrate, the interfacial energy between the film and substrate, and the elastic energy associated with the lattice mismatch between the film and substrate. Using the lattice mismatch and the surface energies for the Ge∕Si heteroepitaxial system, the morphology of islands and the formation of a wetting layer are investigated using two-dimensional simulations. The results show that the wetting angle increases continuously with the increase in the lattice mismatch, and the surface angle of the island on wetting layer varies with the island size. It is demonstrated that the anisotropy of elastic interactions alone is not sufficient to cause surface angle discontinuity or faceting that is observed in experiments.

Ferroelectric domain morphologies in (001) PbZr1−xTixO3 epitaxial thin films were studied using the phase-field approach. The film is assumed to have a stress-free top surface and is subject to a biaxial substrate constraint. Both the electrostatic open-circuit and short-circuit boundary conditions on the film surfaces were considered. The phase-field simulations indicated that in addition to the known tetragonal and rhombohedral phases, an orthorhombic phase becomes stable in films under large tensile constraints. The orthorhombic domain structure contains (100) and (010) 90° domain walls and (110) and (1–10) 180° domain walls. For the rhombohedral phase in a thin film, the domain walls are found to be along {101}, (100), and (010) of the prototypical cubic cell. It is shown that the short-circuit boundary condition and compressive substrate constraint enhance the out-of-plane polarization component while the open-circuit boundary condition and tensile substrate constraint suppress it. It is also shown t...

A 3-dimensional phase-field model is developed to describe the cubic to tetragonal martensitic phase transformation in a thin film attached to a substrate. Elasticity solutions are derived for both elastically anisotropic and isotropic thin films with arbitrary domain structures, subject to the mixed boundary conditions for stress-free and constrained states. The model is applied to an Fe-31%Ni alloy system. The nucleation process as well as the final domain structure strongly depends on the substrate constraint. At a smaller undercooling, the increased strain energy effect results in a lower volume fraction of martensite, a finer domain structure and a longer nucleation period.

Spinodal decomposition in a binary thin film is studied by a three-dimensional (3D) phase field model. A cubic thin film with an (001) orientation is considered. The focus is on the effect of the types of substrate constraint on the morphological evolution during spinodal decomposition as compared to the corresponding bulk. The elastic strain effect is incorporated by solving the elasticity equations for an elastically inhomogeneous thin film with a free surface and constrained by a substrate. Temporal evolution for the composition field, and thus the morphological evolution, is obtained by solving the Cahn-Hilliard equation using a semi-implicit Fourier-spectral method. It is shown that a biaxial substrate constraint has essentially no effect on the spinodally decomposed two-phase morphology which is primarily controlled by the cubically anisotropic elastic interactions. The asymmetry in the strain components along the [100] and [010] directions from the substrate constraint results in the preferential alignment along one of the two directions. In the particular case of a harder phase whose lattice parameter increases with composition, a tensile substrate constraint along the film plane leads to the alignment of two-phase microstructures parallel to the tensile direction.