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The austenite/martensite (fcc/bcc) interface is prevalent across many new classes of high-strength steels, and yet both its fundamental structure and its mechanism of motion remain uncertain in spite of decades of research. Here, atomistic simulations are used to create an fcc-bcc iron interface having a structure and motion that match the major experimental observations on dislocated lath martensite. The simulated interface reveals a defect structure and a mechanism of glissile and athermal propagation that differ in important respects from longstanding assumptions. The atomistically-observed interface defects provide a basis for a parameter-free predictive crystallographic double-shear theory of lath martensite. Predictions of the theory match simulations well and yield very good agreement with experiments on Fe-Ni-Mn and Fe-C. The theory shows that the fcc/bcc lattice parameter ratio is the dominant factor for controlling the “shape” deformation – the overall, in-situ strain associated with the martensitic transformation – which is related to macroscopic toughening, and quantitatively rationalizes many experimental observations. This new understanding about the nature of this special interface provides fundamental insights needed for guiding design of emerging high-strength steels. [ABSTRACT FROM AUTHOR]

Ferroelectric switching in thin films is a local process strongly influenced by the presence and spatial distribution of defects such as dislocations, grain boundaries and preexisting domains. Preexisting ferroelastic domains have been shown to inhibit 180° switching in (001)-oriented epitaxial Pb(Zr 0.2 ,Ti 0.8 )O 3 (PZT) films, but ferroelectric switching pathways around these domains remain unclear. Here, phase field modeling with supporting high resolution transmission electron microscopy is used to investigate ferroelectric switching in PZT thin films around such a ferroelastic domain. We show 180° domain wall motion is arrested at moderate applied biases by the ferroelastic domain through formation of charged 90° domain walls during switching. This leads to an increased applied bias required for complete switching through the thin film. Charged 90° ferroelastic domain walls are found to be partially stabilized by local rotation of the polarization direction and significant broadening of the head-to-head wall to distribute the bound charge, leading to domain walls 5–6 nm in thickness compared to 0.5–2 nm for typical 90° domain walls. Ferroelectric switching continues only at higher applied electric fields. This study provides a more complete picture of the ferroelectric switching pathway around ferroelastic domains than has been previously available and may explain the experimentally observed lower stability of written domain structures around preexisting ferroelastic domain structures in epitaxial ferroelectric thin films. [ABSTRACT FROM AUTHOR]

Impurity atoms segregated in grain boundary (GB) regions can dramatically change the physical and chemical properties of the GBs. Such changes often appear to be attributed to the GB energy reduction and/or solute drag effect. Phase-field models have been utilized to clarify both the thermodynamic and kinetic effects of the GB segregation. In this study, we developed phase-field models for GB segregation that are diffuse interface versions of the classical two-phase model of GB segregation. The thermodynamic state at any point in the system is represented as a mixture of a GB phase and a matrix phase. There are two choices for the thermodynamic relation between the GB phase and the matrix phase that constitute the point: the equal composition condition in model I and the equal diffusion potential condition in model II. Most of the previous PFMs for GB segregation appear to be specific cases of model I. We examined the thermodynamic properties of models I and II, and compared them with each other and the classical two-phase model. Although all the models resulted in the same GB composition, the GB energy and its dependency on the composition at the equilibrium state are quite different from each other. In model I, there is a lower bound to the GB energy, which originates from the equal composition condition. The GB energy from model II shows no such lower bound, and it is represented as the vertical distance between the parallel tangent lines on the free energy diagram, as in the classical two-phase model. Nevertheless, the compositional dependence in the model II is quite different from that in the classical two-phase model. This originates from the different choices for the composition-independent parameter in the models: a constant gradient energy coefficient in model II and a constant GB width in the classical two-phase model. Model I is not suitable for simulations of alloys that show a reduction of the GB energy due to GB segregation below a certain limit (in dilute alloys, about half of the GB energy of pure solvents). Model II is a correct choice for such alloys. [ABSTRACT FROM AUTHOR]

Interdiffusion microstructure maps (IMMs) are drawn on isothermal phase diagrams. They predict how the interdiffusion microstructure varies in a dual alloy when one alloy composition is fixed while the other is varied across a region of the phase diagram. The microstructure is defined in terms of its layers and the velocity direction of boundaries between layers. Previous work involved maps based on experimental, calculated and simulated interdiffusion microstructures. In the current work IMMs for four model systems were obtained from phase field simulations. The IMMs in this study differ from previous work in that one contains a more complicated IMM with seven areas separated by seven lines that meet at a seven-line node and one contains a less complicated IMM with only one area. Also, it was found that the microstructures at all nodes investigated to date are similar by having the microstructure of the initial dual alloy. During interdiffusion treatments the initial interface is stationary and only the amounts of phases on either side of the interface will vary with time. A list of fundamental properties of IMMs is given that combines findings from the current and previous work. In the list are three mechanisms by which microstructures change. One of these had not been seen before. In this mechanism an inversion of the microstructure occurs as the composition crosses from one side to the other of a two-phase region. These fundamentals are the foundation on which IMMs are constructed and can be a guide for their interpretation. [ABSTRACT FROM AUTHOR]

Abstract: The phenomenon of high twin boundary fractions found experimentally for neighboring γ lamellae in fully lamellar TiAl alloys was investigated by phase-field simulations. The nucleation and growth processes during transformation that leads to the lamellar structure were simulated. In particular, the effects of coherency stress and the interfacial energy difference among different types of interfaces and undercooling on the nucleation mechanism were analyzed. It is found that the twin boundary fraction increases with increasing coherency elastic strain energy and increasing interfacial energy difference among different types of interfaces, and with decreasing undercooling. Depending on the relative contributions of these factors, the nucleation events simulated by the Langevin noises could be collective, correlated or independent. These findings could shed light on the control of twin boundary fraction within lamellar structures by adjusting alloy composition and cooling route. [Copyright &y& Elsevier]

Abstract: Using the phase-field crystal model, we investigate the orientation selection of the cubic dendrite growth at the atomic scale. Our simulation results reproduce how a face-centered cubic (fcc) octahedral nucleus and a body-centered cubic (bcc) truncated-rhombic dodecahedral nucleus choose the preferred growth direction and then evolve into the dendrite pattern. The interface energy anisotropy inherent in the fcc crystal structure leads to the fastest growth velocity in the 〈100〉 directions. New {111} atomic layers prefer to nucleate at positions near the tips of the fcc octahedron, which leads to the directed growth of the fcc dendrite tips in the 〈100〉 directions. A similar orientation selection process is also found during the early stage of bcc dendrite growth. The orientation selection regime obtained by phase-field crystal simulation is helpful for understanding the orientation selection processes of real dendrite growth. [Copyright &y& Elsevier]

Abstract: Cracks in brittle solids induced by pyramidal indenters are ideal for toughness evaluation since the indentation stress fields decay rapidly from the contact center and any cracks will be eventually arrested. Thus, if the applied energy release rate can be determined analytically, the material toughness can be deduced by measuring the crack length. However, such a driving force calculation is a nontrivial task because of the complex stress fields; only a number of limit cases can be solved, such as the long half-penny cracks (at least two times larger than the contact size) in the classic Lawn–Evans–Marshall (LEM) model. Important questions such as the evolution from short cracks to median/radial and then to half-penny cracks, the form of the scaling relationship that relates fracture toughness to material hardness and indenter angles, the threshold load for indentation cracking, etc., cannot easily be answered without a detailed knowledge of the co-evolution history of the stress fields and crack morphology. To this end, a finite element model of four-sided pyramidal indentation adopting cohesive interface elements is developed to study the effects of indenter geometry, load, cohesive interface parameters, and material properties on the initiation and propagation of the median/radial/half-penny crack systems. The validity and artifacts of the cohesive interface model are carefully examined, and the crack morphologies under various indentation and material parameters are systematically studied. Numerical predictions lead to a quantitative evaluation of the threshold load for indentation fracture, and an improved method for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, which compare favorably to a large set of experiments in the literature. It is also found that the toughness evaluation method is very sensitive to Poisson’s ratio – an observation that has previously received little attentions. An approximate analysis for short cracks is developed based on the fracture mechanics of annular cracks and the embedded-center-of-dilatation model for indentation-induced residual stress fields. [Copyright &y& Elsevier]

Abstract: The atomistic structure of solid Ni–Al2O3 interfaces at equilibrium was determined by aberration-corrected transmission electron microscopy, from specimens formed during solid-state dewetting of thin Ni films on the (0001) surface of α-Al2O3. It was found that the interface develops a unique mechanism for misfit strain reduction, termed delocalized coherency, via a reconstructed interface structure, contradicting most simulations in the literature, which assume a semi-coherent structure for this system. Based on the experimental work presented here, a structural model was also simulated, showing periodic buckling of the terminating Ni layer (i.e. interface reconstruction). The interface energy was experimentally determined from dewetted Ni particles using Winterbottom analysis, and found to be 2.16±0.2Jm–2 at P(O2)=10−20 atm and T =1623K. [Copyright &y& Elsevier]

Abstract: Using atomistic simulations, we reveal the role of the atomic interface structure on the nucleation of glissile dislocations from a low-energy, atomically flat, incoherent face-centered cubic–body-centered cubic interface with a Kurdjumov–Sachs orientation relationship. Several loading states are simulated to systematically probe the selection of slip systems. Contrary to conventional expectation, the preferred nucleation sites are not always associated with pre-existing misfit dislocations, and the preferred slip systems are not determined solely by the Schmid factor. Amongst the two or more systems that may be geometrically favored, the activated slip system depends on the structure of the nucleation site. The system–site combination is such that the dislocation deposited in the interface after the nucleation event lowers the interfacial energy and has a relatively low self-energy. The fundamental correlations established here apply to interfaces of other orientation relationships that are also flat and have spatially non-uniform shear resistance. [Copyright &y& Elsevier]

Abstract: Vacancy-mediated interdiffusion in coherent Mo/V and Cu/Ni multilayers is simulated to evaluate the effects of coherency stress and vacancy sources/sinks on interface sharpening and the intermixing rate, using the phase field model developed in a previous paper for two limiting cases: ideal vacancy sources/sinks densely distributed or not present at all. Interface sharpening stems from a large diffusion coefficient asymmetry across the interface, which in turn originates from the large difference in vacancy formation and migration energies between the two constituent layers. Remarkable sharpening is found in Mo/V multilayers either with dense or without vacancy sources/sinks, but only in Cu/Ni with a high density of sources/sinks. Sharpening is suppressed by coherency stress in Cu/Ni regardless of the existence of vacancy sources/sinks, but only promoted in Mo/V with a high density of sources/sinks. The intermixing rate is suppressed in Mo/V by the introduction of a high density of vacancy sources/sinks that are parallel or perpendicular to the interfaces, or uniformly distributed in all orientations, but only promoted in Cu/Ni by the introduction of vacancy sources/sinks that are parallel to the interfaces. The intermixing rate is promoted in Mo/V by coherency stress regardless of the existence of vacancy sources/sinks, but promoted in Cu/Ni by coherency stress only when the vacancy sources/sinks are parallel to the interface or not present at all. The effects of that part of coherency stress induced by the mismatch in atomic volumes on interface sharpening and the intermixing rate are opposite to, but dominant over, those of the stress induced by lattice creation/annihilation in vacancy sources/sinks. [Copyright &y& Elsevier]

Abstract: A three-dimensional (3-D) multiphase-field model has been developed in order to study the formation of a micropore constrained to grow in a solid network (i.e. pinching effect). The model accounts for the pressure difference due to capillarity between liquid and gas, the equilibrium condition at triple (solid–liquid–pore) lines, and the partitioning and diffusion of dissolved gases such as hydrogen. From the predicted 3-D morphology of the pore, entities such as the interfacial shape distribution are plotted and analyzed. It is shown that the mean curvature of the pore–liquid surface, and thus also the pressure inside the pore, is uniform. The results are then compared with analytical pinching models. While predicting a similar trend, analytical models tend to underestimate the pore curvature at high solid fractions. Despite the complex morphology of pores reconstructed using high-resolution X-ray tomography, the present phase-field results suggest that a simple pinching model based on a spherical tip growing in between remaining liquid channels is a fairly good approximation. [Copyright &y& Elsevier]

Abstract: A particle-based front tracking method for phase transformation problems is combined with the meshless diffuse approximation method (DAM) and implemented on a two-dimensional unstructured, amorphous grid. The resulting novel method is capable of completely disposing of the grid anisotropy effects common to moving interface problems, as the underlying grid itself has no distinguished direction. The particles track the interface directly and are embedded in the irregular grid by associating each tracking particle with a pair of grid nodes of different phases. This allows for a straightforward treatment of nodes that are subject to a change of phase. The conservation equation at the interface is solved explicitly at the location of the particles. The interface geometry is calculated from the particles’ position by a modified local least squares fitting method. The resulting meshless front tracking method is tested on sample solidification problems in one and two dimensions. An excellent match with analytical and published numerical results is found. [Copyright &y& Elsevier]

Abstract: The interfaces between different materials can be coherent (heteroepitaxial), semi-coherent or incoherent. A semi-coherent interface is one in which the misfit between the two phases is partially or fully accommodated by discrete interfacial dislocations. A precipitate–matrix interface may undergo a transition from coherent to semi-coherent through dislocation nucleation or interactions with pre-existing dislocations during plastic deformation. Dislocation–precipitate interactions can also be modified significantly by the degree of coherency of the interface. In this study, we examine how plasticity mediates the change from coherent to semi-coherent interfaces in the case of a misfitting spherical particle, i.e. how the matrix dislocations relax the misfit of the particle and form dislocation structures on the particle–matrix interface. Various stable dislocation structures on the semi-coherent particles are studied. We also examine how dislocation–particle interactions are influenced by the change in the particle from coherent to semi-coherent. These simulations are performed using a three-dimensional level set dislocation dynamics method. [Copyright &y& Elsevier]

Abstract: Partitioning at phase boundaries of complex steels is important for their properties. We present atom probe tomography results across martensite/austenite interfaces in a precipitation-hardened maraging-TRIP steel (12.2 Mn, 1.9 Ni, 0.6 Mo, 1.2 Ti, 0.3 Al; at.%). The system reveals compositional changes at the phase boundaries: Mn and Ni are enriched while Ti, Al, Mo and Fe are depleted. More specific, we observe up to 27 at.% Mn in a 20nm layer at the phase boundary. This is explained by the large difference in diffusivity between martensite and austenite. The high diffusivity in martensite leads to a Mn flux towards the retained austenite. The low diffusivity in the austenite does not allow accommodation of this flux. Consequently, the austenite grows with a Mn composition given by local equilibrium. The interpretation is based on DICTRA and mixed-mode diffusion calculations (using a finite interface mobility). [ABSTRACT FROM AUTHOR]

Abstract: The partitioning of rotations is considered for two-phase interfaces. In the isotropic, linear elastic approximation, the rotations associated with tilt components of interface dislocations and disconnections partition equally to the two phases. With anisotropic elasticity and with nonlinearities, the partitioning is unequal. Results for linear anisotropic elasticity, average anisotropic elasticity and nonlinear effects as incorporated in an atomistic simulation are compared. The results also apply to most cases of single phase grain boundaries. The results of the atomistic simulations are as predicted in the topological theory of phase transformation. The results have implications for habit plane determination in phase transformations, for the relief of coherency stresses at interfaces, and for boundary conditions in atomistic simulations. [ABSTRACT FROM AUTHOR]

Abstract: We study spacing selection in directional solidification of Al–Cu alloys under transient growth conditions. New experimental results are presented which reveal that the mean dendritic spacing vs. solidification front speed exhibits plateau-like regions separated by regions of rapid change, consistent with previous experiments of Losert and co-workers. Quantitative phase-field simulations of directional solidification with dynamical growth conditions approximating those in the experiments confirm this behavior. The mechanism of this type of change in mean dendrite arm spacing is consistent with the notion that a driven periodically modulated interface must overcome an energy barrier before becoming unstable, in accord with a previous theory of Langer and co-workers. [Copyright &y& Elsevier]

Abstract: A quantitative phase-field model for two-phase solidification processes is developed based on the anti-trapping current approach with the free energy functional formulated to suppress the formation of an extra phase at the interface. This model appropriately recovers the free boundary problem for the motion of interface in the thin-interface limit and, importantly, it is applicable to the solidification process in binary alloy systems with arbitrary values of the solid diffusivities and interfacial energies. The performance of the present model is investigated for the peritectic reaction process in carbon steel. The present model exhibits excellent convergence behavior with respect to the interface thickness. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the early stages of the morphological evolution of intermetallic compounds (IMCs) during lead-free soldering involving liquid Sn-based solder and Cu substrate considering the heterogeneous nucleation of the IMCs. The simulation is performed through the multi-phase-field approach . Initially, the liquid Sn-based solder and the Cu substrate are considered to be at metastable local equilibrium. Nucleation at the solder/substrate interface is modeled by considering it to be a Poisson process. The phase-field simulation accounts for variations in grain boundary diffusion in the η phase and interface energies between the η phase and liquid solder, and uses these variations to investigate the multiplicity of soldering reactions, and make comparisons with previous work . The simulations address the kinetics of the IMC growth during lead-free soldering under the effect of nucleation at an early stage, illustrating the variation in Cu substrate thickness, IMC thickness and number of grains that nucleate or disappear due to grain growth-induced coalescence. [Copyright &y& Elsevier]

Abstract: Using “tunable” interatomic potentials, the dilute heats of mixing for a face-centered cubic–body-centered cubic (fcc–bcc) metal system have been varied in atomistic models, while keeping the Kurdjumov–Sachs crystallographic orientation relationship and the lattice misfit strain constant. As a result of varying the heats of mixing, the atomic structure of the interface is not significantly altered. Interstitial formation energies at interfaces are quite dependent on the heats of mixing, while vacancy formation energies at interfaces are less so. However, variation in heats of mixing has a strong influence on both the interfacial shear strength and the active shear plane at the interface. The critical stress for interface shear increases continuously with decreasing positive heat of mixing, but begins to decrease as the heat of mixing becomes negative since the active shear plane at the interface changes from fcc–bcc to fcc–fcc. The energy landscape for planar faults near the interface was investigated to understand these phenomena. [Copyright &y& Elsevier]

Abstract: A multi-phase field model for quantitative simulations of polycrystalline solidification of binary alloys is introduced. During the free-growth stage of solidification, the model exploits the thin-interface analysis developed by Karma [3] in order to realistically capture bulk phase diffusion and the sharp interface corrections predicted by traditional models of solidification. During grain boundary coalescence, the model is constructed to reproduce the properties of repulsive grain boundaries described by Rappaz et al. [29]. The model provides a very simple mechanism for decoupling of solute and concentration fields at steady state, an important feature for calculating grain boundary energies. [Copyright &y& Elsevier]

Abstract: Molecular dynamics (MD) within the framework of the embedded atom method and the first-principles discrete variational method (DVM) are both used to study the effect of Re in the γ phase, the phase and the interface of Ni-based single-crystal superalloys. From the MD relaxation it is found that the interface only has two atomic configurations, i.e. a coherent region and a misfit dislocation region, and the “cage-like” misfit dislocation networks, consist of {001} edge dislocations winding over the precipitate phase. The MD results also show that the substitution atom Re stabilizes both the γ phase and the phase, and influences the degree of mismatch between γ and . From the simulation results we find that Re atoms have a tendency to cluster in both the γ phase and the phase. Based on the MD simulation we have chosen six clusters of the interface for the DVM study, in which the interatomic energy, the charge distribution, the partial density of states and the electron density difference are all calculated. It is found that a Re atom occupying either a Ni site in the γ phase or an Al site in the phase can strongly enhance the bonding strength between Re and its nearest neighboring atoms, suggesting that the substitution atom Re will influence dislocation motion along the interface. [Copyright &y& Elsevier]

Abstract: We present phase-field simulations of isothermal phase transformations in the peritectic system below and above the peritectic temperature. The physical processes involved are of different natures, involving either a triple junction or a liquid-film-migration (LFM) mechanism. Below the peritectic temperature, one of the solid phases steadily grows along the other. Above the peritectic temperature the phase transformation proceeds via the LFM mechanism. To the best of our knowledge, this mechanism has not been discussed in the literature as a generic process of phase transitions in peritectic systems. In addition to the LFM process, we also simulate melting along the solid–solid interface. Finally, we make a simplified linear stability analysis of the liquid film, supporting our simulation results. [Copyright &y& Elsevier]

Abstract: Atomic-level modeling of materials provides fundamental insights into phase stability, structure and properties of crystalline defects, and to physical mechanisms of many processes ranging from atomic diffusion to interface migration. This knowledge often serves as a guide for the development of mesoscopic and macroscopic continuum models, with input parameters provided by atomistic models. This paper gives an overview of the most recent developments in the area of atomistic modeling with emphasis on interfaces and their impact on microstructure and properties of materials. Modern computer simulation methodologies are discussed and illustrated by several applications related to thermodynamic, kinetic and mechanical properties of materials. Existing challenges and future research directions in this field are outlined. [Copyright &y& Elsevier]

Abstract: Phase-field modeling has been performed to study the domain morphologies of ferroelectric PbTiO3/SrTiO3 superlattice grown on SrTiO3 substrates. Taking into account contributions of the interfacial and depolarization field effects, the polarization, phase transition temperature and critical thickness are calculated as functions of sample dimensions and temperature. The results show that interfacial and depolarization field effects are the main reasons behind the dependence of the domain structures and critical properties (i.e., the phase transition temperature and critical thickness) on the thicknesses of the constituent layers of the PbTiO3/SrTiO3 superlattices. [Copyright &y& Elsevier]

Abstract: The quenching and partitioning (Q&P) process is a new heat treatment for the creation of advanced high-strength steels. This treatment consists of an initial partial or full austenitization, followed by a quench to form a controlled amount of martensite and an annealing step to partition carbon atoms from the martensite to the austenite. In this work, the microstructural evolution during annealing of martensite–austenite grain assemblies has been analyzed by means of a modeling approach that considers the influence of martensite–austenite interface migration on the kinetics of carbon partitioning. Carbide precipitation is precluded in the model, and three different assumptions about interface mobility are considered, ranging from a completely immobile interface to the relatively high mobility of an incoherent ferrite–austenite interface. Simulations indicate that different interface mobilities lead to profound differences in the evolution of microstructure that is predicted during annealing. [Copyright &y& Elsevier]

Abstract: An expression for anisotropic interfacial energy of hexagonal close-packed metals has been formulated which is able to reproduce published data obtained using the modified embedded-atom method, covering the variation in interface energy as a function of orientation for a number of metals. The coefficients associated with the expression can be determined fully by measured or calculated interfacial energies of just three independent crystal planes. Three-dimensional phase-field model simulations using this representation of interfacial energy have been found to yield convincing crystal morphologies. The apparent rate of crystal growth as a function of orientation in the phase-field simulation agrees with predictions made by surface energy theory. [Copyright &y& Elsevier]

Abstract: This paper reports on atomistic simulations of the interactions between the dominant lattice dislocations in γ-TiAl (ordinary screw and 〈101] superdislocations) with all three kinds of γ/γ-lamellar boundaries in polysynthetically twinned (PST) TiAl. The purpose of this study is to clarify the early stage of lamellar boundary controlled plastic deformation in PST TiAl. The interatomic interactions in our simulations are described by a bond order potential for L10-TiAl which provides a proper quantum mechanical description of the bonding. We are interested in the dislocation core geometries that the lattice produces in proximity to lamellar boundaries and the way in which these cores are affected by the elastic and atomistic effects of dislocation-lamellar boundary interaction. We study the way in which the interfaces affect the activation of ordinary dislocation and superdislocation slip inside the γ-lamellae and transfer of plastic deformation across lamellar boundaries. We find three new phenomena in the atomic-scale plasticity of PST TiAl, particularly due to elastic and atomic mismatch associated with the 60° and 120° γ/γ-interfaces: (i) two new roles of the γ/γ-interfaces, i.e. decomposition of superdislocations within 120° and 60° interfaces and subsequent detachment of a single ordinary dislocation and (ii) blocking of ordinary dislocations by 60° and 120° interfaces resulting in the emission of a twinning dislocation. [Copyright &y& Elsevier]

Abstract: Modified embedded-atom method (MEAM) interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems have been developed based on the previously developed MEAM potentials for sub-unary and binary systems. An attempt was made to find a way to determine ternary potential parameters using the corresponding binary parameters. The calculated coherent interface properties, interfacial energy, work of separation and misfit strain energy between body-centered cubic Fe and NaCl-type TiC or TiN were reasonable when compared with relevant first-principles calculations under the same condition. The applicability of the present potentials for atomistic simulations to investigate nucleation kinetics of TiC or TiN precipitates and their effects on mechanical properties in steels is also demonstrated. [Copyright &y& Elsevier]

Abstract: An expression is proposed for the anisotropy of interfacial energy of cubic metals, based on the symmetry of the crystal structure. The associated coefficients can be determined experimentally or assessed using computational methods. Calculations demonstrate an average relative error of <3% in comparison with the embedded-atom data for face-centred cubic metals. For body-centred-cubic metals, the errors are around 7% due to discrepancies at the {332} and {433} planes. The coefficients for the {100}, {110}, {111} and {210} planes are well behaved and can be used to simulate the consequences of interfacial anisotropy. The results have been applied in three-dimensional phase-field modelling of the evolution of crystal shapes, and the outcomes have been compared favourably with equilibrium shapes expected from Wulff’s theorem. [Copyright &y& Elsevier]

Abstract: The effect of an intergranular amorphous film on grain growth behavior has been studied in a faceted model system, BaTiO3. We prepared two kinds of samples with and without intergranular amorphous films but with the same grain size and density. During annealing the samples at 1350°C in air, abnormal grain growth occurred in samples with intergranular amorphous films while grain growth was inhibited in samples with dry boundaries, indicating the presence of a pinning force in samples with dry boundaries. To compare the mobilities of dry and wet boundaries, single crystal and polycrystal bilayer samples with or without amorphous films were prepared and annealed at 1340°C. In contrast to the observed grain growth behavior in polycrystals, the growth of the single crystal into the polycrystal with dry boundaries was faster than that into the polycrystal with wet boundaries, demonstrating the higher mobility of a dry boundary, unlike the conventional understanding. [Copyright &y& Elsevier]

Abstract: The phase-field approach is used to study the formation and ageing of bimodal microstructures in a model Ni-based superalloy. Particular attention is paid to the definition of interfacial energies in the presence of elastic strain fields and to the incorporation of these energies in the phase-field formalism. During a two-step annealing procedure, our model predicts the formation of large anisotropic precipitates (called secondary precipitates) and small, almost isotropic precipitates (called tertiary precipitates). Finally, the phase-field model is used to characterize the ageing of tertiary precipitates. In agreement with experiments, we show that the mean size of the tertiary precipitates first grows as and finally reaches a plateau. This peculiar behavior is explained using phase-field simulations with prescribed geometries and with the development of a simple analytic model. [Copyright &y& Elsevier]

Abstract: A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that the structure and steady-state growth velocity of spatially periodic precipitation fronts depend strongly on the relative magnitudes of the diffusion coefficients. Steady-state solutions always exist for a range of interlamellar spacings that is limited by a fold singularity for low spacings, and by the onset of tip-splitting or oscillatory instabilities for large spacings. A detailed analysis of the simulation data reveals that the hypothesis of local equilibrium at interfaces, used in previous theories, is not valid for the typical conditions of discontinuous precipitation. [Copyright &y& Elsevier]

Abstract: The phase field method has been used to simulate the austenite-to-ferrite phase transformation in steel, for the first time in three-dimensional (3D) space. The effect of the exact morphology of the initial 3D austenitic microstructure is shown to be small, but the nucleus density and the temperature range in which nucleation takes place, both derived from experimental observations, are of primary importance for the kinetics. When 3D simulations are compared to two-dimensional (2D) simulations, it becomes evident that 2D simulations predict faster transformation rates. In the often-used practice of considering the interface mobility as an adjustable model parameter, systematically too low values will be obtained if 2D simulations are compared with experiments. Moreover, unrealistic features can be observed in the simulated 2D microstructures, whereas the 3D microstructures show a realistic representation of the actual microstructure. The overall conclusion is therefore that phase field modelling is distinctly more powerful when applied in 3D space. [Copyright &y& Elsevier]