Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Granasy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Granasy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystal-line solidification obtained using an atomistic phase-field model.
By comparing the grain sizes under different nucleation conditions, the different nucleation mechanisms were investigated. The primitive nuclei origin at some specific interface, and subsequently disperse into the bulk melt with melt flow. The survival probability of nuclei decides the nuclei density in bulk melt, and the growth of survived nuclei finally constitutes the solidified grains. The nucleation process is highly dynamic, evolving and variable with actual experimental condition and production condition.
A vector order parameter phase field model derived from a grand potential functional is presented as a new approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit. In addition, it is shown that grain boundary energy and solute back-d…
Homogeneous nucleation from aluminum (Al) melt was investigated by million-atom molecular dynamics (MD) simulations utilizing the second nearest neighbor modified embedded atom method (MEAM) potentials. The natural spontaneous homogenous nucleation from the Al melt was produced without any influence of pressure, free surface effects and impurities. Initially isothermal crystal nucleation from undercooled melt was studied at different constant temperatures, and later superheated Al melt was quenched with different cooling rates. The crystal structure of nuclei, critical nucleus size, critical t…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the two-dimensional case, where a single orientation field suffices, in three dimensions, minimum three fields are needed. The free energy of grain boundaries is assumed to be proportional to the angular difference between the adjacent crystals expressed here in terms of the differences of the four symmetric Euler parameters. The equations of motion for these fields are ob…
We investigated the homogenous nucleation of the stoichiometric B2 and B33 phases in the Ni50Zr50 alloy using the persistent embryo method and the classical nucleation theory. The two phases become very close competitors at large supercoolings, which is consistent with the experimental observations. In the case of the B2 phase, the linear temperature dependence of the solid-liquid interface (SLI) free energy extrapolated to the melting temperature leads to the same value as the one obtained from the capillarity fluctuation method (CFM). In the case of the B33 phases, the SLI free energy is als…
Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are examined, and it is shown that the antitrapping current is in general not sufficient to remove all thin-interface effects. Second, orientation-field models for polycrystalline solidification are analysed, and it is shown that the standard relaxational equation of motion for the orientation field is incorrect in coherent polycrystalline matter. Third, it is po…
This work provides unambiguous evidence for the occurrence of icosahedral quasicrystal (iQC) enhanced nucleation during selective laser melting of gas atomized commercially-pure Ni powders. This solidification mechanism, which has only been recently reported in a few alloys and has to date never been observed in pure metals, consists on the solidification of grains of the primary phase on the facets of iQCs formed due to the presence of icosahedral short range order in the liquid. The occurrence of iQC enhanced nucleation has been inferred from the observation in the SLM processed pure Ni samp…
Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Toth et al., J. Phys.: Condens. Matter 26, 055001 (2014)], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of di…
Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively parallel computer architectures such as Graphic Processing Units. However, one known drawback of this method is that the discretization of differential terms involving spatial derivatives introduces a spurious lattice anisotropy that can influence the solid-liquid interface dynamics. We find that this influence is significant for the case of polycrystalline …
During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than either solid phase. When the parent or both solid phases are morphologically unstable, i.e., for a small temperature gradient/growth rate ratio ($G/v_p$), one solid phase usually outgrows and covers the other phase, leading to a cellular-dendritic array structure closely analogous to the one formed during monophase solidification of a dilute binary alloy. In contrast, when $G/v_p$ is large enough for both p…
Understanding the underlying mechanism of crystal nucleation during solidification is a fundamental aspect in the prediction and control of materials properties. Classical nucleation theory (CNT) assumes that homogeneous nucleation occurs via random fluctuations within the supercooled liquid, that the structure of the growing clusters resembles the most stable bulk phase, and that the nucleus size is the sole reaction coordinate (RC) of the process. Many materials are, however, known to exhibit multiple steps during crystallization, forming different polymorphs. As a consequence, more complex …
Selective laser melting (SLM) is rapidly evolving to become a mainstream technology. However, the fundamental mechanisms of solidification and microstructure development inherent to the non-equilibrium conditions of this additive manufacturing method, which differ largely from those typical of conventional processing techniques, remain widely unknown. In this work, an in-depth characterization of the microstructure of Al7075 SLM processed samples, built from powder mixtures containing ZrH2 microparticles, demonstrates the occurrence of icosahedral quasicrystal-enhanced nucleation during laser …
The quantitative phase-field approach has been adapted to model solidification in the presence of Metal Matrix Nanocomposites (MMNCs) in a single-component liquid. Nanoparticles of fixed size and shape are represented by additional fields. The corresponding equations of motion are assumed to ensure relaxation dynamics, and can be supplemented by random forces (realizing Brownian motion) or external fields. The nanoparticles are characterized by two model parameters: their mobility and the contact angle they realize with the solid-liquid interface. We investigate the question how grain size dis…
We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a simple numerical implementation based on finite differences and step-wise approximations of parabolic dendritic branches of arbitrary orientation. Results of the two-dimensional model are verified against reference benchmark solutions for steady, unsteady, and buoyant flow, as well as steady-state dendritic growth in the diffusive regime. Simulations of equia…
We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3d, and determine the line free energy in 2d, the height of the nucleation barrier in 2d and 3d for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close packed structures (…
Crystallization represents a fundamental process engendering solidification of a material and determines its microstructure. Driven by complex phenomena at the atomic scale, its understanding for alloys still remains elusive. The present work proposes a large scale molecular dynamics simulation study of the homogeneous crystal nucleation pathways of prototypical undercooled Al-Ni binary alloys. An unsupervised topological learning analysis shows that the nucleation sets in first from a chemical ordering, followed by a bond-orientational ordering of the underlying crystal phase. Our results ind…
In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphisation requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and the liquid states. Taking into account rare nucleation events or structural relaxation under deep undercooling conditions requires much larger length scales and longer time scales than those achievable by \textit{ab initio} molecular dynamics (AIMD). This problem is addressed by means of classical MD simulations using a well established high dimensional neu…
The simulations of the solidification of ternary Al-Cu-Ni alloys by means of a general multi-phase-field model for an arbitrary number of phases reveal that the real microstructure can be generated by coupling the real thermodynamic parameters of the phases and the evolution equations. The stability requirements on individual interfaces for model functions guarantee an absence of "ghost" phases in a $n$-dimensional phase-field space. The special constructed thermal noise terms disturb the stability and can produce the heterogeneous nucleation of product phases in accordance to the energetic an…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the conventional phase-field approaches that rely on spatially averaged (coarse grained) order parameters in capturing freezing, and by the recently developed phase-field crystal models that work on the molecular scale, while employing time averaged particle densities, and are regarded as simple dynamical density functional theories of classical particles. Besi…
Operando study of the evolution of peritectic structures in metal solidification by quasi-simultaneous synchrotron X-ray diffraction and tomography
University of Hull（赫尔大学）；Westlake University（西湖大学）；Diamond Light Source Ltd.（钻石光源有限公司）；Research Complex at Harwell（哈韦尔研究综合体）；Kunming University of Science and Technology（昆明理工大学）
Nucleation during solidification in multi-component alloys is a complex process that comprises the competition between different crystalline phases as well as chemical composition and ordering. Here, we combine transition interface sampling with an extensive committor analysis to investigate the atomistic mechanisms during the initial stages of nucleation in $\text{Ni}_3\text{Al}$. The formation and growth of crystalline clusters from the melt are strongly influenced by the interplay between three descriptors: the size, crystallinity, and chemical short-range order of the emerging nuclei. We d…
We investigate the atomistic mechanism of homogeneous nucleation during solidification in molybdenum employing transition path sampling. The mechanism is characterized by the formation of a pre-structured region of high bond-orientational order in the supercooled liquid followed by the nucleation of the crystalline bulk phase within the center of the growing solid cluster. This precursor plays a crucial role in the process, as it provides a diffusive interface between the liquid and crystalline core, which lowers the interfacial free energy and facilitates the nucleation of the bulk phase. Fur…
In this work, the effect of building direction on the microstructure evolution of laser-powder bed fusion (LPBF) processed AlSi10Mg alloy was investigated. The building direction, as shown in experimentally fabricated parts, can influence the solidification behavior and promote morphological transitions in cellular dendritic microstructures. We develop a thermal model to systemically address the impact of laser processing conditions, and building direction on the thermal characteristics of the molten pool during laser processing of AlSi10Mg alloy. We then employ a multi-order parameter phase f…
The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that indicates the local direction of the crystallographic axes. The free-energy functionals of existing models generally contain a term proportional to the modulus of the orientation gradient, which complicates their mathematical analysis and induces artificial long-range interactions between grain boundaries. We present an alternative model, in which only the square of…
A broad range of computational models have been proposed to predict microstructure development during solidification processing but they have seldom been compared to each other on a quantitative and systematic basis. In this paper, we compare phase-field (PF) and cellular automaton (CA) simulations of polycrystalline growth in a two-dimensional melt pool under conditions relevant to additive manufacturing (powder-bed fusion). We compare the resulting grain structures using local (point-by-point) measurements, as well as averaged grain orientation distributions over several simulations. We expl…
In this research, atomistic molecular dynamics simulations are combined with mesoscopic phase-field computational methods in order to investigate phase-transformation in polycrystalline Aluminum microstructure. In fact, microstructural computational modeling of engineering materials could help to optimize their mechanical properties for industrial applications (e.g. directional solidification for turbine blades). As a result, a multiscale modeling approach is developed to find a relation between manufacturing variables (e.g. temperature) and microstructural properties of crystalline materials …
We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concen-tration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while post-solidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The complete data set, however, shows an unexpected scaling of the nucleation rate densit…
An original thermodynamically consistent large strains-based multiphase phase-field (PF) approach of Ginzburg-Landau type is developed for studying the grain boundary (GB)-induced martensitic transformations (MTs) in polycrystalline materials at the nanoscale considering the structural stresses within the interfaces. In this general PF approach, N independent order parameters are used for describing the austenite (A)<->martensite (M) transformations and N(>1) martensitic variants, and another M independent order parameters are considered for describing M(>1) grains in the polycrystalline sampl…
Nucleation is the onset of a first-order phase transition by which a metastable phase transforms into a more stable one. Such a phase transition occurs when an initial system initially in equilibrium is destabilized by the change of an external parameter like the temperature or the pressure. If the perturbation is small enough, the system does not become unstable but rather stays metastable. In diffusive transformations, the system then evolves through the nucleation, the growth and the coarsening of a second phase. Such a phase transformation is found in a lot of situations in materials scien…
We propose a computationally-efficient approach to multiscale simulation of polycrystalline materials, based on the phase field crystal (PFC) model. The order parameter describing the density profile at the nanoscale is reconstructed from its slowly-varying amplitude and phase, which satisfy rotationally-covariant equations derivable from the renormalization group. We validate the approach using the example of two-dimensional grain nucleation and growth.
A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of i…
By assuming a more realistic nucleation and polarization reversal scenario we build a new statistical switching model for ferroelectrics, which is different from either the Kolmogorov-Avrami-Ishibashi (KAI) model or the Nucleation-Limited-Switching (NLS) model. After incorporating a time-dependent depolarization field this model gives a good description about the retardation behavior in polycrystalline thin films at medium or low fields, which can not be described by the traditional KAI model. This model predicts correctly n=1 for polycrystalline thin films at high Eappl or ceramic bulks in th…
The crystal nucleation from liquid in most cases is too rare to be accessed within the limited timescales of the conventional molecular dynamics (MD) simulation. Here, we developed a "persistent embryo" method to facilitate crystal nucleation in MD simulations by preventing small crystal embryos from melting using external spring forces. We applied this method to the pure Ni case for a moderate undercooling where no nucleation can be observed in the conventional MD simulation, and obtained nucleation rate in good agreement with the experimental data. Moreover, the method is applied to simulate…
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal model…
Schrodinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type materials with capillarity and surface tension, which can undergo liquid-solid or liquid-gas phase transitions. One of the predictions of the theory is a periodic pattern of density inhomogeneities occurring in the form of either bubbles (topological phase), or cells (non-topological phase). Such inhomogeneities are described by solitonic solutions of a logarithmic wave equation, gaussons and kinks, in the vicinity of the liquid-solid phase transition. During the solidification process, …
Numerical simulations are used in this work to investigate aspects of microstructure and microsegregation during rapid solidification of a Ni-based superalloy in a laser powder bed fusion additive manufacturing process. Thermal modeling by finite element analysis simulates the laser melt pool, with surface temperatures in agreement with in situ thermographic measurements on Inconel 625. Geometric and thermal features of the simulated melt pools are extracted and used in subsequent mesoscale simulations. Solidification in the melt pool is simulated on two length scales. For the multicomponent a…
The thermal remagnetization (TR), i.e. the reentrance of magnetization upon heating in a steady-field demagnetized sample, is a common feature to the four types of polycrystalline permanent magnets, mainly utilized for practical purposes, i.e. barium ferrites, SmCo5, Sm2Co17 and NdFeB magnets. The effect is small for pinning controlled and large for nucleation controlled magnets. The effect is strongly dependent on the demagnetization factor and may reach nearly 100 per cent in SmCo5 samples measured in a closed circuit. The TR is very sensitive to a small superimposed steady field. The maximu…
Hexagonal boron nitride (h-BN) has attracted significant attention due to its superior properties as well as its potential as an ideal dielectric layer for graphene-based devices. The h-BN films obtained via chemical vapor deposition in earlier reports are always polycrystalline with small grains due to high nucleation density on substrates. Here we report the successful synthesis of large single-crystal h-BN grains on rational designed Cu-Ni alloy foils. It is found that the nucleation density can be greatly reduced to 60 per mm2 by optimizing Ni ratio in substrates. The strategy enables the …
Many time-dependent deformation processes at elevated temperatures produce significant concurrent microstructure changes that can alter the mechanical properties in a profound manner. Such microstructure evolution is usually absent in mesoscale deformation models and simulations. Here we present an integrated full-field modeling scheme that couples the mechanical response with the underlying microstructure evolution. As a first demonstration, we integrate a fast Fourier transform-based elasto-viscoplastic (FFT-EVP) model with a phase-field (PF) recrystallization model, and carry out three-dime…
We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Phi = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy of body centred cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we prepare the same samples also by slow and mechanically undisturbed deionization in commercial slit cells. These cells…
While biological crystallization processes have been studied on the microscale extensively, models addressing the mesoscale aspects of such phenomena are rare. In this work, we investigate whether the phase-field theory developed in materials science for describing complex polycrystalline structures on the mesoscale can be meaningfully adapted to model crystallization in biological systems. We demonstrate the abilities of the phase-field technique by modeling a range of microstructures observed in mollusk shells and coral skeletons, including granular, prismatic, sheet/columnar nacre, and spri…
The temperature dependencies of the resistivity for the superconducting ruthenocuprates of nominal compositions RuSr2GdCu2O8, Ru0.98Sr2GdCu2O8 and Ru0.5Sr2GdCu2.5O8-d were examined for the magnetic field dependent characteristics of the superconducting transitions. The effect of the insignificant diminishing of the Ru/Cu ratio in parent RuSr2GdCu2O8 was confirmed as relevant for the stabilisation of the superconducting phase. Noted differences in the compared characteristics are interpreted for possible inhomogeneous nucleation of the superconducting phase in the parent ruthenocuprate. The pha…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or repel each other depending on the degree of misorientation between impinging grains, temperature, composition, and stress. To characterize this interaction, we map the multi-phase-field equations for stationary interfaces to a multi-dimensional classical mechanical scattering problem. From the solution of this problem, we derive asymptotic forms for short-range…
