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While biological crystallization processes have been studied on the microscale extensively, there is a general lack of models addressing the mesoscale aspects of such phenomena. 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 sprinkled spherulitic structures. We also compare two possible micromechanisms of calcification: the classical route, via ion-by-ion addition from a fluid state, and a nonclassical route, crystallization of an amorphous precursor deposited at the solidification front. We show that with an appropriate choice of the model parameters, microstructures similar to those found in biomineralized systems can be obtained along both routes, though the time-scale of the nonclassical route appears to be more realistic. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be understood with simple math and simulated by phase-field theory.

Safety valves are the most important safety devices of the pressure system. For safety valves in the vast majority of cases in industrial environment, direct spring-loaded safety valves are used. The most important parameter of the equation of motion is the flow force. The main goal of the analysis was to compare the simulated flow forces with the measured results and validating the computational fluid dynamics model. Simulations were made in ANSYS 2019 R1 code for numerous fixed valve disk positions on different pressures. Results are in good agreement with the measured data.

Spherulites are radial distributions of acicular crystals, common in biogenic, geologic, and synthetic systems, yet exactly how spherulitic crystals nucleate and grow is still poorly understood. To investigate these processes in more detail, we chose scleractinian corals as a model system, because they are well known to form their skeletons from aragonite (CaCO3) spherulites, and because a comparative study of crystal structures across coral species has not been performed previously. We observed that all 12 diverse coral species analyzed here exhibit plumose spherulites in their skeletons, with well-defined centers of calcification (CoCs), and crystalline fibers radiating from them. In 7 of the 12 species, we observed a skeletal structural motif not observed previously: randomly oriented, equant crystals, which we termed "sprinkles". In Acropora pharaonis, these sprinkles are localized at the CoCs, while in 6 other species, sprinkles are either layered at the growth front (GF) of the spherulites, or randomly distributed. At the nano- and micro-scale, coral skeletons fill space as much as single crystals of aragonite. Based on these observations, we tentatively propose a spherulite formation mechanism in which growth front nucleation (GFN) of randomly oriented sprinkles, competition for space, and coarsening produce spherulites, rather than the previously assumed slightly misoriented nucleations termed "non-crystallographic branching". Phase-field simulations support this mechanism, and, using a minimal set of thermodynamic parameters, are able to reproduce all of the microstructural variation observed experimentally in all of the investigated coral skeletons. Beyond coral skeletons, other spherulitic systems, from aspirin to semicrystalline polymers and chocolate, may also form according to the mechanism for spherulite formation proposed here. STATEMENT OF SIGNIFICANCE: Understanding the fundamental mechanisms of spherulite nucleation and growth has broad ranging applications in the fields of metallurgy, polymers, food science, and pharmaceutical production. Using the skeletons of reef-building corals as a model system for investigating these processes, we propose a new spherulite growth mechanism that can not only explain the micro-structural diversity observed in distantly related coral species, but may point to a universal growth mechanism in a wide range of biologically and technologically relevant spherulitic materials systems.

In this paper the back pressure of direct spring loaded safety valves were studied at different blow-down cases. The examined system was described and the different blow-down cases were specified. For back pressure calculation detailed calculation method was described. Results of the calculation were shown on figures and on tables. Simulation method for determining back pressure was also described. Calculated and simulated back pressure values were compared with each other and the results converged very well to each other. The value of the back pressures were higher than 10% of the set pressure in every cases which is not allowed for this type of safety valves. Proposal was given for the stable operation of the safety valve.

One of the most commonly used pressure vessels are the heat exchangers, in which the heat transfer operation takes place, the higher enthalpy medium transmits energy to the other lower enthalpy medium. These equipment are used in refrigeration systems, heat engines, metallurgy, chemical and many other industries. This study presents a theoretical and practical investigation method of the eigenfrequency of such a special heat exchanger, a vertical condensator.

The authors met the following problem in connection with previous industrial assignments: the maximum mass flow through a given pressure control valve which determined according to a sizing guide recommended by some control valve manufacturer, underestimates both the actual value and the value calculated according to EN 60534. In this article, the authors compared these estimations with the calculations according to the EN 60534 standard, as well as with the results provided by the ARI Armaturen fitting manufacturer's own sizing software and the ChemCad simulation software. Our tests were performed on water and nitrogen at 20°C. Pressure of the medium entering the control valve was varied between 3 bara and 30 bara, while the outlet pressure was kept at 2 bara. The maximum flow factor of a globe type valve with V-port plug was taken to be in each case.

The phase-field and lattice Boltzmann methods have been combined to simulate the growth of solid particles moving in melt flow. To handle mobile particles, an overlapping multigrid scheme was developed, in which each individual particle has its own moving grid, with local fields attached to it. Using this approach we were able to simulate simultaneous binary solidification, solute diffusion, melt flow, solid motion, the effect of gravity, and collision of the particles. The method has been applied for describing two possible modes of columnar to equiaxed transition in the Al–Ti system.

International audience; We investigated the Fe-Fe 2 Ti eutectic microstructure obtained by Direct Energy Deposition (DED) with a hypereutectic composition of Fe-17.6 at.% Ti. Ultrafine lamellar spacings as low as 200 nm were achieved, features which otherwise can only be obtained in thin specimens, e.g. by suction casting. However, at interlayer boundaries (ILBs) a globular morphology of the primary Fe 2 Ti phase is observed with halos of the Fe phase. For the given DED conditions the crystalline structure is thus discontinuous across the ILBs. Both 2D and 3D analysis methods were used to quantify the microstructure, including high resolution synchrotron holographic X-ray computed tomography (HXCT). The generic behaviour of eutectic systems under conditions that qualitatively correspond to those of laser additive manufacturing was explored by phase-field modelling for selected nucleation scenarios and alloy compositions spanning from eutectic to hyper-eutectic. While providing valuable insights into microstructure formation, the simulations point out the need to further deepen our understanding about melting under additive manufacturing conditions in order to implement suitable nucleation and / or free growth models. The simulations also show that globular ILBs can be prevented when using exactly eutectic alloy compositions.

A simple phase-field model is used to address anisotropic eutectic freezing on the nanoscale in two (2D) and three dimensions (3D). Comparing parameter-free simulations with experiments, it is demonstrated that the employed model can be made quantitative for Ag–Cu. Next, we explore the effect of material properties and the conditions of freezing on the eutectic pattern. We find that the anisotropies of kinetic coefficient and the interfacial free energies (solid–liquid and solid–solid), the crystal misorientation relative to pulling, the lateral temperature gradient play essential roles in determining the eutectic pattern. Finally, we explore eutectic morphologies, which form when one of the solid phases are faceted, and investigate cases, in which the kinetic anisotropy for the two solid phases is drastically different.

We compare two versions of the phase-field theory for polycrystalline solidification, both relying on the concept of orientation fields: one by Kobayashi et al. [Physica D 140 (2000) 141] [15] and the other by Henry et al. [Phys. Rev. B 86 (2012) 054117] [22]. Setting the model parameters so that the grain boundary energies and the time scale of grain growth are comparable in the two models, we first study the grain coarsening process including the limiting grain size distribution, and compare the results to those from experiments on thin films, to the models of Hillert, and Mullins, and to predictions by multiphase-field theories. Next, following earlier work by Granasy et al. [Phys. Rev. Lett. 88 (2002) 206105; Phys. Rev. E 72 (2005) 011605] [17,21], we extend the orientation field to the liquid state, where the orientation field is made to fluctuate in time and space, and employ the model for describing of multi-dendritic solidification, and polycrystalline growth, including the formation of “dizzy” dendrites disordered via the interaction with foreign particles.

We review recent advances made in modeling heteroepitaxy, two-step nucleation, and nucleation at the growth front within the framework of a simple dynamical density functional theory, the Phase-Field Crystal (PFC) model. The crystalline substrate is represented by spatially confined periodic potentials. We investigate the misfit dependence of the critical thickness in the StranskiKrastanov growth mode in isothermal studies. Apparently, the simulation results for stress release via the misfit dislocations fit better to the PeopleBean model than to the one by Matthews and Blakeslee. Next, we investigate structural aspects of two-step crystal nucleation at high undercoolings, where an amorphous precursor forms in the first stage. Finally, we present results for the formation of new grains at the solid–liquid interface at high supersaturations/supercoolings, a phenomenon termed Growth Front Nucleation (GFN). Results obtained with diffusive dynamics (applicable to colloids) and with a hydrodynamic extension of the PFC theory (HPFC, developed for simple liquids) will be compared. The HPFC simulations indicate two possible mechanisms for GFN.

Significance Using notions from classic materials science, we expand our understanding of the macroscopic morphospace of possible molluscan shell shapes to the level of possible ultrastructures that comprise them. This provides us with a unique opportunity to explore this morphospace using well-developed analytical, theoretical, and numerical tools and to test the effects of a discrete number of parameters on shell biomineralization. The physical model presented here sheds a new light on the evolutionary aspect of molluscan shell ultrastructural fabrication and suggests that the repeated “discovery” of some mineral morphologies partially reflects a series of architectural constraints provided by biomineral growth kinetics., Molluscan shells are a classic model system to study formation–structure–function relationships in biological materials and the process of biomineralized tissue morphogenesis. Typically, each shell consists of a number of highly mineralized ultrastructures, each characterized by a specific 3D mineral–organic architecture. Surprisingly, in some cases, despite the lack of a mutual biochemical toolkit for biomineralization or evidence of homology, shells from different independently evolved species contain similar ultrastructural motifs. In the present study, using a recently developed physical framework, which is based on an analogy to the process of directional solidification and simulated by phase-field modeling, we compare the process of ultrastructural morphogenesis of shells from 3 major molluscan classes: A bivalve Unio pictorum, a cephalopod Nautilus pompilius, and a gastropod Haliotis asinina. We demonstrate that the fabrication of these tissues is guided by the organisms by regulating the chemical and physical boundary conditions that control the growth kinetics of the mineral phase. This biomineralization concept is postulated to act as an architectural constraint on the evolution of molluscan shells by defining a morphospace of possible shell ultrastructures that is bounded by the thermodynamics and kinetics of crystal growth.

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. Besides simpler cases of homogeneous and heterogeneous nucleation, phenomena addressed by these techniques include precursor assisted nucleation, nucleation in eutectic and phase separating systems, phase selection via competing nucleation processes, growth front nucleation (a process, in which grains of new orientations form at the solidification front) yielding crystal sheaves and spherulites, and transition between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies., Open Access Article: https://www.sciencedirect.com/science/article/pii/S0079642519300453

We present nucleation phase field model benchmark problems, expanding on our previous benchmark problems on diffusion, precipitation, dendritic growth, linear elasticity, fluid flow and electrochemistry. Nucleation is the process in which either a new thermodynamic phase or a new structure is created, such as solidification from the melt, or self-assembly of particulates. Based on where the nucleation occurs, it can be divided into two main categories: homogeneous nucleation and heterogeneous nucleation. In the first nucleation benchmark problem, we focus on homogeneous nucleation for both single seed under different initial conditions and multiple seeds. The second nucleation benchmark problem focuses on athermal heterogeneous nucleation and nucleation behavior near the free growth limit with different undercooling driving forces.

Multi-hierarchical self-assembly (MHSA) is a key process responsible for the spontaneous formation of many complex structures. However, because of the complexity of the process, the underlying mechanism remains largely unclear. Thus, a deeper understanding of MHSA is required, especially for the preparation of MHSA systems via bottom-up methodologies. We show here, experimentally and theoretically, that the complex-formation MHSA of peptide nanotube films can be controlled solely by manipulating the experimental parameter of humidity. Furthermore, we identify growth-front nucleation (GFN; the formation of new grains at the perimeter) as the physical background for the observed morphological transitions by correlating experimental observations with phase-field modeling of the morphological evolution. Our findings indicate a simple way to control multi-hierarchical morphologies, crucial for the employment of bottom-up techniques in constructing complex structures for practical applications.

Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This topological property has important consequences for the resulting multi-grain structures: (i) trijunctions may be singular; (ii) for each pair of grains, there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can, (ii) and therefore (iii) cannot be interpreted in the classical picture of grain boundaries. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two new formulations of the model. The first is based on a 3-component unit vector field, while in the second we utilise a 2-component vector field with an additional potential. In both cases, the additional degree of freedom introduced make the order parameter space simply-connected, which removes the topological stability of these defects., Comment: 16 pages, 17 figures in color

In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a log-normal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [R. Kobayashi, J. A. Warren, and W. C. Carter, Physica D 140, 141 (2000)PDNPDT0167-278910.1016/S0167-2789(00)00023-3; H. Henry, J. Mellenthin, and M. Plapp, Phys. Rev. B 86, 054117 (2012)PRBMDO1098-012110.1103/PhysRevB.86.054117] that an insufficient resolution of the small angle grain boundaries leads to a log-normal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our paper indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.

The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at various reduced temperatures in the range $\epsilon\in\left[0,0.5\right]$. While the maximum free energy corresponds to the $\left\{ 100\right\} $ orientation for all $\epsilon$ values, the minimum is realized by the $\left\{ 111\right\} $ direction for small $\epsilon\,(

Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly.

Molluscan shells are a model system to understand the fundamental principles of mineral formation by living organisms. The diversity of unconventional mineral morphologies and 3D mineral-organic architectures that comprise these tissues, in combination with their exceptional mechanical efficiency, offers a unique platform to study the formation-structure-function relationship in a biomineralized system. However, so far, morphogenesis of these ultrastructures is poorly understood. Here, a comprehensive physical model, based on the concept of directional solidification, is developed to describe molluscan shell biomineralization. The capacity of the model to define the forces and thermodynamic constraints that guide the morphogenesis of the entire shell construct-the prismatic and nacreous ultrastructures and their transitions-and govern the evolution of the constituent mineralized assemblies on the ultrastructural and nanostructural levels is demonstrated using the shell of the bivalve Unio pictorum. Thereby, explicit tools for novel bioinspired and biomimetic bottom-up materials design are provided.

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. B 75 (2007) 064107] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed.

Hernádbűd-Várdomb területén 2007-2008-ban geodéziai felméréssel, intenzív felszíni leletgyűjtéssel, régészeti célú légifényképek és geofizikai felmérés segítségével kísérletet tettünk a település szerkezeti rekonstrukciójára. A rekonstrukciómellett elvégeztük az összegyűjtött leletanyag régészeti és környezettörténeti értékelését is.

We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories, and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a new way of constructing the free energy surface, and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism; reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations; enables the use of arbitrary pairwise equilibrium interfacial properties; penalizes multiple junctions increasingly with the number of phases; ensures non-negative entropy production, and the convergence of the dynamic solutions to the equilibrium solutions; and avoids the appearance of spurious phases on binary interfaces. The new approach is tested for multi-component phase separation and grain coarsening.

We discuss the formation of polycrystalline microstructures within the framework of phase field theory. First, the model is tested for crystal nucleation in a hard sphere system. It is shown that, when evaluating the model parameters from molecular dynamics simulations, the phase field theory predicts the nucleation barrier for hard spheres accurately. The formation of spherulites is described by an extension of the model that incorporates branching with a definite orientational mismatch. This effect is induced by a metastable minimum in the orientational free energy. Spherulites are an extreme example of polycrystalline growth, a phenomenon that results from the quenching of orientational defects (grain boundaries) into the solid as the ratio of the rotational to the translational diffusion coefficient is reduced, as is found at high undercoolings. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.

We briefly review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is shown that the phase field theory accurately predicts the nucleation barrier height for this liquid when the model parameters are fixed by independent molecular dynamics calculations. We then address various aspects of polycrystalline solidification and associated crystal pattern formation at relatively long timescales. This late stage growth regime, which is not accessible by molecular dynamics, involves nucleation at the growth front to create new crystal grains in addition to the effects of primary nucleation. Finally, we consider the limit of extreme polycrystalline growth, where the disordering effect due to prolific grain formation leads to isotropic growth patterns at long times, i.e., spherulite formation. Our model of spherulite growth exhibits branching at fixed grain misorientations, induced by the inclusion of a metastable minimum in the orientational free energy. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.

A phase-field theory is applied to model the growth of carbon dioxide hydrate and methane hydrate from a supersaturated solution in water. Temperature- and pressure-dependent thermodynamics for the two systems are accounted for. Simulations of the growth of a planar hydrate film and a circular hydrate nucleus are presented and the interface velocity has been extrapolated from the results to experimental time scales. We discuss how pressure and temperature affects the growth rate and argue that the governing process for the dynamics is the chemical diffusion of the guest molecule in the aqueous solution. We also present results from anisotropic simulations and outline how this will affect the growth.

The formation of two and three-dimensional polycrystalline structures are addressed within the framework of the phase field theory. While in two dimensions a single orientation angle suffices to describe crystallographic orientation in the laboratory frame, in three dimensions, we use the four symmetric Euler parameters to define crystallographic orientation. Illustrative simulations are performed for various polycrystalline structures including simultaneous growth of randomly oriented dendritic particles, the formation of spherulites and crystal sheaves.

A phase-field theory of binary liquid phase separation coupled to fluid flow is presented. The respective Cahn–Hilliard-type and Navier–Stokes equations are solved numerically. We incorporate composition and temperature dependent capillary forces. The free energies of the bulk liquid phases are taken from the regular solution model. In the simulations, we observe Marangoni motion, and direct and indirect hydrodynamic interactions between the droplets. We find that coagulation is dramatically accelerated by flow effects. Possible extension of the model to solidification is discussed.

In this study, we examine the rate-limiting process for the formation of hydrates from aqueous solutions of CO2 and the rate-limiting process when CO2 hydrate dissociates toward pure water. A phase field theory is applied to model the growth and dissociation of the gas hydrate in a system consisting of an aqueous CO2 phase, and an initial hydrate nucleus at constant pressure of 150 bar and a temperature of 274.15 K. The diffusion of CO2 in the aqueous phase is shown to be the governing parameter for the growth and dissociation rates. We investigate concentration profiles at the interface and show that diffusion through Fick’s law in the liquid can account for the behavior of the system. We argue that the released heat has little or no effect on the kinetics of growth and dissociation for the systems in this study, although we cannot exclude the potential effect of released heat on the nucleation stage. Finally, we also discuss the effects of anisotropic crystal growth on crystal morphology and kinetic rates of growth.

Multiphase solidification in multicomponent alloys is pertinent to many commercial materials and industrial processes, while also raising challenging questions from a fundamental point of view. Within the past few years, research activities dedicated to multiphase solidification of ternary and multicomponent alloys experienced considerable amplification. This paper gives an overview of our present understanding in this field and the experimental techniques and theoretical methods research relies on. We start with an introduction to thermodynamic databases and computations and emphasize the importance of thermophysical property data. Then, we address pattern formation during coupled growth in ternary alloys and cover microstructure evolution during successive steps of phase formation in solidifying multicomponent alloys. Subsequently, we review advances made in phase field modeling of multiphase solidification in binary and multicomponent alloys, including various approaches to crystal nucleation and growth. Concluding, we address open questions and outline future prospects on the basis of a close interaction among scientists investigating the thermodynamic, thermophysical and microstructural properties of these alloys.

This article discusses two methods for modeling eutectic solidification using the phase-field approach. First, a multi-phase-field model is used to study the three-dimensional morphological evolution of binary eutectics. Performing the calculations in three dimensions allows observation of both lamellar and rod-like structures as well as transient phenomena such as lamellar fault motion, rod-branching, and nucleation or elimination of phases as solidification progresses. The second approach models multiple eutectic grains where the crystallizing phases have an orientation relationship. This approach is promising for modeling complex solidification microstructures.

The phase field theory of crystal nucleation described in [L. Granasy, T. Borzsonyi, T. Pusztai, Phys. Rev. Lett. 88, 206105 (2002)] is applied for nucleation in hard--sphere liquids. The exact thermodynamics from molecular dynamics is used. The interface thickness for phase field is evaluated from the cross--interfacial variation of the height of the singlet density peaks. The model parameters are fixed in equilibrium so that the free energy and thickness of the (111), (110), and (100) interfaces from molecular dynamics are recovered. The density profiles predicted without adjustable parameters are in a good agreement with the filtered densities from the simulations. Assuming spherical symmetry, we evaluate the height of the nucleation barrier and the Tolman length without adjustable parameters. The barrier heights calculated with the properties of the (111) and (110) interfaces envelope the Monte Carlo results, while those obtained with the average interface properties fall very close to the exact values. In contrast, the classical sharp interface model considerably underestimates the height of the nucleation barrier. We find that the Tolman length is positive for small clusters and decreases with increasing size, a trend consistent with computer simulations., 7 pages, 7 figures

We show that the increase of the interface free energy with deviation from equilibrium seen in recent Monte Carlo simulations [S. Auer and D. Frenkel, Nature (London) 413, 711 (2001)] can be recovered if the molecular scale diffuseness of the crystal–liquid interface is considered. We compare two models, Granasy’s phenomenological diffuse interface theory, and a density functional theory that relies on the type of Ginzburg–Landau expansion for fcc nucleation, that Shih et al. introduced for bcc crystal. It is shown that, in the range of Monte Carlo simulations, the nucleation rate of the stable fcc phase is by several orders of magnitude higher than for the metastable bcc phase, seen to nucleate first in other fcc systems. The nucleation barrier that the diffuse interface theories predict for small deviations from equilibrium is in far better agreement with the simulations than the classical droplet model. The behavior expected at high densities is model dependent. Granasy’s phenomenological diffuse inter...

We apply a single-order-parameter Cahn–Hilliard theory to deduce properties of the fluid–crystal interface from nucleation experiments: The two Cahn–Hilliard parameters (the free energy scale and the coefficient of the square-gradient term) are chosen so that the experimentally determined interfacial free energy of nuclei is recovered. The theory is then used to predict the thickness and free energy of the equilibrium planar interface, and other quantities such as the Tolman length and characteristic thickness, which describe the curvature dependence of the interfacial free energy. The accuracy of the method is demonstrated on systems (Lennard-Jones and ice-water) for which these properties are known. Experimental data available for five stoichiometric oxide glasses are then analyzed. The reduced interfacial free energy (Turnbull’s α) and the interface thickness, we obtained, cover the α=0.28–0.51 and the d=0.8–1.6 nm ranges. For oxide glasses we find that α scales with n−1/3, where n is the number of mol...

Nucleation and growth in unary and binary systems is investigated in the framework of the phase-field theory. Evaluating the model parameters from the interfacial free energy and interface thickness, a quantitative agreement is found with computer simulations and experiments on the ice–water system. The critical undercoolings predicted for a simple binary system are close to experiment. Phase-field simulations for isotropic and anisotropic systems show that due to the interacting diffusion fields the Avrami–Kolmogorov exponent varies with transformed fraction and initial concentration.

Temperature dependence of the magnetic properties of Fe/Ag vacuum evaporated multilayers was studied in a wide range of layer thickness. For Fe thickness larger than 1 nm continuous magnetic layers can be found, but its hyperfine field is significantly lower than that of pure α-Fe at elevated temperatures. It is attributed to a decrease of the Curie temperature due to Ag impurities in the Fe layer. Below 1 nm Fe thickness magnetic relaxation and the formation of a granular alloy with 35 T average hyperfine field was observed. Magnetoresistance results indicate the presence of Fe clusters in the Ag matrix, as well.

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 distribution can be influenced by heterogeneous nucleation on the nanoparticles and by the front-particle interaction. We explore, furthermore, how materials and process parameters, such as temperature, density and size/shape distribution of the nanoparticles, influence microstructure evolution., in Magnesium Technology 2014, John Wiley & Sons, Inc., Hoboken, NJ, USA

Melt-quenched amorphous Fe 92− x B x Zr 7 Cu 1 (2⩽ x ⩽23) ribbons were heat treated to the end of the first crystallization stage. The size of the BCC grains decreases from 20 to 6 nm with increasing B content, while the average thickness of the residual amorphous phase stays approximately constant at about 4 nm. The nanocrystalline BCC phase contains 2–4 at% of dissolved B and Zr, which is also reflected in its modified Curie temperature. The average composition of the residual amorphous regions in the nanocrystalline composite was established as Fe 2 (B 1− y Zr y ), which makes possible a direct comparison of macro- and nanophases of close composition.

The composition dependence of the Curie temperature and the magnetic moment of the nano-size residual amorphous phase in partially crystallized Fe92-xZr7BxCu1 (2 x 23) amorphous alloys were determined by 57Fe M?ssbauer spectroscopy. Both quantities show broad minima and for increasing relative Zr content (i.e. for decreasing B concentration) surpass the usual monotonic decrease observed for the bulk counterparts. The deviation does not scale with the characteristic size of the residual amorphous regions, which was found to be constant, ruling out explanations based on interphase exchange interaction. A magnetovolume origin of the observed anomalous composition dependence and the improved soft-magnetic characteristics of these nanocrystals is proposed.

Eutectic dendrites forming in a model ternary system have been studied using the phase-field theory. The eutectic and one-phase dendrites have similar forms, and the tip radius scales with the interface free energy as for one-phase dendrites. The steady-state eutectic patterns appearing on these two-phase dendrites include concentric rings, and single- to multiarm spirals, of which the fluctuations choose, a stochastic phenomenon characterized by a peaked probability distribution. The number of spiral arms correlates with tip radius and the kinetic anisotropy., Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. E