Electromagnetic levitation containerless processing of metallic materials in microgravity: rapid solidification.

Space levitation processing allows researchers to conduct benchmark tests in an effort to understand the physical phenomena involved in rapid solidification processing, including alloy thermodynamics, nucleation and growth, heat and mass transfer, solid/liquid interface dynamics, macro- and microstructural evolution, and defect formation. Supported by ground-based investigations, a major thrust is to develop and refine robust computational tools based on theoretical and applied approaches. This work is accomplished in conjunction with experiments designed for precise model validation with application to a broad range of industrial processes.

Kinetics of rapid growth and melting of AlNialloying crystals: phase field theoryatomistic simulations revisited.

A revised study of the growth and melting of crystals in congruently melting AlNialloy is carried out by molecular dynamics (MDs) and phase field (PF) methods. An embedded atom method (EAM) potential of Purja Pun and Mishin (200989 3245) is used to estimate the material's properties (density, enthalpy, and self-diffusion) of the B2 crystalline and liquid phases of the alloy. Using the same EAM potential, the melting temperature, density, and diffusion coefficient become well comparable with experimental data in contrast with previous works where other potentials were used.

Rapid eutectic growth: from rod growth to diffusionless solidification.

Numerous experimental data on the rapid solidification of eutectic systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by the suppression of eutectic decomposition due to diffusionless (chemically partitionless) solidification beginning at a high but finite growth velocity of crystals. In the present work, a model is suggested for the diffusionless growth to analyse the atomic diffusion in the rod eutectic couples growing into supercooled liquid.

Thermodynamic description of metastable fcc/liquid phase equilibria and solidification kinetics in Al-Cu alloys.

The thermodynamic description of the fcc phase in the Al-Cu system has been revised, allowing for the prediction of metastable fcc/liquid phase equilibria to undercoolings of Δ = 421 K below the eutectic temperature. Hypoeutectic Al-Cu alloys that are prone to pronounced microsegregation were solidified containerlessly in electromagnetic levitation. Solidus and liquidus concentrations were experimentally determined from highly undercooled samples employing energy-dispersive X-ray analysis.

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model.

The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in colloidal and metallic systems. In the present work, the modified hyperbolic phase-field crystal model for binary systems is presented. This model takes into account slow and fast dynamics of moving interfaces for both concentration and relative atomic number density (which were taken as order parameters).

Amorphization and nanocrystal formation in a Pd-Ni-Cu-P alloy after cooling under different conditions.

Structure formation during solidification of a Pd-Ni-Cu-P melt is studied. It is demonstrated that changes in the heat transfer conditions lead to a nonlinear change in the characteristics of the structure. The article presents the regimes of cooling the samples and the results of their structure and composition studies.

Demonstration of the effect of stirring on nucleation from experiments on the International Space Station using the ISS-EML facility.

The effect of fluid flow on crystal nucleation in supercooled liquids is not well understood. The variable density and temperature gradients in the liquid make it difficult to study this under terrestrial gravity conditions. Nucleation experiments were therefore made in a microgravity environment using the Electromagnetic Levitation Facility on the International Space Station on a bulk glass-forming ZrCuNiAlNb (Vit106), as well as CuZr and the quasicrystal-forming TiZrNi liquids.

Dendrite tips as elliptical paraboloids.

This review article summarizes current theories of the steady-state growth mode of dendrites in the form of elliptical paraboloids. The shape of dendrite tips is analyzed, temperature and solute concentration distributions are described in its vicinity, and a solution of the hydrodynamic problem of a viscous incompressible fluid flowing against a dendrite tip is developed. A significant difference in analytical solutions describing a dendrite tip as an elliptic paraboloid as compared to an axisymmetric morphology is shown.

The hodograph equation for slow and fast anisotropic interface propagation.

Using the model of fast phase transitions and previously reported equation of the Gibbs-Thomson-type, we develop an equation for the anisotropic interface motion of the Herring-Gibbs-Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship 'velocity-Gibbs free energy', Klein-Gordon and Born-Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J.

A review on the theory of stable dendritic growth.

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented.

The shape of dendritic tips: a test of theory with computations and experiments.

This article is devoted to the study of the tip shape of dendritic crystals grown from a supercooled liquid. The recently developed theory (Alexandrov & Galenko 2020 , 20190243. (doi:10.

Kinetics of solid-liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon.

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal-liquid interface featuring an increase up to a maximum at 10-30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson-Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials.

Dendritic growth of ice crystals: a test of theory with experiments.

Motivated by an important application of dendritic crystals in the form of an elliptical paraboloid, which widely spread in nature (ice crystals), we develop here the selection theory of their stable growth mode. This theory enables us to separately define the tip velocity of dendrites and their tip diameter as functions of the melt undercooling. This, in turn, makes it possible to judge the microstructure of the material obtained as a result of the crystallization process.

Traveling waves of the solidification and melting of cubic crystal lattices.

Using the phase field crystal model (PFC model), an analysis of slow and fast dynamics of solid-liquid interfaces in solidification and melting processes is presented. Dynamical regimes for cubic lattices invading metastable liquids (solidification) and liquids propagating into metastable crystals (melting) are described in terms of the evolving amplitudes of the density field. Dynamical equations are obtained for body-centered cubic (bcc) and face-centered cubic (fcc) crystal lattices in one- and two-mode approximations.

Thin interface limit of the double-sided phase-field model with convection.

The thin interface limit of the phase-field model is extended to include transport via melt convection. A double-sided model (equal diffusivity in liquid and solid phases) is considered for the present analysis. For the coupling between phase-field and Navier-Stokes equations, two commonly used schemes are investigated using a matched asymptotic analysis: (i) variable viscosity and (ii) drag force model.

The shape of dendritic tips.

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number.

Fast traveling waves in the phase-field theory: effective mobility approach versus kinetic energy approach.

A phase-field model for small and large driving forces on solidification and melting of a pure substance or alloys is formulated. Derivations of the phase-field model are based on the effective mobility approach and on the kinetic energy approach to analyze fast phase transformation from metastable liquid to solid phase. A hodograph equation (an acceleration-velocity dependent equation of the Gibbs-Thomson type) which predicts the non-linear behavior in the velocity of the crystal-liquid interface is found at the large driving force on transformation and analyzed for different thermodynamic potentials.

Modeling of dendrite growth from undercooled nickel melt: sharp interface model versus enthalpy method.

The dendritic growth of pure materials in undercooled melts is critical to understanding the fundamentals of solidification. This work investigates two new insights, the first is an advanced definition for the two-dimensional stability criterion of dendritic growth and the second is the viability of the enthalpy method as a numerical model. In both cases, the aim is to accurately predict dendritic growth behavior over a wide range of undercooling.

Resistivity Saturation in Metallic Liquids Above a Dynamical Crossover Temperature Observed in Measurements Aboard the International Space Station.

Although a resistivity saturation (minimum conductivity) is often observed in disordered metallic solids, such phenomena in the corresponding liquids are not known. Here we report a saturation of the electrical resistivity in Zr_{64}Ni_{36} and Cu_{50}Zr_{50} liquids above a dynamical crossover temperature for the viscosity (T_{A}). The measurements were made for the levitated liquids under the microgravity conditions of the International Space Station.

Thermodynamics of rapid solidification and crystal growth kinetics in glass-forming alloys.

Thermodynamic driving forces and growth rates in rapid solidification are analysed. Taking into account the relaxation time of the solute diffusion flux in the model equations, the present theory uses, in a first case, the deviation from local chemical equilibrium, and ergodicity breaking. The second case of ergodicity breaking may exist in crystal growth kinetics of rapidly solidifying glass-forming metals and alloys.

Diffusionless (chemically partitionless) crystallization and subsequent decomposition of supersaturated solid solutions in Sn-Bi eutectic alloy.

Results of a study on microstructural evolution of eutectic Sn-57 wt.% Bi processed with cooling rates of 10, 1 K s and approximately 10 K s are presented. In order to distinguish different mechanisms of microstructure formation, a comparison with microstructures of different hypoeutectic alloys with compositions down to below the maximum solubility of Bi in Sn-Bi is undertaken.

Thermo-solutal growth of an anisotropic dendrite with six-fold symmetry.

A stable growth of dendritic crystal with the six-fold crystalline anisotropy is analyzed in a binary nonisothermal mixture. A selection criterion representing a relationship between the dendrite tip velocity and its tip diameter is derived on the basis of morphological stability analysis and solvability theory. A complete set of nonlinear equations, consisting of the selection criterion and undercooling balance condition, which determines implicit dependencies of the dendrite tip velocity and tip diameter as functions of the total undercooling, is formulated.

The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems.

The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived.

Thermo-solutal and kinetic modes of stable dendritic growth with different symmetries of crystalline anisotropy in the presence of convection.

Motivated by important applications in materials science and geophysics, we consider the steady-state growth of anisotropic needle-like dendrites in undercooled binary mixtures with a forced convective flow. We analyse the stable mode of dendritic evolution in the case of small anisotropies of growth kinetics and surface energy for arbitrary Péclet numbers and -fold symmetry of dendritic crystals. On the basis of solvability and stability theories, we formulate a selection criterion giving a stable combination between dendrite tip diameter and tip velocity.

From atomistic interfaces to dendritic patterns.

Transport processes around phase interfaces, together with thermodynamic properties and kinetic phenomena, control the formation of dendritic patterns. Using the thermodynamic and kinetic data of phase interfaces obtained on the atomic scale, one can analyse the formation of a single dendrite and the growth of a dendritic ensemble. This is the result of recent progress in theoretical methods and computational algorithms calculated using powerful computer clusters.