Solute trapping and diffusionless solidification in a binary system

Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to diffusionless (chemically partitionless) solidification at a finite growth velocity of crystals. Special attention is paid to developing a model of rapid solidification which describes a transition from chemically partitioned to diffusionless growth of crystals. Analytical treatments lead to the condition for complete solute trapping which directly follows from the analysis of the solute diffusion around the solid-liquid interface and atomic attachment and detachment at the interface. The resulting equations for the flux balance at the interface take into account two kinetic parameters: diffusion speed $V_{DI}$ on the interface and diffusion speed $V_D$ in bulk phases. The model describes experimental data on nonequilibrium solute partitioning in solidification of Si-As alloys [M.J. Aziz et al., J. Cryst. Growth {\bf 148}, 172 (1995); Acta Mater. {\bf 48}, 4797 (2000)] for the whole range of solidification velocity investigated.Comment: Regular article in Physical Review E, Vol. 76 (2007

Effects of local nonequilibrium in rapid eutectic solidification: Part 1: statement of the problem and general solution

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 suppression of eutectic decomposition due to diffusionless (chemically partitionless) solidification beginning at a high but a finite growth velocity of crystals. A model considering the diffusionless growth is developed in the present work to analyze the atomic diffusion ahead of lamellar eutectic couples growing into supercooled liquid. A general solution of the model is presented from which two regimes are followed. The first presents a diffusion‐limited regime with the existence of eutectic decomposition if the solid–liquid interface velocity is smaller than the characteristic diffusion speed in the bulk liquid. The second shows suppression of eutectic decomposition under diffusionless transformation from liquid to one‐phase solid if the solid–liquid interface velocity overcomes characteristic diffusion speed in the bulk liquid

Analytical solutions to the boundary integral equation: A case of angled dendrites and paraboloids

The boundary integral equation is solved analytically in the case of two‐ and three‐dimensional growth of angled dendrites and arbitrary parabolic/paraboloidal solid/liquid interfaces. The undercooling of a binary melt and the solute concentration at the phase transition boundary are found. The theory under consideration has a potential impact in describing more complex growth shapes and interfaces

Effects of local nonequilibrium in rapid eutectic solidification: Part 2: analysis of effects and comparison to experiment

The developed model of diffusion‐limited and diffusionless solidification of a eutectic alloy describes the relation “undercooling (Δ T )‐velocity ( V )‐interlamellar spacing (λ)” for two cases. Namely, when the solidification front velocity V is smaller than the solute diffusion speed in bulk liquid V D , V V D , the solidification is mainly controlled by kinetic and thermal undercoolings. New expressions for the solute distribution coefficient and slope of the liquidus lines are supplied. The influence of the model parameters on the growth kinetics during eutectic solidification is discussed. Model predictions are compared with experimental data for the solidification of an Fe–B alloy with eutectic composition. Computational results show that the model agrees well with experimental data especially for low and high undercoolings, extending the undercooling range that can be covered by sharp interface modeling

Kinetics of rapid growth and melting of Al 50 Ni 50 alloying crystals: phase field theory versus atomistic simulations revisited *

A revised study of the growth and melting of crystals in congruently melting Al 50 Ni 50 alloy is carried out by molecular dynamics (MDs) and phase field (PF) methods. An embedded atom method (EAM) potential of Purja Pun and Mishin (2009 Phil. Mag. 89 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. In the new revision of MD data, the kinetics of melting and solidification are quantitatively evaluated by the ‘crystal-liquid interface velocity–undercooling’ relationship exhibiting the well-known bell-shaped kinetic curve. The traveling wave solution of the kinetic PF model as well as the hodograph equation of the solid-liquid interface quantitatively describe the ‘velocity–undercooling’ relationship obtained in the MD simulation in the whole range of investigated temperatures for melting and growth of Al 50 Ni 50 crystals

Simulation of crystalline pattern formation by the MPFC method

The Phase Field Crystal model in hyperbolic formulation (modified PFC or MPFC), is investigated as one of the most promising techniques for modeling the formation of crystal patterns. MPFC is a convenient and fundamentally based description linking nano-and meso-scale processes in the evolution of crystal structures. The presented model is a powerful tool for mathematical modeling of the various operations in manufacturing. Among them is the definition of process conditions for the production of metal castings with predetermined properties, the prediction of defects in the crystal structure during casting, the evaluation of quality of special coatings, and others. Our paper presents the structure diagram which was calculated for the one-mode MPFC model and compared to the results of numerical simulation for the fast phase transitions. The diagram is verified by the numerical simulation and also strongly correlates to the previously calculated diagrams. The computations have been performed using software based on the effective parallel computational algorithm

Selection Criterion of Stable Dendritic Growth for a Ternary (Multicomponent) Melt with a Forced Convective Flow

A stable growth mode of a single dendritic crystal solidifying in an undercooled ternary (multicomponent) melt is studied with allowance for a forced convective flow. The steady-state temperature, solute concentrations and fluid velocity components are found for two- and three-dimensional problems. The stability criterion and the total undercooling balance are derived accounting for surface tension anisotropy at the solid-melt interface. The theory under consideration is compared with experimental data and phase-field modeling for Ni 98 Zr 1 Al 1 alloy

Supersymmetry model of a binary mixture with noise of the diffusion flux

Supersymmetry theory of diffusion is elaborated to study analytically a non-equilibrium binary mixture with relaxation of diffusion flux. Within such a scheme, Bose components represent order parameter and amplitude of fluctuations of the diffusion flux, while the mutually conjugated combination of Fermi-components gives the mixture concentration. For above variables, the system of equations is found to describe self-consistent behavior of a binary mixture, when the shortest observable time interval is longer than the flux relaxation time. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/327