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

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

Modeling of convection, temperature distribution and dendritic growth in glass-fluxed nickel melts

Melt flow is often quoted as the reason for a discrepancy between experiment and theory on dendritic growth kinetics at low undercoolings. But this flow effect is not justified for glass-fluxed melts where the flow field is weaker. In the present work, we modeled the thermal history, flow pattern and dendritic structure of a glass-fluxed nickel sample by magnetohydrodynamics calculations. First, the temperature distribution and flow structure in the molten and undercooled melt were simulated by reproducing the observed thermal history of the sample prior to solidification. Then the dendritic structure and surface temperature of the recalescing sample were simulated. These simulations revealed a large thermal gradient crossing the sample, which led to an underestimation of the real undercooling for dendritic growth in the bulk volume of the sample. By accounting for this underestimation, we recalculated the dendritic tip velocities in the glass-fluxed nickel melt using a theory of three-dimensional dendritic growth with convection and concluded an improved agreement between experiment and theory

Theoretical modeling of crystalline symmetry order with dendritic morphology

The stable growth of a crystal with dendritic morphology with n-fold symmetry is modeled. Using the linear stability analysis and solvability theory, a selection criterion for thermally and solutally controlled growth of the dendrite is derived. A complete set of nonlinear equations consisting of the selection criterion and an undercooling balance (which determines the implicit dependencies of the dendrite tip velocity and tip diameter on the total undercooling) is formulated. The growth kinetics of crystals having different lattice symmetry is analyzed. The model predictions are compared with phase field modelling data on ice dendrites grown from pure undercooled water

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields: A test of theory with convection

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields up to 6 T were measured using a high-speed camera. The growth velocities for undercoolings below 120 K are depressed under low magnetic fields, but are recovered progressively under high magnetic fields. This retrograde behavior arises from two competing kinds of magnetohydrodynamics in the melt and becomes indistinguishable for higher undercoolings. The measured data is used for testing of a recent theory of dendritic growth with convection. A reasonable agreement is attained by assuming magnetic field-dependent flow velocities. As is shown, the theory can also account for previous data of dendritic growth kinetics in pure succinonitrile under normal gravity and microgravity conditions. These tests demonstrate the efficiency of the theory which provides a realistic description of dendritic growth kinetics of pure substances with convection

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

Additive manufacturing (AM) processes have many benefits for the fabrication of alloy parts, including the potential for greater microstructural control and targeted properties than traditional metallurgy processes. To accelerate utilization of this process to produce such parts, an effective computational modeling approach to identify the relationships between material and process parameters, microstructure, and part properties is essential. Development of such a model requires accounting for the many factors in play during this process, including laser absorption, material addition and melting, fluid flow, various modes of heat transport, and solidification. In this paper, we start with a more modest goal, to create a multiscale model for a specific AM process, Laser Engineered Net Shaping (LENS™), which couples a continuum-level description of a simplified beam melting problem (coupling heat absorption, heat transport, and fluid flow) with a Lattice Boltzmann-cellular automata (LB-CA) microscale model of combined fluid flow, solute transport, and solidification. We apply this model to a binary Ti-5.5 wt pct W alloy and compare calculated quantities, such as dendrite arm spacing, with experimental results reported in a companion paper