Rapid Solidification Of Binary Alloys Research Articles

An anisotropic lattice Boltzmann - phase field model for dendrite growth and movement in rapid solidification of binary alloys

A model coupling the lattice Boltzmann and the phase field methods with anisotropic effects is proposed, which is used to numerically describe the growth and movement of dendrites in rapid solidification of alloys. The model is quantitatively validated by the simulation of the continuous growth and the drafting-kissing-tumbling phenomenon of two falling particles, and then applied to investigate the effects of dendrite movement and interfacial non-equilibrium on evolution of dendritic patterns for Si-9.0at%As and the CET for Al-3.0wt%Cu alloys. Both the growth and remelt processes of isolated dendrites are studied, and the result reveals the remelting influences on dendrite growth and solute micro-segregation in the condition of directional solidification. This work demonstrates that the proposed model has a wide range of applicability and great potential to simulate the microstructure evolution with various solidification conditions.

Interface kinetics of rapid solidification of binary alloys by atomistic simulations: Application to Ti-Ni alloys

Using molecular dynamics and Monte Carlo simulations we investigate the non-equilibrium interfacial kinetics during rapid solidification of Ti-Ni alloys. According to the existing theories, the kinetic coefficient is related, via an analytical expression, to the equilibrium and non-equilibrium solute concentration profiles across the crystal-melt interface, the interface temperature and velocity, and the drag coefficient. The kinetic coefficient was obtained by deriving these properties from specifically designed atomistic simulations and then fitting using the analytical expression. The results show that the kinetic coefficient is only weakly anisotropic and increases with increasing temperature. The velocity-dependent partition coefficient, as described by two solute trapping models, the continuous growth and the local non-equilibrium models, were fitted to the molecular dynamics simulation results. In addition, molecular dynamics and semi-grand canonical Monte Carlo simulations suggest that complete solute trapping might occur only under certain conditions. This can be explained by the fact that the maximum achievable effective free energy driving force for solidification, which defines the complete solute trapping, is limited by the chemical potential and free energy profiles for the Ti-Ni alloy. The investigations, using molecular dynamics simulations, of the dependence of crystal-melt interface width on solidification velocity show, at high velocities, similar trend to that predicted by the hyperbolic phase field model which is suitable for studies of rapid solidification of alloys.

Nonlinear Dynamics of the Formation of a Periodic Superstructure of Impurity Bands during Rapid Directional Solidification of Binary Alloys

An analytical description is proposed for the nonlinear dynamics of formation of regular impurity superstructures during a rapid solidification of binary alloys supplemented by a numerical model calculation. It is shown that there is a stable limit cycle, and spatial profiles of the impurity concentration in a solid product are calculated. The inclusion of a finiteness of the impurity atom jump velocity is found to lead to very substantial decrease in the cycle sizes and a change in the profiles of impurity superstructures.

Modeling of non-equilibrium solute diffusion upon rapid solidification: effective mobility versus kinetic energy

The effective mobility approach is compared with the kinetic energy approach in terms of sharp interface modeling and phase-field modelling of non-equilibrium solute diffusion upon rapid solidification of binary alloys. The two approaches are equivalent for modelling of long range solute diffusion in bulk phases, but only the effective mobility approach can introduce the non-equilibrium solute diffusion effect to short range solute diffusion at a sharp interface or within a diffuse interface. Addition of the kinetic energy terms results in an unreasonable non-bilinear expression of the flux and thermodynamic driving force in the free energy production of interface migration or phase field propagation, whereas the effective mobility approach allows the thermodynamic extremal principle workable.

Nonlocal diffusion models: Application to rapid solidification of binary mixtures

Various theoretical treatments and models for nonlocal diffusion are briefly reviewed and discussed. The nonlocal effects arise in far from equilibrium processes, which involve extremely fast heat and mass transfer at very small time and length scales. With only diffusive dynamics, the nonlocal models result in a set of transfer equations of parabolic type with an infinite velocity of diffusive disturbances. With the wavelike dynamics, the models lead to a set of transfer equations of hyperbolic type with a finite velocity of diffusive disturbances. Rapid solidification of binary alloys has been used to illustrate the influence of the nonlocal diffusion effects on solute partitioning at the phase interface.

An analytical model for local-nonequilibrium solute trapping during rapid solidification

Updated version of local non-equilibrium diffusion model (LNDM) for rapid solidification of binary alloys was considered. The LNDM takes into account deviation from local equilibrium of solute concentration and solute flux fields in bulk liquid. The exact solutions for solute concentration and flux in bulk liquid were obtained using hyperbolic diffusion equations. The results show the transition from diffusion-limited to purely thermally controlled solidification with effective diffusion coefficient DLNDMb→0 and complete solute trapping KLNDM(v)→1 at v→vDb for any kind of solid-liquid interface kinetics. Critical parameter for diffusionless solidification and complete solute trapping is the diffusion speed in bulk liquid vDb. Different models for solute trapping at the interface with different interface kinetic approaches were considered.

An analytical model for complete solute trapping during rapid solidification of binary alloys

An analytical model has been developed to describe solute partitioning during rapid solidification of binary alloys under local nonequilibrium conditions. The model takes into account the deviations from equilibrium both at the solid–liquid interface according to the kinetic approach of Jackson et al. based on Monte Carlo simulations and in the bulk liquid using local nonequilibrium diffusion model (LNDM). The dimensionless growth parameter β found in the Monte Carlo simulations as the important parameter for solute trapping has been modified for the local nonequilibrium diffusion case. An analytical expression has been developed for the velocity-dependent partition coefficient KLNDM(V) which predicts complete solute trapping and an abrupt transition from diffusion-controlled to diffusionless solidification when the interface velocity V passes through the critical point V=VD. The predictions are in good agreement with the experimental results, molecular dynamic studies, and Monte Carlo computer simulations.

Local non-equilibrium diffusion model for solute trapping during rapid solidification

A local non-equilibrium diffusion model (LNDM) for rapid solidification of binary alloys has been briefly reviewed and used to modify a number of solute trapping models with different solid–liquid interface kinetics. The LNDM takes into account deviation from local equilibrium of a solute diffusion field in bulk liquid on the basis that the exact solutions to hyperbolic diffusion equations govern the solute concentration and solute flux in bulk liquid under local non-equilibrium conditions. The LNDM leads to a velocity-dependent effective diffusion coefficient in bulk liquid ahead of the solid–liquid interface DbLNDM(V), which goes to zero when the interface velocity V→VDb, where VDb is the bulk liquid diffusion speed. The results show an abrupt transition from diffusion-limited to purely thermally controlled solidification, with the diffusion coefficient in bulk liquid DbLNDM(V)=0 and complete solute trapping KLNDM(V)=1 at a finite interface velocity V=VDb for any type of solid–liquid interface kinetics. The bulk liquid diffusion speed VDb is a critical parameter for the transition. The velocity dependence of partition coefficients KLNDM(V) has been calculated for different types of solid–liquid interface kinetics, with allowance for local non-equilibrium diffusion effects. The calculation shows that the local non-equilibrium partition coefficients KLNDM(V) reduce to the standard K(V) at low interface velocity (V≪VDb) and differ substantially at high interface velocity (V∼VDb).

Features of local nonequilibrium recrystallization of binary alloys under the effect of intense pulsed beams of charged particles

Rapid crystallization in binary systems under the effect of high-energy beams of charged particles was described using a model of mass transfer taking into account both the space and time nonlocality. The role of physical constants and parameters of crystallization in the formation of the material microstructure during rapid solidification of binary alloys is evaluated.

Thermoelectric phenomena at rapid solidification of binary alloys

Thermoelectric phenomena at rapid solidification of binary alloys

Novel Monte-Carlo lattice approach to rapid directional solidification of binary alloys

A statistical approach is developed to study the phenomena related to the rapid solidification of binary alloys. We consider a microscopic lattice Hamiltonian containing an Ising-like variable to account for the alloy character of the model and a Potts-like variable to describe the presence of a solid or liquid spot. By means of a suitable set of Monte-Carlo evolution rules for these variables we are able to describe faithfully the advancing of a solid/liquid interface.

Thermal and chemical diffusion in the rapid solidification of binary alloys

Solidification of binary alloys is characterized by the necessity to reject away from the advancing front two conserved quantities: the latent heat released at the solid-liquid interface and the solute atoms that cannot be accommodated in the solid phase. As thermal diffusion is much faster than chemical diffusion, the latter is generally assumed to be the rate limiting mechanism for the process, and the problem is addressed through the isothermal approximation. In the present paper we use the phase-field model to study the planar growth of a solid germ, nucleated in its undercooled melt. We focus on the effects of a noninstantaneous thermal relaxation. The steady growth predicted at large supersaturation in the isothermal limit is prevented. Depending on the value of the Lewis number the growth rate is limited by either mass or heat diffusion; in the latter case we observe a sharp transition between two different regimes, in which originates a nonmonotonic time dependence of the interface temperature. The effects of this transition reflect in the composition of the solidified alloy.

Influence of local nonequilibrium on the rapid solidification of binary alloys

A local-nonequilibrium model of the diffusion of a solute during the rapid solidification of a binary alloy is considered. The model has two characteristic parameters: the diffusion velocity through the interface VDi and the diffusion velocity in the bulk of the liquid phase VD. The influence of local nonequilibrium on the separation of an impurity, the stability of the interface, and the dependence of the temperature of the interface on the velocity of the solidification front is investigated. A comparison with experiment is made.

Homogeneous nucleation ahead of the solid—liquid interface during rapid solidification of binary alloys

In recent rapid solidification experiments on Al—5%Be alloys, a Liquid Phase Nucleation (LPN) model was developed to explain the formation of periodic arrays of randomly-oriented Be-rich particles in an Al-rich matrix. In the LPN model, Be droplets were assumed to nucleate in the liquid ahead of the solid—liquid interface, but no justification for this was given. Here we present a model which considers the geometric constraints (imposed by proximity to the interface) on the number of solute atoms available to form a nucleus. Calculations based on this model predict that nucleation of second-phase particles can be most likely a short distance ahead of the interface in immiscible binary systems such as AlBe. As part of the nucleation calculations, a semi-empirical method of calculating solid—liquid surface tensions in binary systems was developed, and is presented in the Appendix.

A Study of Solute Trapping During Rapid Solidification of Binary Alloys

BACKGROUNDThe very high crystal growth rates which can be produced during pulsed-laser melting provide the opportunity to study non-equilibrium solidification effects under well-defined experimental conditions. In particular, incorporation of solute into the growing crystal in excess of equilibrium solubilities may be achieved. This solute trapping may be pronounced at the highest crystal growth rates and may lead to the absence of microsegregation in non-planar solidification fronts.Crystal/liquid interface kinetics have been treated by considering the diffusive motion of atoms in the liquid. In this treatment, the crystal growth speed can never exceed the maximum diffusive speed of solute in the liquid, hence solute trapping is not possible. More recently, the collision-limited growth model indicates that for metallic and other simple molecular systems, the speed of sound in the liquid should be the upper limit to crystal growth rates. Consequently, in this latter model of solidification, the crystal growth rate can greatly exceed the maximum solute diffusive speed and solute trapping is possible.