Peter Galenko

Diffuse-interface model for rapid phase transformations in nonequilibrium systems

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

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 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 VDI on the interface and diffusion speed VD in bulk phases. The model describes experimental data on nonequilibrium solute partitioning in solidification of Si-As alloys for the whole range of solidification velocity investigated.

Phase-field model with relaxation of the diffusion flux in nonequilibrium solidification of a binary system

Abstract A formalism of the phase-field model for local nonequilibrium solidification of a binary system is developed. The governing equations are derived and comparison with the existing versions of the model is given.

Linear morphological stability analysis of the solid-liquid interface in rapid solidification of a binary system

The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz [Acta Metall. 34, 1663 (1986)]], which is advancing the original treatment of morphological stability by Mullins and Sekerka [J. Appl. Phys. 35, 444 (1964)]] to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the perturbed interface is given in the presence of the local nonequilibrium solute diffusion. Using the developing local nonequilibrium model of solidification, the self-consistent analysis of linear morphological stability is presented with the attribution to the marginal (neutral) and absolute morphological stability of a rapidly moving interface. Special consideration of the interface stability for the cases of solidification in negative and positive thermal gradients is given. A quantitative comparison of the model predictions for the absolute morphological stability is presented with regard to experimental results of Hoglund and Aziz [D. E. Hoglund and M. J. Aziz, in Kinetics of Phase Transformations, edited by M.O. Thompson, M. J. Aziz, and G. B. Stephenson, MRS Symposia Proceedings No. 205 (Materials Research Society, Pittsburgh, 1991), p. 325] on critical solute concentration for the interface breakdown during rapid solidification of Si-Sn alloys.

Change of the kinetics of solidification and microstructure formation induced by convection in the Ni–Al system

The purpose of the present work was to measure the velocity of dendrite growth in undercooled Ni–Al alloy melts as a function of undercooling. The experiments were performed both by containerless electromagnetic levitation on Earth and under reduced gravity conditions during parabolic flight campaigns. While under terrestrial conditions, strong magnetic fields are required to compensate the gravitational force, the forces to compensate disturbing accelerations are decreased by orders of magnitude in reduced gravity. In turn, the alternating electromagnetic fields induce convection, which is strong under terrestrial conditions while much weaker in reduced gravity. The heat and mass transport in front of the solid-liquid interface during solidification controls the dynamics of dendrite growth. By comparing results obtained on Earth and in reduced gravity, it was demonstrated that the change of transport conditions by convection significantly alters the kinetics of solidification and the evolution of grain r...

Analysis of the dispersion relation in spinodal decomposition of a binary system

A model for diffusion and phase separation which takes into account hyperbolic relaxation of the solute diffusion flux is developed. Such a ‘hyperbolic model’ provides analysis of ‘hyperbolic evolution’ of patterns in spinodal decomposition of binary systems. Analytical results for the dispersion relation and critical parameters (such as wavelength and amplification rate of decomposition) are analyzed in comparison with outcomes of classic Cahn–Hilliard theory. It is shown that the hyperbolic model predicts the amplification rate behaviour that is typically observed in experiments on spinodal decomposition.

Evidence of the transition from ordered to disordered growth during rapid solidification of an intermetallic phase

The dendrite growth velocity during solidification is measured on liquid drops of the intermetallic compound Ni50Al50 undercooled by levitation up to 265 K. A sharp increase of the growth velocity is found at a critical undercooling ΔT*≈250 K. In situ diffraction of synchrotron radiation on levitation-processed samples unambiguously shows a transition from ordered to disordered growth at ΔT*. The sharp interface model is extended to describe the transition from ordered to disordered dendrite growth by taking into account the velocity dependence of the order parameter and the kinetic growth coefficient.

The effect of fluid flow on the solidification of Ni2B from the undercooled melt

In this work, we study the effect of fluid flow on the growth dynamics during solidification of tetragonal Ni2B from the undercooled melt. Different experimental techniques are applied to generate varying fluid flow velocities in undercooled samples, electromagnetic levitation under 1 g conditions (1 g EML) and in reduced gravity (μg EML) as well as the melt-fluxing technique and electrostatic levitation. The propagation of the solid-liquid interface apparent on the surface of solidifying samples is observed by high-speed video imaging while the non-contact measurement of the undercooling prior to solidification is accomplished by IR-pyrometry. It is demonstrated that fluid flow has a substantial influence on the growth kinetics. As revealed by an extended sharp-interface model, this effect is mainly attributed to the substantial change in growth kinetics caused by a convection induced transition from dendrites to more faceted solidification structures.

Phase-field modeling of solute trapping: comparative analysis of parabolic and hyperbolic models

Abstract The phase-field model of Wheeler, Boettinger and McFadden is extended to the case of fast solidification in which local non-equilibrium phenomena occur in the bulk phases and within the diffuse solid – liquid interface. Such an extension leads to the characteristic diffusion speeds of atoms (both within the diffuse interface and inside the bulk phases) and to the speed of the interface propagation. As a result, the model is described by a system of hyperbolic equations for the atomic diffusion transport as well as for the phase-field. This model is applied to the problem of solute trapping, which is accompanied by the entrapment of solute atoms beyond chemical equilibrium by a rapidly moving interface. The model predicts the beginning of complete solute trapping and diffusionless solidification at a finite solidification velocity.

Faceting of a rough solid-liquid interface of a metal induced by forced convection

The solid–liquid interface of metallic systems of small entropy of fusion is characterized by a rough interface and dendritic morphology. In contrast, systems of high entropy of fusion like semimetals and semiconductors show smooth interfaces and facetted interfaces. The present work demonstrates that, in an undercooled melt of a metal–metalloid alloy Ni2B of intermediate entropy of fusion, a transition from a rough to a smooth interface is induced by forced convection of the melt. Electrostatic levitation is used to container-less undercool droplets in a quiescent state with no convection while electromagnetic levitation (EML) is used to undercool droplets with forced convection. The growth velocity of the solid phase is monitored as a function of undercooling by a high-speed video camera. The data are analysed within dendrite growth theory. In the case of EML, a transition from a rough to a smooth interface is indicated during dendrite growth in the undercooled melt. This is confirmed by facetted microstructures of samples solidified upon undercooling by EML. Hopper-like crystals are formed like in non-metals as bismuth, halite and ice.