Thermodynamics of rapid solidification and crystal growth kinetics in glass-forming alloys (original) (raw)
Related papers
Modeling of a transition to diffusionless dendritic growth in rapid solidification of a binary alloy
Computational Materials Science, 2009
Diffusionless growth of dendritic crystals results in microsegregation-free microstructures with an initial (nominal) chemical composition of solidifying systems. Normally, a transition from chemically partitioned growth to diffusionless solidification is accompanied by the morphological transition in crystal shape with the appearance of nonlinearity in the kinetic behavior of growing crystals. This phenomenon is discussed using a model of local non-equilibrium rapid solidification. Considering the transition from the solute diffusion-limited growth to purely thermally controlled growth of dendritic crystals, the model predicts the abrupt change of growth kinetics with the break points in the ''dendrite tip velocity-undercooling" and ''dendrite tip radius-undercooling" relationships. It is shown that the abrupt change of growth kinetics occurs with the ending of the transition to purely thermally controlled growth and the onset of diffusionless solidification. To predict the dendrite growth kinetics in a whole region of undercooling, numeric analysis shows that the model has to take into account both anisotropies of solid-liquid interfacial properties. These are anisotropy of surface energy and anisotropy of atomic kinetics of solidification.
… of the Indian Institute of Metals, 2009
The development of microstructure during phase transformations is often best understood by considerations of nucleation in the parent material followed by growth of the new phase. This is a mature research field in alloy solidification, thanks to extensive investigations of nucleation and dendritic growth in cooling alloy melts. Bulk metallic glasses, on the other hand, typically do not form crystals on cooling from above the liquidus to below the glass transition temperature, resulting in very strong hard materials. As BMG toughness can be enhanced by a crystallising anneal, the study of nucleation and growth of crystals in viscous multi-component liquids has become an important topic for study. Such devitrification can lead to crystalline-glass composites or bulk nano-crystalline alloys, and the micro-or nano-structure is controlled by phenomena such as diffusion of solute and heat, and impingement dynamics. The relevance of solidification theories of nucleation, growth and impingement to crystallisation in amorphous alloys is discussed in this paper. The effects of the key differences between phase transformations in alloy casting processes and those in alloy devitrification on development of computational models for process simulation are highlighted.
Crystal–Melt Interfaces and Solidification Morphologies in Metals and Alloys
MRS Bulletin, 2004
When liquids solidify, the interface between a crystal and its melt often forms branching structures (dendrites), just as frost spreads across a window. The development of a quantitative understanding of dendritic evolution continues to present a major theoretical and experimental challenge within the metallurgical community. This article looks at key parameters that describe the interface—excess free energy and mobility—and discusses how these important properties relate to our understanding of crystal growth and other interfacial phenomena such as wetting and spreading of droplets and nucleation of the solid phase from the melt. In particular, two new simulation methods have emerged for computing the interfacial free energy and its anisotropy:the cleaving technique and the capillary fluctuation method. These are presented, along with methods for extracting the kinetic coefficient and a comparison of the results to several theories of crystal growth rates.
Crystallisation kinetics and microstructure development in metallic systems
Progress in Materials Science, 2002
The primary crystallisation of a highly undercooled/supersaturated liquid is considered, and the application to nanocrystallisation by heat treatment of metallic glasses is studied from the thermodynamic, kinetic and microstructural point of view. The thermodynamic evolution is modelled assuming transformation rates low enough to ensure thermal equilibrium to be almost achieved. A mean field approximation is used, which allows us to determine the time evolution of the kinetic variables governing the transformation. The interplay between interface and diffusion controlled growth rate is studied, and both nucleation and crystal growth changes within the transformation are considered as soft mechanisms. The kinetics of the transformation is described in the framework of the Kolmogorov, Johnson and Mehl and Avrami (KJMA) model, which is adequately generalized for primary transformations. The microstructural evolution is described by a populational model, also based on KJMA. The predicted kinetic evolution results are compared to the experimental data on the primary nanocrystallisation of a FINEMET alloy. #
On the transition from diffusion-limited to kinetic-limited regimes of alloy solidification
An abrupt transition from diffusion-limited solidification to diffusionless, kinetic-limited solidification with complete solute trapping is explained as a critical phenomenon which arises due to local non-equilibrium diffusion effects in the bulk liquid. The transition occurs when the interface velocity V passes through the critical point V = V D , where V = V D is the bulk liquid diffusive velocity. Analytical expressions are developed for velocity-temperature and velocity-undercooling functions, using local non-equilibrium partition coefficient based on the Jackson et al. kinetic model and the local non-equilibrium diffusion model of Sobolev. The calculated functions demonstrate a sharp break in the velocity-undercooling and velocity-temperature relationships at the critical point V = V D . At this point the local non-equilibrium solidus and liquidus lines coincide with the T 0 temperature. The relationship to pertinent experiments and the influence of the local non-equilibrium diffusion effects on grain refinement and disorder trapping phenomena are discussed.
Solidification reactions in undercooled alloys
Materials Science and Engineering: A, 1994
It is now recognized that rapid solidification conditions can be achieved with slow cooling rates provided that the liquid is undercooled substantially prior to nucleation. In fact, many of the novel metastable microstructures produced by rapid solidification require the consideration of an undercooled liquid for analysis. In general, rapid solidification techniques involve either constrained growth in which the solid phase formation is limited by the rate of heat extraction or delayed nucleation of the solid followed by unconstrained growth. With delayed nucleation methods such as the droplet emulsion technique direct measurement of undercooling is available for analysis of metastable phase formation. In fine droplet samples an effective nucleation isolation allows for undercoolings of about 0.3 T m with a limit that is usually set by heterogeneous nucleation. Processing variables can be used to control the undercooling and produce a transition in solidification reactions. In this case the use of metastable phase diagrams is important for the analysis of product structures and pathways during solidification and solid state treatments. A key to the understanding of structural evolution is the consideration of competitive nucleation and growth kinetics and thermal history, which can also provide a model for control of solidification reactions as demonstrated in selective alloys.
Influence of local nonequilibrium on the rapid solidification of binary alloys
͑Submitted April 22, 1996͒ Zh. Tekh. Fiz. 68, 45-52 ͑March 1998͒ 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 V Di and the diffusion velocity in the bulk of the liquid phase V D . 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.
Effects of Local Non-Equilibrium Solute Diffusion on Rapid Solidification of Alloys
A conceptual foundation for the study of local non-equilibrium solute diffusion under rapid solidification conditions is proposed. The model takes into account the relaxation to local equilibrium of the solute flux and incorporates two diffusion speeds, VDb, the bulk liquid diffusion speed, and VD~, the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts complete solute trapping and the transition to a purely thermally controlled solidification, which occur abruptly when the interface velocity V equals the bulk liquid diffusion speed VDb. The abrupt change in the solidification mechanism is described by the velocity dependent effective diffusion coefficient D* = D ( l -V2/V&) and the generalized partition coefficient K*. If V > VDb, then D* = 0 and K* = 1. This implies an uudisturbed diffusion field in the liquid (diffusionless solidification) and complete solute trapping at V > VDb. The interface diffusion speed v~i governs solute redistribution at a relatively low interface velocity v -v~i < VDb. The influence of the local non-equilibrium solute transport on the temperature field and interface stability under rapid solidification conditions is also discussed.
arXiv (Cornell University), 2022
The theoretical insights of dynamics most focus on one single dendrite tip at different stages of directional solidification. Through the phase-field model, this paper investigates the evolution in the whole domain during entire directional solidification. Firstly, the evolution of characteristic parameters is obtained, including the solute concentration ahead of interface and tip velocity, demonstrating the dissipative features of solidification. Secondly, by adjusting the diffusion coefficient D L , the dissipation at the interface can be altered. With different D L , different stages during directional solidification are investigated, including planar growth and instability, dendrite growth, and steady-state growth. From the viewpoint of dissipation, the role of solute diffusion in evolution is given out. Even under the local equilibrium conditions, the dissipation at the interface plays an important role in alloy solidification, altered by solute diffusion. Moreover, the competitive influences of tip curvature and velocity are also because of the dissipation.
Amorphization and alloy metastability in undercooled systems
In systems with larger undercoolings, crystal nucleation and growth limitations can expose alloy metastability due either to the suppression of an equilibrium phase or else by the formation of a kinetically favored metastable phase. Under nucleation control, crystallization may be bypassed in bulk volumes as the liquid is uniformly undercooled below the glass transition. Alternatively, during interface reactions, nucleation can be suppressed at early times by larger concentration gradients that can expose several forms of metastability and increase the probability of amorphization. For amorphous phase formation during melt processing the kinetic control may be analyzed in terms of nucleation limitations or growth restrictions. Many metallic glasses require quenching for vitri®cation and often do not have a resolved glass transition upon reheating. The marginal glass formation is related mainly to growth limitations. How- ever, this same kinetic control also provides the foundation for the development of a high density (10 22 m ÿ3 ) of na- nometer sized (20 nm) crystals during primary crystallization. With alternate synthesis routes based upon solid state alloying resulting from deformation, the kinetic pathways to glass formation can be altered to avoid nanocrystallization reactions in marginal glass-forming alloys. These developments present new opportunities for controlling crystallization in multicomponent glasses.